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Precision determination of Vub at an e+e- B factory

Precision determination of Vub at an e+e- B factory. Jik Lee & Ian Shipsey Purdue University. Current Methods of determining V ub I. Endpoint of the inclusive lepton spectrum II. Exclusive decays Methods of determining V ub with small theoretical errors

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Precision determination of Vub at an e+e- B factory

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  1. Precision determination of Vub at an e+e- B factory Jik Lee & Ian Shipsey Purdue University • Current Methods of determining Vub • I. Endpoint of the inclusive lepton spectrum • II. Exclusive decays • Methods of determining Vub with small theoretical errors • 1) Inclusive: low hadronic mass region • 2)Inclusive: endpoint of the q2 spectrum • 3)Exclusive: lattice • Calibration with charm semileptonic decays • Rate and slope in Bl Snowmass July 2001

  2. I. Endpoint Determination of Vub Challenges: Large b to c bkgd Limited understanding of decay spectrum/form factors Large extrapolation (5-20% bu in endpoint) endpoint dominated by several exclusive modes, so models must be used limited by theoretical error • lepton endpoint, beyond the kinematic limit for b  c • 1% of lepton spectrum, (CLEO’93) • Measures |Vub/Vcb| Non-resonant bkgd Endpoint useful as reality check of more precise methods

  3. Vub method II :Exclusive decays * Method 2: exclusive reconstruction require neutrino consistency. * To keep bkgd tractable work in endpoint * Measures Vub * Drawback: extracted Vub relies on poorly known form factors * Model dependence dominates • to reduce theory error by X2 need to know: • how much of the rate is in acceptance ? ~10% • the overall normalization?~ 15% • 2 solutions: theory provides an absolute normalization point (as in bc) • minimise extrapolation i.e. maximize acceptance and test theory CLEO PRD 61 052001 3.3 x 10 6 BB (Averaged with published CLEO Bl) stat sys model

  4. Exclusive Decays and Vub • Beginning to probe distribution • but little discriminating power between models at high lepton energy (where the measurement is performed) • no easy way to choose between models • hard to quantify systematic error associated with a model • although experimental statistical errors on Vub will tend to zero with large data sets dominant uncertainties are theoretical

  5. New Inclusive Methods for Vub • To make major experimental progress in Vub need powerful suppression of b cl provided by full reconstruction of companion B • B tagging efficiency CLEO II/II.V is ~ 2.1 x 10-3 (2.85 x 10-3 in BaBar book, use this number) • technique impractical for (most) analyses with pre-B factory samples, but will be used extensively in future • Assume 1% systematic error in lepton ID, 2% systematic error in tracking. To distinguish bu from bc theoretically: better better q2 spectrum > mhad spectrum > Elepton spectrum But experimental difficulty is in opposite order

  6. Inclusive: Hadronic mass spectrum • select b u with mx< mD(~90% acceptance for b u ) • require: Q(event) =0, 1 lepton/event, missing mass consistent with neutrino • just look at mhad< 1.7 , cut with largest acceptance and hence least theoretical uncertainty, keep bkgd small with p(lepton)>1.4 GeV TRKSIM CLEO III FAST MC

  7. Inclusive: Hadronic mass spectrum • ~100 b ulv events/30 fb-1 : Method attractive with large data samples • Systematic error is dominated by charm leakage into signal region. Depends on S/B ratio & B. Assume B = 0.1 B @ 100 fb-1. • S/B can be improved by vertexing. • B can be reduced as Br(B [D*/D**/D/D ] l) and the form factors in these decays become better measured. B can also be reduced through better knowledge of D branching ratios. • Assume these improvements lead to B = 0.05 B @ 500 fb-1 or higher Ldt. • Then the systematic error dominates for Ldt 1000 fb-1 . • Br(b ulv) ~ 3.4% , Vub~1.7% • Recall theoretical error is ~ 10% year Ldt # bul #b cl Vub Vub Vub (stat) (sys) (expt) 2002 100 fb-1 335 127 3.2% 2.2% 3.9% 2005 500 fb-1 1675 635 1.5% 1.5% 2.1% 2010 2000 fb-1 6700 2540 0.7% 1.5% 1.7%

  8. Inclusive: endpoint q2spectrum • Inclusive q2 endpoint, lose statistics, gain in theoretical certainty • ~40 b ulv events/30 fb-1 Method attractive with VERY large data samples. TRKSIM CLEO III FAST MC look at q2 > 11.6 , and 10.8 keep bkgd small with p(lepton)>1.4 GeV One experimental advantage compared to mhad is that S/B is more favorable 10.8 11.6 S/B: 4/1 18/1

  9. Inclusive: endpoint q2 spectrum • Systematic error is dominated by charm leakage into signal region for q2>10.8 (S/B ratio & B, same issues as mhad) . • Assume B = 1.0 B @ 100 fb-1, and B = 0.2 B @ 500 fb-1 or higher Ldt. • For q2 > 11.6 (S/B = 18/1), systematic error (tracking and lepton ID) dominates @ Ldt 1000 fb-1 • 2000 fb-1Br(b ulv) ~ 3.2% , Vub~1.6%. • Recall theoretical uncertainty ~ (5 – 10) % For q2 > 11.6: year Ldt # bul #b cl Vub Vub Vub (stat) (sys) (expt) 2002 100 fb-1 127 7 4.6 % 3.0% 5.5% 2005 500 fb-1 635 36 2.0 % 1.2% 2.3% 2010 2000 fb-1 2538 144 1.0 % 1.2% 1.6%

  10. Charm Semileptonic Decay and Vub • Semileptonic B decays are used to determine the quark couplings Vub and Vcb as the strong interaction is confined to the lower vertex • In charm semileptonic decays, as Vcs (or Vcd) is known from three generation unitarity the hadronic current can be measured • D system provide a way to test ideas about hadronic physics needed to get Vub Vcb in B decays. Ideas-= HQS, lattice…. model l known unitarity

  11. Charm Semileptonic Decays l • The complexity of the hadronic current depends on the spin of the initial and final state meson and the mass of the final state quark • Simplest case • at same pion energy: • form factor ratio equal by Heavy Quark Symmetry, corrections order 20% • but little known about heavy to light transitions need q2 dependence in both B and D decay to assess the size of the of 1/m corrections. • Lattice also determines the form factors, in principle it may be most precise method. Will concentrate on this method here... B  lv HQS D  l

  12. A lattice determination of Vub • The lattice is capable of predicting the absolute normalization of the form factor in Bl or D l to ~few%.  Vub/Vub ~1-2% • But lattice must be calibrated! • Within the quenched approximation all systematic errors are accounted for and smaller than statistical errors • A comparison of lattice and expt. in D l can give an estimate of the size of the effect of using the quenched approximation • compare lattice to data, if quenching is understood shape should be same STEP ONE: CALIBRATE LATTICE with D l STEP TWO: MEASURE d/dpin Bl STEP THREE: MEASURE (Bl) + lattice Vub

  13. Charm Factory vs. B Factory • The best way to d/dq2 in D l is at a charm factory (e.g. CLEO-c) • Kinematics at threshold cleanly separates signal from background B Factory S/B ~1.3 cf CLEO II S/B 1/3 Charm Factory no background TRKSIM CLEO III FAST MC CLEO II PRD 52 2656 (1995) signal

  14. Step I Calibrate Lattice: Dl • Measure : TRKSIM CLEOIII FAST MC compare to lattice prediction ex: hep-ph/0101023 El-Khadra Note: lattice error large ~15% on normalization but in future 1-few % predicted :

  15. Step II d(Bl)/dq2 TRKSIM CLEO III FAST MC TRKSIM CLEO III FAST MC For the same as D l: compare to lattice prediction ex: hep-ph/0101023 El-Khadra

  16. Step III Vub • If data and lattice agree for 0.4<p<0.8GeV, still need faith that lattice is correct for p > 0.8 GeV. • Lattice can compute rate to few %. How much data would we need to have a comparably small experimental error? • Assume S/B = 10/1 and B = 0.1 B allp • Such large data samples are beyond the reach of existing B factories that expect accumulate ~2000 fb-1 by 2010. • SBF !!! year Ldt # bul S/B Vub Vub Vub (%) (10/1) (stat) (sys) (expt) 2008 1000 fb-1 590(29) 59(3) 4.3(9.8) 1.2 4.5(9.9) ? 10000 fb-1 5900(290) 590(30) 0.7(3.1) 1.2 1.4(3.3) 0.4<p<0.8

  17. Conclusions • All possible theoretically clean measurements are very important, even if they are redundant within the standard model • Must pursue both CP violating and CP conserving measurements (i.e. Vub) to test SM and look for new physics • Inclusive methods will achieve Vub ~ few % (expt) ~ 5 -10% (theory) q2 endpoint is the method of choice. • The first test of CKM at the 10% level will come from this measurement and Vcb , sin2, and Vtd/Vts • If the lattice can reach the predicted accuracy (1-2%) it will become the method of choice for future measurements of Vub (and Vcb) • Lattice must be calibrated. A charm factory can provide crucial tests of lattice predictions. • A ~10,000-20,000 fb-1 data sample is required to attain a total experimental error of 1-2% on Vub commensurate with the lattice error.

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