Michael Kramer¤ - RWTH Aachen Universitymkraemer/susy_qcd.pdf · The hierarchy problem: why is...
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Frontiers in QCD, DESY Hamburg, September 2006
SUSY-particle and MSSM Higgs production at the LHC
Michael Kramer
(RWTH Aachen)
We want to discover and explore models of new physics at the LHC
→ determine masses, quantum numbers, couplings by comparing theory and data
→ need accurate theoretical predictions including higher-order corrections
Michael Kramer Page 1 Frontiers in QCD, September 2006
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The hierarchy problem: why is MHiggs � MPlanck?
Quantum corrections to the Higgs mass have quadratic UV divergencies
� ��
� � ��
→ δm2H ∼ α
π(Λ2 + m2
F )
The cutoff Λ represents the scale up to which the Standard Model remains valid.
→ need Λ of O(1 TeV) to avoid unnaturally large corrections
Most popular new physics models
– Supersymmetry
– Dynamical EWSB
– Extra dimensions
– Little Higgs models
Quantum corrections due to superparticles cancel the quadratic UV divergences
� ���
� � ��
→ δm2H ∼ −α
π(Λ2 + m2
F )
δm2H ∼ α
π(m2
F − m2F ) → no fine-tuning if m ∼< O(1 TeV)
Michael Kramer Page 2 Frontiers in QCD, September 2006
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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 3 Frontiers in QCD, September 2006
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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 4 Frontiers in QCD, September 2006
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Outline
SUSY-particle production at the LHC
MSSM Higgs boson production at the LHC
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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 QCDprocesses, e.g.
g
g
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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 7 Frontiers in QCD, September 2006
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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 8 Frontiers in QCD, September 2006
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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 9 Frontiers in QCD, September 2006
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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
References of LO calculations:
Kane, Leveille, 1982; Harrison, Llewellyn Smith, 1983; Reya, Roy, 1985; Dawson, Eichten, Quigg, 1985; Baer, Tata, 1985,. . .
Michael Kramer Page 10 Frontiers in QCD, September 2006
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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
References of LO calculations:
Kane, Leveille, 1982; Harrison, Llewellyn Smith, 1983; Reya, Roy, 1985; Dawson, Eichten, Quigg, 1985; Baer, Tata, 1985,. . .
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Top-squark production
tL, tR mix to form mass states t1, t2 → potentially small t1 mass
LO cross section
q
q
g
t1
¯t1
g
g
σLO[qq+gg] =α2
sπ
s
[2
27β3 + β
(5
48+
31m2
24s
)+
(2m2
3s+
m4
6s2
)log
1 − β
1 + β
](β2=1−4m2/s)
⇒ no MSSM parameter dependence
LO scale dependence
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 12 Frontiers in QCD, September 2006
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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 13 Frontiers in QCD, September 2006
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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 14 Frontiers in QCD, September 2006
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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 Frontiers in QCD, September 2006
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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 Frontiers in QCD, September 2006
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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
qΓ2q
BR(¯q → χq)
−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2
q)
→ resonance contributions to be subtracted
Michael Kramer Page 17 Frontiers in QCD, September 2006
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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 Frontiers in QCD, September 2006
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MSSM particle production at the LHC
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
References: Beenakker, Hopker, Spira, Zerwas, 1995, 1997; Beenakker, MK, Plehn, Spira, Zerwas, 1998; Baer, Hall, Reno, 1998; Beenakker,
Klasen, MK, Plehn, Spira, Zerwas, 1999; Beenakker, MK, Plehn, Spira, Zerwas, 2000; Berger, Klasen, Tait, 1999-2002; Beenakker, MK, Plehn,
Spira, Zerwas, 2006
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SUSY with R-Parity violation
SUSY models without R-parity allow for resonant single sparticle production
Example: resonant slepton production:
L = λ′ijk
(dRk
dLjνLi
− dRkuLj
lLi
)
→ σLO =λ′2π
12sδ(1 − τ) with τ =
M2
sq
q
S
NLO (SUSY-)QCD corrections sizeable (Dreiner, Grab, MK, Trenkel 2006)
m0 m1/2 A0 tanβ sgn(µ) m( dR) m( dL) m(g) m(νe)
A0
[TeV]ν ~m0.5 1 1.5 2
K-F
acto
r
1.1
1.2
1.3
1.4
1.5
1.6
QCD
QCD + SUSY (A = 0TeV’)
QCD + SUSY (A = 1TeV
QCD + SUSY (A = -1TeV)
SPS 1a’
[TeV]ν ~m0.5 1 1.5 2
K-F
acto
r
1.1
1.2
1.3
1.4
1.5
1.6
QCD
QCD + SUSY (A = 0TeV)
QCD +SUSY (A = 1TeV)
QCD + SUSY (A = -1TeV)
SPS 2
(TeV)ν ~m0.5 1 1.5 2
K-F
acto
r
1.1
1.2
1.3
1.4
1.5
1.6
QCD
QCD + SUSY (A = 0TeV)
QCD + SUSY (A = 1TeV)
QCD + SUSY (A = -1TeV)
SPS 3
λ′
11i = 0.01√
S = 14A
K
∼ 500− 600 ∼ 150∼ 800 ∼ 800 − 900
KK
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SUSY Searches
Hans-Peter Nilles, Physics Reports 110, 1984:
“Experiments within the next 5-10 years will enable us to decide whether su-
persymmetry, as a solution of the naturalness problem of the weak interaction
is a myth or reality”
Hans-Peter Nilles, private communication, quoted from hep-ex/9907042
“One should not give up yet. . . ”
“Perhaps a correct statement is:
it will always take 5-10 years to discover SUSY.”
Michael Kramer Page 21 Frontiers in QCD, September 2006
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A crucial test of the MSSM: the light Higgs
MSSM Higgs sector: two Higgs doublets to give mass to up- and down-quarks
→ 5 physical states: h, H , A, H±
The MSSM Higgs sector is determined by tan β = v2/v1 and MA.
The couplings in the Higgs potential and the gauge couplings are related by super-
symmetry. At tree level one finds Mh ≤ MZ . This relation is modified by radiative
corrections so that
MH ∼< 130 GeV (in the MSSM)
The existence of a light Higgs boson is a generic prediction of SUSY models.
Michael Kramer Page 22 Frontiers in QCD, September 2006
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A crucial test of the MSSM: the light Higgs
One of the SUSY Higgs bosons will be seen at the LHC
ATLAS
LEP 2000
ATLAS
mA (GeV)
tan
β
1
2
3
4
56789
10
20
30
40
50
50 100 150 200 250 300 350 400 450 500
0h 0H A
0 +-H
0h 0H A
0 +-H
0h 0H A
00h H
+-
0h H+-
0h only
0 0Hh
ATLAS - 300 fbmaximal mixing
-1
LEP excluded
but it may look like the SM Higgs. . .
Michael Kramer Page 23 Frontiers in QCD, September 2006
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Higgs production in the MSSM
Higgs production in the SM through
top-quark loops
Ht
g
g
ttH production
g
g
t
t
H
∝ m2top×dPS(ttH)
Michael Kramer Page 24 Frontiers in QCD, September 2006
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Higgs production in the MSSM
Higgs production in the MSSM through
t, b-quark loops + squark loops
Ht, b
g
g
+ Ht
g
g
ttH production and bbH production
g
g
t
t
H
g
g
b
b
H
∝ m2top×dPS(ttH) ∝ m2
b tan β ×dPS(bbH)
Michael Kramer Page 25 Frontiers in QCD, September 2006
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Higgs production in the MSSM
Cross section predictions: light and heavy scalar h and H
[Spira]
10-3
10-2
10-1
1
10
10 2
10 3
10 4
102
gg→H (SM)
gg→H
Hbb–
Htt–
Hqq
HZ HW
tan β = 30Maximal mixing
Ù H
Ù
h
mh/H (GeV)
Cro
ss-s
ectio
n (p
b)
Michael Kramer Page 26 Frontiers in QCD, September 2006
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Higgs production in the MSSM: “gluophobic Higgs”
Ht, b
g
g
+ Ht
g
g
→ interference effects
“Gluophobic Higgs scenario” [Djouadi; Carena et al.; Harlander, Steinhauser; Muhlleitner, Spira]
[Harlander, Steinhauser]
0
20
40
60
80
100
300 400 500 600 700 800 900
σ(pp→h+X) [pb]
m [GeV]t2~
SUSY, NNLO’SUSY, NLOSUSY, LOSM, NNLO’SM, NLOSM, LO
LHC
MSSM parameters
mt1= 200 GeV
mg = 1 TeV
tan β = 10
α = 0
θt = π/4
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Higgs production in the MSSM: associated bbh production
Associated QQ-Higgs production
P
P
g
g
Q
Q′
φ is crucial as a
− Higgs discovery channel
− to measure the heavy-quark–Higgs Yukawa couplings
In the MSSM one has
pp → QQ + h, H, A pp → QQ′ + H±
Relative importance depends on MSSM parameters tan β and MA, eg.:
gMSSMbbh = − sin α
cos βgSM
bbH
tan β�1−→ tan β gSM
bbH (Mh'MA'MZ)
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QQH production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2
s ln(MH/MQ) ∼ α2s
Summation of ln(MH/MQ) terms by using heavy quark PDFs
[Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,. . . ]
MQ � MH-
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Inclusive bbH production: two calculational schemes
4-flavour scheme 5-flavour scheme
+ exact g → bb splitting & mass effects
− no summation of ln(MH/Mb) terms
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb splitting
Comparison at LO
→ strong scale dependence
→ σ(bb → H) � σ(gg → bbH) at µ = MH
→ discrepancy reduced at µF = MH/4
[Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
→ Choice of scale? Impact of HO corrections?
→ comparison at the NLO/NNLO level
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NLO corrections to 4-flavour scheme: gg → bbH
NLO Feynman graphs:
g
g
Q
Q
H
g
g
Q
Q
H + · · ·
Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas; Dawson, Jackson, Orr, Reina, Wackeroth
4-flavour scheme: scale dependence at the LHC (SM Higgs):
[Dittmaier, MK, Spira]
σ(pp → bb_
H + X) [fb]√s = 14 TeVMH = 120 GeVµ0 = mb + MH/2
pTb and pTb_ > 20 GeV
tot
NLO
LO
NLO
LO
µ/µ0
0.1 0.2 0.5 1 2 5 10
10
20
50
100
200
500
1000
2000
5000
10
10 2
10 3
10-1
1 10
Michael Kramer Page 31 Frontiers in QCD, September 2006
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NNLO corrections to 5-flavour scheme: bb → h
Renormalization and factorization scale dependence [Harlander, Kilgore]
0
0.2
0.4
0.6
0.8
1
1.2
10-1
1 10
σ(pp → (bb )H+X) [pb]
µR/MH
LHCMH=120 GeV
µF = MH/4
LONLONNLO
0
0.2
0.4
0.6
0.8
1
1.2
10-1
1 10
σ(pp → (bb )H+X) [pb]
µF/MH
LHCMH=120 GeV
µR=MH
LONLONNLO
Michael Kramer Page 32 Frontiers in QCD, September 2006
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Inclusive Higgs plus bottom-quark production
Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC)
[Harlander, Kilgore; Dittmaier, MK, Spira]
σ(pp → bb_
h + X) [fb]
√s = 14 TeV
µ = (2mb + Mh)/4
Mh [GeV]
bb_
→ h (NNLO)
gg → bb_
h (NLO)10
10 2
10 3
100 150 200 250 300 350 400
– 4-flavour calculation includes Higgs radiation off top loops ≈ −10%
– calculations employ different PDF fits
→ consistent comparison should reveal even better agreement
Michael Kramer Page 33 Frontiers in QCD, September 2006
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Associated Heavy Quark Higgs Production: Status
– gg → h/H + QQ: QCD corrections, full SUSY-QCD in progress[Peng, Wen-Gan, Hong-Sheng, Ren-You, Liang, Yi; Dittmaier, Hafliger, MK, Spira, in preparation]
– gg → A + QQ: QCD corrections [Dittmaier, MK, Spira, preliminary]
– gg → H± + QQ′: (SUSY)-QCD corrections[Peng, Wen-Gan, Ren-You, Yi, Liang, Lei; Dittmaier, Spira, MK, Walcher, in preparation]
– bb → h/H/A: NNLO QCD corrections [Harlander, Kilgore]
MSSM EW corrections [Dittmaier, MK, Muck, in preparation]
– bg → h/H/A + b, bg → H± + t: NLO (SUSY-)QCD corrections[Plehn; Zhu; Campbell, Ellis, Maltoni, Willenbrock; Berger, Han, Jiang, Plehn; Alves, Plehn,. . . ]
⇒ Lots of activity and ongoing calculations. . .
Michael Kramer Page 34 Frontiers in QCD, September 2006
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Summary
Production cross sections (and decay rates) for MSSM SUSY particles and Higgs
bosons are (or will soon be) known at NLO (SUSY-)QCD
→ theoretical uncertainty reduced to ≈ 15%
But still lots of work to be done . . .
– only few results exist for other SUSY models (e.g. RPV SUSY)
– electroweak corrections are only partially known
– many backgrounds (multi-parton processes) are only know at LO
Michael Kramer Page 35 Frontiers in QCD, September 2006