Tests of (non-) Factorization

Transcription

1 Tests of (non-) Factorization Sören Prell Iowa State University INT / SLAC Workshop b c nonleptonic Session May 11, 2005

2 Non-Factorizable B Decays Stuy of moes not ominate by factorizable part of amplitue can give insight to what limit factorization can be expecte to hol A= A + A fact non Concentrate on experimental results for ecays with A non! A fact Designer mesons (some coul be interesting for 2β+γ) Annihilation / W-exchange iagrams May 11, 2005 SLAC / INT QCD workshop 2

3 B Decays to Designer Mesons Mesons with small or zero coupling to vector an axial vector coupling switch off factorizing piece of ecay amplitue Diehl & Hiller, JHEP 0106, 067 (2001)) May 11, 2005 SLAC / INT QCD workshop 3

4 B χ c0/2 K Not allowe in naïve factorization approximation B χ c0 K: charge conjugation invariance B χ c2 K: no J>1 current in HQET lowest-orer Rate coul be enhance in QCDF (similar to χ c1 K?) Belle PRL 88, (2002) 31 M BB + χ = ± 4 Br( B K ) ( ) 10 χ c0 1.8 BaBar PRL 69, (2004) 89 M BB + + Br( B K ) = (2.7 ± 0.7) 10 c0 4 Measure rates comparable to factorization-allowe moes: PDG 2004 averages: Br( B J / ψ K ) = (10.0 ± 0.4) 10 Br( B χ K ) = (6.8 ± 1.2) c Br( B ψ ' K ) = (6.8± 0.4) 10 Enhance ecay rate ue to large re-scattering? Expect a similar rate for B χ c2 K (Colangelo, De Fazio & Pham, PLB 542, 71 (2002)) May 11, 2005 SLAC / INT QCD workshop 4

5 B χ c0/2 K (continue) Search for B χ c0/2 K with χ c0/2 J/ψ γ better sensitivity for B χ c2 K BaBar hep-ex/ (2005) 123 M BB Decay rates 90% C.L. limits for B χ c2 K (*) [in 10-4 ] Limit for B χ c2 K orer of magnitue smaller than measure rate for B χ c0 K (is re-scattering rule out?) May 11, 2005 SLAC / INT QCD workshop 5

6 B χ c0/2 K (continue) but B χ c2 X is observe : Belle PRL 89, (2002) 32 M BB Br( B χ X ) = (1.53 ± 0.27) c Br( B χ X ) = (3.63 ± 0.22 ± 0.34) 10 c1 3 [correcte for fee-own from ψ(2s)] What are the involve exclusive states? higher K resonances, non-resonant multi-boy ecays? B χ c2 K MC Br( B χ K) < c (90% C.L.) May 11, 2005 SLAC / INT QCD workshop 6

7 B Decays to a 0 an a 2 Final States Prouction of a 0/2 strongly suppresse in B ecays 1 a 0, a 2 Αλ 2 (π ʉ, ρ, a 1 ) b c B 0 D + W! a 0 is a secon class current (G-parity violating) Decay constants f(π) =131 MeV, f(a 0 ) = MeV W! a 2 coupling is zero without non-factorizable contribution May 11, 2005 SLAC / INT QCD workshop 7

8 CP Sensitivity 2 contributing tree amplitues with weak phase ifference γ 1 a 0, a 2 Αλ 2 (π ʉ, ρ, a 1 ) b c B 0 D + B 0 Αλ 3 ρ iη e iγ b λ c u D a + 0, a+ 2 (π +, ρ +, a + 1 ) Time-epenent CP violation through interference of mixing an ecay with weak phase ifference 2β + γ May 11, 2005 SLAC / INT QCD workshop 8

9 Expecte branching fractions (x 10-6 ) Diehl & Hiller, hep-ex/ (FA + QCDF), Kim, Lee & Oh, hep-ph/ (ISGW2 HQET) Moe B 0 /B 0! D a + 0 V cb meiate DH / KLO / V ub meiate DH / KLO 2.1 / Uncertain theoretical errors! B 0 /B 0! D (*) a / 1.9 / B 0 /B 0! D a / / B 0 /B 0! D (*) a / / V cb amplitue ominate by non-factorizable contributions V ub amplitue: a 0 (1450) form factor 2 O(2.5x) π form factor 2 V. Chernyak, hep-ph/ Small W! a 0, a 2 coupling suppresses V cb amplitue, but not V ub amplitue Get 2 amplitues of similar size! large CP asymmetries Sensitivity with current ata shoul be O( few 10-5 ) May 11, 2005 SLAC / INT QCD workshop 9

10 Test of the V ub Transition (1): B 0! D s a + 0 W vertex is Cabibbo-favore B 0 b Αλ 3 1 s c u D s a + 0 B 0 D a 226 M BB + S 0 Reconstruct a 0/2 ηπ(100% / 15%) V ub transition not observe BaBar (preliminary) BaBar (preliminary) B 0 D a + S 2 a 0 form factor smaller than expecte? May 11, 2005 SLAC / INT QCD workshop 10

11 Test of the V ub Transition (2): B 0 π a + 0 Not sensitive to α, since here the small a 0 ecay constant creates two ifferent-size amplitues BaBar PRD 70, (2004) 89 M BB BaBar (preliminary) NoB! (π/k) a 0 transition observe final state a 0- π + branching ratio [10-6 ] < 5.1 a 0- K + < 2.1 a 0- K 0 a 00 π + < 3.9 a 00 K + < 5.8 < 2.5 a 00 K 0 < 7.8 May 11, 2005 SLAC / INT QCD workshop 11

12 Test of the V ub Transition (3): B 0 a + 0 l ν Semi-leptonic ecay B 0! a + 0 l ν (V ub measurement) No efficiency loss ue to D branching fractions Experimentally easier than B 0! ρ + l ν BABAR (50 fb -1 ): BR(B 0! ρ + l ν) = (3.3±0.7) x 10 4 B 0 b Αλ 3 1 l ν u a + 0 One shoul look for this moe!!! May 11, 2005 SLAC / INT QCD workshop 12

13 Test of the V cb Transition: B D 0 a 0 Charge B ecay Β! D 0 a 0 Expect same ecay rate as for signal W ʉ b B 0, B c D +, D 0, ʉ, ʉ ominant ecay amplitue, but there s an aitional color-suppresse amplitue for Β! D 0 a 0 Color-suppresse for neutral B gives B 0! D 0 a 0 0 V ub annihilation iagram gives Β! D 0 a 0 No confusion since D has opposite flavor partial D* reconstruction for B 0! D* + a 0 possible? a 0 May 11, 2005 SLAC / INT QCD workshop 13

14 More (but hopeless?) Mesons Decay constants also small for π(1300), b 1, π 2, ρ 3 (Diehl & Hiller, JHEP 0106, 067 (2001)) Dominant meson ecay moes share by mesons from unsuppresse B ecays, e.g. b 1 (1235)! ωπ, but also ρ(1450)! ωπ [CLEO, PRD64, (2001)] π(1300)! ρπ, but also a 1! ρπ Unsuppresse moes will completely swamp the suppresse moes May 11, 2005 SLAC / INT QCD workshop 14

15 Annihilation Diagrams Annihilation W-Exchange Annihilation amplitue suppresse by f B /m B ~ 0.04 w.r.t. similar spectator amplitue typically ignore when non-annihilation amplitues present calculation in factorization approximation unreliable ecays coul be enhance significantly by re-scattering Stuy annihilation amplitues in ecays with small competing spectator amplitue May 11, 2005 SLAC / INT QCD workshop 15

16 B + D (*)+ K S SM preiction (FA) Br( B D K ) = Xing, PRD 53 (1996) If re-scattering is large, ecay amplitue coul be enhance by 1/λ 2 [Blok, Gronau & Rosner, PRL78, 3999 (1997)] May 11, 2005 SLAC / INT QCD workshop 16

17 B + D (*)+ K S CLEO PRD 64 (2001) 9.6 M BB BR(B + D* + Κ 0 ) < (90% C.L.) BaBar (preliminary) Events / GeV Nent = f Gauss + + (1-f) Argus + 0 B D K f = ± S M BB BR(B + D + K 0 ) < BR(B + D* + K 0 ) < (90% C.L.) (90% C.L.) (GeV) m ES May 11, 2005 SLAC / INT QCD workshop 17

18 B + D s (*)+ φ Also, preictions for Cabibbosuppresse moe B + D s (*)+ K S : Br( B D K ) = (1.7± 0.4) s Br( B D K ) = (4.0 ± 0.8) 10 Lu, EPJ C24 (2002) + * s CLEO PLB 319 (1993) 1.2 Br(B + D s φ ) < Br(B + D* s φ ) < M BB (90% C.L.) (90% C.L.) SM Theory BR(B + D s φ ) ~ Lu, EPJ C24 (2002) BR(B + D s φ ) ~ Mohanta, PLB 540 (2002) New physics BR(B + D s φ ) ~ BR(B + D s φ ) ~ Mohanta, PLB 540 (2002) Br(B + D s K ) < Br(B + D* s K ) < Br(B + D s K * ) < Br(B + D* s K * ) < (pqcd) (QCDF) (2HDM) (RPV) (90% C.L.) (90% C.L.) (90% C.L.) (90% C.L.) Sensitivity to B + D s (*) φ/k S with current ata shoul be a few 10-6 May 11, 2005 SLAC / INT QCD workshop 18

19 B 0 D s (*)+ K - BaBar Belle Only observe ecay moe ue to W-exchange Measurements consistent with PQCD (no nee for large re-scattering amplitue?) BR(B 0 D - sk + ) ~ (3.1 ± 1.0) 10-5 BR(B 0 D *- sk + ) ~ (2.7 ± 0.6) 10-5 (pqcd) Lu, EPJ C24 (2002) Belle PRL 89, (2002) 85M BB BaBar PRL 90, (2003) 84 M BB Br( B D K ) = (4.6 ± 1.3) s 1.1 BR(B 0 D - sk + ) = (3.2 ±1.0 ±1.0) 10-5 BR(B 0 D *- sk + ) < (90% C.L.) May 11, 2005 SLAC / INT QCD workshop 19

20 B 0 D s (*)+ D s (*)- Li, Lu, Xiao, J.Phys.G31,273 (2005) Eeg, Fajfer, Hiorth, Prapotkin, NP Proc.Suppl.142, 188 (2005) Sensitivity with current B factory ata sample O(few 10-4 ) May 11, 2005 SLAC / INT QCD workshop 20

21 Summary an Conclusions Designer Mesons: Why is Br(B χ c0 K)! Br(B χ c2 K)? Why no a 0 in B ecays? Coul final states with other esigner mesons be exploite with current ata? Annihilation ecays to charm final states: Only B 0 D s K+ observe so far Experimental limits on other ecay moes getting close to theoretical preictions May 11, 2005 SLAC / INT QCD workshop 21

22 Back-up slies May 11, 2005 SLAC / INT QCD workshop 22

23 Reconstructing B! D (*)+ a 0, D (*)+ a 2 Just like B! D (*)+ ρ, only better Usual D ecay moes D +!K π + π +, D *+!D 0 π + (D 0! K π +, K π + π 0, K π + π π + ) BR(a + 0! ηπ + ) = ominant (assume 1 here) BR(a + 2! ηπ + ) = 15% (70% ρπ not consiere) Combinatorial backgroun less than for B! D (*)+ ρ a, a ηπ ρ π π ! γγ! a + 0, a + 2 are heavy cousins of the ρ: m(a + 0 ) > m(ρ+ ), m(η) > m(π 0 ), Γ(a + 0 ) = < Γ(ρ+ ) May 11, 2005 SLAC / INT QCD workshop 23 γγ Same final state particles!

24 Test of the V cb transition (2): B 0! D + a 0 (2) τ! a 0 ν τ (2n class current), a 2 ν τ ecays Measurement of factorizable contribution (i.e. a 0, a 2 ecay constant) to amplitue (not expecte to be ominant) since no gluon exchange τ W expecte BR(τ! ηπν) ~ 10-5 CLEO limit with 3.5 fb -1: Br(τ! ηπν) <1.4 x 10-4 (95% CL) ʉ ν a 0,a 2 One shoul look for these moes!!! May 11, 2005 SLAC / INT QCD workshop 24