APS 5-MAY-2009 G. Gutierrez, Fermilab Edward A. Bouchet Award Talk “ The top quark mass, a brief...

APS 5-MAY-2009 G. Gutierrez, Fermilab

Edward A. Bouchet Award Talk“The top quark mass, a brief history and present status”

Gaston GutierrezFermilab

This talk is dedicated to the memory of Clicerio

Avilez.


• Concepts of maximum likelihood.

• A brief history of the top quark mass measured by calculating a probability density distribution for every event.

• The current status of the top mass measurements.

• Other application of M.E.M.

• Conclusion.

Outline of the talk


If for an event characterized by a set of measurements one can calculate the probability density function:

then given N events the optimal estimation of the set of parameters is obtained by maximizing

General Maximum Likelihood technique

)|( xP

x

N

iixPL

1

)|()(

1)|(with dxxP


In general we have to sun over all states that can lead to the set of measurements

the sum is over probabilities (amplitudes) if the states do not (do) interfere. For a perfect detector we have

with

Probability calculation

states

ss xPcxP )|()|(

x

)(

)|()|(

xd

dxxP ss

space phase factorflux

|| 2

M

d


Probability calculation for real detectors

)|,()|()(

)|,()|()()|(

xyWydxAdx

xyWydxAxP

s

ss

Detector acceptance(e.g. cuts, trigger, …)

partonicintegral partonic

variables

mapping between partonicand measured variables

measuredvariables

parameters

Integral over measuredVariable (normalization)


Why apply the previous method to the top mass?

• The top mass is an important SM parameter.

• Together with the W mass it constrains the Higgs mass

• Top is a very isolated state, which makes for a cleaner calculation of the pdf.

• No matter which method we use we all need to model the relation between the top mass and the detector measurements.


Kunitaka Kondo

J. Phys. Soc. Japan, 57, 4126 (1988)

J. Phys. Soc. Japan, 60, 836 (1991)

J. Phys. Soc. Japan, 62, 1177 (1993)


R.H. Dalitz and Gary R. Goldstein

Phys. Rev. D45, 1541 (1992)

Proc. Roy. Soc. Lond. A455, 2803 (1999)

J. Mod. Phys. A9, 635 (1994)

Phys. Lett. B287, 225 (1992)

Phys. Rev. D47, 967 (1993) (with K. Sliwa)


D0 experiment

Nature 429,638 (2004)

First complete measurement, including: 1) all detector effects (e.g. reconstruction efficiencies, cuts, trigger, …), 2) correct normalization, 3) background probabilities, 4) MC tests of linearity, 5) pull calculations and 6) estimation of systematic effects.


Run I: Top probability for data events

Left plot show -ln(Ptt) as a function of

Mt for 10-9<Pbkg <10-8 (red arrows in

lower figure).

x=-ln(PB)

x=18.5

x=20.4

x=20.0x=19.4

x=19.2

x=20.5


Run I: Top probability for data events

Left plots show -ln(Ptt) as a function of

Mt for 9.7x10-13 <Pbkg < 9.0x10-12 (red

arrows in lower figure).

x=-ln(PB)x=27.7x=27.2

x=26.7x=26.6

x=25.9

x=25.7


Run I: MC linearity after background selection

Test of linearity of response with MC samples containing large numbers of events.

The number of events in the plot are given before the background cut


Run I: Top mass measurement

Mt= 180.1 3.6 GeV (stat)

This new technique improves the statistical error on Mt from 5.6 GeV [PRD 58 52001,

(1998)] to 3.6 GeV. This is equivalent to a factor of 2.4 in the number of events. The number of extracted signal events is: (11±3)/(0.71 x 0.70 x 0.87)=25 ±7

(a 0.5 GeV shift has been applied, from MC studies)


Run I: W mass check

80.9 ± 2.6 GeV

(GeV) BMWM (GeV) BM

WM

The likelihood minimizes at = 79.4 GeV, with an error of 2.2 GeV. Studies at Mtop= 175 GeV show that there is a systematic shift in MW of 1.5 GeV and an under estimation of the error of 20%. Therefore

BMWM

GeV 6.29.80 WM


Tevatron Run II top quark mass results using M.E.M.


SM Top pair production


lepton+jets top event

p

pt

b

W

qq

W b

t

l


Top and W decay

Wlq

νq’-bar

p = 40 GeV/cThe decay to jets is 3 times more likely than to e and μ

tb W

p ~ 70 GeV/cTop decays to W+b essentially 100 % of the time

Mt = 172 GeV/c2

MW = 80 GeV/c2


Run II: Top mass at D0

There were many improvements in the probability calculations. But the main gain has been to: 1) include a Jet Energy Scale (JES) parameter in the minimization and 2) use a prior from the γ+jet energy calibration.

lepton+jets most recently published result (1 fb-1)


Run II: Top mass at D0

lepton+jets most recently published result (1 fb-1)


Results presented at this conference


Top, W and Higgs masses are related

)/ln(

and 2802.37

)1/()/1(

222

2222

WHt

ZWW

MMcmbar

GeVA

rAMMM

Accurate measurements of the top quark and W boson masses put constraints on the mass of the Higgs boson. Because of the log dependence to have meaningful constraints on the Higgs mass high precision measurement of the W and top quark masses are required.


LEP EWWG as of March 2009

These (almost) lines are EW the predictions.


Higgs limits as of March 2009

The SM Higgs mass limit from the EW fit is: mH<163 GeV/c2 at 95% CL.

Footnote: There is a 3 σ discrepancy between the hadronic and leptonic F-B asymmetries. If any of this two are removed there are big changes in the Higgs mass limits (see M. Chanowitz, PRD 66:073002, 2002 and Fermilab W&C 2/23/2007)


Other applications also presented at this conference


Top-antiquark mass difference measurement


gg HW+W-l+l-Basic selection:• Two opposite sign isolated

leptons• missing transverse momentum

Main backgrounds:• WW, WZ, ZZ• W+jets and Drell-Yang

Geometry help

Use full power of Matrix element


HW+W- in CDF (1.9 fb-1)

Calculate probabilities

Calculate discriminant

Check for observation

If no observation set limit


Conclusion

To conclude I would like to thank my colleagues for the exiting times during the past decade (when all this work was done) and many thanks to the young people that are carrying this work forward.


Backup slides


The general method

N

ii

dxxpNxPeL

1

);();()(

),()()();(1

);( 2121 yxWqfqfdqdqydxPtt

);()();( xPxAccxP

Most people would agree that if the probability of an event could be calculated accurately then the best estimate of a parameter will maximize a likelihood like:

The detector and reconstruction effects are always multiplicative and independent of the parameter to be estimated:

The probability P(x;α) can be calculated as:

Where x is the set of variables measured in the detector, y is the set of parton level variables, dσ is the differential cross section and f(q) are the parton distribution functions. W(x,y) is the probability that a parton level set of variables y will show up in the detector as the set of variables x. The integration reflects the fact that we want to sum over all the possible parton variables y leading to the observed set of variables x.


Transfer function W(x,y)W(x,y) is the probability of measuring x when y was produced (x measured variables, y parton variables):

where Ey energy of the produced quarks Ex measured (and corrected) jet energy py

e produced electron momenta px

e measured electron momenta y

j xj produced and measured jet angles

)(),()(),( 24

1

3 xi

yi

i

xi

yijet

xe

ye EEWppyxW

The energy of the electrons is considered well measured. And due to the excellent granularity of the D calorimeter the angles are also considered as well measured. A sum of two gaussians is used for the jet transfer function (Wjet), the parameters were extracted from MC simulation.


Probability for tt events

2(in) + 18(final) = 20 degrees of freedom

3 (e) + 8 (1..4) + 3 (Pin=Pfinal) + 1 (Ein=Efinal) = 15 constraints

20 – 15 = 5 integrals

Sum over 12 combinations of jets

All values of the neutrino momentum are considered

1 momentum of one of the jets m

1,m

2 top mass in the event

M1,M

2 W mass in the event f(q

1),f(q

2) parton distribution functions (CTEQ4) for qq incident chann.

q1,q

2 initial parton momenta

6 six particle phase space

W(x,y) probability of measuring x when y was produced in the collision

We chose these variables of integration because |M(α)|2 is almost negligible everywhere except near the peaks of the four Breit-Wigners in |M(α)|2.

,

621

21222

22

21

211 ),(

||||

)()(|)(|),(_

combjet

ttyxW

qq

qfqfMdMdmdMdmdxP


Matrix Element

no ttbar spin correlation included s

qt sine of angle between q and t in the q q CM

top quark's velocity in the q q CM g

s strong coupling constant

Leptonic decay

Hadronic decay

Mt, MW pole mass of top and W mt top mass in any eventme ,mdu invariant mass of the e and du (or cs) systemt ,W width of top and W gW weak coupling constant(cos eb,db) angular distribution of the W decay

)2(9

|| 224

2qt

s sFFg

M

22222222

224

)()(

)(cos

)()(4 WWWe

be

tttt

etw

MMmMMm

mmgF

22222222

224

)()(

)(cos

)()(4 WWWud

bd

tttt

udtw

MMmMMm

mmgF

2

2

222 )1()1()( x

m

mxmx

t

Wt


Acceptance Corrections

Detector Acceptance

Likelihood

Production probability

Detector acceptance

N

ii dxxPNxPL

1

);();(ln)(ln

);()();( xPxAccxP Measured probability

N

ii dxxPxAccNxPL

1

);()();(ln)(ln

N

jgenN

VdxxPxAcc

1

112

);()(

)()()( 2121 qfqfdqdqydV n , and Ngen(N) is the number of generated(accepted) events

APS 5-MAY-2009 G. Gutierrez, Fermilab Edward A. Bouchet Award Talk “ The top quark mass, a brief...

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Transcript of APS 5-MAY-2009 G. Gutierrez, Fermilab Edward A. Bouchet Award Talk “ The top quark mass, a brief...