Extract the partial rates We can make fits to the partial decay rates to extract (1) normalization f + (0)|V cx | (2) Form factor shape parameters r 1 and r 2 (or just r 1 ) for series M pole for simple pole α for modified pole r for ISGWII Assuming | V cd |=  (CKM unitarity) 1 σ bands (stat and syst) by FNAL-MILC-HPQCD Introduction Fits to the U Distributions D Tagging at 3770 MeV Summary Form factors as a stringent test of LQCD |V cs | and |V cd | Results Bo Xin, Ian Shipsey, Purdue University, CLEO Collaboration Improved measurements of D meson semileptonic decays to π and K mesons  Goals of CLEO-c semileptonic decay analysis program To provide validation and calibration data for LQCD and other theoretical approaches thereby enabling theory (especially LQCD) to be applied to B physics (|V ub |). To measure |V cs | and |V cd | with a validated theory  We have perform an analysis using CLEO-c’s final data set to meet these goals Most precise branching fraction determinations for D  Ke + and D  πe + Stringent test of LQCD calculations of semileptonic form factors. D  Ke +, D  πe + form factors are found to be in general agreement with LQCD. Best direct measurement of |V cs |, measured to ±1.1%(experimental) ± 10%(theory). |V cd | is measured to ±3.1%(experimental) ± 10%(theory). D  K/πe + Branching fractions Standard D Tags (Tag): One D in the event is fully reconstructed in a hadronic decay mode, the second D decays semileptonically  The three charge +2/3 quarks and three charge -1/3 quarks change identity via the weak interaction with a probability proportional to the elements of the 3x3 unitary Cabibbo-Kobayashi-Maskawa matrix. These nine elements are related to four fundamental parameters of the standard model of particle physics and must be determined by experiment.  Semileptonic decays are the principal process for measuring the CKM matrix elements  Strong interaction effects are confined to the hadronic current and are parameterized by form factors in massless lepton limit For P to P transitions  The theory must predict the absolute normalization of the form factors:  As |V cd | and |V cs | are tightly constrained by the unitarity of the CKM matrix. Measurements of charm semileptonic decay rates and form factors rigorously test the theory (e.g. LQCD)  Validated theory can then be applied to B decays to determine |V ub |, which is the one of the most poorly known CKM matrix elements from fits to M bc from fits to U Pure DD, zero additional particles, ~5-6 charged particles per event ~6.6x 10 5 D 0 and ~4.8 x 10 5 D + tags reconstructed from ~5.4 x 10 6 DD events We tag ~20% of the events, compared to ~0.1% of B’s at the Y(4S) 818 pb (full data set) World’s largest data set at GeV (ρ, η) ~|V ub | Δm d,s l B  l  D HQS Suffer from large theory uncertainty Moriond 09  We perform binned likelihood fits to U distributions in each q 2 bin and tag mode  Signal shapes are taken from signal MC, smeared with double Gaussians  Background shapes are taken from MC with all DD and non-DD decays 4 of 27 U fits S/N~300/1 Signal events~14000 U resolution~10 MeV q 2 resolution~0.008 GeV 2 /c 4 4 of 54 U fits 4 of 42 U fits 4 of 21 U fits S/N~40/1 Signal events~1400 U resolution~10 MeV q 2 resolution~0.008 GeV 2 /c 4  For semileptonic D : U peaks at zero for real semileptonic decays An absolute measurement, independent of the integrated luminosity and number of D mesons in the data sample Precision measurements from BABAR/Belle/CLEO-c. CLEO-c most precise. Theoretical precision lags experiment. 1 σ bands (stat and syst) by FNAL-MILC- HPQCD Modified pole model used to compare with LQCD Form factor measures probability hadron will be formed Assuming | V cs |=  (CKM unitarity) α : CLEO-c prefers smaller value for shape parameter than other experiments f + (0): experiments (1.2%) consistent with LQCD (10%) CLEO-c is most precise. Theoretical precision lags. α : CLEO-c measurements are compatible with LQCD f + (0): experiments (2.9%) consistent with LQCD (10%). CLEO-c is most precise. Theoretical precision lags. arXiv: (accepted PRD Jul ) arXiv: (accepted PRD Jul ) CLEO-c: the most precise direct determination of |V cs | * CLEO-c: νN remains most precise determination * PDG2002 The data determine |V cs(d) |f + (0). To extract |V cs(d) |, we combine the measured |V cs(d) |f + (0) values using the Becher-Hill parameterization with (FNAL-MILC-HPQCD) for f + (0) * * PDG2002 THEORY UNCERTAINITY REMOVED * PDG2002 * The uncertainties on our results are dominated by uncertainties from LQCD  Theoretical precision lags. In particular,  CLEO-c measures form factor normalizations for D  Ke +, D  πe + to 1% and 3%, respectively,  while LQCD predicts them at 10% level.  We are eagerly awaiting more precise LQCD calculations of semileptonic form factors CLEO-c Now CLEO-c full data set + 3-4% theory uncertainties Plots by Sebastien Descortes-Genon & Ian Shipsey See also talk by Descotres-Genon at joint BABAR-Belle-BESIII-CLEO-c Workshop 11/07, Beijing