LFV in meson and baryon decays– TH overview –Diego Guadagnoli
CNRS, LAPTh AnnecyOverview• Short overview of b → s and b → c data
• LFV in B decays: general arguments• LFV in Kaon decays?
• Status of searches

Collider Data

-No direct evidence of BSM at colliders
A coherent set of discrepancies in B decays

 b → s μμ BR data < SMChallenge: B → light meson f.f.’s

D. Guadagnoli, 20th Lomonosov Conferenceb → s μμ BR data < SMb →  μ+μ–

D. Guadagnoli, 20th Lomonosov ConferenceCollider Data

-No direct evidence of BSM at colliders
A coherent set of discrepancies in B decays

 b → s μμ BR data < SM
Challenge: B → light meson f.f.’s➋

B → K* μμ angular data
Challenge: charm loops➌loopprocessesb → s μμ / b → s ee ratios
Challenge: (mostly) stats➍b → c τν / b → c ℓν ratios
Challenge: stats + syst

treeprocesses
D. Guadagnoli, 20th Lomonosov ConferenceMinimal TH considerations(before any fit)

EFT considerations

 Quite remarkably, most data hint at shifts to just 2 eff. couplings
4 GF *α em(μ)
H ( b̄→ s̄ μ μ) = −V tb V tsb̄L γλ s L ⋅ ( C(μ)μ̄γμ+Cλ
910 μ̄ γ λ γ5 μ )4π√2[+ RH-quark ops. + dipoles]

Effects are(mostly) here+ scalar & tensor ops.

➋ Also remarkably, two scenarios stand out:(μ)

dC 9 alone

(μ)

(μ )

dC 9 = −dC 10[Hiller-Schmaltz, 2014]

this op. combination can be written
in terms of SU(2)L invariants[Alonso, Grinstein, M.Camalich, 2014]

well-suited to UV-complete models
D. Guadagnoli, 20th Lomonosov Conference

EFT considerations(μ)(μ )dC=−dCvs.
➋ More on dC (μ)
9109

How to resolve between the two scenarios?
Accurate Bs → μμ measurement
present single-measurement error ≃ 20 %exp combi may soon be able toconfirm or exclude deviations of C10 of O(10%)

D. Guadagnoli, 20th Lomonosov ConferenceMore TH considerations➌ Pattern of Lepton Universality Violation in b → sThe observed new-physics hierarchy:effects in ee≪effects in  ≪ (allowed) effects in 

suggestive of NP coupled dominantly to 3rd gen. SM fermions[Glashow et al., 2015]➍ … which in turn makes it natural to link b → s and b → c data

[Bhattacharya et al., 2015]

Data now allow to disprove some, and to make more precise
some other of these considerations
D. Guadagnoli, 20th Lomonosov Conference1-Wilson-coeff. picture[Carvunis et al., 2102.13390][See Altmannshofer-Stangl, 2103.13370, for a comprehensive discussion including CPV]

D. Guadagnoli, 20th Lomonosov Conference1-Wilson-coeff. picture[Carvunis et al., 2102.13390]

Two scenarios stand out: C9 alone or C9 = – C10(μμ-channel only)

C10 alone also ok, but angular B → K* μμ anomaly unresolved
D. Guadagnoli, 20th Lomonosov ConferenceWhy LFVIf we observe LUV, then, in general
we should expect observable LFV as wellExceptions require that the specific LUV dynamics
has some ad hoc symmetry that prevents LFVModel zero

 All b → s data are explained at one stroke if one assumes(V – A)q × (V – A)ℓ structurewith Wilson-coeff. shift much larger for μμ than for ee Such pattern can be obtained from a purely 3rd-generation interactionof the kind [Glashow et al., 1411.0565]

λH NP = G ( b̄' L γ b' L ) ( τ̄' L γλ τ' L )with

G = 1/Λ 2NP ≪ G F

D. Guadagnoli, 20th Lomonosov ConferenceModel zero

 Note: primed fields in H NP = G ( b̄' L γλ b' L ) ( τ̄' L γλ τ' L )Above the EWSB scale, fields are in the“gauge” basis, not the mass eigenbasis
Mass-basis unitary transformations
induces LUV and LFV effects

massbasisdb' L ≡ (d ' L )3 = ( U L )3 i (d L )i
τ ' L ≡ (ℓ' L )3 = ( U ℓL )3 i (ℓ L )i One can then parametrically relate measured LUV ( RK(*) )to LFV decays such as B → (K) τμ= 2%= 4×10–72(√ R K −1)
BR (B → K ℓ ℓ ) ≃ 2⋅ func.(U ℓL ratios)⋅ BR (B+ → K + μ μ)
RK++±1∓
2BRs ~ 10–8 expected, for generic choices of U matrices
D. Guadagnoli, 20th Lomonosov ConferenceModel zero Note: primed fields in H NP = G ( b̄' L γλ b' L ) ( τ̄' L γλ τ' L )Above the EWSB scale, fields are in the“gauge” basis, not the mass eigenbasis
Mass-basis unitary transformations
induces LUV and LFV effects

massbasisdb' L ≡ (d ' L )3 = ( U L )3 i (d L )i
τ ' L ≡ (ℓ' L )3 = ( U ℓL )3 i (ℓ L )i One can then parametrically relate measured LUV ( RK(*) )to LFV decays such as B → (K) τμ [Glashow et al., 1411.0565]= 2%= 4×10–72(√ R K −1)
BR (B → K ℓ ℓ ) ≃ 2⋅ func.(U ℓL ratios)⋅ BR (B+ → K + μ μ)
RK++±1∓
2BRs ~ 10–8 expected, for generic choices of U matrices
D. Guadagnoli, 20th Lomonosov ConferenceLepton-decay LFV[Feruglio, Paradisi, Pattori, ‘16, ‘17]

 Actually certain LFV decays represent strong constraints
 Given, at the UV matching scaleclose the quark loop
& attach a gauge boson→ two further leptons

D. Guadagnoli, 20th Lomonosov ConferenceLFV in explicit UV-complete models

 Explicit UV-complete constructions (ex. the U1 vector leptoquark)
generally predict B-decay LFV while fulfilling leptonic-LFV limits Example:
models based on the so-called (Pati-Salam)3

 General prediction: large τ → μ effective coupling
due to assumed U(2)5 flavor symmetry and its breaking pattern[Bordone, Cornella, Fuentes-M, Isidori, ‘18]

to compare e.g. withBR(B+ → K+ μ– τ+) < 3.9 × 10–5
[LHCb, 2003.04352]

D. Guadagnoli, 20th Lomonosov ConferenceLFVin Kaon decays?

Main point The putative new dynamics in B decays may yield correlated
effects in suitable K decays.

 Especially interesting examples include

K → π ν ν̄K → (π)μ e

 It turns out that B-physics machines can offer complementary info
on these decays w.r.t. Kaon machines, because of
the large amounts of Kaons produced
the excellent decay-reconstruction capabilities (e.g. for KS )D. Guadagnoli, 20th Lomonosov ConferenceWhy correlated effects
The new physics for B decays can usually be described bytwo-quark { i, j }two-lepton { k, l }operators

New scale Λ may be fixed by size of observed discrepancies( typically Λ = few to 10 x few TeV ) [Di Luzio, Nardecchia, 1706.01868]
The C couplings encode flavor structure. If dynamics tree-level:for new colorless massive bosons
for leptoquarks

In many motivated scenarios, the λ’s entering B decays
and those entering K decays are highly correlated
D. Guadagnoli, 20th Lomonosov ConferenceExample LHCb may well improve existing limits on K → μ e and K+ → π+ μ eL

[Borsato et al., 1808.02006][Alves Jr. et al., 1808.03477]

TH assumptions(V–A) × (V–A), SU(2)L-invariant
qqℓℓ Hamiltonian adopted in[Buttazzo et al., 1706.07808]

to explain B anomalies
CKM-like ansatz for theλ(q) coupling
Agnostic on the λ(ℓ) coupling

D. Guadagnoli, 20th Lomonosov ConferenceStatusof LFV searches

Main points

 Since the connection “measured LUV ⇔ measurable LFV”
was pointed out, many exp searches have been performed
see e.g. [P. de Simone, EPJ WoC 2020] All modes involve two leptons w/ different flavours
Muons are the easiest

Best searches: μe and μτ Sensitivity relies on background control:
combinatorial; semi-lept. or resonant (cc) with mis-ID;

 Challenges to “close the kinematics”
electrons radiatetaus decay, involving missing energy

D. Guadagnoli, 20th Lomonosov ConferenceMany recent stringent searches

at LHCb, 7/8 TeV, 3/fb

at LHCb, 7/8/13 TeV, 9/fb

at LHCb, 7/8 TeV, 3/fb

τ±at LHCb, 7/8 TeV, 3/fb

Notes: some limits are 90%, some other 95% CL; previous limits are from BaBar
D. Guadagnoli, 20th Lomonosov ConferenceConclusions

 As of Moriond 2021, B anomalies hold their ground
One clear hint: beyond-SM LUV

 LUV and LFV are two sides of the same broken symmetryi.e. to prevent LFV requires an additional ad hoc assumption
Generally, models explaining the B anomalies also predict LFV By general arguments, from the measured LUV one can expect
LFV BRs ~ 10 –8 (e.g. in B → K τμ) Using EFT-driven arguments,
K physics offers potential complementary probes

D. Guadagnoli, 20th Lomonosov Conference