Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN.

Experience from Experience from Searches Searches

at the at the TevatronTevatron

Harrison B. Prosper

Florida State University

18 January, 2011

PHYSTAT 2011

CERN

OutlineOutline

h Introduction

h Case Studies

h Search for a rare decay (D0)

h Search for single top (D0)

h Search for Bs0 oscillations (CDF)

h Search for the Higgs (CDF/D0)

h Conclusions

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IntroductionIntroduction

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The Tevatron (1991 – 2011)The Tevatron (1991 – 2011)

Goals:

1. To test the Standard Model (SM)

2. To find hints of new physics

A few key SM predictions:

h jet spectra ✓h existence of top quark ✓h creation of top quarks singly ✓h creation of di-bosons (WW/ZZ/WZ/Wγ/Zγ) ✓h properties of B mesons ✓h existence of Higgs

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“There are known knowns… There are known unknowns… But there are also unknown unknowns.”

Donald Rumsfeld

The Standard Model in ActionThe Standard Model in Action

The observed transverse

momentum spectrum

of jets agrees with

SM predictions over

10 orders of magnitude

This illustrates why we

take our null hypothesis,

the Standard Model,

seriously.

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CDF & D0CDF & D0

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Particle Physics DataParticle Physics Data

Each collision event yields ~ 1MB of data. However, these data are compressed by a factor of ~103 – 104 during

event reconstruction:

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CourtesyCDF

Particle Physics DataParticle Physics Data

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CDF (24 September 1992)proton + anti-proton

3 positron (e+)2 neutrino (ν)3 Jet13 Jet23 Jet33 Jet4

A total of 17 measurements,after event reconstruction

Case StudiesCase Studies

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Search for a Rare Decay (D0)Search for a Rare Decay (D0)

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Search for a Rare Decay (D0)Search for a Rare Decay (D0)

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The goal: test the Standard Model prediction

BF =Bs0 → μ+μ−

Bs0 → everything

=(3.6 ±0.3)×10−9

Bs0

Search for a Rare Decay (D0)Search for a Rare Decay (D0)

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Compress data to the unitinterval using a Bayesian neural network

β = BNN(Data)

Cuts1. β > 0.92. 5.0 ≤ mμμ ≤ 5.8 GeV

define the signal region

Phys.Lett. B693 (2010) 539-544 e-Print: arXiv:1006.3469 [hep-ex]

Search for a Rare Decay (D0)Search for a Rare Decay (D0)

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D0 results (6.1 fb-1) observed backgroundRunIIa na = 256 Ba = 264 ± 13 eventRunIIb nb = 823 Bb = 827 ± 23 events

The likelihood for these data is the 2-count model

p(n|s, μ) = Poisson(na|sa+ μa) Poisson(nb|sb + μb)

where the s and μ are the expected signal and background counts, respectively. The evidence-based prior for the backgrounds istaken to be the product of two normal distributions.

A Search for a Rare DecayA Search for a Rare Decay

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For D0, the branching fraction (BF) is related to be the signals as follows

BF = (4.90 ± 1.00) × 10-9 × sa (RunIIa)

BF = (1.84 ± 0.36) × 10-9 × sb (RunIIb)

The limit BF < 5.1 x 10-8 @ 95% C.L. is derived using CLs, based on the statistic x = log[p(n|BF) / p(n|0)], where p(n|BF) is the likelihood marginalized over all nuisance parameters.

[Recap CLs (Luc’s talk): define p1(BF) = P[x < x0| H1(BF)], reject all BF for which p1(BF) < γ p1(0), and define a (1 – γ) C.L. upper limit as the smallest rejected value of BF.]

Search for Single Top (D0)Search for Single Top (D0)

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Search for Single TopSearch for Single Top

The goal: test the Standard Model prediction that the process

exists and has a total cross section of 3.46 ± 0.18 pb (assuming a top quark mass of mtop=170 GeV).

This corresponds to a production rate of ~ 1 in 1010 collisions.

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p + p→ t+ X

Search for Single TopSearch for Single Top

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S/B ~ 1/260

Search for Single TopSearch for Single Top

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The data are reduced to

M counts described by the

likelihood

where σ (the cross section)

is the parameter of interest

and the εi and μi are nuisance

parameters.

p(n |σ,ε,μ)

= Poisson(ni |ε iσ + μi )i=1

M

∏

Search for Single TopSearch for Single Top

D0 (and CDF) compute the posterior p(σ | n) assuming:

1. a flat prior for π(σ)

2. an evidence-based prior for π(ε, μ)

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Search for Single TopSearch for Single Top

Estimate of “signal significance” using a p-value:

p0 = P[t > t0| H0]

The statistic t is the mode of the the posterior density.

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Search for BSearch for Bss00 Oscillations (CDF) Oscillations (CDF)

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Search for BSearch for Bss00 Oscillations Oscillations

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The goal: test the Standard Model prediction that the oscillation process

exists and is governed by the time-dependent probabilities

with A = 1

Bs0 ↔ Bs

0

Nino T. Leonardo (PhD Dissertation, MIT, 2006)

pBs

0 → Bs0 (t |A,Δm) =

12τ

e−t/τ [1−Acos(Δmt)]

pBs0→ Bs

0 (t |A,Δm) =12τ

e−t/τ [1+ Acos(Δmt)]

There are (at least) two complications:

1. the time of decay t of a B particle is measured with some uncertainty

2. there is background

The probability model is therefore a convolution of a signal plus

background mixture and a resolution function.

The latter is modeled as

a normal with a

variance σ2 that

depends on t.

Search for BSearch for Bss00 Oscillations Oscillations

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Nino T. Leonardo (PhD Dissertation, MIT, 2006)

The likelihood is a product of these functions, one for each measured decay time:

Finding the amplitude A.

For a given oscillation frequency, Δm, a maximum likelihood fit is performed for the amplitude.

It is found that at Δm = 17.8/ps, A = 1.21 ± 0.20, which is consistent with A = 1 and inconsistent with A = 0.

Search for BSearch for Bss00 Oscillations Oscillations

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p(t | A,Δm) ~ N(ti | ′t ,σ i2 )⊗[αP( ′t ) + (1−α)B( ′t )]

i=1

M

∏

Estimating the “signal significance”.

This is done using the likelihood ratio test statistic

Λ = log[p(t | A=0) / p(t | A=1, Δm)],

The significance is

defined to be the

p-value:

p0 = P[Λ < Λ0| H0]

= 8 x 10-8

Search for BSearch for Bss00 Oscillations Oscillations

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CDF, PRL 97, 242003 (2006)

Search for the HiggsSearch for the Higgs

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Search for the HiggsSearch for the Higgs

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Here is all available evidence about the Higgs:

π(s) ≡π(s|H1) = p(s|m,H1)p(m|

100

200

∫ H1)dm p(s | m, H

1) p(m | H

1)

Given the evidence-based prior, π(s), that encodes what we know about the Higgs from the Tevatron and LEP, we could test the Higgs hypothesis with current LHC data by computing a Bayes factor (see Jim Berger’s talk):

or by computing the expected loss (d(N)) (see José Bernardo’s talk)

…just a thought!

Higgs @ CERNHiggs @ CERN

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B01=

Poisson(N |b)π(b)db0

∞

∫Poisson(N |s+b)π(b)π(s)dbds

0

∞

∫0

∞

∫

ConclusionsConclusions

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h Discoveries can be had, in spite of our eclectic, and sometimes muddled, approach to statistics.

h “We” remain ferociously fond of exact frequentist coverage.

h p-values remain king! But Bayes is tolerated.

h CLs still lives…alas!

h Physicists can be taught!