Global fits to radiative b s transitions S ebastien Descotes-Genon - PowerPoint PPT Presentation

Global fits to radiative b → s transitions S´ ebastien Descotes-Genon Laboratoire de Physique Th´ eorique CNRS & Universit´ e Paris-Sud 11, 91405 Orsay, France Rencontres de Moriond - Electroweak session 16 March 2014 LPT Orsay S. Descotes-Genon (LPT-Orsay) Global fits to radiative b → s 16/03/14 1

Effective approach to radiative decays b → s γ and b → s ℓ + 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 10 b → s γ ( ∗ ) : H SM � V ∗ ∆ F = 1 ∝ ts V tb C i Q i + . . . i = 1 Q 7 = e s σ µν ( 1 + γ 5 ) F µν b g 2 m b ¯ [real or soft photon] Q 9 = e 2 s γ µ ( 1 − γ 5 ) b ¯ g 2 ¯ ℓγ µ ℓ [ b → s µµ via Z /hard γ ] Q 10 = e 2 s γ µ ( 1 − γ 5 ) b ¯ g 2 ¯ ℓγ µ γ 5 ℓ [ b → s µµ via Z ] NP changes short-distance C i and/or add new long-distance ops Q ′ i Q 7 → Q 7 ′ ∝ ¯ Chirally flipped ( W → W R ) s σ µν ( 1 − γ 5 ) F µν b (Pseudo)scalar ( W → H + ) s ( 1 + γ 5 ) b ¯ Q 9 , Q 10 → Q S ∝ ¯ ℓℓ, Q P s σ µν ( 1 − γ 5 ) b ¯ Q 9 → Q T ∝ ¯ Tensor operators ( γ → T ) ℓσ µν ℓ S. Descotes-Genon (LPT-Orsay) Global fits to radiative b → s 16/03/14 2

Wilson Coefficients and processes Matching SM at high-energy scale µ 0 = m t and evolving down at µ ref = 4 . 8 GeV C SM = − 0 . 29 , C SM = 4 . 1 , C SM 10 = − 4 . 3 , 7 9 (formulae known up to NNLO + e.m. corrections) C i Observables SM values C eff B ( B → X s γ ) , A I ( B → K ∗ γ ) , S K ∗ γ , B → K ∗ ℓℓ − 0 . 29 7 B ( B → X s ℓℓ ) , B → K ( ∗ ) ℓℓ C 9 4 . 1 B ( B s → µ + µ − ) , B ( B → X s ℓℓ ) , B → K ( ∗ ) ℓℓ C 10 − 4 . 3 C ′ B ( B → X s γ ) , A I ( B → K ∗ γ ) , S K ∗ γ , B → K ( ∗ ) ℓℓ 0 7 C ′ B ( B → X s ℓℓ ) , B → K ( ∗ ) ℓℓ 0 9 C ′ B ( B s → µ + µ − ) , B → K ( ∗ ) ℓℓ 0 10 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 16/03/14 3

B → K ∗ ℓℓ : angular analysis θ l : angle of emission between K ⋆ 0 � K and µ − in di-lepton rest frame � � µ θ K ∗ : angle of emission between K ⋆ 0 � B 0 � K l and K − in di-meson rest frame. µ + 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 ∗ d φ = f i ( θ K ∗ , φ, θ l ) × I i i with 12 angular coeffs I i , interferences between 8 transversity ampl. ⊥ , || , 0 , t polarisation of (real) K ∗ and (virtual) V ∗ = γ ∗ , Z ∗ L , R chirality of µ + µ − pair A ⊥ , L / R , A || , L / R , A 0 , L / R , A t + scalar A s depend on q 2 (lepton pair invariant mass) Wilson coefficients C 7 , C 9 , C 10 , C S , C P (and flipped chiralities) B → K ∗ form factors A 0 , 1 , 2 , V , T 1 , 2 , 3 from � K ∗ | Q i | B � S. Descotes-Genon (LPT-Orsay) Global fits to radiative b → s 16/03/14 4

Four different regions dB(B->K* μμ )/ds x 10 (GeV ) 2 7 γ pole Large recoil Charmonia Low recoil 2 s (GeV ) ℓ < q 2 < 1 GeV 2 ): γ almost real Very large K ∗ -recoil (4 m 2 ( 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 GeV 2 ) 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 16/03/14 5

Hadronic quantities: B → K ∗ form factors 7 independent form factors A 0 , 1 , 2 , V ( O 9 , 10 ) and T 1 , 2 , 3 ( O 7 ) A 2 ( q 2 ) s γ µ ( 1 − γ 5 ) | B ( ǫ, p ) � = − i ǫ µ ( m B + m V ) A 1 ( q 2 ) + i ( p + k ) µ ( ǫ ∗ · q ) � K ∗ ( k ) | ¯ m B + m K ∗ 2 V ( q 2 ) + iq µ ( ǫ ∗ · q ) 2 m K ∗ A 0 ( q 2 ) + ǫ µνρσ ǫ ∗ ν p ρ k σ ˜ q 2 m B + m K ∗ � K ∗ ( k ) | ¯ s σ µν q ν ( 1 + γ 5 ) | B ( ǫ, p ) � = i ǫ µνρσ ǫ ∗ ν p ρ k σ 2 T 1 ( q 2 ) + ǫ ∗ µ ( m 2 B − m 2 V ) T 2 ( q 2 ) − ( p + k ) µ ( ǫ ∗ · q )˜ T 3 ( q 2 ) + q µ ( ǫ ∗ · q ) T 3 ( q 2 ) In the limits of low and large K ∗ recoil, separation of scales Λ and m B q 2 ∼ Λ QCD ≪ m B ) � Large-recoil limit ( [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 0 ( 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 16/03/14 6

Form-factor “independent” observables = Obs. where soft form factors cancel at LO 9 ( s 0 ) + 2 m b M B Zero of forward-back. asym. A FB ( s 0 ) = 0: C eff s 0 C eff 7 = 0 Transversity asymmetries [Kr¨ uger, Matias; Becirevic, Schneider] = | A ⊥ | 2 − | A || | 2 Re [ A L ∗ ⊥ A L || − A R ⊥ A R ∗ || ] P 2 = A re I 3 2 = I 6 s P 1 = A ( 2 ) T = | A ⊥ | 2 + | A || | 2 , = | A ⊥ | 2 + | A || | 2 T 2 I 2 s 8 I 2 s ⊥ || 1.0 1.0 SM SM 0.5 0.5 re � 2 2 P 1 � A T P 2 � A T 0.0 0.0 � 0.5 � 0.5 � 1.0 � 1.0 1 2 3 4 5 6 1 2 3 4 5 6 q 2 � GeV 2 � q 2 � GeV 2 � 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 / 2 P 2 ( 1 − F L ) ] exhausting information in (partially redundant) angular coeffs I i [Matias, Kr¨ uger, Mescia, SDG, Virto, Hiller, Bobeth, Dyck, Buras, Altmanshoffer, Straub. . . ] S. Descotes-Genon (LPT-Orsay) Global fits to radiative b → s 16/03/14 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) F L = I 1 c +¯ S 3 = I 3 +¯ 2 S 3 I 1 c I 3 P 1 = Γ + ¯ Γ + ¯ 1 − F L 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 16/03/14 8

Computation of amplitudes Large recoil: NLO QCD factorisation V , A i , T i = ξ || , ⊥ in A ⊥ , || , 0 (non-factor.) in FFs (factor) + factorisable O ( α s ) + nonpert O (Λ / m b ) A 0 , || , ⊥ = 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 ) ≃ 10 % Low recoil: OPE + HQET A 0 , || , ⊥ = C i × f 0 , || , ⊥ + O ( α s ) corrections + O ( 1 / m b ) corrections f 0 , || , ⊥ ∝ 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 16/03/14 9

SM predictions and LHCb results (1) Present bins Large recoil: [0.1, 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 : [ 10 . 09 , 12 . 89 ] [ 0 . 1 , 1 ] with light resonances, washed out by binning [Camalich, J¨ ager] q 2 > 6 GeV 2 may be affected by charm-loop effects [Khodjamirian et al.] Beauty 12 and EPS 13 : results from LHCb 1.0 1.0 0.8 0.5 0.6 � A FB � � F L � 0.0 0.4 � 0.5 0.2 0.0 � 1.0 0 5 10 15 20 0 5 10 15 20 q 2 � GeV 2 � q 2 � GeV 2 � [SDG, Matias, Virto] = ⇒ blue: SM unbinned, purple: SM binned, crosses: LHCb values S. Descotes-Genon (LPT-Orsay) Global fits to radiative b → s 16/03/14 10

SM predictions and LHCb results (2) 1.0 1.5 0.4 0.5 1.0 0.2 0.5 � P 1 � � P 2 � � � 0.0 0.0 � P 4 0.0 � 0.2 � 0.5 � 0.5 � 0.4 � 1.0 � 1.0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 q 2 � GeV 2 � q 2 � GeV 2 � q 2 � GeV 2 � 1.0 1.0 0.6 0.5 0.4 0.5 0.2 0.0 � � � � � � � P 5 � P 6 � P 8 0.0 0.0 � 0.2 � 0.5 � 0.5 � 0.4 � 1.0 � 0.6 � 1.0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 q 2 � GeV 2 � q 2 � GeV 2 � q 2 � GeV 2 � Meaning of the discrepancy in P 2 and P ′ 5 ? [SDG, Matias, Virto] P 2 same zero as A FB , related to C 9 / C 7 P 5 ′ → − 1 as q 2 grows due to A R ⊥ , || ≪ A L ⊥ , || for C SM ≃ − C SM 9 10 A negative shift in C 7 and C 9 can move them in the right direction S. Descotes-Genon (LPT-Orsay) Global fits to radiative b → s 16/03/14 11