Preliminary Measurement of the Ke3 Form Factor f + (t) M. Antonelli, M. Dreucci, C. Gatti Introduction: Form Factor Parametrization Fitting Function and FSR Corrections Data Sample and Ke3 Selection Efficiency Estimate Fit Results Systematics: Preliminary Studies Preliminary Results Conclusion

Form Factor Parametrization  K l p p´p´ t  (p-p´) 2 The hadronic current in semileptonic decays is parametrized as a function of momenta and form factors: We define t as: In the decay amplitude, f - (t) is multiplied by the lepton mass: It can be neglected for Ke3 decays.

Parametrization of f + (t) and Recent Results  ×10 3   ×10 3 ISTRA (ke3)24.9± ±0.94 KTeV (Ke3)21.67± ±0.78 NA48 (Ke3)28.0±2.40.4±0.9 The constant f + (0) cannot be extracted from experiment. Recent results on slopes:

Fitting Function Where: i and j: t-bin numbers (j=1  t=[-3,-2.5]; j=20  t=[6.5,7.]). A(i,j): Smearing matrix (from MC after selection).  : Distribution density integrated in the bin, for ‘bare’ Ke3 decay.  : Selection efficiency (from MC and data control samples).  =  acctrk)×  kine cut)×  clu)×  tof) F FSR : Includes the effect of the radiated photon in the final state. The slopes are the free parameters of the fit

FSR Correction The photon in the final state soften the pion momentum spectrum. Hence the low-t (high p  ) bins are mostly affected. We correct the ‘bare’ distribution  (t) with that obtained with MC, using the same slope values for both: ´ + = 0.03 and ´´ + = 0. Few percent corrections are observed in the low-t bins. ‘bare’  (t) Ke3  MC t ´ + = 0.03 ´´ + = 0

Data Sample and Selection Data sample: Has been chosen using the same criteria used for the measurement of the main K L BR’s. A total of 328 pb -1 has been divided in 14 periods. Tagging: Events are tagged with K S  +  - decays (  70% ). Emc trigger must be satisfied by clusters associated to K S tracks (  40% mainly TCA). TRK: We look for 2 opposite K L tracks from a vertex (as for K L BR’s) in a fiducial volume (FV): 35<R T <150 cm, |Z|<120 cm (  15% mainly FV, TRK-VTX ~54%). Bkg rejection: Loose kinematical cuts are applied to reject Bkg; missing-energy and -momentum and invariant-mass are calculated to reject:  +  -,  +  -  0,  (  96%). ToF: The final selection is done using ToF technique (  40% mainly TCA).

Bkg Rejection:   E miss (  ) 2 + p miss 2 (MeV)   e   events are rejected by cutting on the sum of missing energy and momentum (squared) in the  mass hypothesis:  (E miss (  ) 2 + p miss 2 >10 MeV ~95% of  events are rejected. Signal efficiency close to 100%.

Bkg Rejection:   E miss (  ) 2 + p miss 2 (MeV)   e   events are rejected by cutting on the sum of missing energy and momentum (squared) in the  mass hypothesis:  (E miss (  ) 2 + p miss 2 >10 MeV ~95% of  events are rejected. Signal efficiency close to 100%.

Bkg Rejection:  E miss (  ) 2 - p miss 2 -M  0 2 (MeV 2 )   e   events are rejected by cutting on the missing mass in the  mass hypothesis: E miss (  ) 2 - p miss 2 < M  0 2 –5000 MeV 2. ~96% of  events are rejected. Signal efficiency close to 100%.

Bkg Rejection:  E miss (  ) 2 - p miss 2 -M  0 2 (MeV 2 )   e   events are rejected by cutting on the missing mass in the  mass hypothesis: E miss (  ) 2 - p miss 2 < M  0 2 –5000 MeV 2. ~96% of  events are rejected. Signal efficiency close to 100%.

Bkg Rejection:  |E miss (  )- p miss | (MeV)  e   events are rejected by cutting on the difference between missing energy and momentum in the  hypothesis; the lesser of the two possibilities (  or  ) has been chosen: |E miss (  )- p miss |> 10 MeV. ~88% of  events are rejected. Signal efficiency about ~96%.

Bkg Rejection:  |E miss (  )- p miss | (MeV)  e   events are rejected by cutting on the difference between missing energy and momentum in the  hypothesis; the lesser of the two possibilities (  or  ) has been chosen: |E miss (  )- p miss |> 10 MeV. ~88% of  events are rejected. Signal efficiency about ~96%.

ToF Selection Kinematic separation is not enough: final contamination is about 12% and we must relay on MC description of bkg; Low discrimination between  and e. The fit result is very sensitive to the amount of bkg and it is not stable for cut variations. A purer sample is needed: TCA: Tracks are associated to clusters, PID with  t(e) -  t(  ). ToF: 2  elliptic cut applied on (  t(e) -  t(  )) vs (  t(e) +  t(  )) where  t(i)=T clu -L trk /c  (m(i)) - L K /c  K.  t(e) -  t(  ) (ns)  t(e) +  t(  ) (ns) K3K3 Ke3 opposite charge Ke3 signal  40%

Signal Purity t S/(S+B) t Signal (A.U.) The ratio of signal (S) and signal plus bkg (S+B) as a function of t shows a behavior: ~ ( /5 t)= ( t) (compare with ´ + ~ 0.025). 10% error on bkg estimate   2% Linear effect are small for ´´ + (  1%) but quadratic terms are important (  100%). Variations are comparable with our final stat. error (6% and 50%). Bkg must be studied carefully. Most of the bkg (total 1%) comes from K  3 where a  is identified as electron.

Efficiency Evaluation Tag: From MC. ACCTRK: From MC corrected with Data/MC efficiencies. TCA: From MC corrected with Data/MC efficiencies. ToF: From MC after tooning of cluster resolutions (‘spaga’technique). Separation of the dataset for slope-measurement and efficiency- measurement not done yet. Is it worth loosing half of the statistics in order to compute the statistical error correctly?

Tag Bias on t-Distribution The tag selection can induce a slope in the t-distribution. The correcion is obtained from MC (systematics discussed later). t  (tag) +e-+e- -e+-e+ 1 period: statistics 1/14

Acceptance-TRK-VTX t  (trk) MC +e-+e- -e+-e+ +e-+e- -e+-e+  (trk) DATA/MC 20% t Low momentum  1% Efficiency for acceptance, tracking, and vertexing is taken from MC. The efficiency is corrected using ratio of data and MC efficiencies from 3  and  e control samples as in the analysis of K L BR’s. The efficiency shows huge variations as a function of t especially for low momenta of the pion. However the variation of the correction (data/MC) is about 1%.

TCA and Cluster Efficiencies Efficiencies measured from  e  control sample selected with tighter cuts on missing energy and momentum. Cut on  t(e (  )) to tag  (e). About 0.1% bkg. Data MC P(MeV)  - endcap  (clu)  (data)/  (MC) Data MC P(MeV) e - barrel  (clu)  (data)/  (MC) Data MC P(MeV)  + endcap  (clu)  (data)/  (MC)

TCA and Cluster Efficiencies As expected, corrections are very different for the two charge modes, due to the different behavior of  + and  -. If not corrected we expect 20% effect on + and up to 200% effect on  +. Final check provided by the comparison of the results for the two charge modes. -e+-e+ +e-+e- t  (data)/  (MC) Low momentum 

Tof Efficiency ToF efficiency taken directly from MC, but after applying to the MC the recipe from K S  e : pezzeto+datizza+smirizza. Agreement observed in  t distribution for  and e selected from control sample used for TCA-CLU.  t(e) (ns) MC sig and bkg + DATA + MC  t(  ) (ns) MC sig and bkg + DATA + MC

MC sig and bkg + DATA + MC BKG?  t(  ) (ns) ToF: Zoom  t(  )

MC sig and bkg + DATA + MC  t(e) (ns) ToF: Zoom  t(e)

Fit Results: Stability Fits are performed separately for each of the 14 periods to check stability, and combining all periods together for the result. We fit both the linear and quadratic approximations of the form factor. The two charge modes are fit separately. Good stability for both. Compatible results. If cluster efficiencies are not applied 15% difference is observed between the two charge modes. period + Fit with linear approximation -e+-e+ +e-+e-

Fit Results With about 2×10 6 selected Ke3 decays we obtain: Linear fit + ×10 3  2  ndf -e+-e+ 28.7±0.7156/181 +e-+e- 28.5±0.6174/181 Combined 28.6±0.5330/363 Quadratic fit + ×10 3  + ×10 3  2  ndf -e+-e+ 24.6±2.11.9±1.0152/180 +e-+e- 26.4±2.11.0±1.0173/180 Combined 25.5±1.51.4±0.7325/362 Correlation matrix

Fit Result:  + e - Data Fit DATA/FIT t Data Fit DATA/FIT t Linear Fit Quadratic Fit

Fit Result:  - e + Data Fit DATA/FIT t Data Fit DATA/FIT t Linear Fit Quadratic Fit

Preliminary Evaluation of Systematics Some of the efficiencies relays on the MC simulation (eventually corrected): Tag, Bkg, ToF, and momentum scale. Some other are corrected with data: TRK, CLU. As a preliminary study we take the maximal variation of the result by changing the selection in the following way: Tag: Looser requirement for K S cluster. Bkg: Reduced using Pid selection. ToF: Use corrections from control sample (pid selection). TRK: Change K L track definition as in K L BR’s. TCA-CLU: Change TCA definition. P Scale: Checks on M 2 and/or E miss -P miss (in progress).

Tag Bias Systematics In the selection the Emc trigger must be satisfied by the K S clusters. We loose this requirement and repeat the measurement without autotrigger request for the tag. Tag Bias  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit (  observed variation,  statistical error of original fit result)

Bkg Systematics Bkg  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit PID - Signal - Bkg Data Bkg, mainly from K  3, is reduced by a factor 3 cutting on PID variable (see K L BR’s). MC PID distribution for signal corrected from control sample to evaluate cut efficiency.

Bkg Systematics Bkg  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit PID - Signal - Bkg Data Bkg, mainly from K  3, is reduced by a factor 3 cutting on PID variable (see K L BR’s). MC PID distribution for signal corrected from control sample to evaluate cut efficiency.

ToF Systematics ToF  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit0.5 — — Quadratic Fit From Ke3 control sample selected with PID and kinematics (Bkg ~0.1%), we measure ToF efficiency for Data and MC. The ratio is used to correct the selection MC efficiency.

TRK systematics TRK  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit Dist(cm) R T (cm) The cut on Dist is the most effective in defining trk quality. We change this cut from 3 (red line) to 1cm (blue line), corresponding to 30% relative variation of the efficiency.

TCA-CLU Systematics TCA-CLU  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit We changed the definition of TCA (30 cm tranverse, 100 cm total). The total distance is reduce to 7 cm corresponding to a relative variation of the efficiency of 40%. -e+-e+ +e-+e- t  (data)/  (MC) d tot =100 cm

TCA-CLU Systematics TCA-CLU  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit We changed the definition of TCA (30 cm tranverse, 100 cm total). The total distance is reduce to 7 cm corresponding to a relative variation of the efficiency of 40%. t  (data)/  (MC) d tot =7 cm -e+-e+ +e-+e-

Momentum Scale Systematics p Scale  + ×10 3  + ×10 3  + ×10 3  + ×10 3 Linear Fit — — Quadratic Fit Momentum scale in KLOE known better than 0.1% (M K,  s,...), corresponding to an error on slopes d  0.2% and d  0.4%. Ongoing checks on M 2 and/or E miss -P miss vs t.

Summary of Systematics Linear Quadratic  + ×10 3  + ×10 3 Tag Bkg ToF TRK TCA-CLU P Scale TOT

Preliminary Results Linear FitQuadratic Fit + =(28.6  0.5  0.8)× =(25.5  1.5  1.9)×10 -3  + = (1.4  0.7  0.7)×10 -3 KTeV NA48 ISTRA+ KLOE + ×10 3 KTeV NA48KLOE ISTRA+  + ×10 3

Conclusions Bkg rejection important: ToF selection. Quadratic slope most sensitive to bkg and efficiency corrections. Different corrections for  + e - and  - e +, but final results in good agreement. Statistical errors comparable with other experiments. First estimate of systematic obtained from maximal variation of fit result by changing selection cuts. Preliminary systematic error comparable with statistical one. At present no separation between control samples and data- sample has been done.

Back of the envelope The effect of a slope (1+  t) not corrected for instance on the efficiency, changes the fit result in the following way (  ): The same can be repeated for a quadratic effect (1+  t+  t 2 ):

Back of the envelope 2 A miscalibration of momenta: p  (1+  ) p ; t  a+bt (a ~0, b ~1+2  )