Measurements of q 2 Dependence of D 0  K  m + n and p  m + n Form Factors.

1. Measurements of q2 Dependence of D0 Km+n and p m+ n Form Factors. • Content ( hep-ex/0410037, PLB 607 (2005) 233) • Part I: Theories of charm semileptonic decays. • Part II: Reconstructing D0Km+n and p m+ n. • Part III: q2 dependence, f+(q2) • Deconvolution approach: Non-parametric analysis. • Parametric fit. • PartVII: Summary APS Meeting April 17, 2005Tampa, FL Doris Y. KimUniversity of IllinoisUrbana-Champaign FOCUS / Doris Kim

2. I: Charm semileptonic decay as tests of LQCD The hadronic complications are contained in the form factors, which can be calculated via non-perturbative Lattice QCD, HQET or quark models. The decay rates are computed from first principles (Feynman diagrams) using CKM matrix elements. f, p, etc. Charm SL decays provide a high quality lattice calibration, which is crucial in reducing systematic errors in the Unitarity Triangle. The techniques validated by charm decays can be applied to beauty decays. FOCUS / Doris Kim

3. Theories of D Pseudoscalar ln decays is the easiest point for LQCD calculation. P at rest in D frame hep-ph/0408306PRL 94 (2005) 011601 cleanest theory highest rate The lattice community is actively fixing the situation and calculating f+ as a function of q2. Simple kinematics  Easy to extract form factors. But a major disconnection exists between experiment and theory. In the past, theories worked best where experiments worked worst. FOCUS / Doris Kim

4. What do we measure? Until quite recently, one required a specific parameterized form to bridge the gap between a theory and an experiment, since neither an experiment nor a theory had clean f+(q2) information. Now we have enough data, hence, • Method I: f+(q2) shape obtained non-parametrically by deconvolution. • Method II: Or fit f+(q2) using specific forms. f+(q2) parameterization (old) pole (old) ISGW1 ISGW2 Updated version. modified pole Spin 1 D*S FOCUS / Doris Kim

5. II. Reconstructing D0 Km+n and p m+ n. Selection 12,840 Km+n • A good muon candidate. • Cerenkov ID for K/p candidates. • Good CL’s for D production/decay vertices, and L/s > 5 between two vertices. • D* tag required, and wrong sign soft p subtraction. cut rs-ws /GeV/c2 MC ws ~ Neutrino Reconstruction • Km rest frame • The D and D* mass constraints the neutrino lies on a cone around the soft pion. • Pick the f that points the D closest to the primary vertex. FOCUS / Doris Kim

6. III.a q2 dependence: Deconvolution approach. A deconvolution matrix is constructed from the number of events generated in the i-th q2 bin that end up reconstructed in the j-th q2 bin. This matrix is then used to correct data for resolution and efficiency. We actually use a 10  10 matrix FOCUS / Doris Kim

7. Correcting for charm backgrounds inD0 Km+n After subtracting known charm backgrounds,f+(q2) is an excellent match to a pole form with mpole= 1.91  0.04  0.05 GeV/c2 or  = 0.32 (CL 87%, 82%). The background only affects the highest q2 bins. FOCUS / Doris Kim

8. III.b Parameterized f+(q2) for D0 Km+n/pm+n n ql D0 Wrest frame m 6574 Km+n events • 2-dim fit: cos ql, q2 • Signal ~ MC with reweighted intensity. • Backgrounds are floated within known uncertainties. 288 pm+n events FOCUS / Doris Kim

9. Comparing to Lattice Gauge Result Km+n FOCUS / Doris Kim

10. Other q2 information in D0 K l n /pl n form factor f+(q²) Based on 820 events single-pole model single-pole model Cleo 2004 Kln pole mass is pln pln pole mass is Kln It disfavors ISGW2 form by ~4.2s Kln Preliminary study pln FOCUS / Doris Kim q² / GeV²

11. Summary of D0 K l n/ p l n Results Clearly the data does not favor the simple Ds* pole New world average for K l n Kln New world average for p l n FOCUS / Doris Kim

12. Question slides FOCUS / Doris Kim