Selected Topics on Open Charm Physics at CLEOc

Selected Topics on Open Charm Physics at CLEO-c Main topics: Overview the CLEO-c experiment and its physics program (3770) D 0 D 0 K+ -, D 0 K-e+ Absolute Hadronic D 0 and D+ Branching Fractions Preliminary Results for Absolute Branching Fractions and Form Factor Measurements in and Batbold Sanghi July, 2006 K+ - Purdue University (CLEO K- e+ Collaboration) Selected Topics on Open Charm Physics from CLEO-c 1

CLEO-c and the CKM Matrix n The CKM matrix provides the only mechanism for CP violation in the SM n An important goal of flavor physics is to measure and (over)constrain the parameters in the CKM matrix (4 parameters) to test the SM n Non-perturbative hadronic effects limit our ability to extract fundamental parameters from experimental measurements n CLEO-c provides unique measurements in the charm sector that test theory and help reduce hadronic uncertainties n CLEO-c tested theory can then be applied to B decay processes to extract CKM matrix elements (especially Vub and Vtd) July, 2006 Selected Topics on Open Charm Physics from CLEO-c Recent status Status with theory errors reduced) 2

An example of a test of Lattice QCD Theories of Strong Interactions (LQCD) n Measure form factors in D l at CLEO-c July, 2006 n validate LQCD calculations form factors n use LQCD to extract Vub from B l Selected Topics on Open Charm Physics from CLEO-c 3

An example of a test of Lattice QCD n m is well measured n But |Vtd| from m has a large uncertainties from f. B Theories of Strong Interactions (LQCD) n measure f. D in D l July, 2006 n validate theoretical calculations f. B ~f. B (LQCD)/ f. D (LQCD) f. D n Use f. B to extract |Vtd| Selected Topics on Open Charm Physics from CLEO-c 4

CLEO-c impact n I will focus on two CLEO-c analyses that have impact on Vcd, Vcs, Vub and Vcd: D semileptonic B’s and form factors in D hadronic branching fractions (Analysis by Cornell, Purdue and CMU) Including: and (Analysis by Purdue and SMU, my main thesis topic) Vud/Vud 0. 1% n e p Vcd/Vcd 7% D CLEO-c l K l l D K Vts/Vts 39% Bd Bs Bs CLEO-c + Lattice QCD +B factories Vub/Vub 15% l B Vcs/Vcs =16% Vtd/Vtd =36% Bd Vus/Vus =1% Vcb/Vcb 5% l B D Vtb/Vtb 29% t W b CLEO-c + Lattice QCD +B factories + ppbar D and Ds leptonic branching fraction July, 2006 Selected Topics on Open Charm Physics from CLEO-c 5

The CLEO-c detector n The main components of the CLEO-c detector were developed for B physics at the Y(4 S). n Minor modifications ¡ Replaced silicon with 6 layer inner drift chamber B field 1. 5 T 1. 0 T Over 20 years of data taking at Y(4 S) Started data taking in the fall of 2003 Note: Log Scale ¡ P/P = 0. 6% at 1 Ge. V E/E = 2% at 1 Ge. V = 5% at 100 Me. V Excelent electron and hadron ID An event taken at (4 S) n Advantages at (3770) ¡ ¡ ¡ July, 2006 Pure DD, no additional particle Low multiplicity High tagging efficiency Selected Topics on Open Charm Physics from CLEO-c 6

CLEO-c data samples Three generations of CLEO-c analyses at the (3770): n Oct-03 through Jan-04: Luminosity = 56 pb 1 all results are published(D hadronic branching fraction) n Sep-04 through Apr-05: Luminosity = 225 pb 1 most analyses are on-going(D semileptonic B’s and form factors) n Future running: projected total Luminosity = 750 pb 1 CLEO-c is also collecting data above the Ds. Dsbar production threshold (goal 750 pb 1) and lower energies at the (2 S). July, 2006 Selected Topics on Open Charm Physics from CLEO-c 7

Absolute Hadronic D 0 and D+ Branching Fractions Introduction and Overview of the Analysis Measurements of Absolute Hadronic Branching Fractions Summary July, 2006 Selected Topics on Open Charm Physics from CLEO-c 8

Overview of Technique Double tagged D Single tagged D e e+ K+ n. Use K + e e+ K+ 3 D 0 modes and 6 D+ modes ¡ K- + , K- + , 0 , K - + , + - ¡ K- + + , K - + + 0 , K s + + + , K - K+ + modes D " K + and K + + normalize many B measurements from other experiments. ¡Reference July, 2006 Selected Topics on Open Charm Physics from CLEO-c 9

Overview of Technique n Determine separately the ¡ n and yields 18=2 (3+6) single tags(ST) and 45(=32 + 62) double tag yields(DT) In a combined 2 fitter (physics/0503050), we extract 9 branching ratios and yields : ¡ ¡ Include both statistical and systematic errors (with correlations): All experimental inputs treated consistently. Efficiency, cross-feed, background corrections performed directly in fit. Some systematic errors for and completely cancelled n Branching fractions are independent of L and cross-sections. n The main variables used in the reconstruction are: July, 2006 Selected Topics on Open Charm Physics from CLEO-c 10

Yield Fits n Unbinned ML fits to MBC (1 D for ST, 2 D for DT) ¡ ¡ ¡ n n Signal function includes ISR, (3770) line shape, beam energy smearing, and detector resolution. Signal parameters from DT fits, then apply to ST. Background: phase space (“ARGUS function”). D and D yields and efficiencies separated. c MBC (log scale) for ST modes: Two dimensional fit allows to separate ¡ ¡ ISR and beam energy spread (causes correlated shifts in the mass of the two D’s) Detector resolution (uncorrelated among these D’s ) DT signal shape Detector resolution R IS y g er & am e b All D 0 DT 2484± 51 July, 2006 Selected Topics on Open Charm Physics from CLEO-c en All D+ DT 1650± 42 11

Systematic uncertainties n Dominant error: MC simulation of tracking, K 0 S, and 0 finding efficiencies: ¡ Correlated errors among all particles of a given type add up quickly. ¡ Missing mass technique measure syst errors by comparing data and MC: Ø Fully reconstruct entire event, but deliberately leave out one particle. Ø Fraction of MM peak where the last particle is found = efficiency. Example: K efficiency from D 0 " K + e ≈ 91% in fiducial volume K found (MC) K not found (MC) + July, 2006 Source Uncertainty (%) Tracking/K 0 s/ 0 0. 7/3. 0/2. 0 Particle ID 0. 3 /1. 3 K Trigger e < 0. 2 E cut 1. 0— 2. 5 per D FSR 0. 5 ST / 1. 0 DT (3770) width 0. 6 Resonant substructure 0. 4— 1. 5 Event environment 0. 0— 1. 3 Yield fit functions 0. 5 Data processing 0. 3 Double DCSD 0. 8 K- + 0, etc. Selected Topics on Open Charm Physics from CLEO-c 12

Fit Results (PRL 95, 121801) n Precision comparable to PDG-04. n Statistical errors: ~2. 0% neutral, ~2. 5% charged from total DT yields. n (systematic) ~ (statistical). ¡ n Many systematic errors are measured in data and will be improved with time. Our MC simulation includes FSR ¡ n The CLEO-c measurement is the single most precise measurement for every mode Using efficiencies without FSR would lead to lower B. NDD includes continuum and resonant production. July, 2006 Selected Topics on Open Charm Physics from CLEO-c 13

Comparisons with other measurements n Reasonable agreement with PDG for all modes ¡ n PDG global fit includes ratios to K- + or K- + +. No FSR corrections in PDG measurements Our measurements are also correlated (through statistics and efficiency systematics). July, 2006 Selected Topics on Open Charm Physics from CLEO-c B(D+ " K- + +) Overall C. L 25. 9% B(D 0 " K +) n Other direct meas. PDG numbers are correlated among modes ¡ n Measurements and errors normalized to PDG. 14

Results for D cross sections n Using a measurement of the luminosity of the data sample (55. 8/pb), we obtain n Our cross sections are in good agreement with BES [Phys. Lett. B 241, 278(1990) ] and higher than those of MARKIII [Phys. Rev. Lett. 60, 89 (1988) ] n CLEO-c inclusive: July, 2006 Selected Topics on Open Charm Physics from CLEO-c PRL 96, 092002 15

Absolute Branching Fractions and Form Factor Measurements in and Introduction and Overview of the Analysis Measurements of Absolute Branching Fractions Measurements of Form Factors Summary July, 2006 Selected Topics on Open Charm Physics from CLEO-c 16

Introduction n Semileptonic decays are an excellent laboratory to study ¡ ¡ n n Gold-plated modes are P P semileptonic transitions as they are the simplest modes for both theory and experiment: ¡ Cabibbo favored : ¡ Cabibbo suppressed : Main goals of the analysis: ¡ ¡ n Weak physics QCD physics Measure efficiency-corrected absolutely-normalized decay rate distributions and form factors Measure form factor parameters to test LQCD and model predictions We analyze both D 0 and D+ decays. By isospin invariance ¡ . This is a nice cross check and adds statistics to improve statistical precision. July, 2006 Selected Topics on Open Charm Physics from CLEO-c 17

Overview of the analysis n Reconstruct one of the two D’s in a hadronic decay channel. It is called a tagging D or a tag. Two key variables in the tagging D reconstruction are: (3770) D 0 D 0 K+ -, D 0 K-e+ ¡ ¡ n n n K- Reconstruct from the remaining tracks and showers the observable particles in the final state of a semileptonic decay. K+ - Define an observable that can be used to separate signal and background as where Emiss and Pmiss are the missing energy and momentum in the event, approximating the neutrino E and P. The signal peaks at zero in U. Branching fractions are obtained as e+ Obtained from Fits to U Obtained from Fits to Mbc July, 2006 Selected Topics on Open Charm Physics from CLEO-c 18

D 0 and D+ tag yields in 281/pb of DATA Examples of Mbc for tag modes in the data ~30% event tagging efficiency ~20% event tagging efficiency Tagging provides a beam of D mesons allowing semileptonic decays to be reconstructed with no kinematic ambiguity July, 2006 Selected Topics on Open Charm Physics from CLEO-c 19

Measurements of Absolute Semileptonic Branching Fractions July, 2006 Selected Topics on Open Charm Physics from CLEO-c 20

Fits to U in 281 pb-1 of Data for N~7000 n Main backgrounds for ¡ ¡ n N~700 Main backgrounds for ¡ ¡ ¡ July, 2006 Electron fakes from kaons Selected Topics on Open Charm Physics from CLEO-c 21

Fits to U in 281 pb-1 of Data for n N~2900 Main backgrounds for ¡ ¡ N~290 n Main Backgrounds for ¡ ¡ July, 2006 Selected Topics on Open Charm Physics from CLEO-c 22

Preliminary Results for BFs July, 2006 Selected Topics on Open Charm Physics from CLEO-c 23

Comparisons with other experiments and projections for 750 pb-1 Statistically limited Systematically limited Reasonable agreement July, 2006 Selected Topics on Open Charm Physics from CLEO-c 24

Measurements of Semileptonic Form Factors July, 2006 Selected Topics on Open Charm Physics from CLEO-c 25

Two Fitting Methods: Fit A and Fit B n The observed decay rate is related to the true decay rate in the following way: in terms of Acceptance and Smearing functions. The fit has to take into account both effects. We have developed and tested two types of fits. n Fit A is a fit to efficiency-corrected and absolutely-normalized d /dq 2 distributions. This fit is a good match for CLEO-c data as the q 2 resolution is excellent. Fit A is our primary fit as the main goal of our analysis is to obtain d /dq 2 and f+(q 2). n Fit B is a fit to the observed decay rate according to a procedure described in D. M. Schmidt, R. J. Morrison and M. S. Witherell in Nucl. Instr. and Meth. A 328 547(1993). The technique makes possible a (multidimensional) fit to variables modified by experimental acceptance and resolution. This method has been used by CLEO several times before, for example, to measure form factor ratios in c e and B D*l. n Both fitting methods were tested using large Monte Carlo samples. Two fits provide cross-checks. July, 2006 Selected Topics on Open Charm Physics from CLEO-c 26

q 2 resolutions and Raw q 2 distributions q 2 resolution D 0→K-e+ν Raw q 2 distribution D 0→K-e+ν q 2 ~ 0. 012 Ge. V 2 7000 events S/B > 300/1 CLEOIII(Y(4 S): q 2 ~ 0. 4 Ge. V 2 CLEO-c( (3770)): q 2 ~ 0. 012 Ge. V 2 Note the background in blue D 0→π-e+ν q 2 ~ D 0→π-e+ν 0. 011 Ge. V 2 July, 2006 700 events S/B ~40/1 Selected Topics on Open Charm Physics from CLEO-c 27

Efficiency corrected and absolutely normalized decay rates (DATA) Subtracting background applying efficiency corrections (matrices) we find absolute decay rates in bins of q 2 (The bin width is equal q 2 max/10, the last bins for D 0 e+ and D+ 0 e+ are 2 and 3 times wider): July, 2006 D 0→K-e+ν D+→Kse+ν D 0→π-e+ν D+→π0 e+ν Selected Topics on Open Charm Physics from CLEO-c 28

Efficiency corrected and absolutely normalized decay rates (DATA) The spectra on the last slide are tabulated here: These rates can be fit to any form factor model w/o knowing CLEO acceptance and resolution July, 2006 Selected Topics on Open Charm Physics from CLEO-c 29

Form Factor Models n Simple pole model : n Modified pole model (BK) [Phys. Lett. B 52, 478, 417(2000) ] : n Series parameterization [. Becher and R. Hill, hep-ph/0509090] n ISGW 2 [Phys. Rev. D 52, 2783, (1985) ] : July, 2006 Selected Topics on Open Charm Physics from CLEO-c 30

Tests of Fit A and B n The fitting techniques were tested by making ensembles of fits to mock data samples with the number of signal events equal to the expected number of events in the data. We have tested: Example: ¡ ¡ ¡ Fits for all 4 form factor models simultaneous fits to isospin conjugate modes fit with two free parameters [f+(0)Vcs and a form factor shape parameter] The fitter is consistent with being unbiased. n The efficiency of fits is tested using the Cramer-Rao inequality: D 0 - e+ 700 events C-R Prediction Our Fits D 0 K - e + 7000 events The fitter is consistent with being fully efficient. July, 2006 Mpole (Ge. V) Selected Topics on Open Charm Physics from CLEO-c 31

Example of a fit (DATA) Modified Pole (BK) Model: July, 2006 D 0→K-e+ν D+→Kse+ν D 0→π-e+ν D+→π0 e+ν Selected Topics on Open Charm Physics from CLEO-c 32

DATA Cross Check 1 By isospin invariance: f+(q 2)Vcs D 0→K e+ν D+→KSe+ν q 2 (Ge. V 2) The plots show: f+(q 2)Vcd D 0→π e+ν D+→π0 e+ν The q 2 spectra for isospin conjugate modes are consistent. July, 2006 q 2 (Ge. V 2) Selected Topics on Open Charm Physics from CLEO-c 33

Cross check 2: Hadron & Electron Spectra & W Helicity n Quantities that are not constrained in the fit are well described D 0→K-e+ν D+→Kse+ν D 0→π-e+ν D+→π0 e+ν Hadron Momentum Electron Momentum cos W July, 2006 Selected Topics on Open Charm Physics from CLEO-c 34

Systematic Uncertainties for Form Factor Shape Parameters n Systematic uncertainties that are independent of q 2 (ex: tag Mbc fit function) do not change the decay rate shape and hence have a negligible contribution to the shape parameter uncertainty n Systematic effects correlated with the hadron (K/KS/ / 0) momentum, change the decay rate distribution and lead to modest systematic uncertainties eff PK(Ge. V) Kaon momentum vs q 2 Kaon ID efficiency Pe(Ge. V) q 2 (Ge. V) Lepton momentum vs q 2 (Ge. V) July, 2006 PK ~ 100 Me. V Few events This correlation is not as strong as the hadron momentum correlation Our studies indicate that the total systematic uncertainty is much smaller than the statistical uncertainty for each semileptonic mode Selected Topics on Open Charm Physics from CLEO-c 35

Fit results with two parameters The shape parameters for modified pole, simple pole model and series parameterization with two parameters : n n The normalization parameter for modified pole model and series parameterization with two parameters : July, 2006 Selected Topics on Open Charm Physics from CLEO-c 36

Comparison with Other Measurements D→K n n e+ ν D → π e+ ν First measurements of form factors for the D+ modes; CLEO-c is the most precise for D→πe+ July, 2006 Selected Topics on Open Charm Physics from CLEO-c 37

Comparison with Other Measurements D → π e+ ν D → K e+ ν n n First measurements of form factors for the D+ modes; CLEO-c is the most precise for D→πe+ July, 2006 Selected Topics on Open Charm Physics from CLEO-c 38

Confidence levels for fits results with 2 parameters The confidence levels for fits with 2 parameters : n n Which parameterization does the data prefer? The confidence levels for all parameterizations are comparable, as the functional forms for the parameterization are similar and the shape parameters are not fixed. However, the CLEO-c data exclude the ISGW 2 (K/ ) , pole (K) and modified pole (K) parameterizations when the shape parameters are fixed to the physical values. July, 2006 Selected Topics on Open Charm Physics from CLEO-c 39

Data vs. physical basis for shape parameters #1: ISGW 2 n Form factor shape parameters in the data for ISGW 2 are inconsistent with the model predictions n Output Physical value for ISGW 2 D 0 K - e + 1. 567 ± 0. 045 1. 131 D 0 - e+ 1. 997 ± 0. 114 1. 410 D+ K 0 e + 1. 476 ± 0. 070 1. 131 D+ -0 e+ 1. 806 ± 0. 209 1. 410 #2: Pole D 0 K - e + n #3: Modified Pole D 0 K - e + Output Physical value for pole 1. 94 ± 0. 04 2. 112 Output Physical Value for effective pole 0. 26 ± 0. 06 ~1. 75 Because the data do not support the physical interpretation of these three parameterizations we use the series parameterization July, 2006 Selected Topics on Open Charm Physics from CLEO-c 40

Fit results with 3 parameters Our main form factor shape and intercept results are for the series parameterization : n n The series is expected to converge rapidly, so only the 1 st few terms are expected to be measurable: we test for three July, 2006 Selected Topics on Open Charm Physics from CLEO-c 41

Interpretation n The fit results for 2 and 3 parameters are consistent with each other; n Noticeable improvement for 2 for D→Ke+ν with 3 parameters; n The modes do not show this trend as they lack the statistics to probe third term in the expansion; n For D → Ke+ν the 3 rd term b 2 is a order of magnitude larger than b 1. This cannot be interpreted as a lack of convergence if the series because both are consistent with zero indicating that the data does not yet have the sensitivity to determine three parameters simultaneously. July, 2006 Selected Topics on Open Charm Physics from CLEO-c 42

Comparison Between Parameterizations Data --- Simple pole D 0→K-e+ν D 0→π-e+ν n --- Modified Pole --- Series with 2 par Series with 3 par D+→Kse+ν D+→π0 e+ν Data and Fit results are normalized to the fit results for the series parameterization with 3 parameters. July, 2006 Selected Topics on Open Charm Physics from CLEO-c 43

Form Factors as a Stringent Test of LQCD n Plotted LQCD results (blue) are recent results of FNAL+MILC unquenched three flavor LQCD [C. Aubin et al. , PRL 94 011601 (2005)] ¡ Vcd = 0. 2238 0. 0029(CKM unitarity, i. e Vcd = Vus) LQCD Lattice systematic uncertainties dominate: DATA FIT ¡ Vcs = 0. 9745 0. 0008(CKM unitarity) ¡ n n The green lines are our fits to CLEO-c data The dashed lines show 1 (stat+syst) regions July, 2006 LQCD Selected Topics on Open Charm Physics from CLEO-c DATA FIT 44

Projections for and f+(0) D 0→π-e+ν The anticipated precision for a larger 750 pb 1 data sample to be collected in the future In these plots, the central values for our projections are equal to the central values from the LQCD results D 0→K-e+ν July, 2006 Selected Topics on Open Charm Physics from CLEO-c 45

Vcs(d) and f+(0) determination n Using Vcd = 0. 2238 0. 0029 (CKM unitarity, i. e Vcd = Vus) Vcs = 0. 9745 0. 0008 (CKM unitarity) n Using LQCD results [C. Aubin et al. , PRL 94 011601 (2005)]: July, 2006 Selected Topics on Open Charm Physics from CLEO-c 46

Summary for D semileptonic studies n I have shown preliminary results for D K/ e+ branching fractions and form factor measurements from the 280/pb data sample collected at (3770). Results of this analysis include: ¡ the most precise branching fraction measurements for these decays ¡ the most precise or first measurements of form factors for these modes ¡ the most precise or first measurements of the efficiency corrected and absolutely normalized decay rates ¡ a stringent test of LQCD calculations of semileptonic form factors July, 2006 Selected Topics on Open Charm Physics from CLEO-c 47

In summary, CLEO-c provides: n unique input to test LQCD, theory capable of solving strongly couple field theory equations, and n input to other experiments that help improve their measurements Thank you July, 2006 Selected Topics on Open Charm Physics from CLEO-c 48

Fit A: a 2 fit to efficiency corrected d /dq 2 n A brief description of the procedure for making Fit A: ¡ ¡ n Create an N x N efficiency matrix, where N is the number of q 2 bins Invert the efficiency matrix Measure raw background subtracted q 2 distributions Use the inverted efficiency matrix to obtain efficiency-corrected and absolutelynormalized d /dq 2 (or the form factor) We make fits form factor parameters to efficiency-corrected and absolutelynormalized d /dq 2 (or the form factor), using the 2 fitter which includes both statistical and systematic errors (with correlations) : ¡ bin migrations, background uncertainty, and efficiency corrections. - the decay rate n - the decay rate estimated from a form factor - the correlation matrix The low number of events in the high q 2 bins can lead to biases in 2 fits, we find that the Bias, if any, is SMALL [~0. 10 (stat. data) ] July, 2006 Selected Topics on Open Charm Physics from CLEO-c 49

Efficiency Matrices n We use 10 q 2 bins for and. For and we use 9 and 8 bins, respectively. The last bin for these two modes are two or three times wider than other bins. o D t no ed ne Full efficiency matrix for 10 bins to a re d e es th Efficiency matrices in a truncated form for 10 bins es bl ta 9 bins 8 bins July, 2006 Selected Topics on Open Charm Physics from CLEO-c 50