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NRW Phanomenologie-Treffen, Januar 2006
SUSY-particle production at Hadron Colliders
Michael Kramer
(RWTH Aachen)
Basics of SUSY particle production at hadron colliders
The calculation of SUSY-QCD corrections
Work done in collaboration with W. Beenakker, R. Hopker, M. Klasen, T. Plehn, M. Spira, P.M. Zerwas
Michael Kramer Page 1 NRW Panomenologie-Treffen, Januar 2006
Introduction: Why Supersymmetrie?
There are many good reasons to study supersymmetric field theoriesand TeV-scale SUSY at colliders:
– SUSY is the unique extension of the Lorentz-symmetry
– SUSY provides a solution to the hierarchy problem
– SUSY allows for gauge coupling unification
– SUSY provides a dark matter candidate
– SUSY can generate EWSB dynamically
– . . .
Michael Kramer Page 2 NRW Panomenologie-Treffen, Januar 2006
The Minimal Supersymmetric Standard Model
The MSSM particle spectrum
Gauge Bosons S = 1 Gauginos S = 1/2
gluon, W±, Z, γ gluino, W , Z, γ
Fermions S = 1/2 Sfermions S = 0(
uL
dL
)(νe
L
eL
) (uL
dL
)(νe
L
eL
)
uR, dR, eR uR, dR, eR
Higgs Higgsinos(
H02
H−
2
)(H+
1
H01
) (H0
2
H−
2
)(H+
1
H01
)
Michael Kramer Page 3 NRW Panomenologie-Treffen, Januar 2006
SUSY particle production at hadron colliders
In the MSSM one imposes a symmetryR = (−1)3B+L+2S
{= +1 SM
= −1 SUSYto avoid proton decay
→ SUSY particles produced pairwise
→ lightest SUSY particle stable (dark matter candidate)
The interactions of MSSM particles are determined by gauge symmetry and SUSY
example: gluonµ, a
p, i
q, j
squark
squark
= −i gs (Ta)ij(p + q)µ
→ no new coupling!
SUSY particles should be produced copiously at hadron colliders through QCD processes, e.g.
g
g
Michael Kramer Page 4 NRW Panomenologie-Treffen, Januar 2006
SUSY particle production at hadron colliders
In the MSSM one imposes a symmetryR = (−1)3B+L+2S
{= +1 SM
= −1 SUSYto avoid proton decay
→ SUSY particles produced pairwise
→ lightest SUSY particle stable (dark matter candidate)
The interactions of MSSM particles are determined by gauge symmetry and SUSY
example: gluonµ, a
p, i
q, j
squark
squark
= −i gs (Ta)ij(p + q)µ
→ no new coupling!
SUSY particles should be produced copiously at hadron colliders through QCD processes, e.g.
g
g
Michael Kramer Page 4 NRW Panomenologie-Treffen, Januar 2006
SUSY particle production at hadron colliders
In the MSSM one imposes a symmetryR = (−1)3B+L+2S
{= +1 SM
= −1 SUSYto avoid proton decay
→ SUSY particles produced pairwise
→ lightest SUSY particle stable (dark matter candidate)
The interactions of MSSM particles are determined by gauge symmetry and SUSY
example: gluonµ, a
p, i
q, j
squark
squark
= −i gs (Ta)ij(p + q)µ
→ no new coupling!
SUSY particles should be produced copiously at hadron colliders through QCD processes, e.g.
g
g
Michael Kramer Page 4 NRW Panomenologie-Treffen, Januar 2006
SUSY particle production at hadron colliders
In the MSSM one imposes a symmetryR = (−1)3B+L+2S
{= +1 SM
= −1 SUSYto avoid proton decay
→ SUSY particles produced pairwise
→ lightest SUSY particle stable (dark matter candidate)
The interactions of MSSM particles are determined by gauge symmetry and SUSY
example: gluonµ, a
p, i
q, j
squark
squark
= −i gs (Ta)ij(p + q)µ
→ no new coupling!
SUSY particles should be produced copiously at hadron colliders through QCD processes, e.g.
g
g
Michael Kramer Page 4 NRW Panomenologie-Treffen, Januar 2006
Squark and gluino cross section at the LHC
0.1 1 1010-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
σjet(ETjet > √s/4)
LHCTevatron
σttbar
σHiggs(MH = 500 GeV)
σZ
σjet(ETjet > 100 GeV)
σHiggs(MH = 150 GeV)
σW
σjet(ETjet > √s/20)
σbbar
σtot
σ (n
b)
√s (TeV)
even
ts/s
ec f
or L
= 1
033 c
m-2
s-1
−→ SUSY signal:
σ(qq + gg + gq) ≈ 2 nb (Mq,g ≈ 300 GeV)
↪→≈ 108squarks & gluinos/year (∫L = 30 fb−1)
Michael Kramer Page 5 NRW Panomenologie-Treffen, Januar 2006
Squark and gluino cross section at the LHC
0.1 1 1010-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
σjet(ETjet > √s/4)
LHCTevatron
σttbar
σHiggs(MH = 500 GeV)
σZ
σjet(ETjet > 100 GeV)
σHiggs(MH = 150 GeV)
σW
σjet(ETjet > √s/20)
σbbar
σtot
σ (n
b)
√s (TeV)
even
ts/s
ec f
or L
= 1
033 c
m-2
s-1
−→ SUSY signal:
σ(qq + gg + gq) ≈ 2 nb (Mq,g ≈ 300 GeV)
↪→≈ 108squarks & gluinos/year (∫L = 30 fb−1)
Michael Kramer Page 5 NRW Panomenologie-Treffen, Januar 2006
SUSY searches at hadron colliders
Distinctive signature due to cascade decays:
multiple jets (and/or leptons) with large amount of missing energy
D_D
_204
7.c.
1
q
q
q
q
q~
~
~
~
—
—
—b
b
l+
l+
g
~g
W— W+t
t
t1
ν
χ1
~χ10
~χ20
Gluino/squark production event topology al lowing sparticle mass reconstruction
3 isolated leptons+ 2 b-jets+ 4 jets
+ Etmiss
~l
+
l-
Such cascade decays allow to reconstructsleptons, neutralinos, squarks, gluinos...in favorable cases with %level mass resolutions
→ LHC discovery reach for squarks and gluinos: Mq,g ∼< 2.5 TeV
Michael Kramer Page 6 NRW Panomenologie-Treffen, Januar 2006
SUSY searches at hadron colliders
Distinctive signature due to cascade decays:
multiple jets (and/or leptons) with large amount of missing energy
D_D
_204
7.c.
1
q
q
q
q
q~
~
~
~
—
—
—b
b
l+
l+
g
~g
W— W+t
t
t1
ν
χ1
~χ10
~χ20
Gluino/squark production event topology al lowing sparticle mass reconstruction
3 isolated leptons+ 2 b-jets+ 4 jets
+ Etmiss
~l
+
l-
Such cascade decays allow to reconstructsleptons, neutralinos, squarks, gluinos...in favorable cases with %level mass resolutions
→ LHC discovery reach for squarks and gluinos: Mq,g ∼< 2.5 TeV
Michael Kramer Page 6 NRW Panomenologie-Treffen, Januar 2006
Current limits on sparticle masses
)2Gluino Mass (GeV/c0 100 200 300 400 500 600
)2S
quar
k M
ass
(GeV
/c
0
100
200
300
400
500
600-1DØ Run II Preliminary L=310 pb
UA
1
UA
2
LEP 1+2
CD
F IB
DØ
IA
DØ IB
DØ II
)10χ∼)<m(q~m(
no mSUGRA
solution
+/-
χ∼LE
P2
l~LEP2
mass limits (roughly)
Mg ∼> 200 GeV
Mq ≈ Mgluino ∼> 300 GeV
Mt1 ∼> 100 GeV
Mχ01 ∼> 50 GeV
Mχ±
1 ∼> 100 GeV
Msleptons ∼> 100 GeV
Michael Kramer Page 7 NRW Panomenologie-Treffen, Januar 2006
Current limits on sparticle masses
)2Gluino Mass (GeV/c0 100 200 300 400 500 600
)2S
quar
k M
ass
(GeV
/c
0
100
200
300
400
500
600-1DØ Run II Preliminary L=310 pb
UA
1
UA
2
LEP 1+2
CD
F IB
DØ
IA
DØ IB
DØ II
)10χ∼)<m(q~m(
no mSUGRA
solution
+/-
χ∼LE
P2
l~LEP2
mass limits (roughly)
Mg ∼> 200 GeV
Mq ≈ Mgluino ∼> 300 GeV
Mt1 ∼> 100 GeV
Mχ01 ∼> 50 GeV
Mχ±
1 ∼> 100 GeV
Msleptons ∼> 100 GeV
Michael Kramer Page 7 NRW Panomenologie-Treffen, Januar 2006
MSSM particle production at hadron colliders
production dynamics
P
P
i
j
¯Q
˜Q
fP
i
f P
i
σ
σ(pp/pp → q¯q) =∫
dx1fPi (x1, µ)
∫dx2f
Pj (x2, µ) σ(ij → q¯q)
+O(Λ/Mq)
→ effective energy for (s)particle production√
s =√
x1x2s <√
s
Michael Kramer Page 8 NRW Panomenologie-Treffen, Januar 2006
MSSM particle production at hadron colliders
Scale dependence
σ =
∫dx1f
Pi (x1, µF )
∫dx2f
Pj (x2, µF )
×∑
n
αns (µR) Cn(µR, µF )
finite order in perturbation theory
→ artificial µ-dependence:
dσ
d ln µ2
R
=
N∑
n=0
αns (µR) Cn(µR, µF )
= O(αs(µR)N+1)
⇒ scale dependence ∼ theoretical
uncertainty due to HO corrections
Example: Stop-pair production at leading order
20
30
40
50
60
70
80
90
100
1
LO
σ(pp → t1t−1+X) [pb]
µ/m(t1)
√s=14 TeV; m(t1) = 200 GeV
→ theoretical uncertainty
∼> ± 100% at LO
⇒ must include NLO corrections
Michael Kramer Page 9 NRW Panomenologie-Treffen, Januar 2006
MSSM particle production at hadron colliders
Scale dependence
σ =
∫dx1f
Pi (x1, µF )
∫dx2f
Pj (x2, µF )
×∑
n
αns (µR) Cn(µR, µF )
finite order in perturbation theory
→ artificial µ-dependence:
dσ
d ln µ2
R
=
N∑
n=0
αns (µR) Cn(µR, µF )
= O(αs(µR)N+1)
⇒ scale dependence ∼ theoretical
uncertainty due to HO corrections
Example: Stop-pair production at leading order
20
30
40
50
60
70
80
90
100
1
LO
σ(pp → t1t−1+X) [pb]
µ/m(t1)
√s=14 TeV; m(t1) = 200 GeV
→ theoretical uncertainty
∼> ± 100% at LO
⇒ must include NLO corrections
Michael Kramer Page 9 NRW Panomenologie-Treffen, Januar 2006
MSSM particle production at hadron colliders
MSSM sparticle pair production
− squarks & gluinos pp/pp → q¯q, gg, qg
− stops pp/pp → tt
− gauginos pp/pp → χ0χ0, χ±χ0, χ+χ−
− sleptons pp/pp → ll
− associated production pp/pp → qχ, gχ
Michael Kramer Page 10 NRW Panomenologie-Treffen, Januar 2006
Top-squark production
tL, tR mix to form mass states t1, t2 → potentially small t1 mass
LO parton reations
q + q → ti + ¯ti (i = 1, 2)
q
q
g
t1
¯t1
g
t
t t1
¯t1
σLO[qq] =α2
sπ
s
2
27β3 (β2 = 1 − 4m2/s)
c.f. top production: σLO[qq] ≈ α2
sπ
s1227 β
→ σtop/σstop ∼ 10 at the Tevatron
g + g → ti + ¯ti (i = 1, 2)
g
g
σLO[gg] =α2
sπ
s
[β
(5
48+
31m2
24s
)+
(2m2
3s+
m4
6s2
)log
1 − β
1 + β
]
⇒ no MSSM parameter dependence
Michael Kramer Page 11 NRW Panomenologie-Treffen, Januar 2006
Top-squark production
tL, tR mix to form mass states t1, t2 → potentially small t1 mass
LO parton reations
q + q → ti + ¯ti (i = 1, 2)
q
q
g
t1
¯t1
g
t
t t1
¯t1
σLO[qq] =α2
sπ
s
2
27β3 (β2 = 1 − 4m2/s)
c.f. top production: σLO[qq] ≈ α2
sπ
s1227 β
→ σtop/σstop ∼ 10 at the Tevatron
g + g → ti + ¯ti (i = 1, 2)
g
g
σLO[gg] =α2
sπ
s
[β
(5
48+
31m2
24s
)+
(2m2
3s+
m4
6s2
)log
1 − β
1 + β
]
⇒ no MSSM parameter dependence
Michael Kramer Page 11 NRW Panomenologie-Treffen, Januar 2006
Top-squark production
tL, tR mix to form mass states t1, t2 → potentially small t1 mass
LO parton reations
q + q → ti + ¯ti (i = 1, 2)
q
q
g
t1
¯t1
g
t
t t1
¯t1
σLO[qq] =α2
sπ
s
2
27β3 (β2 = 1 − 4m2/s)
c.f. top production: σLO[qq] ≈ α2
sπ
s1227 β
→ σtop/σstop ∼ 10 at the Tevatron
g + g → ti + ¯ti (i = 1, 2)
g
g
σLO[gg] =α2
sπ
s
[β
(5
48+
31m2
24s
)+
(2m2
3s+
m4
6s2
)log
1 − β
1 + β
]
⇒ no MSSM parameter dependence
Michael Kramer Page 11 NRW Panomenologie-Treffen, Januar 2006
Top-squark production
tL, tR mix to form mass states t1, t2 → potentially small t1 mass
LO parton reations
q + q → ti + ¯ti (i = 1, 2)
q
q
g
t1
¯t1
g
t
t t1
¯t1
σLO[qq] =α2
sπ
s
2
27β3 (β2 = 1 − 4m2/s)
c.f. top production: σLO[qq] ≈ α2
sπ
s1227 β
→ σtop/σstop ∼ 10 at the Tevatron
g + g → ti + ¯ti (i = 1, 2)
g
g
σLO[gg] =α2
sπ
s
[β
(5
48+
31m2
24s
)+
(2m2
3s+
m4
6s2
)log
1 − β
1 + β
]
⇒ no MSSM parameter dependence
Michael Kramer Page 11 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections
self energies: + · · ·
vertex corrections: + · · ·
box diagrams: + · · ·
+ · · ·
gluon emission: + · · ·
gluon-quark scattering: + · · ·
NLO cross section depends on
squark & gluino masses
stop mixing angle
→ dependence numerically small
NLO cross section near threshold β � 1:
σqq ≈α2
s(µ2)
m2
π
54β
3
×
(1 + 4παs(µ
2)
{−
1
48β+
2
3π2ln
2(8β
2)
−107
36π2ln(8β
2) −
2
3π2ln(8β
2) ln
(µ2
m2
)})
σgg ≈α2
s(µ2)
m2
7π
384β
×
(1 + 4παs(µ
2)
{11
336β+
3
2π2ln
2(8β
2)
−183
28π2ln(8β
2) −
2
3π2ln(8β
2) ln
(µ2
m2
)})
→ large NLO corrections in gg channel
Michael Kramer Page 12 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections
self energies: + · · ·
vertex corrections: + · · ·
box diagrams: + · · ·
+ · · ·
gluon emission: + · · ·
gluon-quark scattering: + · · ·
NLO cross section depends on
squark & gluino masses
stop mixing angle
→ dependence numerically small
NLO cross section near threshold β � 1:
σqq ≈α2
s(µ2)
m2
π
54β
3
×
(1 + 4παs(µ
2)
{−
1
48β+
2
3π2ln
2(8β
2)
−107
36π2ln(8β
2) −
2
3π2ln(8β
2) ln
(µ2
m2
)})
σgg ≈α2
s(µ2)
m2
7π
384β
×
(1 + 4παs(µ
2)
{11
336β+
3
2π2ln
2(8β
2)
−183
28π2ln(8β
2) −
2
3π2ln(8β
2) ln
(µ2
m2
)})
→ large NLO corrections in gg channel
Michael Kramer Page 12 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections
self energies: + · · ·
vertex corrections: + · · ·
box diagrams: + · · ·
+ · · ·
gluon emission: + · · ·
gluon-quark scattering: + · · ·
NLO cross section depends on
squark & gluino masses
stop mixing angle
→ dependence numerically small
NLO cross section near threshold β � 1:
σqq ≈α2
s(µ2)
m2
π
54β
3
×
(1 + 4παs(µ
2)
{−
1
48β+
2
3π2ln
2(8β
2)
−107
36π2ln(8β
2) −
2
3π2ln(8β
2) ln
(µ2
m2
)})
σgg ≈α2
s(µ2)
m2
7π
384β
×
(1 + 4παs(µ
2)
{11
336β+
3
2π2ln
2(8β
2)
−183
28π2ln(8β
2) −
2
3π2ln(8β
2) ln
(µ2
m2
)})
→ large NLO corrections in gg channel
Michael Kramer Page 12 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections: results
reduced scale dependence ∼<15%
(Beenakker, MK, Plehn, Spira, Zerwas)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1
σ(pp– → t1t
−1+X) [pb]
µ/m(t1)
LO
NLO
√s=2 TeV; m(t1) = 200 GeV
K-faktor K = σ(NLO)/σ(LO) ∼ 1 − 1.5
(Beenakker, MK, Plehn, Spira, Zerwas)
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
100 200 300
pp/pp– → t1t
−1+X
K = σ(NLO)/σ(LO)
m(t1)
Tevatron (√s=2 TeV)
LHC
Michael Kramer Page 13 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections: results
reduced scale dependence ∼<15%
(Beenakker, MK, Plehn, Spira, Zerwas)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1
σ(pp– → t1t
−1+X) [pb]
µ/m(t1)
LO
NLO
√s=2 TeV; m(t1) = 200 GeV
K-faktor K = σ(NLO)/σ(LO) ∼ 1 − 1.5
(Beenakker, MK, Plehn, Spira, Zerwas)
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
100 200 300
pp/pp– → t1t
−1+X
K = σ(NLO)/σ(LO)
m(t1)
Tevatron (√s=2 TeV)
LHC
Michael Kramer Page 13 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections: results
reduced scale dependence ∼<15%
(Beenakker, MK, Plehn, Spira, Zerwas)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1
σ(pp– → t1t
−1+X) [pb]
µ/m(t1)
LO
NLO
√s=2 TeV; m(t1) = 200 GeV
K-faktor K = σ(NLO)/σ(LO) ∼ 1 − 1.5
(Beenakker, MK, Plehn, Spira, Zerwas)
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
100 200 300
pp/pp– → t1t
−1+X
K = σ(NLO)/σ(LO)
m(t1)
Tevatron (√s=2 TeV)
LHC
Michael Kramer Page 13 NRW Panomenologie-Treffen, Januar 2006
Top-squark production: NLO cross sections
Tevatron
10-4
10-3
10-2
10-1
1
10
10 2
280 300 320 340 360 380 400 420
10-4
10-3
10-2
10-1
1
10
10 280 100 120 140 160 180 200
NLO
LO
:
: µ = m(t)µ = [ m(t)/2 , m(t) , 2m(t) ]µ = m(t)
m(t2) [GeV]
m(t1) [GeV]
pp– → t t
− + X
σtot[pb]
√S = 1.8 TeV
t1t−1
t2t−2
LHC
10-1
1
10
400 420 440 460 480 500 520 540 560 580 60010
-1
1
10
200 220 240 260 280 300 320 340 360 380 400
NLO
LO
:
: µ = m(t)µ = [ m(t)/2 , m(t) , 2m(t) ]µ = m(t)
m(t2) [GeV]
m(t1) [GeV]
pp → t t− + X
σtot[pb]
√S = 14 TeVt1t
−1
t2t−2
→ small dependence on SUSY-Parameters
Michael Kramer Page 14 NRW Panomenologie-Treffen, Januar 2006
Top-squark searches
• Top-squark search in e±e±+ ≥ 2j final startes (CDF, Phys. Rev. Lett. 83 (1999))
10-1
1
100 110 120 130 140 150
∆MLO
∆MNLO
σNLOσLO
: µ=[m(t)/2 , 2m(t)]: µ=[m(t)/2 , 2m(t)]
m(t1) [GeV]
σ(pp– → t1t
−1 + X) · BR(t1t
−1 → ee + ≥ 2j) [pb]
CDF 95% C.L. upper limit (prel.)
m(χ1o)=m(t1)/2
⇒ Mt1
>
110 ± 15 GeV LO
120 ± 5 GeV NLO
Michael Kramer Page 15 NRW Panomenologie-Treffen, Januar 2006
Current project: associated pp/pp → qχ, gχ production
semi-weak process, but χs are light in most models
pp/pp → gχ q
q
q χ
g
Beenakker, MK, Plehn, Spira, Zerwas; Berger, Klasen, Tait
pp/pp → qχ q
g
q χ
q
LO scale uncertainty O(100%) ⇒ need NLO calculation
Michael Kramer Page 16 NRW Panomenologie-Treffen, Januar 2006
Current project: associated pp/pp → qχ, gχ production
semi-weak process, but χs are light in most models
pp/pp → gχ q
q
q χ
g
Beenakker, MK, Plehn, Spira, Zerwas; Berger, Klasen, Tait
pp/pp → qχ q
g
q χ
q
LO scale uncertainty O(100%) ⇒ need NLO calculation
Michael Kramer Page 16 NRW Panomenologie-Treffen, Januar 2006
Current project: associated pp/pp → qχ, gχ production
semi-weak process, but χs are light in most models
pp/pp → gχ q
q
q χ
g
Beenakker, MK, Plehn, Spira, Zerwas; Berger, Klasen, Tait
pp/pp → qχ q
g
q χ
q
LO scale uncertainty O(100%) ⇒ need NLO calculation
Michael Kramer Page 16 NRW Panomenologie-Treffen, Januar 2006
Current project: associated pp/pp → qχ, gχ production
semi-weak process, but χs are light in most models
pp/pp → gχ q
q
q χ
g
Beenakker, MK, Plehn, Spira, Zerwas; Berger, Klasen, Tait
pp/pp → qχ q
g
q χ
q
LO scale uncertainty O(100%) ⇒ need NLO calculation
Michael Kramer Page 16 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections
+ · · ·
+ · · ·
q
g
q χ
q
g
+ · · ·
q
g
g
χ
q
q
+ · · ·
SUSY breaking in dimensional regularization
g, χ: 2 d.o.f.
g, γ, Z : (n − 2) d.o.f.
→ restauration through finite counter terms
double counting: gg → q¯q → qχq (if mq > mχ)
dσres
dM2= σ(gg → q¯q)
mqΓq/π
(M2 − m2q)2 + m2
qΓ2
q
BR(¯q → χq)
−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2
q)
→ resonance contributions to be subtracted
Michael Kramer Page 17 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections
+ · · ·
+ · · ·
q
g
q χ
q
g
+ · · ·
q
g
g
χ
q
q
+ · · ·
SUSY breaking in dimensional regularization
g, χ: 2 d.o.f.
g, γ, Z : (n − 2) d.o.f.
→ restauration through finite counter terms
double counting: gg → q¯q → qχq (if mq > mχ)
dσres
dM2= σ(gg → q¯q)
mqΓq/π
(M2 − m2q)2 + m2
qΓ2
q
BR(¯q → χq)
−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2
q)
→ resonance contributions to be subtracted
Michael Kramer Page 17 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections
+ · · ·
+ · · ·
q
g
q χ
q
g
+ · · ·
q
g
g
χ
q
q
+ · · ·
SUSY breaking in dimensional regularization
g, χ: 2 d.o.f.
g, γ, Z : (n − 2) d.o.f.
→ restauration through finite counter terms
double counting: gg → q¯q → qχq (if mq > mχ)
dσres
dM2= σ(gg → q¯q)
mqΓq/π
(M2 − m2q)2 + m2
qΓ2
q
BR(¯q → χq)
−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2
q)
→ resonance contributions to be subtracted
Michael Kramer Page 17 NRW Panomenologie-Treffen, Januar 2006
SUSY-QCD corrections: preliminary results
reduced scale dependence
Tevatron
Beenakker, MK, Plehn, Spira, Zerwas
preliminaryσ(pp
_ → q
~ χ2+X)[pb]
√s = 1.96 TeV
LO
NLO
CTEQ5M
Q/m0.1 0.2 0.5 1 2 5 10
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
10-1
1 10
LHC
Beenakker, MK, Plehn, Spira, Zerwas
preliminaryσ(pp→ q
~ χ2+X)[pb]
√s = 14 TeV
LO
NLO
CTEQ5M
Q/m0.1 0.2 0.5 1 2 5 10
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
10-1
1 10
Michael Kramer Page 18 NRW Panomenologie-Treffen, Januar 2006
Summary
NLO SUSY-QCD corrections for MSSM particle production at hadron colliders
→ public code PROSPINO (Beenakker, MK, Plehn, Spira, Zerwas)
10-2
10-1
1
10
10 2
10 3
100 150 200 250 300 350 400 450 500
⇑
⇑ ⇑ ⇑
⇑
⇑⇑
χ2oχ1
+
t1t−1
qq−
gg
νν−
χ2og
χ2oq
NLOLO
√S = 14 TeV
m [GeV]
σtot[pb]: pp → gg, qq−, t1t
−1, χ2
oχ1+, νν
−, χ2
og, χ2oq
Michael Kramer Page 19 NRW Panomenologie-Treffen, Januar 2006
Summary
NLO SUSY-QCD corrections for MSSM particle production at hadron colliders
→ public code PROSPINO (Beenakker, MK, Plehn, Spira, Zerwas)
10-2
10-1
1
10
10 2
10 3
100 150 200 250 300 350 400 450 500
⇑
⇑ ⇑ ⇑
⇑
⇑⇑
χ2oχ1
+
t1t−1
qq−
gg
νν−
χ2og
χ2oq
NLOLO
√S = 14 TeV
m [GeV]
σtot[pb]: pp → gg, qq−, t1t
−1, χ2
oχ1+, νν
−, χ2
og, χ2oq
Michael Kramer Page 19 NRW Panomenologie-Treffen, Januar 2006
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