CKM 2006 Workshop, Nagoya, Japan, Dec , 2006 Leptonic & Semi-Leptonic Charm Decays Sheldon Stone, Syracuse University

S. Stone (Syracuse) CKM 2006 Workshop, Dec , What We Hope to Learn Purely Leptonic Charm Decays D→ + Check QCD calculations including Lattice (LQCD) Look for New Physics Semileptonic decay rates & form-factors QCD checks Use QCD to extract V cq (See talk of M. Artuso) Use d  /dq 2 in conjunction with B decay rates to extract V ub. Use D   to get form-factor for B , at same vv point using HQET (&   Use B   B  K* + -, along with  D   D  K*  at the appropriate q 2 Due to lack of time, many interesting results are omitted   Need f Bs /f B from theory. Measure f D + /f Ds

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Experimental methods  DD production at threshold: used by Mark III, and more recently by CLEO-c and BES-II.  Unique event properties  Only DD not DDx produced  Large cross sections at  (3770):  (D o D o ) = 3.72  0.09 nb  (D + D - ) = 2.82  0.09 nb  Ease of B measurements using "double tags:“ B A = # of A/# of D's  At  (3770) CLEO-c uses beam constrained mass  At 4170 MeV, invariant mass with energy cut World Ave At Y(4S)  (charm) ~ 1 nb   (D S ) ~ 0.15 nb

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Leptonic Decays: D (s)  + Introduction: Pseudoscalar decay constants c and q can annihilate, probability is  to wave function overlap Example : _ In general for all pseudoscalars: Calculate, or measure if V Qq is known (s) or cs

S. Stone (Syracuse) CKM 2006 Workshop, Dec , New Physics Possibilities Another Gauge Boson could mediate decay Ratio of leptonic decays could be modified (e.g.) See Hewett [hep-ph/ ] & Hou, PRD 48, 2342 (1993).

S. Stone (Syracuse) CKM 2006 Workshop, Dec , New Physics Possibilities II Leptonic decay rate is modified by H+ Can calculate in MSSM. Is  m q /m c, so negligible for D + but not for D S (m S /m c ) Leptonic decay for D S gets modified by factor of or where R=tan  /m H See Akeryod [hep-ph/ ] From Akeroyd r

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Old CLEO Measurements of f Ds 1. Detected  &  from D S *→  D S →   decay 2. Used missing energy & momentum in half of the event, to estimate 4-vector. Event half determined using thrust axis 3. Correct 4-vector to get right D S mass value 4. Measured real  background by doing same analysis on D S *→  D S → e  5. Used D* o →  D o → K - (  + ) to measure efficiencies, etc… 6. Used 4.8 fb -1 at or near Y(4S) ( M. Chadha et al. Phys. Rev. D58, (1998))

S. Stone (Syracuse) CKM 2006 Workshop, Dec , New B A B AR Measurements of f Ds Similar analysis to CLEO [1) detect  & , 3) correct P 4, 4) use  e for backgrounds, 5) use D* o →  K - (  + )], but much improved because they use only events: e + e - →“D” x D S * -, where the “D” is a fully reconstructed D o, D + or D* + (B. Aubert et al [hep-ex/ ]) This gives much better S/B and also missing energy resolution Use 230 fb -1

S. Stone (Syracuse) CKM 2006 Workshop, Dec , New CLEO-c Measurement of D S + →  + In this analysis CLEO uses D S *D S events where they detect the  from the D S *→  D S decay They see all the particles from e + e - → D S *D S,  D S (tag) +  + except for the A kinematic fit is used to (a) improve the resolution & (b) remove ambiguities Constraints include: total p & E, tag D S mass,  m=M(  D S )-M(D S ) [or  m= M(  )-M(  )] = MeV, E of D S (or D S *) fixed Lowest  2 solution in each event is kept No  2 cut is applied

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Invariant masses K-K++K-K++ KsK+KsK+    Inv Mass (GeV)  +   K * K * from K s K -    +  Total # of Tags = 19185±325 (stat)

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Tag Sample using  First define the tag sample by computing the MM* 2 off of a  & D S tag Total of 11880±399±504 tags, after the selection on MM* 2 All 8 Modes Data

S. Stone (Syracuse) CKM 2006 Workshop, Dec , The MM 2 (From Simulation) To find the signal events, compute Signal  Signal  → 

S. Stone (Syracuse) CKM 2006 Workshop, Dec , MM 2 Results from 200 pb -1 Clear D S + →  + signal for case (i) Events <0.2 GeV 2 are mostly D S →  +,  →  + in cases (i) & (ii) No D S →e + seen, case (iii) 6 D S →  +,  →  +  in case (i)  + peak Electron Sample DATA 200/pb <0.3GeV in CC DATA 200/pb >0.3GeV in CC 64 events 24 events 12 events Case (i) Case (ii) accepts 99% of  +, 60%  + & K + accepts 1% of  +, 40%  + & K +

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Sum of D S + →  +  +,  →  + Two sources of background A) Backgrounds under invariant mass peaks – Use sidebands to estimate In  +  signal region 2 background (64 signal) Sideband bkgrnd 5.5±1.9 B) Backgrounds from real D S decays, e.g.  +  o  o, or D S →  +,  →  +  o  < 0.2 GeV 2, none in  signal region. Total of 1.3 additional events. B(D S →     ) < 1.1x10 -3 &  energy cut yields <0.1 evts Total background < 0.2 GeV 2 is 6.8 events, out of the events Sum of case (i) & case (ii) K0+K0+  signal line shape

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Branching Ratio & Decay Constant D S + →  + 64  signal events, 2 background, use SM to calculate  yield near 0 MM 2 based on known  ratio B(D S + →  +  (0.657±0.090±0.028)% D S + →  +  + →  + Sum case (i) 0.2 > MM 2 > 0.05 GeV 2 & case (ii) MM 2 < 0.2 GeV 2. Total of 36 signal and 4.8 bkgrnd B(D S + →  +  (7.1±1.4±0.3)% By summing both cases above, find B eff (D S + →  +  (0.664±0.076±0.028)%  f Ds =282 ± 16 ± 7 MeV B(D S + →e +  3.1x10 -4

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Measuring D S + →  +  + → e + B(D S + →  +  B  + → e +  1.3%  is “large” compared with expected B(D S + →Xe +  Technique is to find  events with an e + opposite  D S - tags & no other tracks,  with  calorimeter energy < 400 MeV No need to find  from D S * B(D S + →  +    (6.29±0.78±0.52)%  f Ds =278 ± 17 ± 12 MeV 400 MeV Xe +

S. Stone (Syracuse) CKM 2006 Workshop, Dec , & Weighted Average: f Ds =280.1±11.6±6.0 MeV, the systematic error is mostly uncorrelated between the measurements (More data is on the way) Previously CLEO-c measured M. Artuso et al., Phys.Rev. Lett. 95 (2005) Thus f Ds /f D + =1.26±0.11±0.03 D + →   K0+K0+  

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Comparisons with Theory We are consistent with most models, more precision needed Using Lattice ratio find |V cd /V cs |= 0.22±

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Comparison with Previous Experiments Difficult to average without a clear measurement of B(D S →  + ). In any case CLEO-c result dominates ? ? 280.1±11.6± ± ± 15 ± 6 ± 31 -2

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Limits on New Physics Lepton Universality  (D S + →  +  (D S + →  +  = 9.9±1.7±0.7 SM = 9.72  (D + →  +  (D + →  +  < 4.77 (90% cl) SM = 2.65 Limits on charged Higgs According to Akeryod Unquenched Lattice: f Ds =249±3±16 MeV Our result: 280.1±11.6±6.0 MeV Take m s /m c =0.076 (PDG) Then the ratio of our result/SM gives >1, NP  <1

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Limits on Charged Higgs Mass Can set limits in the tan  - m H ± plane Competitive with CDF But depends on Lattice Model. Don’t take seriously yet Summary of the 95% CL exclusions obtained by LEP & CDF. The full lines indicate the SM expectation (no H ± signal) and the horizontal hatching represents the ±1  bands about the SM expectation.

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Exclusive Semileptonic Decays u Best way to determine magnitudes of CKM elements, in principle is to use semileptonic decays. Decay rate  |V QiQf | 2 u Kinematics:  Matrix element in terms of form-factors (for D  Pseudoscalar +  For = e, f  (q 2 )  0: V QiQf

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Form-Factor Parameterizations In general Modified Pole Series Expansion Hill & Becher, Phys. Lett. B 633, 61 (2006)

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Beam Constrained mass using E miss & P miss to find CLEO-c Exclusive Decays (281 pb -1 ) Both Tagged results & untagged using reconstruction reconstruction has larger statistics but larger systematic errors U = E miss – |P miss | (GeV) 295         29 Samples overlap, so choose only one result

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Exclusive Branching Ratio Summary Theory needs to catch up preliminary D o → K - e + ν D o → π - e + ν (2006)

S. Stone (Syracuse) CKM 2006 Workshop, Dec , CLEO-c Form-Factors Compared to Lattice Lattice predictions* D  Ke f + (0)=0.73±0.03±0.07   =0.50±0.04±0.07 D  e f + (0)=0.64±0.03±0.06   =0.44±0.04±0.07 * C. Aubin et al., PRL (2005) DATA FIT (tagged) LQCD DATA FIT (tagged) LQCD Assume V cd = Assume V cs = Belle.. CLEO-c

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Other Form-Factor Measurements CLEO-c & Belle somewhat disagree with LQCD, Belle  2 28/18 (K) & 9.8/5 (  ) D o  Kℓ & FOCUS LQCD: Aubin et al., PRL94, (2005) ~2.5k signal events 232 signal events Unquenched LQCD Quenched LQCD Simple pole model Kℓ  ℓ Belle q 2 (GeV 2 ) (hep-ex/ ) BELLE: PRL 97, (2006) [hep-ex/ ]

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Pseudoscalar Form Factors D→K e + D→  e +

S. Stone (Syracuse) CKM 2006 Workshop, Dec , D  Form Factors (CLEO-c) Can be used to detemine V ub along with B   D  K*  & B  K* + - (See Grinstein & Pirjol [hep-ph/ ]) D +   - D o   - q2q2 cos   cos  e  Line is projection for fitted R V, R 2 R v = 1.40  0.25  0.03, R 2 = 0.57  0.18  0.06 B(D 0   - e + )= (1.56  0.16  0.09)  B(D +   0 e + )= (2.32  0.20  0.12)  U = E miss – |P miss | (GeV)

S. Stone (Syracuse) CKM 2006 Workshop, Dec , CLEO-c Discovery of D o →K  e + B(D o →K 1 (1270)e + )*B(K 1 (1270) →K -     ) = consistent with ISGW2 prediction

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Conclusions not preliminary f Ds =280.1±11.6±6.0 MeV preliminary f Ds /f D + =1.26±0.11±0.03 preliminary No violation of Lepton Universality observed Accurate semi-leptonic form-factors confronting LQCD & perhaps indicating deviations Much much more to do

CKM 2006 Workshop, Nagoya, Japan, Dec , 2006 The End

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Simp. Pole Mod. Pole Untagged: Form-Factor Results

S. Stone (Syracuse) CKM 2006 Workshop, Dec , D   /Ke : Which Form Factor Parameterization? CLEO preliminary All these models describe the data pretty well (except when forcing pole mass to nominal value in pole model).

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Compare with Limits from Belle  Belle: assumes f B and |V ub | are known, take the ratio to the SM BF. r B =1.13  0.51 Excluded by CLEO-c 95% CL But taking no theoretical error is abhorrent

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Goals in Leptonic Decays f B & f Bs /f B needed to improve constraints from  m d &  m S /  m d. Hard to measure directly (i.e. B    measures V ub f B  but we can determine f D+ & f Ds using D   and use them to test theoretical models (i.e. Lattice QCD)   Constraints from V ub,  m d,  m s & B  

S. Stone (Syracuse) CKM 2006 Workshop, Dec , New CLEO-c Measurements of f Ds Two separate techniques (1) Measure D S + →  + along with D S →  +,  →  +. This requires finding a D S - tag, a  from either D s * - →  D s - or D s * + →  +. Then finding the muon or pion using kinematical constraints (2) Find D S + →  +  → e +  opposite a D s - tag

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Comparisons with Theory We are consistent with most models, more precision needed 280.1±11.6± ± CLEO-c 1.26 ±0.11±0.03

S. Stone (Syracuse) CKM 2006 Workshop, Dec , CLEO-c Untagged D  K(or  ) e

S. Stone (Syracuse) CKM 2006 Workshop, Dec , Define Three Classes Class (i), single track deposits 300 MeV. (accepts 99% of muons and 60% of kaons & pions) Class (ii), single track deposits > 300 MeV in calorimeter & no other  > 300 MeV (accepts 1% of muons and 40% of kaons & pions) Class (iii) single track consistent with electron & no other  > 300 MeV