Precision Measurement of the Top Quark Mass at CDF

Precision Measurement of the Top Quark Mass at CDF

Candidato: Michele Giunta Relatori: Prof. Giorgio Bellettini

Dr. Georgui Velev Relatore interno: Prof. Angelo Scribano

Università di SienaDottorato in Fisica

Siena, 25 Giugno 2007

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Outline

1. Top Quark: introduction2. Decay Channels3. Combinatorics4. Template Method5. Improvement to TM:

3Best6. BLUE7. Sanity Checks8. Mass Measurement9. Results

Michele Giunta, 25/06/07

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The Top Quark


In the Standard Model, there are 3 generations of elementary matter fermions. Four bosons (not including gravity) carry interactions among them. Fermions and bosons get masses through their interaction with the yet-to-be discovered Higgs boson.

Each generation comprises a lepton and a quark doublet. Members differ in one unit of

electric charge. The third generation of quarks was discovered in 1977 when the b-quark was observed in a bound b-antib state and soon understood to be a down quark type.

After that discovery it was expected its doublet to be completed by a “top” quark.The enormous mass of the top quark delayed discovery by about 20 years.

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Why Top Mass


• In the SM the top and the W masses include a contribution by Higgs virtual loops. These contributions can be computed as a function of the MH and by correlating the Mtop and MW masses one gets indirect but important information on MH.

• The top lifetime is so short the it decays before hadronizing. This unique feature makes it possible to measure its mass as the invariant mass of its decay products, as currently done for unstable non-elementary particles.

It is important to measure the top quark properties, primarily its mass, to proof the validity of the SM.

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Top Discovery


Evidence for the top quark was announced in 1994 by the CDF experiment at the Fermilab Tevatron by observing an excess of top-like events in two decay channels and reconstructing 6 events (19.3 pb-1 data), showing a mass of about 175 GeV.

Full discovery was reached with more statistics and announced in 1995 by the CDF and the other Tevatron experiment, DØ.

Tevatron

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The Tevatron


The last particle accelerator of the Fermilab chain, the Tevatron, is a proton syncrotron accelerating the proton and antiproton beams in opposite direction from 150 to 980 GeV to provide about 2 TeV CM energy.

Top luminosity reached: 286·1030cm-2s-1

Integrated luminosity: up to today ~2.5 fb-1 on tape2 more years of data-taking scheduled (6 fb-1)

CDFCDF

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The CDF Detector


Tracking system:• L00, SVX, ISL• COT Calorimeters:

• Electromagnetic• Hadronic

Muon chambers:• CMP, CMU• CMX

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The top quark is expected single or in ttbar pairs.

The expected production cross section of single top is about 3 times smaller, detection efficiency is lower and separation from BKG is more difficult. Even if some evidence has been shown, single top production has not been demonstrated yet.

Our analysis addresses t-tbar production.

Top Production


~85% ~15%Strong production

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Warning!


From now on we shall consider only:• ttbar pair production

TTBAR SYSTEM

SINGLE TOP

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Top Decay Channels


The top decades ~100% in Wb.The W decay is shared among the allowed channels: e, , , ud(x3), cs(x3).

Depending on the decay of the W, there are the following 3 t-tbar decay channels(“lepton” = e or ):

DILEPTON : (2/9)·(2/9) = 4.9%SEMILEPTONIC : 2·(2/9)·(6/9) = 29.6% ALL HADRONIC : (6/9)·(6/9) = 44.4%

Weak decay

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Warning!


SEMILEPTONIC

DILEP, ALLHAD From now on we shall consider only:• ttbar pair production• semileptonic decay channel

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L+J: Combinatorics


The detector measures energy and direction of four jets.

With no information on jet flavour (b-tagging) we cannot assign uniquely jets to partons.

A number of t-tbar reconstructions are possible for each event.

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Combinations Count


• 4 objects: 4! = 24 combinations (jet-to-parton associations)

• The two light jets (u,d,s) given to the W can be swapped: 12 combs.

• The 2nd degree equation for the neutrino longitudinal momentum has in general 2 different solutions: 24 combs

• 1 b-tag: 3!=6 combinations for jets. W, pz( 6 combs again. Ambiguity on the b-side: hadronic or leptonic? : 12 combs

• 2 b-tag: 2 combinations for W jets. W, pz (: again 2 combs. Ambiguity on the b-side: hadronic or leptonic? : 4 combs

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Warning!


PRETAG SAMPLE

2TAG, 1TAG, 0TAGFrom now on we shall consider only:• ttbar pair production• semileptonic decay channel• pretag data sample

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Analysis Methods


Template (TM): the shape of reconstructed masses from the data sample is compared to MC predictions (templates) for discrete input top masses. Parametric are functions used to smooth discrete MC samples. Simple method, low CPU needed.

Matrix element (ME): To each observed event and possible reconstruction of it, a probability of having been produced in that specific kinematic configuration is associated. A transfer function describes how a produced signal/BG would be seen by the detector.Difficult estimate of systematics, smaller data samples, heavy CPU usage, but better use of the information.

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Warning!


TEMPLATE

MATRIX ELEMENT

From now on we shall consider only:• ttbar pair production• semileptonic decay channel• pretag data sample• Template method

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TM: Analysis Procedure


BKG estimation: ratios, #events

Kinematic Fit

Selection

Final (LH) Fit

Establish cuts to select MC signals and BKG events and real data.

Compute relative/absolute contaminations of BKG in the data sample.

Associate to each reconstructed event a top mass and a reconstruction quality factor (2).

Perform a LH fit to data.

Mass TemplatesAnd BKG Samples

Obtain mass shapes for the BKG and for a number of MC generated top masses: [155;195] GeV stepping by 2.5 GeV. Parametrize them.

Selection

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Event Selection


The same selection cuts are applied to MC signal, MC BKG, data. The criteria for an event to be accepted are as standard in CDF top studies.

trigger electron Et>20 GeV or muon pT>20 GeV/c dilepton veto MET > 20 GeV ≥4 jets with ET>15 GeV cosmic veto lepton solation > 0.1 |z|<60cm track reconstruction quality… BKG

s

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Backgrounds


We must evaluate the amount of background (BKG).

BKG process BKG fractions BKG templates

• W+light jets • W+H.F. • non-W (QCD) • diboson • Single Top (<1 evt)

We estimate the relative contribution of each process to the total BKG

We get the BKG templates by reconstructing events as t-tbar

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BKG Estimation


NUMBER OF EVENTS:By applying the selection to data, we find 700 events. A kinematical 2 cut accepts 645 events.

RATIOS:The BKG fractions had been computed for tagged events in the course of the cross-section measurement with 695 pb-1.We correct by MC to pretag events and normalize to our 1030 pb-1 sample.

W+L.F. 63.3W+H.F. 13.9Non-W 14.6Diboson 8.2

BKG %

Total 700 645Signal 353 339W+L.F. 223 194W+H.F. 49 43Non-W 46 45Diboson 27 25

Any 2 2<91 fb-1

We can run a constrained fit

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Combination Sorting


In the classical TM, all the possible jet-to-parton assignments are reconstructed. The reconstruction 2 gauges how well a combination can fit the t-tbar assumption.

The reconstructions are sorted by increasing 2

and the mass associated to the minimum 2 is entered the mass spectrum.

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Template Final Fit


Mtop, stat

A maximum likelihood technique fits the data mass distribution in terms of a BKG and of a mass-dependent signal template. The Mtop for which the LH is maximum indicates the top mass measure.

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Our Analysis


We developed an improved Template Method and analyzed the 1030 pb-1 data sample accordingly

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2 Rank


In the subsample of events where the 4 t-tbar decay quarks generate the 4 leading jets, only about 50% of times the best 2 is found to correspond to the correct jet/parton association. The rest of times, it is distributed on the other rank bins as in the figure.

To recover part of the neglected information we exploit not only the best, but also the second and the third best reconstructions (3Best2 Method)

Does the best 2 indicate the correct jets-to-parton assignement?

3Best2s

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3Best 2s


Yes, First

No: skip

Yes, Second

Yes, Third

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Multiple 2 Analysis


Comb 1

TMT

M1, 1

Comb 3

TMT

Comb 2

TMT

M2, 2 M3, 3

Combine results Mcomb, comb

Three Mass template sets and three BKG templates are generated, one for each combination.

We perform three independent Top mass measurements.

Results are combined after taking correlations into account

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Template Parameterization


I

II

III

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BKG Parameterization


I II III

BLUE

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BLUE


The combined mass is a linear combination of the input masses.

The weights are constrained.

The are

obtained by imposing the combination to have the smallest 2The correlation factors are related to the

covariances in the error matrix.

Best Linear Unbiassed Estimate [L. Lyons D. Gibaut, How to combine correlated estimates

of a single physical quantity, NIMA A270 (1988), pp 110, 117.]

PE

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Pseudo-Experiments


Pseudo-Experiments (PE) are data-similar sets of MC events.

Each PE: 645 total events out of which 306 ± (=44) BKG.

The MC events are fished out from the MC samples.Example: • take the Mtop=170 GeV MC• extract 337 events (fluctuation!) from it• join with 308 events piked from the BKG samples (using the correct ratios) • fit as they were the data set• repeat.

Correlations (cov1,2, cov1,3, cov2,3) were computed from 2000 PEs.

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How to Apply BLUE


Mtop TEMPLATES:

• A set of 2K PEs is created for each Mtop. The distributions of the 3

best combinations are fitted preserving their correlations and the mass correlation factors 12, 13, 23 are determined.

• For the n-th event, 1(n), 2(n), 3(n) are determined and the

average values 1, 2, 3 are calculated.

• The BLUE mass and error mB,n and B,n are computed for each PE.

• The mB and B are determined by fitting to Gaussians their

distributions..

SYSTEMATIC ERRORS and DATA:The correlation factors 12(175), 13 (175), 23 (175) from the mass

template Mtop=175 GeV are used (see next slide).

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Correlation Factors


To measure the DATA w/ BLUE, we cannot study the correlation factors (data is one single experiment).

Systematic uncertainties must be measured in the same conditions as data.

We must compute the s from a MC sample.

We must use the same s as for data.

How could we choose the best triplet? We picked a value in the middle of the mass range and showed that the measure is insensitive to other choices.

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Alpha Weights


The values of 1,2,3 as a function of Mtop

are the mean values of their distributions.

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BLUE mass/error Distributions


Michele Giunta 11-30-06 prebless

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BLUE Masses


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2Best 2s


How much does the third combination contribute?

To check this, we turn the third combination off and measure the different precision on MC simulations

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2Best 2s


The 3rd combination itself improves the overall stat error by about 1 more % (about 13% of the BLUE improvement). It would not be worth studying the fourth combination. Sanity

Checks

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Sanity Checks


Before applying the method to data, “sanity checks” are made on simulated events in order to assess its ability to correctly reconstruct a top mass.

Sanity checks include:

• Minput vs Moutput plots• Pull = (Mfit-Mtrue)/fit distributions• Blind masses study

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Min vs Mout


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Pull Distribution for Mtop=175 GeV


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Average Pulls vs Mtop


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BLUE Pulls


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Blind Masses


This test is preliminary to accessing the data. We do not know the real mass for these 5 samples. The test is passed if the residuals between our measure and the nominal value is consistent with zero.

Random order blind samples.

The Pythia samples are shifted up by the generator systematic uncertainty.

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Systematic Uncertainties


The correlation factors used are: 12(175) =

0.372813(175) =

0.297923(175) =

0.3314

Data!

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Data Measurement


MBLUE = 168.9 ± 2.2stat ± 4.2syst GeV/c2

This result is obtained with no use of b-tag information.

Kolmogorov-Smirnov test on the data fit: KS(first) = 0.904KS(second) = 0.998 KS(third) = 0.953

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How likely is our BLUE improvement by 5% on the statistical error?From the PEs for Mtop=175 GeV we found that we could have

been luckier but that the result was not unlikely at all.

23% 77%

BLUE Improvement


Data

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Among Other Results


Our result fits well into the full picture of CDF

top mass measurements.

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Aknowledgements


Questa tesi è stata possibile grazie all’aiuto ed alla collaborazione di molte persone:

- dei miei relatori: G. Bellettini, A. Scribano, G. Velev (FNAL)- del prof. L. Lyons (Oxford)- del mio tutor a Fermilab G. Chlachidze (FNAL)- del mio collega bielorusso F. Prokoshin (Dubna)- delle discussioni con G. Punzi, F. Bedeschi, G. Latino, A. Annovi, G. Compostella.- delle enormi forze dispiegate dai fisici e dagli ingegneri che negli anni hanno immaginato, studiato, creato e mantenuto sistemi complessi come CDF ed il Tevatron- della posta elettronica (CERN)

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Backup

slides

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“Quark”


"Three quarks for Muster Mark!Sure he hasn't got much of a barkAnd sure any he has it's all beside the mark."

In 1963 Gell Mann named “quarks” the three constituents hidden in the nucleon. He took the name from “The Finnegan’s wake” by James Joyce.

The word “quark” is probably an onomatopeia for the albatros cry.

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B-tagging


B-tagging (SECVTX)The b-hadron lifetime is long enough to allow B hadrons to travel O(mm) before decaying.Their decay originates a secondary vertex within the jet. The main b-tagging CDF SECVTX algorithm relies on this signature.

By mean of suitable algorithms we can attempt to separate b-jets (and c-jets) from u,d,s jets in several ways:SECVTX: finds secondary vertices.JETPROB: gauges the number of tracks missing the primary vertex.SLT: finds a soft lepton inside the jet.OTHERS: NN algorithms exploit many detailed signatures of b-jets.

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Channels


Ogni canale di decadimento ha i suoi pregi e difetti, a seconda della possibilità di triggerare e della quantità di fondi.

DILEPTONFacile trigger (due leptoni), ma difficoltà di ricostruzione (due neutrini, una MET). Per risolvere l’ambiguità si possono studiare le correlazioni con altre variabili cinematiche e pesare le soluzioni.Piccolo fondo: anche senza b-tag, S/B~10; con b-tag anche 50.

SEMILEPTONICTrigger dato da un leptone di high-Pt, almeno 4 jet e MET. Rapporto S/N circa 1 senza b-tag, altrimenti migliore: può arrivare a 20 con 2 b-tag. Golden channel.

ALL HADRONICCanale molto abbondante, ma trigger affidato ai 6 jet che vengono scelti di alta energia. Forte presenza di fondo: S/B~1/8-1/6

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Data/MC Comparison


Confronti data/MCDopo la selezione, si controlla l’accordo di dati e MC confrontando distribuzioni cinematiche, ad esempio:

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Data Selection


Reproduce selectionas from winter06Top Prop Group

x-sec study

Our selection:nosi GRL

JetCorr06b

We reconstruct kinematically

the data events and apply a 2<9 cut

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BKG Ratios


Based on on the 695 pb-1 goodsilicon BG for tagged events, we estimated (note 8430) 219 BG events out of 468 candidates in the pretag sample.

Out of 219 BGs: 141 W+mistags 31 W+H.F. 30 non-W 17 diboson <1 Single Top

Renormalized to 100%

Overall <9 cut efficiency for the combined BG

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Sample Composition


goodsi nosi

695 pb-1 760 pb-

1

goodsi nosi955 pb-1 1030

pb-1

Candidates

Estimated BGs

468 482

219 239

700

347

Candid. 2<9

Est. BG 2<9

446

239*0.882= 211

645

347*0.882= 306

S/N ratio 1.11 1.11

*700/482lum

BG estimation available BG estimation wanted

In order to allow for the overall rate fluctuations, rather than normalizing to the luminosity we normalized the expected background in 1030 pb-1 to the number of candidates actually observed, i.e. 700 candidates. This gives an estimated background of 347 events.

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BKG Estimation


The analysis runs with constrained BG.

To estimate amount and composition of BG in or data we start from the known background in the 695pb-1 tagged sample.

We write the likelihood of tagging Ntag events out of N and to observe a specific BG composition (same as in Run1 -> PRD63 032003). We use the binomial distribution B to model Ntag and Gauss distributions Gi to represent the probability density for the occurrence of signal and BGs:

tagevent is the tag efficiency for tagging a ≥4 jets event. It depends on the BG processes tag efficiencies, the ttbar tag efficiency and on the Top fraction f in the sample.

We maximize this likelihood using MINUIT and we extract f. The number of BG events for each contribution is obtained as well.

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BKG Estimation


The quantity minimized to get the Top fraction f.

The table reports the BG contribution studied and the index used.

The efficiency in tagging an event depends on the Top fraction f.

Number of tagged events.

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Tagged Samples corr. Comb.


MC events nel L+Jquando è possibile associare correttamente i 4 leading jet ai 4 partoni (b, bbar, u, d ad esempio), possiamo anche verificare quale fosse la giusta combinazione. Si può fare solo sul MC perchè in quel caso possiamo risalire alla configurazione partonica.

L’ambiguità combinatoria porta ad un ulteriore fondo nel segnale: il fondo combinatorio.

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Why a second peak in the BKG 1st comb?


In BG non-Top events the most likely best jet combination is frequently found as follows:1) The fitter orders jets by decreasing energy. It first tries to form the W mass (which

is about 81 GeV) by using the two leading jets. 2) Next the fitter forms the Top mass by adding the b-jet. The less energetic jets are

often left to do that. Those jets are often close to the 15 GeV transverse energy cut.

3) The fitter would thus indicate a Top mass close to the W mass plus the energy of such a b-jet, which amounts to about 105-115 GeV as in the peak in question.

4) The second and third combinations would correspond to assignments of higher energy jets as b-jets, and the Top mass would result larger – with a larger chi2 since the W mass is still imposed on the hadronic W by the fitter – and the peak at low mass would smeared.5) As a check of this interpretation we made a test by increasing the 15 GeV jet Pt cut and we observed this peak disappearing.

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Accelerator Energies


Quanta energia serve per produrre una coppia ttbar?

Con un collider del tipo LEP, e+e-, la soglia è circa 360 GeV. LEP, che ha terminato le attività nel 2000, è arrivato a 208 GeV (LEP2) nel CdM.

Con un collider adronico, dove i proiettili sono i partoni, l’energia necessaria (ai protoni accelerati) è di circa 3 volte tanto (ma dipende dalle funzioni di struttura).Il Tevatron è stato il primo collider a porsi nelle condizioni di produrre ttbar.

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Top@LHC


tt(LHC)=825±150 pb(~100 volte Tevatron)

Significa 8 milioni di coppie ttbar all’anno (una al secondo)

a bassa luminosità: LHC sarà una top factory!

LHC avrà una tale produzione di Top da poter usare i suoi decadimenti per calibrare i detectors.Sono previste misure di precisione della massa e di altre quantità, ma il Top potrebbe presto diventare un fondo nelle misure dell’Higgs Boson!

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Syst in other Top Studies


lum pb-1 Generator JES L5 JES L7This study 1030 0.8 2.8 2.53Best 6770 108 0.6 2.4 1.47532 0tag 318 2.7 1.97532 1tagT 318 2.3 2.27532 combined 318 0.3 2.2 2.10tag CDF 7063 194 0.1 2.5 2.2Pretag 6853 194 1.2 3.2 1.9

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Top Studies


• Mass• Cross section• Production mechanism (qq, gg)• W helicity (il W da Top appare longitudinale 70% e left 30%. Studi violazione P.)

• Charge (Il b quark ha carica =-1/3. t->W+b oppure t->W-b ?)• Lifetime• Search for t’• Single Top• Risonanze ttbar

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Other Top Physics


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EndBacku

p slides

La scoperta del Top

CDF ha dimostrato l’ EVIDENZA (3) sperimentale dell’esistenza del Top quark nel 1994 studiando il canale dileptonico (S/B molto favorevole). Lo studio utilizzava il b-tag SVX (SLT) ed evidenziò un numero di candidati di 6(7) con un numero di BG atteso di 2.3±0.3 (3.1±0.3).

La SCOPERTA (5) è stata annunciata da CDF e D0 congiuntamente il 2 marzo 1995.

• CDF Collaboration, Phys.Rev.Lett. 74, 2626 (1995)

• D0 Collaboration, Phys.Rev.Lett. 74, 2632 (1995)

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Top production


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Precision Measurement of the Top Quark Mass at CDF