# Presentation: 528586

## Measurements of q2 Dependence of D0  K +  and + Form Factors.

- Doris Y. KimUniversity of IllinoisUrbana-Champaign

** ****Content  ( ****hep-ex/0410037,****                  PLB 607 (2005) 233** **)**
-  Part I: Theories of charm semileptonic decays.
-  Part II: Reconstructing D0 ** **K +  and +
-  Part III: q2 dependence, f+(q2)
-  Deconvolution approach: Non-parametric analysis.
-  Parametric fit.
-  Part VII: Summary

**Measurements of q****2**** Dependence of**** D****0**** ******** K******** ********+**** ******** and ****************+******** Form Factors.**

- APS Meeting April 17, 2005Tampa, FL

- FOCUS / Doris Kim

- 4/17/2005

## I: Charm semileptonic decay as tests of LQCD

**I: Charm semileptonic decay as tests of LQCD**

- The decay rates are computed from first principles (Feynman diagrams) using CKM matrix elements.

- 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.*

- FOCUS / Doris Kim

- 4/17/2005

**Notes:**
This example is Cabbibo-allowed decays. Cabbibo-suppressed ones: pi, rho, etc. Fully-explicit decay rate canbe calculated from first principles (eg, Feynman diagrams. No final-state interactions to worry about!
QCD complications are contained in form factors.
1 (+1) for pseudoscalar-l-
3 (+1) for vector-l-
Form factors can be predicted by HQET, LGT, Quark models: Though today, I’ll talk about LQCD only.
Shape measurement determines form factor ratios for vector-l-
Branching ratio measures absolute FF scale times VCS, VCD
Measurements + FF predictions can determine CKM matrix elements

## Theories of D Pseudoscalar l decays

**Theories of D******** Pseudoscalar *****l***** ********decays**

- But a major disconnection exists between experiment and theory. In the past, theories worked best where experiments worked worst.

**Simple kinematics ********  Easy to extract form factors.**

- FOCUS / Doris Kim

- 4/17/2005

**Notes:**
Here is illustration of this important disconnect in existing published charm semileptonic form factor data. The configuration that was easiest for theorists to compute left the daughter quark at rest in the rest frame of the parent which happens when qsq = qsqmax. In this configuration, one is automatically satisfying the condition that the lattice spacing is short on the scale of the deBroglie wavelength of the daughter.  The p**3 as a function of q**2 plot illustrates  that the rate falls off dramatically one approaches qsq max  Finally I show two commonly appearing parameterizations for crossing the divide between observation and prediction.  A pole dominance form where the spectroscopic pole would be the lowest vector c sbar state or the Ds**.  Another form in the literature is the Isgur-Wise form which is exponential in f+ with suggested slope values. If one is not running at the 3770, qsq resolution is terrible and hence one is essentially forced to use one or the other of these forms to extrapolate.   To make a truly incisive test of theory one needs to measure the form factor in a region where there is still substantial rate as well a strong theoretical prediction.
By the way, Aida f+/f0 may not be the experimentally measured f+/f-!.

## What do we measure?

**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. Now we have enough data, hence,**

**What do we measure?**

- (old) ISGW1

-  Method I:  f+(q2) shape obtained non-parametrically by deconvolution.
-  Method II: Or fit  f+(q2) using specific forms.

- (old) pole

- modified pole

- f+(q2) parameterization

- ISGW2

**Updated version****.**

**Spin 1 D*****S**

- FOCUS / Doris Kim

- 4/17/2005

**Notes:**
M(D*s) = 2.112 for K l nu, m(D*) = 2.010 for pi l nu

## II. Reconstructing D0  K +  and +

** ****A good muon candidate.**
** ****Cerenkov ID for K/******** candidates.**
** ****Good CL’s for D production/decay vertices, and L/******** > 5 between two vertices.**
** ****D* tag required, and wrong sign soft ****************subtraction******

**II. ****Reconstructing D****0**** ******** K******** ********+**** ******** and ****************+******

- Selection

**~**

**cut**

**rs-ws**

**MC ws**

- 12,840 K + ** **

- Neutrino Reconstruction

-  K rest frame
-  The D and D* mass constraints the  neutrino lies on a cone around the soft pion.
-  Pick the **** that points the D closest to the primary vertex.

**/GeV/c****2**

- FOCUS / Doris Kim

- 4/17/2005

## III.a q2 dependence: Deconvolution approach.

**We actually use a 10 ******** 10 matrix**

**A deconvolution matrix  is constructed from the number of events generated in the i-th  q****2**** bin that end up reconstructed  in the  j-th q****2**** bin. This matrix is then used to correct data for resolution and efficiency.**

- FOCUS / Doris Kim

- 4/17/2005

## Correcting for charm backgrounds inD0  K +  

- The background only affects the highest q2 bins.

- After subtracting known charm backgrounds,** **f+(q2) is an excellent match to a pole form with mpole= 1.91  0.04  0.05 GeV/c2 or **** = 0.32  (CL 87%, 82%).

- FOCUS / Doris Kim

- 4/17/2005

**Notes:**
Background is 12.6%, non-negligible.

## III.b Parameterized f+(q2) for D0  K +  / +  

**III.b Parameterized ****f****+****(q****2****) for ****D****0**** ******** K******** ********+**** ****** **/************ ********+**** ******

**6574 K******** ********+**** ********events**

**288************ ********+**** ********events**

-  2-dim fit: cos l, q2
-  Signal ~ MC with reweighted intensity.
-  Backgrounds are floated within known uncertainties.

- FOCUS / Doris Kim

- 4/17/2005

## Comparing to Lattice Gauge Result

**Comparing to Lattice Gauge Result**

**K******** ********+**** ******

- FOCUS / Doris Kim

- 4/17/2005

## Other q2 information in D0  K l  /l 

**Other q****2**** information in D****0**** ******** K******** ****l******** ******** /************l******** ******

- lpole mass is

******l******

**Kl******

- It disfavors ISGW2 form by ~4.2

**q2 / GeV2**

- Kl

- l

- Cleo 2004 lpole mass is

**Preliminary study**

- FOCUS / Doris Kim

- 4/17/2005

**Notes:**
Cleo claims a qsq resolution of 0.4 GeVsq. The igws2 form has a chisq/dof =f 18. the other forms are consistent.  they evidently assign the pion mass when computing the qsq in kmunu events so that the kinematic range is the same (very goofy!).  this causes a larger resolution correction.   The correlations are roughly rho12=–75%

## Summary of D0  K l  l Results

**Summary of D****0**** ******** K******** ****l******** ************ ****l******** ********Results**

- K*l*

- New world average for **K******** ****l******** ******

- New world average for ********** ****l******** ******

- FOCUS / Doris Kim

- 4/17/2005

**Notes:**
Cleo claims a qsq resolution of 0.4 GeVsq. The igws2 form has a chisq/dof =f 18. the other forms are consistent.  they evidently assign the pion mass when computing the qsq in kmunu events so that the kinematic range is the same (very goofy!).  this causes a larger resolution correction.   The correlations are roughly rho12=–75%

## Question slides

- FOCUS / Doris Kim

- 4/17/2005