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SUSY and Exotica
by
Ben Allanach (University of Cambridge)
Talk outline
• SUSY Fits• Impact of LHC data• SUSY Tactics• Exotica andAFB(tt)
Please ask questions while I’m talking
SUSY and Exotica B.C. Allanach – p. 1
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A Problem With the Higgs Bo-sonThe Higgs boson mass receivesquantum correctionsfrom heavy particles in the theory:
h hF
F
λ λ ∼ − aλ2
16π2
∫
dnk
k2 −m2F
+ . . .
Quantum correction to Higgs mass:
mphysh = 126 GeV/c2 = mtree
h +O(mF/100).
mF ∼ 1019 GeV/c2 is heaviest mass scale present.
SUSY and Exotica B.C. Allanach – p. 2
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Electroweak BreakingBothHiggs get vacuum expectation values:(
H01
H−1
)
→(
v10
) (
H+2
H02
)
→(
0
v2
)
and to getMW correct, match withvSM = 246 GeV:
v1
v2β
vSM tan β = v2v1
L = httLH02 tR + hbbLH
01bR + hτ τLH
01τR
⇒ mt
sin β=
htvSM√2
,mb,τ
cos β=
hb,τvSM√2
.
SUSY and Exotica B.C. Allanach – p. 3
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Supersymmetric Copies
H
SUSY and Exotica B.C. Allanach – p. 4
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Supersymmetric Copies
H × 2 H × 2
SUSY and Exotica B.C. Allanach – p. 4
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ImplementationWe use
• 95% C.L. direct search constraints• ΩDMh2 = 0.1143± 0.02 micrOMEGAs
• δ(g − 2)µ/2 = (29.5± 8.8)× 10−10 Stöckingeret al
• B−physics observables includingSusyBSGBR[b → sγ]Eγ>1.6 GeV = (3.52± 0.38)× 10−4,
BR(Bs → µµ) < 1.1× 10−8 micrOMEGAs
• Electroweak dataW Hollik, A Weberet al
2 lnL = −∑
i
χ2i + c =
∑
i
(pi − ei)2
σ2i
+ c
SUSY and Exotica B.C. Allanach – p. 5
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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 and Exotica B.C. Allanach – p. 6
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ATLAS Weighted Fits
Allanach, Khoo, Lester and Williams Mar, 2011
0 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
0.2
0.4
0.6
0.8
1Allanach, Khoo, Lester and Williams Mar, 2011
0 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
0.2
0.4
0.6
0.8
1
Again, we assumeA0-tan β independence andinterpolate acrossm0 andm1/2. CMS 35 pb−1,ATLAS 35 pb−1, CMS 1 fb−1
SUSY and Exotica B.C. Allanach – p. 7
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CMS/ATLAS Weighted Fits
0
0.02
0.04
0.06
0.08
0.1
0.12
0 500 1000 1500 2000 2500 3000mqL
/GeV
Allanach, Khoo, Lester and Williams, Mar 2011
Incl. ATLASExcl. CMS/ATLAS
Incl. CMS
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 500 1000 1500 2000
mg/GeV
Allanach, Khoo, Lester and Williams, Mar 2011
Incl. ATLASExcl. ATLAS
Incl. CMS
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 100 200 300 400 500mχ1
0/GeV
Allanach, Khoo, Lester and Williams, Mar 2011
Incl. ATLASExcl. ATLAS
Incl. CMS
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 200 400 600 800 1000meR
/GeV
Allanach, Khoo, Lester and Williams, Mar 2011
Incl. ATLASExcl. ATLAS
Incl. CMS
SUSY and Exotica B.C. Allanach – p. 8
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Prospects for SUSYStill look good! 5fb−1 expected before christmas
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
-6 -4 -2 0 2 4 6
log10(σSUSY/pb)
Allanach, Khoo, Lester and Williams, Mar 2011
Incl. ATLASExcl. ATLAS
Incl. CMS
SUSY and Exotica B.C. Allanach – p. 9
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pMSSM Fits25 pMSSM input parametersare:M1,2,3, At,b,τ,µ, mH1,2
, tan β,
mdR,L= msR,L
, muR,L= mcR,L
, meR,L= mµR,L
, mt,b,τR,L
mt, mb(mb) αs(MZ)MS, α−1(MZ)
MS, MZ . Combined Bayesianfita:
Measurement Fit(Log)Observable 0
0
1
1
2
2
3
3
measσ| / fit - Omeas|O
[GeV]Wm 0.025±80.399 80.402
[GeV]ZΓ 0.0025±2.4952 2.4964
lepeffθ 2sin 0.0012±0.2324 0.2314
10 10× µ
(g-2)δ 9.02±30.20 26.74
l0R 0.025±20.767 20.760
bR 0.00066±0.21629 0.21962
cR 0.0030±0.1721 0.1723
eA 0.0021±0.1513 0.1483
bA 0.020±0.923 0.935
cA 0.027±0.670 0.685
FBbA 0.0016±0.0992 0.1040
FBcA 0.035±0.071 0.074
4 10×) γ s X→BR(B 0.42±3.55 3.42
)ν τ → u
BR(BR 0.32±1.11 1.00
sB M∆R 0.40±1.15 1.00
0-∆ 0.0289±0.0375 0.0748
2hCDMΩ 0.02±0.11 0.13
aS.S. AbdusSalam, BCA, F. Quevedo, F. Feroz, M. Hobson, PRD81
(2010) 985012,arXiv:0904.2548SUSY and Exotica B.C. Allanach – p. 10
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Spectrum
0.1 0.12 0.14mh
2 4mA ≈ mH ≈ mH±
−4 −2 0 2µ[×103]
0.5 1 1.5 2mχ0
1
1 2 3mχ0
2
0.5 1 1.5 2mχ0
3
2 4mχ0
4
1 2 3mχ
±
1
2 4mχ
±
2
0 2 4mg
Obtained withMultiNesta algorithm in 16 CPUyears. Prior dependence isuseful: which predictionsarerobust?
aFeroz, Hobsonarxiv:0704.3704
SUSY and Exotica B.C. Allanach – p. 11
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Collider SUSY ProductionStrong sparticle production and decay to dark matterparticles.
q
q
q,g
χ01χ0
1
p
Interaction
q
q
7 TeV7 TeV
q,g
q q~ ~
p
Any (light enough) dark matter candidate that couplesto hadrons can be produced at the LHC
SUSY and Exotica B.C. Allanach – p. 12
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αT , MET , MT2 SearchesCMS: jets and missing energyarXiv:1101.1628
L = 35 pb−1. HT =∑Njet
i=1 |pjiT | > 350 GeV.
∆HT ≡∑
ji∈A|pji
T | −∑
ji∈B|pji
T |.(1)
One then calculates
αT =HT −∆HT
2√
H2T −H/2T
> 0.55(2)
whereH/T =
√
(∑Njet
i=1 pjix )2 + (∑Njet
i=1 pjiy )2.
SUSY and Exotica B.C. Allanach – p. 13
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CueMT2
m(i)T
2(pT
(i), /qT(i)) ≡ 2
∣
∣
∣pT
(i)∣
∣
∣
∣
∣
∣/qT(i)∣
∣
∣− 2pT
(i) · /qT(i)
where/qT(i) is the missing transverse momentum from
i. The variableMT2 is defined by:
MT2(pT(1),pT
(2), /pT) ≡ min∑ /qT
=/pT
max(
m(1)T ,m
(2)T
)
The minimization is over all values of/qT(1,2)
consistent with∑
/qT= /pT
. For the SUSY search,the unknown undetected particle masses are set tozero inMT2.
SUSY and Exotica B.C. Allanach – p. 14
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MT2 Search
[GeV]T2m
0 100 200 300 400 500 600
−1nu
mbe
r of
eve
nts/
10G
eV/ 1
00pb
1
10
210
310 SUSY signal (SPS1a)
)τ, µ (l = e, −l+ l→ Z
νν → Z )τ, µ (l = e, ν l→ W
t t QCD
0 100 200 300 400 500 600
1
10
210
310
Figure 1: Only cuts: Nj > 1, pT > 50 GeV,L =
100pb−1 at√s = 7 TeV. Barr, Gwenlan PRD80 (2009) 074007.
SUSY and Exotica B.C. Allanach – p. 15
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MT2 v EmissT
BCA, Barr, Dafinca, Gwenlan, JHEP 1107 (2011) 104,
arXiv:1105.1024
SUSY and Exotica B.C. Allanach – p. 16
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Compressed Spectra
SUSY and Exotica B.C. Allanach – p. 17
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Compressed Spectra IILeCompte, Martin,arXiv:1105.4304
SUSY and Exotica B.C. Allanach – p. 18
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BenchmarksCurrently wea are devising SUSY benchmark models.It’s imminent.
• CMSSM, NUHM, mAMSB, mGMSB, RPV andsome simplified models (via pMSSM) aredefined.
• Defining interesting parameter planes:identifying important parameters which controlthe masses of sparticles in each case.
• Discrete set of points along monotonic lines: nextpoint for the experiments to study is defined asthe lightest one that is not ruled out to 95% CL.
aS.S. AbdusSalam, BCA H. Dreiner, J. Ellis, S. Heinemeyer,
M. Kramer, M. Mangano, K.A. Olive, S. Rogerson, L. Roszkowski,
M. Schlaffer, G. WeigleinSUSY and Exotica B.C. Allanach – p. 19
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AFB(tt)AFB =
N(yt > yt)−N(yt > yt)
N(yt > yt) +N(yt > yt)
AFB(CDF )lj+ll = (20.9± 6.6)%,
AFB(D0)lj = (19.6± 6.5)%,
SUSY and Exotica B.C. Allanach – p. 20
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CDF
Seems to be increasing with mass. Lepton charge isnice verification.
SUSY and Exotica B.C. Allanach – p. 21
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Mtt
SUSY and Exotica B.C. Allanach – p. 22
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AFB Exotica
Must notdisturbσtt or dσtt/dMtt
• axigluonsa
• Z ′/W ′b
aFrampton et alSUSY and Exotica B.C. Allanach – p. 23
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LHC AsymmetryDefined LHC charge asym
AC =N(|yt| > |yt|)−N(yt > |yt|)N(|yt| > |yt|) +N(yt > |yt|)
SM discovery would take 60 fb−1 at 5σ, but newphysics quicker (Z ′ takes 2 fb−1)
ACMSC = −1.6±3±1% AATLAS
C = −2.4±1.6±2.3%
SUSY and Exotica B.C. Allanach – p. 24
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Models• Z ′ modelis rather odd: only contains a vertex
couplingutZ ′, egMZ ′ = 800 GeV,gZ = 3.4:predicts significantsame sign tops.
• W ′ models also covered by LHC experiments bynow.
• Heavyaxigluon models eg 2 TeV,gq=-gt=2.4 areruled out by LHCmjj searches
• Recent proposala: axigluonsg =0.4-0.8,M = 50− 90 GeV. They evade jet data becausethe have massesbelow current limits.Non-resonant production suppresses new physicscontribution toσtt.
aKrnjaic,arXiv:1109.0648SUSY and Exotica B.C. Allanach – p. 25
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Shopping ListThings that the CMS/ATLAS always provide that weneed:
• Cuts and numbers of events observed past them• Expected background numbers with systematic
errors
We could really do with:• Keeping in mind: we can’t combine analyses that
use the same events: much better to keep theeventsdisjoint. Doesn’t preclude fully inclusiveanalysis, but make the others as disjoint aspossible.
• Likelihood versus predicted number of eventspast cuts (before efficiency correction). Ideally,sanitizedRooStatsSUSY and Exotica B.C. Allanach – p. 26
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Shopping List IIFailing that, then we must calculate the likelihood:
• Systematic errors on signals: perhaps at least arange over parameter space in one model. Ideally,it would be parameterised in terms of importantquantities.
• Other contours (eg 1/5 sigma exclusion contours)so we can check our likelihood away from 95%excluded region.
• Numbers in histogram plotsattached toarXivpublication
SUSY and Exotica B.C. Allanach – p. 27
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Summary• LHC analyses providing a nice amount of
information for interpretation of data. There’salways room for improvement...
• SUSY is late to the party, but not late enough tobe reported missing
• CMSSMcould well be discovered this/next year• Current searches reach squark and gluino masses
of 980 GeV. This will be extended to∼ 1100GeV next year, covering much of the good-fitregion.
• tt asymmetry situation extremelymurky. Manyheavy axigluon models now ruled out.
SUSY and Exotica B.C. Allanach – p. 28
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Supplementary Material
SUSY and Exotica B.C. Allanach – p. 29
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CMS αT SearchCMS: jets and missing energyarXiv:1101.1628
L = 35 pb−1. HT =∑Njet
i=1 |pjiT | > 350 GeV.
∆HT ≡∑
ji∈A|pji
T | −∑
ji∈B|pji
T |.(3)
One then calculates
αT =HT −∆HT
2√
H2T −H/2T
> 0.55(4)
whereH/T =
√
(∑Njet
i=1 pjix )2 + (∑Njet
i=1 pjiy )2.
SUSY and Exotica B.C. Allanach – p. 30
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Results
SUSY and Exotica B.C. Allanach – p. 31
![Page 33: SUSY and Exoticaconference/zhang_170217.pdf · • Exotica and AFB(t¯t) Please ask questions while I’m talking SUSY and Exotica B.C. Allanach – p. 1 . A Problem With the Higgs](https://reader033.vdocuments.site/reader033/viewer/2022050609/5fb01f68fcffb61fdc2ae6ed/html5/thumbnails/33.jpg)
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 onm(NLSP ).
MT2(pT(1),pT
(2), /pT) ≡ min∑ /qT
=/pT
max(
m(1)T ,m
(2)T
)
SUSY and Exotica B.C. Allanach – p. 32
![Page 34: SUSY and Exoticaconference/zhang_170217.pdf · • Exotica and AFB(t¯t) Please ask questions while I’m talking SUSY and Exotica B.C. Allanach – p. 1 . A Problem With the Higgs](https://reader033.vdocuments.site/reader033/viewer/2022050609/5fb01f68fcffb61fdc2ae6ed/html5/thumbnails/34.jpg)
Candidate Event: HighET (j)
SUSY and Exotica B.C. Allanach – p. 33
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MSSM Exclusion: SimplifiedModel
SUSY and Exotica B.C. Allanach – p. 33