Global analysis of b sll anomalies

Transcription

1 Global analysis of b sll anomalies Joaquim Matias Universitat Autònoma de Barcelona LIO Conference on Flavour, Composite Models and Dark Matter In collaboration with: S. Descotes-Genon, L. Hofer and J. Virto Based on: DMV 13 PRD88 (2013) , DHMV 14 JHEP 1412 (2014) 125, JM 12 PRD86 (2012) , HM 15 JHEP 1509(2015)104, DHMV All originated in Frank Krueger, J.M., Phys. Rev. D71 (2005) November 25, 2015

2 Goal of this talk This talk will try to answer the following questions: What does the global fit on b sll tell us about Wilson coefficients? Which Wilson coefficients/scenarios receive a dominant NP contribution? What does other approaches using different observables and methodology obtain? Are the alternative explanations (factorizable power corrections and charm) raised to explain (some) anomaly on the fit really robust? Where those explanations fail in front of a possible New Physics explanation? What can we expect in the near future?

3 Motivation Since long time ago... b sγ and b sll Flavour Changing Neutral Currents have been used as our portal to explore the fundamental theory beyond SM. Analysis in a model-independent approach effective Hamiltonian: 10 b sγ( ) : H F SM =1 VtsV tb C i O i +... i=1 O 7 = e g 2 m b sσ µν (1 + γ 5 )F µν b O 9 = e2 g 2 sγ µ (1 γ 5 )b lγ µ l O 10 = e2 g 2 sγ µ (1 γ 5 )b lγ µ γ 5 l SM Wilson coefficients up to NNLO + e.m. corrections at µ ref = 4.8 GeV [Misiak et al.]: NP changes short distance C i C SM i C SM 7 = 0.29, C SM 9 = 4.1, C SM 10 = 4.3 Our Aim: To disentangle hadronic effects from New Physics effects. = C NP i and induce new operators, like O 7,9,10 = O 7,9,10(γ 5 γ 5 ) Our Tool: A global analysis of b sll, b sγ will allow to test these Wilson coefficients with an unprecedented precision.

4 THE OBSERVABLES

5 Rare b s processes Inclusive B X s γ (BR)... C ( ) 7 B X s l + l (dbr/dq 2 )... C ( ) 7, C( ) 9, C( ) 10 Exclusive leptonic B s l + l (BR)... C ( ) 10 Exclusive radiative/semileptonic B K γ (BR, S, A I )... C ( ) 7 B K l + l (dbr/dq 2 )... C ( ) 7, C( ) 9, C( ) 10 B K l + l (dbr/dq 2, Optimized Angular Obs.).. C ( ) 7, C( ) 9, C( ) 10 B s φl + l (dbr/dq 2, Angular Observables)... C ( ) 7, C( ) 9, C( ) 10 Λ b Λl + l (None so far) etc.

6 The optimized observables P ( ) i come from the angular distribution B d K 0 ( K π + )l + l with the K 0 on the mass shell. It is described by s = q 2 and three angles θ l, θ K and φ d 4 Γ( B d ) dq 2 d cos θ l d cos θ K dφ = 9 32π J(q2, θ l, θ K, φ) = i J i (q 2 )f i (θ l, θ K, φ} µ θl µ + φ B 0 K θ K π+ K 0 θ l : Angle of emission between and µ in di-lepton rest frame. θ K : Angle of emission between and K in di-meson rest frame. φ: Angle between the two planes. K 0 q 2 : dilepton invariant mass square. J i (q 2 ) are function of transversity amplitudes of K : A L,R,,0 and they depend on FF and Wilson coefficients. Notice LHCb uses θl LHCb = π θl us. Ongoing discussion on φ LHCb versus φ theory irrelevant for the fit (checked explicitly) (sign of S 7,8 or P 6,8 ). (Zwicky)

7 Four regions in q 2 Four regions in q 2 : very large K -recoil (4ml 2 < q2 < 1 GeV 2 ): γ almost real. large K -recoil/low-q 2 : E K Λ QCD or 4ml 2 q2 < 9 GeV 2 : LCSR-FF charmonium region (q 2 = mj/ψ 2,...) betwen 9 < q2 < 14 GeV 2. low K -recoil/large-q 2 : E K Λ QCD or 14 < q 2 (m B m K ) 2 : LQCD-FF

8 The distribution (massless case) including the S-wave and normalized to Γ full : 1 Γ full d 4 Γ dq 2 dcos θ K dcos θ l dφ = 9 [ 3 32π 4 F T sin 2 θ K + F L cos 2 θ K +( 1 4 F T sin 2 θ K F L cos 2 θ K ) cos 2θ l P 1F T sin 2 θ K sin 2 θ l cos 2φ + ( ) 1 F T F L 2 P 4 sin 2θ K sin 2θ l cos φ + P 5 sin 2θ K sin θ l cos φ F T F L (P 6 sin 2θ K sin θ l sin φ 1 ) 2 P 8 sin 2θ K sin 2θ l sin φ ] +2P 2 F T sin 2 θ K cos θ l P 3 F T sin 2 θ K sin 2 θ l sin 2φ (1 F S ) + 1 Γ W S full in blue the set of relevant observables P 1,2, P 4,5. the S-wave terms are (see discussion [HM 15]) not all free observables: W S Γ full = 3 [ F S sin 2 θ l + A S sin 2 θ l cos θ K + A 4 S 16π sin θ K sin 2θ l cos φ +A 5 S sin θ K sin θ l cos φ + A 7 S sin θ K sin θ l sin φ + A 8 S sin θ K sin 2θ l sin φ ] Basis (massless): {Γ K,A FB or F L, P 1, P 2, P 3, P 4, P 5, P 6 } and only 4 of {F S, A S, A 4 S, A5 S, A7 S, A8 S } are independent.

9 Theoretical description of B K l + l : low-q 2 There are basically two theory approaches: 1. Improved-QCDF approach: QCDF+exploit symmetry relations at large-recoil (limit) among FF: m K E m B m B +m V (q2 K ) = m B+m K 2E A 0(q 2 ) = m B+m K 2E A 1 (q 2 ) = T 1 (q 2 ) = m B 2E T 2(q 2 ) = ξ (E) A 1 (q 2 ) m B m K m B A 2 (q 2 ) = m B 2E T 2(q 2 ) T 3 (q 2 ) = ξ (E) Transparent, valid for ANY FF parametrization (BZ, KMPW,...) and easy to reproduce.

10 Theoretical description of B K l + l : low-q 2 There are basically two theory approaches: 1. Improved-QCDF approach: QCDF+exploit symmetry relations at large-recoil (limit) among FF: m K E m B m B +m V (q2 K ) = m B+m K 2E A 0(q 2 ) = m B+m K 2E A 1 (q 2 ) = T 1 (q 2 ) = m B 2E T 2(q 2 ) = ξ (E) A 1 (q 2 ) m B m K m B A 2 (q 2 ) = m B 2E T 2(q 2 ) T 3 (q 2 ) = ξ (E) Transparent, valid for ANY FF parametrization (BZ, KMPW,...) and easy to reproduce. Dominant correlations automatically implemented in a transparent way via SYMMETRIES.

11 Theoretical description of B K l + l : low-q 2 There are basically two theory approaches: 1. Improved-QCDF approach: QCDF+exploit symmetry relations at large-recoil (limit) among FF: m K E m B m B +m V (q2 K ) = m B+m K 2E A 0(q 2 ) = m B+m K 2E A 1 (q 2 ) = T 1 (q 2 ) = m B 2E T 2(q 2 ) = ξ (E) A 1 (q 2 ) m B m K m B A 2 (q 2 ) = m B 2E T 2(q 2 ) T 3 (q 2 ) = ξ (E) Transparent, valid for ANY FF parametrization (BZ, KMPW,...) and easy to reproduce. Dominant correlations automatically implemented in a transparent way via SYMMETRIES. Construction of FFI observables P ( ) i : at LO in 1/m b, α s and large-recoil limit (EK large): A L,R ξ A L,R ξ A L,R 0 ξ We add all Symmetry Breaking corrections in our computation to relations above:

12 Theoretical description of B K l + l : low-q 2 There are basically two theory approaches: 1. Improved-QCDF approach: QCDF+exploit symmetry relations at large-recoil (limit) among FF: m K E m B m B +m V (q2 K ) = m B+m K 2E A 0(q 2 ) = m B+m K 2E A 1 (q 2 ) = T 1 (q 2 ) = m B 2E T 2(q 2 ) = ξ (E) A 1 (q 2 ) m B m K m B A 2 (q 2 ) = m B 2E T 2(q 2 ) T 3 (q 2 ) = ξ (E) Transparent, valid for ANY FF parametrization (BZ, KMPW,...) and easy to reproduce. Dominant correlations automatically implemented in a transparent way via SYMMETRIES. Construction of FFI observables P ( ) i : at LO in 1/m b, α s and large-recoil limit (EK large): A L,R ξ A L,R ξ A L,R 0 ξ We add all Symmetry Breaking corrections in our computation to relations above: known α s factorizable and non-factorizable corrections from QCDF. factorizable power corrections (using a systematic procedure for each FFp, see later) non-factorizable power corrections including charm-quark loops. Minor drawback: You should use the freedom to define ξ, to identify an optimal scheme that minimizes your sensitivity to factorizable power corrections. A blind choice like in (J.C. 12 & 14) enlarges artificially their impact.

13 Theoretical description of B K l + l : low-q 2 There are basically two theory approaches: 1. Improved-QCDF approach: QCDF+exploit symmetry relations at large-recoil (limit) among FF: m K E m B m B +m V (q2 K ) = m B+m K 2E A 0(q 2 ) = m B+m K 2E A 1 (q 2 ) = T 1 (q 2 ) = m B 2E T 2(q 2 ) = ξ (E) A 1 (q 2 ) m B m K m B A 2 (q 2 ) = m B 2E T 2(q 2 ) T 3 (q 2 ) = ξ (E) Transparent, valid for ANY FF parametrization (BZ, KMPW,...) and easy to reproduce. Dominant correlations automatically implemented in a transparent way via SYMMETRIES. Construction of FFI observables P ( ) i : at LO in 1/m b, α s and large-recoil limit (EK large): A L,R ξ A L,R ξ A L,R 0 ξ We add all Symmetry Breaking corrections in our computation to relations above: known α s factorizable and non-factorizable corrections from QCDF. factorizable power corrections (using a systematic procedure for each FFp, see later) non-factorizable power corrections including charm-quark loops. Minor drawback: You should use the freedom to define ξ, to identify an optimal scheme that minimizes your sensitivity to factorizable power corrections. A blind choice like in (J.C. 12 & 14) enlarges artificially their impact.

14 Theoretical description of B K l + l : low-q 2 2. Full FF approach: Compute correlations from a specific LCSR computation. Parametric correlations easy, but Borel parameters choice delicate. Use of EOM. Factorizable O(α s ) and factorizable p.c. included in a particular LCSR parametrization. Less general, attached to a single FF parametrization with all inner choices included. Extra pieces that need to be added: known α s non-factorizable corrections from QCDF. non-factorizable power corrections and charm-quark loop effects Usually applied to S i = (J i + J i )/(dγ + dγ) highly dependent on FF-error estimate. Minor drawback: Do the results of the fit depend on the details of a particular non-perturbative Form Factor computation and their small error size?

15 Theoretical description of B K l + l : low-q 2 2. Full FF approach: Compute correlations from a specific LCSR computation. Parametric correlations easy, but Borel parameters choice delicate. Use of EOM. Factorizable O(α s ) and factorizable p.c. included in a particular LCSR parametrization. Less general, attached to a single FF parametrization with all inner choices included. Extra pieces that need to be added: known α s non-factorizable corrections from QCDF. non-factorizable power corrections and charm-quark loop effects Usually applied to S i = (J i + J i )/(dγ + dγ) highly dependent on FF-error estimate. Minor drawback: Do the results of the fit depend on the details of a particular non-perturbative Form Factor computation and their small error size? Amplitude analysis. Not a FF treatment but a different approach to data based on exploiting the symmetries of the distribution. They fit for the amplitudes after fixing 3 of them to zero by means of the symmetries. The outcome is a set of parameters α, β, γ that contain the information on WC and FF. They naturally produce unbinned results.

16 Theoretical description of B K l + l : low-q 2 2. Full FF approach: Compute correlations from a specific LCSR computation. Parametric correlations easy, but Borel parameters choice delicate. Use of EOM. Factorizable O(α s ) and factorizable p.c. included in a particular LCSR parametrization. Less general, attached to a single FF parametrization with all inner choices included. Extra pieces that need to be added: known α s non-factorizable corrections from QCDF. non-factorizable power corrections and charm-quark loop effects Usually applied to S i = (J i + J i )/(dγ + dγ) highly dependent on FF-error estimate. Minor drawback: Do the results of the fit depend on the details of a particular non-perturbative Form Factor computation and their small error size? Amplitude analysis. Not a FF treatment but a different approach to data based on exploiting the symmetries of the distribution. They fit for the amplitudes after fixing 3 of them to zero by means of the symmetries. The outcome is a set of parameters α, β, γ that contain the information on WC and FF. They naturally produce unbinned results.

17 Theoretical description of B K l + l : large-q 2 It corresponds to large q 2 O(m b ) above Ψ mass, i.e., E K is around GeV or below. OPE in E K / q 2 or Λ QCD / q 2 (Buchalla et al) NLO QCD corrections to the OPE coeffs (Greub et al) Lattice QCD form factors with correlations (Horgan et al proceeding update) ±10% on angular observables to account for possible Duality Violations. Estimates on BR from GP (5%) and BBF (2%) using Shifman s model. Existence of c c resonances in this region (clearly seen ψ(4160) in B K µ + µ ), require to take a long bin. Candidates / (25 MeV/c 2 ) LHCb data total nonresonant interference resonances background m µ + µ [MeV/c 2 ]

18 A few properties of the relevant observables P 1,2 The idea of exact cancellation of the poorly known soft form factors at LO at the zero of A FB was incorporated in the construction of the transverse asymmetry (this is the meaning of the word clean ) P 1 and P 2 observables function of A and A amplitudes P 1 : Proportional to A 2 A 2 Test the LH structure of SM and/or existence of RH currents that breaks A A P 2 : Proportional to Re(A i A j ) Zero of P 2 at the same position as the zero of A FB P 2 is the clean version of A FB. Their different normalizations offer different sensitivities. - - ( ) ( ) P 3 and P 6,8 are proportional to ImA ia j and small if there are no large phases. All are < 0.1. P CP i are all negligibly small if there is no New Physics in weak phases.

19 Brief Discussion on: P 5 and P ( ) P 5 was proposed for the first time in DMRV, JHEP 1301(2013)048 P 5 = 2 Re(AL 0 AL AR 0 AR = Re[n 0 n 2 ]. A 0 2 ( A 2 + A 2 ) n 0 2 ( n 2 + n 2 ) ) with n 0 = (A L 0, AR 0 ), n = (A L, AR ) and n = (A L, AR ) If no-rhc n n (H +1 0) P 5 cos θ 0, (q 2 )

20 Brief Discussion on: P 5 and P 4 P 5 was proposed for the first time in DMRV, JHEP 1301(2013)048 P 5 = 2 Re(AL 0 AL AR 0 AR = Re[n 0 n 2 ]. A 0 2 ( A 2 + A 2 ) n 0 2 ( n 2 + n 2 ) ) - - ( ) with n 0 = (A L 0, AR 0 ), n = (A L, AR ) and n = (A L, AR ) If no-rhc n n (H +1 0) P 5 cos θ 0, (q 2 ) In the large-recoil limit with no RHC [ A L, (1, 1) C9 eff C [ ˆm b ŝ Ceff 7 ]ξ (E K ) A R, (1, 1) C9 eff + C ˆm b ŝ [ [ ] A L 0 C9 eff C ˆm b C7 ]ξ eff (E K ) A R0 C9 eff + C ˆm b C7 eff ξ (E K ) Ceff 7 ] ξ (E K ) In SM C SM 9 + C SM 10 0 AR, AL, In P 5 : If CNP 9 < 0 then A R 0,, AR and AL 0,, AL and due to, P 5 gets strongly reduced.

21 Brief Discussion on: P 5 and P 4 P 5 was proposed for the first time in DMRV, JHEP 1301(2013)048 P 5 = 2 Re(AL 0 AL AR 0 AR = Re[n 0 n 2 ]. A 0 2 ( A 2 + A 2 ) n 0 2 ( n 2 + n 2 ) ) - - ( ) with n 0 = (A L 0, AR 0 ), n = (A L, AR ) and n = (A L, AR ) If no-rhc n n (H +1 0) P 5 cos θ 0, (q 2 ) In the large-recoil limit with no RHC [ A L, (1, 1) C9 eff C [ ˆm b ŝ Ceff 7 ]ξ (E K ) A R, (1, 1) C9 eff + C ˆm b ŝ [ [ ] A L 0 C9 eff C ˆm b C7 ]ξ eff (E K ) A R0 C9 eff + C ˆm b C7 eff ξ (E K ) Ceff 7 ] ξ (E K ) In SM C SM 9 + C SM 10 0 AR, AL, In P 5 : If CNP 9 < 0 then A R 0,, AR and AL 0,, AL and due to, P 5 gets strongly reduced.

22 Brief Discussion on: P 5 and P 4 P 4 was proposed for the first time in DMRV, JHEP 1301(2013)048 P 4 = 2 Re(AL 0 AL +AR 0 AR ) = Re[n 0 n 2 ]. A 0 2 ( A 2 + A 2 ) n 0 2 ( n 2 + n 2 ) - ( ) with n 0 = (A L 0, AR 0 ), n = (A L, AR ) and n = (A L, AR ) If no-rhc n n (H +1 0) P 4 cos θ 0, (q 2 ) In the large-recoil limit with no RHC [ A L, (1, 1) C9 eff C [ ˆm b ŝ Ceff 7 ]ξ (E K ) A R, (1, 1) C9 eff + C ˆm b ŝ [ [ ] A L 0 C9 eff C ˆm b C7 ]ξ eff (E K ) A R0 C9 eff + C ˆm b C7 eff ξ (E K ) Ceff 7 ] ξ (E K ) In SM C SM 9 + C SM 10 0 AR, AL, In P 4 :If CNP 9 < 0 then A R 0,, AR and AL 0,, AL due to + what L loses R gains (little change).

23 History of global b sll fits (I) From recent Bobeth s talk at cern year arxiv: group/programs authors method EOS CB/Hiller/van Dyk χ DGMR Descotes-Genon/Ghosh/JM/Ramon χ EOS CB/Hiller/van Dyk χ APS Altmannshofer/Paradisi/Straub χ EOS CB/Hiller/van Dyk/Wacker χ EOS Beaujean/CB/van Dyk/Wacker bayesian AS Altmannshofer/Straub χ SuperISO Hurth/Mahmoudi χ DMRV Descotes-Genon/JM/Ramon/Virto χ 2 χ 2 means frequentist. global fits: combination of observables governed by b sll and b sγ Public software: EOS, SuperIso, HEPfit and private codes DHMV, AS,...

24 History of global b sll fits (II) year arxiv: group/programs authors method DMV Descotes-Genon/JM/Virto χ 2 Anomaly AS Altmannshofer/Straub χ EOS Beaujean/CB/van Dyk bayesian HLMW Horgan/Liu/Meinel/Wingate χ SuperISO Hurth/Mahmoudi χ GNR Ghosh/Nardecchia/Renner bayesian SuperIso Hurth/Mahmoudi/Neshatpour χ / AS Altmannshofer/Straub χ EOS Beaujean/CB/Jahn bayesian DHMV Descotes-Genon/Hofer/Matias/Virto χ 2 1/fb dataset from LHCb first analysis done using optimized observables the B K µ + µ anomaly is described in /fb dataset from LHCb the anomaly is confirmed.

25 Global Fits to Wilson coefficients: History and Results 2013 with 1fb 1 Situation in 2013: Descotes-Genon, Matias, Virto C 9 NP SM 68.3 C.L 95.5 C.L 99.7 C.L Includes Low Recoil data Only 1,6 bins P 2 P 5 db/dq 2 GeV q GeV q 2 GeV B± K ± µ + µ C9 NP = 0.0 binned LHCb q 2 (GeV) 2 Our statement in July 2013 DMV 13: We found that the Standard Model hypothesis C NP 7 = 0, C NP 9 = 0 has a pull of 4.5σ. Other groups later on confirmed the relevance of C 9 using FFD-observables (Altmannshofer, Straub ), low-recoil (Horgan et al ), Bayesian approach (Beaujean, Bobethm Van Dyk ). [low-recoil C 9 NP < 0], [3.7 σ third bin], [2.9σ in second bin]

26 FIT 2015

27 Theory and experimental updates in 2015 fit BR(B X s γ) see talk J. Virto New theory update: B SM sγ = (3.36 ± 0.23) 10 4 (Misiak et al 2015) +6.4% shift in central value w.r.t 2006 excellent agreement with WA BR(B s µ + µ ) New theory update (Bobeth et al 2013), New LHCb+CMS average (2014) BR(B X s µ + µ ) New theory update (Huber et al 2015) BR(B K µ + µ ) : LHCb Lattice form factors at large q 2 (Bouchard et al 2013, 2015) B (s) (K, φ)µ + µ : BRs & Angular Observables LHCb Lattice form factors at large q 2 (Horgan et al 2013) BR(B Ke + e ) [1,6] (or R K ) and B K e + e at very low q 2 LHCb 2014, 2015

28 Fit 2015: Statistical Approach Frequentist approach: χ 2 (C i ) = [O exp O th (C i )] j [Cov 1 ] jk [O exp O th (C i )] k Cov = Cov exp + Cov th. We have Cov exp for the first time Calculate Cov th : correlated multigaussian scan over all nuisance parameters Cov th depends on C i : Must check this dependence For the Fit: Minimise χ 2 χ 2 min = χ2 (C 0 i ) (Best Fit Point = C 0 i ) Confidence level regions: χ 2 (C i ) χ 2 min < χ σ,n In a model with a single free param. C 9 the fit result measurement of C 9 (confidence interval). Pull SM tells you how much in this model the measured value of C 9 is in tension with C 9 = C SM 9

29 Message 1 NO SINGLE MEASUREMENT HAVE A PULL LARGER THAN 3.3σ (several deviations 2-3σ) GLOBAL ANALYSIS TELLS YOU HOW MUCH C NP i = 0 (SM) (i=9 for instance) IS DISFAVOURED COMPARED TO THE BEST FIT POINT THIS OBVIOUSLY CAN BE LARGER THAN 3σ if deviations are consistent

30 SM predictions and Pulls 2015: B K µµ: What s new in 2015? R K LHCb BaBar Belle LHCb R K = Br (B+ K + µ + µ ) Br (B + K + e + e ) = ± SM It deviates 2.6σ from SM. Data on B + K + µ + µ is below SM in all bins at large and low-recoil q 2 [GeV 2 /c 4 ] Also neutral mode: 10 7 BR(B 0 K 0 µ + µ ) Standard Model Experiment Pull [0.1, 2] 0.63 ± ± [2, 4] 0.65 ± ± [4, 6] 0.64 ± ± [6, 8] 0.64 ± ± [15, 19] 0.90 ± ±

31 Message 2 THERE ARE COMMON NEW PHYSICS MECHANISMS ABLE TO EXPLAIN P 5 and R K

32 SM predictions and Pulls 2015: BR(B V µµ) 10 7 BR(B 0 K 0 µ + µ ) Standard Model Experiment Pull [0.1, 2] 1.26 ± ± [2, 4.3] 0.84 ± ± [4.3, 8.68] 2.52 ± ± [16, 19] 1.66 ± ± BR(B + K + µ + µ ) Standard Model Experiment Pull [0.1, 2] 1.31 ± ± [2, 4] 0.79 ± ± [4, 6] 0.94 ± ± [6, 8] 1.15 ± ± [15, 19] 2.59 ± ± BR(B s φµ + µ ) Standard Model Experiment Pull [0.1, 2.] 1.81 ± ± [2., 5.] 1.88 ± ± [5., 8.] 2.25 ± ± [15, 18.8] 2.20 ± ±

33 SM predictions and Pulls 2015: P i (B K µµ) and P i (B s Φµµ) New 3fb 1 dataset confirms the anomaly in P 5 in bins [4,6] and [6,8] P 1 (B K µ + µ ) Standard Model Experiment Pull [15, 19] 0.64 ± ± P 2 (B K µ + µ ) Standard Model Experiment Pull [0.1, 0.98] 0.12 ± ± [6, 8] 0.38 ± ± P 5 (B K µ + µ ) Standard Model Experiment Pull [0.1, 0.98] 0.67 ± ± [2.5, 4] 0.49 ± ± [4, 6] 0.82 ± ± [6, 8] 0.94 ± ± [15, 19] 0.57 ± ± P 1 (B s φµ + µ ) Standard Model Experiment Pull [15, 18.8] 0.69 ± ± P 4 (B s φµ + µ ) Standard Model Experiment Pull [15, 18.8] 1.30 ± ±

34 Result of the fit with 1D Wilson coefficient 2015 This is the first analysis: - using the basis of optimized observables (B K µµ and B s φµµ) - using the full dataset of 3fb 1 : Coefficient Best fit 1σ 3σ Pull SM C NP [ 0.04, 0.00] [ 0.07, 0.04] 1.1 C NP [ 1.32, 0.89] [ 1.71, 0.40] 4.5 C NP [0.34, 0.84] [ 0.11, 1.41] 2.5 C NP [ 0.01, 0.04] [ 0.05, 0.09] 0.7 C NP [0.21, 0.77] [ 0.33, 1.35] 1.8 C NP [ 0.46, 0.08] [ 0.84, 0.28] 1.4 C NP 9 = C NP [ 0.40, 0.00] [ 0.74, 0.55] 1.0 C NP 9 = C NP [ 0.88, 0.51] [ 1.27, 0.18] 4.1 C NP 9 = C NP [ 1.28, 0.88] [ 1.62, 0.42] 4.8 (no R K ) C9 NP = C10 NP = C9 NP = NP 0.68 [ 0.49, 0.49] [ 1.36, 0.15]

35 Result of the fit with 2D Wilson coefficient constrained and unconstrained Coefficient Best Fit Point Pull SM p-value (%) (C7 NP, CNP 9 (C9 NP, CNP 10 ) ( 0.00, 1.11) ) ( 1.16, 0.35) (C NP 9, CNP 7 ) ( 1.16, 0.02) (C NP 9, CNP 9 ) ( 1.15, 0.77) (C NP 9, CNP 10 ) ( 1.23, 0.38) (C NP 9 = C NP 9, C NP 10 = CNP 10 ) ( 1.17, 0.26) (C NP 9 = C NP 9, C NP 10 = CNP 10 ) ( 1.14, 0.04) (C NP 9 = C NP 9, C NP 10 = CNP 10 ) ( 0.68, 0.26) (C NP 9 = C NP 10, CNP 9 = C NP 10 ) ( 0.74, 0.26) C NP 9 always play a dominant role All 2D scenarios above 4σ are quite indistinguishable. We have done a systematic work to check what are the most relevant Wilson Coefficients to explain all deviations, by allowing progressively different WC to get NP contributions and compare the pulls.

36 QUESTION 1: Branching Ratios versus Angular Observables P i? 3 3 Branching Ratios Branching Ratios 2 Angular Observables P i All 2 Angular Observables P i All 1 1 NP C 9' 0 NP C C 9 NP C 9 NP 3 Branching Ratios 3 Branching Ratios 2 Angular Observables P i All 2 Angular Observables P i All 1 1 NP C 10 NP C10' 0 NP C 10 NP C10' C NP NP 9 C 9' C NP NP 9 C 9' Figure: Angular observables (FFI at LO P i ) dominates clearly over Branching ratios

37 QUESTION 2: B K µµ, B K µµ and B s φµµ? 3 3 B KΜΜ B K ΜΜ 2 B s ΦΜΜ 2 All B KΜΜ B K ΜΜ B s ΦΜΜ All 1 1 NP C 9' 0 NP C C 9 NP C 9 NP 3 B KΜΜ 3 B KΜΜ 2 B K ΜΜ B s ΦΜΜ 2 B K ΜΜ B s ΦΜΜ All All 1 1 NP C 10 NP C10' 0 NP C 10 NP C10' C NP NP 9 C 9' C NP NP 9 C 9' Figure: The hierarchy of importance for the fit: B K µµ, B s φµµ and B K µµ

38 QUESTION 3: Which information and constraints provide each region? 3 Only large recoil Only bins within 1,6 region 2 Only low recoil All 1 NP C 9' C 9 NP Figure: We show the 3 σ regions allowed by large-recoil only (dashed green), by bins in the [1-6] range (long-dashed blue), by low recoil (dot-dashed purple) and by considering all data (red, with 1,2,3 σ contours). Low-recoil is strongly constraining! Important implications for power corrections and charm. Bins [1,6] are perfectly coherent with the full large-recoil.

39 Impact of B Ke + e under hypothesis of maximal Lepton Flavour Universal Violation

40 1D-Coefficient Best fit 1σ 3σ Pull SM C NP [ 1.34, 0.93] [ 1.71, 0.47] C NP 9 = C NP [ 0.81, 0.50] [ 1.15, 0.21] C NP 9 = C NP [ 1.28, 0.88] [ 1.62, 0.43] 4.9 C NP 9 = C NP 10 = CNP 9 = C NP [ 0.83, 0.49] [ 0.19, 0.19] 4.4 2D-Coefficient Best Fit Point Pull SM (C7 NP, CNP 9 (C9 NP, CNP 10 (C9 NP, CNP 7 ) (0.00, 1.13) ) ( 1.11, 0.32) ) ( 1.20, 0.03) (C9 NP, 9 ) ( 1.23, 0.61) (C9 NP, 10 ) ( 1.32, 0.34) (C9 NP = C9 NP, C NP 10 = CNP 10 ) ( 1.23, 0.39) (C9 NP = C9 NP, C NP 10 = CNP 10 ) ( 0.99, 0.03) 4.5 (C9 NP = C9 NP, C NP 10 = CNP 10 ) ( 0.70, 0.22) (C9 NP = C10 NP, 9 = C NP 10 ) ( 0.69, 0.27) The strong correlations among form factors of B K µµ and B Kee assuming no NP in B Kee enhances the NP evidence in muons. Notice that we use all bins in B K µµ while R K is only [1,6]. All theory correlations included. Only scenarios explaining R K get an extra enhancement of σ

41 Fits considering Lepton Flavour (non-) Universality ( μμ) + ( ) [ ] ( μμ) + ( ) [ ] μμ μμ - = μ μ = - μ If NP-LFUV is assumed, NP may enter both b see and b sµµ decays with different values. For each scenario, we see that there is no clear indication of a NP contribution in the electron sector, whereas one has clearly a non-vanishing contribution for the muon sector, with a deviation from the Lepton Flavour Universality line.

42 Prediction for LFU tests observables C NP C NP C NP R K [1, 6] R K [1.1, 6] R φ [1.1, 6] SM 1.00 ± ± 0.01 [1.00 ± 0.01] 1.00 ± 0.01 C NP 9 = ± ± 0.08 [0.84 ± 0.02] 0.84 ± = C NP = ± ± 0.14 [0.74 ± 0.04] 0.74 ± C NP 9 = C NP 10 = ± ± 0.03 [0.69 ± 0.01] 0.69 ± = 1.15, C NP = ± ± 0.12 [0.76 ± 0.03] 0.76 ± C NP 9 = 1.16, C NP 10 = ± ± 0.07 [0.75 ± 0.02] 0.76 ± 0.01 C NP 9 = 1.23, C NP = ± ± 0.11 [0.75 ± 0.02] 0.76 ± = C NP = 1.17, CNP 10 = C NP = ± ± 0.12 [0.71 ± 0.04] 0.71 ± Table: Predictions for R K, R K, R φ at the best fit point of different scenarios of interest, assuming that NP enters only in the muon sector, and using the inputs of our reference fit, in particular the KMPW form factors for B K and B K, and BSZ for B s φ. In the case of B K, we also indicate in brackets the predictions using the form factors in BSZ.

43 Updated plot of C.L 95.5 C.L 99.7 C.L Includes Low Recoil data [ ] Only 1,6 bins C 9 NP 0 SM Figure: For the scenario where NP occurs in the two Wilson coefficients C 7 and C 9, we compare the situation from the analysis in Fig. 1 of Ref. DMV 13(on the left) and the current situation (on the right). On the right, we show the 3 σ regions allowed by large-recoil only (dashed green), by bins in the [1-6] range (long-dashed blue), by low recoil (dot-dashed purple) and by considering all data (red, with 1,2,3 σ contours).

44 A CRUCIAL QUESTION: How much the fit results depend on the details? Two first strong tests

45 TEST 1: Does the fit result depend on method IQCDF-KMPW or Full-FF-BSZ? Two examples of Form Factor determinations (left KMPW, right BSZ): form factor F i BK ( ) (0) b i 1 f + BK fbk f T BK V BK A BK A BK A BK T BK T BK T BK Table: The B K ( ) form factors from LCSR and their z-parameterization. Interestingly in this update from BZ to BSZ, relevant FF from BZ moved towards KMPW. For example: V BZ (0) = T1 BZ (0) = The size of uncertainty in BSZ = size of error of p.c. we use. B K B s φ B s K A 0 (0) ± ± ± A 1 (0) ± ± ± A 12 (0) ± ± ± V (0) ± ± ± T 1 (0) ± ± ± T 2 (0) ± ± ± T 23 (0) ± ± ± Table: Values of the form factors at q 2 = 0 and their uncertainties.

46 TEST 1: Does the fit result depend on method IQCDF-KMPW or Full-FF-BSZ? NO Full Form Factor approach Full Form Factor approach Full Form Factor approach 2 Soft Form Factor approach 2 Soft Form Factor approach 2 Soft Form Factor approach NP C 9' 0 NP C 10 0 NP C 10 NP C10' C 9 NP C 9 NP C NP NP 9 C 9' Figure: We show the 3 σ regions allowed using form factors in BSZ 15 in the full form factor approach (long-dashed blue) compared to our reference fit with the soft form factor approach (red, with 1,2,3 σ contours). The results of the fit using (IQCDF-KMPW) or (Full-FF-BSZ) are perfectly consistent. The fact that our regions are slightly larger points that our estimate of uncertainties (power corrections, etc.) is conservative.

47 TEST 2: Does the fit result depend on using P i or S i observables? NO 3 3 Angular Observables S i Angular Observables S i 2 Angular Observables P i All P i 2 Angular Observables P i All P i 1 1 NP C 9' 0 NP C C 9 NP C 9 NP The results of the fit using P i observables or S i observables are perfectly consistent. The highest sensitivity to NP of the optimized observables due to the shielding on FF details induces a small albeit systematic improvement in significance for the P i. Does the error predictions on individual observables depend significantly on FF choice? anomaly [4,6] bin P 5 error SIZE [pull] S 5 error SIZE [pull] Full-FF-BSZ 10% [2.7σ] 12% [2.0σ] IQCDF-KMPW 10% [2.9σ] 40% [1.2σ] Yes for S i, Not for P i.

48 Message 3 Only in a global fit thanks to correlations it is basically the same to use: Optimized observables P i. FF dependent observables S i. BUT when testing individual observables with data: Optimized observables P i are robust. FF dependent observables S i are largely choice dependent.

49 Hadronic Uncertainties: Power corrections and charm loop Frequent naïve statement: Uncertainties are underestimated? It is important to understand what the uncertainties are and how they are treated before been able to ask the question.

50 Hadronic uncertainties: power corrections and charm While in the past focusing in one single anomaly was logical..., now it is not a good idea neither an acceptable approach to focus all the attention on one single observable. BECAUSE now we have several deviations so a global view is compulsory: and the correction question is: Can I explain all (or quasi) with the same solution?

51 Hadronic uncertainties: power corrections and charm While in the past focusing in one single anomaly was logical..., now it is not a good idea neither an acceptable approach to focus all the attention on one single observable BECAUSE now we have several deviations so a global view is compulsory. The correction question is: What is more natural a solution consistent with all anomalies and tensions or an ad-hoc (and unclear) solution different for each anomaly?

52 Hadronic Uncertainties I: Factorizable Power corrections

53 Factorizable Power Corrections General idea: : Parametrize power corrections to form factors: F(q 2 ) = F soft (ξ, (q 2 )) + F αs (q 2 q 2 q 4 ) + a F + b F mb 2 + c F mb 4... (JC 12) a F, b F, c F... represent the deviation to the SFF+ known α s in the full form factor F (taken e.g. from LCSR) V(q 2 ) = m B + m K m B ξ (q 2 ) + V αs (q 2 ) + V Λ (q 2 ), A 1 (q 2 ) = 2E m B + m K ξ (q 2 ) + A αs 1 (q2 ) + A Λ 1(q 2 ), A 2 (q 2 ) = m B m B m K [ ξ (q 2 ) ξ (q 2 ) ] + A αs 2 (q2 ) + A Λ 2(q 2 ), A 0 (q 2 ) = E m K ξ (q 2 ) + A αs 0 (q2 ) + A Λ 0(q 2 ), T 1 (q 2 ) = ξ (q 2 ) + T αs 1 (q2 ) + T Λ 1 (q 2 )... STEP 1: Define the SFF ξ, to all orders by means of a factorisation scheme CHOICE.

54 STEP 2: The CHOICE of scheme is fundamental will yield accurate predictions for different observables depending on the scheme choice if not all correlations among errors are known not all choices are appropriate. In the scheme we use (Beneke-Feldmann 01) SFF are defined by: ξ (1) (q2 ) m B m B + m K V(q 2 ) ξ (1) (q2 ) m B + m K 2E A 1 (q 2 ) m B m K m B A 2 (q 2 ), Power corrections V Λ (q 2 ) and a combination of A Λ 1 (q2 ) and A Λ 2 (q2 ) are absorbed in ξ,.

55 STEP 2: The CHOICE of scheme is fundamental will yield accurate predictions for different observables depending on the scheme choice if not all correlations among errors are known not all choices are appropriate. In the scheme we use (Beneke-Feldmann 01) SFF are defined by: ξ (1) (q2 ) m B m B + m K V(q 2 ) ξ (1) (q2 ) m B + m K 2E A 1 (q 2 ) m B m K m B A 2 (q 2 ), Power corrections V Λ (q 2 ) and a combination of A Λ 1 (q2 ) and A Λ 2 (q2 ) are absorbed in ξ,. Size of power corrections: The fit to the difference between SFF+ F αs and full-ff is O(Λ/m b ) and is scheme dependent. â (1) F ˆb (1) F ĉ (1) F r(0 GeV 2 ) r(4 GeV 2 ) r(8 GeV 2 ) A 1 (KMPW) ± ± ± % 6% 5% A 1 (BZ) ± ± ± % 1% 3% A 2 (KMPW) ± ± ± % 11% 10% A 2 (BZ) ± ± ± % 1% 5% T 1 (KMPW) ± ± ± % 2% 2% T 1 (BZ) ± ± ± % 7% 6% where r = (a F + b F q 2 /m 2 B + c F /m 4 B )/FF (q2 ) represents the percentatge of p.c.

56 STEP 2: The CHOICE of scheme is fundamental will yield accurate predictions for different observables depending on the scheme choice if not all correlations among errors are known not all choices are appropriate. In the scheme we use (Beneke-Feldmann 01) SFF are defined by: ξ (1) (q2 ) m B m B + m K V(q 2 ) ξ (1) (q2 ) m B + m K 2E A 1 (q 2 ) m B m K m B A 2 (q 2 ), Power corrections V Λ (q 2 ) and a combination of A Λ 1 (q2 ) and A Λ 2 (q2 ) are absorbed in ξ,. Size of power corrections: The fit to the difference between SFF+ F αs and full-ff is O(Λ/m b ) and is scheme dependent. â (1) F ˆb (1) F ĉ (1) F r(0 GeV 2 ) r(4 GeV 2 ) r(8 GeV 2 ) A 1 (KMPW) ± ± ± % 6% 5% A 1 (BZ) ± ± ± % 1% 3% A 2 (KMPW) ± ± ± % 11% 10% A 2 (BZ) ± ± ± % 1% 5% T 1 (KMPW) ± ± ± % 2% 2% T 1 (BZ) ± ± ± % 7% 6% where r = (a F + b F q 2 /m 2 B + c F /m 4 B )/FF (q2 ) represents the percentatge of p.c. This confirms power corrections are typically of order 10% (or smaller in BZ) for relevant FF as expected from dimensional arguments.

57 STEP 2: The CHOICE of scheme is fundamental will yield accurate predictions for different observables depending on the scheme choice if not all correlations among errors are known not all choices are appropriate. In the scheme we use (Beneke-Feldmann 01) SFF are defined by: ξ (1) (q2 ) m B m B + m K V(q 2 ) ξ (1) (q2 ) m B + m K 2E A 1 (q 2 ) m B m K m B A 2 (q 2 ), Power corrections V Λ (q 2 ) and a combination of A Λ 1 (q2 ) and A Λ 2 (q2 ) are absorbed in ξ,. Size of power corrections: The fit to the difference between SFF+ F αs and full-ff is O(Λ/m b ) and is scheme dependent. â (1) F ˆb (1) F ĉ (1) F r(0 GeV 2 ) r(4 GeV 2 ) r(8 GeV 2 ) A 1 (KMPW) ± ± ± % 6% 5% A 1 (BZ) ± ± ± % 1% 3% A 2 (KMPW) ± ± ± % 11% 10% A 2 (BZ) ± ± ± % 1% 5% T 1 (KMPW) ± ± ± % 2% 2% T 1 (BZ) ± ± ± % 7% 6% where r = (a F + b F q 2 /m 2 B + c F /m 4 B )/FF (q2 ) represents the percentatge of p.c. This confirms power corrections are typically of order 10% (or smaller in BZ) for relevant FF as expected from dimensional arguments.

58 In the older scheme (first Beneke-Feldmann) SFF are defined by (also JC 14): ξ (2) (q2 ) T 1 (q 2 ), ξ (2) (q2 ) m K E A 0(q 2 ). Power corrections associated to T Λ 1 (q2 ) and A Λ 0 (q2 ) are absorbed in ξ,. Problems of T 1 choice: Extracting T 1 (0) from data on B K γ is plagued of assumptions (as done in JC 12): 1) assumption of no NP in C ( ) 7 2) ignoring possible non-factorizable power corrections. Taking T 1 from LCSR and use it to define ξ is also non-optimal (as done in JC 14). [ ] A L,R = N C + 9±10 [Vsff+αs (q 2 ) + V Λ ] + C + 7 [Tsff+αs 1 (q 2 ) + T1 Λ ] + O(α s, Λ/m b,...) If one is interested in obtaining accurated predictions for observables dominated by C 9 (like P 5 ) better to have a good control of p.c on V than in T 1. T 1 may be a good choice for observables dominated by C 7. Problem of A 0 choice (minor): P i observables do not depend on A 0 (q 2 ) FF. A 0 choice would be a good choice for lepton-mass suppressed observables.

59 In the older scheme (first Beneke-Feldmann) SFF are defined by (also JC 14): ξ (2) (q2 ) T 1 (q 2 ), ξ (2) (q2 ) m K E A 0(q 2 ). Power corrections associated to T Λ 1 (q2 ) and A Λ 0 (q2 ) are absorbed in ξ,. Problems of T 1 choice: Extracting T 1 (0) from data on B K γ is plagued of assumptions (as done in JC 12): 1) assumption of no NP in C ( ) 7 2) ignoring possible non-factorizable power corrections. Taking T 1 from LCSR and use it to define ξ is also non-optimal (as done in JC 14). [ ] A L,R = N C + 9±10 [Vsff+αs (q 2 ) + V Λ ] + C + 7 [Tsff+αs 1 (q 2 ) + T1 Λ ] + O(α s, Λ/m b,...) If one is interested in obtaining accurated predictions for observables dominated by C 9 (like P 5 ) better to have a good control of p.c on V than in T 1. T 1 may be a good choice for observables dominated by C 7. Problem of A 0 choice (minor): P i observables do not depend on A 0 (q 2 ) FF. A 0 choice would be a good choice for lepton-mass suppressed observables.

60 STEP 3: A correct treatment of power corrections require to respect the correlations among them: a) kinematic correlations among QCD form factors at maximum recoil b) from the renormalization scheme definition of the soft form factors ξ and ξ. STEP 4: The error estimate in previous table â F â F a F â F + â F, ˆb F ˆb F b F ˆb F + ˆb F, ĉ F ĉ F c F ĉ F + ĉ F. comes from F Λ F O(Λ/m b ) 0.1F error assignment larger than size of p.c. itself for â. IN SUMMARY: Each set of observables has an optimal scheme choice, a non-optimal choice may induce artificially large corrections. Interestingly an independent computation using full-ff (BSZ) that has embedded the correlations of a specific LCSR computation gives predictions in good agreement with us for the P i.

61 What does the fit tells you about IMPACT of POWER CORRECTIONS: 3 Only large recoil % 2 Only bins within 1,6 region Only low recoil All % % 1 NP C C 9 NP We show the impact in the fit of increasing power corrections up to 40% At a certain point p.c.-sensitive observable become subdominant and low-recoil dominates. even if power corrections diverge we still get a pull from low-recoil.

62 Hadronic Uncertainties II: Non-factorizable power corrections and long distance charm contributions

63 B K l l : Corrections to QCDF at low-q 2 Non-factorizable power corrections (amplitudes): subleading new unknown non-perturbative. SCET/QCDF at leading power in 1/m b : Factorization of matrix elements into form factors, light-cone distribution amplitudes and hard-scattering kernels. c c loops (resonant and non-resonant contributions) Single out in the amplitude T i in K γ H eff B the piece not associated to FF: Ti had = T i ( C ) 7 0 where r i (s) = r a i e iφa i Multiply each amplitude i = 0,, with a complex q 2 -dependent factor. ( ) 1 + r i (q 2 ) T had i T had i + ri b e iφb i (s/mb 2 ) + r i c e iφc i (s/mb 2 )2 and r a,b,c i [0, 0.1] and φ a,b,c i [ π, π]

64 Charm-loop contributions General considerations on resonances: Low-q 2 : q GeV 2 to limit impact of J/ψ tail. LHCb interesting test split [4.3, 8.68] [4, 6], [6, 8] Large-q 2 : quark-hadron duality violations Model estimate yield 2-5% for BR(B K µµ) [BBF, GP] Assumed similar size for BR and angular observables B K µµ. We enlarge it up to 10% as a correction to each amplitude. At Large-recoil two type of contributions: C BK 9 = δc BK ( ) 9,pert + s iδc BK ( ),i 9,non pert - Short distance (hard-gluons) LO included in C 9 C 9 + Y (q 2 ) higher-order corrections via QCDF/HQET. - Long distance (soft-gluons) Only existing computation KMPW 10 using LCSR. Partial computation yields C BK 9 > 0 (s i = 1) enlarges the anomaly. Our c.v. is s i = 0 to be 10 conservative C9 c c, B K, M q 2 GeV 2 C9 c c, B K, M q 2 GeV 2

65 B K l + l : Impact of long-distance c c loops DHMV Inspired by Khodjamirian et al (KMPW): C 9 C 9 + s i δc LD(i) 9 (q 2 ) Notice that KMPW implies s i = 1, but we vary it independently s i = 0 ± 1, i = 0,, (Zwicky) δc LD,(, ) 9 (q 2 ) = a(, ) + b (, ) q 2 [c (, ) q 2 ] b (, ) q 2 [c (, ) q 2 ] δc LD,0 9 (q 2 ) = a0 + b 0 [q 2 + s 0 ][c 0 q 2 ] b 0 [q 2 + s 0 ][c 0 q 2 ] δ ( ) δ - ( ) - ( ) Obtaining from fitting the long-distance part to KMPW.

66 Is reasonable to expect a huge-charm contribution?? Attempt 1 (Valli, Silvestrini et al.): Introduce an arbritary parametrization of charm-loop h λ = h (0) λ + h(1) λ q2 + h (2) λ q4 with (λ = 0, ±) So many free parameters allows to fit any shape predictivity is rather low. This approach is in trouble if R K and other sensitive LFV observables like R K are confirmed. non pert. g = C9 /(2C 1 ) They force the fit (red points) to agree on the very low-q 2 with KMPW. This has two problems: At very low-q 2 there are other problems they forgot (lepton mass effects). By forcing the fit to agree at very low-q 2 can induce an artificial tilt of your fit. More interestingly the blue points where KMPW is not imposed is perfectly compatible with C 9 C SM 9 constant+kmpw similar to us!!.

67 Attempt 2 (Lyon, Zwicky 14 unpublished): An attempt more near to a prediction was presented by LZ 14 (left plot). Using e + e hadrons to build a model of c c resonances at low-recoil in B K µµ, then extrapolating it at large-recoil via dispersion relations, and assuming that it holds in the same way for B K µµ However a large charm contribution (q 2 ) should be seen in bin [6,8] being above [4,6] bin ( ) Different curves on left correspond to different hypothesis of the impact at low-q 2 from high-q 2. Smooth behaviour of data does not favour claims on large-long distance charm q 2 effects in [6,8] bin.

68 Cross check: Bin by Bin analysis of C 9 in three scenarios - - Result of bin-by-bin analysis of C 9 in 3 scenarios. - - ( ) Notice the excellent agreement of bins [2,5], [4,6], [5,8]. Strong argument in favour of including the [5,8] region-bin. = First bin is afflicted by lepton-mass effects. (see Back-up slides) = ( ) We do not find indication for a q 2 -dependence in C 9 neither in the plots nor in a 6D fit adding a i + b i s to C9 eff for i = K, K, φ. disfavours again charm explanation. 2nd and 3rd plot test if you allow for NP in other WC the agreement of C 9 bin by bin improves as compared to 1st plot. ( ) Figure: Determination of C 9 from the reference fit restricted to

69 Impact on the fit: Charm-loop dependence NP C s i 4 s i 2 s i 1 C BK 9 = δc BK ( ) 9,pert + s iδc BK ( ),i 9,non pert (same for B s φ) Increasing the range allowed for s i makes low-recoil and B K µµ dominate more and more C 9 NP A comparison of our charm error estimate with other estimates (BSZ) shows a good agreement even if systematically we take a larger error size and we have an extra non-factorizable error. Example in the anomaly bin P 5[4,6] : our estimate hep-ph/ is BSZ estimate in hep-ph/ is ±0.05

70 Message 4 Factorizable power corrections: The fit to factorizable power corrections show they are of order 10% as expected from dimensional arguments. The freedom to define ξ, allows you find an optimal scheme with minimal sensitivity to power corrections. Our results are in excellent agreement with a different approach/methodology/ff set. In summary a careful computation of power corrections shows they are perfectly under control. Charm-loop contributions: R K, nor the future R K or R φ cannot be explained with a charm contribution. The behaviour of bin [6,8] versus [4,6] in observables like P 5 precludes it. A 6-D fit or a bin-by-bin analysis does not find indication for a q 2 -dependence in C 9. In summary three arguments against a large-charm explanation of all the anomalies. Even if one can try to find alternative explanations for individual deviations (with not much success...), at the end of the day one has to rely on a different explanation for each deviation, contrary to a shift in the Wilson Coefficients which explains all at the same time.

71 Does the alternative explanations to NP raised in literature: factorizable power corrections and charm stand a serious and accurate analysis? NO

72 A glimpse into the future: Wilson coefficients versus Anomalies C NP 9 C NP 10 C 9 R K P 5 [4,6],[6,8] B Bs φµµ B Bs µµ best-fit-point of global fit + [100%] X + [36%] X [32%] + [21%] X [36%] C 10 + [75%] [75%] X Table: A checkmark ( ) indicates that a shift in the Wilson coefficient with this sign moves the prediction in the right direction to solve the corresponding anomaly. B Bs µµ is not an anomaly but a very mild tension. C NP 9 < 0 is consistent with all anomalies. This is the reason why it gives a strong pull. C10 NP, C 9,10 fail in some anomaly. BUT C10 NP is the most promising coefficient after C 9. C 9, C 10 seems quite inconsistent between the different anomalies and the global fit.

73 Z particle a possible explanation In [DMV 13] we proposed to explain the anomaly in B K µµ with a Z gauge boson contributing to O 9 = e 2 /(16π 2 ) ( sγ µ P L b)( lγ µ l), with specific couplings as a possible explanation of the anomaly in P 5. l Z l + b s B (s) B K q b s Z s b B(s) L q = ( ) sγ ν P L b sb L + sγ ν P R b sb R + h.c. Z ν L lep = ( µγ ν P L µ µ µ L + µγ ν P R µ µ µ R +... ) Z ν The Wilson coefficients of the semileptonic operators are: C NP {9,10} = 1 s 2 W g2 SM 1 1 M 2 Z sb L µµ {V,A}, C{9 NP λ,10 } = 1 ts with the vector and axial couplings to muons: µµ V,A = µµ R ± µµ L. sb L 1 sb sw 2 g2 SM MZ 2 R µµ {V,A} λ ts, with same phase as λ ts = V tb V ts (to avoid φ s) like in MFV. Main constraint from M Bs ( sb L,R ).

74 A Z model can belong to the following categories: no-coupling non-zero couplings Pull SM C 9 no-right-handed quark & no-muon-axial coupling sb L 0, µµ V 0 4.9σ (C 9, C 10 ) no-right-handed quark coupling sb L 0, µµ V 0, µµ A 0 4.8σ (C 9, C 9 ) no-muon-axial coupling sb L 0, sb R 0,, µµ V 0 4.9σ (C 10, C 10 ) no-muon-vector coupling sb L 0, sb R 0, µµ A 0 - (C 9, C 10 ) no-left-handed quark coupling sb R 0, µµ V 0, µµ A 0 - Example: C NP 9 = 1.1, µµ V /M Z = 0.6 TeV 1 and bs L /M Z = TeV 1 If NP enters all four semileptonic coefficients, the following relationships hold: C NP 9 C NP 10 = CNP 9 C NP 10 = µµ V µµ A, C NP 9 C NP = CNP 10 9 C NP = sb L 10 sb R. Many ongoing attempts to embed this kind of Z inside a model [U.Haisch, W.Altmannshofer, A.Buras, D. Straub,..]

75 Conclusions of this talk The global analysis of b sl + l with 3 fb 1 dataset shows that the solution we proposed in 2013 to solve the anomaly with a contribution C NP 9 1 is confirmed and reinforced. We take full dataset and optimized basis of observables. The fit result is very robust and does not show a significant dependence nor on the method used to compute observables neither on the observables used once correlations are correctly included. We have shown that the treatment of uncertainties entering the observables in B K µµ is indeed under good control and the alternative explanations to New Physics are indeed not in very solid ground. Near future? Maybe C 10 will become significant soon. A heavy Z (1-2 TeV) with bs-coupling is a viable explanation for many (not all) scenarios.

76 TECHNICAL Conclusions of this talk Robustness of the FIT: The results of the fit using P i (optimized-ffi) or S i (FFD) and IQCDF-KMPW or Full-FF-BSZ results are in very good agreement. Low sensitivity to details of FF computation. Any scenario including C NP 9 gets a large-pull. 2D scenarios still indistinguishable More data needed. Robustness of hadronic uncertainties of OBSERVABLES: Factorizable power corrections: The Fit to full FF in an appropriate scheme gives 10% in agreement with dimensional arguments. A correct FF choice + correlations among p.c. is essential not to artificially inflate errors. c c loops: We include LO and NLL perturbative contributions to C eff 9 also long distance (following KMPW) with both signs to be conservative. Three reasons why a huge charm contribution cannot explain all deviations: R K cannot be explained. The behaviour of bin [6,8] versus [4,6] in observables like P 5. A 6-D fit or a bin-by-bin analysis does not find evidence for a new-q 2 dependence. Any set of observables is equivalent in terms of accuracy for the predictions on individual observables? NO, P i observables are stable under FF changes, S i depend largely on the choice.

77 Back-up slides

78 Bin [0.1,0.98] lepton-mass effect LHCb naturally given the limited statistics takes the massless lepton limit. They measure: 1 d 3 (Γ + Γ) d(γ + Γ)/dq 2 = 9 dω 32π [ 3 4 (1 F LHCb L which is modified once lepton masses are considered 1 d 3 (Γ + Γ) d(γ + Γ)/dq 2 = 9 [ dω 32π ) sin 2 θ K + FL LHCb cos 2 θ K ] LHCb (1 FL ) sin 2 θ K cos 2θ l FL LHCb cos 2 θ K cos 2θ l ˆ F T sin 2 θ K + ˆF L cos 2 θ K + 1 ] 4 F T sin 2 θ K cos 2θ l F L cos 2 θ K cos 2θ l +... where ˆF T,L and F L,T are [JM 12]. All our observables are thus written and computed in terms of the longitudinal and transverse polarisation fractions F L,T J 2c F L = d(γ + Γ)/dq 2 F T = 4 d(γ + Γ)/dq 2 ˆF L = J 2s J 1c d(γ + Γ)/dq 2 WHEN measured value ˆF L is used instead of F L SM prediction is shifted towards the data in 1st bin F L [0.1,0.98] = , P 2 [0.1,0.98] = , P 4 [0.1,0.98] = , P 5 = [0.1,0.98]

79 δc 7 = 0.1 δc 9 = 1 δc 10 = 1 δc 7 = 0.1 δc 9 = 1 δc 10 = 1 P 1 [0.1,.98] + δc i δc i P 1 [6,8] + δc i δc i P 1 [15,19] + δc i δc i P 2 [2.5,4] + δc i δc i P 2 [6,8] + δc i δc i P 2 [15,19] + δc i δc i P 4 [6,8] P 4 [15,19] P 5 [4,6] P 5 [6,8] + δc i δc i δc i δc i δc i δc i δc i δc i

80 Correlations play a central role If one wants to solve the anomalies exhibited in b sµµ processes through power corrections, it is important not to focus on one single observable, like P 5, alone but on the full set. Illustrative example. Let s do the following exercise: Assume you take the non-optimal scheme-2 as in (JC 14) and helicity basis a V± = 1 [( 1 + m ) ( K a 1 1 m ) ] K a V. 2 m B m B Notice that taking a V in a range ±0.1 correspond to an absurd 33% power correction in KMPW. because a 10% in KMPW corresponds to 0.03 in a V. accepting values like (a V = 0.1, a V + = 0) would imply that BSZ computation of A 1 (q 2 ) is wrong by several sigmas. An explanation of P 5 [4,6], P 2 [4,6] and P 1 [4,6] within SM requires a 20% correction. Adding P 5 [6,8] no common solution found even beyond 20%.