1 Doris Y. Kim, University of Illinois Urbana-Champaign Content Part I: Theories of Charm Semileptonic decays Part II: q 2 dependence in Pseudo- scalar l  decays  Part III: Vector l  decays  D +  K* 0   analysis (not so simple!)  Form factors of  Ds   Part V: Future of Semileptonic decays. Semileptonic Charm Decays and QCD ISMD Sonoma July 27, 2004

2 I: Charm semileptonic decay as tests of LQCD The decay rates are computed from first principles (Feynman diagrams) using CKM matrix elements. The hadronic complications are contained in the form factors, which can be calculated via non-perturbative Lattice QCD, HQET or quark models. 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.  etc.

3 II: Pseudoscalar l  decays But a major disconnection exists between experiment and theory. In the past, theories worked best where experiments worked worst. cleanest theory highest rate is the easiest point for LQCD calculation. P at rest in D frame Simple kinematics  Easy to extract form factors. The lattice community is actively fixing the situation and calculating f+ as a function of q 2. hep-lat/ preliminary

4 Comparing Pole versus ISGW forms in D  l The difference between these forms can be quite dramatic in  decays. Especially since  decay gets quite close to the D* pole. ISGW1 f + (q 2 ) parameterization pole 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 + (q 2 ) information. ISGW2Updated one.

5 Brand new q 2 information in D  l /Kl Preliminary Cleo 2004  e  pole mass is  e Ke It disfavors ISGW2 form by ~4.2  form factor f+(q²) single-pole model Based on 820 events q² / GeV² Kl  l q² / GeV² Preliminary K 

6 Summary of D  l /Kl  Results Clearly the data does not favor the simple Ds* pole Consistent w/ SU(3) breaking A big advance in precision! Kl BR

7 III: D  vector  decays H 0 (q 2 ), H + (q 2 ), H - (q 2 ) are helicity-basis form factors computable by LQCD right-handed  + left-handed  + Two amplitudes get sumed over W polarization using D-matrices Helicity FF are combinations of one vector and two axial form factors. Two observables parameterize the decay

8 Interference in D +  K*  Yield 31,254 Data MC K*  interferes with S- wave K  and creates a forward-backward asymmetry in the K* decay angle with a mass variation due to the varying BW phase. (2002) F-B asymmetry The S-wave amplitude is about 7% of the (H 0 ) K* BW with a 45 o relative phase Focus “ K* ” signal It ’ s the same relative phase as the LASS (1988) matches model -15% F-B asymmetry!

9 K*  form factors Results are getting very precise and unquenched calculations for incisive tests of the theory would be very desirable. acoplanarity Precision tests of the model. Due to interference

Direct measurement of  (D+  K*  / K  ) Use upstream K s (~10%) so that both the numerator (K  ) and denominator (K s  ) leave 3 tracks in FOCUS  -strip Theory S-wave corrected Old quark model

11 The D s  form factor enigma Theoretically, the Ds  l form factors should be within 10% of D+  K*l  The r V values were consistent, but r 2 for Ds  l was 2  higher than D+  K*l  But the (2004) FOCUS measurement obtained a consistent r 2 value as well! D s   versus D+  K*l circa 1999 circa 2004

12 The future of charm SL physics Precision neutrino closure in D  e. Cleo-c and Bes III: Run at  (3770) with high luminosity and modern detectors.  D o D o, D o  K -  + K-K- K+K+ ++  Extremely clean events! CLEO-c yellow book: 1 fb -1 MC U = E miss - P miss Prelim. data (60 pb -1 ) Pavlunin APS(2004) Yellow book 1 fb -1 (MC) The q 2 impasse afflicting SL data for the last 20 years shall be solved, finally.

13 Summary Consistent FF for D +  K*  & D s +   s-wave interference in D +  K*  F-B asymmetry V(q 2  0) problem D +  K*  q 2 < 0.2 New CLEO 2004 D  e /Ke  result V/PS ratio

14  (D+  K*  / K  ) circa 1993 circa 1993

15 Some more tests of the K*  model Generally the model tracks the data rather well … A dramatic mismatch is seen at very low q 2 suggesting a V(q 2  0) problem Focus has a preliminary analysis of the K* 0 line shape.  K* 0 )  is seen as less than PDG by  ~1.6 MeV.