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Semileptonic Charm Decays. Doris Y Kim University of Illinois. Content I : Why We Study Charm Semileptonic Decays. II : Recent Analyses on Semileptonic BF, from BES and CLEO-c. III : Form Factors for PseudoScalar l n, from BaBar, Belle, CLEO-c, & FOCUS.

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## Semileptonic Charm Decays

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**Semileptonic Charm Decays**Doris Y KimUniversity of Illinois Content I: Why We Study Charm Semileptonic Decays. II: Recent Analyses on Semileptonic BF, from BES and CLEO-c. III: Form Factors for PseudoScalar l n,from BaBar, Belle, CLEO-c, & FOCUS. IV: Vector l n Form Factors from CLEO-c. BEACH 2006July 5, 2006**I. Charm Semileptonic Decays as Tests of QCD**The hadronic complications are contained in the form factors, which can be calculated via non-perturbative lattice QCD, HQET, quark models, etc. BF (decay rate) study provides a measurement of |Vcq|2 f, 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. Improvement of CKM @ beauty sector.**An Example of Semileptonic Decays: CLEO-c** K- K+ - e+ (~117 events) Events / 10 MeV U ( = Emiss – |Pmiss| ) CLEO-c (56/pb) &BESBF relative to PDG 04**II. Inclusive Semileptonic BF.**Inclusive BF vs sum of exclusive BF CLEO-c 281 pb-1 • Consistent with the known exclusive modes saturating the inclusive B . • Some room for new modes? Extrapolated below 0.2 • Consistent with SL isospin symmetry:**V/PS Anomaly in (DK*ln) / ( K l n)**DATA Data (2004) Predictions • Early V/PS predictions were 1.5 – 2 larger than known data ( the A1 form factor problem ). • Since 1995 predictions have stabilized close to data. Plot courtesy of BES • Recent V/PS measurements are consistent: FOCUS (04) CLEO(05) two new BES(06). The V/PS anomaly is rapidly fading away.**III. D Pseudoscalar ln Form Factors**Rate P3 This process can give a clean measurement of CKM angles and powerful tests of LQCD. Unfortunately the rate vanishes at highest q2 where sensitivity to the form of f+(q2) is greatest.This is also the zero recoil limit where theory calculations are cleanest. What do we know about f+(q2) ? **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 **R.J. Hill’s† New Approach to f(q2)**Hill makes a complex mapping that pushes the cut singularities far from maximum q2. z q2 cut physical Form factors are given by a simple Taylor series for |z | << 1 Illustrate with Bendata[Hill (06)] • For Bp: The cut is very close to the maximum q2andf+ (q2) as q2 q2max • 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. Pf+ (z) f+ (q2) 2.5x 10x -z q2 Charm data?? †R.J. Hill hep-ph/0606023 (FPCP06)**FOCUS (2004) non-parametricD0 Km+n analysis**After subtracting known charm backgrounds, f+(q2) is an excellent match to a pole form withmpole= 1.91 0.04 0.05 GeV/c2 or = 0.32 (CL 87%, 82%). The background only affects the highest q2 bins.**The New Results from Belle (2006)**unquenched LQCDquenched LQCDsimple pole model fit results One “effective” pole D0 Kl n modified pole D0 pln Plot courtesy of L. Widhalm**LQCD, FOCUS & BaBar: q2 and z-trans**Hill transformation gives a nearly linear f(Z) for DK data. The expansion should converge very rapidly since |z| << 1 in this decay ~100K From Hill (06) BaBarFOCUS 13K -z Plus some new results from CLEO-c**Preliminary Untagged DK/p e n from CLEO-c**Modified pole CKM info 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**IV. D Vector l n Decay**Korner+Schuler (1990) Present in K* l nu H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD A new factor h0 (q2) is needed to describe s-wave interference piece.**KS / GS model for H and H0**K&S write H and H0 as linear combinations of two axial and one vector form factors. Two approaches are used to parameterizethem: Spectroscopic pole dominance Versus B&K style “effective” poles The traditional method. • V(q2) essentially same as B&K with one physical and one effective 1- poles. • A1(q2) forced to be one effective 1+ pole • A2(q2) has two effective 1+ poles But spectroscopic pole dominance should work poorly at high q2 Need for alternative…**Spectroscopic Pole Dominance DV l n Fits**R2 D+ K*l+ n RV RV time R2 The latest results FOCUS (2004) on Dsf m nform factors are consistent with those for D+. Experimental results are very consistent with small errors. But must we trust/rely on spectroscopic pole dominance? **A non-parametric Approach**D: M+M- M0 Disentangle helicity form factors based on their different angular bin populations. cosL cosV**Non-parametric D+ Kp+e+n Form Factors (281 pb1)**CL = 24% FOCUS model CL = 40% Low q2 peaking of H0 and h0 is very apparent. Apart from interference term the CL are rather good. CL = 59% CL = 0.2%**Pole Mass Sensitivity in Data**MV=2.1 MA=2.5 Constant Ai & V Data fits spectroscopic poles and constant form factors equally well.**Preliminary Z transform of PS-V decay by Hill**Pf H 0(z) CLEO data D+ Kp+e+n -z Analysis of CLEO non-parametric data by R.J. Hill(private communication) The Hill- transformed CLEO non-parametric H0 data seems nearly constant. For DK* decays, the z range is 4 small than for DK. Hence, one expects that the H0 data is nearly constant after transformation, which is confirmed in data**Confirming the s-wave in D+ Kp+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.**Summary**• Inclusive BF of semileptonic decays from CLEO-c. • From 281/pb at (3770), much better than the PDG 04. SL(D0)/ SL(D+) = 1. Known decay modes almost saturating. • 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. • Form Factor measurements for D V l n from CLEO-c 281/pb and FOCUS. • H+, H, H0 appear consistent with the spectroscopic pole dominance model and consistent with Hill. • Not covered here & Coming soon: Exclusive BF decays, rare decays, Ds semileptonic decays, more form factors, etc. • Looking forward to new data from B factories, CLEO-c, BES III, and next-next-generation charm experiments.**Search for D-wave Kp**Add a D-wave projector Guard against “phase cancellation” by showing above and below the K* q2 GeV2**FOCUS D0 Km+n analysis**12,840 Km+n Dm cut RS-WS MC WS Lab frame • A good muon candidate. • Cerenkov ID for K/p candidates. • L/s > 5 between two good vertices. • D* tag required, and wrong sign soft p subtraction. Km frame • Fixed Target Neutrino closure • Jump to 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. q2 reconst q2 actual**Expected q2 Dependence of Helicity FF**Only 0 helicity components can survive at q2 0because of V-A helicity laws.**Comparing CLEO-c & FOCUS Results**Data 2472 PreliminaryCLEO D+ Kpen FOCUS D+ Kpmn Data 11397 q2 res q2 res

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