Semileptonic Charm Decays Doris Y Kim University of

Semileptonic Charm Decays Doris Y Kim University of Illinois BEACH 2006 July 5, 2006 Content I: Why We Study Charm Semileptonic Decays. II: Recent Analyses on Semileptonic BF, from BES and CLEO-c. III: Form Factors for Pseudo. Scalar l n, from Ba. Bar, Belle, CLEO-c, & FOCUS. IV: Vector l n Form Factors from CLEO -c. 1

I. Charm Semileptonic Decays as Tests of QCD BF (decay rate) study provides a measurement of |Vcq|2 f, etc. The hadronic complications are contained in the form factors, which can be calculated via non-perturbative lattice QCD, HQET, quark models, 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. 2 Improvement of CKM @ beauty sector.

Events / 10 Me. V An Example of Semileptonic Decays: CLEO-c (~117 events) K- K+ U ( = Emiss – |Pmiss| ) e+ CLEO-c (56/pb) & BES BF relative to PDG 04 3

II. Inclusive Semileptonic BF. Inclusive BF vs sum of exclusive BF mode D 0 Xe+n CLEO-c 281 pb-1 B (6. 46 ± 0. 17 ± 0. 13)% Si Bi (D 0 Xe+n) (6. 1 ± 0. 2)% D+ Xe+n (16. 13 ± 0. 20 ± 0. 33)% Si Bi (D+ Xe+n) (15. 1 ± 0. 5)% • Consistent with the known exclusive modes saturating the inclusive B. • Some room for new modes? Extrapolated below 0. 2 • Consistent with SL isospin symmetry: 4

V/PS Anomaly in (D K*l n) / ( K l n) Data (2004) DATA Predictions • Early V/PS predictions were 1. 5 – 2 larger than known data ( the A 1 form factor problem ). • Since 1995 predictions have stabilized close to data. • Recent V/PS measurements are consistent: FOCUS (04) CLEO(05) two new BES(06). The V/PS anomaly is rapidly fading away. Plot courtesy of BES 5

III. D Pseudoscalar l n Form Factors Rate P 3 This process can give a clean measurement of CKM angles and powerful tests of LQCD. Unfortunately the rate vanishes at highest q 2 where sensitivity to the form of f+(q 2) is greatest. This is also the zero recoil limit where theory calculations are cleanest. What do we know about f+(q 2) ? 6

Pole Dominance Parameterization: D K l n / l n Dispersion Ds * <Mpole> is 5. 1 s lower than Ds* Integral term is important But there is a less model dependent way of dealing with f + singularities 7

R. J. Hill’s† New Approach to f (q 2) z q 2 Hill makes a complex mapping that pushes the cut singularities far from maximum q 2. cut physical Form factors are given by a simple Taylor series for |z | << 1 Illustrate with B en data [Hill (06)] For B : The cut is very close to the maximum q 2 and f+ (q 2) as q 2 max P f+ (z) f+ (q 2) 10 x q 2 †R. J. 2. 5 x Hill hep-ph/0606023 (FPCP 06) -z After z mapping, the physical and cut region are far apart. The f+ (z) data is well fit with just a straight line as a polynomial. Charm data? ? 8

FOCUS (2004) non-parametric D 0 K m+ n analysis The background only affects the highest q 2 bins. After subtracting known charm backgrounds, f+(q 2) is an excellent match to a pole form with mpole= 1. 91 0. 04 0. 05 Ge. V/c 2 or = 0. 32 (CL 87%, 82%). 9

The New Results from Belle (2006) fit results unquenched LQCD simple pole model One “effective” pole mass (Ge. V) Kln 1. 82 ± 0. 04 stat ± 0. 03 syst ln 1. 97 ± 0. 08 stat ± 0. 04 syst D 0 Kl n modified pole Kln 0. 52 ± 0. 08 stat ± 0. 06 syst ln 0. 10 ± 0. 21 stat ± 0. 10 syst D 0 ln Plot courtesy of L. Widhalm 10

LQCD, FOCUS & Ba. Bar: q 2 and z-trans ~100 K Hill transformation gives a nearly linear f(Z) for D K data. The expansion should converge very rapidly since |z| << 1 in this decay From Hill (06) Ba. Bar FOCUS 13 K -z Plus some new results from CLEO-c 11

Preliminary Untagged D K/ e n from CLEO-c CKM info Modified pole Neutrinos are determined by energy-momentum balance AND the recoil D tagging method is not used. Slightly lower than previous measurements charm vector semileptonic decays 12

IV. D Vector l n Decay Korner+Schuler (1990) Present in K* l nu H 0(q 2), H+(q 2), H-(q 2) are helicity-basis form factors computable by LQCD A new factor h 0 (q 2) is needed to describe s-wave interference piece. 13

KS / GS model for H and H 0 K&S write H and H 0 as linear combinations of two axial and one vector form factors. Two approaches are used to parameterize them: Spectroscopic pole dominance Versus B&K style “effective” poles The traditional method. • V(q 2) essentially same as B&K with one physical and one effective 1 - poles. But spectroscopic pole dominance should work poorly at high q 2 Need for alternative… • A 1(q 2) forced to be one effective 1+ pole • A 2(q 2) has two effective 1+ poles 14

Spectroscopic Pole Dominance D V l n Fits D+ K* l+ n RV RV R 2 time R 2 The latest results FOCUS (2004) on Ds m n form factors are consistent with those for D+. Experimental results are very consistent with small errors. But must we trust/rely on spectroscopic pole dominance? 15

cos. L A non-parametric Approach 7 8 9 4 5 6 1 2 3 D: M+ M- M 0 Disentangle helicity form factors based on their different angular bin populations. cos. V 16

Non-parametric D+ K +e+n Form Factors (281 pb 1) CL = 24% FOCUS model CL = 40% Low q 2 peaking of H 0 and h 0 is very apparent. CL = 59% CL = 0. 2% Apart from interference term the CL are rather good. 17

Pole Mass Sensitivity in Data MV=2. 1 MA=2. 5 Constant Ai & V Data fits spectroscopic poles and constant form factors equally well. 18

Preliminary Z transform of PS-V decay by Hill Analysis of CLEO non-parametric data by R. J. Hill (private communication) The Hill- transformed CLEO non-parametric H 0 data seems nearly constant. P H 0(z) CLEO data D+ K + e+ n -z For D K* decays, the z range is 4 small than for D K. Hence, one expects that the H 0 data is nearly constant after transformation, which is confirmed in data 19

Confirming the s-wave in D+ K + e+ n FOCUS CLEO-c The disappearance of the interference above the pole implies the above phase relationships between the BW and the s-wave amplitude. 20

Summary (1) Inclusive BF of semileptonic decays from CLEO-c. • From 281/pb at (3770), much better than the PDG 04. SL(D 0)/ SL(D+) = 1. Known decay modes almost saturating. (2) Active Form factor analyses for D Pseudoscalar l n by several experiments are compared to the latest unquenched light-flavor LQCD results, B&K model & Hill transformation. (3) Form Factor measurements for D V l n from CLEO-c 281/pb and FOCUS. • H+, H 0 appear consistent with the spectroscopic pole dominance model and consistent with Hill. (4) Not covered here & Coming soon: Exclusive BF decays, rare decays, Ds semileptonic decays, more form factors, etc. (5) Looking forward to new data from B factories, CLEO-c, BES III, and next-generation charm experiments. 21

Question slides 22

Search for D-wave K Add a D-wave projector Guard against “phase cancellation” by showing above and below the K* q 2 Ge. V 2 23

FOCUS D 0 K m+ n analysis 12, 840 K m+ n Dm cut RS-WS MC WS • A good muon candidate. • Cerenkov ID for K/ candidates. • L/s > 5 between two good vertices. • D* tag required, and wrong sign soft subtraction. Km frame • Jump to Km rest frame • The D and D* mass constraints the neutrino lies on a cone around the soft pion. q 2 reconst Fixed Target Neutrino closure • Pick the that points the D closest to the primary vertex. Lab frame q 2 actual 24

Expected q 2 Dependence of Helicity FF Only 0 helicity components can survive at q 2 0 because of V-A helicity laws. 25

Comparing CLEO-c & FOCUS Results Preliminary CLEO D+ K en q 2 Data 2472 res FOCUS D+ K mn Data 11397 q 2 res 26