Global fits to radiative b s transitions

Global fits to radiative b s transitions Sébastien Descotes-Genon Laboratoire de Physique Théorique CNRS & Université Paris-Sud 11, 9145 Orsay, France Rencontres de Moriond - Electroweak session 16 March 214 LPT Orsay S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 1

Effective approach to radiative decays b sγ and b sl + l Flavour-Changing Neutral Currents enhanced sensitivity to New Physics effects analysed in model-independent approach effective Hamiltonian integrating out all heavy degrees of freedom 1 b sγ( ) : H F SM =1 VtsV tb C i Q i +... i=1 Q 7 = e g 2 m b sσ µν (1 + γ 5 )F µν b [real or soft photon] Q 9 = e2 g 2 sγ µ (1 γ 5 )b lγ µ l [b sµµ via Z /hard γ] Q 1 = e2 g 2 sγ µ (1 γ 5 )b lγ µ γ 5 l [b sµµ via Z ] NP changes short-distance C i and/or add new long-distance ops Q i Chirally flipped (W W R ) Q 7 Q 7 sσ µν (1 γ 5 )F µν b (Pseudo)scalar (W H + ) Q 9, Q 1 Q S s(1 + γ 5 )b ll, Q P Tensor operators (γ T ) Q 9 Q T sσ µν (1 γ 5 )b lσ µν l S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 2

Wilson Coefficients and processes Matching SM at high-energy scale µ = m t and evolving down at µ ref = 4.8 GeV C SM 7 =.29, C SM 9 = 4.1, C SM 1 = 4.3, (formulae known up to NNLO + e.m. corrections) C i Observables SM values C7 eff B(B X s γ), A I (B K γ), S K γ, B K ll.29 C 9 B(B X s ll), B K ( )ll 4.1 C 1 B(B s µ + µ ), B(B X s ll), B K ( )ll 4.3 C 7 B(B X s γ), A I (B K γ), S K γ, B K ( )ll C 9 B(B X s ll), B K ( )ll C 1 B(B s µ + µ ), B K ( )ll B X s γ: strong constraints on C 7, C 7 [Misiak, Gambino, Steinhauser... ] B X s ll: not accurate enough expt [Misiak, Bobeth, Gorbahn, Haisch, Huber, Lunghi... ] B s µµ: recent th. and exp. progress [talks from C. Bobeth and M. Gorbahn] B K ( )ll: recent th. and exp. progress S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 3

B K ll: angular analysis µ l µ + B K K + θ l : angle of emission between K and µ in di-lepton rest frame θ K : angle of emission between K and K in di-meson rest frame. φ: angle between the two planes q 2 : dilepton invariant mass square d 4 Γ dq 2 d cos θ l d cos θ K dφ = f i (θ K, φ, θ l ) I i i with 12 angular coeffs I i, interferences between 8 transversity ampl.,,, t polarisation of (real) K and (virtual) V = γ, Z L, R chirality of µ + µ pair A,L/R, A,L/R, A,L/R, A t + scalar A s depend on q 2 (lepton pair invariant mass) Wilson coefficients C 7, C 9, C 1, C S, C P (and flipped chiralities) B K form factors A,1,2, V, T 1,2,3 from K Q i B S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 4

Four different regions 7 2 db(b->k*μμ)/ds x 1 (GeV ) γ pole Large recoil Charmonia Low recoil 2 s (GeV ) Very large K -recoil (4m 2 l < q2 < 1 GeV 2 ): γ almost real (C 7 /q 2 divergence and light resonances) Large K -recoil (q 2 < 9 GeV 2 ): energetic K (E K Λ QCD : form factors from light-cone sum rules LCSR) Charmonium region (q 2 = m 2 ψ,ψ... between 9 and 14 GeV2 ) Low K -recoil (q 2 > 14 GeV 2 ): soft K (E K Λ QCD : form factors lattice QCD) S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 5

Hadronic quantities: B K form factors 7 independent form factors A,1,2, V (O 9,1 ) and T 1,2,3 (O 7 ) K (k) sγ µ(1 γ 5 ) B(ɛ, p) = iɛ µ(m B + m V )A 1 (q 2 ) + i(p + k) µ(ɛ A 2 (q 2 ) q) m B + m K +iq µ(ɛ q) 2m K q 2 Ã (q 2 ) + ɛ µνρσɛ ν p ρ k σ 2V (q 2 ) m B + m K K (k) sσ µνq ν (1 + γ 5 ) B(ɛ, p) = iɛ µνρσɛ ν p ρ k σ 2T 1 (q 2 ) + ɛ µ(m 2 B m 2 V )T 2 (q 2 ) (p + k) µ(ɛ q) T 3 (q 2 ) + q µ(ɛ q)t 3 (q 2 ) In the limits of low and large K recoil, separation of scales Λ and m B Large-recoil limit ( q 2 Λ QCD m B ) [LEET/SCET, QCDF] two soft form factors ξ (q 2 ) and ξ (q 2 ) O(α s ) corr. from hard gluons [computable], O(Λ/m B ) [nonpert] [Charles et al., Beneke and Feldmann] Low-recoil limit (E K Λ QCD m B ) [HQET] three soft form factors f (q 2 ), f (q 2 ), f (q 2 ) O(α s ) corr. from hard gluons [computable] and O(Λ/m B ) [nonpert] [Grinstein and Pirjol, Hiller, Bobeth, Van Dyk... ] S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 6

Form-factor independent observables = Obs. where soft form factors cancel at LO The concept of clean observables: origin and benefits Zero of forward-back. asym. A FB (s ) = : C9 eff(s ) + 2 m bm B s Transversity asymmetries C7 eff = 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 [Krüger, the word Matias; clean ) Becirevic, Schneider] [Kruger, J.M 5] [Becirevic et al. 12] P 1 = A (2) T = I 3 A 2 A 2 2I 2s 2 + A 2, Are T 2 = I 6s = Re[AL A L AR AR P 1 = A (2) T (q2 ) = J3 = A 2 A 2 2J 2s A 2 + A 2 P 2 = Are T 2 = J6s = Re(AL A L AR AR II ) 8J 2s A 8I 2 + A 2s A 2 2 + A 2 where A, correspond to two transversity amplitudes of the K. 1. 1. SM SM ] P1 A T 2 P2 A T re 2 1. 1 2 3 4 5 6 q GeV 1. 1 2 3 4 5 6 q GeV 6 form-factor independ. obs. at large recoil (P 1, P 2, P 3, P 4, P 5, P 6 ) + 2 form-factor dependent obs. (Γ, A FB, F L... ) [A FB = 3/2P 2 (1 F L )] Both asymmetries exhibit an exact cancellation of soft form factors not only at a point (like A FB) but in the full low-q 2 range. First examples of clean observables that could be measured. A (2) T is constructed to detect presence of RH currents (A A in the SM), A re T complements AFB since it contains exhausting similar information, information but a theoretically in (partially better controlled redundant) way. angular coeffs I i [Matias, Krüger, Mescia, SDG, Joaquim Matias Universitat Autònoma de Barcelona Physik B Institut, K l + l Virto, Hiller, Bobeth, Dyck, Buras, Altmanshoffer, Universität a portal forzurich New Physics: Theory + Experimental Based Perspectives on: S. Descotes, Straub... JM, ] S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 7

Sensitivity to form factors P i designed to have limited sensitivity to ffs S i CP-averaged version of I i (A i for CP-asym) P 1 = 2S 3 F L = I 1c + Ī1c S 3 = I 3 + Ī3 1 F L Γ + Γ Γ + Γ different sensivity to form factors inputs for given NP scenario (form factors from LCSR: green [Ball, Zwicky] vs gray [Khodjamirian et al.]) S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 8

Computation of amplitudes Large recoil: NLO QCD factorisation in A,, (non-factor.) in FFs (factor) V, A i, T i = ξ, + factorisable O(α s ) + nonpert O(Λ/m b ) A,, = C i ξ, + factorisable O(α s ) + nonfactorisable O(α s ) + nonpert O(Λ/m b ) either compute A with ξ, extracted from V, A i (check T i OK) or compute A from V, A i, T i + nonfactorisable corrections nonperturbative corrections O(Λ/m b ) 1% Low recoil: OPE + HQET A,, = C i f,, + O(α s ) corrections + O(1/m b ) corrections f,, CL(A 1, A 2 ), A 1, V + O(1/m b ) corrections HQET relations between V, A i and T i nonperturbative corrections smaller O(C 7 Λ/m b, α s Λ/m b ) S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 9

SM predictions and LHCb results (1) Present bins Large recoil: [.1, 2], [2,4.3], [4.3,8.68] and [1,6] GeV 2 Low recoil: [14.18,16], [16,19] GeV 2 c c resonances : [19, 12.89] [.1, 1] with light resonances, washed out by binning [Camalich, Jäger] q 2 > 6 GeV 2 may be affected by charm-loop effects [Khodjamirian et al.] Beauty 12 and EPS 13 : results from LHCb 1. 1. A FB F L.8.6.4.2 1. 5 1 15 q GeV 5 1 15 q GeV [SDG, Matias, Virto] = blue: SM unbinned, purple: SM binned, crosses: LHCb values S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 1

SM predictions and LHCb results (2) 1. 1.5.4 1. XP4 \.2 XP2 \ XP1 \ - -.2 - -.4-1. -1. 5 1 q 2 HGeV2 L 15 2 1. 5 1 q 2 HGeV2 L 15 2.6.4 5 q 2 HGeV2 L 1 15 2 5 q 2 HGeV2 L 1 15 2 1. XP8 \ XP6 \ XP5 \.2 -.2 - - -.4-1. -.6-1. 5 1 q 2 HGeV2 L 15 2 5 1 q 2 HGeV2 L 15 2 Meaning of the discrepancy in P2 and P5? [SDG, Matias, Virto] P2 same zero as AFB, related to C9 /C7 L SM ' C SM P5 1 as q 2 grows due to AR 1, A, for C9 A negative shift in C7 and C9 can move them in the right direction S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 11

Global fit to radiative decays [SDG, Matias, Virto] C 9 NP 4 2 SM 68.3 C.L 95.5 C.L 99.7 C.L Includes Low Recoil data Only 1,6 bins Standard χ 2 frequentist analysis B K µµ: P 1, P 2, P 4, P 5, P 6, P 8, A FB B X s γ, B X s µµ: Br B s µµ: Br 2 4.15.1 5 5.1 5 C i (µ ref ) = C SM i + C NP i B K γ: A I and S K γ Several B K µµ sets [LHCb] full: 3 fine large-recoil bins dashed: 3 fine large-recoil bins + low-recoil bins orange: 1 large recoil-bin only Form factors from LCSR [Khodjamirian et al.], extrapolated if needed Large recoil: Soft form factors ξ, + QCDF Low recoil: Full form factors V, A i + HQET for T i S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 12

Only C 7, C 9 Pull of SM value for each C i [ χ 2 i = χ 2 (C i = ) min Ci χ 2 (C i )] pull for C 9 4σ, pull for C 7 3σ once both C9 NP and C7 NP included, low pulls for the other C i s consistent pattern favouring C9 NP 1.5 [added to C9 SM 4.1] 1.5 1. P 2 P 4 P 5 2 4 6 8 2 4 6 8 1. 2 4 6 8 P 2 2 4 6 8 P 5 1. 2 4 6 8 grey: SM; red: C NP 9 1.5; blue: LHCb S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 13

C 9 = 1.5 P 1 P 2 P 4 1. 5 1 15 1.5 1. 1. 5 1 15 P 5 1. 1. 5 1 15 5 1 15 S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 14

Other scenarios SM operators + chirally flipped Coefficient 1 σ 2 σ 3 σ C7 NP [ 5, 1] [ 6, 1] [ 8, 3] C9 NP [ 1.6,.9] [ 1.8,.6] [ 2.1,.2] C1 NP [.4, 1.] [ 1.2, 2.] [ 2., 3.] C7 NP [ 4, 2] [ 9, 6] [.14,.1] C9 NP [.2,.8] [.8, 1.4] [ 1.2, 1.8] [.4,.4] [ 1.,.8] [ 1.4, 1.2] C NP 1 Large-recoil shape of P 2 and P 5 favours CNP 7 < and C9 NP < No other NP contrib favoured (small pulls once C7 NP and C9 NP ) C 9, C 9 scenario C9 NP 1.6, C9 NP 1.5 improves large-recoil P 5 low-recoil dilute effect, allow C 9 < or > P 5 1. 2 4 6 8 P 5 1. 2 4 6 8 S. Descotes-Genon (LPT-Orsay) Global fits to radiative b snp NP NP16/3/14 15

With exp. correlations: two scenarios 4 2 b sγ, Bs ΜΜ, Bs Xsll 68.3 C.L P 1, P 2, P 4, P5, P6, P8, AFB CORRELATIONS 95.5 C.L 99.7 C.L Includes Low Recoil data Only 1,6 bins 4 2 68.3 C.L 95.5 C.L 99.7 C.L Includes Low Recoil data Only 1,6 bins C 9 NP SM NP C 9' SM 2 2 b sγ, Bs ΜΜ, Bs Xsll P 1, P 2, P 4, P5, P6, P8, AFB CORRELATIONS 4.15.1 5 5.1 5 7 4 4 2 2 4 C 9 NP NP in C 7, C 9 NP in C 9, C 9 For C 7, C 9 scenario 4.2σ (large-recoil), 3.5σ (large + low recoil), 2.7σ ([1-6] bin) same conclusions hold if P i, P i, F L rather than P i, P i, A FB S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 16

Global fit with S i, A i [Altmannshofer, Straub] Frequentist frame: S i, A i, A FB, Br(B K µµ), Br(B K µµ), with wide [1-6] at large recoil + low recoil S K γ, Br(B X s γ), A CP (b sγ), Br(B X s ll), Br(B s µµ) Amplitudes from full form factors LCSR [Ball, Zwicky] + non-factorisable corrections + O(Λ/m b ) non fact. C9 NP.9 with less significance due to use of S i, [1,6] bins, F L Need for C9 NP > due to low-recoil B(B K µ + µ ) Re C 9 ' 3 2 1 1 2 3 F L S 5 S 4 A FB B K ΜΜ Equivalent analysis for with LHCb F L, A FB, S 3,4,5,7,8 with three low-recoil bins (but no B K µµ) 2.7 σ for C NP 7, CNP 9 Best fit point C NP 7 = 2, C NP 9 = 1.76 No need for C NP 9 3 2 1 1 2 3 S. Descotes-Genon (LPT-Orsay) 9 Global fits to radiative b s 16/3/14 17

Global fit with Bayesian approach [Beaujean, Bobeth, Van Dyk] C9 6 5 4 3 2 1.4.3.2.1 2 3 4 5 6 7.2.3.4.6 C 7 Bayesian analysis: P i, F L, A FB, Br(B K µµ), Br(B K µµ), Br(B K γ), C K γ, S K γ, Br(B X s γ), A CP (b sγ), Br(B X s ll), Br(B s µµ) wide [1-6] at large recoil + low recoil Priors on nuisance parameters (form factors, Λ/m b corrections) SM with decent p-values from χ 2 min if shift of 1 2% Λ/m b corrections to amplitudes (but N dof? asymptotic?) 2 σ dev. from SM for NP in 7,9,1 only C7 NP = ±2, C9 NP =.3±.4, C1 NP =.4±.3 Bayes factors favour NP in SM operators + chirally flipped operators, either generic or restricted to (C 9, C 9 ) S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 18

Analysis based on lattice QCD form factors B K ll and B s φll form factors [Horgan et al.] db/dq 2 (1 7 GeV 2 ) C 9 5 4 3 2 1 1 2 1.2 1..8.6.4.2 B K µ + µ 15 16 17 18 19 1σ 2σ 3 2 1 1 2 3 3σ C9 NP SM Lattice simulations (staggered + NRQCD) Main problem in BRs [ previous studies] SM predictions 3% higher than experiment (similar to results using [Ball, Zwicky]) (blue and pink : SM, dashed: C NP 9 = C NP 9 = 1.1) Frequentist with only large-recoil B q V ll: dγ/dq 2, F L, S 3, S 4, S 5, A FB for B K ll; dγ/dq 2, F L, S 3 for B s φll 2 low-recoil bins: C9 NP = 1.1 ±, C NP 9 = 1.1 ± 1. Last low-recoil bin: C9 NP = 1.1 ±.7, C NP =.4 ±.7 9 S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 19

A-S claim that C 9 > and opposite size of C 9 using [1-6] bins and low-recoil B K µ µ. In DMV 13 C9 NP using ALL bins we or C NP found: large-recoil prefers C 9 >? NP 9 <, while low-recoil prefers C9 NP > oth P i (left) and S i (center) analysis confirm the same conclusion. See C9 NP C9 NP correlation. [1-6] bins for B K 68.3 C.L 95.5 C.L µµ q 2 Includes Low Recoil data 2 dependence Only 1,6 bins of P 5 C NP SM SM 9 < better agreement for 1st and 3rd bins of P 5 b sγ, Bs ΜΜ, Bs Xsll C NP 99.7 C.L P 1, P 2, P 4, P5, P6, P8, AFB 9 > worse agreement CORRELATIONS 4 for 1st and 3rd bins of P 5 2 2 4 C 9 NP NP C 9' 4 2 68.3 C.L 95.5 C.L 99.7 C.L Includes Low Recoil b sγ, Bs ΜΜ, Bs Xsll S 3, S 4, S 5, S 7, S 8, A FB, F L 4 2 2 4 C 9 NP P5 ' 1. 1. SM C 9 NP 1.5, C9 ' NP C 9 NP 1.5, C9 ' NP 1.5 C 9 NP 1.5, C9 ' NP 1.5 5 1 15 integrated value over [1, 6] almost same: no sensitivity < improves agreement with data for 1st and 3rd bin in P 5 and tiny decrease [1-6]: 8 7. > worsen the fit to data for 1st and 3rd bin in P 5 and tiny improves [1-6]: 8 9 data Low-recoil B(B K µ + µ ) LHCb his problem 15 is opaque if the total [1-6] bin is used. nonresonant [14.18,22] good agreement with SM f A.S 13 best fit point is used interference P 5 gets worst: P 5 [4.3,8.68] (A S) bestfit =.74 (data.19 ±.16) 1 resonances background favours C NP uim Matias Universitat Autònoma de Barcelona Physik B Institut, K l + l Universität a portal forzurich New Physics: Theory + Experimental Based Perspectives on: S. Descotes, JM Candidates / (25 MeV/c 2 ) 5 38 4 42 44 46 [MeV/c 2 ] m µ + µ 9 + C9 NP, C NP 9 > in [Altmannshofer, Straub], low-recoil 3 bins with 2% uncertainty to account for ψ(416) in first large-recoil bin q 2 S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 2

Fluctuation of the data? [Matias, Serra] Redundancy in angular coefficients ] P 2 = 1 2 [P 4 P 5 + 1βl ( 1 + P 1 + P 4 2)( 1 P 1 + βl 2P 2 5 ) if no new CPV phase in C i s and negligible P 3,5,8 (Im[A ia j ]) Corrections from binning can be computed and are small, apart from [.1-2] and [1-6] bins P2 2 3 4 5 6 7 8 9 P 2 : Gray: SM prediction, blue: data, red: C NP 9 = 1.5, green: relation [2.4,3]:.2σ measured vs relation [4.3,8.68]: 2.4σ measured vs relation, 1.9σ rel. vs NP best fit, 3.6σ rel. vs SM More consistent for (P 2, P 5 ) in the future if third-bin P 5 goes down (closer to SM) and third-bin P 2 goes up (away from SM) S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 21

Charm-loop effects Charmonium resonances Large recoil: q 2 6-7 GeV 2 to avoid J/ψ tail Low recoil: quark-hadron duality sum of res. integrated over wide bin perturbative computation toy models suggest small corrs, but large bin = less q 2 sensitivity Short-distance non-resonant (hard gluons) LO included C 9 C 9 + Y (q 2 ), dependence on m c (which scheme) higher-order short -dist QCD via QCDF/HQET Long-distance non-resonant (soft gluons) C BK ( ) 9 using LCSR [Khodjamirian, Mannel, Wang] For B K, C BK ( ) 9 < tend to increase the need for C9 NP B b γ c s K K C9 c c, B K, M1 4 2 2 4 2 4 6 8 1 12 q 2 GeV 2 (a) (b) S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 22

Impact of C BK ( ) 9 and m c [SDG, Matias, Virto] 1. C 9 NP gets more negative C 9 cc,pert, C9 cc,ld cc,pert C 9 mc 1 GeV cc,ld C 9 C cc,pert cc,ld 9 C 9 C 9 cc,pert mc 1.4 GeV 1. C 9 NP gets less negative 1.5 2 4 6 8 Shifts induced by change in m c and long-distance gluons in c c loops S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 23

1/m b corrections [Camalich, Jäger] SM preds with same central values but larger errors P 4 FF=soft form factor + O(α s ) corrections + O(Λ/m b ) Fix soft form factors ξ, ξ from 2 form factors [LCSR] Then compare predictions for the other form factors.8.6.4.2.2.4.6.8 1 2 3 q 2 GeV 2 P 5 1.2.8.4.4.8 1.2 1 2 3 q 2 GeV 2 P 6.4.2.2.4 1 2 3 q 2 GeV 2 [Camalich, Jäger] assume C 7 = C SM 7 and extract from B(B K γ) the very accurate value ξ () = T 1 () =.277 ± 13 = Need large O(Λ/m b ) to predict other form factors in agreement with other approaches (LCSR, Dyson-Schwinger eqs.... ) [SDG, Matias, Virto] ξ () =.31 +.2.1 from LCSR 1% O(Λ/m b ) enough for QCDF and LCSR to agree for all FFs S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 24

Outlook b sγ( ) transition Very interesting playing ground for FCNC studies Many observables, more or less sensitive to hadronic unc. Intriguing LHCb results for B K µµ, supporting C9 NP And a lot theoretical discussions on accuracy of computations and/or interpretation in terms of NP How to improve? Exp: finer binning in [1, 6] region, other expts (ATLAS and CMS?) Exp: refine B K µµ and impact of ψ(416) Th: form factors from lattice on a larger q 2 range? Th: c c loops, soft-gluon exchanges, quark/hadron duality Both: cross check with other modes/observables Only the beginning of the story... more very soon! S. Descotes-Genon (LPT-Orsay) Global fits to radiative b s 16/3/14 25