Lepton flavor nonuniversality

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1 Lepton flavor nonuniversality + in b s processes Nejc Košnik 6OJWFSTJUZ PG -KVCMKBOB 'BDVMUZ PG.BUIFNBUJDT BOE 1IZTJDT Moriond EW La Thuile, March

2 Outline Introduction Effective theory analysis UV realizations: Z model, light leptoquarks Additional cross checks and LFV Conclusion Lepton flavor nonuniversality in b sl + l processes 2

3 Muon discovery H. Yukawa proposes scalar meson theory of proton-neutron interaction 35 Cosmic ray meson discovery 37 [Neddermeyer] The discovered meson is not interacting strongly 47 [Conversi] Pion and unexpected muon were discovered μ - π system, π μν There is a muon I. Rabi: who ordered that A. Pais: divine laughter, muon is useless as a constituent Heavy, unstable electron, mμ ~ 200 me 3 N. Košnik, FMF, Nov. 2, 15

4 Introduction Lepton Flavor Universality (LFU) first observed in the framework of Fermi theory u νe,νμ G e F G µ F J µ quark = n µ (1 a 5 )p J µ lep = e µ (1 5)e + µ µ (1 5)µ d e, μ G F p 2 J lep,µ J µ had LFU predicted in the SM on the level of gauge couplings. Broken only by lepton Yukawa couplings. Well tested in pion, kaon decays, Z decays (LEP): C`V = 1 CÀ = sin 2 W Lepton flavor nonuniversality in b sl + l processes 4

5 Introduction LHCb seen hints of LFU in b sμμ transition (2014) R K = B(B! Kµ+ µ ) q 2 2[1,6] GeV 2 B(B! Ke + e ) q2 2[1,6] GeV 2 =0.745 ± ±0.036 [LHCb, ] 2.6σ below the LFU prediction, RK = 1 First proposal and prediction of RK, RK*, RXs in 2003 Very precise due to efficient cancellation of hadronic uncertainties. e and μ are almost massless. [Kruger, Hiller, hep-ph/ ] [LHCb ] missing muons or too many electrons? Lepton flavor nonuniversality in b sl + l processes 5

6 Effective operator analysis Standard Model + dim-6 operators at NP scale Λ Λ Q i (HD µ H)( q µ q) ( q µ V µ q)h qq `` Higgs current dipoles 4-fermion Matching onto low energy effective Lagrangian t h W,Z t b O (0) 7 = e (4 ) 2 m b( s µ P R(L) b)f µ O (0) 9 = e2 (4 ) 2 ( s µp L(R) b)( ` µ`) O (0) 10 = e2 (4 ) 2 ( s µp L(R) b)( ` µ 5`) O (0) S = e2 (4 ) 2 ( sp R(L)b)( ``) O (0) P = e2 (4 ) 2 ( sp R(L)b)( ` 5`) 1. no tensor currents 2. scalar combinations CS=-CP, CS =CP' 3. C9,SM=-C10,SM=4.2 Lepton flavor nonuniversality in b sl + l processes 6 [Grinstein, Camalich, Alonso, ] [Grinstein, Camalich, Alonso, ] [See talk by Gudrun Hiller]

7 Effective operator analysis Global b sμμ data prefer: decrease muonic decay rate B Kμμ, less attractive: increase electronic rate B Kee Scalar operators CS=-CP, CS =CP for muons: disfavoured by Br(Bs μμ) Scalar operators CS=-CP, CS =CP for electrons can decrease RK: in conflict with rate of B Kee (Axial)vector operators, chiral vector currents: can affect μ or e C µ 9 = Cµ 10 O (0) 7 = e (4 ) 2 m b( s µ P R(L) b)f µ O (0) 9 = e2 (4 ) 2 ( s µp L(R) b)( ` µ`) O (0) 10 = e2 (4 ) 2 ( s µp L(R) b)( ` µ 5`) O (0) S = e2 (4 ) 2 ( sp R(L)b)( ``) O (0) P = e2 (4 ) 2 ( sp R(L)b)( ` 5`) [0.5, 1] negative contribution towards B Kμμ, Bs μμ [See talks by Lars Hofer and Johannes Albrecht] [Hiller, Schmaltz, ] [Hiller, Schmaltz, ] Lepton flavor nonuniversality in b sl + l processes 7

8 Related LFU observables [Kruger, Hiller, hep-ph/ ] sensitive to right-handed quark current [Hiller, Schmaltz, ] [G. Hiller, EPS 2015] [Altmannshofer, Straub, ] Lepton flavor nonuniversality in b sl + l processes 8

9 Lμ-Lτ Z model Gauge the leptonic number difference: U(1)Lμ - Lτ, massless boson Z μ At this point we have vector-couplings of Z to either muons or taus Spontaneously break U(1) by a VEV of a scalar Φ, charged under U(1). mz = g vφ Vector-like quarks charged under U(1) mix with SM quarks and give dim-6 operators: C µ 9 = C 9 C 0µ 9 = C0 9 [Altmannshofer, Gori, Pospelov, Yavi, ] [Altmannshofer, Yavin, ] Lepton flavor nonuniversality in b sl + l processes 9

10 Lμ-Lτ Z model Starting from the global fit to b sμμ data LFU observables are predicted to be ~20% below the SM values [Altmannshofer, Yavin, ] Analogous modes, b s τ τ, should be enhanced by 20% w.r.t. SM predictions cf. [Altmannshofer, Gori, Pospelov, Yavi, ] [Altmannshofer, Yavin, ] Lepton flavor nonuniversality in b sl + l processes 10

11 Scalar leptoquark models Representations of scalar LQs under SU(3) SU(2) U(1) (3, 2) 7/6 (3, 2) 1/6 ( 3, 3) 1/3 ( 3, 1) 4/3 Increases B Kμμ Decreases B Kμμ Proton destabilizing Proton destabilizing Yukawa couplings Qe R (3, 2) 1/6 Ld R Q C i 2 ~ L d C R`R Q C i 2 ~ Q u C R u R L = Y ij L i i 2 d Rj = Y ij `Li d Rj (2/3) + Lk (V PMNS ) ki d Rj ( 1/3) Y = 0 Y µs Y µb A Couplings designed for B Kμμ LFU violation but flavour conservation SU(2) doublet correlations with B Kνν Lepton flavor nonuniversality in b sl + l processes 11

12 Scalar leptoquark model - μ (3, 2) 1/6 (Y µs µ L s R + Y µb µ L b R ) (2/3) [Becirevic,NK,Fajfer, ] right-left couplings b μ s μ C 0 10 = C 0 9 = 2 p 2G F V tb V ts Y µb Y µs m 2. Increasing B Kμμ implies larger Bs μμ! B(B +! K + µ + 8 µ ) q 2 2[15,22]GeV2 =(8.5 ± 0.3 ± 0.4) 10 [LHCb, ] B(B s! µ + µ ) exp =( ) 10 9 [LHCb+CMS, ] Lepton flavor nonuniversality in b sl + l processes 12

13 RK prediction C9 = -C10 R K (C 0 10) =1.001(1) 0.46 Re[C 0 10] 0.094(3) Im[C 10 0 ]+0.057(1) C Remaining form factor uncertainties RK contours Vs. prediction (green) R pred. K =0.88 ± 0.08 RK by LHCb (gray): 0.75 ± 0.12 Lepton flavor nonuniversality in b sl + l processes 13

14 Relating Bs mixing and RK b s μ μ s b With imposed RK constraint, effect in BsBs is increasing with mass Upper mass limit for the LQ of the order 100 TeV. Lepton flavor nonuniversality in b sl + l processes 14

15 Scalar leptoquark model - e (3, 2) 1/6 (Y es µ L s R + Y eb µ L b R ) (2/3) [Hiller, Schmaltz, ] b s C 0 10 = C 0 9 = 2 p 2G F V tb V ts Y eb Y es m 2. e e Increased B Kee implies decrease in Bs ee C ! Y eby es m 2 1 (24TeV) 2 Lepton flavor nonuniversality in b sl + l processes 15

16 Further remarks on LQs Scalars: ( 3, 3) 1/3 ( 3, 1) 1/3 Both states may destabilize the proton ( 3, 3) 1/3 implements a favorable C µ 9 = Cµ 10 scenario ( 3, 1) 1/3 cf. Hiller, Schmaltz, has loop level contributions towards B Kμμ and treelevel contributions to B D(*)τν (3, 3) 2/3 cf. Neubert, Bauer, Vector conserves baryon number, implements C µ 9 = Cµ 10 scenario and also contributes to B D(*)τν cf. Fajfer, NK, Lepton flavor nonuniversality in b sl + l processes 16

17 Relating LFUv to Lepton Flavor Violation Even with LFU violation, LFV can be avoided. [Grinstein, Camalich, ] In leptoquark models, LFV is closely tied to LFUV. b s Y = 0 Y µs Y µb A Universality lost, flavour conserved! μ μ For LFV one needs to affect electronic and muonic decay modes simultaneously: Y = 1 Y es Y eb Y µs Y µb A LFU LFU μ eγ, ϒ eμ, Φ eμ Bs eμ, B Keμ Lepton flavor nonuniversality in b sl + l processes 17

18 Relating LFUv to Lepton Flavor Violation Consider vector LQ (3, 3) 2/3 that addresses RK and R(D)* puzzles: Inevitable LFV in τ-μ sector. Bounds from τ μγ, B Kτμ, B Kνν apply strongest by far [BaBar, ] [Fajfer, NK, ] Lepton flavor nonuniversality in b sl + l processes 18

19 Conclusions & Outlook R K measurement is very clean observable, it shows a hint of LFU violation Test in additional LFU ratios: R K at high q 2, R K*, R Φ, R K* /R K, (Axial)-vector O 9 ( ), O 10 ( ) operators are the simplest solution, consistency with global b sμμ data requires O 9 Z or light leptoquarks naturally realize these operators Each model offers additional specific predictions Lepton flavour violation expected but not guaranteed Lepton flavor nonuniversality in b sl + l processes 19

20 Backup Lepton flavor nonuniversality in b sl + l processes 20

21 LQ specific predictions: B Kνν L = Y ij L i i 2 d Rj = Y ij `Li d Rj (2/3) + Lk (V PMNS ) ki d Rj (charge -1/3) ( 1/3) SM: flavour diagonal contributions [Altmannshofer et al, ] LQ: mixed flavor contributions b s νi νj Lepton flavor nonuniversality in b sl + l processes 21

22 LQ specific predictions: B Kνν Sum the widths over all neutrinos i, j Correction of the SM q 2 spectrum and branching fraction: Lepton flavor nonuniversality in b sl + l processes

23 LFV LFV (LFUV in different channels) (Bs eμ and B Keμ can be measured) if and only if (LFUV in bottomonium and Φ can be measured) b s μ e b b s s μ μ e e B(! µµ) B(! ee) B(! µµ) B(! ee) Lepton flavor nonuniversality in b sl + l processes 23

24 Decay spectrum d dq 2 (B! Kµ+ µ )=2a µ (q 2 )+ 2 3 c µ(q 2 ) in terms of Wilson coefficients and form factors h a`(q 2 )=C(q 2 ) q 2 F P (q 2 ) 2 + (q2 ) 4 h c`(q 2 )=C(q 2 ) F A (q 2 ) 2 + F V (q 2 ) 2 +4m 2`m 2 B F A (q 2 ) 2 +2m` m 2 B m 2 K + q 2 Re F P (q 2 )FA(q 2 ) (q 2 ) i 2 ` (q 2 ) F A (q 2 ) 2 + F V (q 2 ) 2 4 i F V (q 2 )=(C 9 + C 0 9) f + (q 2 )+ F A (q 2 )=(C 10 + C10)f 0 + (q 2 ) apple F P (q 2 )= m`(c 10 + C10) 0 f + (q 2 ) 2m b m B + m K (C 7 + C 0 7) f T (q 2 ) m 2 B m 2 K q 2 f 0 (q 2 ) f + (q 2 ) Form factors (with full correlations) taken from HPQCD lattice calculation [Bouchard et al, ] Lepton flavor nonuniversality in b sl + l processes 24