# Presentation: 898567

## Semileptonic Charm Decays and QCD

- Doris Y. Kim, University of Illinois Urbana-Champaign

** ****Content**
-  Part I: Theories of Charm Semileptonic decays
-  Part II: q2 dependence in Pseudo-scalar l decays
-  Part III: Vector l decays
-  D+  K*0  analysis (not so simple!)
- Form factors ofDs   
-  Part V: Future of Semileptonic decays.

**Semileptonic Charm Decays and QCD**

- ISMD Sonoma July 27, 2004

- E791

- E687

## I: Charm semileptonic decay as tests of LQCD

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

- The hadronic complications are contained in _the form factors_, which can be calculated via non-perturbative _Lattice QCD_, HQET or quark models.

- 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.*

**Notes:**
This example is Cabbibo-allowed decays. Cabbilo-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

## II: Pseudoscalar l decays

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

**is the easiest point for LQCD calculation.**

***P***** at rest**** in D frame**

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

- The lattice community is actively fixing the situation and calculating f+ as a function of q2.

**hep-lat/0309107 preliminary**

**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-!.

## Comparing Pole versus ISGW forms in Dl

**The difference between these forms can be quite dramatic in ******** ****decays. **

**Especially since ******** ****decay gets **_**quite**_** close to the D* pole. **

**ISGW1**

- f+(q2) parameterization

- pole

**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+(q2) information.

**ISGW2**

**Updated one.**

**Notes:**
Finally to the right I compare the qsq dependence and momentum spectrum predicted by the ISGW and pole form in previous data. You can see how non-linear the pole form is at the high qsq end.  Both forms appear consistent with the present lattice calculations but could be easily distinguished from 1 inverse fb of 3770 running.  I slightly tuned the ISGW parameter to match the slope of the pole form at low q^2.

Alpha slope could be measured to 4% in pilnu or klnu. Presently measured to about 12% only in K*mn

I tuned the alpha parameter from 0.32 to 0.26 to match the low qsq slope.This means forms are tuned to hi Ppi since inversely related.  This is not the quenched approximation. the shaded regions are the range where the groups can control systematic uncertainties. the lower limit cuts out a region where extrapolations in P and the light quark mass are difficult.

## Brand new q2 information in Dl/Kl

**Preliminary Cleo 2004 ********e********pole mass is **

**It disfavors ISGW2 form by ~4.2******

**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 Dl/KlResults

- Summary of Dl/KlResults

**Consistent w/ SU(3) breaking**

- K*l*

**BR**

**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%

## III: Dvector   decays

**H****0****(q****2****), H****+****(q****2****), H****-****(q****2****) are helicity-basis form factors computable by LQCD**

**Notes:**
Here is a diagram showing the internal angles in terms of which the decay rate is expressed.  We call these the weak decay angle, the vector or strong decay angle, and the acoplanarity angle.  You get a fairly scary looking expression for the decay intensity but when written in this amplitude form all of the pieces are easy to understand in terms of “helicity” basis form factors that describe the  amplitude for the W to be in each of its three allowed spin states. These helicity basis form factors are combinations axial and vector pole forms shown here.  The form factors are traditionally fit two just two “form factor ratios”.

## Interference in D+ K* 

**Yield **** 31,254**

**Data****MC**

** ****K********* interferes with S- wave K******** and creates a forward-backward asymmetry in the K* decay angle with a  mass variation** **due to the varying BW phase.**

- (2002)

**The S-wave amplitude is about 7% of the (H****0****) K* BW with a 45****o**** relative phase**

**Focus “K*” signal**

**It’s the same relative phase as the LASS (1988)**

**Notes:**
Are these isodoublet phase differences from LASS
One interesting complication to semileptonic decay was published by Focus in 2002.  Although the Kpi mass peak of focus looked pretty much like a pure K*, there was an interesting asymmetry on the K* decay angle below and above the K* peak The forward backward asymmetry as a function of kpi mass was consistent with s-wave amplitude interfering with the K* breit wigner which of course changes phase as a function of mass. This interference also created a previously unobserved  asymmetry in the acoplanarity between the K* and virtual W decay planes.

##  K*form factors

**Results are getting very precise and unquenched calculations for incisive tests of the theory would be **_**very desirable**_**.**

**Notes:**
The s-wave interference was discovered in the process of measuring the K*munu form factor ratios.  Here are is a comparison of these measurements for RV and R2 compared quark model and lattice gauge theory.   On the right we probe some neat features of the model by showing how the acoplanarity distribution changes as a function of the K* decay angle.

## Direct measurement of  (D+K* / K)

- Direct measurement of  (D+K* / K)

**Use upstream K****s****  (~10%) so that both the numerator (K********) and  denominator  ****(K****s**** ********) leave 3 tracks in FOCUS ********-strip **

**S-wave corrected**

**Old quark model**

**Notes:**
Originally, the theory expected the BR to be 1. During 90’s new experiment and theory results got lower values. His results indicates that unseen semileptonic decays modes of D+ are unlikely.

## The Ds form factor enigma

- The Ds form factor enigma

**Theoretically, the ****Ds********l************form factors should be within 10% of  ****D+ ********K*l******** The r****V**** values were consistent, but r****2**** for ****Ds********l************was  2 ******** higher than  ****D+ ********K*l******

**But the (2004) FOCUS measurement obtained a consistent r****2**** value as well!**

**D****s**** ******versus **D+ ********K*l******

- circa 1999

- circa 2004

**Notes:**
Here is another result from FOCUS which bears a long standing enigma concerning the Ds to phi mu nu decay. One always expected that these form factors should lie within 10% of those for K* mu nu.  If we look at the older data we find the Rv values were consistent but the r2 values for phi mu nu (red averages) were a factor of two larger than the for D+ to K*munu (blue averages).  New precise measurements from focus changes this picture. They get an R2 for phimunu which is very consistent with K*munu.

## The future of charm SL physics

**Precision neutrino closure in D ********e********.**

**Cleo-c and Bes III: Run at  ********(3770) with high luminosity and modern detectors.**

**The q****2**** impasse afflicting SL data for the last 20 years shall be solved, finally.**

**Notes:**
Resolution got improved for neutrino closure.

## Summary

##  (D+K* / K) circa 1993

## Some more tests of  the K*model 

**Generally the model tracks the data rather well...**

**Focus has a preliminary analysis of the K*****0**** line shape.  ********K*****0****)********is seen as less than PDG by********~1.6 MeV.**