# Presentation: 707255

## Direct Measurement of the W boson Decay Width at DØNeeti Parashar

**Northeastern**** University**
**Boston, Massachusetts**
**U.S.A.**

**DPF Meeting, College of William and Mary, VA, USA.**
**	****	**** ****24 May, 2002**

**Notes:**
I would like to present a measurement of the W boson decay width done at D0 at Fermilab, using a direct method.

## Outline

**Introduction**
**Event Selection**
**Monte Carlo Simulation**
**Background Estimation**
***W***** Width Determination**
**Systematic Uncertainty**
**Conclusions**

**Notes:**
The outlijne of my talk is the following.
I shall begin with an introduction to the motivation for this measurement. Then I shall present the analysis strategy, starting with the event selection, background estimation, simulations done with the Monte Carlo, the determination of the W width, including the sources of systematic uncertainties and finally concluding with the results.

## Introduction

***W***** decay width, *********W***** ****, is an important parameter in the Standard Model (SM)**
**In pp collisions, *****W*****’s are**** **
**produced**** ****by process:**** ****ud ******** W**
**decay**** ****leptonic:**** ****W ******** *****l*********; *****l***** = e, ******** ******** **
**    ****hadronic:**** ****W ******** *****q*****’*****q*****; *****q*****’ or q = *****u*****, *****d*****, *****s*****,*****c***** or *****b***** (not t)**
**Considering 3 color charges, total of 9 decay channels yield a total width of ~ 9********(*****W ************ e*********) **
**Including QCD corrections, the SM prediction for the full width is given by**

- GeV

**Notes:**
The W decay width is a derived quantity in SM. There are 3 leptonic decay channels and 6 hadronic decay channels (taking the 3 color charges into consideration) for the W boson, which lead to the SM prediction for the full width of the W boson.
.........
Historically, the accurate determination of the W width was available through an indirect measurement using the ratio R of the W-> ev and Z ->ee cross sections, which uses the W and Z cross-sections as calculated in the SM and the Z -> ee branching fraction from LEP. It also assumes the coupling of the W to the leptons in order to determine full width. D0 published its indirect result with ....

So what is the motivation for doing a direct measurement of  this quantity? One obvious one is to test the predictions that the SM has made. In addition, the direct measurement explores the region above the W mass  pole, where possible new phenomena such as additional heavy W (W prime) can contribute. Also, it is desirable to have more than one method of measuring a given property. 

## Introduction

-  **Indirect measurement**
**Assumes *****W***** coupling to lepton to determine ********(*****W***** *********e*********)**
******(*****W*****)/********(*****Z*****) from theory and Br(*****Z*****0 *********ee*****) from LEP**
**Measured by UA1, UA2, LEP, CDF, DØ**
**DØ result (2000):**
**CDF result (1995):**

- GeV

- GeV

**Motivation for Direct Measurement**

** ****a test of SM**
** ****a probe for possible new physics**

**Notes:**
The W decay width is a derived quantity in SM. There are 3 leptonic decay channels and 6 hadronic decay channels (taking the 3 color charges into consideration) for the W boson, which lead to the SM prediction for the full width of the W boson.
.........
Historically, the accurate determination of the W width was available through an indirect measurement using the ratio R of the W-> ev and Z ->ee cross sections, which uses the W and Z cross-sections as calculated in the SM and the Z -> ee branching fraction from LEP. It also assumes the coupling of the W to the leptons in order to determine full width. D0 published its indirect result with ....

So what is the motivation for doing a direct measurement of  this quantity? One obvious one is to test the predictions that the SM has made. In addition, the direct measurement explores the region above the W mass  pole, where possible new phenomena such as additional heavy W (W prime) can contribute. Also, it is desirable to have more than one method of measuring a given property. 

## Direct Measurement

**The total decay width, ********W****, of the *****W***** could be measured by the transverse mass m****T ****of *****W*********e******** **
**m****T**** spectrum is sensitive to the *****W***** decay width, particularly in the high end**
**Theoretical input of ********(*****W*****)/********(*****Z*****) not required**
**Radiative corrections to *********W***** can be observed**

**Notes:**
The direct measurement relies on the fact that the width can be obtained from the line shape of the transverse mass of W, because the Breit-Wigner (width) component of the line shape falls off more slowly at high mt than the resolution does. The transverse mass is given by ........, where pt and pe are the transverse momenta and phi-e and phi-v are the azimuthal angles of the elctron and the neutrino respectively.

This figure shows the mt spectrum shape expected for different values of width and indicates the sensitivity of the tail of the distribution to the width.

The advantage is that the theoretical inputs for sig ( )....., which may be sensitive to non-SM coupling of the W boson are not required.
The radiative corrections to decay width could be observed by this measurement.

## Event Selection

***W***** ********e******** ****event selection**
**1994-1995 Run I data, 85 pb****-1**

**“****Loose” Electrons**
**Fiducial region:**** ****|********|< 1.1** **in central  calorimeter (CC)**
**High EM fraction:**** ****f****em**** ****> 0.9**
**Isolation of EM cluster:**** ****f****iso****< 0.15**** **
**Shower shape**** consistent with that   expected for e: ********2**** < 100**

**“****Tight” Electrons**
**     “****Loose” Electrons AND**
**Track match:**** ********trk**** < 5**
**4-variable likelihood**** ****(**2,trk,fem,fiso**)  4vl ****< 0.25**

**Missing** **E****T****> 25 GeV**
**p****T****(*****W*****) < 15 GeV**

**Notes:**
We select W ->ev events for this analysis, which are selected offline. The data samplewas collected during the 1994-1995 run of the Tevatron collider with an integrated luminosity of 85 ...   We require the electron to be a tight electron, which means it should satisfy the following conditions.
The e should be in the center of the calorimeter.
It should deposit at least 90% of the energy in the EM section of the calorimeter and
Should be isolated from other calorimeter energy deposits.
A shower shape measure by chi-sq , consistent with that expected of an EM shower is compared
To increase the likelihood that the cluster is due to an electron and not a photon, a charged track from the central tracking system is required to point to the center of the EM cluster. The variable sigma(trk) quantifies the quality of the match.

To a good approximation these 4 variables are independent of each other for electron showers. So a tight electron satisfies all of these conditions.
The missing energy corresponding to the neutrino is required to be > 25 GeV and the
W transverse momentum < 15 GeV.

## Event Selection

***W***** transverse mass**

**A typical *****W ************ e********* event in Run I**

** ****Total *****W *****candidates = 24487**

***  ******W *****candidates in m****T****  bins****	**

**	****(45, 200)  2447**
**	****(75, 200)  6286**
**           ****(90, 200)    319**

**Notes:**
A typical W-> ev event looked like this in Run I.  The red color corresponds to the EM energy deposited for the electron and the magenta for the momentum imbalance for the neutrino. This is the transverse mass spectrum of the w-> ev candidates after applying all of the cuts imposed. We are left with 24487 candidates. In the 90-200 Gev there are 319 events.  

## Zee event selection

**To study **
**	****Electron Efficiency**
**                   ****&**
**	****Monte Carlo (MC) simulation**
**Both electrons are in CC region and “tight”**
**p****t****(e) > 25 GeV**
**Invariant mass of dielectron pair**
**     ****60 GeV < m****ee**** < 120 GeV**
**Total candidates = 1997**

**Notes:**
We use the z->ee candidate sample to calibrate both the data and the Monte Carlo. We require both the electrons to be in the central region and should be tight each with pt > 25 GeV. The invariant mass of the dielectron pair is required to satisfy the range from 60 – 120 GeV.

This figure shows the inv. mass distribution of the Z->ee candidates. 
The histogram is the MC and the black dots with the error bars is the data.

## Monte Carlo

**A fast Monte Carlo, also used in the *****W***** mass analysis**
**Three main steps**
***W(Z)***** boson production**
**For MRSA, β = 0.00852 ******** 0.00013**
**For CTEQ4M, ****β = 0.00852 ******** 0.00012**
***W(Z)***** boson decay**
**Include W ********e******
**Detector simulation**
**Parameterized simulation**
**Parameters need to be constrained from real data (Z********ee, ****π****0****, etc)**

**Notes:**
We use the Monte Carlo simulation to model the transverse mass spectrum. . The Monte Carlo used is called CMS after Columbia Michigan State. It is a fast MC. The tran. Mass spectrum is modeled in 3 steps
W boson production
We first simulate the production of the W by generating its four momentum and other event characteristics. To lowest order, the mass of the W is given by this formula, .....   where m is the inv. mass of the W generated, M is the pole mass and this quantity is the parton luminosity. To evaluate this we, generate w->ev events using different PDF models and then select events using the same kinematic and fiducial contraints as for the W and Z data samples.  The resulting event distribution is proportional to the parton luminosity, which we parameterize with the function ......, where beta is obtained from a fit of the MC events to above. 
W boson decay
	The decay of the W is used to calculate the transverse  momentum of the electron and other decay products. The W-.tau nu is included in this since it cannot be distinguished from W -.ev events.
3.   Parameterized detector simulation
Finally we apply a a parameterized detector simulation to simulate the detector response and resolution to obtain electron and recoil momenta. The parameters are constrained using real data with Z ->ee, pions, J/psi etc.

## Background

**Multijet events**
**Energy is mis-measured (missing E****t****)**
**The other passes electron cuts (fake electron)**
**Z ******** *****ee***
**One electron is missing or mis-measured**
**HERWIG *****Z***** events and GEANT simulation**
**MC sample passed through *****W***** selection cuts**
**Normalized, total = 102**
**W ********e******
**Same signature as *****W***** ******** *****e***********, but at low p****t**
**Included in MC**

**Three main backgrounds to *****W***** ******** *****e********* sample**
** **

**Notes:**
Backgrounds are processes that mimic our signal, and can affect the shape of the trans. Mass spectrum and skew the measurement of the width. There are 3 main backgrounds.
One large potential source is due to multijet events in which one jet is misdientified as an electron and the energy in the event is mismeasured, thereby yielding large missing Et., or the other passes our electron selection criteria. 

Another source of background is due to Z->ee  events in which one electron is undetected. This results in momentum imbalance with the event now being topologically indistinguishable from W -> ev events. This bkgd is estimated using MC events generated by HERWIF, processed thru GEANT simulation of the D0 detector and passed thru the W selection. After normalizing it to the size of the data we estimate 102 events.

W -> taunu events in which the tau decays into an e and two neutrinos are indistinguishable from W -> ev events. The size of this bkgd is small, and it tends to add events with low values of mt, and is included in MC.

## Multijet Background

**Method (Data based)**
**Loose sample:          N  =     N****s ****+   N****b**
**Tight (data) sample:  N****t**** = ********e****N****s ****+ ********j****N****b**
**Background in data  N****b****= ********j****(********e****N- N****t****)/(********e****-********j****)**
**The difference between loose and tight                           samples is the *****e***** requirement cuts**
**Efficiencies**
******e****: electron efficiency**
**Use Z*********ee***** data**
******e****=0.8633 ****±0.0118**
******j****: jet efficiency**
**Use non-isolated data without missing E****t ****requirement**
**Calculate ********j ****in low missing E****t**** region (0-10 *****GeV*****)**
******j ****= 0.0583 ****±0.0016**

**Notes:**
I shall explain a bit as to how the multijet bkgd is estimated, since this is the dominant one. The method used is called the Matrix method, which uses 2 sets of data, each containing both signal and background. The difference is that of e cut on the two samples. The number of multijet bkgd events in the tight sample is given by  ...........So the task is to determine the electron efficiency and jet efficiency.  

Electron efficiency is the fraction of loose electrons that pass the tight electron criteria.
We use Z-> ee data and get 86%.
Jet efficiency is the fraction of loose electrons found in multijet events that also pass tight electron criteria. And this number is about 5.8%.

## Inclusive number 
         368±32
In 90 <mT< 200 GeV  25.4±2.2
Background distribution vs. mT
Smooth background with exponential function in tail

**         ****368****±32**
**In 90 <m****T****< 200 GeV****  ****25.4****±****2.2**
**Background distribution vs. m****T**
**Smooth background with exponential function in tail**

**Multijet Background**

**Notes:**
The total multijet bkgd is estimated to be 368 events in <200 GeV Mt bin. This is a trans. Mass distribution for the multijet events. We fit the distribution to an exponenetial function of the form ......., which is repsresented by this line here.

## Fast MC simulation
Generate W  e events with different W 
Run through W selection cuts
Normalize MC to data with background subtracted
Add background
QCD background
Zee background
Calculate likelihood for different W
Calculate likelihood data vs. MC
Find W at maximum likelihood
Find statistical uncertainty

**Generate *****W***** ******** e******** events with different *********W***** **
**Run through *****W***** selection cuts**
**Normalize MC to data with background subtracted**
**Add background**
**QCD background**
**Z********ee background**
**Calculate likelihood for different *********W***
**Calculate likelihood data vs. MC**
**Find *********W***** ****at maximum likelihood**
**Find statistical uncertainty**

*******W***** Determination**

**Notes:**
The next step is to determine the width , which we do using our fast MC simulation. So we generate w_ev events with different gamma ...........
Then we perform bin log-likelihood fits. The log likelihood is the product of the probabilities of the events coming from a given distribution. 
Gamma W is estimated at maximum likelihood for which statistical uncertainty is also evaluated.

## W Determination

**For fitting region m****T****(****90,200****)**** with 319 events**
-                      ******W**** =2.231****+0.145****/-0.138**** GeV**
******2****=22.6/22 and Kolmogorov-Smirnov test, *****k***** = 0.434**

**Notes:**
This plot here shows the results of log-likelihood fit of the to MC templates for different gamma W. For our fitting region of 90-200 GeV with 319 events gamma W is   .........
With chi-sq = ....and a Kolmogorov Smirnov test yields kappa = 0.434, which is evidence of a good fit.

The plot on the right is a comparison of data to the MC templates for best fit. Black circles with error bars are the data. The solid line of the histogram corresponds to the MC templates with gamma W = 2.23 normalized to the expected no of W events. The shaded area is the background.

## Uncertainties

| Parameter | Value |  (MeV) |
| --- | --- | --- |
| Hadronic Energy Resolution | 0.49  0.14 | 55 |
| Electron Energy Scale | 0.95450.0008 | 41 |
| Background (ensemble) | N=40 | 39 |
| Luminosity slope dependence | (8.52  0.12)E-3 |  28 |
| Electron Energy Resolution | 0.0115 +0.0027-0.0036 | 27 |
| PDF(MRSA, MRST, CTEQ5M, CTEQ4M) | - | 27 |
| Hadronic Energy Scale | 0.6930.060 | 22 |
| Background (uncertainty) | - | 15 |
| W mass | 80.436  0.037 | 15 |
| Wpt theory | 0.58  0.06 | 12 |
| Radiative corrections | 0.3  0.1 | 10 |
| Angular calibration of e trajectory | 0.998  0.001 | 10 |
| Selection bias | - | 9 |
| Systematic Uncertainty | - | 99 |
| Statistical Uncertainty | - | +145 / -138 |
| Total Uncertainty | - | +176 / -170 |

**Notes:**
This table lists the sources of systematic uncertainties that can alter the shape of the transverse mass distribution and the total uncertainty on the W width measurement.

## Conclusions

**(hep-ex/0204009, submitted to PRD)**
**Consistent with SM**
**CDF+D0 direct measurement (preliminary)**
**Preliminary world average**

**Conclusions**

- GeV

- GeV

- GeV

- GeV

**Notes:**
We have measured gamma W directly from the shape of the trans mass psectrum of W. The measured value is consistent with the SM prediction.
Results from Do and CDF have been combined  together and with all of this the world average for the direct measurement is 2.135

This analysis shall be even more important in RunII when the indirect measurement shall be limited by statistical uncertainty.