Improving acceptance for Higgs events at CDF

Anno A ademi o 2006/2007

Tesi di Laurea Spe ialisti a

Improving a eptan e for Higgs events at CDF

Tesi di Federi o Sforza

Introdu tion vii

1 Standard Model of Elementary Parti les and Higgs Physi s 1

1.1 Standard Modelof ElementaryParti les . . . 1

1.1.1 Gauge Theory . . . 2

1.1.2 Standard ModelTheory . . . 4

1.2 HiggsMe hanism . . . 6

1.2.1 Spontaneous Symmetry Breaking inSM . . . 7

1.3 Experimental LimitsonHiggsBoson Mass . . . 9

1.4 HiggsProdu tionand Sear h atthe Tevatron . . . 11

1.4.1 HiggsProdu tion and De ay . . . 12

1.4.2

W H

Sear h atthe Tevatron . . . 15

2 The Tevatron Collider and the CDF II experiment 19 2.1 The Tevatron . . . 19

2.1.1 Proton and AntiprotonProdu tion . . . 19

2.1.2 Collisionand Performan e . . . 21

2.2 The CDF Dete tor . . . 23

2.2.1 Overview and Coordinate system . . . 24

2.2.2 Tra kingSystem . . . 26

2.2.3 Central OuterTra ker . . . 29

2.2.4 CalorimeterSystem . . . 30

2.2.5 OtherDete tors . . . 34

2.3 Trigger and DataHandling . . . 37

2.3.1 CDF Software Framework . . . 40

3 Physi al Obje ts Re onstru tion 43

3.1 Tra ks Re onstru tion . . . 44

3.1.1 Tra kingAlgorithms . . . 45

3.2 Calorimeter Ele tronIdenti ation . . . 47

3.3 Muon Identi ation . . . 49

3.4 Primary Vertex Identi ation . . . 50

3.5 Neutrino Identi ation . . . 50

3.6 Jet Identi ation . . . 50

3.6.1 CDF Cone Algorithm. . . 52

3.6.2 JetCorre tions . . . 54

3.7 Se ondary Vertex Tagging . . . 57

3.7.1 The Se Vtx Algorithm . . . 59

3.7.2 TaggingPerforman es and S ale Fa tors . . . 61

4 Event Sele tion and Signal A eptan e 65 4.1 Data Sampleand Run Interval . . . 65

4.2 Event Sele tion Requirements . . . 66

4.3 Forward Tra king E ien y Study . . . 70

4.4 WH Signal A eptan e . . . 71

5 Ba kground Analysis 75 5.1 Overview of the Ba kground Composition . . . 75

5.1.1 Ba kground Estimate . . . 76

5.2 Non-

W

QCDBa kground . . . 77

5.2.1 Tagged non-

W

Ba kground . . . 79

5.3 Heavy Flavor Ba kground . . . 80

5.4 Light Flavors/Mistags . . . 84

5.5 Ele troweak and TopBa kground . . . 87

5.6 Ba kground Summary . . . 88

6 Comparison of Kinemati Quantities 95 6.1 Kinemati Comparison . . . 95

7 Con lusions 105 7.1 Shapes Comparison . . . 106

7.2 Signal Improvements . . . 106

7.3 Future Prospe t . . . 107

A Trigger E ien y Studies 109 A.1

MET

_

PEM

Trigger Path . . . 109

C Tight Ele trons and Muons 115

The Standard Model of elementary parti les predi ts the existen e of the

Higgs boson as the responsable of the ele troweak symmetry breaking, the

pro ess by whi h fermions and ve tor bosons a quire mass. Probably the

Higgs existen e is one of the most important questions in the present high

energy physi s resear h.

This work on erns the sear h of

W H

asso iate produ tionat the CDF II experiment (Collider Dete tor at Fermilab). Even if

W H

produ tion is one of the favouredsear h hannels, the expe ted ross se tion isvery tiny:

0.1

_{∼ 0.2 pb for m}

H

< 140 GeV/c

2

,

(1)

thereforeitisoffundamentalimportan etoexploit themaximum apability

of the dete tor.

This analysis sear hs for

W H

eventsin the de ay hannel:

W

±

H

→ e

±

_νb¯b.

(2)

Appropriate utsareappliedtosele t andidateevents: oneele tronis

re on-stru ted through a alorimetri lusterin the forward regionof the dete tor

(

1.2 <

|η| < 2.8

) with a tra k mat hed to it, the neutrino is revealed as missing energy and at least one jet ompatible with

b

-hadrons de ay must be identied.

This kindofsele tionimprovesthe CDF a eptan einatwofoldway: as

rst istan ethe signal andthe ba kground arestudied inthe forward region

ofthedete tor,thatpartisnotfullyexploitedbe auseuptonowmostofthe

analysesarebasedonthewellknown entralpartofthedete tor. Asase ond

istan ea new set of tra k re onstru tion algorithmsistested, this grantsan

Standard Model of Elementary

Parti les and Higgs Physi s

Thepresent physi stheoriesof Natureidentify fourkindsof fundamental

in-tera tions: gravitational,ele tromagneti ,weak and strongintera tion. The

Standard Model of elementary parti le (SM) unies and des ribes in an

ex- ellent way the last three intera tions, it leaves out gravitational for e, that

is,however, negligibleatatomi and subatomi s ale.

The theory is veried with high a ura y and predi ted the existen e of

new parti les (like the

W

and

Z

bosons or the

top

quark) that were later dis overed. The SM predi ts the existen e of a not yet dis overed parti le,

the Higgs boson, an essential element to introdu e parti le masses in the

equation of motion[1, 2,4℄.

Indire t limits an be posed onthe expe ted Higgsmass and produ tion

ross se tion on the basis of SM assumptions and of the most re ent

ele -troweak measures. At the moment the dire t experimental limitsare above

the SMexpe tationbut the high-energy physi s ommunity ispushingforth

in the sear h. The Tevatron, being the most powerful hadron ollider

ur-rently inoperation, plays afundamentalrole inthis sear h.

1.1 Standard Model of Elementary Parti les

High energy parti le physi s inquires nature at fundamental level, its

on-stituentsandthe basi intera tions. Intheoreti alphysi slanguageparti les

are quantum lo alelds intera ting via the ex hange of for e-mediator

ve -tor bosons. A free eld is ompletely des ribed only by spin and mass, the

SM introdu es intera tions through gauge symmetries, with new quantum

The fundamental building blo ks of matter observed up to now are the

spin

1/2

elds (fermioni elds) alled quarks and leptons and the spin

1

ve tor boson elds alledgauge bosons.

Theleptonsaredividedintothreegeneration orfamilies andare grouped

ina leftweak isospin doublet 1

and a rightweak isospin singlet. Also quarks

are divided into three avor families but weak isospin lassi ation mixes

quarkdoublets ofdierentfamilies,besidesthere isthe olor quantum

num-berto take into a ountstrong intera tion.

The for e mediators are

W

±

,

Z

0

,

γ

, that arry ele troweak for e, and

g

(gluons), whi h mediate strong intera tion. A short summary of the SM fundamentalparti lesis reported inTable (1.1).

Generation Proprieties

1st 2nd 3rd Spin(

~

) Charge(

e

) Intera tion



u

d





s

c





t

b



1/2



+2/3

−1/3



EM,Weak,Strong



ν

e

e





ν

µ

µ





ν

τ

τ



1/2



0

−1



EM,Weak

GaugeBoson Mass(GeV/

2

) Spin(

~

) Charge(

e

) Intera tion

γ

0

1

0

EM

W

80.4

1

_±1

EM,Weak

Z

91.2

1

0

EM,Weak

g

0

1

0

Strong

Table1.1: Quarks,leptonsand gaugebosonsinStandardModelandsomeof

their hara teristi s,for ea h parti leexists the orresponding antiparti le.

1.1.1 Gauge Theory

The SM is a lo al quantum eld theory based on a lo al gauge symmetry

and on the least-a tion prin iple to onstrains the form of the equation of

motion.

The importan e of gauge invarian e omes dire tly from free Dira

La-grangian, the equation that des ribes freefermioni elds:

L

_{(x) = ¯}

_ψ(x)(iγ

µ

_∂

_µ

_{− m)ψ(x),}

(1.1)

where

ψ

istheDira eldofmass

m

and

γ

µ

arethe Dira 'smatri es. Eq.1.1

satises the global

U(1)

symmetry transformation:

ψ(x)

_{→ e}

iQα

ψ(x),

(1.2)

with the ele tri harge

Q

and the spa e independent parameter

α

(

x

is a spa e-time 4-ve tor). The Noether theorem[4℄ states that when a symmetry

appears in a Lagrangian there is a orresponding onserved urrent. In the

ase of the Dira eld:

∂

µ

j

µ

= 0,

(1.3)

with the urrent 4-ve tor

j

µ

₌

_{−Q ¯}

_ψγ

µ

_ψ

. This leads to the onservation of

the harge, i.e the time omponent of

j

µ

(integrated over the spa e).

An elegantway tointrodu eintera tion inthe freeLagrangian istoshift

fromthe global, i.e. spa e independent,

U(1)

transformationtoa lo al

U(1)

transformation,i.e. with aspa e dependent parameter

α(x)

:

ψ(x)

_{→ e}

iQα(x)

ψ(x),

(1.4)

tomaintainthegaugeinvarian e onditionintheLagrangian1.1, a ovariant

derivative

D

µ

is introdu ed:

∂

µ

→ D

µ

= ∂

µ

+ iQA

µ

,

D

µ

ψ(x)

→ e

iQα(x)

D

µ

ψ(x),

(1.5)

where it was dened a new ve tor eld

A

µ

transforming in the following manner:

A

µ

→ A

µ

−

1

Q

∂

µ

α(x).

(1.6)

The nal result is the QED Lagrangian:

L

_QED

_{= ¯}

_ψ(x)(iγ

µ

_D

_µ

_{− m)ψ(x) −}

1

4

F

µν

F

µν

_,

(1.7)

where

F

µν

≡ ∂

µ

A

ν

− ∂

ν

A

µ

is the ovariantkineti term of

A

µ

. If the Euler-Lagrangeequation[4℄ is applied,we obtain the Dira equation of motion for

a eld

ψ

undergoing ele tromagneti intera tion:

(iγ

µ

∂

µ

− m)ψ(x) = Qγ

µ

A

µ

ψ(x),

(1.8)

the for e is mediated by the massless ve tor eld

A

µ

. A mass term in the form

1

2

m

2

_A

1.1.2 Standard Model Theory

TheSMisbasedonagaugegroup

SU(2)

⊗ U(1)

2

.

SU(2)

isthe non-Abelian groupof the spin algebra(the so- alledweakisospin)and itis hara terized

by three generators linked to three gauge ve tor elds, beyond the ve tor

eld produ edby

U(1)

group generator.

Ele troweakintera tion anbeexplainedwithasimpliedmodel

ontain-ing only two spin

1/2

, elementary, massless, fermions,

f

and

f

′

, su h that

Q

f

= Q

f

′

+ 1

(

Q

is the ele tri harge).

Weakintera tion is built from V-A urrents. Left and right omponents

are dened and they are olle ted intoa leftdoubleteld and intotwo right

singletelds:

ψ

1

≡

 f

L

(x)

f

′

L

(x)



,

ψ

2

≡ f

R

(x)

ψ

3

≡ f

R

′

(x),

(1.9) with:

f

L,R

(x) =

1

2

(1

± γ

5

)f (x),

f

¯

L,R

(x) =

1

2

f (x)(1

¯

± γ

5

),

(1.10)

f

′

L,R

(x) =

1

2

(1

± γ

5

)f

′

_(x),

_f

_¯

′

L,R

(x) =

1

2

f

¯

′

(x)(1

± γ

5

).

(1.11) The leptoni se tor of the SM an be explained by su h pattern: we dene

T

3

as the third omponent of weak isospinand

Y

(the hyper harge) as

U(1)

partofthe intera tion,the Gell-Mann-Nishijimarelationbinds

Q

,

T

3

and

Y

:

Q = T

3

+

Y

2

.

(1.12)

The left doublet with

T

3

=

±1/2

,

Y = 1

is the harged lepton

f

plus the orresponding neutrino

f

′

, while the right singlet with

T

3

= 0

,

Y =

−2

is onlythe hargedlepton.

The ele troweak intera tion is introdu ed through

SU(2)

⊗ U(1)

gauge transformation:

ψ

j

(x)

→ ψ

j

′

(x) = e

i

τ

2

·~

α(x)+iY

j

β(x)

ψ

j

(x),

(1.13)

inthe free eld Lagrangian:

L

_{(x) =}

3

X

j=1

i ¯

ψ

j

(x)γ

µ

∂

µ

ψ

j

(x),

(1.14) 2

anda ovariantderivativeisintrodu edinEq. 1.14tomaintaingauge invari-an e:

L

_I

_{(x) =}

3

X

j=1

i ¯

ψ

j

(x)D

µ

j

∂

µ

ψ(x)

j

,

(1.15)

with

D

_µ

j

= ∂

µ

− ig

τ

2

· ~

W

µ

(x)

− ig

′

_Y

j

B

µ

(x).

(1.16) Eq.1.16 ontains threeve torbosons (

W

~

µ

)from

SU(2)

generators,one(

B

µ

) from

U(1)

generator and four oupling onstants:

g

,

g

′

_Y

j

(

j = 1, 2, 3

). After some algebrathe Lagrangian1.15 an be writtenin the form:

L

_I

_{(x) = L}

_CC

_{(x) + L}

_{N C}

_(x),

(1.17) witha harged urrent ontribution(

L

CC

)andaneutral urrent ontribu-tion (

L

N C

). The harged urrent ontributionis seen only by left doublet elds:

L

_CC

_{(x) =}

g

2

√

2

n ¯

_f(x)γ

µ

₍₁

− γ

5

)f

′

(x)

1

√

2

W

+

µ

(x) + h.c.

o

,

(1.18) with

W

+

µ

(x)

alinear ombinationof

W

1

µ

(x)

and

W

2

µ

(x)

. Eq.1.18isthe orre t Lagrangian for harged urrent behaviormediated by the

W

boson.

The fermion ouplingto

Z

0

and photonis produ edina similarway: an

appropriateorthogonallinear ombinationof neutralve tor elds

B

µ

(x)

and

W

0

µ

(x)

produ e the orre tfermion oupling:

L

_{N C}

_{(x) = L}

A

N C

(x) + L

N C

Z

(x) :

(1.19)

L

A

N C

(x) =

3

X

j=1

¯

ψ

j

(x)γ

µ

g

τ

3

2

sin θ

W

+ g

′

_Y

j

cos θ

W

ψ

j

(x)A

µ

(x),

(1.20)

L

Z

N C

(x) =

3

X

j=1

¯

ψ

j

(x)γ

µ

g

τ

3

2

cos θ

W

+ g

′

_Y

j

sin θ

W

ψ

j

(x)Z

µ

(x),

(1.21)

θ

W

is the Weinberg angle and the generi four oupling onstants have now a physi al meaning:

g sin θ

W

= e,

(1.22)

g

′

_{cos θ}

W

Y

1

= e(Q

f

− 1/2),

g

′

cos θ

W

Y

2

= eQ

f

,

(1.23)

g

′

cos θ

W

Y

3

= eQ

f

′

(1.24) The pre eding equations are the ore of the Standard Model. Anyway the

masses of the eld donot appear: the spontaneous symmetry breaking and

1.2 Higgs Me hanism

Spontaneous breaking of symmetry is based on the possibility, in systems

with innite degrees of freedom, to have a Lagrangian invariant under a

group

G

of transformation that produ es non symmetri states.

AtoyHiggsme hanism[5℄ anberealizedinLagrangiandensityofs alar

ele trodynami s:

L

_{(x) =}

₋

1

4

F

µν

(x)F

µν

_{(x) +}

(1.25)

(∂

µ

+ ieA

µ

(x))φ

†

(x)

 · (∂

µ

− ieA

µ

(x))φ(x)



−µ

2

φ

†

_(x)φ(x)

_{− h}

_φ

†

_(x)φ(x)



2

where

h > 0

,

µ

2

_{< 0}

,

φ(x)

is the s alar eld undergoing ele tromagneti intera tionviatheAbeliangaugeeld

A

µ

_(x)

,the lastpartoftheLagrangian

is the Higgs potential. Eq. 1.25 maintains invarian e under the lo al gauge

transformation:

φ(x)

_{→ φ}

′

_{(x) = e}

iα(x)

_φ(x)

_A

µ

(x)

→ A

′

µ

(x) = A

µ

(x) +

1

5

∂

µ

α(x)

(1.26) The solution to the equation of motion orresponds to the minimal energy

solutionastosaythe va uumexpe tationvalues ofthe eldsinlowestorder

perturbation theory. Be ause of

µ

2

_{< 0}

there isnot only one trivialsolution

φ(x) = 0

, but there exista set of degenerate solutionswith

|φ

2

_{| =}

−µ

2

h

=

λ

2

2

.

This ree t the underlying gauge symmetry:

φ(x) =

λ

√

2

e

iα(x)

(see Fig. 1.1).

Gauge freedom allows to hoose

α(x)

su h that

φ

′

_(x)

is real and the lowest

Figure1.1: Symmetrybreakingdependingfrom

µ

2

parameter:

µ

2

_{> 0}

onthe left,

µ

2

_{< 0}

on the right. state is

φ(x) =

λ

√

2

. To rst order we an write:

φ

′

_{(x) =}

_√

1

2

[λ + φ

1

(x)],

φ

2

(x) = 0,

A

′

Repla ingEq.1.27inEq.1.25and writingtheLagrangianinpowers of

φ

1

(x)

one obtains:

L

_{(x) =}

₋

1

4

B

µν

(x)B

µν

_{(x) +}

1

2

e

2

_λ

2

_B

µ

(x)B

µ

(x)

(1.28)

+e

2

_λB

µ

(x)B

µ

φ

1

(x) + +

1

2

e

2

_λB

µ

(x)B

µ

φ

2

1

(x)

+

1

2

∂

µ

_φ

1

(x)∂

µ

φ

1

(x) + 2µ

2

φ

2

1

(x)



+

µ

2

λ

φ

3

1

(x) +

µ

2

4λ

2

φ

4

1

(x)

−

1

4

λ

2

_µ

2

_.

Ea hline inEq. 1.28 has aphysi almeaning:

- the rst line des ribesa massive ve tor eld withmass

|eλ|

instead of the originalmassless gauge eld;

- the se ond line is the intera tion of the ve tor eld with the neutral

s alar eld with ouplingstrength

e

2

_λ

and

1

2

e

2

;

- the third line is the free s alar Lagrangian of a parti le, alled Higgs,

with mass

M

H

=

p−2µ

2

;

- the lastline isthe self intera tion of the s alareld.

Spontaneoussymmetry breaking takes pla ein Eq.1.25, the initial omplex

s alareld (two degrees offreedom) andthe masslessve tor eld(othertwo

degrees of freedom for the heli ity states) turns into a s alar real (neutral)

parti le (one degree of freedom) and a massive ve tor boson (three degrees

of freedom).

1.2.1 Spontaneous Symmetry Breaking in SM

Spontaneoussymmetry breaking anbeappliedalsoto Eq.1.9to give mass

to

W

±

and

Z

0

bosons. Two omplex s alar elds are introdu ed to adapt

Higgs me hanism to gauge groups

SU(2)

⊗ U(1)

. They form an isodoublet with respe t to

SU(2)

group:

φ(x)

_≡

 φ

+

_(x)

φ

0

_(x)



,

(1.29)

where the eld

φ

+

_(x)

is the harged omponent of the doublet and

φ

0

_(x)

is

neutral. SM Lagrangian with the added Higgspotentialgives:

V

H

(x)

≡ −µ

2

φ

†

(x)φ(x)

− h

φ

†

(x)φ(x)



2

with

h > 0

and

µ

2

_{< 0}

. Eq. 1.27 states that the neutral s alar eld

φ

0

_(x)

hasava uumexpetationvalueof

λ

√

2

,sothat (atrst order)theeld1.29 is:

φ(x) = e

λ

i

~

τ · ~

θ(x)



0

1

√

2

(λ + χ(x))



,

(1.31)

wherethe

SU(2)

gaugefreedomisexpli it; itpermitstogaugeaway threeof thefour omponentsofeld

φ(x)

,onlyonereals alar eldremains:

φ

0

_{(x) =}

1

√

2

(λ + χ(x))

. Last se tion of SM Lagrangian omes out omposing all the pre eding equation:

L

_{(x) =}

1

4

g

2

_λ

2

_W

†

µ

(x)W

µ

(x) +

1

1

(g

2

_{+ g}

′2

_)λ

2

_Z

µ

(x)Z

µ

(1.32)

+

1

2

g

2

_λW

†

µ

(x)W

µ

(x)χ(x) +

1

4

g

2

_W

†

µ

W

µ

χ

2

(x)

+

1

4

(g

2

_{+ g}

′2

_)λZ

µ

(x)Z

µ

(x)χ(x) +

1

8

g

2

_Z

µ

(x)Z

µ

(x)χ

2

(x)

+

1

2

∂

µ

_χ(x)∂

µ

χ(x) + 2µ

2

χ

2

(x)



+

µ

2

λ

χ

3

_{(x) +}

µ

2

4λ

2

χ

4

_(x)

−

1

₄

λ

2

µ

2

,

Eq. 1.32 has to be added to SM Lagrangian. We on lude that nowthe

Z

0

and

W

±

bosons have a quired mass:

M

W

=

1

₂

λg,

(1.33)

M

Z

=

1

₂

λ

√

g

x

+ g

′x

=

1

₂

_{cos θ}

λg

_w

.

(1.34)

Some parametersare now onstrained, for example:

M

Z

=

_cosθw

M

W

>

M

W

,

(1.35)

G

_√

F

2

=

g

2

8M

2

W

,

(1.36)

however Higgs mass,

M

χ

=

p−2µ

2

(sometimes

M

H

isused), remains a free parameter tobe measured by experiments. Higgsme hanism generates also

fermion massesif a Yukawa ouplingis added:

L

_{(x) = c}

_f

′

"

( ¯

f(x), ¯

f

′

(x))

L

 φ

+

_(x)

φ

0

_(x)



#

f

_R

′

(x)

(1.37)

+c

f

"

( ¯

f (x), ¯

f

′

(x))

L

 − ¯

φ

0

_(x)

φ

−

_(x)



#

f

R

(x) + h.c.,

therefore,after symmetry breaking,fermion masses have the form:

m

f

=

−c

f

λ

√

2

,

m

f

′

=

−c

f

′

λ

√

2

,

(1.38)

where the onstants

c

f

and

c

f

′

an be derived by measures of the fermion masses.

1.3 Experimental Limits on Higgs Boson Mass

Limits on the Higgs mass ome both from dire t sear hes or from a urate

ele troweak measurements that indire tly onstrain SMparameters.

Dire t Experimental Limits: the most important dire t limit on the

Higgs mass omes from LEP experiments[7℄. The experiment performed a

dire tHiggssear husing

2461 pb

−1

ofdataata enterofmassenergybetween

189

and

209

GeV.Channelsusedwere

e

+

_e

−

_{→ Z}

0

_H

,with

Z

0

de ayingintoall

possible modesand

H

→ b¯b

,and the hannelwith

H

→ τ

+

_τ

−

and

Z

0

_{→ q¯q}

.

Figure 1.2 shows re onstru ted Higgs mass distribution. No signi ant

mass peak was found, so a

95%

onden e level lowermass limitwas estab-lished:

m

H

> 114.4 GeV/c

2

(1.39) However the ALEPH experiment laimed some in onsisten y of observed

data with expe ted ba kground.

Indire t Experimental Limits: Indire t Higgsmass estimates are done

in a model dependent way, assuming the orre tness of SM with the Higgs

me hanismin luded. A urate mass measurements of the heavierSM

parti- les, like

W

±

,

Z

0

and topquark,posetheoreti allimitsonthe allowedHiggs

mass.

Infa tthemassofthoseparti lesisin reasedbyloopdiagram orre tions

asshowninFigure1.3. The ontributionofHiggsmasstogaugebosonmasses

has the following form[8℄:

ρ =

M

2

W

M

2

Z

(1

− sin

2

θ

W

)

= 1 + ∆ρ,

(1.40)

∆ρ

≡

3G

F

8π

2

√

₂

M

2

t

+

√

2G

F

16π

2

M

2

t

 11

3

ln

M

2

H

M

2

W

+ ...

(1.41)

where

G

F

is the Fermi oupling onstant,

θ

W

is Weinberg angle,

M

t

,

M

W

,

Figure1.2: Re onstru ted Higgs boson mass obtained fromtwosele tion at

LEP.MonteCarlopredi ted ba kground(yellow)andStandardModelHiggs

boson signal (red) for amass of

115

GeV/

2

is shown together with data.

Figure 1.3: Radiative loop ontribution to masses of ele troweak obje ts.

Pre ision measurements of the gauge bosons and of the top quark masses

an providea limitonthe SM Higgs boson mass.

Higgs boson. Figure 1.4 shows the limitson

M

H

, derived by

M

W

and

M

top

measures. Contour urvesare obtained varying experimentalmass values of

Figure 1.4: SM relationship between

M

t

,

M

W

and

M

H

. Contour urves are obtainedvaryingexperimentalmassvaluesof

±σ

[9,10℄. Thearrowlabeledas

∆α

showstheglobalvariationif

α(M

Z

)

is hangedbyonestandarddeviation.

DØ with Higgsmass asa free parameter inSM we derive the

∆χ

2

urve in

Figure 1.5. The preferred value orresponds to the minimum of the urve

and gives

M

H

= 76

+33

−24

GeV/

2

at

68%

CL. If alsoLEP-2dire t sear h limit is in luded (yellow regionin Fig. 1.5), itgives:

114.4 < M

H

< 182 GeV/c

2

,

(1.42)

95%

CL onstraint derived both fromdire t and indire t sear hes.

1.4 Higgs Produ tion and Sear h at the T

eva-tron

The Tevatron

p¯

p

ollider, with

√

s = 1.96

TeV enter-of-mass energy, is the only pla e were operative experiments an explore the Higgs existen e in a

mass range

100

− 200

GeV/

2

Figure 1.5:

∆χ

2

distribution as a fun tion of

M

H

from a global t of ele -troweakparameters measured at LEP, SLD, CDF, DØand NuTeV.

manydierent hannels. During2003theCDFandDØWorkingGroup[11℄

estimatedhowmu hdatashouldbe olle ted fora

5σ

dis overy,

3σ

eviden e ortoex ludeHiggsofgiven masswith

95%

CL(see Fig.1.6). Su hstudyhas not been updated re ently, and therefore an be onsidered not more than

anindi ationof the physi s rea h of the Tevatron.

1.4.1 Higgs Produ tion and De ay

The Higgs produ tion pro esses a essible at the Tevatron are gluon fusion

and ve tor boson asso iate produ tion (see Fig. 1.7). Their ross se tion

have been al ulated taking into a ount also QCD radiative orre tions[6℄.

Resultsare plottedin Figure1.8for all mass range.

Higgs mass value xes also the bran hing ratios and the allowed de ay

hannels(see Fig.1.9). On thebasis of theHiggsWorkingGroup sensitivity

study, the sear hes for the Higgs are divided in two ategories: high Higgs

mass sear hes,with

M

H

> 140

GeV

/c

2

,andlowHiggsmass sear hes,with

M

H

< 140

GeV

/c

2

.

In the high mass region, the main Higgsde ay hannels are

W

+

_W

−

Figure 1.6: Prospe t of sensitivity and integrated luminosity for the SM

Higgsboson sear h asa fun tion of

M

H

atthe Tevatron.

Figure 1.7: Tree diagrams for Higgs (

φ

) produ tion at the Tevatron. Left: Higgsprodu tion asso iated with a ve tor boson (

V

). Right: Higgs produ -tion through gluon fusion.

Z

0

_Z

0

. The pro esses investigated are:

p¯

p

_{→ H → W W}

∗

_{→ lνjj and lν¯l¯ν,}

(1.43)

p¯

p

_{→ H → ZZ}

∗

_{→ lljj and l¯lν ¯ν,}

(1.44)

p¯

p

_{→ W}

±

_H

_{→ l}

±

_{νW W}

∗

_{→ lνlνlν,}

(1.45)

p¯

p

→ W

±

_H

_{→ l}

±

_{νW W}

∗

_{→ lνlνjj.}

(1.46)

The leansignatureoftwove tor bosonsde ayingtoleptonsisanadvantage

for ba kground reje tion but in many ases the ve tor bosons de ay into

1.0

0.1

100

120

140

160

180

200

gg→H

WH

ZH

m

_H

(GeV/c

2

₎

SM Higgs cross section (HIGLU, V2HV)

Figure1.8: Higgsprodu tion ross se tionsasafun tion of

m

H

atthe T eva-tron enter of mass energy

√

s = 1.96

TeV[6℄.

1

0.1

10

-2

10

-3

bb

_

WW

ττ

_gg

ZZ

cc

_

Zγ

γγ

120

140

160

180

200

100

m

H

(GeV/c

2

)

SM Higgs branching ratios (HDECAY)

Belowthe

W

+

_W

−

threshold, fermioni bran hing ratio is favored and is

proportionaltothe fermionmass squared:

Γ(H

_{→ f ¯}

f) =

_N

c

G

F

m

2

f

4

√

2π

m

H

β

3

_,

(1.47)

the favored de ay hannelis

H

→ b¯b

.

Inthelowmassregionthesear hisfo usedon

V H

produ tion(where

V

is eithera

W

ora

Z

boson). Eventhoughtheseare nottheprimaryprodu tion modes,theyaretheeasiertobedete ted. ThemainHiggsprodu tionmodeis

bygluonfusionbut,duetothehadroni environment,this hannelhasavery

large ba kground from QCDpro esses. The hannels urrently investigated

inthe lowmass region are:

p¯

p

_{→ W H → lνb¯b,}

(1.48)

p¯

p

→ ZH → l

+

_l

−

_b¯b,

(1.49)

p¯

p

→ ZH → ν ¯νb¯b.

(1.50) Thebran hingfra tionof

W

±

and

Z

0

toleptonsfurtherredu ethenumberof

expe ted events but the leansignature of anisolated leptonand aneutrino

providesa simple signature for triggeringand ba kgroundreje tion.

1.4.2

W H

Sear h at the Tevatron

The hannel

W H

→ lνb¯b

is exploited both atCDF II and DØ experiments and it is one of the most promising for the low Higgs mass region.

W H

analysesarebasedontheleptonplusneutrinosele tionandonthesu essive

identi ationof one ormore

b

-jets(i.e. jets produ ed by

b

quarks).

Theusualapproa histooptimizethesignaltoba kgroundsigni an ein

dierent

b

-jettagging ategory(seese tion3.7). Variousstudiesarefo alized onthe optimizationof analysistools,su h asneural-networkdis riminators,

jet re onstru tion algorithms or

b

-taggers. Other works (and this thesis is among them) aim to in rease the signal a eptan e. Figure 1.10 shows the

a eptan e for

W H

events in the last CDF analysis performed at CDF[13℄ with an integrated luminosity of

1.9

fb

−1

olle ted in the

W H

→ eνb¯b

,

W H

_{→ µνb¯b}

hannels inthe entralpart of the dete tor.

CDF II and DØ experiments are getting near to the SM limit on the

Higgs produ tion but further renement and more integrated luminosity is

ne essary. Figure1.12 shows the experimentallimitsfound in

W H

analysis on the

σ(p¯

p

→ W H) × BR(H → b¯b)

, both at DØ experiment, with an integrated luminosity of

1.7

fb

−1

[12℄, and at CDF II experiment, with an

integrated luminosityof

1.9

fb

−1

Figure1.10: A eptan e for

W H

→ lνb¯b

events with

l = e

,

µ

in the entral regionof CDF dete tor for dierent

b

-tagging ategories[13℄.

Figure1.12 displaystheupperlimitat

95%

CLonHiggsprodu tionafter the ombination of all the low mass and high mass hannels of the Higgs

)

2

(GeV/c

H

m

105

110

115

120

125

130

135

140

145

)

b

b

→

BR(H

×

WH)

→

p

(p

σ

Limit /

0

10

20

30

40

50

60

70

-1

DØ Preliminary, L=1.7 fb

b

b

ν

l

→

WH

Observed Limit

Expected Limit

Figure1.11: Experimentallimitson

σ(p¯

p

→ W H) × BR(H → b¯b)/SM

expect

for the DØ experiment with

1.7

fb

−1

(top) and for the CDF II experiment

with

1.9

fb

−1

(bottom). CDF II limits (bottom) are quoted for dierent

b

-tagging ategories.

1

10

10

2

110 120 130 140 150 160 170 180 190 200

1

10

10

2

m

_H

(GeV/c

2

)

95% CL Limit/SM

Tevatron Run II Preliminary, L=0.9-1.9 fb

-1

D

∅

Expected

CDF Expected

Tevatron Expected

Tevatron Observed

LEP Limit

SM

Figure 1.12:

95%

CL upper limit on Higgs produ tion at the Tevatron. The limit is obtained ombining all the sear h hannels of CDF II and

The Tevatron Collider and the

CDF II experiment

The stru ture of CDF II (ColliderDete torat Fermilabfor RUN

2

) experi-mentisdes ribed inthis hapter. The three mainse tions des ribe:

proton-antiproton beams produ tion and a eleration, the CDF dete tor

omposi-tion and main hara teristi s, the trigger and data a quisitionsystem.

2.1 The Tevatron

TheTevatron olliderisaproton-antiprotonstoragering, ir ulara elerator

lo ated at the Fermi National A elerator Laboratory (FNAL or Fermilab),

50

Km west from Chi ago (Illinois, U.S.A.). With a enter-of-mass energy of

√

s = 1.96

TeV, itis the word highestenergy a elerator[15℄ inoperation. Proton-antiproton produ tion and a eleration is a te hnologi al

hal-lengeandinvolvesthesimultaneousoperationofseverala eleratorma hines.

Figure2.1shows aviewofTevatron omplexand ofitsvariousse tions[16℄.

2.1.1 Proton and Antiproton Produ tion

The rst stage, proton extra tion and initial a eleration, is done by the

PreA elerator(PreA ). Hothydrogengas mole ules(

H

2

)are splittedbyan intense lo alele trostati eld and harged with two ele trons;

H

−

ions are

a elerated up to

750

KeV by a Co k roft-Walton a eleratorevery

66

ms. PreA ionsour e

1

onstantlyprodu esbeamsat

15

Hzrateandsendthem to the Lina : a linear a elerator that in rease the ions energy

750

KeV to

1

Figure 2.1: S hemati view of Tevatron a elerator omplex at Fermilab,

dierent olors markdierenta elerator se tions.

400

MeV. It is made by two se tions: a low energy drift tube and a high energy oupled avity atthe end.

Thenexta elerationstageismadebya ir ulara elerator(syn hrotron)

of

75

m radius alled Booster. The insertion of a thin arbon foil strips o ele trons from the

400

MeV ions and a sweep, from

∼ 38

to

∼ 53

MHz in radio-frequen y (RF), arries resultingprotons to an energy of

8

GeV. The use of negative ions permits more inje tion of parti lesfrom the Lina ,

oth-erwise the magneti eld needed to at h the protons would alsoki k away

protonsalreadyinsidetheBooster. Bun hesareextra ted whenabout

8

·10

Resultingbun hes are inje tedintoanotherlargersyn hrotron, the Main

Inje tor: it has a radius of more than

0.5

Km, 18 a elerating avities and onventional magnets. It an a elerate protons up to

120

or

150

GeV, de-pending of the use:

120

GeV protons are used to sta k antiprotons, while

150

GeV protons are used to ontinue the a eleration hain into Tevatron main ring.

The Antiproton Sour e is not an a elerator but it is essential to obtain

andstoreantiprotons. Thisma hineis omposedbyseveral omponents(see

Fig.2.1): rst thereisatargetstationwherethe

120

GeVprotons, extra ted from Main Inje tor, ollide with a ni kel target and antiprotons of

8

GeV are sele ted from all the resulting parti les. Typi ally, 21 antiprotons are

olle ted for ea h

10

6

protonson target.

Afterprodu tion, antiprotonshavealarge spatialand momentumspread

while a eleration into Main Inje tor requires narrow pa kets. The

De-bun her is a triangular shape syn hrotron, with a mean radius of

90

m, where sto hasti ooling and bun h rotation[17℄ is applied. Pra ti ally the

bun h signalis pi ked up and analyzedfromone side of the ringand then it

is orre ted onthe other side.

In the laststage ofantiprotonprodu tionthe antiprotonbeamis sentto

the A umulator, asmaller syn hrotron(with amean radiusof

75

m)inside Debun herring,whereantiprotonsarestoredandsomemore oolingmethods

are applieduntildesired antiprotonintensity is rea hed and antiprotons an

be sentto the Re y ler.

The Re y ler is an antiproton a umulator of in reased a eptan e

lo- ated in the same tunnel of the Main Inje tor. It an store many more

antiprotons than the A umulator. Originally it was built to re over

an-tiprotons at the end of a Tevatron run but, at the moment, has the only

(very important) fun tion to store antiprotons before the inje tion in the

lasta eleratorma hine. Thisimportantnew featureboostedTevatron

per-forman e inthe lastyears.

2.1.2 Collision and Performan e

Last a eleration stage takes pla e into the Tevatron. With a radius of one

kilometer this is the largest of the Fermilaba elerators, and, thanks to

su-per ondu ting magnets,it an storeand a elerate

p¯

p

beamsfromanenergy of

150

GeV (Main Inje tor result)to

980

GeV.

∼ 10

12

and

∼ 10

11

parti les, are inje ted into the Main Ringat point 2

F0.

Protonand antiprotonbun hes are kept

∼ 0.5

mmthin and share the same beam pipe,the magnetsandva uumsystem, separatedby

5

mmintwonon interse ting orbits. Beam ontrolisobtained through nearly 1000

super on-du tingmagnets

6

m long, ooled to

4.3

K and apableof

4.2

Telds. Beside energy, the other fundamental parameter of an a elerator is the

instantaneous luminosity (

L

), as the rate of a physi al pro ess with ross se tionsigma is:

dN

dt

= L σ.

(2.1)

Highenergypermitsaninsighttoin rediblysmalls alephysi sbutonlyvery

highinstantaneousluminosityand verylargeintegrated (intime)luminosity

allow to see rare events. Figure 2.2 shows the produ tion ross se tion of

dierent physi al pro esses. Due to the tiny ross se tions we deal with in

most of this work, we willbe using pi obarns (pb) where 1

pb = 10

−36

_cm

2

.

Theinstantaneousluminosityofana elerator,usuallymeasuredin m

−2

s

−1

, isgiven by:

L

₌

N

p

N

p

¯

Bf

4πσ

x

σ

y

,

(2.2)

where

N

p

and

N

p

¯

arethe numberofprotonsandantiprotons perbun h,

B

is the number ofbun hes inside a elerator,

f

isthe bun h rossing frequen y,

σ

x

and

σ

y

arethe beamdimensionsinthe planetransverse totheintera tion point. Inside the Tevatron the 36

p¯

p

bun hes have a rossing frequen y of

396

nsand,atintera tionpoints,quadrupolemagnetsfo usbeamsin

≈ 30 µ

s spots.

Whileseveral parameters are (almost)xed beinglinked tothe

a elera-tors latti e, higher luminosities have been a hieved in Run II thanks to the

in reased antiproton sta k rate. At this moment the re ord instantaneous

luminosity is

L

= 2.85

· 10

32

m

−2

s

−1

obtained on 18February 2007.

CDFwritesontapeabout

80%

ofthetotalintegratedluminositydelivered by the Tevatron (see Fig.2.3), ine ien y are due todete tor alibration or

monitoring stores not used to olle t physi s quality data. On this side,

another important re ord is the

≈ 40

pb

−1

per week integrated luminosity

ontape[19℄.

This analysisuse data olle ted up tothe endof 2006 that orrespond to

about

1.4

fb

−1

, a halfof the total now ontape.

2

TheTevatronisdividedintosixse tions(seeFig.2.1)andea hjun tionzone,named

formAtoF,hasadierentfun tion: mostimportantareasareB0,D0andF0,therst

Figure2.2: Produ tion rossse tionof physi alpro essesatCDF.The

num-ber of expe ted events in

1

fb

−1

of integrated luminosity is reported on the

right

y

-axis. Higgs ross se tion varies with the Higgsmass.

2.2 The CDF Dete tor

CDF II dete tor is a multi-purpose solenoidal dete tor situated at BØ

in-tera tionpointalongthe Tevatronmaina eleratorring. Thanksto harged

parti le tra king, fast proje tive alorimetry and ne grained muon

dete -tion, the CDF II dete tor an measure energy, momentum and harge of

most parti lesresulting from

1.96

TeV

p¯

p

ollisions.

The rst original design goba k to 1981 but CDF underwent many

up-grades during the past twenty years. The last and most extensive upgrade

started in 1996 and ended in 2001 when Tevatron RUN II started. At the

presentCDFIIexperimentisoperatedbyaninternational ollaborationthat

Store Number

Total Luminosity (pb

-1

)

0

500

1000

1500

2000

2500

3000

3500

1000

2000

3000

4000

5000

1

4

7 10 1 4

7 101 4 7 1 4 7101 7 101 4

2002

2003

2004

2005 2006 2007

Year

Month

Delivered

To tape

Figure2.3: Integratedluminositydeliveredby theTevatron(red)and stored

by CDF (blue)[18℄.

2.2.1 Overview and Coordinate system

The dete tor is omposed by many subse tions (subdete tors) for a total of

about 5000 tons of metaland ele troni s, alength of

∼ 16

m and adiameter of

∼ 12

m. The dete tor isapproximatelyof ylindri alshape withaxialand forward-ba kward symmetry about the BØ intera tion point. Before going

further we des ribe the oordinate system used at CDF and through this

thesis.

BØistakenasthe originofCDF right-handed oordinatesystem:

x

-axis is horizontal pointing North

3

,

y

-axis is verti al pointing upward and

z

-axis is along beam line pointing along proton dire tion, it identies forward

and ba kward regions, respe tively at

z > 0

, East, and

z < 0

, West. Sometimesit is onvenienttowork in ylindri al(

r

,

z

,

φ

) oordinates where the azimuthal angle

φ

is on the

xy

-plane and is measured from the

x

-axis. The

xy

-plane is alled transverse, quantities proje ted on it are noted with a T subs ript. Two useful variables are the transverse momentum,

p

T

, and energy,

E

T

, of aparti le:

~p

T

≡ p sin(θ),

E

T

≡ sin(θ).

(2.3) 3

Besides Cartesian oordinates, another system is ommonly used in

ol-lider physi s,in it the polarangle

θ

is repla ed by pseudorapidity:

η

≡ − ln[tan(θ/2)].

(2.4)

If

(E, ~p)

is the 4-momentum of a parti le, the pseudorapidity is the high energy approximation (

p

≫ m

) of the rapidity:

y =

1

2

ln

E + p cos(θ)

E

− p cos(θ)

p≫m

→

1

2

ln

p + p cos(θ)

p

− p cos(θ)

=

− ln[tan(θ/2] = η.

(2.5) ALorentzboostalongthe

z

ˆ

dire tionaddsa onstant

ln(γ + γβ)

to

y

, there-forerapiditydieren es are invariant. In hadroni ollidersintera tions take

pla e between the (anti)proton onstituents whi h arry only a fra tion of

the energy of the nu leonso resultingparti les usually have momentum

im-balan es along

z

ˆ

. As a result statisti al distribution of nal state parti les isroughlyatin

y

,thismakes

η

agoodparameterfordete torsegmentation. Figure2.4shows a3D ross-se tionoftheCDFdete torandofitsvarious

subdete tors. Thepartinsidethe

1.4

Tsuper ondu tingsolenoid ontainsthe integratedtra kingsystem: threesili onsubdete tors(theLayerØØ,the

Sili- onVertex dete torII andtheIntermediateSili onLayers)aretheinner ore

of CDF II. The high resolution apability of sili on mi rostrips is ne essary

to have good tra k resolution near intera tion point, where parti le density

ishigher. Afterwardan open elldrift hamber(theCentral Outer Tra ker)

overs until

r

≃ 130

m, in the region

|η| < 1.0

, the extended lever arm providesvery good momentum measurement (

∆P

T

/P

2

T

≃ 10

−3

(GeV /c)

−1

). Calorimeter systems are lo ated outside the super ondu ting solenoid.

Theyare basedonshower sampling alorimeters madeofsequentiallayers of

high-Zpassiveabsorbersanda tivesignalgeneratorplasti s intillators. The

system is omposed by towers with

η

− φ

segmentation, ea h one divided in ele tromagneti and hadroni part,they overtheregionupto

|η| ≃ 3.6

(

θ

≃

3

◦

)andare organized intwomainse tion: theCentralCalorimeter overing

the region

|η| . 1.1

and the Plug Calorimeter extending the overage up to

|η| ≃ 3.6

. While the entral alorimeter is un hanged sin e 1985, the Plug alorimeter a tivepart was ompletelyrepla ed for Run II,repla ing

gas hambers with plasti s intillator tiles to better ope with the higher

luminosity.

TheoutermostpartofCDFdete tor, outside alorimeters,iso upiedby

the muon dete tors. They are multiple layers of drift hambers arranged in

various subse tions whi h over the region

|η| . 1.5

. Onlyhigh penetrating harged parti les, su h asmuons, an go a ross the entire dete tor.

Figure 2.4: 3D ross se tion of CDF II dete tor, various subdete tor have

dierent olors.

Otherdete torsareusedforabetterparti leidenti ation, alibrationor

monitoring. Howeveradetailedstudy of the entire CDF dete torisfar from

the s ope of this work. The next paragraphs will fo alize on tra king and

alorimetersystemswhi hplay asigni antroleinthe analysis. A omplete

des ription of CDF II dete tor an befound in[20,21℄.

2.2.2 Tra king System

The traje toryof a harged parti le with non-zero momentum in auniform

magneti eld in va uum is a helix. A tra king dete tor identies

(possi-bly with a minimal perturbation) some points, hits, along parti le path so

that it is possible to obtain momentum measures by re onstru ting the

he-lix parameters 4

. A s hemati view of CDF tra king volume an be seen in

Figure2.5: the threemain omponentsare the super ondu ting magnet,the

sili on subdete tors and the entraldrift hamber.

Figure 2.5: Viewof CDF tra king volume and alorimeter disposition.

The solenoidalmagnet, made by NbTi/Cusuper ondu ting oils,

main-tains a bendingmagneti eld with a entralvalue of

1.4116

Tesla, oriented along the positive

z

ˆ

dire tion and nearly uniform in allthe tra king volume (

r . 150

m and

|z| . 250

m). The momentum threshold for a parti le to radiallyes apethemagneti eldis

p

T

&

0.3

GeV/

c

and theradialthi kness of the oilis

0.85

radiationlengths (

X

0

).

Sili on System

The sili on system is the rst tra king subdete tor en ountered by parti les

oming from the primary intera tion vertex. Semi ondu tor dete tors oer

ex ellent spatial resolution and fast response time. Therefore itpermits the

re onstru tion of displa ed se ondary verti es produ ed from the de ay of

long lived

b

-hadrons 5

.

CDF employs

∼ 7

m

2

sili on a tive-surfa e for a total of 722,432

dif-ferent hannels read by about 5500 integrated ustom hips. The omplete

5

Corre tidenti ationof

b

-hadronsisfundamentalinmanyanalysese.g.

b

-hadronsare oneofthe de ayprodu ts of

top

quarkandalso Higgs boson hasahigh bran hingratio to

b

quark.

sili on tra king dete tor is displayed in Figure2.6. Of the three subsystems

buildingCDF ore, the LayerØØ[22℄ (LØØ) is the innermost. It onsistsof

a single layer of single-sided sili on sensors dire tly mounted on the beam

pipe at radii, alternating in

φ

, of

1.35

m or

1.62

m, overing the region

|z| . 47

m. During the onstru tion of the SVXII mi rovertex (see below) CDF realized that the multiple s attering due to the presen e of read-out

ele troni sand ooling systemsinstalledinsidetra kingvolumewasgoingto

degrade the impa t parameter resolution. LØØ was designed to re over it

thanks to its proximity to the beam. Furthermore, being made of

state-of-the-art radiation-tolerant sensors, it will ensure a longer operating lifetime

tothe entire system.

Figure2.6: Sideandfrontviewofintegratedsili ontra kingsystem atCDF.

The main omponent of the sili on system is SVX II[23℄, the Sili on

VerteX dete tor is made of three ylindri al barrels for a total length of

about

96

m along

z

, overing the luminosity region until

2.5σ

z

, and with a pseudo-rapidity range

|η| . 2

. Ea h barrel is divided in twelve identi al wedges in

φ

, arranged in ve on entri layers between radii

2.4

m and

10.7

m. Ea hlayer isdivided into independent longitudinalread-out units, alled ladders. Ea h ladder onsists of a low-mass support for a

double-sided sili on mi rostripdete tors. Threeout of ve layers ombine an

r

− φ

measureononesidewith

90

◦

stereomeasureontheother,theremainingtwo

layers ombinean

r

−φ

measurewithasmallangle

r

−z

stereomeasure (with tilt angle of

1.2

◦

). The highly parallel ber based data a quisition system

ISL[24℄ (Intermediate Sili onLayers)istheoutermost ofthethreesili on

subdete tors,radiallylo atedbetweenSVXIIandthedrift hamber overing

the region

|η| . 2

. It is divided in three barrels segmented into

φ

wedges. The entral barrel (

|η| . 1

) is made of one layer of sili on sensors at radius of

22

m, insteadthe two outer barrels (

1 .

|η| . 2

) are made of two layers at radii of

20

m and

28

m. Its purpose is tostrengthen the CDF tra king in the entral region and to add pre ision hits in a region not fully overed

by the drift hamber. This improvesthe tra kingat large

η

and alsoallows sili on stand alonetra k re onstru tion in the whole region

|η| < 2

.

The omplete sili on subdete tor (LØØ, SVXII and ISL) has an

asymp-toti resolutionof

40 µ

minimpa tparameterandof

70 µ

malong

z

dire tion. The total amount of materialvaries roughly as:

0.1X

0

sin(θ)

(2.6)

inthe entralregionanddoublesintheforwardregionbe auseofthepresen e

of read-out ele troni s, ooling system and supportframes[25℄.

2.2.3 Central Outer Tra ker

The Central Outer Tra ker[26℄ (COT)isanopen- elldrift hamberused for

harged parti les tra king at large radii. It has an hollow- ylindri al

geom-etry and overs

43.3 < r < 132.3

m,

|z| . 155

m. Figure 2.5 shows that COT fully overs the entral region (

|η| . 1

) with some residual apability up to

|η| ≈ 2

TheCOT(seeFig.2.7)isstru turedintoeightsuper-layers ea hdivided

into

φ

ells; ea h ell ontains twelve sampling wires, spa ed

0.583

m, to olle t the ions produ ed by passing harged parti les. The disposition of

the ells has a

χ = 35

◦

tilt with respe t to the hamber radius to partially

ompensatethe Lorentz angle of the drifting ele trons in the magneti eld

and obtain the best resolution 6

.

The nal stru ture has 8x12 sampling planes alternated with planes of

potentialwires (seeFig.2.8),

96

hitsare measuredfor aparti le rossingthe entire COT (

|η| < 1

). Four super-layers employ sense-wires parallel to the beamaxisformeasuresin

r

−φ

plane,theotherfourinterspa ingsuper-layers are alled stereo super-layers be ause their wires are alternately anted at

6

Ele tronsdriftingin agaswithinanele tromagneti eld

( ~

E, ~

B)

movewithanangle

χ

_{≃ arctan}

v(E,B=0)B

_kE

, where

k

is empiri al parameter of gas and ele tri eld and

Figure 2.7: A

1/6

se tion of the COT end-plate with the eight super-layers stru ture and the disposition of ellslots.

anglesof

+2

◦

and

−2

◦

withrespe t tothe beamlineandareused tomeasure

r

− z

oordinates. The appliedele tri drifteld (seeFig. 2.8)is

1.9

kV/ m. A

50 : 50

gas admixture of argon and ethane bubbled through isopropyl al ohol (

1.7

%) onstantly ows in the amber volume. The obtained drift velo ity is about

100 µ

m/ m for a maximum drift spa e of

0.88

m. The materialof theCOT isabout

0.017X

0

, mostly on entratedinthe innerand outershell.

2.2.4 Calorimeter System

Lo ated immediately outside the solenoid, the alorimeter system at CDF

overs a solid angle of nearly

4π

around

p¯

p

intera tion point and has the fundamentalrole to measure energies of ele trons, photons, parti le lusters

(jets) and the imbalan e intransverse energy ow (signature of neutrinos).

The lo ation of alorimeter se tions is visible in Figure 2.5. Both Plug

and Central are sampling alorimeters divided in an ele tromagneti

se -tion (lead/s intillator), optimized to olle t all the energy of ele trons and

photons, and a subsequent hadroni se tion (iron/s intillator), thi ker and

optimized for hadron energy measurement. Calorimeters have an in-depth

segmentation, ner near the ollision point and oarser outward. The

η

− φ

planeismapped inre tangular ells, ea hone orrespondingtothe

indepen-Figure 2.8: Left: equipotential line inside one of the COT super-layer ell.

Right: layout of sense-wires, eld-wires and shaper-wires onside one COT

ell.

CEM CHA,WHA PEM PHA

Energy Resolution

14%/

√

E

75%/

√

E

16%/

√

E

80%/

√

E

Angular Coverage

|η| < 1.1

|η| < 1.3

1.1 <

|η| < 3.6 1.3 < |η| < 3.6

Absorber lead iron lead iron

Longitudinal Depth

19X

0

,

1λ

4.5λ

21X

0

,

1λ

7λ

Table 2.1: Main hara teristi s of CDF alorimeter system.

paragraphs explains in more detail the omposition of the dierent

subse -tions and Table 2.1 summarizes their main hara teristi s. Thanks to the

fast response ofs intillators, signalsfrom alorimetersare qui kly pro essed

and used at various triggerlevels.

Central Calorimeter

The entralregionof the dete tor is overed by the CentralEle tromagneti

(CEM) and the CentralHAdroni (CHA) alorimeters[27℄, orrespondingto

the pseudo-rapidity region

|η| < 1.1

and

|η| < 0.9

respe tively.

The CEM is a hollow ylinder lo ated at

173 < r < 208

m, divided in four

180

◦

ar hes ea h omposed by12azimuthalse tions(

∆φ = 15

◦

) and10

pseudo-rapidityse tions(

∆η

≃ 0.11

)foratotalof478instrumentedtowers 7

.

The CHA overs region

|η| < 0.9

and it is divided into 9x12

η

− φ

tow-ers orresponding to CEM segmentation for a total of 384 towers. Central

hadroni alorimeter overing isextended up to

|η| ≃ 1.3

thanks tothe end-Wall HAdron Calorimeter[28℄ (WHA). It has same

φ

segmentation and six additional

η

towers: the rst threeoverlap CHA and the lastthreeextend

η

overage.

Figure 2.9 shows a wedge of the entral alorimeter system. Ea h CEM

se torisasamplingdevi emadeof31layersofpolystyrenes intillator(

5

mm thi k)radiallyalternatedwithlayersofaluminum- ladlead(

3.18

mmthi k). Some of the 30 lead layers are repla ed by a ryli (Plexiglas) as a fun tion

of

θ

to maintain a uniform thi kness in

X

0

. As parti les lose energy into

Figure 2.9: Stru ture of a wedge of CDF entral alorimeter.

the absorber medium, the blue light emitted by a tive s intillator medium

is olle ted by thin barsof blue-to-greenwave-lengthshifter a ryli material

pla edonthe sides of ea h towerthat bring the lighttotwophotomultiplier

tubesoutside CHA.

CEM ontains also the Central Ele tron Strip hambers (CES) and the

CentralPreshower dete tor (CPR). CES is a multi-wireproportional

ham-ber pla ed at a radial depth of

∼ 6X

0

and is used to determine shower position and transverse shower development with an a ura y of

∼ 0.2

m. CPR is a layer of nely segmented s intillatorslo ated immediatelyoutside

thesolenoidandisusedtomonitorphoton onversionstartedinthetra king

region.

The stru ture of hadroni alorimetersis similarto ele tromagneti ones

butabsorbermaterialsare 32steel,

2.5

m-thi k,layersinCHAand15steel,

The total thi kness of ele tromagneti se tionis nearly uniformand

or-responds to

19

radiation length (

X

0

) or

1

intera tion length (

λ

int

). Based ontestbeamdata, theCEM energy resolutionforanele tron goingthrough

the enter of a tower isfound tobe:

σ

E

E

=

13.5%

pE(GeV)

⊕ 2%.

(2.7)

Thetotalthi knessofhadroni se tionis

∼ 4.5λ

int

andtheirenergyresolution is:

σ

E

E

=

50%

pE(GeV)

⊕ 3%,

σ

E

E

=

75%

pE(GeV)

⊕ 4%.

(2.8) respe tively for CHAand WHA.

Forward Calorimeter

Plug alorimeters[29℄ are two identi al stru tures, east and west, that over

region

1.1 .

|η| . 3.6

. Figure 2.10 shows the stru ture of plug alorime-ters, ina way similar to the entraldevi e: there is a Plug Ele troMagneti

alorimeter se tion (PEM), a Plug PReshower (PPR) dete tor before the

alorimeter, a Plug Ele tromagneti Shower-maximum dete tor (PES)

em-bedded(at

6X

0

)andasubsequentPlugHAdroni alorimeter se tion(PHA). Ele tromagneti se tion is

21X

0

thi k and is omposed by 23 anular plates, of

2.77

m outer diameter and aninner hole for the beam pipe made of

4.5

mmthi kleadabsorber. Towers haveasegmentationwith

∆η

and

∆φ

varying as Table 2.2 shows, with an azimuthal-angle overing of

7.5

◦

down

to

η = 2.11

and of

15

◦

further. A tive elements are

4

mm thi k s intillator tiles read-out by embedded wavelength shifters onne ted to PMT. All is

assembled intriangularshapepizza-pans whi hen loseasli eofa

∆φ = 15

◦

se tor. Two layers are dierent: rst s intillator layer is

10

mmthi k and is usedasapreshowerdete tor, PES layeris madebytwostripsofs intillators

thatprovideshowermaximumpositionmeasurementwith

∼ 1

mma ura y. Hadroni se tion is about

7λ

int

thi k and segmented in

∆φ = 30

◦

for

a total of 12 se tions of 23 iron

5

m-thi k layers alternated with

6

mm s intillator a tive material layers. The hara teristi plug shape is due to

the growing radii of the layers far from intera tion point to mat h WHA

overage. Energy resolution is:

σ

E

E

=

16%

pE(GeV)

⊕ 1%,

σ

E

E

=

74%

pE(GeV)

⊕ 4%.

(2.9)

Figure2.10: Elevationview of one quarter of the CDF Plug alorimeter.

|η|

Range

∆φ

∆η

0.

_{− 1.1(1.2H)}

15

◦

_{∼ 0.1}

1.1(1.2H)

_{− 1.8 7.5}

◦

_{∼ 0.1}

1.8

− 2.1

7.5

◦

_{∼ 0.16}

2.1

_{− 3.64}

15

◦

_0.2

_{− 0.6}

Table 2.2: CDF II alorimeter segmentation,

H

stands for the hadroni se -tion.

respe tively for PEM and PHA. Figure 2.11 shows the segmentation of a

∆φ = 15

◦

se tor and des ribes the distributionof triggertowers.

2.2.5 Other Dete tors

This analysis is based onre onstru ted jets and ele trons whi h mainlyuse

alorimeterand tra king apabilityofthe CDF dete tor, however other

sub-dete tors data are used indire tly or play a key role in other important

Figure 2.11: Segmentation of the plug alorimeter and tower disposition

inside one wedge.

Muon Dete tors

Muons loose very little of their energy into the tra king volume and in the

alorimeter system 8

so only they, ex ept neutrinos and parti les going into

the  ra ks of the dete tor, pass throughout.

Muon subsystems[30℄ are organized in four subdete tors: the Central

MUon dete tor (CMU) overs region

|η| . 0.6

, the Central Muon Upgrade (CMP) is pla ed over CMU and over a

∼ 2.4λ

int

steel shielding to redu e hadrons es aping from CHA, the Central Muon eXtention (CMX) overs

region

0.6 <

|η| < 1.0

and the Intermediate MUon system (IMU) rea h

|η| ≃ 1.5

. The

η

− φ

overage and subdete tors disposition issummarizedin Figure2.12.

Ea h muon subsystem is omposed by arrays of azimuthal, single wire,

re tangular, drift hambers overplayed in dierent patterns (to an el hits

position ambiguities) and oupled with s intillators (to grant fast timing

measures). Singlehitresolutionisof

∼ 0.25

mmin

η

−φ

plane,thankstothe measure of the dieren eof drift ele tron arrivaltimes between neighboring

ells, and of

∼ 1.2

mmalong

z

thanks tothe measure of the dierent harge olle ted atthe end of ea h wire. When a tra k-segment results from three

mat hingradiallayers(astub)anda orrespondingCOTtra kpointoutward

toit, amuon andidate isidentied.

8

Muonsfrom

Z

0

de ays,forinstan e,depositonaverageabout

0.4

GeVinthe ele tro-magneti portion ofthe alorimeter and

4

GeVin thehadroni one.