[PPT] - Global Fits to MSSM Models by Ben Allanach (University of PowerPoint Presentation

SLIDE 1

Global Fits to MSSM Models

by

Ben Allanach (University of Cambridge)

Talk outlinea

LHC SUSY Searches
SUSY fits to Indirect Data
Effect of Searches

Please ask questions while I’m talking

aBCA, arXiv:1102.3149;

BCA, Khoo, Lester, Williams, arXiv:1103.0969

Global Fits to MSSM Models B.C. Allanach – p. 1

SLIDE 2

Supersymmetric Copies

H

Global Fits to MSSM Models B.C. Allanach – p. 2

SLIDE 3

Supersymmetric Copies

H × 2 ˜ H × 2

Global Fits to MSSM Models B.C. Allanach – p. 2

SLIDE 4

Electroweak Breaking

Both Higgs get vacuum expectation values: H0

1

H−

1

→

v1

H+

2

H0

2

→

v2

and to get MW correct, match with vSM = 246 GeV:

v1 v2 β vSM tan β = v2

v1

L = ht¯ tLH0

2tR + hb¯

bLH0

1bR + hτ ¯

τLH0

1τR

⇒ mt sin β = htvSM √ 2 , mb,τ cos β = hb,τvSM √ 2 .

Global Fits to MSSM Models B.C. Allanach – p. 3

SLIDE 5

CMS αT Search

CMS: jets and missing energy arXiv:1101.1628 L = 35 pb−1. HT = Njet

i=1 |pji T| > 350 GeV.

∆HT ≡

ji∈A

|pji

T| −

ji∈B

|pji

T|.

(1) One then calculates αT = HT − ∆HT 2

H2

T − H

/2

T

> 0.55 (2) where H /T =

(Njet

i=1 pji x )2 + (Njet i=1 pji y )2.

Global Fits to MSSM Models B.C. Allanach – p. 4

SLIDE 6

Results

Global Fits to MSSM Models B.C. Allanach – p. 5

SLIDE 7

ATLAS 0-lepton, jets and / pT

meff = p(j)

T + p

/T, m(i)

T 2(pT (i), /

qT

(i)) ≡ 2

pT (i)

/ qT

(i)

− 2pT (i) · / qT

(i)

where / qT

(i) is the transverse momentum of particle

(i). For each event, it is a lower bound on m(NLSP). MT2(pT

(1), pT (2), /

pT) ≡ min

/ qT =/ pT

max
m(1)

T , m(2) T

Global Fits to MSSM Models

B.C. Allanach – p. 6

SLIDE 8

Candidate Event: High ET(j)

Global Fits to MSSM Models B.C. Allanach – p. 7

SLIDE 9

MSSM Exclusion: Simplified Model

gluino mass [GeV]

250 500 750 1000 1250 1500 1750 2000

squark mass [GeV]

250 500 750 1000 1250 1500 1750 2000

= 10 pb

SUSY

σ = 1 pb

SUSY

σ = 0.1 pb

SUSY

σ )

1

χ ∼ Squark-gluino-neutralino model (massless =7 TeV s ,

1

= 35 pb

int

L 0 lepton combined exclusion

ATLAS

0 lepton combined exclusion q ~ LEP 2 FNAL MSUGRA/CMSSM, Run I D0 MSUGRA/CMSSM, Run II CDF MSUGRA/CMSSM, Run II Observed 95% CL limit Median expected limit σ 1 ± Expected limit

Global Fits to MSSM Models B.C. Allanach – p. 7

SLIDE 10

SUSY Dark Matter

astro-ph/0608407

χ0

1

χ0

1

p p′ σ

Global Fits to MSSM Models B.C. Allanach – p. 8

SLIDE 11

SUSY Prediction of Ωh2

Assume relic in thermal equilibrium with

neq ∝ (MT)3/2exp(−M/T).

Freeze-out with Tf ∼ Mf/25 once interaction

rate < expansion rate (teq critical)

microMEGAs uses calcHEP to automatically

calculate relevant Feynman diagrams for some given model Lagrangian: flexible.

darkSUSY, IsaRED has MSSM annihilation

channels hard-coded.

Both darkSUSY and micrOMEGAs calculate

(in-)direct predictions.

Global Fits to MSSM Models B.C. Allanach – p. 9

SLIDE 12

WMAP+BAO+Ia Fits

Global Fits to MSSM Models B.C. Allanach – p. 10

SLIDE 13

WMAP+BAO+Ia Fits

ΩDMh2 = 0.1143 ± 0.0034 Power law ΛCDM fit

Global Fits to MSSM Models B.C. Allanach – p. 10

SLIDE 14

Universality

Reduces number of SUSY breaking parameters from 100 to 3:

tan β ≡ v2/v1
m0, the common scalar mass (flavour).
M1/2, the common gaugino mass (GUT/string).
A0, the common trilinear coupling (flavour).

These conditions should be imposed at MX ∼ O(1016−18) GeV and receive radiative corrections ∝ 1/(16π2) ln(MX/MZ). Also, Higgs potential parameter sgn(µ)=±1.

Global Fits to MSSM Models B.C. Allanach – p. 11

SLIDE 15

Implementation

We use

95% C.L. direct search constraints
ΩDMh2 = 0.1143 ± 0.02 Boudjema et al
δ(g − 2)µ/2 = (29.5 ± 8.8) × 10−10 Stöckinger et al
B−physics observables including

BR[b → sγ]Eγ>1.6 GeV = (3.52 ± 0.38) × 10−4

Electroweak data W Hollik, A Weber et al

2 ln L = −

i

χ2

i + c =

i

(pi − ei)2 σ2

i

+ c

Global Fits to MSSM Models B.C. Allanach – p. 12

SLIDE 16

Additional observables

δ(g − 2)µ 2 ∼ 13 × 10−10 100 GeV MSUSY 2 tan β µ µ γ ˜ ν χ±

i

µ µ γ χ0

1

˜ µ BR[b → sγ] ∝ tan β(MW/MSUSY )2 b s γ ˜ ti χ±

i

b s γ t H±

Global Fits to MSSM Models B.C. Allanach – p. 13

SLIDE 17

mSUGRA Global Fits

There are 3 methodologies of doing these type of global fits:

Markov Chain Monte Carlo: BCA et al; Ruiz de

Austri et al: primary interpretation is Bayesian.

MultiNest: Ruiz de Austri et al: Bayesian

interpretation only.

Minimising χ2/Profile likelihood: Buchmueller

et al. Impressive array of electroweak

bservables. Moving to a hybrid approach.

Frequentist interpretation only.

Global Fits to MSSM Models B.C. Allanach – p. 14

SLIDE 18

Application of Bayes’

L ≡ p(d|m, H) is pdf of reproducing data d assuming pMSSM hypothesis H and model parameters m p(m|d, H) = p(d|m, H)p(m, H) p(d, H) p(m|d, H) is called the posterior pdf. We will compare p(m, H) = c with a different prior. p(m0, M1/2|d, H) =

do p(m0, M1/2, o|d, H)

Called marginalisation.

Global Fits to MSSM Models B.C. Allanach – p. 15

SLIDE 19

Log Fits

0.2 0.4 0.6 0.8 1

B.C. Allanach, Feb 2011

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 m1/2 (TeV) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 m0 (TeV) 0.2 0.4 0.6 0.8 1

B.C. Allanach, Feb 2011

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m1/2/TeV 10 20 30 40 50 60 tanβ

Choose priors on SM parameters set from data. Priors

n SUSY parameters up to 4 TeV: flat in tan β, A0,

ln(m0), ln(m1/2).

Global Fits to MSSM Models B.C. Allanach – p. 16

SLIDE 20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) P/P(max) 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4 0.2 0.4 0.6 0.8 1 P/P(max) 0.5 1 1.5 2 M1/2 (TeV) 0.5 1 1.5 2 2.5 3 3.5 4 m0 (TeV)

flat tan β flat µ, B

BCA, Cranmer, Weber, Lester, arXiv:0705.0487 http://users.hepforge.org/˜allanach/benchmarks/kismet.html

200 400 600 800 1000 1200 1400 1600 1800 2000 375 750 1125 1500

m1/2 (GeV) m0 ( GeV)

L = 1 fb-1 10 fb-1 100 fb-1 300 fb-1

g

~

( 1 ) g

~

( 1 5 ) g

~

( 2 ) g

~

( 2 5 ) g

~

( 3 ) q

~(2500)

q

~(2000)

q

~(1500)

q

~(1000)

Mh limit b → s γ limit Charged LSP

CMS

tan β = 35

Killer Inference for Susy METeorology

BCA, Cranmer, Weber, Lester, arXiv:0705.0487

Global Fits to MSSM Models B.C. Allanach – p. 17

SLIDE 21

200 400 600 800 1000 1200 1400 1600 1800 2000 375 750 1125 1500

m1/2 (GeV) m0 ( GeV)

L = 1 fb-1 10 fb-1 100 fb-1 300 fb-1

g

~

( 1 ) g

~

( 1 5 ) g

~

( 2 ) g

~

( 2 5 ) g

~

( 3 ) q

~(2500)

q

~(2000)

q

~(1500)

q

~(1000)

Mh limit b → s γ limit Charged LSP

CMS

tan β = 35

Killer Inference for Susy METeorology

BCA, Cranmer, Weber, Lester, arXiv:0705.0487

Bayesian 1 Bayesian 2

Global Fits to MSSM Models B.C. Allanach – p. 18

SLIDE 22

Collider SUSY Dark Matter Production

Strong sparticle production and decay to dark matter particles.

q q q,g χ0

1

χ0

1

p Interaction q q

7 TeV 7 TeV

q,g q q ~ ~ q q p

Any (light enough) dark matter candidate that couples to hadrons can be produced at the LHC

Global Fits to MSSM Models B.C. Allanach – p. 19

SLIDE 23

Validation of CMS Analysis

Used SOFTSUSY3.1.7, Herwig++-2.4.2 and fastjet-2.4.2 to simulate 10000 signal events αT distributions with HT > 350 GeV: αT distributions for SUSY point LM0 m0 = 200, m1/2 = 160, A0 = −400, tan β = 10 by my simulation (solid) and CMS’ (dashed).

Global Fits to MSSM Models B.C. Allanach – p. 20

SLIDE 24

CMS Validation II

tan β = 3 tan β = 30

∆χ2 approx tan β, A0 independent ⇒ interpolate it across m0 and m1/2, then re-weight fit with ∆χ2.

Global Fits to MSSM Models B.C. Allanach – p. 21

SLIDE 25

CMS Weighted Fits

0.2 0.4 0.6 0.8 1

B.C. Allanach, Feb 2011

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 m1/2 (TeV) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 m0 (TeV) 0.2 0.4 0.6 0.8 1

B.C. Allanach, Feb 2011

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 m1/2 (TeV) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 m0 (TeV)

Global Fits to MSSM Models B.C. Allanach – p. 22

SLIDE 26

Validation of ATLAS Analysis

Information Σ(i) = (n(i)

s , n(i) b , σ(i) s , σ(i) b ), expected

number of events past cuts λ( Σ(i), δs, δb) = n(i)

s (1 + δs · σ(i) s ) + n(i) b (1 + δb · σ(i) b ),

[GeV] m

200 400 600 800 1000

[GeV]

1/2

m

150 200 250 300 350 400

>0. µ = 0, = 3, A β MSUGRA/CMSSM: tan =7 TeV s ,

1

= 35 pb

int

L > 1000 GeV

eff

0 lepton 3j m

ATLAS

1 6 . 1 1 8 1 7 . 8 8 . 8 5 9 . 6 5 3 . 5 2 5 . 6 6 5 . 5 9 4 . 5 1 4 . 8 8 1 6 . 3 1 6 . 6 1 9 . 9 1 4 . 6 1 1 . 1 7 . 2 8 1 . 8 8 . 2 4 7 . 5 3 . 8 8 5 . 5 6 4 . 2 4 4 . 6 4 4 . 7 3 . 3 1 3 . 5 7 2 . 5 2 . 2 1 2 1 . 3 2 . 7 2 3 1 5 . 5 1 3 . 3 1 . 6 8 . 6 3 6 . 2 6 4 . 7 6 5 . 6 7 2 2 . 3 1 9 . 7 2 2 . 4 1 5 . 4 1 2 . 5 1 2 1 . 3 7 . 1 8 6 . 6 2 5 . 7 2 4 . 8 3 3 . 9 9 3 . 7 5 2 . 9 7 2 . 6 9 2 . 2 2 1 . 6 5 1 . 5 7 1 9 . 1 2 . 4 1 9 . 9 1 8 . 9 1 6 1 3 . 3 1 7 . 9 2 7 . 8 8 6 . 6 9 1 9 . 7 2 3 2 4 . 7 1 9 . 4 1 6 . 2 1 4 1 2 . 7 9 . 7 8 6 . 5 6 7 . 3 1 4 . 8 8 4 . 5 3 . 4 9 3 . 4 2 . 5 3 1 . 8 7 1 . 5 2 1 . 2 5 2 . 1 1 7 . 8 2 1 . 7 2 . 2 1 5 . 7 1 2 . 2 1 1 . 4 9 . 4 9 7 . 9 4 5 . 9 9 1 6 . 6 2 . 1 1 8 . 7 1 6 . 6 1 4 . 8 1 3 . 2 1 1 . 3 8 . 8 7 . 5 6 . 1 9 4 . 5 7 3 . 5 3 2 . 7 9 2 . 2 1 . 8 7 1 . 3 5 1 . 5 . 8 1 5 1 3 . 1 1 3 . 4 9 . 3 6 7 . 2 9 5 . 6 3 3 . 7 9 2 . 7 2 2 . 7 1 . 5 9 1 . 3 5 1 . 5 . 8 7 8 . 6 3 1 9 . 4 7 1 . 1 8 . 3 6 . 6 4 . 5 3 . 1 5 2 . 2 2 1 . 5 8 1 . 2 9 . 9 6 5 . 7 7 . 5 9 9 . 4 7 2 7 . 5 5 7 . 4 5 6 . 3 4 . 3 7 3 . 4 3 2 . 3 2 1 . 4 6 1 . 2 3 1 . 3 . 8 2 2 . 6 4 . 4 5 1 . 4 5 5 . 3 4 4 . 8 7 4 . 5 6 3 . 5 5 2 . 7 8 1 . 8 5 1 . 1 7 . 8 9 7 . 7 5 2 . 5 8 5 . 4 8 6 . 3 8 1 . 2 8 9 3 . 3 6 3 . 5 9 3 . 1 2 . 2 7 1 . 7 1

> 1000 GeV

eff

0 lepton 3j m Observed 95% CL limit Median expected limit

Global Fits to MSSM Models B.C. Allanach – p. 23

SLIDE 27

Validation of ATLAS Analysis II

For Poisson distribution p, Psys(n(i)

, δs, δb|

Σ(i)) = 1 N(i)p

n(i)
|λ
e− 1

2(δ2 b+δ2 s),

Pm(n(i)

|

Σ(i)) =

dδs
dδb Psys(n(i)
, δs, δb).

Global Fits to MSSM Models B.C. Allanach – p. 24

SLIDE 28

Validation of ATLAS Analysis III

Found σC = 0.6, σD = 0.3 provide a reasonably good fit - by hand. n = (n(C)

, n(D)
),

λ = (λC, λD) P( n| λ) = p(n(D)

|λD) p(n(D)
− n(C)
|λC − λD).

(3)

Global Fits to MSSM Models B.C. Allanach – p. 25

SLIDE 29

ATLAS Weighted Fits

Allanach, Khoo, Lester and Williams Mar, 2011

0.2 0.4 0.6 0.8 m1/2 (TeV) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 m0 (TeV) 0.2 0.4 0.6 0.8 1

Allanach, Khoo, Lester and Williams Mar, 2011

0.2 0.4 0.6 0.8 m1/2 (TeV) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 m0 (TeV) 0.2 0.4 0.6 0.8 1

Again, we assume A0-tan β independence and interpolate across m0 and m1/2.

Global Fits to MSSM Models B.C. Allanach – p. 26

SLIDE 30

CMS/ATLAS Weighted Fits

0.02 0.04 0.06 0.08 0.1 0.12 500 1000 1500 2000 2500 3000 mqL/GeV

Allanach, Khoo, Lester and Williams, Mar 2011

Incl. ATLAS
Excl. CMS/ATLAS
Incl. CMS

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 500 1000 1500 2000 mg/GeV

Allanach, Khoo, Lester and Williams, Mar 2011

Incl. ATLAS
Excl. ATLAS
Incl. CMS

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 100 200 300 400 500 mχ1

0/GeV

Allanach, Khoo, Lester and Williams, Mar 2011

Incl. ATLAS
Excl. ATLAS
Incl. CMS

0.02 0.04 0.06 0.08 0.1 0.12 0.14 200 400 600 800 1000 meR/GeV

Allanach, Khoo, Lester and Williams, Mar 2011

Incl. ATLAS
Excl. ATLAS
Incl. CMS

Global Fits to MSSM Models B.C. Allanach – p. 27

SLIDE 31

Prospects for SUSY

Look good! 5fb−1 expected over the next couple of years

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

6
4
2

2 4 6 log10(σSUSY/pb)

Allanach, Khoo, Lester and Williams, Mar 2011

Incl. ATLAS
Excl. ATLAS
Incl. CMS

Global Fits to MSSM Models B.C. Allanach – p. 28

SLIDE 32

Summary

LHC analyses providing a nice amount of

information for interpretation of data. There’s always room for improvement...

Validation step very important for us when we’re

interpreting experiments’ results.

CMSSM could well be discovered this year
Current searches reach squark and gluino masses
f 775 GeV. This will be extended to 1000 GeV,

covering much of the good-fit region.

Global Fits to MSSM Models B.C. Allanach – p. 29

SLIDE 33

Other work

Shortly after my first, the Mastercode

collaborationa performed fits of CMSSM, NUHM, VCMSSM, mSUGRA to CMS and ATLAS 1l data based on an informed guess of the likelihood function, fitted to the exclusion

contours. Validated against one point. CMSSM

results very similar to our analysis.

More recently Akula et alb examined ATLAS 0

and 1-lepton analyses at varying A0, tan β in a scan, showing where the indirect constraints apply.

aarXiv://1102.4585 barXiv://1103.1197

Global Fits to MSSM Models B.C. Allanach – p. 30

SLIDE 34

Log Fits

0.2 0.4 0.6 0.8 1

Allanach, Khoo, Lester and Williams Mar, 2011

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m1/2/TeV 10 20 30 40 50 60 tanβ 0.2 0.4 0.6 0.8 1

Allanach, Khoo, Lester and Williams Mar, 2011

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m1/2/TeV 10 20 30 40 50 60 tanβ

Before (left) and after (right) ATLAS 0-lepton exclusion limits.

Global Fits to MSSM Models B.C. Allanach – p. 31

SLIDE 35

Supplementary Material

Global Fits to MSSM Models B.C. Allanach – p. 32

SLIDE 36

Checking A0-tan β Indepen- dence

Choose samplings from the global fit at random and perform simulation on them. Then compare with m0 − m1/2 interpolation at tan β = 3 and find how good the approximation is.

Global Fits to MSSM Models B.C. Allanach – p. 33

SLIDE 37

Markov-Chain Monte Carlo

Metropolis-Hastings Markov chain sampling consists

f list of parameter points x(t) and associated

posterior probabilities p(t). x(t), p(t) x(t+1), p(t+1) r

p(r) r σ

P =min(p(t+1)/p(t), 1) Final density of x points ∝ p. Required number of points goes linearly with number of dimensions.

Global Fits to MSSM Models B.C. Allanach – p. 34

SLIDE 38

Ice Cube

Neutralinos can become trapped in the sun ˜ h0 − Z coupling σχ0p,SD ∝ [|N1d|2 − |N1u|2]2 dominates. A⊙ ≡ σv/V : ˙ N = C⊙ − A⊙N2, Γ = 1 2A⊙N2 = 1 2 C⊙ tanh2 √ C⊙A⊙ t⊙

dNνµ

dEνµ = C⊙FEq 4πD2

ES

dNν dEν Inj Nev ≈ dNνµ dEνµ dσν dy Rµ((1 − y) Eν) Aeff dEνµ dy

Global Fits to MSSM Models B.C. Allanach – p. 35

SLIDE 39

Naturalness priors

0.5 1 1.5 2 2.5 3 3.5 log10(prior) 0.5 1 1.5 2 2.5 3 3.5 4 m0 (TeV) 10 20 30 40 50 60 tanβ

Global Fits to MSSM Models B.C. Allanach – p. 36

SLIDE 40

Potential Problem

Often, people use a flat Q(x). The trouble with this “blind drunk” sampling is the following situation: Either large or small proposal widths σ lead to low efficiencies of sampling. Our proposal is to determine a Q(x) closer to P(x) semi-automatically.

Global Fits to MSSM Models B.C. Allanach – p. 37

SLIDE 41

Bank Sampling

Figure 1: Bank points determined from previous runs: want to have at least one point in each maximum. Knowledgeable drunk

Global Fits to MSSM Models B.C. Allanach – p. 38

SLIDE 42

Proposal Distribution

Qbank(x; x(t)) = (1−λ)K(x; x(t))+λ

N

i=1

wiK(x; y(i)) wi are a set of N weights: N

i=1 wi = 1, 0 < λ < 1,

while K is the proposal distribution. With probability (1 − λ) propose a local Metropolis step of the usual kind, i.e. “close” to the last point in the chain. With probability λ, teleport to the vicinity

f one of the number of “banked” points, chosen with

weight wi from within the bank.

Global Fits to MSSM Models B.C. Allanach – p. 39

SLIDE 43

Example Distribution

f2D(x) = circ(x; c1, r1, w1) + circ(x; c2, r2, w2) where c1 = (−2, 0), r1 = 1, w1 = 0.1, c2(+4, 0), r2 = 2, w2 = 0.1 and circ(x; c, r, w) = 1 √ 2πw2 exp

−(|x − c| − r)2

2w2

.

2.5 2.5 5 x 2 2 y 1 2 3 4 5 f2 D 2.5 2.5 5 x 1 2

Global Fits to MSSM Models B.C. Allanach – p. 40

SLIDE 44

Bank vs Metropolis

10 000 samples for MCMC and bank sampling:

x

4
2

2 4 6 8 y

6
4
2

2 4 6 x

4
2

2 4 6 8 y

6
4
2

2 4 6 Global Fits to MSSM Models B.C. Allanach – p. 41

SLIDE 45

Safety with respect to λ

10 bank samplers, with 10 bank points generated in each circle: 10 000

samples. All started from x = −2. Correct x = 2. λ ≈ 1 is

importance sampling limit.

) λ (

10

log

6
5
4
3
2
1

<x>

3
2
1

1 2 3 x

4
2

2 4 6 8 y

6
4
2

2 4 6

Q: What values of λ are “safe”? A: [0.001, 0.9]

Global Fits to MSSM Models B.C. Allanach – p. 42

SLIDE 46

LHC Cross-sections

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

6
4
2

2 4 6 log10σ/fb strong weak gaugino slepton 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log10(σstrong/fb) log10(σweak/fb) P/P(max)

6 -4 -2 0

2 4 6 8 10 0.5 1 1.5 2 2.5 3 3.5 4 4.5

(a) (b)

0.2 0.4 0.6 0.8 1 log10(σstrong/fb) log10(σslepton/fb) P/P(max)

6 -4 -2 0

2 4 6 8 10

10
8
6
4
2

2 4 0.2 0.4 0.6 0.8 1 log10(σweak/fb) log10(σslepton/fb) P/P(max) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

10
8
6
4
2

2 4

(c) (d)

Global Fits to MSSM Models B.C. Allanach – p. 43

SLIDE 47

Collider Check

Need corroboration with direct detection. If we can pin particle physics down, a comparison between the predicted relic density and that observed is a test of the cosmological assumptions used in the prediction.a Thus, if it doesn’t fit, you change the cosmology until it does.

aBCA, G. Belanger, F. Boudjema, A. Pukhov, JHEP 0412 (2004)

020.; M. Nojiri, D. Tovey, JHEP 0603 (2006) 063

Global Fits to MSSM Models B.C. Allanach – p. 44

SLIDE 48

CMSSM Regions

After WMAP+LEP2, bulk region diminished. Need specific mechanism to reduce overabundance:

˜

τ coannihilation: small m0, m˜

τ1 ≈ mχ0

1.

Boltzmann factor exp(−∆M/Tf) controls ratio

f species. ˜

τ1χ0

1 → τγ, ˜

τ1˜ τ1 → τ ¯ τ.

Higgs Funnel: χ0

1χ0 1 → A → b¯

b/τ ¯ τ at large tan β. Also viaa h at large m0 small M1/2.

Focus region: Higgsino LSP at large m0:

χ0

1χ0 1 → WW/ZZ/Zh/t¯

t.

˜

t coannihilation: high −A0, m˜

t1 ≈ mχ0

1.

˜ t1χ0

1 → gt, ˜

t˜ t → tt

aDatta, Djouadi, Drees, hep-ph/0504090

Global Fits to MSSM Models B.C. Allanach – p. 45

SLIDE 49

Comparison

LHS: allowing non thermal-χ0

1 contribution

RHS: only χ0

1 dark matter

(flat priors)

Global Fits to MSSM Models B.C. Allanach – p. 46

SLIDE 50

Annihilation Mechanism

Define stau co-annihilation when m˜

τ is within 10% of

mχ0

1 and Higgs pole when mh,A is within 10% of

2mχ0

1.

mechanism flat prior natural prior h0−pole 0.025 0.07 A0−pole 0.41 0.14 ˜ τ−co-annihilation 0.26 0.18 rest 0.31 0.61 b, τ ¯ b, ¯ τ χ0

1

χ0

1

h0, A0 ˜ τ χ0

1

τ γ τ

Global Fits to MSSM Models B.C. Allanach – p. 47

SLIDE 51

Comparison

200 400 600 800 1000

m1/2 [GeV]

3000
2500
2000
1500
1000
500

500 1000 1500 2000 2500 3000

A0 [GeV]

CMSSM, µ > 0, tanβ = 10 ∆χ

2, 90% CL

∆χ

2, 68% CL

best fit

0.2 0.4 0.6 0.8 1 M1/2 (TeV) A0 (TeV) P/P(max) 0.2 0.4 0.6 0.8 1

3
2
1

1 2 3

J Ellis et al

Fix tan β = 10 and all SM inputs
Restrict m0, M1/2 < 1 TeV.
Same fits!

Global Fits to MSSM Models B.C. Allanach – p. 48

SLIDE 52

No Dark Matter Fits

0.02 0.04 0.06 0.08 0.1 0.12 0.14 20 40 60 80 100 120 140 P per bin ΩDMh2 µ>0 µ<0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) P/P(max) 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

Huge χ2 from the dark matter relic density.

Global Fits to MSSM Models B.C. Allanach – p. 49

SLIDE 53

Volume Effects

Can’t rely on a good χ2 in non-Gaussian situation ρ x

Global Fits to MSSM Models B.C. Allanach – p. 50

SLIDE 54

Likelihood and Posterior

Q: What’s the chance of observing someone to be pregnant, given that they are female? Likelihood p(pregnant | female, human) = 0.01 Posterior p(female | pregnant, human) = 1.00

Global Fits to MSSM Models B.C. Allanach – p. 51

SLIDE 55

Sanity Check

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mh (GeV) mχ1

0 (TeV)

L/L(max) 80 90 100 110 120 130 140 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mA (TeV) mχ1

0 (TeV)

L/L(max) 0.5 1 1.5 2 2.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mτ (TeV) mχ1

0 (TeV)

L/L(max) 0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.01 0.02 0.03 0.04 0.05 0.06 0.5 1 1.5 2 2.5 3 3.5 4 L per bin m (TeV) RH slepton gluino LH squark light stop Global Fits to MSSM Models B.C. Allanach – p. 52

SLIDE 56

LHC vs LC in SUSY Measure- ment

LHC (start date 2007) produces strongly

interacting particles up to a few TeV. Precision measurements of mass differences possible if the decay chains exist: possibly per mille for leptons, several percent for jets.

ILC has several energy options: 500-1000 GeV,

CLIC up to 3 TeV. Linear colliders produce less strong particles but much easier to make precision measurements of masses/couplings. Q: What energy for LC? Q: What do we get from LHCa?

aLHC/ILC Working Group Report: hep-ph/0410364

Global Fits to MSSM Models B.C. Allanach – p. 53

SLIDE 57

Convergence

We run 9×1 000 000 points. By comparing the 9 independent chains with random starting points, we can provide a statistical measure of convergence: an upper bound r on the excepted variance decrease for infinite statistics.

1 1.2 1.4 1.6 1.8 2 10 20 30 40 50 60 70 80 90 100 r step/10000 upper bound

Global Fits to MSSM Models B.C. Allanach – p. 54

SLIDE 58

LHC SUSY Measurements

˜ b2 ˜ g χ0

2

˜ l χ0

1

b b l+ l−

100 200 300 400 50 100 150

205.7 / 197 P1 2209. P2 108.7 P3 1.291

Mll (GeV) Events/0.5 GeV/100 fb-1

m2

ll = (m2

χ0 2

−m2

˜ l )(m2 ˜ l −m2 χ0 1

) m2

˜ l

Q: Can we measure enough of these to pin SUSYa down?

aBCA, Lester, Parker, Webber, JHEP 0009 (2000) 004

Global Fits to MSSM Models B.C. Allanach – p. 55

SLIDE 59

Predicting Ωh2

Not much left that’s allowed but edge measurements allow reasonable Ωh2 errora for 300 fb−1.

20 40 60 0.05 0.1 0.15 0.2

59.34 / 54 Constant 38.39 Mean 0.1046 Sigma 0.1966E-01

Ωh2 Experiments/bin

Q: What about other bits of parameter space?

aM Nojiri,

G Polesello, D Tovey, JHEP 0603 (2006) 063, hep-ph/0512204.

Global Fits to MSSM Models B.C. Allanach – p. 56

SLIDE 60

Bulk Region

M Nojiri, G Polesello, D Tovey, JHEP 0603 (2006) 063, hep-ph/0512204. for 300 fb−1. SPA point m0 = 70 GeV, m1/2 = 250 GeV, A0 = −300 GeV, tan β = 10, µ > 0: Ωh2 = 0.108. Put in mmax

ll

, mmax

llq ,

mlow

lq , mhigh lq

, mmin

llq , mlL − mχ0

1, mmax

ll

(χ0

4), mmax ττ , mh.

˜ χ0

1 ˜

χ0

1 → ℓ+ℓ−

40% ˜ χ0

1 ˜

χ0

1 → τ +τ −

28% ˜ χ0

1 ˜

χ0

1 → ν¯

ν 3% ˜ χ0

1˜

τ1 → Zτ 4% ˜ χ0

1˜

τ1 → Aτ 18% ˜ τ1˜ τ1 → ττ 2%

Global Fits to MSSM Models B.C. Allanach – p. 57

SLIDE 61

Neutralino mass matrix

Neutralino masses measured: χ0

1,2,4 but need mixing

matrix to determine couplings. Left with tan β.       M1 −mZcβsW mZsβsW M2 mZcβcW −mZsβcW −mZcβsW mZcβcW −µ mZsβsW −mZsβcW −µ       (4)

Global Fits to MSSM Models B.C. Allanach – p. 58

SLIDE 62

Neutralino mass matrix

Neutralino masses measured: χ0

1,2,4 but need mixing

matrix to determine couplings. Left with tan β.

0.986 0.988 0.99 0.992 20 0.02 0.04 0.06 0.08 0.1 20 0.12 0.125 0.13 0.135 0.14 20 0.02 0.04 0.06 0.08 20 tanβ abs(Z11) abs(Z12) abs(Z13) abs(Z14)

Global Fits to MSSM Models B.C. Allanach – p. 58

SLIDE 63

Slepton/A0 Higgs

Γ(χ0

2 → ˜

lRl)/Γ(χ0

2 → ˜

τ1τ) then helps determine θτ for a given tan β. Exclusion of A0 helps you to exclude A0 appearing in cascade decays. Meaurement

f mh provides constraints in mA − tan β plane.

0.025 0.05 0.075 0.1 200 400 600 800 m(A) (GeV) Ωh2 Global Fits to MSSM Models B.C. Allanach – p. 59

SLIDE 64

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) L/L(max) 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tan β m0 (TeV) L/L(max) 10 20 30 40 50 60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tan β m1/2 (TeV) L/L(max) 10 20 30 40 50 60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tan β A0 (TeV) L/L(max) 10 20 30 40 50 60

2
1.5
1
0.5

0.5 1 1.5 2

Global Fits to MSSM Models B.C. Allanach – p. 60

SLIDE 65

v 60-1

SLIDE 66

Uncertainties in Relic Density

Bulk region: ˜ B ˜ B → Z, h → l¯

l. Coannihilation: ˜

τχ0

1 → τ + X

Figure 3: Bulk/coannihilation region. Full: SoftSusy, dotted: SPheno.

Global Fits to MSSM Models B.C. Allanach – p. 61

SLIDE 67

Focus Point

Figure 4: Focus point region. Full: SoftSusy, dot- ted: SPheno, dashed: SuSpect. Higgsino LSP an- nihilates into ZZ/WW

Global Fits to MSSM Models B.C. Allanach – p. 62

SLIDE 68

High tan β

BCA, Belanger, Boudjema, Pukhov, Porod, hep-ph/0402161. Baer et al

Figure 5: High tan β region. Full: SoftSusy, dotted: SPheno, dashed: SuSpect. Get annihilation into A.

Global Fits to MSSM Models B.C. Allanach – p. 63

SLIDE 69

SUSY Kinematics: a Reminder

Take a particle decaying into 2 particles, eg H0 → b¯ b. We define the invariant mass of the b¯ b pair such that: H0(p) b(pb) ¯ b(p¯

b)

pµ = (

m2

H + p2, p) = pµ b + pµ ¯ b

⇒ p2 = m2

H = (pb + p¯ b)2

Is invariant in boosted frames Question: What happens to invariant mass in SUSY cascade decays, where we miss the final particle?

Global Fits to MSSM Models B.C. Allanach – p. 64

SLIDE 70

Cascade Decay

χ0

2

˜ l χ0

1

l+ l− pµ

˜ l = (m˜ l, 0)

pµ

l± = (|pl±|, pl±)

pµ

χ0

1,2 = (

mχ0

1,2

2 + |pχ0

1,2|2, pχ0 1,2)

The invariant mass of the l+l− pair is m2

ll = (pl+ + pl−)µ(pl+ + pl−)µ = p2 l+ + p2 l− + 2pl+ · pl−

= 2|pl+||pl−|(1 − cos θ)≤ 4|pl+||pl−|. Momentum conservation: ⇒ pχ0

2 + pl+ = 0,

pl− + pχ0

1 = 0.

Energy conservation:

mχ0

2

2 + |pl+|2 = m˜ l + |pl+|,

⇒ |pl+| =

m2

χ0 2

−m2

˜ l

2m˜

l

. Similarly |pl−| =

m2

˜ l −m2 χ0 1

2m˜

l

.

Global Fits to MSSM Models B.C. Allanach – p. 65

SLIDE 71

Edge to Mass Measurements

width S5 width O1 χ0

1

17 22 ˜ lR 17 20 χ0

2

17 20 ˜ q 22 20

50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 m1 (GeV) ml (GeV)

Mass differences well constrained, but overall mass scale not so well constrained by LHC

Global Fits to MSSM Models B.C. Allanach – p. 66

SLIDE 72

Fitting to SUSY Breaking Model

200 300 400 500 600 360 380 400 420 440 460 480 Spheno Isajet Softsusy Suspect

m1/2 [GeV] m0 [GeV]

200 300 400 500 600 1.6 1.8 2. 2.2 2.4 Softsusy Spheno Suspect Isajet

tan β m0 [GeV]

Experimenters pick a SUSY breaking point
They derive observables and errors after detector

simulation

We fita this “data” with our codes

aBCA, S Kraml, W Porod, JHEP 0303 (2003) 016

Global Fits to MSSM Models B.C. Allanach – p. 67

SLIDE 73

Edge Fitting at S5 and O1

50 100 150 200 50 100 150 mll (GeV) dσ/dmll (Events/100fb-1/0.375GeV) (a) 100 200 300 400 200 400 600 800 1000 mllq (GeV) dσ/dmllq (Events/100fb-1/5GeV) (b) 100 200 300 400 200 400 600 800 1000 High mlq (GeV) dσ/dmlq (Events/100fb-1/5GeV) (c1) 200 400 600 200 400 600 800 1000 Low mlq (GeV) dσ/dmlq (Events/100fb-1/5GeV) (c2) 50 100 150 200 400 600 800 1000 mllq (GeV) dσ/dmllq (Events/100fb-1/5GeV) (d) 20 40 60 80 100 200 400 600 800 1000 mhq (GeV) dσ/dmhq (Events/100fb-1/5GeV) (e) 50 100 150 200 50 100 150 mll (GeV) dσ/dmll (Events/100fb-1/0.375GeV) (a) 100 200 300 200 400 600 800 1000 mllq (GeV) dσ/dmllq (Events/100fb-1/5GeV) (b) 100 200 200 400 600 800 1000 High mlq (GeV) dσ/dmlq (Events/100fb-1/5GeV) (c1) 100 200 300 400 200 400 600 800 1000 Low mlq (GeV) dσ/dmlq (Events/100fb-1/5GeV) (c2) 20 40 60 200 400 600 800 1000 mllq (GeV) dσ/dmllq (Events/100fb-1/5GeV) (d) 20 40 60 80 200 400 600 800 1000 mzq (GeV) dσ/dmzq (Events/100fb-1/5GeV) (e)

Global Fits to MSSM Models B.C. Allanach – p. 68

SLIDE 74

Edge Positions

endpoint S5 fit O1 fit mll 109.10±0.13 70.47±0.15 mllq edge 532.1±3.2 544.1±4.0 lq high 483.5±1.8 515.8±7.0 lq low 321.5±2.3 249.8±1.5 llq thresh 266.0±6.4 182.2±13.5 Best case lepton mass measurements can be as accurate as 1 per mille, but jets are a few percent

Global Fits to MSSM Models B.C. Allanach – p. 69

SLIDE 75

2 α

−1

log (E/GeV)

M GUT M SUSY i 10

3 1

Run to MZ

❄

Run to MS. Calculatea sparticle pole masses.

❄

MX. Soft SUSY breaking BC.

❄

REWSB, iterative solution of µ

❄

Run to MS.

❄

Get gi(MZ), ht,b,τ(MZ).

✛

SOFTSUSY

aBCA, Comp. Phys. Comm. 143 (2002) 305.

Global Fits to MSSM Models B.C. Allanach – p. 70

SLIDE 76

Other Observables

Often more complicated, eg mllq edge: max (m2

˜ q − m2 χ0

2)(m2

χ0

2 − m2

χ0

1)

m2

χ0

2

, (m2

˜ q − m2 ˜ l )(m2 ˜ l − m2 χ0

1)

m2

˜ l

, (m˜

qm˜ l − mχ0

2mχ0 1)(m2

χ0

2 − m2

˜ l )

mχ0

2m˜

l

Also mhigh

lq

, mlow

lq , llq threshold a, M 2 T2(m) =

min/

p1+/ p2=/ pT

max
m2

T(pl1 T, /

p1, m), m2

T(pl2 T , /

p2, m)

,

max[MT2(mχ0

1)] = m˜

l] for dislepton production.

a

minimum where

Global Fits to MSSM Models B.C. Allanach – p. 71

SLIDE 77

Same order prior

We wish to encode the idea that “SUSY breaking terms should be of the same order of magnitude” p(m0|MS) = 1 √ 2πw2m0 exp

− 1

2w2 log2( m0 MS )

,

p(A0|MS) = 1 √ 2πe2wMS exp

− 1

2e2w A2 M 2

S

,

We don’t know SUSY breaking scale MS: p(m0, M1/2, A0, µ, B) = ∞ dMS p(m0, M1/2, A0, µ, B|MS) p(MS)

Global Fits to MSSM Models B.C. Allanach – p. 72

SLIDE 78

Naturalness

M 2

Z = tan 2β

m2

H2 tan β − m2 H1 cot β

− 2µ2

Cancellation implied by sparticle mass bounds. Quantify by f = maxx{d ln M 2

Z

d ln x } where x ∈ {M1/2, m0, A0, µ, B}. We will choose the prior to be 1/f.

Global Fits to MSSM Models B.C. Allanach – p. 73

SLIDE 79

Fine Tuning

Compare with usual definition of fine-tuning: f = maxp d ln MZ d ln p

10
5

5 10 500 1000 1500 2000 2500 m0 (GeV) ln(REWSB) ln(sameOrder w=1) ln(sameOrder w=2) ln(1/fine-tuning)

SPS1a Point M1/2 = 250 GeV tan β = 10 GeV A0 = −100 GeV

Global Fits to MSSM Models B.C. Allanach – p. 74