Radiative and rare semileptonic B decays (news 2009/2010) Miko� laj Misiak (University of Warsaw )
# 1. New, more precise determination of B ( B → X s l + l − ) by Belle. Slide from T. Ijima at Lepton-Photon 2009: ∆ (stat.) much larger Detailed property of B X s ll than ∆ (syst.) Linear scale Log scale (M ll > 0.2 GeV/c 2 ) BELLE 605fb -1 BELLE 605fb -1 BELLE Data Data Data 605fb 605fb -1 MC Data MC MC For entire MXs region 0.33 6 Br B Br B ( ( X ee X ee ) ) (4 56 1 15 (4.56 1.15 ) 10 ) 10 + − 0.76 0 76 6 6 → → = = ± ± × × (3 66 (3.66 ) 10 ) 10 + + − × S 0.40 − 0.77 − 0.16 6 Br B ( X µµ ) (1.91 1.02 ) 10 + − → = ± × S 0.18 − 0.19 6 Br B Br B ( ( X X ) ) (3.33 (3.33 0.80 0.80 ) 10 ) 10 + − → → = ± ± × × S S 0 24 0.24 − Note: Measured Br (M(XS):0.2-2.0 GeV/c 2 ) 28 x [1.10 0.002] --- based on signal MC
Dilepton mass spectrum in ¯ B → X s l + l − . d B ( ¯ B → X s l + l − ) × 10 5 m b dm l + l − 1 0.8 0.6 perturbative 0.4 with non-perturbative c ¯ c using “naive” factorization [F. Kr¨ uger, L.M. Sehgal 0.2 hep-ex/9603237] 1 2 3 4 5 m l + l − [GeV]
� � B ( X s → l + l − ) = 3 . 66 +0 . 76 × 10 − 6 New HFAG average (2009): − 0 . 77 ⇒ Non-SM sign of C 7 is excluded at more than 4 σ [P. Gambino, U. Haisch, MM, (as compared to 3 σ that we’ve had so far) PRL 94 (2005) 061803] using (4 . 5 ± 1 . 0) × 10 − 6 . provided C 9 , 10 remain unchanged. L QCD × QED ( q, l ) + 4 G F 10 2 V ∗ � √ L = ts V tb i =1 C i ( µ ) O i ( q = u, d, s, c, b , l = e, µ ) c Γ ′ (¯ s Γ i c )(¯ i b ) , i = 1 , 2 , | C i ( m b ) | ∼ 1 q Γ ′ (¯ s Γ i b ) Σ q (¯ i q ) , i = 3 , 4 , 5 , 6 , | C i ( m b ) | < 0 . 07 em b s L σ µν b R F µν , 16 π 2 ¯ i = 7 , C 7 ( m b ) ∼ − 0 . 3 O i = gm b s L σ µν T a b R G a 16 π 2 ¯ µν , i = 8 , C 8 ( m b ) ∼ − 0 . 15 e 2 s L γ µ b L )(¯ lγ µ γ 5 l ) , i = 9 , 10 16 π 2 (¯ | C i ( m b ) | ∼ 4
Inclusive decay rates and the sign of C 7 s = q 2 l + l − ˆ m 2 b ts V tb | 2 d Γ( ¯ B → X s l + l − ) = G 2 F m 5 b, pole | V ∗ α em 2 s ) 2 × (1 − ˆ 48 π 3 d ˆ s 4 π � 4 + 8 � � � s ) | 2 + | C eff s ) | 2 + 12 Re | C eff s ) | 2 | C eff C eff s ) C eff ∗ × (1 + 2 ˆ s ) 9 ( ˆ 10 ( ˆ + 7 ( ˆ 7 ( ˆ 9 ( ˆ s ) + R 1 , ˆ s ts V tb | 2 B → X s γ ) Eγ>E 0 = G 2 F m 5 b, pole | V ∗ α em s = 0 ) | 2 + R 2 Γ( ¯ 4 π | C eff 7 ( ˆ 8 π 3 are conveniently expressed in terms of the so-called effective coefficients C eff i ( ˆ s ) = C i ( µ b ) + (loop corrections) ( ˆ s ) . The quantities R i stand for small bremsstrahlung contributions and for the non-perturbative corrections . s gn C 7 ( µ b ) = (“sign of the b → sγ amplitude”). This sign matters for the ¯ B → X s l + l − rate and (even more) for the forward-backward asymmetry: − 1 dy d 2 Γ( ¯ B → X s l + l − ) � 1 � � �� s ) 2 Re C eff ∗ sC eff s ) + 2 C eff A FB = s gn y ∼ (1 − ˆ 10 ( ˆ s ) ˆ 9 ( ˆ 7 ( ˆ s ) + R 3 , d ˆ s dy where y = cos θ l and θ l is the angle between the momenta of ¯ B and l + in the dilepton rest frame. Forward-backward asymmetries for the exclusive ¯ B → K ( ⋆ ) l + l − modes are defined analogously.
AD 2005 model-independent constraints on additive new physics contributions to C 9 , 10 at 90% C.L. 15 15 2 SM-like sign of C 7 non-SM sign of C 7 non-SM 12 12 (surroundings 1.5 of the origin) 9 9 allowed allowed 1 allowed 6 6 eff eff eff � � � C C C 10,NP 10,NP 10,NP 0.5 3 3 0 0 0 � 3 � 3 � 1.5 � 1 � 0.5 0 0.5 � 12 � 9 � 6 � 3 0 3 � 12 � 9 � 6 � 3 0 3 eff � eff eff C � � 9,NP C C 9,NP 9,NP The three lines correspond to three different values of B ( ¯ B → X s γ ) × 10 4 : the experimental central value and borders of the 90% C.L. domain for this branching ratio. The dot at the origin indicates the SM case for C 9 , 10 . The SM values have been assumed for C 1 , ..., C 6 and for C 8 . New physics in C 8 would have little effect provided one accepts the bound B ( b → charmless) NP = 3.7% @ 95% C.L. [DELPHI, PLB 426 (1998) 193]. In the rightmost plot, the maximal MFV MSSM ranges for C 9 , NP and C 10 , NP are indicated by the dashed cross. They were obtained in hep-ph/0112300 by A. Ali, E. Lunghi, C. Greub and G. Hiller who scanned over the following parameter ranges: 2 . 3 < tan β < 50 , 0 < M 2 < 1 TeV , − 1 TeV < µ < 1 TeV , 78 . 6 GeV < M H ± < 1 TeV , 90 GeV < M � t 1 , 2 < 1 TeV , − π t < π 2 < θ � 2 , M � ν ≥ 50 GeV .
# 2. Updated forward-backward asymmetries in B ( B → K ∗ l + l − ) . Slide from T. Ijima at Lepton-Photon 2009: B K*ll : FB Asymmetry A FB extracted from fits to 657 M BB , 384M BB , 657 M BB 384M BB submitted to PRL, arXiv: 0904.0770 PRD79, 031102(R) (2009) SM SM SM C 7 =-C 7 SM C 7 =-C 7 SM 7 7 C 7 =-C 7 SM SM SM SM C 9 C 10 =-(C 9 C 10 ) SM C 7 =-C 7 C 7 C 7 SM & & C 9 C 10 =-(C 9 C 10 ) SM A FB exceeds SM ? 25
# 3. Updated B ( B → X s γ ) measurement by Belle. A. Limosani et al , arXiv:0907.1384, PRL 103 (2009) 241801. B× 10 4 for each E min Averages for each E min rescaled to E min [GeV] = 1 . 6 GeV γ γ γ Babar, hep-ex/0607071 4 4 HFAG 88.5 M B ¯ B 0808.1297 3.5 3.5 3 3 SM, hep-ph/0609232 Belle, arXiv:0907.1384 657 M B ¯ B 2.5 2.5 Cleo, hep-ex/0108032 9.7 M B ¯ B 1.6 1.7 1.8 1.9 2 2.1 2.2 1.6 1.7 1.8 1.9 2 2.1 2.2 The displayed measurements are only the fully-inclusive, no-hadronic-tag ones. Other methods (included in the HFAG average): • Semi-inclusive (systematics-limited), • With hadronic tags of the recoiling B meson (not necessarily fully reconstructed). Low systematic errors, but statistics-limited at present.
b ) corrections to Γ 77 ( ¯ # 4. Evaluation of O ( α s Λ 2 /m 2 B → X s γ ) and moments of the photon spectrum. [T. Ewerth, P. Gambino and S. Nandi, arXiv:0911.2175, NPB 830 (2010) 278]. α 2 Γ 77 | E γ >E 0 = Γ (0) λ 1 − 9 λ 2 ( µ ) α s ( µ ) s ( µ ) 1 + + π f pert . NLO ( δ ) + π 2 f pert . NNLO ( δ ) 77 2 m 2 b � � + λ 1 α s ( µ ) λ 2 ( µ ) α s ( µ ) − 3+4 ln δ + g 1 ( δ ) + g 2 ( δ ) + . . . 3 m 2 6 δ 2 m 2 b π b π M. Neubert, 2005 δ = 1 − 2 E 0 5 m b δ , ln 2 δ , ln δ , 4 g 1 , 2 contain ln δ 1 δ , 3 and non-singular terms. 2 s ( δ ) 1 s ( δ )+ g 1 ( δ ) 0 � 1 1.5 1.6 1.7 1.8 1.9 2.0 E 0
# 5. Clarification of quark-hadron duality issues in ¯ B → X s l + l − [M. Beneke, G. Buchalla, M. Neubert and C. Sachrajda, arXiv:0902.4446, EJPC 61 (2009) 439]. If the intermediate J/ψ and ψ ′ resonances are included, Γ( ¯ B → X s l + l − ) ex- ceeds the perturbative Γ( b → X s l + l − ) by around two orders of magnitude. Is the quark-hadron duality violated here? G.B. 2000: No, because we need to resum Coulomb-like interactions in the c ¯ c state. BBNS 2009: Yes, because we need to resum Coulomb-like interactions in the c ¯ c state. Both answers are satisfactory, because they differ only linguistically, while the physics remains the same.
Technically: Coulomb resummation effects get washed out after smearing over q 2 in the correlator (as in b → sc ¯ c ), but not in the squared correlator (as in b → se + e − ). Pedagogical toy model: consider ficticious leptons (heavy l 1 instead of b , and massless l 2 instead of s ) to single out bound-state effects in the c ¯ c system only. c and l 1 → l 2 e + e − are described by: The decays l 1 → l 2 c ¯ l 2 l 2 l 2 l 1 l 1 l 1 l 1 l 1 l 1 c c c c c c c c e (a) (b) e In the case (b), we integrate imaginary part of the correlator Π( q 2 ) of two c currents. In the case (a), we get | Π( q 2 ) | 2 . c ¯ In the acknowledgments, thanks to Tobias Hurth for persistent encouragement .
# 6. Many BSM studies... Let’s have a look at the past 2 weeks. # 6a. G. Degrassi and P. Slavich, arXiv:1002:1071 (Feb 4th) Evaluation of the NLO QCD corrections to R b and b → sγ in generic MVF two-Higgs-doublet models. � � u i T ( a ) g 1 − γ 5 1+ γ 5 V ij d j H + � 3 A i − A i L H + = − i,j =1 ¯ u m u i d m d j ( a ) + h . c . √ R 2 2 2 m W A u = 0.3 8 7 Type III Type C 6 m H + = 100 GeV -4 BR(B->X s γ ) / 10 5 4 3 2 m H + = 400 GeV 1 0 0 10 20 30 40 50 60 A d Question: Do the two-loop b → sγ matching results agree analytically with those from hep-ph/9904413 (C. Bobeth, J. Urban, MM)?
# 6b. Fourth generation (congratulations to George Hou!) # 6b1. arXiv:1002.0595 (Feb 3rd), A. Soni et al. , 46pp. # 6b2. arXiv:1002.2216 (Feb 10th), A. J. Buras et al. , 87pp. Scans over the SM4 parameter space (Fig. 16 from the latter paper): BS1 (yellow) BS2 (green) BS3 (red) LO b → sγ matching for 4th gen. S ψφ 0 . 04 ± 0 . 01 0 . 04 ± 0 . 01 ≥ 0 . 4 Br( B s → µ + µ − ) (2 ± 0 . 2) · 10 − 9 (3 . 2 ± 0 . 2) · 10 − 9 ≥ 6 · 10 − 9 Would the left plot remain qualitatively the same for q 2 ∈ [1 , 6] GeV 2 and/or with the updated HFAG result for the full q 2 range?
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