30
Experience Experience from Searches from Searches at the at the Tevatron Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

Embed Size (px)

Citation preview

Page 1: 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

Page 2: Experience from Searches at the Tevatron 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

PHYSTAT 2011 Harrison B. Prosper 2

Page 3: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

IntroductionIntroduction

PHYSTAT 2011 Harrison B. Prosper 3

Page 4: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 4

Page 5: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

PHYSTAT 2011 Harrison B. Prosper 5

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

Donald Rumsfeld

Page 6: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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.

PHYSTAT 2011 Harrison B. Prosper 6

Page 7: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

CDF & D0CDF & D0

PHYSTAT 2011 Harrison B. Prosper 7

Page 8: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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:

PHYSTAT 2011 Harrison B. Prosper 8

CourtesyCDF

Page 9: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

Particle Physics DataParticle Physics Data

PHYSTAT 2011 Harrison B. Prosper 9

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

Page 10: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

Case StudiesCase Studies

PHYSTAT 2011 Harrison B. Prosper 10

Page 11: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 11

Page 12: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 12

The goal: test the Standard Model prediction

BF =Bs0 → μ+μ−

Bs0 → everything

=(3.6 ±0.3)×10−9

Bs0

Page 13: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 13

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]

Page 14: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 14

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.

Page 15: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

A Search for a Rare DecayA Search for a Rare Decay

PHYSTAT 2011 Harrison B. Prosper 15

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.]

Page 16: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 16

Page 17: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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.

PHYSTAT 2011 Harrison B. Prosper 17

p + p→ t+ X

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

Search for Single TopSearch for Single Top

PHYSTAT 2011 Harrison B. Prosper 18

S/B ~ 1/260

Page 19: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

Search for Single TopSearch for Single Top

PHYSTAT 2011 Harrison B. Prosper 19

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

Page 20: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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)

PHYSTAT 2011 Harrison B. Prosper 20

Page 21: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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.

PHYSTAT 2011 Harrison B. Prosper 21

Page 22: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 22

Page 23: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

Search for BSearch for Bss00 Oscillations Oscillations

PHYSTAT 2011 Harrison B. Prosper 23

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)]

Page 24: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 24

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

Page 25: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 25

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

i=1

M

Page 26: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 26

CDF, PRL 97, 242003 (2006)

Page 27: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

Search for the HiggsSearch for the Higgs

PHYSTAT 2011 Harrison B. Prosper 27

Page 28: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

Search for the HiggsSearch for the Higgs

PHYSTAT 2011 Harrison B. Prosper 28

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)

Page 29: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

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

PHYSTAT 2011 Harrison B. Prosper 29

B01=

Poisson(N |b)π(b)db0

∫Poisson(N |s+b)π(b)π(s)dbds

0

∫0

Page 30: Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

ConclusionsConclusions

PHYSTAT 2011 Harrison B. Prosper 30

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!