Charm Form Factors from from B -Factories A. Oyanguren BaBar Collaboration (IFIC –U. Valencia)

Charm Form Factors Arantza Oyanguren CIPANP V cd  Exclusive charm semileptonic decays: form factors Parameterized in terms of form factors q 2 =  p  p    =  p M  p X   which depend on q 2 =  p  p    =  p M  p X   Purpose: Lattice-QCD - Validate Lattice-QCD calculations - Discriminate between models describing hadronic effects

Charm Form Factors Arantza Oyanguren CIPANP Several models for form factor parameterization Simple pole ISGW2 Taylor expansion t  q 2 |z| << 1 Modified pole D  Physical region D  K

Charm Data Samples B A B AR & BELLE 530 fb -1 CLEO-c & BES III 0.57 fb -1  DD ~6 nb ~10 9 D (s) (*)(**) Much more statistics: ~10 9 D (s) (*)(**) Less background Better q 2 resolution Arantza Oyanguren CIPANP  cc ~1.3 nb 0.XX fb fb -1

Measurements at B-Factories Arantza Oyanguren CIPANP Full reconstruction : Partial reconstruction D  K/  D  K/  - good resolution (~ CLEO-c) - low efficiency - worse resolution* (*) not really an issue since the shape of the form factors is smooth - high efficiency D  K e D  K e D s  K + K - e D s  K + K - e Phys. Rev. D 76, (2007) Phys. Rev. D 78, (RC) (2008) Phys. Rev. Lett. 97, (2006) From continuum events:

D  K/  at BELLE Arantza Oyanguren CIPANP Full reconstruction : Continuum events, 282fb -1 Tag-side: Tag-side: D or D*, D  Kn , D*  D  /    mass constrained vertex fits, Prob. >0.1% Signal-side: Signal-side: D* +  D 0  + s (+ additional primary mesons)   p D*sig = p beam –p D(*)tag – p primary  p D0  p D0 from D* + and soft  + s + kinematic fit  D 0  K - + D 0  - +  D 0  K - + and D 0  - +  q 2 =(p + p miss ) 2  reconstruction: p miss = p D0 – p K or  - p   q 2 =(p + p miss ) 2 Primary mesons D* - D0D0 K+K+ -- -- Tag-side D0D0 ++ K-K- + Signal-side D* +

D  K/  at BELLE Arantza Oyanguren CIPANP D 0 candidates in the signal side: Normalized events Right sign Wrong sign   Background subtracted from wrong combinations of  s and kaon from the D tag : candidates evts/0.02 GeV  309  830 signal D evts 141 evts  D 0  K - + D 0  - +  D 0  K - + and D 0  - + reconstructed from the remaining particles   m 2 =p miss 2 (|m 2 | < 0.05 GeV 2 /c 4 ) m 2 (GeV 2 /c 4 ) data MC   Absolute normalization (  K(  ) /  D0 ~70%) B( D 0  K - + ) = e: (3.45  0.10  0.19)%  : (3.45  0.10  0.21)% B( D 0  - + ) = e: (2.79  0.27  0.16)   : (2.31  0.26  0.19)  D 0  K -  + D 0  -  + 6% bkg 25% bkg

D  K/  at BELLE Arantza Oyanguren CIPANP Form factors: D 0  K - + D 0  - +  q 2 =(p + p miss ) 2  q 2 ~15 MeV 2 m pole = 1.82  0.04  0.03 GeV m pole = 1.97  0.08  0.04 GeV  pole = 0.52  0.08  0.06  F + (0)=    pole = 0.10  0.21  0.10  F + (0)=   D 0  K - + D 0  - +  F  + (0) 2 |V cd | 2 / F K + (0) 2 |V cs | 2 =    2 /dof= 34/28  2 /dof= 28/18, 34/23  2 /dof= 6.2/10  2 /dof= 9.8/5, 3.4/5

D  Ke at BaBar Arantza Oyanguren CIPANP D* +  D 0  +, D 0  K - e + D* +  D 0  +, D 0  K - e + Define two hemispheres: Impose soft  +, K - and e + in the same hemisphere  Compute D direction (- p all tracks  K,e )  Fit p D = p K +p e +p Constraints using m D and m D* Compute q 2 =(p D – p K ) 2 (1c or 2c fit)  Compute the missing energy in the e +  hemisphere  (4S) rest frame  From p K,p e, computed E and D 0 direction Continnum events, 75fb -1 Partial reconstruction

D  Ke at BaBar Arantza Oyanguren CIPANP events (13% bkg)  m =m(K - e +  + )-m(K - e + )  m (GeV/c 2 ) Peaking cc =46% Non-peaking cc= 31% BB= 21% D 0  K - e + candidates: BB cc K e ** Lepton hemisphere   Background reduced from event shape and event topolgy   Control from data (D 0  K -  +, K -  +  0 )

D  Ke at BaBar Arantza Oyanguren CIPANP Simple pole and ISGW2 form factors with default parameters excluded ISGW2,  I= Model predictions ISGW2 m pole = m D*s data Form factor:  q 2 ~ MeV 2 Unfolded distribution: m pole =   GeV  pole =   D 0  K - + D 0  K - + r 1 = -2.5  0.2  0.2 r 2 = 0.6  6.0  5.0 z expansion:   /NDF  Simple pole mpole = mD*s   /NDF  QM light cone ( PRD41(90)3394)

D  Ke at BaBar Arantza Oyanguren CIPANP B (D  Ke ) (%) BaBar BELLE CLEO-c  Branching ratio relative to D  Kπ: Using the world average for Br(D 0  K -  + ) = 3.80 ± 0.07 % Form factor normalization:

Measurements at B-Factories Arantza Oyanguren CIPANP Form factors D  K : m pole (GeV/c 2 ) Form factors D  : f + (0)  pole m pole (GeV/c 2 ) CLEO-c BELLE BaBar FOCUS f + (0)  pole CLEO-c BELLE BaBar FOCUS LQCD CLEO-c BELLE BaBar LQCD CLEO-c BELLE CLEO-c BELLE LQCD BELLE CLEO-c LQCD

D s  K - K + e at BaBar Arantza Oyanguren CIPANP Partial reconstruction D s   e +  K + K - Similar reconstruction to D  Ke Continnum events, 214 fb -1 But vector final state (3 form factors)  The decay rate depends on 4 variables: q 2,  v,  ,  q 2,  v,  ,  and 2 form factor ratios: A 1 (q 2 ), A 2 (q 2 ), and V(q 2 ) shapes:  Simple pole form factors   Key channel for lattice validations ( s and c quarks)   Key to study the S-wave component of the K + K - system r 2 = A 2 (0)/A 1 (0) r v = V (0)/A 1 (0) 1 + (D sJ (2460), D s1 (2536)) : m A = 2.5 GeV/c (D s *) : m V = 2.1 GeV/c 2

D s  K - K + e at BaBar Arantza Oyanguren CIPANP events (18% bkg) D s  K - K + e + candidates: asymmetry First evidence of a S-wave component 70% peaking (  )

D s  K - K + e at BaBar Arantza Oyanguren CIPANP Form factors: Fit in 4D, using pole form factor shapes: First measurement of the q 2 dependence First measurement of the S-wave component ( f 0 ) F 10 = r 0 f 10 (q 2 ) A f0 (m) Amplitude Simple pole form factor f 0 amplitude (Flatté) S+P Interference of the S-wave with the 

D s  e at BaBar Arantza Oyanguren CIPANP (Corrected for mass range and S wave contribution) Form factors Form factors (fixed m A =2.5GeV) (fixed m A =2.5GeV) r V =   and r 2 =   Comparison with LQCD Form factor normalization: Branching fraction measured relatively to D s + →  + : Branching fraction measured relatively to D s + →  + :

Summary and conclusions Arantza Oyanguren CIPANP Very precise measurements are performed at B factories, complementary to charm threshold results D  e Ongoing at BaBar: D  e (more difficult but feasible) D  K  e D  K  e (including K  S-wave component) High statistics to perform accurate measurements having control on systematics Charm form factors are decisive for Lattice-QCD validation BaBar  D  Ke and D s   e form factors from BaBar BELLE  D  K and D   form factors from BELLE BaBar  First measurement of the S-wave in D s  K + K - e from BaBar Charm form factors at B-Factories: Impressive experimental improvement in the past years