talk outline - university of california, irvinesusy06.physics.uci.edu/talks/1/allanach.pdf ·...

mSUGRA Fits and NaturalnessPriors

by

Ben Allanach (University of Cambridge)BCA, Lester, PRD73 (2006) 015013 hep-ph/0507283

BCA, PLB365 (2006) 123 hep-ph/0601089

Talk outline

• Constraints on SUSY models• Implications

SUSY Dark Matter and Colliders B.C. Allanach – p.1/24

Constraints on SUSY ModelsmSUGRA well-studied in literature: eg Ellis, Olive et al PLB565

(2003) 176; Roszkowski et al JHEP 0108 (2001) 024; Baltz, Gondolo, JHEP 0410 (2004) 052;. . .

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mh = 114 GeV

m0

(GeV

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m1/2 (GeV)

tan β = 10 , µ > 0

mχ± = 104 GeV

SUSY Dark Matter and Colliders B.C. Allanach – p.2/24

Shortcomings• Really, would like to combine likelihoods from

different measurements a

• Typically only 2d scans, but in general we haveαs(MZ), mt, mb, m0, M1/2, A0, tan β to vary

• Effective 3d type scan done b whichparameterises a 2d surface of correct Ωh2

• Baltz et al managed to perform a 4d scan, but lostthe likelihood interpretation. They used theimpressive Markov Chain Monte Carlotechnique.

aDone in 2d in Ellis et al, hep-ph/0310356bEllis et al, hep-ph/0411218

SUSY Dark Matter and Colliders B.C. Allanach – p.3/24

LikelihoodL ≡ p(d|m) is pdf of reproducing data d assumingmSUGRA model m (which depends on parameters).

p(m|d) = p(d|m)p(m)

p(d)

p(m1|d)

p(m2|d)=

p(d|m1)p(m1)

p(d|m2)p(m2)

We will compare p(mi) = 1 with a naturalness prior:1/(mi fine tuning).

SUSY Dark Matter and Colliders B.C. Allanach – p.4/24

Naturalness

M 2Z = tan 2β

[

m2H2

tan β − m2H1

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 theprior to be 1/f .

SUSY Dark Matter and Colliders B.C. Allanach – p.5/24

Markov-Chain Monte CarloMarkov chain consists of list of parameter points x(t)

and associated likelihoods L(t)

1. Pick a point at random for x(1)

2. Pick a point around x(t) (say with a Gaussianwidth) as the potential new point.

3. If L(t+1) > L(t), the new point is appended ontothe chain. Otherwise, the proposed point isaccepted with probability L(t+1)/L(t). If notaccepted, a copy of x(t) is added on to the chain.

Final density of x points ∝ L. Required number ofpoints goes linearly with number of dimensions.

SUSY Dark Matter and Colliders B.C. Allanach – p.6/24

ImplementationInput parameters are: m0, A0, M1/2, tan β

• mt = 172.7 ± 2.9 GeV• mb(mb)

MS = 4.2 ± 0.2 GeV,• αs(MZ)MS = 0.1187 ± 0.002.

For the likelihood, we also use• ΩDMh2 = 0.1125+0.0081

−0.0091

• δ(g − 2)µ/2 = (19 ± 8.4) × 10−10

• BR[b → sγ] = (3.52 ± 0.42) × 10−5

lnL = −1

2

∑

i

(pi − mi)2

2σ2i

+ cSUSY Dark Matter and Colliders B.C. Allanach – p.7/24

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SUSY Dark Matter and Colliders B.C. Allanach – p.8/24

Annihilation MechanismDefine stau co-annihilation when mτ is within 10% ofmχ0

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

2mχ0

1.

mechanism flat prior natural priorh0−pole 0.025 0.07A0−pole 0.41 0.14

τ−co-annihilation 0.26 0.18rest 0.31 0.61

b, τ

b, τ

χ01

χ01

h0, A0τ

χ01

τ

γ

τ

SUSY Dark Matter and Colliders B.C. Allanach – p.9/24

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Tevatron upper boundTevatron sensitivity

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SUSY Dark Matter and Colliders B.C. Allanach – p.10/24

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SUSY Dark Matter and Colliders B.C. Allanach – p.11/24

95% CL Upper Limits onMasses

particle flat prior natural priorh0 0.123 0.120A0 1.45 1.50χ0

1 0.65 0.45χ±

1 1.20 0.85g 3.25 2.30eR 1.90 1.90qL 3.20 2.45t1 2.45 1.80

P(500 GeV ILC>χ01χ

01, χ±

1 χ±1 ) ILC=0.7,0.33

P(800 GeV ILC>χ01χ

01, χ±

1 χ±1 ) ILC=0.93,0.58

SUSY Dark Matter and Colliders B.C. Allanach – p.12/24

Summary• Markov chains bring out the multi-dimensionality

of the space: is a lot less constrained than in 2d• Still, current data is constraining• Likelihood of LHC-friendly chain

qL → χ02 → lR → χ0

1 is 24±4%

• Tevatron has 32% chance of seeing Bs → µµ raredecay.

• Good news for ILC: light gauginos• Ruiz de Austri, Trotta, Roszkowski

hep-ph/0602028 confirms and extends our study.

SUSY Dark Matter and Colliders B.C. Allanach – p.13/24

Supplementary Material

SUSY Dark Matter and Colliders B.C. Allanach – p.14/24

ConvergenceWe run 9×1 000 000 points. By comparing the 9independent chains with random starting points, wecan provide a statistical measure of convergence: anupper bound r on the excepted variance decrease forinfinite statistics.

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step/10000

upper bound

SUSY Dark Matter and Colliders B.C. Allanach – p.15/24

SUSY Prediction of Ωh2

• Assume relic in thermal equilibrium withneq ∝ (MT )3/2exp(−M/T ).

• Freeze-out with Tf ∼ Mf/25 once interactionrate < expansion rate (teq critical)

• We use microMEGAs a: Ωh2 ∝ 1/< σv > tosolve coupled Boltzmann equations

• Generate SUSY spectrum with SOFTSUSY b

linked with SLHA c

aBelanger et al, CPC 149 (2002) 103bBCA, CPC 143 (2002) 305cBCA et al, JHEP0407 (2004) 036

SUSY Dark Matter and Colliders B.C. Allanach – p.16/24

Additional observables

δ(g − 2)µ

2∼ 13 × 10−10

(

100 GeVMSUSY

)2

tan β

µ µ

γ

ν

χ±i

µ µ

γ

χ01

µ

BR[b → sγ] ∝ tan β(MW/MSUSY )2

b s

γ

ti

χ±i

b s

γ

t

H±

SUSY Dark Matter and Colliders B.C. Allanach – p.17/24

mSUGRA RegionsAfter WMAP+LEP2, bulk region diminished. Needspecific mechanism to reduce overabundance:

• τ coannihilation: small m0, mτ1≈ mχ0

1.

Boltzmann factor exp(−∆M/Tf ) controls ratioof species. τ1χ

01 → τγ, τ1τ1 → τ τ .

• Higgs Funnel: χ01χ

01 → A → bb/τ τ at large

tan β. Also via a h at large m0 small M1/2.• Focus region: Higgsino LSP at large m0:

χ01χ

01 → WW/ZZ/Zh/tt.

• t coannihilation: high −A0, mt1≈ mχ0

1.

t1χ01 → gt, tt → tt

aDatta, Djouadi, Drees, hep-ph/0504090SUSY Dark Matter and Colliders B.C. Allanach – p.18/24

LHC SUSY Measurements

qL χ02 l χ0

1

q l+ l−

m2ll = (pl1 + pl2)

2

edge position measuresa

√

(m2

χ02

−m2

l)(m2

l−m2

χ01

)

m2

l0

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400

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205.7 / 197

P1 2209.

P2 108.7

P3 1.291

Mll (GeV)

Eve

nts/

0.5

GeV

/100

fb-1

aBCA, C Lester, A Parker, B Webber, JHEP 09 (2000) 004

SUSY Dark Matter and Colliders B.C. Allanach – p.19/24

2

α−1

log (E/GeV)

MG

UT

MSU

SY

i

10

3

1

Run to MZ

?

Run to MS. Calculate a 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.SUSY Dark Matter and Colliders B.C. Allanach – p.20/24

Uncertainties in Relic DensityBulk region: BB → Z, h → ll. Coannihilation: τχ0

1→ τ + X

Figure 1: Bulk/coannihilation region. Full:SoftSusy, dotted: SPheno.

SUSY Dark Matter and Colliders B.C. Allanach – p.21/24

Focus Point

Figure 2: Focus point region. Full: SoftSusy, dot-ted: SPheno, dashed: SuSpect. Higgsino LSP an-nihilates into ZZ/WW

SUSY Dark Matter and Colliders B.C. Allanach – p.22/24

High tan βBCA, Belanger, Boudjema, Pukhov, Porod, hep-ph/0402161. Baer et

al

Figure 3: High tan β region. Full: SoftSusy, dotted:SPheno, dashed: SuSpect. Get annihilation into A.

SUSY Dark Matter and Colliders B.C. Allanach – p.23/24

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SUSY Dark Matter and Colliders B.C. Allanach – p.24/24