CALCULATION OF A e iδ :

Transcription

1

2 H weak = G F V pb Vpd 2 C 1µ)O p 1 + C 2µ)O p 2 + C i µ)o i + C 7γ O 7γ + C 8g O 8g p=u,c i=3,..,10 A e iδ f H weak B = k C k µ) }{{} f O k µ) B }{{} pert. QCD non pert. QCD CALCULATION OF A e iδ : use of FLAVOUR isospin, SU3)) symmetries [Gronau, Rosner et. al ] QCD factorization [Beneke, Buchalla, Neubert, Sachrajda 1999)] M 1 M 2 O i B = dωdudvφ B ω)th i ω, u, v)φ M 1 u)φ M2 v) PQCD approach [Keum, Sanda, Li 2001)] M 1 M 2 O i B = dk i dωdudvφ B ω, k 3 )TH i ω, u, v, k i )φ M1 u, k 1 )φ M2 v, k 2 ) LIGHT-CONE SUM RULE METHOD [Khodjamirian 2001)]

3 f O k µ) B ππ O 1 B = [ ] [ π dγ µu 0 π uγ µ b B 1 + Oα s, Λ QCD /m b ) = imb 2 }{{} Bπ m2 π ) 1 + Oα Λ ] QCD s, ) m b naive factorization B P TRANSITION FORM FACTORS FROM LCSR: f + Bπ 0) = f Bπ 0 0) = fbπ T 0) = ± [G. Duplančić, A. Khodjamirian, Th. Mannel, B.M., N. Offen 2008)] extraction of the V ub matrix element from exclusive B decays: exp. V ub f + Bπ 0) V ub = 3.5 ± 0.4 ± 0.2 ± 0.1) 10 3 SU3) BREAKING SU3) f K /f π, f BK /f Bπ, m s... ) B K form factors f + BK 0) = f 0 BK 0) = , f T BK 0) = 0.38 ± 0.05 B s K form factors f + Bs K 0) = f 0 Bs K 0) = , f T Bs K 0) = 0.30 ± 0.05 predicted SU3) breaking: [G. Duplančić, B.M.2008)] f + BK 0) f + = Bπ 0), f + Bs K 0) f + = Bπ 0), fbk T 0) fbπ T = ), f T Bs K 0) fbπ T = ) A fact B s K + K ) A fact B d π + π ) = f K f + Bs K m2 K ) m 2 Bs m2 K f π f + Bπ m2 π) mb 2 = m π

4 DIFFERENT TOPOLOGIES CONTRIBUTING: π + π + B 0 d B 0 d g, γ, Z π q, c π a) emission - T b) emission - C c) penguin - P q,c, P C EW π + B 0 d π d) annihilation - E e) annihilation - A f) penguin annihilation - PA,PE

5 "!! λ EMISSION TOPOLOGY - nonfactorizable OΛ/m b ) corrections from Õ 1 = dγ a λa µ 2 u)uγµ 2 b) [Khodjamirian 2001)] r ππ) E = [ ) ] [ + soft r ππ,6) E = [ 2.7 ± 0.4) 10 2 ] hard QCDF ) + i PENGUIN CONTRIBUTIONS: [Khodjamirian, Mannel, BM 2003), Khodjamirian, Mannel, Urban 2002)] ) ] 10 2 hardqcdf r ππ) Pq = r ππ) P b = [ )] i ) r ππ) Pc 10 2 r ππ) 8g [ = i ) = )] 10 2 ANNIHILATION: [Khodjamirian, Mannel, Melcher, BM 2005)] r ππ) A = [ )] i , R ππ,6) A = 2f B F S π m2 B ) m b f πf + = Bπ 0), r ππ,5,6)) A 0

6 decay BR10 6 ) BR10 6 ) th a CP a CP) th B π 0 π ) 0.06 ± ) B 0 π + π 5.16 ± ) 0.38 ± ) B 0 π 0 π ± ) ) B π 0 K 12.9 ± ) ± ) B 0 π + K 19.4 ± ) ) ± B π K ± ) ± ) B 0 π 0 K ± ) ) B K 0 K ) ) ± B 0 K 0 K ) ) B 0 K + K ) - 0 0) 0.23 ± 0.14 B 0 s π+ π 0.57 ± ) - 0 0) B 0 s π0 π ) - 0 0) B 0 s π K ± ) 0.39 ± ) 0.15 ± 0.19 B 0 s π0 K ) ) B 0 s K 0 K 0 < ) ) B 0 s K + K 26.5 ± ) ) Table: 20 30% error in LCSR results has to be considered;...) = QCDF default results; LCSR predictions are more or less in the ballpark of QCDF results

7 topological amplitudes PA EW and PE EW neglected): tree-dominated decays 2 AB π π 0 = T + C) + P EW + P C EW T, C, E, A λ u = V ub V ud P, P EW, PE... λ u + λ c penguin-dominated decays A B0 π + π = T + E) + P PC EW + PE + 2PA A B 0 π 0 π 0 = C E) P + PEW PC EW PE 2PA A B π K0 = A ) + P 1 3 P C EW + PE 2 AB π 0 K = T + A ) + P P C EW + PE + [C K ) + P EW,K ], A B0 π + K = T ) + P P C EW + PE 2 A B0 π 0 K0 = P P C EW PE + [C K )] A B K K 0 = A) + P 1 PEW + PE 3 A B0 K0 K 0 = P 1 PEW + PE + 2PA 3 annihilation-dominated decay A B 0 K K + = E) + 2PA

8 topological amplitudes - B s decays PA EW and PE EW neglected): tree-dominated decays A Bs π K + = T ) + P PC EW + PE 2 A Bs π 0 K 0 = C) P + P EW PC EW PE penguin-dominated decays A Bs K 0 K 0 = P 1 3 P C EW + PE + 2PA A Bs K K + = T + E ) + P P C EW + PE + 2PA annihilation-dominated decay A Bs π + π = E ) + 2PA

9 S = 0 decays B ππ B K K B s π K T 10 8) C 10 8) P 10 8) P EW 10 8 ) P C EW 10 8 ) E 10 8) A 10 8) PE 10 8) PA 10 8) PE EW 10 8 ) PA EW 10 8 ) S = 1 decays B s ππ B s K K B π K T 10 8) C K 10 8 ) P 10 8) P EW 10 8 ) P C EW 10 8 ) E 10 8) A 10 8) PE 10 8) PA 10 8) PE EW,K 10 8 ) PA EW 10 8 )

10 PUZZLES in B ππ, πk, KK decays predicted BRs for penguin-dominated B PP decays are systematically somewhat lower than the measurements color-suppressed tree-dominated B π 0 π 0 BR is predicted too low direct CP asymmetries a CP B 0 π + K ), a CP B 0 π + π ) and a CP B s π K + ) disagree with the data in the sign a CP B πk) = a CP B π 0 K ) a CP B π + K ) = ± by including the most recent Belle results; expected a CP B πk) = 0 annihilation-dominated decays B K + K and B s π + π cannot be explained, unless by introducing ad hoc large annihilation contribution with a large phase SOLUTIONS? large C/T -amplitude with a large phase for a CP and BR of π 0 π 0 puzzle large P EW -amplitude with a large phase for B Kπ puzzle large PE-amplitude with a large phase for puzzles in S = 1 modes but not for π 0 π 0 problems large FSI - D, D exchange for color-suppressed neutral modes π 0 π 0, π 0 K 0

11 SOLUTIONS for B s) PPP = π, K) puzzles with the LCSR input? [ M. Jung, A. Khodjamirian, BM, in preparation] Preliminary! we plan to use CKMfitter with the LCSR input decay constants, form factors, different contributions and topologies) to perform the fit to B s) PPP = π, K) decays we use different scenarios, trying to minimize the input, and to obtain all BRs and CP asymmetries simultaneously isospin decomposition of amplitudes - a relative phase is introduced which is varied in a full range annihilation topologies - extracted from the measured annihilation dominated decays predictions for B s decays

12 ISOSPIN PHASE general isospin decomposition - B ππ amplitudes: AB π π 0 ) = π π 0 H eff B = 3 2 A 2, A B 0 π + π ) = π + π H eff B 0 = A 2 + A 0e δ I, A B 0 π 0 π 0 ) = π 0 π 0 H eff B 0 = 2A 2 A 0e δ I, A 2 = 1 ) T + C) + P EW + P C EW 3 A 0 = 1 ) 2T C + 3E) + 3P P EW + P C EW 3 + 3PE + 6PA PEEW + PAEW in A 0 amplitude we miss a proper treatment of nonemission topologies penguin and/or annihilation diagrams) and final state effects we introduce a relative phase between the isospin amplitudes, δ I : BRB π + π ) a CPB π + π )

13 BRB π 0 π 0 ) a CPB π 0 π 0 ) a CPB π 0 K ) a CPB π + K ) - unfortunatelly, this does not solve the B πk puzzle, since asymmetries flip the sign simultaneously BR sb πk) still a bit too low

14 PENGUIN PHASE unique nonperturbative phase is added to the penguin amplitudes calculated in LCSRs r P, r 8g, r 7γ) - P, P C EW : - it does not solve the problems in B ππ decays tree-dominated) - influence on the penguin-dominated B πk decays: BRB π 0 K ) a CPB π 0 K ) BRB π + K ) a CPB π + K ) again the same situation, adjusting a CPB π + K ) spoils a CPB π 0 K ) prediction

15 BRB π K 0 ) a CPB π K 0 ) BRB π 0 K 0 ) a CPB π 0 K 0 )

16 ANNIHILATION PHASE pengin-annihilation part PA is fitted to the data using recently measured penguin-dominated decays B K + K and B s π + π fitted values: S = 0 decays B ππ B K K PA 10 8) PAfit) 10 8) 0.09 ± ± 0.03 S = 1 decays B s ππ B s K K PA 10 8) PA fit) 10 8) 0.43 ± ± 0.13 predictions: decay BR10 6 ) BR10 6 ) th a CP a CP) th B 0 π + π 5.16 ± ) 6.8 ± ± ) fig B 0 π 0 π ± ) 0.29 ± ) [0.26,0.66] B 0 K 0 0 K ) 1.2 ± ) fig B 0 K + K ) 0.08 ± ) [-0.23,0.23] 0.23 ± 0.14 B 0 s π+ π 0.57 ± ) 0.63 ± ) [-0.01,0.01] B 0 s K 0 K 0 < ) [13.7, 29.0] ) [-0.15,0.10] B 0 s K + K 26.5 ± ) [12.5,27.2] ) [-0.10,0.17]

17 a CPB π + π ) a CPB K 0 K 0 ) CKMfitter is needed for a more reliable fit

18 CONCLUSIONS LCSRs are providing the input for the factorizable contributions - form factors and decay constants within LCSRs the predictions for penguins and the annihilation part finite!) are given predictions for BR s are in the ballpark of QCDF results with the LCSRs 1/m b -effects are calculable the puzzles remain! adding arbitrary phases to isospin and penguin parts does not bring an agreement with the data more elaborated fits will be done by using CKMfitter [M. Jung, A. Khodjamirian, B.M., in preparation] pessimistic view: hadronic final-state interactions are probably more important that we have first thought - inelastic intermediate states can mix up different toplogies; effects are not accessible with QCD techniques B PP decays, with the current set of data remain a challenge!

19