Talk outline - University of California, Irvinesusy06.physics.uci.edu/talks/1/allanach.pdf ·...
Transcript of 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
)
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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coannihilationrest
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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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r
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
100
200
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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