S UPERSYMMETRY
AT THE
LHC
Tilman Plehn
Edinburgh/Munich
– TeV–scale supersymmetry
– Inclusive signals
– Exclusive measurements
– SUSY parameters
Tilman Plehn: Susy at the LHC – p.1
T E V–S CALE S UPERSYMMETRY
Bright side
– 3 running gauge couplings meet — GUT gauge group
– 2 Higgs doublets — radiative symmetry breaking
– R parity — stable proton yields dark matter
– local supersymmetry – including gravity?
– rich LHC phenomenology — no nasty surprises
[if you can do SUSY you can do everything]
Dark side
– unknown SUSY breaking
→ masses, couplings, phases...
→ e.g. hierarchical spectrum?
– flavor physics and SUSY breaking
→ CKM and lepton flavor?
– 2 Higgs doublet model
→ µ parameter and SUSY breaking?
fermion
→ sfermion
gluon
→ gluino
gauge bosons
Higgs bosons
→ neutralinos
gauge bosons
Higgs bosons
→ charginos
f L , fR
f˜L , f˜R
Gµ
g̃
γ, Z
h o , H o , Ao
χ̃o
i
W±
H±
±
χ̃
i
spin
1/2
0
1
1/2
1
0
1/2
d.o.f.
1+1
1+1
n-2
2
2+3
3
4·2
1
0
2·3
2
1/2
2·4
Majorana
Majorana
Dirac
⇒ as many as exclusive analyses as possible
Tilman Plehn: Susy at the LHC – p.2
S USY TOOLS
Supersymmetric parameter conventions
– comparison of specialized codes crucial
[remember: e.g. Comphep–Pythia–Isajet]
⇒ fix SUSY conventions once for all
soft breaking parameters [e.g. ±At ]
scale dependence of couplings, masses [e.g. m(q = TeV, v, mt )?]
definitions of mass matrixes, mixing angles [e.g. t̃L,R up or down?]
SUSY Les Houches Accord
[Allanach, Skands et al.]
– spectrum generators: SoftSusy, SPheno, FeynHiggs,...
– multi-purpose Monte Carlos: Pythia, Herwig, Sherpa
– matrix element generators: Whizard, Smadgraph
– NLO cross sections: Prospino2
– NLO decay rates: Sdecay
– SUSY parameter extraction: Fittino, Sfitter
– dark matter: Micromegas
⇒ fixed parameter convention and read-write format
[list still growing]
Tilman Plehn: Susy at the LHC – p.3
I NCLUSIVE S USY S IGNALS
Supersymmetry at the LHC
(1) possible discovery — signals for new physics, exclusion of parameter space
(2) measurements — masses, cross sections, decays
(3) parameter studies — MSSM Lagrangean, SUSY breaking
⇒ at least 10% precision to be matched at LHC
[theorist’s nightmare, yet unsolved]
10 3
SUSY signals in Prospino2
∗
– jets and E
/ T : pp → q̃ q̃ , g̃g̃, q̃g̃
– funny tops: pp → t̃1 t̃∗1
10 2
– tri-leptons: pp →
χ̃02 χ̃−
1
1
10
0 ¯ −
0
˜¯
[χ̃0
2 → `` → χ̃1 ``; χ̃1 → χ̃1 `ν̄]
– bottoms and E
/ T : pp → b̃1 b̃∗1
−
⇑
10
– like sign dileptons: pp → g̃g̃
[g̃ → ũū → χ̃+
1 dū or c. c.]
−
10
−
−
σtot[pb]: pp → g̃g̃, q̃q̃, t̃1t̃1, χ̃o2χ̃+1, ν̃ν̃, χ̃o2g̃, χ̃o2q̃
⇑
t̃1t̃1
⇑
⇑
χ̃o2χ̃+1
-1
⇑
-2
100
150
⇑ ⇑
χ̃o2q̃
g̃g̃
−
q̃q̃
√S = 14 TeV
χ̃o2g̃
NLO
LO
−
ν̃ν̃
200
m [GeV]
250
300
350
400
450
500
Tilman Plehn: Susy at the LHC – p.4
I NCLUSIVE S USY S IGNALS
Supersymmetry at the LHC
(1) possible discovery — signals for new physics, exclusion of parameter space
(2) measurements — masses, cross sections, decays
(3) parameter studies — MSSM Lagrangean, SUSY breaking
⇒ at least 10% precision to be matched at LHC
[theorist’s nightmare, yet unsolved]
10
−
−
−
−
σtot[pb]: pp → g̃g̃, q̃q̃, t̃1t̃1, χ̃o2χ̃+1, ν̃ν̃, χ̃o1g̃, χ̃+1q̃
SUSY signals in Prospino2
∗
– jets and E
/ T : pp → q̃ q̃ , g̃g̃, q̃g̃
– funny tops: pp → t̃1 t̃∗1
– like sign dileptons: pp → g̃g̃
10
[g̃ → ũū → χ̃+
1 dū or c. c.]
– tri-leptons: pp → χ̃02 χ̃−
1
10
-1
NLO
LO
⇑
⇑
⇑
−
q̃q̃
-2
−
10
−
t̃1t̃1
χ̃o2χ̃+1
ν̃ν̃
0 ¯ −
0
˜¯
[χ̃0
2 → `` → χ̃1 ``; χ̃1 → χ̃1 `ν̄]
– bottoms and E
/ T : pp → b̃1 b̃∗1
√S = 2 TeV
1
-3
100
⇑
150
χ̃+1q̃
200
g̃g̃
⇑χ̃ g̃
⇑
250
⇑
o
1
300
350
400
m [GeV]
450
500
Tilman Plehn: Susy at the LHC – p.5
S USY M ASS M EASUREMENTS
Spectra from cascade decays
– decay g̃ → q̃ q̄ → χ̃02 q q̄ → µ+ µ− q q̄ χ̃01
– cross sections some 100 pb
– thresholds & edges
µ
q
q
µ
[better not via Z or to τ ]
[more than 3 × 105 events]
χ̃o2
~
q
~
µ
χ̃o1
g̃
[Hinchliffe, Paige...; Cambridge ex-ph]
2
2
2
2
2
classical m2
`` < (mχ̃0 − m`˜)(m`˜ − mχ̃0 )/m`˜
2
1
– detector resolution, calibration, systematic errors, shape analysis?
– cross sections as additional input?
[Lester...]
⇒ q̃L cascade reconstruction great for SPS1a
Gluino mass
[mass differences better]
m∼χ 0
m~l m∼χ 0
R
1
[Gjelsten, Miller, Osland]
m~q - m∼χ 0
– now four jets instead of two
L
1
1
– b̃L instead, all jets b-tagged
0
100
m~q
L
m~g
1
mg~ - mb~
2
1
R
1
mχ∼0 - mχ∼0
m~l - mχ∼0
m~g- m∼χ 0
– jet identification crucial
⇒ gluino mass to ∼ 1%
statistical error dominant
2
m~b - m∼χ 0
1
1
m~b
200
300
400
Sparticle masses and mass differences [GeV]
1
500
600
Tilman Plehn: Susy at the LHC – p.6
S USY S PIN D ETERMINATION
How to make sure it is SUSY
– assume neutralino is found in cascades
⇒ if fermion, then weakly interacting Majorana
[that’s what we call a neutralino]
⇒ compare with a model where gluino is a boson: universal extra dimensions
[Cheng, Dobrescu,...; mass spectra degenerate — ignore this information; cross section factor 10 larger — ignore this as well]
Slepton cascade
[Smillie, Webber]
– decay chain χ̃02 → ``˜∗ → ``¯χ̃01
– compare with first KK Z and `
– initial-state asymmetry pp → q̃g̃
[q̃/q̄˜ ∼ 2]
– trick: mass variables, ‘normalized angles’ [Barr]
m
b = mj` /mmax
most promising
j`
A = [σ(j`+ ) − σ(j`− )]/[σ(j`+ ) + σ(j`− )]
– assume hierarchical SPS1a spectrum [dashed SUSY]
⇒ SUSY spins accessible
Tilman Plehn: Susy at the LHC – p.7
S USY S PIN D ETERMINATION
How to make sure it is SUSY
– assume neutralino is found in cascades
⇒ if fermion, then weakly interacting Majorana
[that’s what we call a neutralino]
⇒ compare with a model where gluino is a boson: universal extra dimensions
[Cheng, Dobrescu,...; mass spectra degenerate — ignore this information; cross section factor 10 larger — ignore this as well]
Slepton cascade
[Smillie, Webber]
– decay chain χ̃02 → ``˜∗ → ``¯χ̃01
– compare with first KK Z and `
– initial-state asymmetry pp → q̃g̃
[q̃/q̄˜ ∼ 2]
– trick: mass variables, ‘normalized angles’ [Barr]
m
b = mj` /mmax
most promising
j`
A = [σ(j`+ ) − σ(j`− )]/[σ(j`+ ) + σ(j`− )]
– assume non-hierarchical UED spectrum [dashed SUSY]
⇒ SUSY spins accessible
Tilman Plehn: Susy at the LHC – p.8
S USY M ATRIX E LEMENTS
Complex final states: SUSY-Madgraph
[Hagiwara, Kanzaki, TP, Rainwater, Stelzer]
– Majoranas and fermion number violation in Madgraph
– complete set of Feynman rules
Squarks and gluinos plus jets
[Denner, Eck, Hahn, Küblbeck]
[400+ processes compared with Whizard and Sherpa]
[TP, Rainwater, Skands]
– cascade studies sensitive to jets?
– SUSY-Madevent: g̃g̃+2j and ũL g̃+2j
[pT ,j > 100 GeV]
⇒ Phythia shower tuned at Tevatron?
σ [pb]
σ0j
σ1j
σ2j
tt̄600
1.30
0.73
0.26
g̃g̃
4.83
2.89
1.09
ũL g̃
5.65
2.74
0.85
dσ/dpT [pb/GeV]
⇒ SUSY will be fine, top harder
pT,j (pp→tt̄j)
1
10
dσ/dpT [pb/GeV]
10
10
10
10
max
pT,j
(pp→tt̄jj)
min
pT,j
(pp→tt̄jj)
pT,j≥50 GeV
pT,j≥50 GeV
pT,j≥50 GeV
|ηj|<5, ∆Rjj>0.4
KPythia=1.8
-1
-2
LHC:
Susy-MadGraph
Pythia: pT2 (power)
pT2 (wimpy)
2
Q (power)
2
Q (wimpy)
2
Q (tune A)
max
pT,j
(pp→ũLũLjj)
pT,j (pp→ũLũLj)
-3
-4
-5
0
pT,j≥50 GeV
|ηj|<5, ∆Rjj>0.4
KPythia=1.25
min
pT,j
(pp→ũLũLjj)
pT,j≥100 GeV
pT,j≥100 GeV
LHC: sps1amod
Susy-MadGraph
Pythia: pT2 (power)
pT2 (wimpy)
2
Q (power)
2
Q (wimpy)
2
Q (tune A)
100
200
300
400
0
100
200
300
400
0
100
200
300
400 GeV
Tilman Plehn: Susy at the LHC – p.9
S USY M ATRIX E LEMENTS
Complex final states: SUSY-Madgraph
[Hagiwara, Kanzaki, TP, Rainwater, Stelzer]
– Majoranas and fermion number violation in Madgraph
– complete set of Feynman rules
Squarks and gluinos plus jets
[Denner, Eck, Hahn, Küblbeck]
[400+ processes compared with Whizard and Sherpa]
[TP, Rainwater, Skands]
– cascade studies sensitive to jets?
– SUSY-Madevent: g̃g̃+2j and ũL g̃+2j
[pT ,j > 100 GeV]
⇒ Phythia shower tuned at Tevatron?
σ [pb]
σ0j
σ1j
σ2j
tt̄600
1.30
0.73
0.26
g̃g̃
4.83
2.89
1.09
ũL g̃
5.65
2.74
0.85
dσ/dpT [pb/GeV]
⇒ SUSY will be fine, top harder
max
pT,j
(pp→g̃g̃jj)
pT,j (pp→g̃g̃j)
pT,j≥50 GeV
|ηj|<5, ∆Rjj>0.4
KPythia=1.75
-2
10
-3
10
-4
min
pT,j
(pp→g̃g̃jj)
pT,j≥100 GeV
pT,j≥100 GeV
LHC: sps1a
Susy-MadGraph
Pythia: pT2 (power)
pT2 (wimpy)
2
Q (power)
2
Q (wimpy)
2
Q (tune A)
dσ/dpT [pb/GeV]
10
10
10
10
max
pT,j
(pp→ũLũLjj)
pT,j (pp→ũLũLj)
-3
-4
-5
0
pT,j≥50 GeV
|ηj|<5, ∆Rjj>0.4
KPythia=1.25
min
pT,j
(pp→ũLũLjj)
pT,j≥100 GeV
pT,j≥100 GeV
LHC: sps1amod
Susy-MadGraph
Pythia: pT2 (power)
pT2 (wimpy)
2
Q (power)
2
Q (wimpy)
2
Q (tune A)
100
200
300
400
0
100
200
300
400
0
100
200
300
400 GeV
Tilman Plehn: Susy at the LHC – p.10
S USY PARAMETERS
SUSY parameters from observables
– parameters: weak-scale MSSM Lagrangean
– measurements: masses or edges
branching fractions [MSMlib, Sdecay]
cross sections [Prospino2, MSMlib],...
– errors: general correlation, statistics & systematics & theory
– problem in grid: huge phase space, local minimum?
problem in fit: domain walls, starting values, global minimum?
– assume we know how SUSY is broken
⇒ mSUGRA
– include some indirect constraints
– fit m0 , m1/2 , A0 , tan β, sign(mu)
[Allanach]
⇒ who believes in mSUGRA?
m0 (TeV)
First go at problem
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
L/L(max)
0 0.20.40.60.8 1 1.21.41.61.8 2
M1/2 (TeV)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
mSUGRA useful testing ground for methods
Tilman Plehn: Susy at the LHC – p.11
S USY PARAMETERS
SUSY parameters from observables
– parameters: weak-scale MSSM Lagrangean
– measurements: masses or edges
branching fractions [MSMlib, Sdecay]
cross sections [Prospino2, MSMlib],...
– errors: general correlation, statistics & systematics & theory
– problem in grid: huge phase space, local minimum?
problem in fit: domain walls, starting values, global minimum?
10
8
6
CMSSM, µ > 0
2
– assume we know how SUSY is broken
χ (today)
First go at problem
⇒ mSUGRA
– include more indirect constraints
4
tanβ = 10, A0 = 0
tanβ = 10, A0 = +m1/2
[Weiglein, Stöckinger,...]
tanβ = 10, A0 = -m1/2
2
tanβ = 10, A0 = +2 m1/2
– fit m0 , m1/2 , A0 , tan β, sign(mu)
tanβ = 10, A0 = -2 m1/2
0
⇒ who believes in mSUGRA?
0
200
400
600
800
1000
m1/2 [GeV]
mSUGRA useful testing ground for methods
Tilman Plehn: Susy at the LHC – p.12
S USY PARAMETERS
SUSY parameters from observables
– parameters: weak-scale MSSM Lagrangean
– measurements: masses or edges
branching fractions [MSMlib, Sdecay]
cross sections [Prospino2, MSMlib],...
– errors: general correlation, statistics & systematics & theory
– problem in grid: huge phase space, local minimum?
problem in fit: domain walls, starting values, global minimum?
Sfitter/Fittino [Lafaye, TP, Zerwas; Bechtle, Desch, Wienemann]
– (1) grid for closed subset
(2) fit of remaining parameters
(3) complete fit
– LHC better than expected
– LHC+ILC without assumptions
– SUSY breaking bottom–up
tanβ
M1
M3
Mτ̃
L
Mτ̃
R
Mµ̃
L
Mq̃3
L
M
t̃R
M
b̃R
Aτ
At
Ab
LHC
10.22±9.1
102.45±5.3
578.67±15
fix 500
ILC
10.26±0.3
102.32±0.1
fix 500
197.68±1.2
LHC+ILC
10.06±0.2
102.23±0.1
588.05±11
199.25±1.1
SPS1a
10
102.2
589.4
197.8
129.03±6.9
135.66±0.3
133.35±0.6
135.5
198.7±5.1
198.7±0.5
198.7±0.5
198.7
498.3±110
497.6±4.4
521.9±39
501.3
fix 500
420±2.1
411.73±12
420.2
522.26±113
fix 500
504.35±61
525.6
fix 0
-507.8±91
-784.7±35603
-202.4±89.5
-501.95±2.7
fix 0
352.1±171
-505.24±3.3
-977±12467
-253.5
-504.9
-799.4
Tilman Plehn: Susy at the LHC – p.13
O UTLOOK
LHC phenomenology
– pheno-experimental efforts very strong in Scotland and northern England
– lots of new tools on the market, waiting to be tested
– We will be able to do amazing things at the LHC
⇒ come to Georg’s talk for we still need in the future of HEP...
Tilman Plehn: Susy at the LHC – p.14