Measuring with B ρρ and ρπ Andrei Gritsan LBNL May 14, 2005 U. of WA, Seattle Workshop on Flavor Physics and QCD
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
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 0 0 1-1 < 1.1 (90%) BABAR (230 10 6 ) ρ ρ + 2 0 2 30 ± 4 ± 5 0.978 ± 0.014 +0.021 0.029 BABAR (89/230 10 6 ) ρ 0 ρ + 1 1 0 23 +6 5 ± 6 0.97+0.03 0.07 ± 0.04 BABAR (89 106 ) 32 ± 7 +4 7 0.95 ± 0.11 ± 0.02 BELLE (85 10 6 ) ωρ + -1-1 2 12.6 +3.7 3.3 ± 1.6 0.88+0.12 0.15 ± 0.03 BABAR (89 106 ) ωρ 0 0 0-2 < 3.3 (90%) BABAR (89 10 6 ) 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
Issue 1: Isospin Triangles have to close Enforce isospin relation in toy MC generated with measured values: input (10 6 ) output (10 6 ) B 00 0.6 ± 0.3 0.8 ± 0.3 B + 30.0 ± 6.4 34.0 ± 5.6 B +0 26.0 ± 6.0 19.9 ± 3.9 A(ρ 0 ρ 0 ) + A(ρ + ρ )/ 2 = A(ρ 0 ρ + ) 2 + 1 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 0 0 1 2 3 B 00 (10-6 ) 0 10 20 30 40 50 60 B +- (10-6 ) 0 10 20 30 40 50 60 B +0 (10-6 )
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 + 2 + 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 -30-20 -10 0 10 20 30
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 0.00 0.25 0.50 0.75 1.00 P / T 0.00 0.25 0.50 0.75 1.00 C / T wrong 180 : possible large C / T (could use for constraints) phase assumption could be used (e.g. Gronau/Lunghi/Wyler)
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 ) 0.8 10 6 not resolved ambiguities (8/180 ) each solution to few at 10ab 1 10ab 1 20 eff error (degrees) 15 10 eff -30-20 -10 0 10 20 30 5 0 10 2 10 3 10 4 luminosity (fb -1 )
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 2 + 1 Ā + 2 L 1 A + Ā 00 L 2 L A 00 L A +0 L = Ā 0 L eff -120-80 -40 0 40 80 120
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%
Projection to Higher Luminosity Strongly depends on true values 10 ab 1 5 ab 1 2 ab 1 1 ab 1 0.5 ab 1
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
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 ) 30 25 20 15 10 5 s + = 1.5 GeV/c 2 Interference s 0 = 1.5 GeV/c 2 s = 1.5 GeV/c 2 5 4 3 2 1 0 22 23 24 25 26 27 0 0 5 10 15 20 25 30 s + (GeV 2 /c 4 )
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 1.8 ± 0.6 ρ + π ρ π + 24.0 ± 2.5 ρ + π 0 12.0 ± 2.0 ρ 0 π + 9.1 1.3 +1.4 Q2B isospin analysis unfruitful (12 params): sin(2 + θ + ), sin(2 + θ + ), sin(2 + θ 00 ) A + 2 + A + 2 + 2A 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
Dalitz analysis of B ρπ Dalitz-time analysis of B π + π π 0 by BABAR (213 10 6 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 ) = ( 67+28 31 ± 7) = (113 +27 17 ± 6) at 68% CL C.L. 1 0.8 0.6 BABAR preliminary using isospin without isospin C.L. 1 0.8 0.6 BABAR preliminary 0.4 0.4 0.2 0.2 0-180 -120-60 0 60 120 180 δ + (deg) 0 0 30 60 90 120 150 180 (deg)
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
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 1.2 1 C K M f i t t e r Moriond 05 B ππ B ρπ B ρρ WA Combined CKM fit 1 CL 0.8 0.6 0.4 0.2 0 0 20 40 60 80 100 120 140 160 180 (deg)