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Precision Determination of Vub at e+e- B Factory: Insights from Jik Lee & Ian Shipsey

This document presents advanced methods for determining the quark coupling Vub at e+e- B factories, focusing on inclusive and exclusive decays. It details challenges in endpoint determination due to large backgrounds, theoretical errors, and model dependence. The analysis covers lepton spectrum endpoints and charm semileptonic decays, emphasizing the importance of experimental techniques like full reconstruction and B-tagging for improving measurement precision. As data samples grow, insights will enable better extraction of Vub and understanding of B decays.

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Precision Determination of Vub at e+e- B Factory: Insights from Jik Lee & Ian Shipsey

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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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