Misure dell’angolo a del Triangolo Unitario Fabrizio Bianchi University of Torino and INFN-Torino

Outline Introduction to the measurement of a Results from the B-factories: B p+ p-, p± p0, p0 p0 B r+ r-, r± r0, r0 r0 B0 (r p)0 Summary and outlook

CKM Matrix I SM accounts for flavor changing quark transition through the coupling of the V-A charged current operator to a W boson: where: Vij are the elements of the CKM matrix i, j run on the three quark generations

Wolfenstein Parameterization CKM Matrix II CKM matrix can be regarded as a rotation from the quark mass eigenstates (d, s, b) to a set of new states (d’, s’, b’) with diagonal coupling to u, c, t Complex matrix described by 4 independent real parameters (including one phase) l~ 0.22 sinθC Cabibbo angle Wolfenstein Parameterization 2 ® 1 ~l 3 ® 2 ~l2 3 ® 1 ~l3 h changes sign under CP

Product of 1st and 3rd columns Unitarity Triangle Product of 1st and 3rd columns (1 of 6 relations) Can be represented as a triangle in the complex plane a = f2 g = f3 b = f1 Dividing all sides by

Normalized Unitarity Triangle h Apex at r, h a g b r

Inc. penguin contribution Measuring a Access to a from the interference of a b→u decay (g) with B0B0 mixing (b) Inc. penguin contribution

From aeff to a: Isospin Analysis Gronau and London, Phys. Rev. Lett. 65, 3381 (1990) Assume SU(2) symmetry among amplitudes Neglecting EW Penguins: is a pure tree mode. The triangles share a common side.

PEP-II

Luminosity

BABAR Detector

Time Dependent Analysis Outline Fully reconstruct the B decaying to a CP eigenstate. Tag the flavor of the other B. Mis-tag probability measured in Bflav sample. Measure Dt. Extract S and C with a ML fit on a signal enriched sample. Signal PDF from MC. Background PDF from MC or sidebands

Variables used in the ML fit Event Topology Combine variables in F or N signal signal PID info: DIRC + dE/dX (BaBar) Aerogel + dE/dX (Belle) Dt background background

:results (preliminary) 347 million BB hep-ex/0607106 :results (preliminary) Background Signal B0tag mES B0tag mES DE DE Npp = 675±42 sPlot

:results (preliminary) 535 million BB hep-ex/0608035 :results (preliminary) Npp = 1464±65

:results (preliminary) C =−A :results (preliminary) 347 million BB Cpp = - 0.16 ± 0.11 ± 0.03 Spp = - 0.53 ± 0.14 ± 0.02 BaBar (Spp, Cpp) = (0.0, 0.0) excluded at 3.6 s Average 535 million BB Belle Cpp = - 0.55 ± 0.08 ± 0.05 Spp = - 0.61 ± 0.10 ± 0.04 2.3 s discrepancy Observation of Direct CPV at 5.5 s Observation of mixing-induced CPV at 5.6 s

(preliminary) Np±p0 = 572 ± 53 Np0p0 = 140 ± 25 347 million BB hep-ex/0607106 Np±p0 = 572 ± 53 Np0p0 = 140 ± 25

a constraint from Da = a - aeff Da a a 1- C.L. |Da| < 41o at 90% C.L. a a 1- C.L. Frequentist interpretation: use only the B→pp branching fractions and isospin-triangle relations. No stringent constraint from pp system alone  need rr and rp

The analysis Worse than pp at first sight: However: V V final state. Mixture of CP = +1 and -1: need to know each fraction However: ~100% longitudinally polarized (~pure CP-even state) no need for elaborate angular analysis Branching fraction for B0 g r+r- is larger than p+p- Branching fraction for B0 g r0r0 is small (~1.1x10-6) small penguin pollution

results (preliminary) 347 million BB results (preliminary) hep-ex/0607098

275 million BB results PRL 96, 171801 (2006) Nrr = 194±32

results (preliminary)

results (preliminary) 232 million BB results (preliminary) hep-ex/0607092 Nr+r0 =390 ± 49

results (preliminary) 347 million BB results (preliminary) hep-ex/0607097 Nr0r0 = 98 ± 32 ± 22 3.0 s evidence

a constraint from a hep-ex/0607098 PRL 96, 171801 (2006) at 68.3% C.L. Use BR(B->r0r0)<1.1 X 10-6 a Frequentist interpretation: use only the B→ρρ branching fractions, polarization fractions and isospin-triangle relations. First evidence of B→r0r0 Constraint on a is less stringent

The Dalitz analysis r+p- r-p+ B0 r0p0 p+p-p0 B0 Monte Carlo A. Snyder and H. Quinn, Phys. Rev. D, 48, 2139 (1993) r+p- r-p+ r0p0 B0 p+p-p0 B0 Monte Carlo Time-dependent Dalitz-plot analysis assuming isospin simmetry. 26 coefficients of the bilinear form factor terms occurring in the decay rate are measured with a UML fit. Physically relevant quantities are derived from subsequent fits to these coefficients. Interference provides information on strong phase difference r(1450) and r(1700) are included

analysis (preliminary) 347 million BB hep-ex/0608002 m’ and q’ are the transformed Dalitz variables

analysis (preliminary) 449 million BB hep-ex/0609003 Dalitz + Isospin (pentagon) analysis 26(Dalitz) + 5(Br(rp), Br(r+p0), Br(r0p+), A(r+p0), and A(r0p+)) r+p- r-p+ r0p0 Signal SCF BB bkg continuum mass helicity

a constraint from (preliminary) [0,8]o U [60,95]o U[129,180]o at 68.3% C.L. 1- C.L. 1- C.L. a (deg) a (deg)

a constraints Belle rp result is not included. It will weakens the suppression of solutions around 0o and 180o. CKMfitter http://ckmfitter.in2p3.fr/ UTfit http://utfit.dreamhosters.com/ a constraints Global Fit B-Factories aB-Factories = [ 93 ] º +11 -9 aB-Factories = [92 ± 7]o (SM Solution) aGlobal Fit = [93 ± 6]o Nice agreement aGlobal Fit = [ 98 ] º +5 -19

Pending Issues Cpp = - 0.16 ± 0.11 ± 0.03 Discrepancy on Cpp Solutions at 0o and 180o should be (more) suppressed. Using rp: nice suppression from BaBar, not from Belle. Background modeling. Interference with other resonances or non-resonant component in rp, rr modes. Subtleties on statistical analysis with small statistics. Cpp = - 0.16 ± 0.11 ± 0.03 Cpp = - 0.55 ± 0.08 ± 0.05

Uncertainties on a extraction Possible contribution of EW penguin and isospin breaking effect. EW penguin effect seems to be small (~2°). Other isospin breaking effect ~ O(1°). [M.Gronau and J.Zupan PRD 71, 074017(2005)] I=1 contribution due to finite width of r mass (rr mode). [A.Falk et al. PRD 69, 011502(R)] Too small to be an issue at B-factories

Summary and Outlook The three modes are complementary. Need to study them all. Good agreement between the CKM fit (a determined by others) and direct measurements. Still a lot to do. Refine previous analysis and exploit new ideas: a from B->a1p ? Constraint on a from B0->r+r- and B+->K*0r+ [M. Beneke et al., Phys. Lett. B638, 68(2006)] Doubling of statistics at the B-factories is much needed. Looking forward to LHC and to a Super B-Factory.

Backup Slides

Trickle injection at the B Factories Best shift, no trickle Best shift, LER only trickle Nov 2003 Best shift, double trickle Mar 2004 PEP-II: ~5 Hz continuous KEKB: at ~5-10 min intervals PEP-II Lumi HER current LER current

Detection of Internally Reflected Cherenkov light The high optical quality of the quartz preserves the angle of the emitted Cherenkov light. The measurement of this angle, in conjunction with knowing the track angle and momentum from the drift chamber, allows a determination of the particle mass. qc = arcos (1/nb)

DIRC: Control samples for p and K Projection for 2.5 < p < 3 GeV/c

Time Dependent CP Asymmetry mixing decay Amplitude ratio CP eigenvalue

:results (preliminary) Cpp = - 0.16 ± 0.11 ± 0.03 Spp = - 0.53 ± 0.14 ± 0.02 (Spp, Cpp) = (0.0, 0.0) excluded at 3.6 s

:results (preliminary) App = + 0.55 ± 0.08 ± 0.05 Spp = - 0.61 ± 0.10 ± 0.04 Observation of Direct CPV at 5.5 s Observation of mixing-induced CPV at 5.6 s

a constraint from

a constraint from

formalism Direct CP Violation CP violation in the interference with and without B mixing.

parameters (prelim)

Direct CP violation in Significance for non-zero DCPV: BaBar: 3.0 s Belle: 2.4 s

Differences in peak height Courtesy of Marcella Bona Differences in peak height