flavors of fundamental particles -- table

| **[[flavor (particle physics)|flavors]] of [[fundamental particle|fundamental]] [[fermions]] in the**
 **[[standard model of particle physics]]:** |                |                   |                  |
|--|----------------|-------------------|------------------|
| [[generation of fermions]] | 1st generation | 2nd generation    | 3d generation    |
| **[[quarks]]** ($q$) |   |   |   |
| up-type  |  [[up quark]] ($u$)  | [[charm quark]] ($c$)  | [[top quark]] ($t$)   |
| down-type  | [[down quark]] ($d$) | [[strange quark]] ($s$) | [[bottom quark]] ($b$) |
| **[[leptons]]** |   |   |  |
| charged  |   [[electron]] | [[muon]] | [[tauon]] |
| neutral  | [[electron neutrino]] | [[muon neutrino]] | [[tau neutrino]]  |
|  |   |  |   |
| **[[bound states]]:** |  |  |  |
| **[[mesons]]** | **[[light mesons]]**:
 [[pion]] ($u d$)
 [[ρ-meson]] ($u d$)
 [[ω-meson]] ($u d$)
 [[f1-meson]]
 [[a1-meson]] | **[[strange quark|strange]]-mesons**:
 [[ϕ-meson]] ($s \bar s$),
 [[kaon]], [[K*-meson]] ($u s$, $d s$)
 [[eta-meson]] ($u u + d d + s s$)

 **[[charm quark|charmed]] [[heavy mesons]]**:
 [[D-meson]] ($ u c$, $d c$, $s c$)
 [[J/ψ-meson]] ($c \bar c$)  | **[[bottom quark|bottom]] [[heavy mesons]]**:
 [[B-meson]] ($q b$)
 [[ϒ-meson]] ($b \bar b$) |
| **[[baryons]]** | **[[nucleons]]**:
 [[proton]] $(u u d)$
 [[neutron]] $(u d d)$  |  |  |


flavors of higher toposes -- list

**flavors of [[higher topos theory|higher toposes]]**

* [[1-topos]]

  * [[(0,1)-topos]]

  * [[(1,1)-topos]] = [[topos]]

  * [[(2,1)-topos]]

  * [[(n,1)-topos|$(n,1)$-topos]]

  * [[(∞,1)-topos]] ([[n-localic (infinity,1)-topos|$n$-localic]])

    $\;\;\;\;$ [[model topos]]

* [[2-topos]]

  * [[(2,2)-topos]] ([[n-localic 2-topos|$n$-localic]])

  * [[(∞,2)-topos]]

* [[n-topos|$n$-topos]]

  * [[(∞,n)-topos|$(\infty,n)$-topos]]


flavors of modal logics and relations -- table

| type of [[modal logic]] | [[relation]] in its [[Kripke frames]] |
|--|--|
| [[K modal logic]] | any [[relation]] |
| [[K4 modal logic]] | [[transitive relation]] |
| [[T modal logic]] | [[reflexive relation]] |
| [[B modal logic]] | [[symmetric relation]] |
| [[S4 modal logic]] | [[reflexive relation|reflexive]] & [[transitive relation]] |
| [[S5 modal logic]] | [[equivalence relation]] |

> (following [BdRV (2001) Table 4.1 ](modal+logic#BlackburnDeRijkeVenema01); cf. [Fagin, Halpern, Moses & Vardi (1995) Thm. 3.1.5](epistemic+modal+logic#FaginHalpernMosesVardi95))


flavour (particle physics)

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

#Contents#
* table of contents
{:toc}

## Idea

The [[fermion]] [[fundamental particles]] in the [[standard model of particle physics]] arrange in three "[[generation of fundamental particles|generations]]". Between generations, particles differ in their [[mass]] and in further properties referred to as _flavor quantum numbers_, but otherwise their interactions are the same, to high accuracy. Hence _flavor physics_ refers to the [[phenomenology]] of processes that do involve or depend on flavor quantum numbers, notably when flavor changes through interactions via the [[weak nuclear force]] and [[Yukawa interactions]].

For the [[leptons]] these flavor quantum numbers are _[[electron]] number_, _[[muon]] number_ and _[[tauon]] number_ as well as the corresponding three _[[neutrino]] numbers_.

For the [[quarks]] the flavor quantum numbers are _[[isospin]]_, _[[charm quark|charm]]_, _[[strange quark|strange]]-ness_,  _[[bottom quark|bottom]]-ness_ and _[[top quark|top]]-ness_.

See [yotams](#yotams) for a good quick introduction.

## Properties

### The flavor problem
 {#TheFlavorProblem}

In the [[standard model of particle physics]], the sector involving [[flavor physics]] -- hence the [[Higgs boson]] [[interaction]] with the [[generations of fermions]], hence the [[Yukawa coupling]]- and [[CKM matrix]]-sector in the [[Lagrangian density]] of the [[Einstein-Yang-Mills-Dirac-Higgs theory]] that defines the standard model --  has some striking characteristics different from the sector that does not:

> slide grabbed from [Altmannshofer 14](spring)

> slide grabbed from [Isidori 16](#Isidori16)

(Note that Isidori's slide collects all terms with a [[Higgs boson]] factor, including the pure Higgs terms reflecting the [[cosmological constant]] and the [[hierarchy problem]], and hence "all the problematic terms", while the flavor sector proper consists of those terms involving
Higgs and [[quark]] factors.)

Broadly, _the flavor problem_ (see the references [below](#ReferencesFlavorProblem)) is the fact that the nature and principles behind the flavor sector of the standard model are much less understood than those of the gauge sector (the "color sector"). More concretely, the flavor problem in models going beyond the standard model (such as [[GUT]] models and/or the [[MSSM]]) is that introducing any New Physics while satisfying observational constraints on flavor physics seems to demand a high level of [[fine-tuning]] in the flavor sector.

Moreover, all observed [[CP violation]] is related to flavor-changing [[interactions]].

Finally, due to [[confinement]], the flavor-changing transitions between [[quarks]] are not seen in isolation by collider [[experiments]], but are only seen via the induced decays of the [[mesons]] and/or [[baryons]] that the [[quarks]] are [[bound state|bound]] in. This way the flavor problem is tied to the [confinement problem](confinement#OpenProblem) and hence to the problem of formulating [[QCD]] [[non-perturbative quantum field theory|non-perturbatively]] (e.g. via [[AdS/QCD]]).

All this suggests that the flavor sector is controlled by mechanisms that are not understood or identified yet.

### Experimental "anomalies"

Due to the [flavor problem](#TheFlavorProblem), the flavor sector of the [[standard model of particle physics]] is the least well understood in detail. Indeed, thete are persistent and growing discrepancies between SM-predictions and experimental measurements in the flavor sector:

#### Flavor anomaly

[[flavor anomalies]] reflect a discrepancy in [[B-meson]] decays between [[experiment]] ([[LHCb]], [[Belle experiment|Belle]], [[BaBar experiment|BaBar]]) and theoretical computations, which keeps being seen at a global [[statistical significance]] of $\sim 4\sigma$ across all experiments and decay channels. If these [[flavour anomalies]] are real they signify New Physics in the flavor sector.

See at _[[flavour anomalies]]_ for more.

#### Cabibbo anomaly

See at _[[Cabibbo anomaly]]_ and _[[V_cb puzzle]]_.

#### $(g-2)$ anomaly

See at _[[(g-2) anomaly]]_.

### Geometric engineering on D8-branes
 {#GeometircEngineeringInDBranes}

In [[geometric engineering of QFT|geometric engineering]] of [[flavor physics]] in [[intersecting D-brane models]], the flavour degrees of freedom come from [[open strings]] ending on [[spacetime]]-filling [[D-branes]] called "[[flavor branes]]" ([Karch-Katz 02](#KarchKatz02)).

Specifically in the [[Sakai-Sugimoto model]] [[geometric engineering of QFT|geometrically engineering]] something close to actual [[quantum chromodynamics]] ([Sakai-Sugimoto 04](#SakaiSugimoto04), [Sakai-Sugimoto 05](#SakaiSugimoto05)), flavour is encoded in the presence of [[D8-branes]] in the model:

Here we are showing

1. the [[color charge|color]] [[D4-branes]];

1. the [[flavour (particle physics)|flavor]] [[D8-branes]];

   with

   1. the [[5d Chern-Simons theory]] on their [[worldvolume]]

   1. the corresponding [[4d WZW model]] on the boundary

   both exhibiting the [[meson fields]];

1. the [[baryon]] [[D4-branes]]

   (see at _[WSS-model -- Baryons](WSS+model#Baryons)_);

1. the [[Yang-Mills monopole]] [[D6-branes]]

   (see at _[[D6-D8-brane bound state]]_);

1. the [[NS5-branes]] (often not considered here).

## Related concepts

* [[light and heavy flavor]]

* [[CKM matrix]]

* [[Yukawa coupling]]

* [[color charge]]

* [[flavour anomaly]]

* [[Cabibbo anomaly]], [[V_cb puzzle]]

* [[flavor brane]]

* [[quantum hadrodynamics]]

  * [[hadron supersymmetry]]

  * [[hadron Kaluza-Klein theory]]

## References

### General

A good quick account is in

* {#yotams} yotams, _What is flavor?_ ([pdf](https://webhome.weizmann.ac.il/home/yotams/notes/ep1_flavor.pdf), [[yotamsFlavor.pfd:file]])

Textbook accounts:

* [[Robert E. Marshak]], Chapter 3 of: *Conceptual Foundations of Modern Particle Physics*, World Scientific 1993 ([doi:10.1142/1767](https://doi.org/10.1142/1767))

* {#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]])

Lecture notes:

* [[Yuval Grossman]], _Introduction to flavor physics_, CERN Yellow Report CERN-2010-002, pp. 111-144 ([arXiv:1006.3534](https://arxiv.org/abs/1006.3534))

* [[Benjamin Grinstein]], _TASI-2013 Lectures on Flavor Physics_ ([arXiv:1501.05283](https://arxiv.org/abs/1501.05283))

* [[Yuval Grossman]], Philip Tanedo, _Just a Taste: Lectures on Flavor Physics_, Chapter 4 in: _Anticipating the Next Discoveries in Particle Physics (TASI 2016)_ ([arXiv:1711.03624](https://arxiv.org/abs/1711.03624),  [doi:10.1142/9789813233348_0004](https://doi.org/10.1142/9789813233348_0004))

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

With an emphasis on [[CP-violation]]:

* [[Antonio Pich]], _Flavour Dynamics and Violations of the CP Symmetry_, Lectures at the 2017 and 2019 CERN - Latin-American Schools of High-Energy Physics ([arXiv:1805.08597](https://arxiv.org/abs/1805.08597))

With an emphasis on the [[neutrino]]-sector:

* Zhi-zhong Xing, _Flavor structures of charged fermions and massive neutrinos_ ([arXiv:1909.09610](https://arxiv.org/abs/1909.09610))

See also

* Wikipedia, Flavour (particle physcs)

* Fernando Abreu de Souza, Gero von Gersdorff, _A Random Clockwork of Flavor_ ([arxiv:1911.08476](https://arxiv.org/abs/1911.08476))

On [[flavour physics]] and [[flavour anomalies]] seen at the [[LHCb experiment]]:

* [[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

Survey and outlook:

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

* Vladimir V. Gligorov, *Overview of quark flavour results*, talk at [ICHEP 2022](https://www.ichep2022.it/) (Bologna, 2022) [[infn:171923](https://agenda.infn.it/event/28874/contributions/171923/), [pdf](https://agenda.infn.it/event/28874/contributions/171923/attachments/94847/130108/Vladimir_Gligorov.pdf)]

### The flavour problem
 {#ReferencesFlavorProblem}

On the [[flavour problem]]:

* [[Gino Isidori]], _Kaon decays and the flavour problem_, Annales Henri Poincare 4 (2003) S97-S109 ([arXiv:hep-ph/0301159](https://arxiv.org/abs/hep-ph/0301159))

  (emphasis on [[kaon]] [[scattering|decays]])

* {#Isidori16} [[Gino Isidori]], _The flavor problem_, 2016 ([pdf](https://indico.cern.ch/event/504502/contributions/2147710/attachments/1287372/1915547/SWHEPPS_Talk.pdf), [[IsidoriFlavor16.pdf:file]])

* {#Altmannshofer14} [[Wolfgang Altmannshofer]], _The Flavor Puzzle_, Aspen 2014 ([pdf](https://www.aspenphys.org/science/colloquia/2014_slides/altmannshofer.pdf), [[AltmannshoferFlavorProblem.pdf:file]])

In relation to the [[neutrino mass problem]]:

* {#Xing19} Zhi-zhong Xing, _Flavor structures of charged fermions and massive neutrinos_ Physics Reports Volume 854, 20 April 2020, Pages 1-147 ([arXiv:1909.09610](https://arxiv.org/abs/1909.09610), [doi:10.1016/j.physrep.2020.02.001](https://doi.org/10.1016/j.physrep.2020.02.001))

On the [[flavor problem]] in the [[MSSM]]:

* [[Stuart Raby]], _SUSY Flavor Problem_, In: _Supersymmetric Grand Unified Theories_. Lecture Notes in Physics, vol 939 ([doi:10.1007/978-3-319-55255-2_7](https://doi.org/10.1007/978-3-319-55255-2_7))

### Flavour anomalies

Outlook on the field of flavour physics in view of [[LHCb]]-measurement of [[flavour anomalies]] and [[CP violation]]:

* [[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_ ([arxiv:1910.10662](https://arxiv.org/abs/1910.10662))

See also

* {#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))

On [[flavour physics]] and potential [[flavour anomalies]] in [[kaon]]-[[scattering|decays]]:

* {#Buras16} [[Andrzej Buras]], _The Revival of Kaon Flavour Physics_,  EPJ Web Conf. Volume 129, 2016  ([arXiv:1609.05711](https://arxiv.org/abs/1609.05711), [doi:10.1051/epjconf/201612900050](https://doi.org/10.1051/epjconf/201612900050))

* {#Buras18} [[Andrzej Buras]], _The Return of Kaon Flavour Physics_, Acta Phys. Pol. B 49, 1043 (2018) ([doi:10.5506/APhysPolB.49.1043](https://www.actaphys.uj.edu.pl/index_n.php?I=R&V=49&N=6#1043))

### Geometric engineering on flavor branes

The [[geometric engineering of QFT|geometric engineering]] of flavour physics in [[intersecting D-brane models]] ([[flavor branes]] in [[AdS/QCD]]) was originally understood in

* {#KarchKatz02} [[Andreas Karch]], [[Emanuel Katz]],  _Adding flavor to AdS/CFT_, JHEP 0206:043, 2002 ([arxiv:hep-th/0205236](https://arxiv.org/abs/hep-th/0205236))

and then developed in detail for [[QCD]] on [[D8-branes]] in the [[Sakai-Sugimoto model]]:

* {#SakaiSugimoto04} [[Tadakatsu Sakai]], [[Shigeki Sugimoto]], _Low energy hadron physics in holographic QCD_, Prog.Theor.Phys.113:843-882, 2005 ([arXiv:hep-th/0412141](https://arxiv.org/abs/hep-th/0412141))

* {#SakaiSugimoto05} [[Tadakatsu Sakai]], [[Shigeki Sugimoto]], _More on a holographic dual of QCD_, Prog.Theor.Phys.114:1083-1118, 2005 ([arXiv:hep-th/0507073](https://arxiv.org/abs/hep-th/0507073))

[[!include flavor on heterotic M5-branes -- references]]

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