Measurement of the ratio R=BR(t->Wb)/BR(t->Wq) at CDF

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Corso di Laurea Magistrale in Fisica Anno Accademico 2010/2011

Tesi di Laurea Magistrale

Measurement of the ratio

B(t → W b)/B(t → W q)

at CDF

Tesi di Pierfrancesco Butti

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Introduction

In the Stardard Model of elementary particles, the top quark completes the third quark generation. It was directly observed in 1995 during Tevatron Run I with √

s = 1.8 TeV by both CDF and D0 experiments [1, 2, 3]. It is the most massive elementary known particle up until now, with a mass of 172.7 ± 1.1(stat + syst) GeV/c2 _{[4], about 35 times larger than the mass oft the next heavy quark and very}

close to the scale of the electroweak symmetry breaking.

Produced at the Tevatron in proton-antiproton collisions via strong interac-tions, top quark decays through weak interaction to a W boson and a down-type quark q (d,s,b) before forming hadrons, giving the possibility to study the prop-erties of a bare quark. In the Standard Model the decay rate is proportional to |Vtq|2, the Cabibbo-Kobayashi-Maskawa (CKM) matrix element. Since the

as-sumption of three generation of quarks and the unitarity of the CKM matrix lead to |Vtb| = 0.99915+0.00003−0.00005 [7], it can be assumed that top quark decays exclusively

to W b. On the other hand, if more than three generation of quarks are allowed, the constraint on |Vtb|is removed and lower values are possible, affecting top cross

section measurements, B mixing and CP violation.

A direct measurement of |Vtb| matrix element can be obtained measuring the

single top production cross section, but a value can be extracted from the top quark decay rate in the t¯t channel. It is possible to define R as the ratio of the branching fractions: R = B(t → W b) B(t → W q) = |Vtb| 2 |Vtb|2+ |Vts|2+ |Vtd|2 (1) expected to be 0.99830+0.00006

−0.00009 if the previous constraints are assumed.

In this analysis we measured directly the the ratio of the branching fractions R using a data sample corresponding to 7.5 fb−1 _{collected at the CDF detector}

with √s =1.96 TeV. The analysis is performed in the lepton plus jets (l+jets) channel, where one W boson, coming from t¯t → W+_qW−_q_¯_{, decays hadronically}

while the second decays in a charged lepton and a neutrino. CDF performed several measurements of R both during Run I and Run II, combining the l+jets channel with the dilepton channel, where both of W bosons produced by top pairs decay leptonically. The last measurement found a central value of R = 1.12+0.21_−0.19(stat)+0.17_0.13 (syst) using an integrated luminosity of 162 pb−1, extracting R > 0.61 at 95% CL [5]. The DØ collaboration has measured recently R, using 5.4 fb−1_{, with a simultaneous fit on the top pair production cross section, in the}

l+jets and dilepton channels. Their result is R = 0.90 ± 0.04(stat+syst) and R > 0.79 at 95% CL [6].

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Since the uncertainty on the central value measured by CDF was dominated by the statistical error, we decided to perform a new measurement adding the new datasets.

My analysis is based on the determination of the number of b-jets in t¯t events using the l+jets sample with more than three jets in the final state. We consider events in which the charged leptons are either electrons or muons. Identification of jets coming from b-quark fragmentation (b-jet tagging) is performed by the SecVtx algorithm, based on the reconstruction of displaced secondary vertices.

We divided our sample in subsets according to the type of lepton, number of jets in the final states and events with zero, one or two tags. The comparison between the total prediction, given by the sum of the expected t¯t events and background estimate, and the observed data in each subsample is made using a Likelihood function. Our measured value for R is the one which maximizes the Likelihood, i.e. gives the best match between the observed events and the prediction.

Our final measurement of R is obtained recursively performing a simultaneous fit also the top pair production cross section. We obtain R = 0.92+0.08

−0.07 (stat+syst)

and σp ¯p→t¯t= 7.4 ± 0.9(stat+syst) pb. Assuming the unitarity of the CKM matrix

and three generation of quarks we obtained |Vtb| = 0.96 ± 0.04 (stat+syst), in

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Chapter 1 Standard Model of Elementary

Particles and Higgs Physics

The Standard Model of Elementary Particles is a gauge theory that explains the dynamics of the known subatomic particles, describing the electromagnetic, weak and strong nuclear interactions. Even if the theory is far from being complete be-cause it does not include general relativity, it is verified with a very good accuracy. The discovery of new particles predicted in the model, the vector bosons W± _and

Z0 _{(1983, CERN) and the top (t) quark (1995, Fermilab), lent credibility to it.}

There is still one particle, predicted by the Standard Model, that has not yet been discovered: the Higgs Boson. Introduced by the Higgs mechanism to give mass to SM particles in the equations of motion keeping at the mean time the renormaliz-abilty of the theory.

It is very interesting to study top quark properties, such as its electric charge, the heliciy of the W boson in t → W b decay or branching fraction B(t → W b), because the comparison of these measurements with SM prediction is a powerful tool in searching for new physics. In addition it is possible to set a constrain on the mass range of the last yet to be observed SM predicted particle, the Higgs boson, using top quark and W masses linked to the Higgs particle trough radiative correction [8].

1.1 Standard Model

Experiments so far revealed four fundamental forces, or interactions: gravity, elec-tromagnetism, the weak interaction, and the strong interaction [20]. Theoretical insights and relative experimental proofs have collected in the Standard Model (SM) picture of elementary particles and fundamental interactivity which, how-ever, does not include gravity1.

The SM is a Quantum Field Theory, belonging to the class of gauge theories, providing a mathematical description of particles and interactions that incorpo-rates quantum mechanics and special relativity by construction. According to

1_{The fourth force, the gravity, is far weaker. It is roughly 40 orders of magnitude smaller than}

the strong nuclear force and is not expected to contribute significantly to the physical processes which are of current interest in high energy particle physics.

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this theoretical framework the interactions between fermions is introduced by re-quiring the invariance of the Lagrangian with respect to an arbitrary transforma-tion of the fields describing the particles according to the local symmetry group SU (3)_C⊗SU (2)_L⊗U (1)_Y. The underscript C is a reminder that SU(3) represents the symmetry group of the colored strong interactions of quantum chromodynam-ics (QCD). L indicates that the SU(2) group contains left-handed weak isospin doublets and Y is a reminder that the U(1) group contains the right-handed weak hypercharge singlets. These quantities are connected to the electric charge Q through the Gell-Mann - Nishijima relation,

Q = Y

2 + T3 (1.1)

Together, the SU (2)L⊗ U (1)Y groups govern the unified electroweak force.

The elementary particles are representations of the symmetry group: all particles are defined by quantum local fields, with well-defined transformation properties under Poincaré group transformations. While the kinematics of the particles is completely defined by special relativity, the SM focus on the description of their dynamics, that is the study of the general structure of interactions and their in-terpretation trough symmetry principle.

In the SM the known constituents of matter are spin 1

2 fermions, while their

in-teractions are mediated by spin 1 particles, called intermediate gauge bosons (see Table 1.1 and 1.2).

Fermions are divided in two classes, leptons, that can only interact trough elecro-magnetic and weak interaction, and quarks, that can interact also trough strong nuclear force.

1.1.1 Bosons

SM interactions are mediated by spin-1 bosons, which are the generators of the symmetry group. The 8 colored gluons g are the massless mediators of the strong force, i.e. they are the generators of the group SU(3)C. The photon γ, W± and Z

are the force carriers of the electroweak interactions, i.e. they are the generators of the group SU(2)L⊗ U (1)Y.

The gauge bosons and their properties are summarized in Table 1.1.

1.1.2 Fermions

There are six types of leptons (plus their anti-particles) in the SM. These are the electron, muon, tau (e, µ, τ) and their respective neutrinos (νe, νµ, ντ).

Leptons are described as doublets of the SU(2)L group with their associate

neu-trinos, as left-handed eigenstates (with -1 eigenvalue chirality), one for each gen-eration. As the Goldhaber et al. experiment [21] proved, neutrinos with positive chirality eigenvalues do not exist. This is the reason why the right-handed fermions in the SM are singlet for SU(2)L.

Quarks have fractional electric charge and a quantum property called color simi-lar to the electric charge of electromagnetism. Color is the source of their strong

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Generations Proprieties 1st 2nd 3rd T3 Y Q Leptonic Sector νe e L νµ µ L ντ τ L +1₂ −1₂ −1 0 −1 eR µR τR 0 -2 -1 Quark Sector ∗u ∗d L ∗c ∗s L ∗t ∗b L +1₂ −1 2 1 3 +2₃ −1 3 ∗u_R ∗c_R ∗t_R 0 +4₃ +2₃ ∗dR ∗sR ∗bR 0 −2₃ −1₃

Table 1.1: Leptons and quark in Standard Model and some of their properties. Gauge Boson Charge Mass (GeV/c2₎ _Interaction

γ 0 0 EM

W± ±1 80, 399 ± 0, 023 EM,Weak

Z0 ₀ _{91, 1876 ± 0, 0021} Weak

g 0 0 Strong

Table 1.2: Gauge bosons in Standard Model and some of their properties. Charges expected is in unit of e.

interaction, and comes in three states conventionally named red r, green g and blue b. Quarks and their properties are listed in Table 1.1.

1.2 The Cabibbo-Kobayashi-Maskawa Matrix

Quark mass eigenstates are not exactly the same as the electroweak eigenstates. The quark eigenstates of electroweak charged current interactions are given by

u d0 , c s0 , t b0

where the mixing is described by the unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix, whose elements specify the strength of the coupling in each transition

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between quarks i and j.   d0 s0 b0  =   Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb  ·   d s b  

Here the different Vij are constants to consider in calculation of Feymann vertices

connecting the quark i with the quark j and are fundamental in calculating pro-cesses amplitude and cross section.

Although there are 9 elements in the CKM matrix, imposing unitarity, they found that CKM matrix is function of only 4 free parameters2_{, which can be expressed}

as 3 angles and one CP (charge-parity) violating phase. This corresponds to the CKM form: V =   c1 −s1c3 −s1s3 s1c2 c1c2c3− s2s3eiδ c1c2s3+ s2c3eiδ s1s2 c1s2c3− c2s3eiδ c1s2s3 + c2c3eiδ  

where s and c refer to sin and cos and their subscript the angle θi and δ is then

the CP violating phase. Thus there are four parameters which are θ1, θ2, θ3 and δ.

CP violation, though very small, is now well established with CPT (charge, parity and time operations) is believed to be the preserved underlying symmetry.

In a similar way it is possible to parametrize the CKM matrix in terms of A, λ, η and ρ according to the Wolfenstein parametrization, which emphasize the relative amplitudes of the elements of the matrix, showing that transitions across two quark generations, or more generally transitions that involve further off-diagonal elements of the CKM matrix elements are suppressed with respect to transitions involving diagonal elements. This parametrization maintains the unitarity to O(λ4₎_:

V = 



1 − λ2_/2 _λ _Aλ3_{(ρ − iη)}

−λ 1 − λ2/2 Aλ2

Aλ3(1 − ρ − iη) −Aλ2 ₁



+ O(λ4)

In the SM the unitary of the CKM matrix must hold:

3 X i=1 VijVik∗ = 3 X i=1 VjiVki∗ = δij (1.2)

Expanding eq. 1.2 for any j and k yields nine equations, of which the six equations involving the off-diagonal elements of δij describe triangles in the complex plane.

These six triangles fall into two groups of three, differing only by their orientation in the complex plane: these are the so-called unitary triangles.

The free parameters of the CKM matrix are not specified by the theory and must be determined by experiments. The study of processes involving flavor-changing charged weak interaction (i.e. matter-antimatter oscillations of mesons or weak decays) allows the measurements of physical observables (oscillation fre-quencies, decay rates) that depend on real quantities such as the moduli of ele-ments |Vij| in various combinations. These measurements can be converted into

measurements of the length of the sides and interior angles of the unitary triangle.

2_{Five parameters in the CKM matrix can be eliminated redefining quark fields up to a phase}

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1.3 Quantum Chromodynamics

Quantum chromodynamics (QCD) is the theory of the strong interactions between quarks and gluons. Quarks carry a single color charge while gluons, which are mediator of color flow are bicolored (i.e. carrying color and anti-color). In SU(3)C

the three colors give nine total color states for the gluon: an octet and a color singlet. However, the singlet is colorless and so in nature there are only 8 possible colored gluons. Quarks only exist in colorless bound states with integer charge.

Colored partons3 will be confined in objects which are, as a whole, colorless. We

can only observe color singlet quark-antiquarks bound states (mesons) or of three quarks or three antiquarks (baryons). Mesons and baryons are collectively denoted as hadrons and, being composed of quarks, are subject to strong interactions.

The feature of the strong force is that the coupling becomes increasingly large with separation distance. The coupling constant of QCD (αS) is a running function

of the momentum transferred in the interaction, qµ_{, which is approximately given}

by

αS(q2) =

12π

(33 − 2nf) log(q2/Λ2QCD)

(1.3) where Λ ∼ 0.1 GeV and nf is the number of quark flavors whose mass is greater

than the q2 _{of interest [22].}

At very large q2 _{(corresponding to very short approach distances) α}

S becomes

increasingly small. This phenomena is known as asymptotic freedom. This prop-erty allows, for high-q2interaction, perturbative expansion of QCD processes which

remain finite. This is often the case of the collisions at Tevatron, where it is pos-sible to calculate interaction cross sections as perturbative expansions.

When highly energetic quarks or gluons are produced in high energy physics experiment a process called hadronization or showering takes place: after a parton is produced in an interaction, the potential with the parton system of origin, tries to keep it bound until the strength reaches a breaking point where a q¯q pairs are created. The new partons are approximately collinear with the original parton and combine into meson or baryons in such a way that a spray of colorless particles is observed which move close to the same direction. The final state in which we observe the parton generated in the interaction is a collimated jet.

Most of the fragmentation process is non-perturbative and not completely the-oretically under control, since during the fragmentation process the particle ener-gies become successively smaller and perturbative QCD is no longer applicable. Phenomenological models are usually applied in order to describe completely jet features [23]. These models are relevant to Monte Carlo code that describes the jet formation and properties.

1.3.1 The Higgs Mechanism

An explicit mass term in the interaction Lagrangian cannot be accepted because it would violate gauge symmetry. The gauge invariance of SU(2)L⊗ U (1)Y implies

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massless fermions and weak bosons, in total contradiction with reality. The most accredited theory to give mass to the W and Z bosons is based on the interaction with the so-called Higgs field which is a result of a spontaneously broken symmetry arising in the SU (2)L ⊗ U (1)Y electroweak sector. The predicted Higgs boson

resulting from this broken symmetry is supposed to generate the fermion masses as well.

Spontaneous breaking of symmetry is based on the possibility, in systems with infinite degrees of freedom, to have a Lagrangian invariant under a group G of transformation that produces non symmetric states.

The Higgs mechanism was proposed by P. Higgs [26, 27, 28] in 1964 and has been fully incorporated into the Standard Model by Weinberg and Salam [29, 30] in the SU(2)L⊗ U (1)Y theory.

This mechanism provides masses to fermions, at the price of introducing a new spin-0 scalar gauge field, the Higgs boson. However, it is the only particle in the SM which has yet to be discovered.

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Chapter 2 Top quark Production at Tevatron

The top quark is the last discovered fundamental particle. It was observed in 1995 by the CDF and DØ Collaborations at the Tevatron, Fermilab. Top quark completes the third quark generation and interacts with other particles trough electroweak and strong forces. The last combination of measurements performed at Tevatron yields to a top-quark mass of mt =172.7 ± 1.1(stat + syst) GeV/c2

and it results as the heaviest fundamental particle known so far. Its mass is about 35 times bigger than its weak partner, the bottom quark, and this result can be used, with a measurement of W mass, to set limits on Higgs boson mass. Given this mass predicted lifetime τ ≈ 5 × 10−25_{s is one order of magnitude smaller than}

the time scale for hadronization. The top quark decays trough weak interaction without forming bound states. This leads to the possibility to study a bare quark with well defined properties, not disturbed by the hadronization process. In the Standard Model theory the CKM matrix forces the top quark to decay with a very high probability into a b quark and a W boson, while the decays in light flavor quarks (down or strange) are suppressed by small values of |Vtd| and |Vts|.

2.1 Top-pair Production through Strong

Interac-tion

The Standard Model theory can be used to calculate cross sections and decay rates only for elementary particles, evaluating the matrix element M of the process and integrating it on all possible final states. However, at the Tevatron, the collisions are between compound particles, protons and antiprotons, made up respectively of two u and one d and their antiparticles. These quarks are called valence quarks and are bound by virtual gluons that can split into quark-antiquarks pairs, called sea quarks. In this scheme the total momentum P of the proton (antiproton) is shared between all the constituents, called partons. The fraction of the momentum carried by parton i is given by Pi = xi·P and its distribution is described by Parton

Distribution Functions (PDFs) fi(xi, µ2), corresponding to the probability to find

the given parton inside the hadron with momentum fraction xi, when probed at

an energy scale µ2. In the top-quark production the typical energy scale of the

interaction is usually set to the order of the top mass µ = mt. Since the Tevatron is

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Figure 2.1: Parton distribution function for µ = mt [12]

a symmetric p¯p collider, the square of the center of mass energy of two interacting partons is defined by

ˆ

s = (x1Pp+ x2Pp¯)2 = 4x1x2s (2.1)

where s is the square of the center of mass energy of the colliding protons and antiprotons (√s = 1.96TeV at the Tevatron). The minimum square center of mass energy of the interacting partons requested to produce a couple t¯t is ˆsmin = 4m2t.

This value leads to momentum fractions greater than x1x2 ≥

ˆ smin

s ≈ 0.032 (2.2)

For this fraction values the partons responsible of the production of the top-pairs are mostly valence quarks, as can be seen from the Figure 2.1.

Figure 2.2: Leading order Feynman diagram of the t¯t production via quark anni-hilation

For Tevatron√s is calculated that rougly the 85% of production cross section is due to quark-antiquark annihilation while the remaining fraction is gluon-gluon fusion [13]. The t¯tproduction cross section is calculated performing an integration of the cross section corresponding to the hard process (ˆσ (ˆs, mt)) over the PDFs

and summing on all the interacting partons, in the following way: σp ¯p→t¯t( √ s, mt) = X i,j=q,¯q,g Z ˆ σij−>t¯t(ˆs, mt) fi(xi, mt)fj(xj, mt)dxidxj (2.3)

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Figure 2.3: Leading order Feynman diagrams of the t¯t production via gluon fusion The parton-parton cross section can be calculated as a perturbation series in the strong coupling constant αs(m2t). The LO Feynman diagrams of t¯t production are

shown in Figure 2.2 and in Figure 2.3. At the NLO contributions due to initial and final state radiation, gluon splitting and bremsstrahlung are added to the leading order calculation. The current NNLLO approximated top pair production cross section at Tevatron is 7.22 +0.31+0.71

−0.47−0.55

pb [14] for a top quark with mass mt= 173.3

GeV/c2_.

2.2 Single-Top production via weak interaction

The single top-quarks production via electroweak interaction is predicted by the SM as well. Two electroweak production modes are dominating at Tevatron: the t-channel process and the s-channel process, where s and t are the Mandelstam variable involved in the transition matrix element.

In p¯p collisions the third electroweak production mode, the W t production, since the small predicted cross section, is negligible.

Since electroweak top-quark production proceeds via a W tb vertex, it provides the unique opportunity of the direct measurement of the CKM matrix element |Vtb|.

All three production modes are distinguished by the virtuality Q2 _{= −q}2, where

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Figure 2.4: s-channel (left) and t-channel (right) single top Feynman diagrams.

2.2.1 t-channel

In t-channel production a virtual spacelike W boson (q2 _{= t < 0}_{) strikes a b}

quark inside the proton or antiproton. The predicted NLO cross-section at the Tevatron is σ = 1.98+0.28

−0.22 pb [31, 32], assuming mt = 175 GeV/c2. The overall

uncertainty includes the choice of the factorization scale (±4%), the choice of PDF parameterization (+11.3%

−8.1% ), and the uncertainty in the top-quark mass ( +6.9% −7.5%).

2.2.2 s-channel Production Mode

In s-channel production, a timelike W boson (q2 _{= s > (m}

t+ mb)2) is produced

by the fusion of two quarks. At the Tevatron, the predicted cross section at NLO is σ = 0.88+0.12

−0.11 pb [31, 32] for mt = 175 GeV/c2. Here, the uncertainty includes

±2% due to the factorization scale, +4.7%_−3.9% due to the PDF parameterization and

+10.0%

−11.7% due to the uncertainty in the top-quark mass.

The NLO contributions to the s-channel will mostly lead to additional soft light quarks, since the probability of the gluon to split into a heavy quark-antiquark pair is quite low.

2.2.3 W t Production Mode

In the associated production an on-shell (or close to on-shell) W boson is produced in conjunction with the top quark. The predicted NNNLO cross-section at next-to-leading logarithmic (NLL) accurancy of this production mode at the Tevatron for mt = 175 GeV/c2 is σ = 0.26 ± 0.06 pb [35].

Since this cross section is negligible, the further discussion is restrained on the t and s-channel single top-quark production modes.

2.2.4 General Properties of Electroweak Single Top-Quark

Production

Interference between s and t-channel diagrams are null and their separation is maintained at NLO. Higher order corrections lead to nonzero interference terms. Recent results show, that those terms are heavily color-suppressed and wont pre-vent a meaningful separation of both channels [33].

The s and t channel processes are dominated by contributions from u and d quarks coupling to the W boson. Contributions from s or c sea-quarks in the

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initial state are small, an effect of only about 7% for t-channel and about 2% for s-channel production [35, 36]. There are also other electroweak production modes than those involving the W tb vertex. But the channels involving a W td or W ts vertex are strongly suppressed, since the involved CKM matrix elements are small. The contribution of such processes to the total single top-quark cross-section is about 1% and thus negligible at the Tevatron. The same circumstance is valid for the top quark decay. Nearly 100% decay into a b quark and a W boson. Decays into d or s quarks are strongly CKM suppressed.

As already mentioned, electroweak single top-quark production provides the unique opportunity to measure the value of the CKM matrix element |Vtb|. The

single top-quark production cross-section is directly proportional to |Vtb|2, hence

its measurement yields a direct extraction of the size of |Vtb|.

|Vtb| is determined experimentally to be very close to unity, under the SM

assumption of a unitary 3×3 CKM matrix. By only assuming that the branching ratio (BR) for a top quark decaying into a W boson and a b quark is 100%, BR(t → W b) = 1, which is equivalent to |Vtb| |Vtd|, |Vts|, the experimental

extraction of the matrix element is feasible without assuming neither the 3×3 structure of the CKM matrix nor its unitarity.

Theoretical new physics models beyond the SM exist which predict a signifi-cant deviation of |Vtb| from unity [37]. One minimal extension of the SM is the

introduction of a t0 _{quark with a mass around the electroweak scale and an electric}

charge of 2/3. Through a mixing with the SM top quark, this specific model imple-ments a rescaling of the third row to conserve its unitarity and wouldn’t interfere with the first and second row of the CKM matrix.

The scenario of a whole fourth generation of fermions is another interesting extension of the SM allowing for a value of |Vtb|considerably deviant from unity.

Contrary to general accepted opinion, a unitary 4×4 quark mixing matrix could provide sizeable mixing between the SM quarks and the fourth generation, assuming no correlations to a lepton mixing matrix [38]. In this model |Vtd| and

|Vts|could differ by a factor of 3 from the SM values as well as |Vtb|could be as low

as 0.75. The non-observation of those effects in other processes could be explained by huge cancellations due to virtual corrections of heavy b0 _{and t}0 _{quarks. The}

most stringent bounds on the mixing with the fourth generation is expected to be obtained from direct measurements of the third row CKM matrix elements. Preliminary lower limits from the CDF Collaboration on the mass of a b0 _{and a t}0

quark have been measured to be mb0 > 325GeV/c2 [39] and m_t0 > 311GeV/c2[40] at the 95% C.L., respectively.

2.3 Previous measurements of the top quark

branch-ing fraction ratio

Measurements of R were performed in CDF, first in RunI and then RunII.

The first measurement was performed using only 80 pb−1 _{in the lepton plus}

four jet samples. The idea behind the measurement technique was based on the calculation of the efficiency to tag a b in a event and on the determination of the

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Figure 2.5: The upper plot shows the negative likelihood function at the minimum and the likelihood as a function of R in the inset. The lower plot shows 95% (red), 90% (green) and 68% (yellow) confidence level bands. The measurement of R = 1.12 implies R > 0.61 at the 95%.

Parameter Value Lower Limit

σp ¯p→t¯t 7.74+0.67−0.57(stat+syst) (pb)

-R 0.90 ± 0.04(stat+syst) > 0.92 |Vtb| 0.95±0.02(stat+syst) > 0.96

Table 2.1: Summary of DØ measurement results.

number of selected events with a model in which R was one of the free parameters. According to the number of tags requested (zero, one or two) data was organized in bins. The background was computed using a kinematical-base analysis and by comparing observed and expected number of events in each bin R was fit. This analysis was reiterated with the final Run I CDF data set (109 pb −1_{) using also}

data collected in the t¯t→ llνν channel. The final result, R = 0.94+0.31

−0.24(stat + syst)

or R > 0.56 at 95 % C.L. was the first measurement of this quantity [112].

CDF performed a new analysis at the beginning of Run II, using 169 pb−1

[5]. Several improvements in the estimate of the backgrounds in different tag bins were applied. The result R > 0.61 and |Vtb| > 0.78 at 95 % CL (assuming three

generation of quarks and the unitarity of the CKM matrix) was again largely dominated by the statistics of the sample. In Figure 2.5 we show this result.

The most precise R measurement to date was performed by the DØ Collabo-ration using 5.4 fb−1 _{[6]. It was obtained using both the lepton plus jet and the}

dilepton channels. This analysis fits simultaneously R and the top pair produc-tion cross secproduc-tion σp ¯p→t¯t. A new method to calculate the number of t¯t events was

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t¯t → W bW ql and t¯t → W qlW ql for a top quark of mass mt = 172.5 GeV1. The

number of t¯t events in the i-th tag bin was described as a function of R and of the efficiencies to tag t¯t events with zero, one or two light quark jets.

Using a maximum likelihood technique, contents of each jet bin in data are compared to expectations and σt¯tand R are extracted. The results are summarized

in Figure 2.6 showing the confidence level intervals. The measured value for the branching fraction ratio, cross section and |Vtb|are summarized in Table 2.1

Figure 2.6: Confidence Level bands calculated by Feldman-Cousins technique. The dotted line is in correspondance of the measured value.

1_{Here q}

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Chapter 3 The Tevatron Collider and the CDF

II experiment

3.1 The Tevatron accelerator

The Tevatron [42, 43] is a proton-antiproton synchrotron located at Fermilab (FNAL) near Chicago (USA). It produces p¯p collisions with a center of mass en-ergy√s = 1.96 TeV and it was the highest energy accelerator before the start of Large Hadron Collider (LHC), in Geneve.

The high technology apparatus responsible of the production of the resulting p¯p beams used for collision, constitued by many sub-systems as the protons and an-tiproton sources, the pre-accelerators and storage rings for antimatter, is described briefly in the next sections. Collisions took place in designed interactions points where are installed the CDF and DØ detectors. A scheme of the Tevatron accel-erator complex is shown Figure 3.1.

The machine started operating in 1983. From 1985 to September, 2011 provided p¯p collisions at center of mass energy ≈ 2 TeV (1.6 TeV, 1.8 TeV and finally 1.96 TeV).

It was shut down on September 30, 2011. However, as most of this thesis was written before Tevatron shut down we will use the present tense to describe its operations.

3.1.1 The proton source

The process leading to the p¯p collisions starts with a Cockroft-Walton electro-static preaccelerator (PreAc) and its Proton Source, which contains an hydrogen ions source. Hydrogen gas is ionized into electrons and H+ _{ions and the latter are}

accelerated and strike on a cathode surface made of vapor coated cesium, charac-terized by a low work function. The H+ _{ions can absorb two electrons from the}

cathode and transform into hydrides H−_{, that are accelerated to an energy of 750}

keV by the PreAc. The H−_{beams produced in this way at a 15 Hz rate are focused}

by magnetic lenses and sent to a linear accelerator (Linac).

The Linac [44] uses H− _{ions due to the nature of its magnet power supply}

system, which resonates at 15 Hz. It is made of two sections: the first is the low 15

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Figure 3.1: Schematic view of the Tevatron accelerator complex

energy one, constitued by five drift tube cavities, which accelerates the ions to an energy of 116 MeV while the second is the high energy one, constitued by seven RF stations, that accelerate the hydrides to 400 MeV and collect them into bunches.

The next step of the acceleration process is performed by the Booster [45], a synchrotron of 75m radius, working at the same duty cycle as the Linac, constituted by a series of conventional magnets with 18 RF cavities interspersed. The H−_ions,

exiting from the Linac, are bent through thin carbon foils to strip off the electrons and the remaining protons are guided into the ring and accelerated by the RF cavities to an energy of 8 GeV. The use of negative ions permits injection of more particles from the Linac without losing the protons already inside the Booster. The final "batch" inside the Booster contains about 5 · 1012 _{protons and it is divided}

in 84 bunches, with a spacing time of about 19 ns, each one consisting of 6 · 1010

protons.

3.1.2 The Main Injector

The proton beam generated by the Booster is guided to the Main Injector [46] (MI), an oval synchrotron with a mean radius of 0.5 km, that can accelerate particles, using radio frequency systems, in the energy range between 8 GeV and 150 GeV. The MI can operate in different ways: for example, it can accelerate 8 GeV protons from Booster to 120 GeV for the antiproton production, it can accept antiprotons from the Recycler and can accelerate particles to 150 GeV, injecting them to the Tevatron for the last stage of the process. The first operation mode is one of the simplest tasks of the MI, where two batches from the Booster are merged together, with a procedure called "slip stacking", and sent on the target station to produce

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antiprotons. The Antiprotons Source (AS) will be described in more details below. The most complex scenario is the so called Collider Mode. In this mode the MI has to feed the Tevatron with protons and antiprotons at 150 GeV and has to prepare them in bunches more intense than the ones which come out from the Booster. The process that has been developed to achieve the latter task is called coalescing. The Collider Mode is organized in a sequence of steps:

• Only 7 of the bunches at 8 GeV produced by the Booster are extracted to Main Injector.

• This short batch is accelerated to 150 GeV.

• At this energy, the bunches are coalesced: that is, pushed together to form one high intensity bunch.

• The coalesced bunch is injected into Tevatron in a single turn.

• These steps are repeated until 36 coalesced bunches are injected to the Teva-tron.

• The 8 GeV antiprotons produced in the AS and stored in the Accumulator in 4 groups are injected in opposite direction with respect to the protons in the MI

• The antiprotons are accelerated to 150 GeV, the groups are coalesced in 4 bunches and then are extracted to the Tevatron in the opposite direction with respect to the protons. This procedure is repeated for 9 times, until 36 antiproton coalesced bunches are delivered.

3.1.3 The antiproton source and accumulation

The Antiproton Source [47] refers to an apparatus made up of a target station, two rings called the Debuncher and the Accumulator and the transfer lines that connect this rings to the Main Injector. The process to produce an antiproton beam that can be used in Tevatron collisions is long, between 10 and 20 hours, and can be summarized in a series of steps:

• A single bunch of protons, made up of two proton bunches from the Booster, is accelerated to 120 GeV and, before the extraction from tne MI, is narrowed in time at the expense of increasing the momentum spread (∆p/p), in a procedure known as bunch rotation. After the extraction the proton bunch spot is reduced by quadrupole magnets.

• The bunch hits a target in nickel to produce a shower of secondary particles. The target is kept in rotation to reduce asymmetrical depletion. Immediately downstream of the target module is the Lithium Lens module, designed to focus a portion of the 8 GeV pbars coming off of the target, reducing their an-gular spread. It was used instead of conventional quadrupoles because it can focus in both transverse planes. Lithium was used because is the least-dense

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solid conductor which minimizes the antiproton loss (18% of antiprotons focused are absorbed or scattered while passing trough the lens)

• A pulsed dipole magnet is situated after the lens. Its function is to select the negative particles and to discard the particles with the wrong charge-to-mass ratio from the beam and guide them on a graphite beam-dump.

• The production of antiprotons is a very inefficient process: typically just 1 or 2 antiprotons are selected every 105 protons colliding on the target. The

sur-viving particles are sent to the Debuncher, a rounded triangular synchrotron with a mean diameter of 180 metres. The purpose of the Debuncher is to reduce momentum spread by bunch rotation, by adiabatic debunching and by stochastic cooling to maximize the efficiency in the the transfer to the Accumulator. The antiprotons remain in the Debuncher until next bunch of protons is extracted from MI to the AS.

• The purpose of the Accumulator, a triangular shaped synchrotron housed in the same tunnel as the Debuncher, is to collect and accumulate antiprotons at 8 GeV. Both RF and stochastic cooling systems are used to cool the particles to desired momentum and to minimize the transverse beam size • When the Accumulator cannot store more antiprotons, they are transferred

to the MI, where they will be accelerated to 150 GeV and then injected to Tevatron, or to the Recycler ring, where they are stored at 8 GeV.

3.1.4 The Recycler

The Recycler Ring [48] is an antiproton accumulator of increased acceptance lo-cated in the same tunnel of the MI. It was degnigned to achieve three tasks: first to recover the antiprotons at the end of Tevatron collisions, collecting and cooling them in new re-usable bunches. Since the antiproton production rate decreases as the beam-current in the Accumulator rises, the Recycler was designed to store more antiprotons and maximize the AS efficiency; the Recycler uses permanent magnets in order not to lose the antiproton beam if the Fermilab power is lost for an hour.

The Recycler was never used to achieve the first task because of the enormous antiproton loss in the deceleration process from 1 TeV to 8 GeV, but the use of the Recycler allowed to increase the antiproton production and, consequently, boosted Tevatron performance since its introduction (2004).

3.1.5 The Tevatron Ring and Performance

The last stage of particles acceleration takes place in the Tevatron ring, a syn-chrotron with a radius of 1 km, where the beams collide at a final center of mass energy p(s) = 1.96 TeV. The beam control is obtained by the use of supercon-ducting coils, capable of a up to 4.2 T magnetic field at a temperature around 4.3 K, cooled by liquid helium. The two beams in the ring share the same beampipe,

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circulating in opposite directions on two non-intersecting helical orbits, kept sep-arated by electrostatic separators. They contains both 36 bunches, grouped in three trains, separated by an abort gap of 2.6 µs. These gaps are necessary to keep a proper and safe environment for the collision and for the removal of the beam at Tevatron run end or in case of malfunction. The bunches in every single train have a time spacing of 396 ns. Each proton bunch contains ∼ 1012 _particles,

while the antiproton one is made up of ∼ 1011 _{particles. The beams are focused}

and brought to collision in two determinated points of the accelerator, called BØ and DØ where are respectively present CDF and DØ detectors. In this points the beams are focused by quadrupole magnets, reducing the transverse size in a procedure called low β∗ _squeeze_{, to achieve the maximum possible luminosity.}

Istantaneous luminosity (L ) is an important parameter of an accelerator and it is proportional to the data taken in a unit time. It is given by

L = NpNp¯Bf

2π σ2 p + σp2¯

(3.1)

where Np and Np¯ are respectively the number of protons and antiprotons in each

bunch, B is the number of bunches, f is the revolution frequency and σp and σp¯are

respectively the rms of a gaussian fit on the proton and antiproton beams section. The istant luminosity values for Run II are noticeably higher with respect to Run I thanks mainly to an higher rate in antiproton production after the introduction of the Recycler ring. Continuous upgrades lead to the record instantaneous lumi-nosity of L = 4.31 · 1032 _cm2 _s1 _{on 4}th _{of May 2011. In Figure 3.2 is reported the}

peak luminosity as a function of time from the start of Run II. The blue triangles show the peak luminosity at the beginning of each store. Since the luminosity drops as the particles continue to collide with each other during the life of the store, the average of the last 20 peaks is marked by a red square, to display the peak luminosity in a format that is easier to follow.

The amount of data collected is proportional to the integrated luminosity, given by the integral of instantaneous luminosity over time Lint =

R

L dt. It is a very important parameter since for a given physical process with a given cross section σ, usually measured in picobarn (pb), the number of event N is given by

N =Lintσ (3.2)

In Figure 3.3 we show the Run II weekly integrated luminosity as a function of time where it can be seen a steady improvement since the Run II start. The CDF detector does not acquire on tape all data delivered. As can be seen from Figure 3.4 the average efficiency in collecting the delivered luminosity is about 85%. The sources of this reduction are due to the trigger dead time, bad beam conditions that do not allow the detector to operate and the choice to use part of the data acquired for detector studies, calibration and monitoring. The collision data used in the analysis described in this thesis were taken from February 2002 to March 2011 and correspond to an integrated luminosity of 7.52 fb−1_{. The Tevatron}

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Figure 3.2: Graphic of Tevatron peak luminosity since the start of RunII [50].

3.2 The CDF II detector

The Collider Detector at Fermilab [41], commonly called CDF, is a 5000 ton solenoidal detector, built to study p¯p collisions at the Tevatron and it is located in the interaction point called BØ . Event analysis is based on the combination between precision charged particle tracking, momentum analysis, fast projective calorimetry and fine grained muon detection.

Tracking systems are contained in a superconducting solenoid, 1.5 m in radius and 4.8 m in length, which generates a 1.4 T magnetic field parallel to the beam axis. Calorimetry and muon systems are located outside the solenoid. The original de-sign of the detector was developed in 1981 and the partially completed apparatus detected the first p¯p collision in October 1985. Since then CDF underwent many upgrades and some detector components and the data acquisition system were completely rebuilt for the Tevatron Run II. The basic goal for CDF is to measure the momentum, energy and, if possible, the identity of particles produced in p¯p collisions over as large a fraction of the solid angle as possible. To accomplish this task the detector was designed to sourround the interaction region with layers of different detector components, described in the next subsections.

3.2.1 Detector coordinates system

The events registered by CDF can be described using a cartesian coordinate sys-tem centered in the nominal point of interaction. The z axis is coincident with the beamline and points in the proton beam direction, while the x is set in the accelerator plane pointing outward the ring and the y axis points up. The x-y

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Figure 3.3: Graphic of Tevatron integrated luminosity [50].

plane is usually called the transverse plane and the quantities projected on this plane are marked with a T subscript, while the regions at z > 0 and z < 0 are respectively called forward and backward and corresponds to ongoing p (¯p). Because of the simmetry of the detector a cylindrical or a polar coordinates system are also used. The first one uses r as the distance from z axis in the transverse plane and φ as the azimuthal angle, starting from the x axis and defined positive in the anti-clockwise direction. The second one instead uses r as the distance from the interaction point, φ as the azimuthal angle and θ as the polar angle, starting from the positive direction of the z axis. Since the colliding beams are un-polarized, the production of the physics objects is invariant under rotation around the beam line axis. The azimuthal and the polar angles are respectively described by:

φ = arctany

x θ = arctan

px2_{+ y}2

z (3.3)

A very important quantity that is commonly used instead of the polar angle θ is the pseudorapidity defined by

η = − ln tan θ 2 (3.4) and can be extracted from the high energy limit (E m) of the rapidity y defined by y = 1 2ln E + p cos θ E − p cos θ (3.5)

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Figure 3.4: Graphic of the comparison for CDF luminosity delivered and on tape as a function of the store number (bottom) and of the date (top). [51]

Figure 3.5: CDF detector isometric view

For instance if an object is emitted at θ=90° it has a pseudorapity η=0. It can be shown that this quantity transforms linearly under Lorentz boosts along z direc-tion, so the η intervals are Lorentz invariant. This property is particularly useful at hadron colliders where the interactions take place between hadron constituents that carry only fractions of the nucleon momentum and so the events are boosted along z direction. At high energy the resulting distribution of product particles is, in good approximation, flat in η, so the detector components are designed to be uniformly segmented in this parameter. A very useful Lorentz invariant quantity that can be introduced to parameterize the distance between two particle is the Lorentz invariant ∆R defined by:

∆R =p∆η2_{+ ∆φ}2 (3.6)

This parameter is used to define a cone around a single particle and it is of great important in the jet reconstruction algorithm.

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Since the quadrimomentum balance can be applied only on the transvers plane, due to the unknown longitudinal fraction of quadrimomentum carried by the inter-action partons in the hard process, it is very useful to introduce a set of variables. Therefore we define the transverse energy ET and the transverse momentum pT as

ET = E · sin(θ) and pT = p · sin(θ) = pz/ sinh η

A charged particle moving into a homogeneous magnetic field, in this case oriented along the beam direction, performs a helicoidal trajectory that can be uniquely described by a set of 5 parameters:

C - Is the half curvature of the trajectory defined by C = q/2R, where q is the charge of the particle and R is the helix radius. It is related to the transverse momentum, in GeV, by

pT = 0.15 ·

qB

|C| (3.7)

where B is espressed in Tesla and C in m−1_.

d0 - Is the signed impact parameter defined as the minimum distance between

the z-axis and the projection of the helix on the transverse plane shown in Figure 3.6 . d0 = q q x2 0+ y20− R (3.8) where x0 and y0 are the coordinates of the center of the helix projected onto

the transversal plane while R is its radius. φ0 - Is the azimuthal angle of the track at its vertex.

λ - Is the cotangent of the polar angle between the track at the vertex and the z-axis. The longitudinal component of the momentum is given by

pz = pT · λ (3.9)

3.2.2 Tracking system

Situated just outside of the beam pipe, in the central region of the CDF II de-tector, there is the Tracking System, an apparatus capable to measure with high precision and minimum perturbation the trajectory of charged particles produced by Tevatron interactions. The whole system seats inside a magnetic field of 1.4 T, oriented along the positive z direction, generated by a solenoidal magnet made by niobium-titanium/aluminum superconducting coils refrigerated by helium [52]. The presence of the magnetic field constrains the charged particles to follow heli-coidal trajectories whose radius projected on the transversal plane is related to the transverse momentum of the particles (pT). In Figure 3.7 it is possible to notice

that the tracking system is made up of two subsystems: the first one, located next to the beam pipe, is the Silicon Tracker surrounded by a drift chamber called Central Outer Tracker.

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Figure 3.6: Helix Parametrization

Figure 3.7: Schematic view of the inner tracking system and plug calorimeters at CDF

Silicon tracker

The silicon microstrip system is responsible of high precision and fast recon-struction of charged particle trajectories. This detector is capable of reconrecon-struction of secondary vertices displaced from the primary ones in an event and real-time triggering using the impact parameter d0. Both of these features are of

fondamen-tal importance in the reconstruction of the b-jets used for top decay studies. The silicon tracker is divided in three subsystems:

• Layer 00 (L00): Layer00 [53, 54] is a single-sided silicon detector, providing a full azimuthal coverage, directly mounted on the beam pipe on a carbon fiber support structure with integrated colling system. To prevent gaps,the L00 was build on two overlapping and alternating in φ layers as shown in Figure 3.8. The inner one (128 strips) has a radius of 1.35 cm, while the outer (256 strips) has a radius of 1.62 cm. This detector covers the region

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|z| ≤ 47cm (η ≤ 4). Since L00 is very close to the primary interaction point, it provides a very precise track reconstruction and was designed to recover the loss in the impact parameter resolution due to the presence of read-out electronics and cooling systems of the SVXII subsystem. L00 was built using the radiation-hard silicon sensors that are also used in the LHC detectors.

Figure 3.8: Left: Full view of SVX II barrels. Right: Transversal view of the Layer00 and the first two layers of the SVXII

• Silicon Vertex Detector II (SVX II): The SVX II [55, 56, 57] is the main component of the silicon tracking system. The detector design is the barrel geometry comprised of layers of silicon microstrip detectors supported by disc shaped bulkheads perpendicular to the beam pipe. The SVX II is made up of three barrels modules, each one constituted by five cylindrical layers of ladders divided into 12 sections, for a total length of 96 cm and covering the region |η| ≤ 2. The silicon sensors, unlike for L00, are double-sided, feature that provides a 3D vertex reconstruction. The SVX II provides up to five r-φ measurements, but since the strips on the backside of the sensors in layers 0,1 and 3 are perpendicular to the axis aligned strips, it is possible to combine r-φ measurement with a precise determination of the z coordinate. In addition, the strips of the remaining two layers, named small angle stereo, are rotated by 1.2° to provide an unique 3D reconstruction.

The average axial pitch of the silicon ladders is around 60 µm. Figure 3.8 shows both the full view of the SVXII barrels and the transversal view. • Intermediate Silicon Layer (ISL):

The ISL [57, 58] is a double sided silicon micro-strip detector consisting of three layers situated in three different regions and radii. The central layer is at r=22 cm from the beam and it is very important in connecting the trajectories reconstructed by the SVX II and the ones tracked by the COT. It covers the region with |η| ≤ 1. There are then two forward layers situated at r=20 cm and r=28 cm in the region with 1 ≤ |η| ≤ 2, where COT does

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not provide a good coverage, to enhance track reconstruction efficiency and acceptance.

The whole silicon system is made to provide a 3D track reconstruction with a total resolution on the impact parameter d0 and on the interaction point z0 of 40 µm

and 70 µm respectively.

Central Outer Tracker (COT)

The COT [59] is a cylindrical drift chamber designed to substitute the old CDF central drift chamber, not usable at the Run II luminosity. The detector is 310 cm long in the z direction, covers 43.3 ≤ r ≤ 132.3 cm in radial direction and spans the entire azimuthal angle providing a full coverage for |η| ≤ 1, coverage that decreases up to |η| ≈ 2. The COT contains 30,240 sense wires. Approximately half of them are axial and the other half are at small stereo angle |ϕ| = 2°. They provide a 3D track reconstruction, accurate information in r-φ, a less accurate information in r-z and a measurement of pT.

The COT is constituted by 96 sense wires grouped in eight superlayers which in turn are divided in φ into supercells. The structure of the COT and the layout of supercells are represented of Figure 3.9. The supercells are tilted by 35° with respect to the axial direction to compensate for the Lorentz angle of the drifting electrons due to the presence of the magnetic field. The COT was built to ensure that the maximum drift time is less than the bunch spacing time in order to operate correctly during Run 2. The best performance is obtained when the COT is filled with a gas mixture of argon/ethane/CF4 (50:35:15) giving a maximum drift time of around 100 ns, that allows a good track reconstruction during 108 bunch operations with a spacing time of 132 ns1_{. The resolution on the hit position is}

about 140 µs while the resolution on the measurement of the transverse momentum is σ_pT

p2 T

= 0.0015 (GeV/c)−1.

Figure 3.9: (left) Tranversal section of the COT. It is shown in more detail the structure of a superlayer. (right) Schematic layout of three supercells of the second superlayer

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3.2.3 Time of Flight Detector

The time of flight detector (TOF) [60] is made by 216 bars of plastic scintillators, each one covering 1.7° in φ and connected to PMTs, and it is installed just outside the COT, covering the region with η ≤ 1. The primary physics motivation is to provide charged kaon identification to improve efficiency in B physics analyses. The TOF is capable to provide two standard deviation separation between K±

and π± _{for momenta up to 1.6 GeV/c. Besides that, the TOF detector is used}

in triggering of highly ionizing particles or cosmic rays, since it can provide fast information available to the first-level trigger.

3.2.4 Calorimetric systems

The calorimetry system is located outside the solenoid that surrounds the tracking system, and its purpose is to measure the energy and the direction of neutral and charged particles exiting out from the inner region of the detector. For a correct measurement of the total energy of an event the calorimetric system has to cover as much region in η as possible and must be thick enough to let the particles lose all their energy inside the detector. Particles hitting the calorimeters can interact electromagnetically (as electrons and photons do) or hadronically (mesons or barions produced during the hadronization processes). Since the interaction are different, two types of calorimeters were built: an inner sampling calorimeter (lead/scintillator), optimized to collect the energy of EM particles, and an outer sampling calorimeter (iron/scintillator), thicker and studied for hadron energy reconstruction. The total coverage is up to |η| < 3.6, provided by the so called "central" and "plug" calorimeters. Each calorimeter is divided in η − φ sections, called towers, designed to point to the center of the detector, in order to provide information on particle position.

The system is divided in central (up to |η| < 1.1) and plug (1.1 < |η| < 3.6). In

Coverage Thickness Pos Res ((rφ, z)) E res

CEM |η| < 1.1 18X0 (1λ0) 0.2, 0.2 13.5%√_E T ⊕ 1.5% CHA |η| < 0.9 4.7λ0 10, 5 √50%_E T ⊕ 3% PEM 1.3 < η < 3.6 23.2X0 (1λ0) √16%_E T ⊕ 1% PHA 1.3 < η < 3.6 6.7λ0 √80%_E T ⊕ 5% WHA 0.7 < η < 1.3 4.7λ0 10 5 √75%_E T ⊕ 4%

Table 3.1: Some properties of various electromagnetic and hadronic calorimeters. X0 is the radiation length while λ0 is the interaction length. The values for

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the Table 3.1 are summarized some properties of the calorimetric system.

The central calorimeter

• The central region of the calorimetric system is made up of the CEM (elec-tromagnetic), CHA and WHA (hadron calorimeters) [61, 62], providing a complete covering in the azimuthal region and, respectively, a coverage of the |η| < 1.1 and |η| < 0.9 regions. The electromagnetic calorimeter is seg-mented in a series of ∆η × ∆φ = 0.11 × 15· projective towers, called wedges, whose structure is shown in Figure 3.10. The wedge is a sampling device made up of 31 layers of polystyrene scintillator with 30 interleaved lead-aluminium layers. In order to mantain a constant radiation length thickness as polar angle varies, some of the lead-aluminum layers are substituted by acrylic ones. The blue light generated into the active material is collected by blue-to-green wavelength shifters and guided to PMTs placed outside the module. The CHA and WHA modules have a structure very similar to the electromagnetic ones. In fact the modules are projective towers each cov-ering approximately 0.1 unit in pseudorapidity and 15 (grad) in azimuthal angle, matching those of the electromagnetic calorimeter which are in front of them. Absorber materials are 32 steel layers, 2.5 cm thick, in CHA and 15 steel layers, 5.1 cm thick, in WHA both interleaved with acrylic scintillator. In addition CEM modules contain the Central Electron Strip (CES) cham-bers and Central Preshower detector (CPR). The strip chamcham-bers, located at ≈ 6 X0 determine shower position and transverse development at shower

maximum by measuring the charge deposition on orthogonal strips and wires. The result leads to a better reconstruction of electromagnetic object prop-erties. CPR is as preshower detector and can collect the energy deposit originated by interaction of particles with tracking system and solenoid ma-terial. This detector is used to help separating pions from electron and photons, since the latter deposit a greater amount of energy in the chamber and provides a precise measurement of the electromagnetic shower position.

The plug calorimeter

• The plug calorimeter [63, 64] covers the region with 1.1 ≤ |η| ≤ 3.6 and it is constituted by two identical parts, called East and West. A schematic view of the plug calorimeter is shown in Figure 3.11 (right) where is possible to notice that the structure of the detector is similar to the central calorimeter one: there is a front electromagnetic compartment, PEM, and a rear hadronic one, PHA. Briefly, the PEM is made up of 22 sets of alternating layers of absorber (lead) and polystirene scintillator, with a thickness of 4mm. The scintillating layers are organized in projective towers that are distributed in φ sections as shown in figure 3.11 (left). Just behind the 4th_{lead absorber, the}

PEM incorporates a Shower-Max Position detector (PES), placed at 6 X0,

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Figure 3.10: Schematic view of a CEM wedge.

obtained from the first tile of scintillators that, for this scope, is thicker than the other. The PHA has a similar structure to the PEM, but the thickness of the scintillators is 6mm and the absorbers are made up of iron. As in the central calorimeter detector the read out is obtained trough PMTs

3.2.5 Muon Detectors

Since muons lose very little of their energy into the tracking and the calorimeter systems, the muons detectors [67, 68] are situated behind most of CDF detector material. In figure 3.12 we show the geometry coverage of the muon subsystems. This detector is organized in four subdetectors:

• The central muon detector (CMU) is located right outside the CHA behind 5.5 interaction lengths (λ0) of detector material. It covers a pseudorapidity

region of |η| < 0.68. It is a barrel with inner and outer radii respectively of ri = 347 cm and ro = 396 cm, consisting of 4 drift tube layers sectioned

by wedge matching the CHA towers: 3 sections of 4 tubes per layer per 15°. Each tube operates in proportional mode, with a maximum drift time of 0.8 µs, a multiple scattering resolution of 12/(p[GeV]) cm and a longitudinal resolution of δz ≈ 10 cm.

• The central muon upgrade detector (CMP) is placed over the CMU be-hind 7.8 λ0 of detector material that includes 60 cm thick steel slabs, in

order contain the hadrons escaping from the CHA. The CMP contains four layer of rectangularly arrayed drift tubes. The rapidity extension of the

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Figure 3.11: At left is represented a transversal view of a quarter of the CDF plug calorimeter. At right is shown the tower segmentation of the calorimeter

Figure 3.12: η - φ coverage of the muon detector system. The shape is not regular because of the obstruction by structural elements.

CMP detector is |η| ≤ 0.68 . Also the CMP works in proportional mode, with a maximum drift time of 1.4 µs and a multiple scattering resolution of 15/(p[GeV]) cm. There is a layer of scintillators (CSP) mounted outside the CMP to provide timing information with a resolution of 1-2 ns

• The central muon extension detector (CMX) consists of conical sections facing toward the interaction point behind 6.2 λ0 of detector material,

ex-tending the central muon detector coverage to 0.65 ≤ |η| ≤ 1.0. The CMX is made up of two folds of 4 layers of rectangular drift tubes with a multiple scattering resolution of 13/(p[GeV]) cm and the longitudinal position reso-lution of δz ≈ 14 cm. Two layers of scintillators (CSX) are mounted on the external surfaces of the CMX, one layer on the upper surface and one on the lower surface, in order to provide timing information.

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• The intermediate muon detector (IMU) is placed behind 6.2 - 20 λ0 of

material, depending on the rapidity. The IMU is made up of two barrels extending the CDF geometric muon acceptance in the range 1.0 ≤ |η| ≤ 1.5. It contains 4 layers of proportional drift tubes (BMU), with a maximum drift time of 0.8 µs, a multiple scattering resolution of (13-25)/(p[GeV]) cm and the longitudinal position resolution is δz ≈ 16.5 cm. There are three layers of scintillators that provide timing information: BSU-F,BSU-R and TSU.

3.2.6 Cherenkov luminosity counters

Since a measurement of the luminosity based on measurements of the beam param-eters has an uncertainty greater than 15%, CDF measures the collider luminosity using the Cherenkov Luminosity Counters (CLC) [69], made up of two symmetri-cal modules designed to determine the rate of inelastic processes per bunch cross-ing. The detector is placed in a high pseudorapidity region of 3.7 < |η| < 4.7, with each module constituted by 48 conical, gaseous, Cherenkov counters pointing toward the interaction point.

(a) (b)

Figure 3.13: Schematic view of the CLC in CDF (a) and time distribution of East and West modules of CLC (b). The p¯p collisions deposti a coincidence signal in the two modules

The cones are arranged in concentric manner with the smaller counters, 110 cm long and with an initial diameter of 2 cm, at the center and the biggest, 180 cm long and with an initial diameter of 6 cm, outward. The shape and orientation are designed to enhance the collection of particles outgoing from the interaction region. The collisions are measured by time coincidences between the two modules (called East and West) with a time resolution of 100 ps. The various signal shapes on CLC can provide a measurement of the average number of inelastic collisions per bunch crossing (µ) with an uncertainty around 4%2_.

The instantaneous luminosity L can be extracted from:

µfbc = σp ¯p,in·L · (3.10)

2_{The number n of p¯}_{p interaction in a bunch crossing follows a Poisson distribution with mean}

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where fbc is the bunch crossing rate in Tevatron, is the CLC acceptance for

inelastic scattering and σp ¯p,in is the inelastic p¯p cross section obtained by

extrapo-lating at √s = 1.96 TeV the combined results for the inelastic p¯p cross section of CDF and E811 at √s = 1.8 TeV measurements [70].The value used for the cross section is σp ¯p,in = 60.7 ± 2.0 mb. The evaluation of the uncertainties of different

factors in Eq. 3.10 leads to a total uncertainty of 5.8% on instantaneous luminosity value.

3.3 CDF Trigger and Data handling

3.3.1 CDF Trigger system

At the Tevatron the total crossing rate, due to the organization of the beam in three trains of 12 bunches with a spacing time of 396 ns, as described previously in the chapter, is 2.53 MHz. Since the maximum tape writing speed is ≈ 100 Hz, it is necessary a system that select only interesting physics events from the over-whelming background. This task is performed by the trigger, that selects events online and decides if the information can be written on tape, and subsequently fully reconstructed offline, or has to be discarded.

The CDF trigger is organized in a three level architecture (L1, L2 and L3 shown in Fig. 3.14 (a)), each one providing a rate reduction sufficient to allow the processing in the next level with minimal deadtime. The first two levels are hardware based while the third one is a software filter that runs on a processor farm.

The final decision taken by each level is based on a set of programmable condi-tions that increases in complexity and selectivity as detector read-out and data elaboration becomes available.

(a) (b)

Figure 3.14: The CDF II trigger system. In figure (a) is shown the diagram of the three levels trigger. In figure (b) is shown the L1 and L2 trigger subsystems [71].

Measurement of the ratio R=BR(t->Wb)/BR(t->Wq) at CDF

Tesi di Laurea Magistrale