Measuring α with B ρρ and ρπ

Transcription

1 Measuring with B ρρ and ρπ Andrei Gritsan LBNL May 14, 2005 U. of WA, Seattle Workshop on Flavor Physics and QCD

2 Outline Minimal introduction = arg[v td Vtb/V ud Vub] with b u and mixing penguin pollution with /VtbV td is a problem B ρρ proved to be successful due to small pollution and 100% CP-even isospin analysis like in B ππ (Gronau/London) B ρ 0 ρ 0 is the key B ρπ proved to be successful with Dalitz analysis (interference) quasi-two-body isospin analysis is not feasible

3 Part I: B ρρ Decays T T + C C + P P Tree Ù Ù Ï Penguin Ï Ù Ï Ù Ø Ù Ù Ù Ù Ù Ù Õ Õ B decay T C P B (10 6 ) f L = A 0 2 /Σ A m 2 N B B ρ 0 ρ < 1.1 (90%) BABAR ( ) ρ ρ ± 4 ± ± BABAR (89/ ) ρ 0 ρ ± ± 0.04 BABAR ( ) 32 ± ± 0.11 ± 0.02 BELLE ( ) ωρ ± ± 0.03 BABAR ( ) ωρ < 3.3 (90%) BABAR ( ) ρ ρ +, ρ 0 ρ +, ωρ + : large decay rate with tree (compared to ππ) Confirm f L 1 CP-even eigenstate ρ ρ + ρ 0 ρ 0, ωρ 0 : small penguin great for Unitarity Triangle

4 Issue 1: Isospin Triangles have to close Enforce isospin relation in toy MC generated with measured values: input (10 6 ) output (10 6 ) B ± ± 0.3 B ± ± 5.6 B ± ± 3.9 A(ρ 0 ρ 0 ) + A(ρ + ρ )/ 2 = A(ρ 0 ρ + ) Ā + 2 L 1 A + Ā 00 L 2 L A 00 L A +0 L = Ā 0 L B 0 ρ 0 ρ 0 B 0 ρ + ρ B + ρ + ρ B 00 (10-6 ) B +- (10-6 ) B +0 (10-6 )

5 Measuring with ρρ like with ππ A ρ ρ + (t) = C + L cos( m B t) S + L sin( m B t) sin(2 + eff ) = Im( q p 2 + = arg( A+ L A +0 L Ā + L )/ λ = S + A + L ) arg(ā+ L Ā 0 L ) L / 1 C L 2 = + eff + + BABAR: A +0 L 1 Ā + 2 L 1 A + Ā 00 L 2 L A 00 L = Ā 0 L + eff = (100 ± 9) + = (0 ± 11) = (100 ± 14) eff

6 Issue 2: Penguin and Tree Size Extract Penguin (P) and Color-suppressed tree (C) amplitudes t-convention: dominant t-penguin V tbv td, P/T weak phase correct 90 : T dominates, P C P / T C / T wrong 180 : possible large C / T (could use for constraints) phase assumption could be used (e.g. Gronau/Lunghi/Wyler)

7 Issue 3: What is the true branching of B ρ 0 ρ 0 (1) set only limits on ρ 0 ρ 0 straight-forward but unlikely (2) B(ρ 0 ρ 0 ) not resolved ambiguities (8/180 ) each solution to few at 10ab 1 10ab 1 20 eff error (degrees) eff luminosity (fb -1 )

8 Measuring with ρ 0 ρ 0 Unique to B ρρ (vs. ππ): B 0 ρ 0 ρ 0 π + π π + π measure eff 00 with A ρ0 ρ0(t) need high statistics 00 from the same triangle Limited resolution due to long sides systematics in B + and B 0+ (assume 7% here) 2 00 Real advantage: resolving triangle ambiguities Ā + 2 L 1 A + Ā 00 L 2 L A 00 L A +0 L = Ā 0 L eff

9 Resolving Ambiguities with ρ 0 ρ 0 and ρ + ρ Triangle orientations should match for 00 and + (A) opposite orientations (B) the same orientations ρ 0 ρ 0 ρ + ρ ρ 0 ρ 0 Could resolve ambiguities with ρ 0 ρ 0 could completely resolve if Branching systematics 1%

10 Projection to Higher Luminosity Strongly depends on true values 10 ab 1 5 ab 1 2 ab 1 1 ab ab 1

11 Conclusion on ρρ and Open Issues B ρ 0 ρ 0 unique, may allow precision few together with ρ + ρ 0 Challenges: broad ρ I=1 contribution, isospin-breaking, interference high background and B cross-feed branching B +0 and B + systematics down to few % even relative Υ(4S) B + B vs. B 0 B0 matters for B +0 /B + assume f L (ρ 0 ρ 0 ) = 1, lesson of φk : other contributions to ρρ? We learn to deal with challenges as we accumulate statistics

12 Resolving (90 ) Ambiguities Unresolved ambiguity (90 ) measure sin(2) in individual channels (ππ, ρπ, ρρ, etc) Angular-time analysis of B 0 ρ + ρ could solve: Im(A (t)a (t) ) and Im(A 0 (t)a (t) ) cos(2) sin( mt) hopeless in near future given f L 98% Dalitz-time analysis of B 0 π + π π 0 interference e.g. ρ + π and ρ π + cos(2) sin( mt) proposed by Snyder/Quinn recently measured by BABAR s (GeV 2 /c 4 ) s + = 1.5 GeV/c 2 Interference s 0 = 1.5 GeV/c 2 s = 1.5 GeV/c s + (GeV 2 /c 4 )

13 Part II: B ρπ Decays (1) How small is B ρ 0 π 0? (BABAR 1.4 ± 0.7, BELLE 5.1 ± 1.8) (2) B ρ ± π not CP eigenstate B decay HFAG B (10 6 ) ρ 0 π ± 0.6 ρ + π ρ π ± 2.5 ρ + π ± 2.0 ρ 0 π Q2B isospin analysis unfruitful (12 params): sin(2 + θ + ), sin(2 + θ + ), sin(2 + θ 00 ) A A A 00 = A +0 + A 0+ = T 1 A + A + + A0+ 2 A+0 2 = T 2 better if very small ρ 0 π 0 Lipkin/Nir/Quinn/Snyder, Gronau

14 Dalitz analysis of B ρπ Dalitz-time analysis of B π + π π 0 by BABAR ( B B) key: time-dependence and interference of ρ + π and ρ π + A ± 3π(t) 2 = e t /τ B 0 4τ B 0 [ 16/26 free parameters (incl. strong phase): A 3π 2 + A 3π 2 ( A 3π 2 A 3π 2) cos( mt) ± 2Im [ A 3π A ] ] 3π sin( mt) δ + = arg A(ρ π + ) A(ρ + π ) = ( ± 7) = ( ± 6) at 68% CL C.L BABAR preliminary using isospin without isospin C.L BABAR preliminary δ + (deg) (deg)

15 Dalitz model is the key: Open issues in B ρπ phenomenology of all resonances and phases currently model ρ(770), ρ(1450), ρ(1700), same P/T absent S-wave (e.g. f 0 (600) or σ), etc B 0 ρ 0 π 0 ignore time-dependence at the moment Projection to higher statistics: many more degrees of freedom than in ρρ very different results depending on amplitude parameters ρ 0 π 0 rate alone is not as crucial as ρ 0 ρ 0

16 Summary Best constraints from B ρρ and B 0 ρπ π + π π 0 B ρρ improvement depends on ρ 0 ρ 0, understanding of ρ + ρ, ρ + ρ 0 current error 13, ambiguities not solved B ρπ Dalitz (interf.) and time of ρ + π and ρ π +, some ρ 0 π 0 current error 23, ambiguities solved, likely improve C K M f i t t e r Moriond 05 B ππ B ρπ B ρρ WA Combined CKM fit 1 CL (deg)