flavour anomaly

***

**Update Dec 2022.** At long last, the [[LHCb collaboration]] in Dec 2022 announced ([LHCB22](#LHCB22)) that they had all along been mis-attributing hadronic backgrounds in the measurement of kaonic decays of B-mesons to electron pairs (as some people had [suspected](http://resonaances.blogspot.com/2021/03/thoughts-on-rk.html?showComment=1617397775790&m=1#c6699295970247538741)), and that fixing this makes the apparent anomaly in $R_K$, $R_{K^{\ast}}$ disappear, and with it most of the other apparent anomalies, too ([CFFPSV22](#CFFPSV22)). For more see [below](#FixingTheBackgrounds).

This seems to mean that all the discussion on this page here is essentially obsolete as far as its particle physics content goes -- what remains is maybe just of historical/sociological interest.

***

+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
### Context
#### Fields and quanta
+--{: .hide}
[[!include fields and quanta - table]]
=--
=--
=--

#Contents#
* table of contents
{:toc}

## Idea
 {#Idea}

In the current [[standard model of particle physics]] the [[fundamental particles]] in the three [[generations of fermions]] have identical properties from one generation to the next, except for their [[mass]], a state of affairs referred to as _[[lepton]] [[flavour physics|flavour]] universality_ (LFU). A possible violation of lepton flavour universality (LFUV) is also called a _[[flavour in particle physics|flavour]] anomaly_, which, if confirmed, would be a sign of "New Physics" (NP) beyond the [[standard model of particle physics|standard model]].

The presence -- or not -- of flavour anomalies is part of the general _[[flavour problem]]_ of the [[standard model of particle physics]].

Flavor universality pertains in particular to ([[semileptonic decay|semi]]-)[[leptonic decays]] of [[bottom quarks]], denoted $b$ (in the third [[generation of fundamental particles|generation]]), into [[electron]]/[[positron]] pairs, denoted $e^+ e^-$ (in the first [[generation of fundamental particles|generation]]) or [[muon]]/[[antiparticle|anti]][[muon]] pairs, denoted $\mu^+ \mu^-$ (in the second [[generation of fundamental particles|generation]]), the latter two jointly denoted $\ell^+ \ell^-$ (for "[[leptons]]") in this context.

Since [[quarks]] never appear in isolation (due to [[confinement]]) but always as [[bound states]] to [[hadrons]], [[scattering amplitude|decays]] specifically of [[bottom quarks]] manifest themselves in [[leptonic decays]] of [[mesons]] that contain $b$ -- [[B-mesons]], denoted $B$ --

\begin{imagefromfile}
  "file_name": "bsllprocesses.jpg",
  "width": 570,
  "caption": "from [Cartelle 18](#Cartelle18)"
\end{imagefromfile}

or as [[leptonic decays]] of [[baryons]] that contain $b$ -- [[Lambda baryons]], denoted $\Lambda_b$ (measured only more recently ([LHCb 19120.8139](#LHCb191208139))).

\begin{imagefromfile}
  "file_name": "AltmannshoferRKDecay.jpg",
  "width": 300,
  "float": "right",
  "margin": {
    "top": -30,
    "right": 0,
    "bottom": 10,
    "left": 20,
    "unit": "px"
  },
  "caption": "from [Altmannshofer 14](flavor+problem#Altmannshofer14)"
\end{imagefromfile}

Hence flavour universality in the [[standard model of particle physics]] demands, for example, that the _[[ratios]]_ of decay rates (branching fractions) of [[B-mesons]] into [[electrons]] are the same as into [[muons]], hence that the [[ratio]]

\[
  \label{RKInIntroduction}
  R_K
  \;=\;
  \frac{
    B \to K \mu^+ \mu
  }{
    B \to K e^+ e^-
  }
\]

(where $K$ is a [[kaon]], a [[meson]] containing a [[strange quark]])

is essentially equal to 1. Any [[statistical significance|significant]] departure of this [[observable]] from 1 would be a _flavour anomaly_ and would mean that there are fundamental processes at play which are not described by the current [[standard model of particle physics]] ("New Physics").

Moreover, in the [[standard model of particle physics|standard model]] the decays involved here are "forbidden" (have vanishing decay rate) at [[tree level]], so that only [[loop orders]] contribute to any possible flavour anomaly. But these loop contributions are sensitive to effects from putative undiscovered [[fundamental particles]] which "run in the loops" as [[virtual particles]], and which thus may show up as a flavour anomaly even if their [[mass]] is too large for them to be seen as scattering products (i.e. as actual, non-[[virtual particles]]).

{#CleanObservablesInIntroduction} Finally, in forming the "branching" [[ratios]] (eq:RKInIntroduction) it is expected (see e.g. [Nabeebaccus & Zwicky 2022](#NabeebaccusZwicky22))
that "hadronic uncertainties cancel out", namely that [[non-perturbative effects]] of [[QCD]], which remain largely unknown (due to the [open problem of confinement](confinement#OpenProblemConfinementReferences)), contribute the same (unknown) factor to numerator and denominator and hence do not affect the ratio ([Hiller & Krüger 2004](#HillerKrueger04), see also [Isidori et al. 2021](#IsidoriEtAl21)). Also [[QED]]-[[radiative corrections]], while not cancelling out in this way, have been argued to be negligible ([Bordone, Isidori and Pattori 2016](#BordoneIsidoriPattori16), but see [CFFPSSV 2021](#CFFPSSV21) for cautionary remarks). Therefore these branching ratios are regarded as "clean observables" in that their value, to relevant precision, is unambiguously predicted by the [[standard model of particle physics]].

This way, tests of lepton flavour universality through measurement of branching ratios like (eq:RKInIntroduction) provide a means to potentially detect "New Physics" (effects not described by the present [[standard model of particle physics|standard model]]) via *indirect* high-luminosity/high-[[precision experiment]] (see e.g. [Brambilla et al. 2014, Section 5](#Brambilla14) [AHRS 2020](#AHRS20)), complementary to traditional high-energy *direct* detection measurements.

Notice that the channel $R_K$ (eq:RKInIntroduction) is just one among the more prominent of several channels in which flavour anomalies may and have been seen. There are other decay channels of [[B-mesons]] such as with differing spectator quarks ([LHCB 2021](#LHCB21)) and there are also flavour anomalies in decays of, for instance, [[kaons]] ([Buras 16](kaon#Buras16), [Buras 2018](kaon#Buras18)) as well as in angular observables ([LHCb 2020](#LHCb2012)).

See [Alonso 2019](#Alonso19) for general introduction to an audience with basic background in [[quantum field theory]].

## Statistical significance
 {#StatisticalSignificance}

While the [[statistical significance]] of the [[flavour anomalies]] in every single decay channel is about $2\sigma$-$3\sigma$ (around $4 \sigma$ for some), the observations across channels are all compatible with each other, with a high joint/global statistical significance.

[Garisto 20](#Garisto20):

> Alone, each notable B physics result is only a few-sigma discrepancy. But taken together, the aggregate of the results is—depending on whom you ask—a 5- to 7-sigma deviation from the standard model estimates.

and quoting [[Gino Isidori|Isodori]]:

> "We’ve seen a lot of anomalies here and there popping up and going back, but this time I think it’s different… . For the first time, it’s not just one thing that doesn't fit with the other, but it's a coherent set of things."

Moreover, there are other types of anomalies currently observed in the data (such as in the [[anomalous magnetic moment]] of the [[muon]] and in the [[mass]] of the [[W-boson]]) which have been argued to possibly have a joint origin with the anomalies in $B$-meson decays (see [below](#RelationToOtherAnomalies) for more).

It is expected that if the ongoing evaluation of the data of [[LHC]]'s Run 2 confirms the measurements of Run 1, then the [[statistical significance]] of the effect in each decay channel separately is expected to have reached 5 [[standard deviations|σ]] ([Crivellin et. al 18, p. 12](#CrivellinEtAl18), [Zupan 19, 4.6](#Zupan19), in [HMSN 21](#HMSN21) this is expected for Run 3 data) and hence conventionally count as detection of flavour anomaly (see [here](statistical+significance#ParticlePhysics)), which would make it the first established "new physics" seen at the [[LHC]]. Extrapolation based on [LHCb Collaboration 18](#LHCbCollaboration18) predicts a [[statistical significance]] between 6 and 10 $\sigma$ by the year 2025 ([LKLR 19, p. 12](#LKLR19)).

### Up to 2019

Indications of flavour anomalies have been observed (first suggested in [Hiller 2002](#Hiller02), [Koppenburg 2007](#Koppenburg07), for introduction and review see [Koppenburg 21](#Koppenburg21)) consistently and with increasing [[statistical significance]] around $2$ [[standard deviations|σ]] in [[B meson]] [[scattering amplitude|processes]] in various decay channels and by a number of independent [[experiments]]: the [[LHCb experiment]], the [[Belle experiment]] and the [[BaBar experiment]]:

\begin{center}
\begin{imagefromfile}
  "file_name": "FlavourAnomaliesByChannels.jpg",
  "width": 590,
  "caption": "table grabbed from [BGV 19](#BGV19)"
\end{imagefromfile}
\end{center}

\begin{imagefromfile}
  "file_name": "FlavourAnomalyAt4Sigma.jpg",
  "width": 320,
  "float": "right",
  "margin": {
    "top": 0,
    "right": 10,
    "bottom": 10,
    "left": 0,
    "unit": "px"
  },
  "caption": "graphics grabbed from [Dey 18](#Dey18)"
\end{imagefromfile}

The global (all channels and experiments combined) tension  with the standard model by end of 2018 had [[statistical significance]] around $4.1$ [[standard deviations|σ]] ([Strumia et al. 17](#StrumiaEtAl17), [Cartelle 18, slide 22/25](#Cartelle18), [Dey 18, slide 16/23](#Dey18), [HAMN 18, p. 4](#HAMN18), [Bouchard-Cao-Owen 19](#BouchardCaoOwen19)). Various authors see the global tension (i.e. of all decay channels jointly) at over $5 \sigma$ ([CCDGMV 17](#CCDGMV17), [CFMVV 17](#CFMVV17) [CGMS 18](#CGMS18), [Dordei 18, slide 12](#Dordei18)), which traditionally qualifies as detection (see [here](statistical+significance#ParticlePhysics)), some authors already quote $5.3 \sigma - 5.8 \sigma$ ([ACDGMM 19](#ACDGMM19)) or $5-6 \sigma$ ([Kumar-London 19](#KumarLondon19), [Kumar 19](#Kumar19)).

More recent measurements in March 2021 make even just the combination of the particularly "clean" observables reach $4\sigma - 4.6\sigma$, see [below](#SignificanceMarch2021) for more recent references.

### Updates in 2019

This situation was confirmed with the completed measurements presented at [Moriond 2019](http://moriond.in2p3.fr/2019/), which showed ([Straub 19](#Straub19), [Allanach 19](#Allanach19)) smaller mean discrepancy but also had smaller uncertainty, thus keeping the [[statistical significance]] of the apparent anomaly essentially unaffected. But [Caria 19, slide 9](#Caria19)  reported new measurements by [[Belle collaboration|Belle]] ([Belle 1910](#Belle1910))
according to which the previous [[statistical significance]] of $3.8 \sigma$ in the $R_D$ channel would decrease to $3.1 \sigma$ or $2.8 \sigma$ ([Gambino-Jung-Schacht 19 (6)](V_cb+puzzle#GambinoJungSchacht19)).  See [LHCb 19, p. 2](#LHCb19) for how the new numbers come about. The [[statistical significance]] over all sectors is still seen $\gt 4 \sigma$ ([London 19, p. 7](#London19)) or $\sim 3\sigma$ ([Jaiswal-Nandi-Patra 20](#JaiswalNandiPatra20)). Moreover, the theoretical prediction is being corrected further away from these measured values ([BDKL 20, footnote 1](#BDKL20)).

Comprehensive assessments of the situation after [Moriond 2019](http://moriond.in2p3.fr/2019/) are given in [AHMSN 19](#AHMSN19), [Descotes-Genon 19](#DescotesGenon19), [Bardhan-Ghosh 19](#BardhanGhosh19), [Alguero 19](#Alguero19) and agree that the flavour anomalies have been confirmed:

>  It appears the reason is that, given the amount of independent measurements (~180!) a smaller deviation because of new physics is easier to accommodate than a large one. Thus the new measurements actually fit better with new physics.

> (Axel Maas, reporting from [ALPS2019](https://indico.cern.ch/event/757995/),
 [tweet, 23 Apr 2019](https://twitter.com/axelmaas/status/1120653147947655168))

\begin{center}
\begin{imagefromfile}
  "file_name": "ZupanFlavourAnomaly.jpg",
  "width": 690,
  "caption": "from [Zupan 19](#Zupan19), see also [LHCb19, Fig. 5](#LHCb19)"
\end{imagefromfile}
\end{center}

There is the claim ([DGKV 19](#DGKV19)) that the discrepancy with the standard model increases further if non-trivial [[hadron|hadronic]] [[form factors]] are taken into account:

\begin{imagefromfile}
  "file_name": "DescotesGenonBsll19FormfactorCorrectionA.jpg",
  "width": 600
\end{imagefromfile}

\begin{imagefromfile}
  "file_name": "DescotesGenonBsll19FormfactorCorrectionB.jpg",
  "width": 600,
  "caption": "from [Descotes-Genon 19b](#DescotesGenon19b)"
\end{imagefromfile}

and also that the discrepancy increases further with [[QED]]-corrections taken into account ([Mishra-Mahajan 20,p. 20-21](#MishraMahajan20)).

### Updates in 2020

[Smith 20](#Smith20) on behalf of [LHCb 2003.04831](#LHCb200304831) (see also [Lopes 20](#Lopes20), [CERN Courier 200311](#CERNCourir200311)):

\begin{center}
\begin{imagefromfile}
  "file_name": "SmithAtLHCbFlavourAnomalies.jpg",
  "width": 540
\end{imagefromfile}
\end{center}

From [Crivellin-Mueller-Saturnino 20a](#CrivellinMuellerSaturnino20a) (where "LQ" is [[leptoquark]]):

\begin{imagefromfile}
  "file_name":
  "CrivellinEtAl.jpg",
  "width": 500
\end{imagefromfile}

[Virto 21, p.6](#Virto21) points out (their emphasis):

> **Both $R_K$ and $P'_5$ have moved towards the Standard Model, but this actually improves the New Physics fits.** $[$...$]$

> The set of $b \to s \ell \ell$ anomalies are alive and a global coherence remains after the measurements in 2019 and 2020. While some key measurements have central values that have moved towards the Standard Model predictions, the overall consistency of the data and the global tension with respect to the Standard Model has not diminished (in fact this may even enhance the significance for New Physics). The New Physics fit is a good fit (with $p$-values in the ballpark of 50%), and the SM pull is high $[$...$]$. In addition, data sets from all different experiments are compatible $[$...$]$.

The [[statistical significances]] of pull away from the [[standard model of particle physics|standard model]] for [[effective field theory|effective]] New Physics models:

\begin{imagefromfile}
  "file_name": "AlgueroBsll19Fits.jpg",
  "width": 600,
  "caption": "from [Alguero 19](#Alguero19)"
\end{imagefromfile}

\begin{imagefromfile}
  "file_name": "Koppenburg20PullSummary.jpg",
  "width": 600,
  "caption": "from [Koppenburg 20](#Koppenburg20)"
\end{imagefromfile}

### Updates in 2021
 {#UpdatesIn2021}

{#SignificanceMarch2021} New measurements reported by [[LHC]] [in March 2021](https://home.cern/news/news/physics/intriguing-new-result-lhcb-experiment-cern) for the first time see deviation in a single decay channel at a statistical significance above $3.1 \sigma$.

Implications for the significance across channels:

[HLN 21](#HLN21):

> Naive combination of $R_K$ and $R_{K*}$ measurements shows a deviation from the standard model above $4 \sigma$

[Geng et al. 21](#GengEtAl21):

> Motivated by $[\cdots]$  LHCb's new measurements $[\cdots]$ we quantify the combined level of discrepancy with the Standard Model and fit values of short-distance Wilson coefficients. A combination of the clean observables $R_K$, $R_{K^\ast}$, and $B_s \to \mu \mu$ alone results in a discrepancy with the Standard Model at $4.0 \sigma$, up from $3.5 \sigma$ in 2017. One-parameter scenarios with purely left-handed or with purely axial coupling to muons fit the data well and result in a $\sim 5 \sigma$ pull from the Standard Model.

[AlSt 21](#AltmannshoferStangl21):

> With the recent updates $[...]$ the case for new physics inrare B decays has been further strengthened. $[...]$ Even if only the theoretically  clean  LFU observables  $[...]$ are considered, muon specific $[$ Wilson coefficients for New Physics$]$ improve over the Standard Model by $\sqrt{\Delta^2} \simeq 4.7 \sigma$.

[CFFIN 21](#CFFIN21):

> With the recent result $[$ of [[LHCb]] $]$, for the first time a single observable affected by negligible theoretical uncertainties exhibits a deviation from the SM exceeding the $3 \sigma$ level. Equally striking is the overall coherence of the picture that emerges, especially in $b \to s \ell^+ \ell^-$ −transitions.  As we shall show in this paper, combining all the $b \to s \ell^+ \ell^-$−observables in a very conservative way, the significance of the New Physics (NP) hypothesis formulated in 2014–2015 of a purely left-handed LFU-violating contact interaction has now reached a [[statistical significance|significance]] of $4.6 \sigma$.

> $[\ldots]$  A more structural way of addressing the flavor structure of the model is the idea of implementing [[GUT|Pati-Salam unification]]

[LIOS 21](#LIOS21):

> we obtain the global significance to be 3.9 standard deviations

[MT 21](#MarzoccaTrifinopoulos21):

> the combined significance of the deviation reaches $4.7\sigma$. Furthermore, taking into account also less theoretically-clean observables $[\ldots]$ the overall significance of the deviations  in  this  channel  is  raised  to  even  above  $6\sigma$, depending on the specific SM prediction employed

[Davighi 21](#Davighi21):

> A highly conservative method for combining the various $b \to s \ell \ell$ anomalies, including the look-elsewhere effect, estimates their global significance to be 3.9σ. The  combined  set  of  discrepancies are by and  large self-consistent with a common new physics origin involving muons.

[Chang 21](#Chang21):

> From the global fits to various $b \to  s l^+ l^-$−data, the discrepancy is more than $5\sigma$ from the SM predictions. The new result ([59](https://arxiv.org/abs/2103.11769)) further strengthens the lepton flavor universality violation. This anomaly alone convincingly indicates New Physics

[CFFIN 21](#CFFIN21):

> striking is the overall coherence of the picture that emerges, especially in $b \to s \ell^+ \ell^-$ −transitions.  As we shall show in this paper, combining all the $b \to s \ell^+ \ell^-$−observables in a very conservative way, the significance of the New Physics (NP) hypothesis formulated in 2014–2015 of a purely left-handed LFU-violating contact interaction has now reached a [[statistical significance|significance]] of $4.6 \sigma$.

### Updates in 2022
 {#UpdatesIn2022}

[Alise et al. 22](#AliseEtAl2222):

> We critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment. $[\cdots]$ the deviations from the Standard Model are at the 4.7σ level when including only the hadronic insensitive observables while it increases to 6.1σ when including also the hadronic sensitive ones.

> $[...]$ Scalar [[leptoquarks]], either a singlet or a doublet of weak interactions, can explain all the anomalies.

[ACMM 22](#ACMM22):

> when combining all tests of LFUV (like $R_{K^+}$ ) with $B$ decays involving muon pairs [...], one finds a preference for new physics (NP) hypotheses of more than 7σ compared to the [[standard model of particle physics|SM]]. Note that such a high significance is only possible since all measurements are compatible with each other, i.e. they form a coherent picture

[PBD22](#PBD22):

> We have used our improved scalar, vector and tensor [[form factors]] calculated in $N_f = 2+1+1$ [[lattice QCD]] [...] Our improved form factors significantly sharpen the tension, which becomes particularly strong in the  region below the charmonium resonances. For $1.1 \lt  q^2 \lt 6 GeV^2$ we find a tension of 4.7σ for $B^+ \to K^+ \mu^+ \mu^-$ and 3.6σ for $B^0 \to K^+ \mu^+ \mu^-$ with LHCb ’14A and 3.3σ for $B^+ \to K^+ e^+ e^-$ with LHCb ’21

[PBD22b](#PBD22b):

> We present the first fully relativistic determination of the scalar, vector and tensor form factors for $B \to K$ decays. [...] Using these form factors, we can calculate the SM branching fraction for $B \to K e(\mu)+ e(\mu)^-$ [...] We find tensions above $3\sigma$ in the ratio of our result with LHCb, and above$5\sigma$ in one instance for the low $q^2$ bin.

[Mahmoudi 2022](#Mahmoudi22):

> The updated NP fits to rare B decays [...] follow the same trend as with the previous set of results favouring in particular new physics contributions in the Wilson coefficient $C^\mu_9$, with an increased significance. [...] The projections for clean observables, show that if the current tensions remain, $R_K$ can establish NP with 5σ significance already with less than 20 $fb^{-1}$ of data. The main source of theory uncertainty in global fits is due to non-local hadronic contributions. However, different fits with different setups, inputs and statistical frameworks show a remarkable agreement so that the experimental observation of the discrepancy in these observables would be a clear sign of physics beyond the SM.

[IKW22](#IKW22):

> Incorporating several recent developments of determinations of the $B \to D^{(\ast)}$ form factors in the Standard Model (SM), we observe a 4.1σ deviation from the SM predictions.

> present data deviates from the SM predictions at 4.3σ.

\linebreak

[Soni 2022](#Soni22):

> For almost a decade now, there have been persistent indications from all three major B-facilities of lepton universality violations (LUV) [1], [2–10], with a combined significance of 4.5σ [11]. In tree-level charge current decays, B → D(∗)τ(l)ν, the reactions involving τ seem to differ more from those involving muon or electron than predicted by the SM. Another class of reaction that is
presenting an even stronger indications of lepton flavor universality violations is flavor changing
neutral current decays which, in the SM are loop-level. At the quark-lepton level this is b → sl+l − for l = µ or e. The corresponding ratios of such reactions, RK(∗) etc which in the SM are supposed to be unity within O(few %), experimentally at LHCb [9] are found to be significantly different
from unity i.e. O(≈ 30%) at around 3 or even possibly ≈ 4σ. Moreover, another rather strong indication of new physics (NP) that has been strengthened
this year is the muon (g-2) anomaly. For well over a decade this was already around 3.5σ being the difference between the experimental measurements at BNL from about 2002 [12] to around 2006 [13] and the theory predictions based on dispersion relations, data driven approach [14].

> Recent confirmation by the Fermilab $(g-2)$ Collaboration [15] of the old BNL result has now increased the deviation from the data-driven theory prediction from the SM to about 4.2σ.
The main point to bear in mind is that there are three anomalies, RD(∗) , RK(∗) and muon (g-2), and each of these is over three σ.

> So, the chances of at least one of these surviving the test of time and leading us to new physics is rather high,

\linebreak

### Fixing the backgrounds
 {#FixingTheBackgrounds}

However, [LHCB22](#LHCB22) claims that re-analysis of hadronic backgrounds in kaonic decays makes the decay rate in the electron channel go down, so that the ratio $R_K$, $R_{K^\ast}$ over the corresponding muon channel is accurately described by the standard model (cf. [A. Maas, 20 Dec 2022](https://twitter.com/axelmaas/status/1605159026441986049)).

This seems to make all the apparent anomalies disappear.

[CFFPSV22](#CFFPSV22):

> we show that current data no longer provide strong hints for NP.

\linebreak

## Relation to other anomalies
 {#RelationToOtherAnomalies}

There is possibly a relation between the [[flavour anomalies]] to anomalies currently observed in other processes, notably to the [anomalies](anomalous+magnetic+moment#Anomalies) observed in the [[anomalous magnetic moment]] of the [[electron]] and/or the [[muon]] (e.g. [Chiang-Okada 17](#ChiangOkada17)) which might point to a common origin in the [[flavour sector]] (e.g. [Crivellin-Hoferichter 20](#CrivellinHoferichter20)):

\begin{center}
  \begin{imagefromfile}
    "file_name": "CrivellinRandAHints.jpg",
    "width": 300,
    "caption": "graphics from [Crivellin-Hoferichter 20](#CrivellinHoferichter20)"
  \end{imagefromfile}
\end{center}

> (here "$R$" refers to [[flavour anomalies]] in various channels, "$a$" refers to anomalies in the the [[anomalous magnetic moments]] of the [[electron]] and the [[muon]], "LFUV" is shoft for "Lepton Flavor Universality Violation", and the numbers are the [[statistical significances]] of the effects seen)

\begin{imagefromfile}
  "file_name": "CrivellinHintsForNewPhysics21.jpg",
  "width": 600,
  "margin": {
    "top": -30,
    "right": 0,
    "bottom": 10,
    "left": 20,
    "unit": "px"
  },
  "caption": "from [Crivellin 21, slide 15](#Crivellin21)"
\end{imagefromfile}

Indeed, [[leptoquark]] models preferred by the flavour anomalies (see [below](#Leptoquarks)) are also a candidate explanation of the anomaly seen at over 4$\sigma$ [[statistical significance]] in the [[anomalous magnetic moment]] of the [[muon]], see [there](anomalous+magnetic+moment#Anomalies).

Some authors therefore begin to speak jointly of _muon anomalies_ ([GST 21](#GST21)).

{#KoppenburgListOfAnomalies} Here is a list of experiments, all somehow related to [[muons]], which see deviations (shown in blue) from the theoretical expectation (shown in orange):

\begin{imagefromfile}
  "file_name": "KoppenburgFlavourAnomaliesApril2021.jpg",
  "width": 600,
  "margin": {
    "top": -30,
    "right": 0,
    "bottom": 10,
    "left": 20,
    "unit": "px"
  },
  "caption": "from [Koppenburg Scholarp.](#KoppenburgScholarpedia)"
\end{imagefromfile}

(This is as of April 2021, see [here](http://www.scholarpedia.org/article/Rare_decays_of_b_hadrons#Prospects) for the source text with more details; also [Koppenburg 21, slide 44](#Koppenburg21). For more data points and updates see [Koppenburg Fl. Anom.](#KoppenburgAnomalies))

\linebreak

\begin{imagefromfile}
  "file_name": "KoppenburgFlavourAnomaliesPattern.jpg",
  "width": 600,
  "margin": {
    "top": -30,
    "right": 0,
    "bottom": 10,
    "left": 20,
    "unit": "px"
  },
  "caption": "from [Koppenburg 21, slide 53](#Koppenburg21)"
\end{imagefromfile}

A [[leptoquark]]-model meaning to explain all of the [[flavour anomalies]], the [[(g-2)-anomaly]] and the [[Cabibbo anomaly]] at once: [Marzocca-Trifinopoulos 21](#MarzoccaTrifinopoulos21).

In [ACMM22](#ACMM22) it is argued (see [footnote 3](https://arxiv.org/pdf/2201.08170.pdf#page=2)) that also the huge anomaly reported by [CDF collaboration 2022](W-boson#CDF22) in the [[mass]] of the [[W-boson]] is compatible with (in fact predicted by) the $B$-meson decay anomalies.

\linebreak

## Status and Outlook
 {#Outlook}

In conclusion, with currently available data, the observed flavour anomalies are possible signs of New Physics beyond the current [[standard model of particle physics]].

\begin{center}
\begin{imagefromfile}
  "file_name": "DordeiConclusion.jpg",
  "width": 740,
  "caption": "graphics taken from [Dordei 18, slide 22](#Dordei18)"
\end{imagefromfile}
\end{center}

\linebreak

\begin{imagefromfile}
  "file_name": "TuningFLavourAnomaliesInterlocking.jpg",
  "width": 560,
  "margin": {
    "top": -30,
    "right": 0,
    "bottom": 10,
    "left": 20,
    "unit": "px"
  },
  "caption": "from [Tuning 20](#Tuning20)"
\end{imagefromfile}

\linebreak

In any case, further and more sensitive experiments are needed to  confirm and explore the effect, such as possibly the "[HL-LHC](http://hilumilhc.web.cern.ch)" or "HE-LHC" experiment. General outlook, prospects and suggestions for future collider design in this respect are discussed in detail in [Allanach-Gripaios-You 17](#AllanachGripaiosYou17), [Crivellin et al.  18](#CrivellinEtAl18).

From [Isidori 19, slide 6](#Isidori19):

\begin{center}
\begin{imagefromfile}
  "file_name": "IsidoriExpectations19.jpg",
  "width": 610
\end{imagefromfile}
\end{center}

\linebreak

Outlook on the [[Belle II experiement]] to confirm the flavour anomalies, if real ([HHJLQV 20](#HHJLQV20)):

> With $[$ ... $]$ [[Belle II]], we are at the brink of a new era in [[quark]] [[flavour physics]] $[...]$ we present a phenomenological study of  the potential for [[Belle II]] to reveal possible new physics in the inclusive decay channel

> ([p. 15](#HHJLQV20):) We see that [[flavour anomalies|anomalies]] in the exclusive sector can be confirmed at the [[statistical significance|5σ]] level by inclusive measurements if the true values of $C_{9,10}^{\mu NP}$ are at the current best-fit point of the exclusive fits

> ([p. 16](#HHJLQV20):)  After including $B_s \to \mu^+ \mu_-$, the reach in the $[C_9^{\mu NP}, C_{10}^{\mu NP}]$ plane improves considerably.  Exclusive [[flavour anomalies|anomalies]] could be confirmed at the [[statistical significance|6σ]] level.

> ([p. 20](#HHJLQV20):) Should  the  true  value  of $C_9^{NP}$ and $C_{10}^{NP}$ be at  the current best-fit points of the global fits, an analysis of inclusive $\bar B_ \to X_s \ell^+ \ell^-$ at [[Belle II]] with $50 ab^{-1}$ of data will exclude the SM point $C_9^{NP} = C_{10}^{NP} = 0$ at the level of $\sim 5$[[statistical significance|σ]].  This again underlines the necessity of a full angular analysis of $\bar B_ \to X_s \ell^+ \ell^-$ at [[Belle II]].

From [Guadagnoli & Koppenburg 2022](#GuadagnoliKoppenburg22):

> The main final message is that all the instruments necessary to fully establish the putative new effects are at hand, thanks to running experiments and their upgrades. Therefore this subject stands concrete chances to usher genuinely unexpected discoveries.

\linebreak

## Possible models

Candidate [[model (in theoretical physics)|models]] of "New Physics" beyond the [[standard model of particle physics]] that could possibly explain the flavour anomalies (if indeed they are real) includes the following:

### Leptoquarks and Grand unified theory
 {#Leptoquarks}

One promising [[model (in theoretical physics)|model]] that could potentially explain the apparently observed flavour anomalies are
[[leptoquarks]], which naturally arise in, and hence potentially point to, [[grand unified theory]] (GUT) [[model (in theoretical physics)|models]], such as notably the [[Pati-Salam model]] ([Heek-Teresi 18](#HeekTeresi18), [Heek-Teresi 19](#HeekTeresi19))

(see [Bauer-Neubert 15](#BauerNeubert15), [CCDM 16](#CCDM16), [Crivellin 17](#Crivellin17), [Falkowski17](#Falkowski17), [Mueller 18](#Mueller18), [Matsuzaki-Nishiwaki 18](#MatsuzakiNishiwaki18), [Monteux-Rajaraman 18](#MonteuxRajaraman18), [AMST 18](#AMST18), [BDFKFS 18](#BDFKFS18), [Crivellin 18](#Crivellin18), [MMR 18](#MMR18), [Kumar-London 19, section 2.2.1](#KumarLondon19), [MVT 19](#MVT19), [AMM 19](#AMM19), [MVK 19](#MVK19), [Cata-Mannel 19](#CataMannel19))

From [Crivellin 18, p. 2](#Crivellin18):

> the global fit $[$ to [[flavour anomalies]] $]$ even shows compelling evidence for New Physics $[$... $]$ The vector [[leptoquark]] (LQ) $SU(2)_L$ singlet with hypercharge $-4/3$ arising in the famous [[Pati-Salam model]] is capable of explaining all the $[$[[flavour anomalies|flavour]] $]$ anomalies and therefore several attempts to construct a [[UV completion]] for this LQ to address the anomalies have been made. It can give a sizeable effect in $b \to c(u)\tau \nu$ data without violating bounds from $b \to s(d)\nu \bar \nu$ and/or direct searches, provides (at [[tree level]]) a $C_9 = - C_{10}$ solution to $b \to s \ell^+ \ell^-$ data and does not lead to [[proton decay]] at any order in [[perturbative quantum field theory|perturbation theory]].

From [GMV 20, Figure 9](#GMV20), showing fits of leptoquark models (labeled $S_i$) to a variety of [[observables]]:

\begin{center}
\begin{imagefromfile}
  "file_name": "GherardiEtAlLeptoquarkFits.jpg",
  "width": 600
\end{imagefromfile}
\end{center}

In [CFFPV20](#CFFPV20):

> In the Standard Model Effective Theory (SMEFT) [41, 42], the significance of NewPhysics from the global $b \to s \ell^+ \ell^-$ analysis increases with the inclusion of new data, reaching a maximum of almost 6σ for the simple hypothesis of a non-vanishing $[$[[leptoquark]] contribution$]$.

If it is a [[GUT]]-model containing the [[leptoquarks]], then this seems to prefer embedding into a [[Randall-Sundrum model]] ([Blanke & Crivellin 18](#BlankeCrivellin18), [Crivellin 18](#Crivellin18)) or similar ([FMIPS21](#FMIPS21)), hence a setup broadly as in [[intersecting D-brane models]].

### Other
 {#PossibleModelsOther}

Other possible [[model (in theoretical physics)|models]] besides [[leptoquarks]] ([above](#Leptoquarks)) which have been proposed as possible explanations of the apparently observed flavour anomalies include the following:

* [[Z'-boson]]

  ([Gauld-Goertz-Haisch 13](#GauldGoertzHaisch13),  [D'Ambrosio-Iver-Piccinini-Polosa 19](#DAmbrosioIverPiccininiPolosa19))

* [[composite Higgs boson]]

  ([Marzocca 18](#Marzocca18))

* [[dark matter]]

  ([Baek 19](#Baek19), [CCMRM 19](#CCMRM19))

* [[right-handed neutrinos]]

  ([MMR 19](#MMR19))

## Related concepts

* [[flavour (particle physics)]]

* [[Cabibbo anomaly]]

* [[V_cb puzzle]]

* [[(g-2) anomaly]]

## References
 {#References}

### General

Early suggestion to look for New Physics in B-meson decays:

* {#Hiller02} [[Gudrun Hiller]], *$b \to s \ell^+ \ell^-$ decays in and beyond the Standard Model*, AIP Conf. Proc. 549:614-618, 2002 ([arXiv:hep-ph/0008092](https://arxiv.org/abs/hep-ph/0008092))

* [[Gudrun Hiller]], *Physics reach of rare b-decays*, Nucl. Phys. Proc. Suppl. 115 (2003) 76-81 ([arXiv:hep-ph/0207121](https://arxiv.org/abs/hep-ph/0207121))

* [[Gudrun Hiller]], *Phenomenology of New Physics* ([arXiv:hep-ph/0308180](https://arxiv.org/abs/hep-ph/0308180))

and specifically concerning the [[LHCb]]-experiment

* {#Koppenburg07} [[Patrick Koppenburg]], _Selection of $B_u \to \ell \ell K$ at LHCb and Sensitivity to $R_K$_, 2007 ([cern:1027442](http://cds.cern.ch/record/1027442), [pdf](http://cds.cern.ch/record/1027442/files/lhcb-2007-034.pdf))

On the branching ratios being "clean", i.e. with small theoretic uncertainty:

early arguments:

* {#HillerKrueger04} [[Gudrun Hiller]], F. Krüger, *More Model-Independent Analysis of $b \to s$ Processes*, Phys. Rev. D69 : 074020, 2004 ([arXiv:hep-ph/0310219](https://arxiv.org/abs/hep-ph/0310219))

regarding [[QED]]-[[radiative corrections]]:

* {#BordoneIsidoriPattori16} [[Marzia Bordone]], [[Gino Isidori]], Andrea Pattori, *On the Standard Model predictions for $R_K$ and $R_{K^\ast}$*, Eur. Phys. J. C 76, 440 (2016). ([arXiv:1605.07633](https://arxiv.org/abs/1605.07633), [doi:10.1140/epjc/s10052-016-4274-7](https://doi.org/10.1140/epjc/s10052-016-4274-7))

* [[Gino Isidori]], Saad Nabeebaccus, Roman Zwicky, *QED Corrections in $\bar B \to \bar K \ell^+ \ell^-$ at the Double-Differential Level* ([arXiv:2009.00929](https://arxiv.org/abs/2009.00929))

comprehensive analysis:

* {#IsidoriEtAl21} [[Gino Isidori]], Davide Lancierini, Abhijit Mathad, Patrick Owen, Nicola Serra, Rafael Silva Coutinho, *A general effective field theory description of $b \to s l^+ l^-$ lepton universality ratios* ([arXiv:2110.09882](https://arxiv.org/abs/2110.09882))

cautionary remarks:

* {#CFFPSSV21} Marco Ciuchini, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini, Mauro Valli, *New Physics without bias: Charming Penguins and Lepton Universality Violation in $b \to s \ell^+ \ell^-$ decays* ([arXiv:2110.10126](https://arxiv.org/abs/2110.10126))

General introduction to the issue in [[B-meson]] decays:

* {#KoppenburgScholarpedia} [[Patrick Koppenburg]], [[Zdenek Dolezal]], [[Maria Smizanska]], _Rare decays of b hadrons_, Scholarpedia, 11(6):32643 ([doi:10.4249/scholarpedia.32643](http://dx.doi.org/10.4249/scholarpedia.32643))

* Simone Bifani, Sebastien Descotes-Genon, Antonio Romero Vidal, Marie-Helene Schune, _Review of Lepton Universality tests in B decays_, Journal of Physics G: Nuclear and Particle Physics, Volume 46, Number 2 (2018) ([arXiv:1809.06229](https://arxiv.org/abs/1809.06229))

* {#Alonso19} Rodrigo Alonso, _Lepton (non-) unversality in (flavor changing) neutral current B decays_, Proceedings of [FPCP2019](https://fpcp2019.triumf.ca/) ([arXiv:1907.01716](https://arxiv.org/abs/1907.01716))

and for [[charm quark]] physics:

* [[Alexey Petrov]], _Theory of rare charm decays into leptons_ ([arXiv:1704.03862](https://arxiv.org/abs/1704.03862))

Detailed introduction and survey as of May 2021;

* {#Koppenburg21} [[Patrick Koppenburg]], *Penguin B decays*, 2021 ([cds:2767155](https://cds.cern.ch/record/2767155), [pdf](https://cds.cern.ch/record/2767155/files/Koppenburg-20210519-Usach.pdf))

Up-to-date plots of observed anomalies:

* {#KoppenburgAnomalies} [[Patrick Koppenburg]], *Flavour Anomalies* [[anomalies.htlm](https://www.nikhef.nl/~pkoppenb/anomalies.html)]

Textbook account:

* Marina Artuso, [[Gino Isidori]], Sheldon Stone, *New Physics in $b$ Decays*, World Scientific (2020) $[$[doi:10.1142/9789811251306](https://www.worldscientific.com/doi/abs/10.1142/9789811251306_0001)$]$

See also

* CERN, _[LHCb flavour anomalies continue to intrigue](https://home.cern/scientists/updates/2017/06/lhcb-flavour-anomalies-continue-intrigue)_, June 2017

* Vasudevan Mukunth, _[A Similar Anomaly Has Showed up in Three Physics Experiments Since 2009. What’s Happening?](https://thewire.in/science/b-mesons-kaons-flavour-changing-neutral-currents)_, 2017

* Diego Guadagnoli, _On the status of flavor anomalies_, 2016 ([web](http://indico.ictp.it/event/7627/session/78/contribution/486/))

Comprehensive overview of the latest world-averaged results to be found at:

* {#HFLAV} _[Heavy Flavour Averaging group](https://hflav.web.cern.ch/)_ (HFLAV)

  * _[Semileptonic B-decays](https://hflav.web.cern.ch/content/semileptonic-b-decays)_

  * _[Rare B decays](https://hflav.web.cern.ch/content/rare-b-decays)_

  * _[B decays to charm final states](https://hflav.web.cern.ch/content/b-hadron-decays-open-or-hidden-charm-hadrons)_

Brief review from the point of view of [[non-perturbative effect|non-perturbative]] [[QCD]]:

* {#Brambilla14} Brambilla et al., Section 5 of: _[[QCD and strongly coupled gauge theories - challenges and perspectives]]_, Eur Phys J C Part Fields. 2014; 74(10): 2981 ([arXiv:1404.3723](https://arxiv.org/abs/1404.3723), [doi:10.1140/epjc/s10052-014-2981-5](https://link.springer.com/article/10.1140%2Fepjc%2Fs10052-014-2981-5))

On $R_K$ beingba "clean" observable with negligible theoretical error:

* {#NabeebaccusZwicky22}
Saad Nabeebaccus, Roman Zwicky, *On the $R_K$ Theory Error* [[arXiv:2209.09585](https://arxiv.org/abs/2209.09585)]

### Experimental results

#### Before fixing the backgrounds

* [[LHCb collaboration]], _Differential branching fractions and isospin asymmetries of $B \to K^{(\ast)}\mu^+ \mu^-$ decays_, JHEP 06 (2014) 133 ([arXiv:1403.8044](https://arxiv.org/abs/1403.8044))

* [[LHCb collaboration]], _Test of lepton universality using $B^+\to K^+ \ell^+ \ell^-$ decays_, Phys. Rev. Lett. 113, 151601 (2014) ([arXiv:1406.6482](https://arxiv.org/abs/1406.6482))

* [[LHCb collaboration]], _Angular analysis and differential branching fraction of the decay $B^0_s \to \phi \mu^+ \mu^-$_, JHEP09(2015)179 ([arXivL1506.08777](https://arxiv.org/abs/1506.08777))

* [[LHCb collaboration]], _Differential branching fraction and angular analysis of $\Lambda^0_b \to \Lambda \mu^+ \mu^-$ decays_, JHEP 06 (2015) 115; JHEP 09 (2018) 145 ([arXiv:1503.07138](https://arxiv.org/abs/1503.07138))

* [[LHCb collaboration]], _Test of lepton universality using $B^0\to K^{\ast 0} \ell^+ \ell^-$ decays_, JHEP 08 (2017) 055 ([arXiv:1705.05802](https://arxiv.org/abs/1705.05802))

* [[LHCb collaboration]], _Measurement of the ratio of the $B^0 \to D^{\ast -} \tau^+ \nu_\tau$ and $B^0 \to D^{\ast - }\mu^+ \nu_\mu$ branching fractions using three-prong τ-lepton decays_ ([arXiv:1708.08856](https://arxiv.org/abs/1708.08856))

* [[Belle collaboration]], _Measurement of the $\tau$ lepton polarization and $R(D^\ast)$ in the decay $\bar B \to D^\ast \tau^- \bar \nu_\tau$ with one-prong hadronic τ decays at Belle_ ([arXiv:1709.00129](https://arxiv.org/abs/1709.00129))

* [[Belle collaboration]], _Measurement of the $D^{\ast -}$ polarization in the decay $B^0 \to D^{\ast -} \tau^+ \nu_\tau$_ ([arXiv:1903.03102](https://arxiv.org/abs/1903.03102))

* [[LHCb collaboration]], _Search for lepton-universality violation in $B^+ \to K^+ \ell^+ \ell^-$ decays_ ([cern:2668514](https://cds.cern.ch/record/2668514))

* [[Belle Collaboration]], _Test of lepton flavor universality in $B \to K^\ast \ell^+ \ell^-$ decays at Belle_ ([arXiv:1904.02440](https://arxiv.org/abs/1904.02440))

* {#LHCb19} [[LHCb collaboration]], _Lepton flavour universality in charged-current $B$ decays_ ([arXiv:1907.01500](https://arxiv.org/abs/1907.01500))

* {#Belle1910} [[Belle collaboration]], _Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^\ast)$ with a semileptonic tagging method_, Phys. Rev. Lett. 124, 161803 (2020)
([arXiv:1910.05864](https://arxiv.org/abs/1910.05864), [doi:10.1103/PhysRevLett.124.161803](https://doi.org/10.1103/PhysRevLett.124.161803))

* {#LHCb191208139} [[LHCb collaboration]], _Test of lepton universality with $\Lambda^0_b\to p K^-\ell^+\ell^-$ decays_ ([arXiv:1912.08139](https://arxiv.org/abs/1912.08139))

  also:

  CERN courier, _[Debut for baryons in flavour puzzle](https://cerncourier.com/a/debut-for-baryons-in-flavour-puzzle/)_, 20 Dec. 2019

  CERN news, _[LHCb explores the beauty of lepton universality](https://home.cern/news/news/physics/lhcb-explores-beauty-lepton-universality)_, 15 Jan 2020

  (first measurement of lepton universality for $\Lambda^0_b$ [[Lambda baryons]], finding the [[flavour anomaly]] at (only) 1 [[standard deviation|sigma]] but pointing in the same direction as seen in other channels)

* {#LHCb200304831} [[LHCb collaboration]], _Measurement of CP-averaged observables in the $B^0 \to K^{\ast 0} \mu^+ \mu^-$ decay_, Phys. Rev. Lett. 125, 011802 ([cds:2712641](http://cds.cern.ch/record/2712641), [arXiv:2003.04831](https://arxiv.org/abs/2003.04831), [doi:10.1103/PhysRevLett.125.011802](https://doi.org/10.1103/PhysRevLett.125.011802))

* [[LHCb collaboration]], _Measurement of CP-averaged observables in the $B^0\to K^{\ast 0} \mu^+ \mu^-$ decay_ ([spire:1784890](https://inspirehep.net/literature/1784890), [arXiv:2003.04831](https://arxiv.org/abs/2003.04831))

* {#Gerick20} David Gerick on behalf of the [[LHCb collaboration]], _Rare Decays at LHCb:  recent results_, talk at _[Implications of LHCb measurements and future prospects](https://indico.cern.ch/event/857473/)_, October 2020 ([pdf](https://indico.cern.ch/event/857473/contributions/4060371/attachments/2133689/3593528/Implications2020_LHCbRareDecays_DavidGerick.pdf))

* {#LHCb2012} [[LHCb collaboration]], _Angular analysis of the $B^+ \to K^{\ast + } \mu^+ \mu^-$ decay_ ([arXiv:2012.13241](https://arxiv.org/abs/2012.13241))

* {#LHCB21} [[LHCb collaboration]], *Tests of lepton universality using $B^0 \to K^0_S l^+ l^-$− and $B^+ \to K^\ast \ell^+ \ell^-$ decays* ([arXiv:2110.09501](https://arxiv.org/abs/2110.09501))

* Gregory Max Ciezarek on behalf of the [[LHCb collaboration]]: *First joint measurement of $R(D^\ast)$ and $R(D^0)$ at LHCb*, LHC seminar (2022) [[indico:1187939](https://indico.cern.ch/event/1187939), slides: [pdf](https://indico.cern.ch/event/1187939/attachments/2530158/4353109/dtaunu_CERNSeminar.pdf)]

More accurate predictions from [[lattice QCD]] of the expected branching ratios:

* {#PBD22} W. G. Parrott, C. Bouchard, C. T. H. Davies, *Standard Model predictions for $B \to K \ell^+ \ell^-$, $B \to K \ell^-_1 \ell^+_2$ and $B \to K \nu \bar\nu$ using form factors from Nf=2+1+1 lattice QCD* [[arXiv:2207.13371](https://arxiv.org/abs/2207.13371)]

* {#PBD22b} W. G. Parrott, C. Bouchard, C. T. H. Davies, *The search for new physics in $B \to K \ell^+ \ell^-$ and $B \to K \nu^+ \nu^-$ using precise lattice QCD form factors* [[arXiv:2210.10898](https://arxiv.org/abs/2210.10898)]

#### After fixing the backgrounds

Announcement that hadronic backgrounds had been mis-identified all along and observation that fixing this makes at least the anomaly in $R_K$ disappear:

* {#LHCB22} [[LHCb collaboration]], *Test of lepton universality in $b \to s \ell^+ \ell^-$ decays LHCb collaboration* [[arXiv:2212.09152](https://arxiv.org/abs/2212.09152)]

  [[LHCb collaboration]], *Measurement of lepton universality parameters in $B^+ \to K^+ \ell^+ \ell^-$ and $B^0 \to K^{\ast 0} \ell^+ \ell^-$ decays* [[arXiv:2212.09153](https://arxiv.org/abs/2212.09153)]

  $\,$

  anonymous but informative Twitter thread on what happened: [here](https://twitter.com/particleist/status/1605151216094572547)

  $\,$

  Davide Castelvecchi, *[Hint of crack in standard model vanishes in LHC data](https://www.nature.com/articles/d41586-022-04545-z)*, Nature News (20 Dec 2022)

  $\,$

  *[Standard Model survives its biggest challenge yet](https://bigthink.com/starts-with-a-bang/standard-model-survives/)*

Re-analysis finding that thereby essentially all the anomalies disappear:

* {#CFFPSV22} Marco Ciuchini, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini, Mauro Valli, *Constraints on Lepton Universality Violation from Rare B Decays* [[arXiv:2212.10516](https://arxiv.org/abs/2212.10516)]

  > show that current data no longer provide strong hints for NP.

### Review and outlook
 {#ReferencesReviewAndOutlook}

* Elena Graverini, _Flavour anomalies: a review_, in _Proceedings of the [13th International Conference on Beauty, Charm and Hyperon hadrons (BEACH 2018)](http://inspirehep.net/record/1621649)_ ([arXiv:1807.11373](https://arxiv.org/abs/1807.11373))

* {#Guadagnoli17} Diego Guadagnoli, _Flavour anomalies on the eve of the Run-2 verdict_,  Modern Physics Letters AVol. 32, No. 07, 1730006 (2017) ([arXiv:1703.02804](https://arxiv.org/abs/1703.02804))

* Greory Ciezarek, Manuel Franco Sevilla, Brian Hamilton, Robert Kowalewski, Thomas Kuhr, Vera Lüth, Yutaro Sato, _A challenge to lepton universality in B-meson decays_, Nature 546, 227–233 (2017) ([doi:10.1038/nature22346](https://doi.org/10.1038/nature22346))

* [CernCourier](https://cerncourier.com/), _[Beauty quarks test lepton universality](https://cerncourier.com/beauty-quarks-test-lepton-universality/)_, March 2018

* {#Cartelle18} Paula Alvarez Cartelle on behalf of the [[LHCb collaboration]], _New results on flavor anomalies at LHCb_, April 2018 ([pdf](https://cds.cern.ch/record/2311960/files/FlavourAnomaliesLHCbAlvarez.pdf))

* {#Dey18} Biplab Dey on behalf of the [[LHCb collaboration]], _Flavor anomalies at LHCb_, May 2018 ([[DeyFlavourAnomalies2018.pdf:file]])

* Vera Lüth, _A Challenge to Lepton Universality in B Meson Decays_, Invited tall at [7th Symposium on Symmetries in Subatomic Physics (SSP 2018)](https://indico.cern.ch/event/651952/) at RWTH Aachen University (Germany), June 11-15, 2018 ([arXiv:1808.02587](https://arxiv.org/abs/1808.02587))

* {#Dordei18} Francesca Dordei, _Lepton flavour universality at LHCb_, August 2018 ([cern:2634813](http://cdsweb.cern.ch/record/2634813), [pdf](http://cdsweb.cern.ch/record/2634813/files/dordei_nufact.pdf))

* {#Adamczyk19} Karol Adamczyk ([[Belle collaboration]]), _Semitauonic B decays at Belle/Belle II_, Proceedings of the [10th International Workshop on the CKM Unitarity Triangle](https://ckm2018.physi.uni-heidelberg.de/) (CKM 2018), Heidelberg, Germany, September 17-21, 2018 ([arXiv:1901.06380](https://arxiv.org/abs/1901.06380))

* {#BouchardCaoOwen19} Christopher Bouchard, Lu Cao, Patrick Owen, _Summary of the 2018 CKM working group on semileptonic and leptonic b-hadron decays_ ([arXiv:1902.09412](https://arxiv.org/abs/1902.09412))

* {#Zupan19} Jure Zupan, _Introduction to flavour physics_ ([arXiv:1903.05062](https://arxiv.org/abs/1903.05062))

* {#Straub19} David Straub on behalf of [[LHCb collaboration]], _Search for lepton-universality violation in $B^+ \to K^+ \ell^+ \ell^-$ decays_, talk at [Moriond 2019](http://moriond.in2p3.fr/2019/EW/) ([pdf](http://moriond.in2p3.fr/2019/EW/slides/6_Friday/2_afternoon/4_straub-moriond-2019.pdf))

* {#Allanach19} [[Ben Allanach]], _Finding Z's responsible for $R_{K^{(\ast)}}$_, talk at [Moriond 2019](http://moriond.in2p3.fr/2019/EW/) ([pdf](http://moriond.in2p3.fr/2019/EW/slides/6_Friday/2_afternoon/5_Allanach.pdf))

* {#DescotesGenon19} Sebastien Descotes-Genon, _B-physics anomalies, fluctuations and patterns:a status report_, talk at [ALPS2019](https://indico.cern.ch/event/757995/) ([web](https://indico.cern.ch/event/757995/contributions/3315334/), [pdf](https://indico.cern.ch/event/757995/contributions/3315334/attachments/1832940/3002267/slides_alps.pdf))

* {#BardhanGhosh} Debjyoti Bardhan, Diptimoy Ghosh, _B-meson charged current anomalies: the post-Moriond status_ ([arXiv:1904.10432](https://arxiv.org/abs/1904.10432))

* {#Alguero19} Marcel Alguero, _Emerging patterns of New Physics with and without Lepton Flavour Universal contributions_, talk at [bsll2019](https://indico.in2p3.fr/event/18646/) ([pdf](https://indico.in2p3.fr/event/18646/contributions/74403/attachments/54790/71933/Marcel_Alguero_Lyon.pdf), [[AlgueroBsll19.pdf:file]])

* Jon Butterworth, Section 1 in: _Highlights of EPS HEP 2019_, talk at [eps-hep2019](http://eps-hep2019.eu/)
 ([arxiv:1910.12768](https://arxiv.org/abs/1910.12768))

* [[Antonio Pich]], _Flavour Anomalies_, PoS LHCP2019 (2019) 078 ([arxiv:1911.06211](https://arxiv.org/abs/1911.06211), [spire:1765034](https://inspirehep.net/literature/1765034))

* {#London19} David London, _Anomalies in B Decays: A Sign of New Physics?_,
talk at [XIth International Symposium on Quantum Theory and Symmetries](http://www.crm.umontreal.ca/2019/QTS2019/index_e.php), July 1-5, 2018 Centre de recherches mathématiques, Montréal, Canada ([arxiv:1911.06238](https://arxiv.org/abs/1911.06238))

* Barbara Gallavotti, starring [[Gino Isidori]], _How Particle Physics Works: Episode II - The New Analysis_, June 2019 ([youtube](https://www.youtube.com/watch?v=krWPeFLLBFY))

* {#JaiswalNandiPatra20} Sneha Jaiswal, Soumitra Nandi, Sunando Kumar Patra, _Updates on SM predictions of $\vert V_{c b}\vert$ and $R(D^{(\ast)})$  in $B\to D^\ast \ell \nu_\ell$ decays_ ([arXiv:2002.05726](https://arxiv.org/abs/2002.05726))

* {#Smith20} Eluned Smith on behalf of the [[LHCb collaboration]], _Update of the $B^0 \to K^{\ast 0} \mu^+ \mu^-$ angular analysis at LHCb_, 2020 ([[SmithatLHCbOnFlavourAnomalies2020.pdf:file]])

  (on [LHCb2003.04831](#LHCb200304831))

* {#Lopes20} Ana Lopes, _[New LHCb analysis still sees previous intriguing results](https://home.cern/news/news/physics/new-lhcb-analysis-still-sees-previous-intriguing-results)_, CERN News 2020

  (on [LHCb2003.04831](#LHCb200304831))

* {#CERNCourir200311} CERN Courier, _[Anomalies persist in flavour-changing B decays](https://cerncourier.com/a/anomalies-persist-in-flavour-changing-b-decays/)_, March 13 2020

  (on [LHCb2003.04831](#LHCb200304831))

* {#Koppenburg20} [[Patrick Koppenburg]], _Beauty 2019 -- Conference summary_ ([arXiv:2001.11796](https://arxiv.org/abs/2001.11796))

* {#Virto21} [[Javier Virto]], _Anomalies in $b \to s \ell \ell$ transitions and Global Fits_ ([arXiv:2103.01106](https://arxiv.org/abs/2103.01106))

* {#AltmannshoferStangl21} [[Wolfgang Altmannshofer]], [[Peter Stangl]], _New Physics in Rare B Decays after Moriond 2021_ ([arXiv:2103.13370](https://arxiv.org/abs/2103.13370))

* {#CFFIN21} Claudia Cornella, Darius A. Faroughy, [[Javier Fuentes-Martin]], [[Gino Isidori]], [[Matthias Neubert]], _Reading the footprints of the B-meson flavor anomalies_ ([arXiv:2103.16558](https://arxiv.org/abs/2103.16558))

* {#LIOS21} Davide Lancierini, [[Gino Isidori]], Patrick Owen, Nicola Serra, _On the significance of new physics in $b \to s \ell^+ \ell^-$ decays_ ([arXiv:2104.05631](https://arxiv.org/abs/2104.05631))

* {#HMSN21} T. Hurth, F. Mahmoudi, D. Martinez Santos, S. Neshatpour, *More Indications for Lepton Nonuniversality in $b \to s \ell^+ \ell^-$ ([arXiv:2104.10058](https://arxiv.org/abs/2104.10058))

* {#Crivellin21} [[Andreas Crivellin]], *Heavy Flavours -- Theory*, talk at [LHCP, Paris 2021](https://indico.cern.ch/event/905399/) ([[CrivellinLHCP2021.pdf:file]])

* {#LancieriniMoise21} Davide Lancierini, R. Dan Moise, *[Anomalous measurements: recent results deepen flavour puzzle](https://ep-news.web.cern.ch/content/anomalous-measurements-recent-lhcb-results-deepen-flavour-puzzle)*, CERN EP Newsletter 21st June 2021  ([arXiv:2107.06337](https://arxiv.org/abs/2107.06337))

* {#GengEtAl21} Li-Sheng Geng, Benjamín Grinstein, Sebastian Jäger, Shuang-Yi Li, Jorge Martin Camalich, Rui-Xiang Shi, *Implications of new evidence for lepton-universality violation in $b \to s \ell^+ \ell^-$ decays*, Phys. Rev. D **104** (2021) 035029  ([arXiv:2103.12738](https://arxiv.org/abs/2103.12738), [doi:10.1103/PhysRevD.104.035029](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.035029))

* David London, Joaquim Matias, *$B$ Flavour Anomalies: 2021 Theoretical Status Report* ([arXiv:2110.13270](https://arxiv.org/abs/2110.13270))

* Valerio Gherardi, *New Physics Hints from Flavour* ([arXiv:2111.00285](https://arxiv.org/abs/2111.00285))

* [[Monika Blanke]], *Theory Perspective on Heavy Flavour Physics*, talk at [10th Edition of the Large Hadron Collider Physics Conference](https://indico.cern.ch/event/1109611/) (2022) [[arXiv:2207.07354](https://arxiv.org/abs/2207.07354), talk slides and recording: [indico.cern:4686945](https://indico.cern.ch/event/1109611/contributions/4686945)]

* F. Mahmoudi, *Theoretical Review of Rare B Decays* [[arXiv:2208.05755](https://arxiv.org/abs/2208.05755)]

* {#IKW22} Syuhei Iguro, Teppei Kitahara, Ryoutaro Watanabe, *Global fit to $b \to c \tau \nu$ anomalies 2022 mid-autumn* [[arXiv:2210.10751](https://arxiv.org/abs/2210.10751)]

* Ashutosh Kotwal, Joaquim Matias, Andrea Mauri, Tom Tong, Lukas Varnhorst, *Round table on Standard Model Anomalies* [[arXiv:2211.13030](https://arxiv.org/abs/2211.13030)]

Further outlook:

* {#AllanachGripaiosYou17} [[Ben Allanach]], Ben Gripaios, Tevong You, _The Case for Future Hadron Colliders From $B \to K^{(\ast)}\mu^+ \mu^-$ Decays_, JHEP03(2018)021 ([arXiv:1710.06363](https://arxiv.org/abs/1710.06363))

* {#LHCbCollaboration18} [[LHCb collaboration]], _Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era_ ([arXiv:1808.08865](https://arxiv.org/abs/1808.08865))

* {#CrivellinEtAl18} A. Cerri, [[Andreas Crivellin]] et. al. _Opportunities in Flavour Physics at the HL-LHC and HE-LHC_, Report from Working Group 4 on the [Physics of the HL-LHC, and Perspectives at the HE-LHC](https://indico.cern.ch/event/686494/) ([arXiv:1812.07638](https://arxiv.org/abs/1812.07638))

* [[Gino Isidori]], *Hints of New Physics from flavor-changing processes*, talk at SPS Annual Meeting, Lausanne, Aug. 2018 ([pdf](https://indico.cern.ch/event/716246/contributions/3097683/attachments/1709141/2754825/SPS_Lausanne.pdf))

* {#Isidori19} [[Gino Isidori]], _Flavor physics & CP violation_, talk at [Symposium on the European Strategy for Particle Physics](https://indico.cern.ch/event/808335/timetable/#20190513.detailed) 2019 ([pdf](https://indico.cern.ch/event/808335/contributions/3365125/attachments/1842875/3022853/Granada_GI_13May.pdf))

* {#LKLR19} Luca Di Luzio, Matthew Kirk, Alexander Lenz, Thomas Rauh, _$\Delta M_s$ theory precision confronts flavour anomalies_ ([arXiv:1909.11087](https://arxiv.org/abs/1909.11087))

* {#Grinstein19} [[Benjamin Grinstein]], _A path to flavor_, talk at _[Implications of LHCb measurement and future prospects](https://indico.cern.ch/event/769902/)_ CERN 2019 ([pdf](https://indico.cern.ch/event/769902/contributions/3582540/attachments/1926501/3193107/Grinstein-high-res.pdf), [[GrinsteinFlavor2019.pdf:file]], [indico:3582540](https://indico.cern.ch/event/769902/contributions/3582540))

* [[Monika Blanke]], _Flavour Physics from Present to Future Colliders_, talk at [LFC19: Strong dynamics for physics within and beyond the Standard Model at LHC and Future Colliders](https://indico.ectstar.eu/event/55/) (2019) ([arxiv:1910.10662](https://arxiv.org/abs/1910.10662))

* {#CrivellinHoferichter20} [[Andreas Crivellin]], Martin Hoferichter, _Beta decays as sensitive probes of lepton flavor universality_ ([arXiv:2002.07184](https://arxiv.org/abs/2002.07184))

* {#Garisto20} Dan Garisto, _The Era of Anomalies_, [Physics 13, 79 (2020)](https://physics.aps.org/articles/v13/79)

* {#Tuning20} [[Niels Tuning]], _Recent results from LHCb_, Nikhef 2020 ([nikhef event:2253](https://indico.nikhef.nl/event/2253), [pdf](https://indico.nikhef.nl/event/2253/material/slides/0.pdf), [[TuningFlavourAnomaly20.pdf:file]])

  > In recent years a number of results in flavour physics have drawn some attention due to tensions with respect to Standard Model predictions. An overview of these results will be shown, together with a few recent results from this Spring, both on the flavour anomalies and 'classical' flavour physics

* Florian U. Bernlochner, Manuel Franco Sevilla, Dean J. Robinson, Guy Wormser,  _Semitauonic b-hadron decays: A lepton flavor universality laboratory_ ([arXiv:2101.08326](https://arxiv.org/abs/2101.08326))

* {#GGJLMCS21} Li-Sheng Geng, Benjamín Grinstein, Sebastian Jäger, Shuang-Yi Li, Jorge Martin Camalich, Rui-Xiang Shi, _Implications of new evidence for lepton-universality violation in $b \to s \ell^+ \ell^-$ decays_ ([arXiv:2103.12738](https://arxiv.org/abs/2103.12738))

* [[Riccardo Barbieri]], Section 5 of: _A view of flavour physics in 2021_ ([arXiv:2103.15635](https://arxiv.org/abs/2103.15635))

* {#GuadagnoliKoppenburg22} Diego Guadagnoli, [[Patrick Koppenburg]], *Lepton-flavor violation and lepton-flavor-universality violation in b and c decays* [[arXiv:2207.01851](https://arxiv.org/abs/2207.01851)]

* {#Soni22} Amarjit Soni, *Precision tau physics: Challenge for Theory, on and off the lattice* [[arXiv:2211.05839](https://arxiv.org/abs/2211.05839)]

Outlook for [[Belle II]] to confirm the [[flavour anomalies]], if they are real:

* {#HHJLQV20} Tobias Huber, Tobias Hurth, Jack Jenkins, Enrico Lunghi, Qin Qin, K.Keri Vos, _Phenomenology of inclusive $\bar B \to X_s \ell^+ \ell^-$ for the Belle II era_ ([arXiv:2007.04191](https://arxiv.org/abs/2007.04191))

Emphasis of [[non-perturbative effects]]:

* {#Nierste18} Ulrich Nierste, _Flavour Anomalies: Phenomenology and BSM Interpretations_, talk at [Planck 2018](https://indico.desy.de/indico/event/18498/), Bonn 2018 ([pdf](https://indico.desy.de/indico/event/18498/session/5/contribution/52/material/slides/0.pdf))

* Saeed Kamali, _New physics in inclusive semileptonic $B$ decays including nonperturbative corrections_ ([arXiv:1811.07393](https://arxiv.org/abs/1811.07393))

Emphasis of higher [[loop order]]-effects:

* {#CGMS18} [[Andreas Crivellin]], Christoph Greub, Dario Müller, Francesco Saturnino, _Importance of Loop Effects in Explaining the Accumulated Evidence for New Physics in B Decays with a Vector Leptoquark_, Phys. Rev. Lett. 122, 011805 (2019) ([arXiv:1807.02068](https://arxiv.org/abs/1807.02068))

Emphasis of effects of [[hadron|hadronic]] [[form factors]]:

* {#DGKV19} Sébastien Descotes-Genon, Alexander Khodjamirian, [[Javier Virto]], _Light-Cone Sum Rules for $B \to K \pi$ Form Factors and Applications to Rare Decays_ ([arXiv:1908.02267](https://arxiv.org/abs/1908.02267))

* {#DescotesGenon19b} Sebastien Descotes-Genon, _Light-cone sum rules for $B \to K \pi$ form factorsand applications to rare decays_, talk at [bsll2019](https://indico.in2p3.fr/event/18646/) ([pdf](https://indico.in2p3.fr/event/18646/contributions/74316/attachments/54770/71918/slides_bslllyon.pdf), [[DescotesGenonBssl19.pdf:file]])

Emphasis of [[QED]]-corrections:

* {#MishraMahajan20} Dayanand Mishra, Namit Mahajan
On the Impact of Soft Photons on  $B \to K \ell^+ \ell^-$ ([arXiv:2010.10853](https://arxiv.org/abs/2010.10853))

Textbook account:

* {#Buras20}  [[Andrzej Buras]], _Gauge Theory of Weak Decays_, (2020) ([doi:10.1017/9781139524100](https://doi.org/10.1017/9781139524100), [CERN review](https://cerncourier.com/a/the-hitchhikers-guide-to-weak-decays/) by [[Gino Isidori]])

Original articles:

* {#StrumiaEtAl17} Guido D'Amico, Marco Nardecchia, Paolo Panci, Francesco Sannino, [[Alessandro Strumia]], Riccardo Torre, Alfredo Urbano,

  _Flavour anomalies after the $R_{K^\ast}$ measurement_,

  J. High Energ. Phys. (2017) 2017 ([arXiv:1704.05438](https://arxiv.org/abs/1704.05438))

* Andrea  Mauri, Nicola Serra, Rafael  Silva  Coutinho, _Towards establishing Lepton Flavour Universality violation in $\bar B \to \bar K^\ast \ell^+ \ell^-$ decays_ ([arXiv:1805.06401](https://arxiv.org/abs/1805.06401))

* {#CCDGMV17} Bernat Capdevila, [[Andreas Crivellin]], Sébastien Descotes-Genon, Joaquim Matias, [[Javier Virto]], _Patterns of New Physics in $b \to s \ell^+ \ell^-$ transitions in the light of recent data_, JHEP 1801 (2018) 093 ([arXiv:1704.05340](https://arxiv.org/abs/1704.05340))

* {#CFMVV17} Alejandro Celis, [[Javier Fuentes-Martin]], Avelino Vicente, [[Javier Virto]], _Gauge-invariant implications of the LHCb measurements on Lepton-Flavour Non-Universality_, Phys. Rev. D 96, 035026 (2017) ([arXiv:1704.05672](https://arxiv.org/abs/1704.05672))

* [[Monika Blanke]], [[Andreas Crivellin]], Stefan de Boer, Teppei Kitahara, Marta Moscati, Ulrich Nierste, Ivan Nišandžić, _Impact of polarization observables and $B_c \to \tau \nu$ on new physics explanations of the $b \to c \tau \nu$ anomaly_ ([arXiv:1811.09603](https://arxiv.org/abs/1811.09603))

* [[Monika Blanke]], [[Andreas Crivellin]], Stefan de Boer, Teppei Kitahara, Marta Moscati, Ulrich Nierste, Ivan Nišandžić, _Addendum: "Impact of polarization observables and $B_c \to \tau \nu$ on new physics explanations of the $b \to c \tau \nu$ anomaly"_ ([arXiv:1905.08253](https://arxiv.org/abs/1905.08253))

* {#KumarLondon19} Jacky Kumar, David London, _New physics in $b \to s e^+ e^-$?_, Phys. Rev. D 99, 073008 (2019) ([arXiv:1901.04516](https://arxiv.org/abs/1901.04516), [doi:10.1103/PhysRevD.99.073008](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.99.073008))

* Domagoj Leljak, Blazenka Melic, Monalisa Patra, _On lepton flavour universality in semileptonic $B_c \to \eta_c, J/\psi$ decays_ ([arXiv:1901.08368](https://arxiv.org/abs/1901.08368))

* {#SGGJC19} Rui-Xiang Shi, Li-Sheng Geng, Benjamín Grinstein, Sebastian Jäger, Jorge Martin Camalich, _Revisiting the new-physics interpretation of the $b \to c \tau \nu$ data_ ([arXiv:1905.08498](https://arxiv.org/abs/1905.08498))

Cautionary remarks include

* _[Some B Meson Decay Anomalies Disappear In Run-2 Data](http://dispatchesfromturtleisland.blogspot.com/2017/05/some-b-meson-decay-anomalies-disappear.html)_

* {#Caria19} Giacomo Caria on behalf of the [[Belle collaboration]], _Measurement of $R(D)$ and $R(D^\ast)$ with a semileptonic tag at Belle_, Moriond, EW  22/03/2019 ([pdf](http://moriond.in2p3.fr/2019/EW/slides/6_Friday/3_YSF/1_gcaria_moriond2019.pdf))

In contrast, an argument that the threshold [[statistical significance]] for flavour anomalies should be taken to be $3\sigma$ instead of $5 \sigma$ is made in

* {#Lyons13b} Louis Lyons, _Discovering the Significance of 5 sigma_ ([arXiv:1310.1284](https://arxiv.org/abs/1310.1284))

* {#Dorigo15} [[Tommaso Dorigo]], _Extraordinary claims: the $0.000029\%$ solution_, EPJ Web of Conferences 95, 02003 (2015) ([doi:10.1051/epjconf/20159502003](https://doi.org/10.1051/epjconf/20159502003))

Discussion of possible $b \to d$ anomalies:

* Aleksey V. Rusov, _Probing New Physics in $b \to d$ Transitions_ ([arXiv:1911.12819](https://arxiv.org/abs/1911.12819))

### In hadronic decays

* Marzia Bordone, Nico Gubernari, Tobias Huber, Martin Jung, Danny van Dyk, _A puzzle in B¯0(s)→D+(s){π−,K−} decays and extraction of the fs/fd fragmentation fraction_ ([arXiv:2007.10338](https://arxiv.org/abs/2007.10338))

* Syuhei Iguro, Teppei Kitahara, _Implications for new physics from novel puzzle in B¯0(s)→D(∗)+(s){π−,K−} decays_ ([arXiv:2008.01086](https://arxiv.org/abs/2008.01086))

* Eleftheria Malami, _Exploring New Physics in B→πK Decays_ ([arXiv:2008.08468](https://arxiv.org/abs/2008.08468))

### Relation to $(g-2)$-anomalies

Beyond their possible common origin in [[leptoquarks]], further possible joint explanation of [[flavour anomalies]] and the [anomalies](anomalous+magnetic+moment#Anomalies) observed in the [[muon]] [[anomalous magnetic moment]]:

* Geneviève Bélanger, Cédric Delaunay, Susanne Westhoff, _A Dark Matter Relic From Muon Anomalies_,  Phys. Rev. D 92, 055021 (2015) ([arXiv:1507.06660](https://arxiv.org/abs/1507.06660))

* {#ChiangOkada17} Cheng-Wei Chiang, Hiroshi Okada, _A simple model for explaining muon-related anomalies and dark matter_ ([arXiv:1711.07365](https://arxiv.org/abs/1711.07365))

* Junichiro Kawamura, Stuart Raby, Andreas Trautner, _Complete Vector-like Fourth Family and new $U(1)'$ for Muon Anomalies_ ([arXiv:1906.11297](https://arxiv.org/abs/1906.11297))

* Lorenzo Calibbi, M.L. López-Ibáñez, Aurora Melis, Oscar Vives, _Muon and electron $g-2$ and lepton masses in flavor models_ ([arXiv:2003.06633](https://arxiv.org/abs/2003.06633))

* A. S. de Jesus, S. Kovalenko, F. S. Queiroz, K. Sinha, C. Siqueira, _Vector-Like Leptons and Inert Scalar Triplet: Lepton Flavor Violation, $g-2$ and Collider Searches_ ([arXiv:2004.01200](https://arxiv.org/abs/2004.01200))

* Shaikh Saad, _Combined explanations of $(g-2)_\mu$, $R_{D^\ast}$, $R_{K^\ast}$ anomalies in a two-loop radiative neutrino mass model_ ([arXiv:2005.04352](https://arxiv.org/abs/2005.04352))

* K. S. Babu, P. S. Bhupal Dev, Sudip Jana, Anil Thapa, _Unified Framework for $B$-Anomalies, Muon $g-2$, and Neutrino Masses_ ([arXiv:2009.01771](https://arxiv.org/abs/2009.01771))

* Sang Quang Dinh, Hieu Minh Tran, _Muon $g-2$ and semileptonic $B$ decays in BDW model with gauge kinetic mixing_ ([arXiv:2011.07182](https://arxiv.org/abs/2011.07182))

### Possible explanations/models

#### General EFT parameterization

General [[effective field theory]] parametrization:

* {#HAMN18} T. Hurth, A. Arbey, F. Mahmoudi, S. Neshatpour, _New global fits to $b \to s$ data with all relevant parameters_, Proceedings of the [Seventh Workshop on Theory, Phenomenology and Experiments in Flavour Physics](https://agenda.infn.it/event/14359/), Capri, 8-10 June 2018 ([arXiv:1812.07602](https://arxiv.org/abs/1812.07602))

* Srimoy Bhattacharya, Aritra Biswas, Zaineb Calcuttawala, Sunando Kumar Patra, _An in-depth analysis of $b \to c(s)$ semileptonic observables with possible $\mu \to \tau$ mixing_ ([arXiv:1902.02796](https://arxiv.org/abs/1902.02796))

* {#ACDGMM19} Marcel Algueró, Bernat Capdevila, Sébastien Descotes-Genon, Pere Masjuan, Joaquim Matias, _What $R_K$ and $Q_5$ can tell us about New Physics in $b \to s \ell \ell$ transitions?_ ([arXiv:1902.04900](https://arxiv.org/abs/1902.04900))

* Marcel Algueró, Bernat Capdevila, [[Andreas Crivellin]], Sébastien Descotes-Genon, Pere Masjuan, Joaquim Matias, [[Javier Virto]], _Addendum: "Patterns of New Physics in $b \to s \ell^+ \ell^-$ transitions in the light of recent data"_ ([arXiv:1903.09578](https://arxiv.org/abs/1903.09578))

* Ashutosh Kumar Alok, Amol Dighe, Shireen Gangal, Dinesh Kumar, _Continuing search for new physics in $b \to \mu s s$ decays: two operators at a time_ ([arXiv:1903.09617](https://arxiv.org/abs/1903.09617))

* Marco Ciuchini, António M. Coutinho, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini, Mauro Valli, _New Physics in $b \to s \ell^+ \ell^-$ confronts new data on Lepton Universality_ ([arXiv:1903.09632](https://arxiv.org/abs/1903.09632))

* Jason Aebischer, [[Wolfgang Altmannshofer]], Diego Guadagnoli, Meril Reboud, [[Peter Stangl]], David M. Straub, _B-decay discrepancies after Moriond 2019_ ([arXiv:1903.10434](https://arxiv.org/abs/1903.10434))

* Alakabha Datta, Jacky Kumar, David London, _The $B$ Anomalies and New Physics in $b \to s e^+ e^-$_ ([arXiv:1903.10086](https://arxiv.org/abs/1903.10086))

* Ashutosh Kumar Alok, Dinesh Kumar, Suman Kumbhakar, S Uma Sankar, _Impact of $D^\ast$ polarization measurement on solutions to $R_D$-$R_{D^\ast}$ anomalies_ ([arXiv:1903.10486](https://arxiv.org/abs/1903.10486))

* Pere Arnan, [[Andreas Crivellin]], Marco Fedele, Federico Mescia, _Generic Loop Effects of New Scalars and Fermions in $b \to s \ell^+ \ell^-$ and a Vector-like 4th Generation_ ([arXiv:1904.05890](https://arxiv.org/abs/1904.05890))

* {#AHMSN19} A. Arbey, T. Hurth, F. Mahmoudi, D. Martinez Santos, S. Neshatpour, _Update on the $b \to s$ anomalies_ ([arXiv:1904.08399](https://arxiv.org/abs/1904.08399))

* Pouya Asadi, David Shih, _Maximizing the Impact of New Physics in $b \to c \tau \nu$ Anomalies_,  ([arXiv:1905.03311](https://arxiv.org/abs/1905.03311))

* J. E. Chavez-Saab, Marxil Sánchez, Genaro Toledo, _$R_{D^\ast}$ or $R_{D_\pi}$: closing the theoretical gap?_ ([arXiv:1905.03394](https://arxiv.org/abs/1905.03394))

* Suman Kumbhakar, Ashutosh Kumar Alok, Dinesh Kumar, S Uma Sankar, _Resolving $R_D$ and $R_{D^\ast}$ anomalies_ ([arXiv:1905.03513](https://arxiv.org/abs/1905.03513))

* Jyoti Saini, Dinesh Kumar, Shireen Gangal, S. B. Dasm, _Probing signatures of beyond standard model physics through $B_s^\ast \to \mu^+ \mu^-$ decay_ ([arXiv:1905.03933](https://arxiv.org/abs/1905.03933))

* David London, _CP Violation in $\bar B^0 \to D^{\ast +} \ell^- \bar \nu_\ell$_ ([arXiv:1906.07752](https://arxiv.org/abs/1906.07752))

* Marta Moscati, _New Physics in $b \to c \tau \nu$: Impact of Polarisation Observables and $B_c \to \tau \nu$_ ([arXiv:1906.08035](https://arxiv.org/abs/1906.08035))

* Damir Becirevic, Marco Fedele, Ivan Nisandzic, Andrey Tayduganov, _Lepton Flavor Universality tests through angular observables of $\bar B \to D^{(\ast) \ell \bar \nu}$ decay modes_ ([arXiv:1907.02257](https://arxiv.org/abs/1907.02257))

* Ashutosh Kumar Alok, Suman Kumbhakar, S. Uma Sankar, _Discriminating new physics scenarios in b→sμ+μ− via transverse polarization asymmetry of K∗ in B→K∗μ+μ− decay_ ([arXiv:2001.04395](https://arxiv.org/abs/2001.04395))

* Suman Kumbhakar, Ashutosh Kumar Alok, Dinesh Kumar, S. Uma Sankar, _New Physics solutions for $b \to c \tau \bar \nu$ anomalies after Moriond 2019_ ([arXiv:2001.06344](https://arxiv.org/abs/2001.06344))

* Florian U. Bernlochner, Stephan Duell, Zoltan Ligeti, Michele Papucci, Dean J. Robinson, _Das ist der HAMMER: Consistent new physics interpretations of semileptonic decays_ ([arXiv:2002.00020](https://arxiv.org/abs/2002.00020))

* Andrei Angelescu, Darius A. Faroughy, Olcyr Sumensari, _Lepton Flavor Violation and Dilepton Tails at the LHC_ ([arXiv:2002.05684](https://arxiv.org/abs/2002.05684))

* Kingman Cheung, Zhuo-Ran Huang, Hua-Dong Li, Cai-Dian Lü, Ying-nan Mao, Ru-Ying Tang, _Revisit to the $b \to c \tau \nu$ transition: in and beyond the SM_ ([arXiv:2002.07272](https://arxiv.org/abs/2002.07272))

* Soumia Lebbal, Noureddine Mebarki, Jamal Mimouni, _Lepton Flavor Universality Violation in a 331 Model in $b \to s l^+ l^-$ Processes_ ([arXiv:2003.03230](https://arxiv.org/abs/2003.03230))

* {#AHRS20} Rafael Aoude, Tobias Hurth, Sophie Renner, William Shepherd, _The impact of flavour data on global fits of the MFV SMEFT_ ([arXiv:2003.05432](https://arxiv.org/abs/2003.05432))

* Aritra Biswas, Soumitra Nandi, Ipsita Ray, Sunando Kumar Patra,
_New physics in $b\to s \ell \ell$ decays with complex Wilson coefficients_ ([arXiv:2004.14687](https://arxiv.org/abs/2004.14687))

* {#BDKL20}   Bhubanjyoti Bhattacharya, Alakabha Datta, Saeed Kamali, David London, _A Measurable Angular Distribution for $\bar B \to D^\ast \tau^- \bar \nu_\tau$ Decays_ ([arXiv:2005.03032](https://arxiv.org/abs/2005.03032))

* N. Penalva, E. Hernández, J. Nieves, _$\bar B_c \to \eta_c$, $\bar B_c \to J/\psi$ and $\bar B \to D^{(\ast)}$ semileptonic decays including new physics_ ([arXiv:2007.12590](https://arxiv.org/abs/2007.12590))

* Aishwarya Bhatta, Rukmani Mohanta, _Implications of new physics in $B \to K_1 \mu^+ \mu^-$−decay processes_ ([arXiv:2011.05820](https://arxiv.org/abs/2011.05820))

* S. Neshatpour, T. Hurth, F. Mahmoudi, _Searching for New Physics with $ B^0 \to K^{\ast 0} \mu^+ \mu^-$  ([arXiv:2012.07408](https://arxiv.org/abs/2012.07408))

In relation to [[electroweak field|electroweak]] [[precision measurements]]:

* Lina Alasfar, Aleksandr Azatov, Jorge de Blas, Ayan Paul, Mauro Valli, _B anomalies under the lens of electroweak precision_ ([arXiv:2007.04400](https://arxiv.org/abs/2007.04400))

* Ashutosh Kumar Alok, Suman Kumbhakar, Jyoti Saini, S Uma Sankar, _New physics in $b \to s e^+ e^-$: A model independent analysis_ ([arXiv:2011.14668](https://arxiv.org/abs/2011.14668))

* T. Hurth, F. Mahmoudi, S. Neshatpour, _Model independent analysis of the angular observables in B0→K∗0μ+μ− and B+→K∗+μ+μ−_ ([arXiv:2012.12207](https://arxiv.org/abs/2012.12207))

* Jorge Alda, Jaume Guasch, Siannah Penaranda, _Anomalies in B mesons decays: A phenomenological approach_ ([arXiv:2012.14799](https://arxiv.org/abs/2012.14799))

* Jorge Alda, Jaume Guasch, Siannah Penaranda, *Anomalies in B mesons decays: Present status and future collider prospects* ([arXiv:2105.05095](https://arxiv.org/abs/2105.05095))

#### Leptoquarks

explanation via assumption of [[leptoquarks]]:

* {#BauerNeubert15} Martin Bauer, [[Matthias Neubert]], _One Leptoquark to Rule Them All: A Minimal Explanation for $R_{D^{(\ast)}}$, $R_K$ and $(g-2)_\mu$_, Phys. Rev. Lett. 116, 141802 (2016) ([arXiv:1511.01900](https://arxiv.org/abs/1511.01900))

* Yi Cai, John Gargalionis, Michael A. Schmidt, Raymond R. Volkas, _Reconsidering the One Leptoquark solution: flavor anomalies and neutrino mass_ ([arXiv:1704.05849](https://arxiv.org/abs/1704.05849))

* {#CCDM16} Estefania Coluccio Leskow, [[Andreas Crivellin]], Giancarlo D'Ambrosio, Dario Müller, _$(g-2)_\mu$, Lepton Flavour Violation and Z Decays with Leptoquarks: Correlations and Future Prospects_, Phys. Rev. D 95, 055018 (2017) ([arXiv:1612.06858](https://arxiv.org/abs/1612.06858))

* {#Crivellin17} [[Andreas Crivellin]], _New Physics in Flavour Observables_ ([arXiv:1706.00929](https://arxiv.org/abs/1706.00929))

* {#Falkowski17} [[Adam Falkowski]], _[Leptoquarks strike back](http://resonaances.blogspot.com/2015/11/leptoquarks-strike-back.html)_, November 2017

* {#Mueller18} Dario Müller, _Leptoquarks in Flavour Physics_, EPJ Web of Conferences 179, 01015 (2018) ([arXiv:1801.03380](https://arxiv.org/abs/1801.03380))

* {#MatsuzakiNishiwaki18} Shinya Matsuzaki, Kenji Nishiwaki, Kei Yamamoto, _Simultaneous interpretation of K and B anomalies in terms of chiral-flavorful vectors_ ([arXiv:1806.02312](https://arxiv.org/abs/1806.02312))

* {#MonteuxRajaraman18} Angelo Monteux, [[Arvind Rajaraman]], _B Anomalies and Leptoquarks at the LHC: Beyond the Lepton-Quark Final State_, Phys. Rev. D 98, 115032 (2018) ([arXiv:1803.05962](https://arxiv.org/abs/1803.05962))

* {#AMST18} Ufuk Aydemir, Djordje Minic, Chen Sun, Tatsu Takeuchi, _$B$-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry_, JHEP 09 (2018) 117 ([arXiv:1804.05844](https://arxiv.org/abs/1804.05844))

* {#BDFKFS18} Damir Bečirević, Ilja Doršner, Svjetlana Fajfer, Nejc Košnik, Darius A. Faroughy, Olcyr Sumensari, _Scalar leptoquarks from GUT to accommodate the $B$-physics anomalies_, Phys. Rev. D 98, 055003 (2018) ([arXiv:1806.05689](https://arxiv.org/abs/1806.05689))

* {#KumarLondonWatanabe18} Jacky Kumar, David London, Ryoutaro Watanabe, _Combined Explanations of the $b \to s \mu^+ \mu^-$ and $b \to c \tau^- \bar \nu$ Anomalies: a General Model Analysis_, Phys. Rev. D 99, 015007 (2019) ([arXiv:1806.07403](https://arxiv.org/abs/1806.07403))

  (reviewed in [Kumar 19](#Kumar19))

* {#MMR18} Tanumoy Mandal, Subhadip Mitra, Swapnil Raz, _$R_{D^{(\ast)}}$ in minimal leptoquark scenarios: impact of interference on the exclusion limits from LHC data_ ([arXiv:1811.03561](https://arxiv.org/abs/1811.03561))

* Jason Aebischer, [[Andreas Crivellin]], Christoph Greub, _QCD Improved Matching for Semi-Leptonic B Decays with Leptoquarks_ ([arXiv:1811.08907](https://arxiv.org/abs/1811.08907))

* Michael J. Baker, [[Javier Fuentes-Martin]], [[Gino Isidori]], [[Matthias König]], _High-pT Signatures in Vector-Leptoquark Models_ ([arXiv:1901.10480](https://arxiv.org/abs/1901.10480))

* {#MVT19} Ivo de Medeiros Varzielas, Jim Talbert, _Simplified Models of Flavourful Leptoquarks_ ([arXiv:1901.10484](https://arxiv.org/abs/1901.10484))

* Natascia Vignaroli, _Seeking leptoquarks in the $t \bar t$ plus missing energy channel at the high-luminosity LHC_ ([arXiv:1808.10309](https://arxiv.org/abs/1808.10309))

* {#AMM19} Ufuk Aydemir, Tanumoy Mandal, Subhadip Mitra,
_Addressing the $R_{D^{(\ast)}}$ anomalies with an S1 leptoquark from $SO(10)$ grand unification_,  Phys. Rev. D 101, 015011 (2020) ([arXiv:1902.08108](https://arxiv.org/abs/1902.08108))

* {#MVK19} Ivo de Medeiros Varzielas, Stephen F. King, _Origin of Yukawa couplings for Higgs and leptoquarks_ ([arXiv:1902.09266](https://arxiv.org/abs/1902.09266))

* {#CataMannel19} Oscar Cata, Thomas Mannel, _Linking lepton number violation with $B$ anomalies_ ([arXiv:1903.01799](https://arxiv.org/abs/1903.01799))

* Bhubanjyoti Bhattacharya, Alakabha Datta, Saeed Kamali, David London, _CP Violation in $\bar B^0 \to D^{\ast +} \mu^- \bar \nu_\mu$_ ([arXiv:1903.02567](https://arxiv.org/abs/1903.02567))

* Han Yan, Ya-Dong Yang, Xing-Bo Yuan, _Phenomenology of $b \to c \tau \bar \nu$ decays in a scalar leptoquark model_ ([arXiv:1905.01795](https://arxiv.org/abs/1905.01795))

* Alakabha Datta, Divya Sachdeva, John Waite, _A unified explanation of $b \to s\mu^= \mu^-$ anomalies, neutrino masses and $B \to \pi K$ puzzle_ ([arXiv:1905.04046](https://arxiv.org/abs/1905.04046))

* Andrei Angelescu, _Single Leptoquark Solutions to the $B$-physics Anomalies_, contribution to the [2019 EW session](http://moriond.in2p3.fr/2019/EW/) of the [54th Rencontres de Moriond](http://moriond.in2p3.fr/2019/) ([arXiv:1905.06044](https://arxiv.org/abs/1905.06044))

* Oleg Popov, Michael A. Schmidt, Graham White, _$R_2$ as a single leptoquark solution to $R_{D^{(\ast)}}$ and $R_{K^{(\ast)}}$_ ([arXiv:1905.06339](https://arxiv.org/abs/1905.06339))

* [[Andreas Crivellin]], Francesco Saturnino, _Correlating Tauonic B Decays to the Neutron EDM via a Scalar Leptoquark_ ([arXiv:1905.08257](https://arxiv.org/abs/1905.08257))

* {#CrivellinSaturnino19} [[Andreas Crivellin]], Francesco Saturnino, _Explaining the Flavor Anomalies with a Vector Leptoquark (Moriond 2019 update)_ ([arXiv:1906.01222](https://arxiv.org/abs/1906.01222))

* {#BGV19} Innes Bigaran, John Gargalionis, Raymond R. Volkas, _A near-minimal leptoquark model for reconciling flavour anomalies and generating radiative neutrino masses_ ([arXiv:1906.01870](https://arxiv.org/abs/1906.01870))

* {#Malinsky19} [[Michal Malinský]], _Lepton non-universality in $B$-decays in the minimal leptoquark gauge model_ ([arXiv:1906.09174](https://arxiv.org/abs/1906.09174))

* Jordan Bernigaud, Ivo de Medeiros Varzielas, Jim Talbert, _Finite Family Groups for Fermionic and Leptoquark Mixing Patterns_ ([arXiv:1906.11270](https://arxiv.org/abs/1906.11270))

* Junichiro Kawamura, Stuart Raby, Andreas Trautner, _Complete Vector-like Fourth Family and new $U(1)'$ for Muon Anomalies_ ([arXiv:1906.11297](https://arxiv.org/abs/1906.11297))

* Leandro Da Rold, Federico Lamagna, _A vector leptoquark for the B-physics anomalies from a composite GUT_ ([arXiv:1906.11666](https://arxiv.org/abs/1906.11666))

* {#Kumar19} Jacky Kumar, _Combined explanation of the B-anomalies_, Proceedings for FPCP 2019 ([arXiv:1907.00416](https://arxiv.org/abs/1907.00416))

  (review of [KumarLondonWatanabe18](#KumarLondonWatanabe18))

* C. Hati, J. Kriewald, J. Orloff, A.M. Teixeira, _A nonunitary interpretation for a single vector leptoquark combined explanation to the B-decay anomalies_ ([arXiv:1907.05511](https://arxiv.org/abs/1907.05511))

* [[Javier Fuentes-Martin]], [[Gino Isidori]], [[Matthias König]], Nudzeim Selimovic, _Vector Leptoquarks Beyond Tree Level_ ([arxiv:1910.13474](https://arxiv.org/abs/1910.13474))

* Shaikh Saad, Anil Thapa, _A Common Origin of Neutrino Masses and $R_{D^\ast}$, $R_{K^\ast}$ Anomalies_ ([arXiv:2004.07880](https://arxiv.org/abs/2004.07880))

* P. S. Bhupal Dev, Rukmani Mohanta, Sudhanwa Patra, Suchismita Sahoo, _Unified explanation of flavor anomalies, radiative neutrino mass and ANITA anomalous events in a vector leptoquark model_ ([arXiv:2004.09464](https://arxiv.org/abs/2004.09464))

* Suman Kumbhakar, Rukmani Mohanta, _Investigating the effect of $U_1$ vector leptoquark on $b \to u \tau \bar\nu$ mediated B decays_ ([arXiv:2008.04016](https://arxiv.org/abs/2008.04016))

* {#GMV20} Valerio Gherardi, [[David Marzocca]], Elena Venturini, _Low-energy phenomenology of scalar leptoquarks at one-loop accuracy_ ([arXiv:2008.09548](https://arxiv.org/abs/2008.09548))

* {#CrivellinMuellerSaturnino20a} [[Andreas Crivellin]], Dario Mueller, Francesco Saturnino, _Leptoquarks in Oblique Corrections and Higgs Signal Strength: Status and Prospects_ ([arXiv:2006.10758](https://arxiv.org/abs/2006.10758))

* {#CFFPSV20} Marco Ciuchini, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini, Mauro Valli, _Lessons from the $B^{0,+} \to B^{\ast, 0,+} \mu^+ \mu^-$ angular analysis_ ([arXiv:2011.01212](https://arxiv.org/abs/2011.01212))

* J. Kriewald, C. Hati, J. Orloff, A. M. Teixeira, _A combined explanation of the B-meson decay anomalies with a single vector leptoquark_ ([arXiv:2012.06315](https://arxiv.org/abs/2012.06315))

* Andrei Angelescu, Damir Bečirević, Darius A. Faroughy, Florentin Jaffredo, Olcyr Sumensari, _On the single leptoquark solutions to the B-physics anomalies_ ([arXiv:2103.12504](https://arxiv.org/abs/2103.12504))

* {#HLN21} [[Gudrun Hiller]], Dennis Loose, Ivan Nišandžić, _Flavorful leptoquarks at the LHC and beyond: Spin 1_ ([arXiv:2103.12724](https://arxiv.org/abs/2103.12724))

* {#GST21} [[Admir Greljo]], [[Peter Stangl]], Anders Eller Thomsen, _A Model of Muon Anomalies_ ([arXiv:2103.13991](https://arxiv.org/abs/2103.13991))

* [[Andreas Crivellin]], Luc Schnell, *Complete Set of Feynman Rules for Scalar Leptoquarks* ([arXiv:2105.04844](https://arxiv.org/abs/2105.04844))

\linebreak

[[leptoquarks]] for explaining both the [[flavour anomalies]] and the [(g-2)-anomalies](anomalous+magnetic+moment#Anomalies):

* Mingxuan Du, Jinhan Liang, Zuowei Liu, Van Que Tran, *A vector leptoquark interpretation of the muon $g-2$ and $B$ anomalies* ([arXiv:2104.05685](https://arxiv.org/abs/2104.05685))

* Hyun Min Lee, *Leptoquark Option for B-meson Anomalies and Leptonic Signatures* ([arXiv:2104.02982](https://arxiv.org/abs/2104.02982))

* {#MarzoccaTrifinopoulos21} [[David Marzocca]], Sokratis Trifinopoulos, *A Minimal Explanation of Flavour Anomalies: B-Meson Decays, Muon Magnetic Moment, and the Cabbibo Angle* ([arXiv:2104.05730](https://arxiv.org/abs/2104.05730))

* Kayoung Ban, Yongsoo Jho, Youngjoon Kwon, Seong Chan Park, Seokhee Park, Po-Yan Tseng, *A comprehensive study of vector leptoquark on the B-meson and Muon $g-2$ anomalies* ([arXiv:2104.06656](https://arxiv.org/abs/2104.06656))

* {#Chang21} We-Fu Chang, *One colorful resolution to the neutrino mass generation, three lepton flavor universality anomalies, and the Cabibbo angle anomaly* ([arXiv:2105.06917](https://arxiv.org/abs/2105.06917))

* Alexandre Carvunis, [[Andreas Crivellin]], Diego Guadagnoli, Shireen Gangal, *The Forward-Backward Asymmetry in $B \to D^\ast \ell \nu$: One more hint for Scalar Leptoquarks?* ([arXiv:2106.09610](https://arxiv.org/abs/2106.09610))

* {#AliseEtAl2222} Alessandra D'Alise  et al.,  *Standard model anomalies: Lepton flavour non-universality, g-2 and W-mass* $[$[arXiv:2204.03686](https://arxiv.org/abs/2204.03686)$]$

* Jason Aebischer, [[Gino Isidori]], Marko Pesut, Ben A. Stefanek, Felix Wilsch, *Confronting the vector leptoquark hypothesis with new low- and high-energy data* [[arXiv:2210.13422](https://arxiv.org/abs/2210.13422)]

\linebreak

[[leptoquarks]] within a [[Randall-Sundrum model]]:

* {#Crivellin18} [[Andreas Crivellin]], _Explaining the Flavour Anomalies with the Pati-Salam Vector Leptoquark_, PoS LHCP2018 (2018) 269 ([spire:1713260](http://inspirehep.net/record/1713260), [doi:10.22323/1.321.0269](https://doi.org/10.22323/1.321.0269))

* {#BlankeCrivellin18} [[Monika Blanke]], [[Andreas Crivellin]], _$B$ Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background_, Phys. Rev. Lett. 121, 011801 (2018) ([arXiv:1801.07256](https://arxiv.org/abs/1801.07256))

or similar [[intersecting D-brane models|brane models]]:

* {#FMIPS21} [[Javier Fuentes-Martin]], [[Gino Isidori]], Julie Pagès, Ben A. Stefanek, *Flavor Non-universal Pati-Salam Unification and Neutrino Masses*, Physics Letters B Volume 820, 10 September 2021, 136484 ([arXiv:2012.10492](https://arxiv.org/abs/2012.10492), [talk recording](https://www.youtube.com/watch?v=ko4R8S8XYV4&t=2s))

[[leptoquarks]] particularly as fields in a [[grand unified theory]]:

* {#HeekTeresi18} Julian Heeck, Daniele Teresi, _Pati-Salam explanations of the B-meson anomalies_, JHEP 12 (2018) 103 ([arXiv:1808.07492](https://arxiv.org/abs/1808.07492))

* {#HeekTeresi19} Julian Heeck, Daniele Teresi, _Pati-Salam and lepton universality in B decays_ ([arXiv:1905.05211](https://arxiv.org/abs/1905.05211))

* Shyam Balaji, Michael A. Schmidt, _A unified $SU(4)$ theory for the $R_D^{(\ast)}$ and $R_K^{(\ast)}$ anomalies_ ([arXiv:1911.08873](https://arxiv.org/abs/1911.08873))

* Mario Fernández Navarro, Stephen F. King, *$B$-anomalies in a twin Pati-Salam theory of flavour* [[arXiv:2209.00276](https://arxiv.org/abs/2209.00276)]

and in relation to [[axions]]:

* [[Javier Fuentes-Martin]], Mario Reig, Avelino Vicente, _4321... axion!_ ([arXiv:1907.02550](https://arxiv.org/abs/1907.02550))

and in relation to [[gauge coupling unification]]:

* Purushottam Sahu, Aishwarya Bhatta, Rukmani Mohanta, Shivaramakrishna Singirala, Sudhanwa Patra, *Flavour anomalies and dark matter assisted unification in $SO(10)$ GUT* [[arXiv:2204.06392](https://arxiv.org/abs/2204.06392)]

[[leptoquarks]] as possible explanation also of the anomalies seen in the [[ANITA experiment]]

* Bhavesh Chauhan, Subhendra Mohanty, _A common leptoquark solution of flavor and ANITA anomalies_ ([arXiv:1812.00919](https://arxiv.org/abs/1812.00919))

Leptoquarks as [[dark matter]]-candidates:

* Francesco D'Eramo, Nejc Košnik, Federico Pobbe, Aleks Smolkovič, Olcyr Sumensari, _Leptoquarks and Real Singlets: A Richer Scalar Sector Behind the Origin of Dark Matter_ ([arXiv:2012.05743](https://arxiv.org/abs/2012.05743))

#### $Z'$-boson

explanations via assumption of [[Z'-bosons]]:

* {#GauldGoertzHaisch13} Rhorry Gauld, Florian Goertz, Ulrich Haisch, _An explicit Z'-boson explanation of the $B \to K^\ast \mu^+ \mu^-$ anomaly_, JHEP01(2014)069 ([arXiv:1310.1082](https://arxiv.org/abs/1310.1082))

* Richard H. Benavides, Luis Muñoz, William A. Ponce, Oscar Rodríguez, Eduardo Rojas, _Minimal $Z^\prime$ models for flavor anomalies_ ([arXiv:1812.05077](https://arxiv.org/abs/1812.05077))

* {#DAmbrosioIverPiccininiPolosa19} G. D'Ambrosio, A. M. Iyer, F. Piccinini, A.D. Polosa, _Confronting $B$ anomalies with atomic physics_ ([arXiv:1902.00893](https://arxiv.org/abs/1902.00893))

* P. Ko, Takaaki Nomura, Chaehyun Yu, _$b \to s \mu^+ \mu^-$ anomalies and related phenomenology in $U(1)_{B_{3-x_\mu L_\mu - x_\tau L_\tau}}$ flavor gauge models_ ([arXiv:1902.06107](https://arxiv.org/abs/1902.06107))

* Joe Davighi, _Connecting neutral current $B$ anomalies with the heaviness of the third family_, Contribution to the [2019 QCD session](http://moriond.in2p3.fr/2019/QCD/) of the [54th Rencontres de Moriond](http://moriond.in2p3.fr/2019/) ([arXiv:1905.06073](https://arxiv.org/abs/1905.06073))

* [[Wolfgang Altmannshofer]], Joe Davighi, Marco Nardecchia, _Gauging the accidental symmetries of the Standard Model, and implications for the flavour anomalies_ ([arXiv:1909.02021](https://arxiv.org/abs/1909.02021))

* [[Ben Allanach]], _$U(1)_{B_3-L_2}$ Explanation of the Neutral Current $B$−Anomalies_ ([arXiv:2009.02197](https://arxiv.org/abs/2009.02197))

* [[Andreas Crivellin]], Claudio Andreas Manzari, Marcel Alguero, Joaquim Matias, _Combined Explanation of the $Z \to b \bar b$ Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, $\tau \to \mu \nu \nu$ and $b \to s \ell^+ \ell^-$ Data_ ([arXiv:2010.14504](https://arxiv.org/abs/2010.14504))

* {#Davighi21} Joe Davighi, *Anomalous $Z'$ bosons for anomalous B decays* ([arXivL2105.06918](https://arxiv.org/abs/2105.06918))

* Rigo Bause, [[Gudrun Hiller]], Tim Höhne, Daniel F. Litim, Tom Steudtner, *B-Anomalies from flavorful $U(1)'$ extensions, safely* ([arXiv:2109.06201](https://arxiv.org/abs/2109.06201))

  > (in view of [[Higgs field]] [metastability](Higgs+field#MassAndVacuumInstability))

* Disha Bhatia, Nishita Desai, Amol Dighe, Frugal $U(1)_X$ models with non-minimal flavor violation for $b \to s \ell \ell$ anomalies and neutrino mixing* ([arXiv:2109.07093](https://arxiv.org/abs/2109.07093))

* {#ACMM22} Marcel Algueró, [[Andreas Crivellin]], Claudio Andrea Manzari, Joaquim Matias, *Unified Explanation of the Anomalies in Semi-Leptonic $B$ decays and the $W$ Mass*, Physical Review D (2022) [[arXiv:2201.08170](https://arxiv.org/abs/2201.08170)]

#### Dark matter
 {#ReferencesDarkMatter}

Possible joint explanation of the [[flavour anomalies]] and [[dark matter]]:

* Basabendu Barman, Debasish Borah, Lopamudra Mukherjee, Soumitra Nandi, _Correlating the anomalous results in $b \to s$ decays with inert Higgs doublet dark matter and muon $(g-2)$_, Phys. Rev. D 100, 115010 (2019) ([arXiv:1808.06639](https://arxiv.org/abs/1808.06639))

* {#Baek19} Seungwon Baek, _Scalar dark matter behind $b \to s \mu \mu$ anomaly_ ([arXiv:1901.04761](https://arxiv.org/abs/1901.04761))

* {#CCMRM19} D.G. Cerdeno, A. Cheek, P. Martin-Ramiro, J.M. Moreno, _B anomalies and dark matter: a complex connection_ ([arXiv:1902.01789](https://arxiv.org/abs/1902.01789))

* {#BiswasShaw19} Anirban Biswas, Avirup Shaw, _Reconciling dark matter, $R_{K^{(\ast)}}$ anomalies and $(g-2)_\mu$ in an $L_\mu-L_\tau$ scenario_ ([arXiv:1903.08745](https://arxiv.org/abs/1903.08745))

* Da Huang, António P. Morais, Rui Santos, _Anomalies in $B$ Decays and Muon $g-2$ from Dark Loops_ ([arXiv:2007.05082](https://arxiv.org/abs/2007.05082))

#### F-theory
 {#ReferencesFTheory}

Realization in [[F-theory]] of [[GUT]]-models with [[Z'-bosons]] and/or [leptoquarks]] addressing the [[flavour anomalies]] and the [(g-2) anomalies](anomalous+magnetic+moment#Anomalies):

* Miguel Crispim Romao, Stephen F. King, George K. Leontaris, _Non-universal $Z'$ from Fluxed GUTs_, Physics Letters B Volume 782, 10 July 2018, Pages 353-361 ([arXiv:1710.02349](https://arxiv.org/abs/1710.02349))

* A. Karozas, G. K. Leontaris, I. Tavellaris, N. D. Vlachos, _On the LHC signatures of $SU(5) \times U(1)'$ F-theory motivated models_ ([arXiv:2007.05936](https://arxiv.org/abs/2007.05936))

#### Other

Other possible explanations of the flavour anomalies:

[[composite Higgs boson]]:

* {#Marzocca18} [[David Marzocca]], _Addressing the B-physics anomalies in a fundamental Composite Higgs Model_, JHEP07(2018)121 ([arXiv:1803.10972](https://arxiv.org/abs/1803.10972))

* [[Andreas Crivellin]], Dario Müller, Christoph Wiegand, _$b \to s \ell^+ \ell^-$ Transitions in Two-Higgs-Doublet Models_ ([arXiv:1903.10440](https://arxiv.org/abs/1903.10440))

* [[Peter Stangl]], _Flavour anomalies and (fundamental) partial compositeness_ ([arXiv:1907.05158](https://arxiv.org/abs/1907.05158))

[[right-handed neutrino]]:

* {#MMR19} Carlo Marzo, Luca Marzola, Martti Raidal, _Common explanation to the $R_{K^{(\ast)}}$, $R_{K^{(\ast)}}$ and $\epsilon'/\epsilon$ anomalies in a 3HDM+$\nu_R$ and connections to neutrino physics_ ([arXiv:1901.08290](https://arxiv.org/abs/1901.08290))

* Luigi Delle Rose, Shaaban Khalil, Simon J.D. King, Stefano Moretti, _$R_K$ and $R_{K^\ast}$ in an Aligned 2HDM with Right-Handed Neutrinos_ ([arXiv:1903.11146](https://arxiv.org/abs/1903.11146))

* Rusa Mandal, Clara Murgui, Ana Peñuelas, [[Antonio Pich]], _The role of right-handed neutrinos in $b \to c \tau \bar \nu$ anomalies_ ([arXiv:2004.06726](https://arxiv.org/abs/2004.06726))

[[MSSM]]:

* Dris Boubaa, Shaaban Khalil, Stefano Moretti, _Explaining B decays anomalies in SUSY models_ ([arXiv:2004.07939](https://arxiv.org/abs/2004.07939))

[[MSSM]] with [[R-parity]]-violation

* {#WangYangYuan19} Dong-Yang Wang, Ya-Dong Yang, Xing-Bo Yuan, _$b \to c \tau \bar \nu$ decays in supersymmetry with R-parity violation_ ([arXiv:1905.08784](https://arxiv.org/abs/1905.08784))

* Quan-Yi Hu, Lin-Lin Huang,
_Explaining $b\to s \ell^+ \ell^-$ data by sneutrinos in the R-parity violating MSSM_ ([arXiv:1912.03676](https://arxiv.org/abs/1912.03676))

* Quan-Yi Hu, Ya-Dong Yang, Min-Di Zheng, _Revisiting the B-physics anomalies in R-parity violating MSSM_ ([arXiv:2002.09875](https://arxiv.org/abs/2002.09875))

* Wolfgang Altmannshofer, P. S. Bhupal Dev, Amarjit Soni, Yicong Sui, _Addressing $R_{D^\ast}$, $R_{K^\ast}$, muon $g-2$ and ANITA anomalies in a minimal R-parity violating supersymmetric framework_ ([arXiv:2002.12910](https://arxiv.org/abs/2002.12910))

[[Horava-Witten theory]]-type [[KK-compactification]]:

* Jong-Phil Lee, _$B$ anomalies in the nonminimal universal extra dimension model_ ([arXiv:1906.07345](https://arxiv.org/abs/1906.07345))

Exotic [[Higgs field]] couplings to a [[hidden sector]]:

* Jared A. Evans, [[Philip Tanedo]], Mohammadreza Zakeri, _Exotic Lepton-Flavor Violating Higgs Decays_ ([arxiv:1910.07533](https://arxiv.org/abs/1910.07533))

Unparticles:

* Jong-Phil Lee, _B anomalies with unparticles_ ([arXiv:2012.11852](https://arxiv.org/abs/2012.11852))

[[!include application of holographic QCD to B-meson physics -- references]]

[[!redirects flavour anomalies]]

[[!redirects flavor anomaly]]
[[!redirects flavor anomalies]]

[[!redirects lepton flavour universality violation]]
[[!redirects LFUV]]


flavours of cobordism cohomology theories -- table

**flavors of [[bordism homology theories]]/[[cobordism cohomology theories]], their [[Brown representability theorem|representing]] [[Thom spectra]] and [[cobordism rings]]**:

[[bordism homology theory|bordism theory]]$\;$[[M(B,f)]] ([[B-bordism]]):

* [[MFr]]

* [[MO]], [[MSO]], [[MSpin]], [[MString]], ...

* [[MU]], [[MSU]], ...

  [[Ravenel's spectrum|MΩΩSU(n)]]

  [[MP-theory|MP]], [[MR-theory|MR]]

* [[MSpin^c|MSpinc]]

* [[MSp]]

relative bordism theories:

* [[MOFr]], [[MUFr]], [[MSUFr]]

[[equivariant bordism homology theory|equivariant bordism theory]]:

* [[equivariant MFr]]

* [[equivariant MO]]

* [[equivariant MU]]

[[global equivariant bordism homology theory|global equivariant bordism theory]]:

* [[global equivariant mO]],

* [[global equivariant mU]]

algebraic:

* [[algebraic cobordism]]

[[!redirects cobordism cohomology theories -- contents]]


flavours of cohomotopy -- table

| flavours of
**[[Cohomotopy]]**
[[generalized cohomology|cohomology theory]]  | [[cohomology]]
 ([[homotopy theory|full]] or [[rational homotopy theory|rational]]) |  [[equivariant cohomology]]
 ([[equivariant homotopy theory|full]] or [[rational equivariant homotopy theory|rational]])|
|--|--|--|
| **[[non-abelian cohomology]]** | [[Cohomotopy]]
 (full or [[rational Cohomotopy|rational]])| [[equivariant Cohomotopy]] |
| **[[twisted cohomology]]**
 (**[[parametrized homotopy theory|full]]** or **[[rational parameterized stable homotopy theory|rational]]**) | [[twisted Cohomotopy]] |  twisted equivariant Cohomotopy |
| **[[generalized (Eilenberg-Steenrod) cohomology|stable cohomology]]**
 (**[[stable homotopy theory|full]]** or **[[rational stable homotopy theory|rational]]**) |  [[stable Cohomotopy]] |  [[equivariant stable Cohomotopy]] |
| **[[differential cohomology
]]** | [[differential Cohomotopy]] | equivariant differential cohomotopy |
| **[[persistent homotopy|persistent cohomology]]** | [[persistent Cohomotopy]] | persistent equivariant Cohomotopy |