SUSY-QCD corrections to MSSM Higgs boson production via gluon fusion

0.09 MB·English

by  M. Muhlleitner

SUSY-QCD corrections to MSSM Higgs boson
0
production via gluon fusion
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0
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n
a
J

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1 MargareteMühlleitner
∗

InstituteforTheoreticalPhysics,ITP(KIT)
]
h E-mail: [email protected]
p
- HeidiRzehak
p
InstituteforTheoreticalPhysics,ITP(KIT)
e
h E-mail: [email protected]
[

MichaelSpira
1
v PaulScherrerInstitute,PSI(VilligenPSI)
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E-mail: [email protected]
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In the MSSM scalar h,H productionis mediatedby heavyquarkand squarkloops. Thehigher
.
1
order QCD correctionshave been obtainedsome time ago and turned out to be large. The full
0
0 SUSY QCD correctionshave been obained recently including the full mass dependenceof the
1
loopparticles. We describeourcalculationandpresentfirstnumericalresults. We also address
:
v
thequestionofthepropertreatmentofthelargegluinomasslimit,i.e. theconsistentdecoupling
i
X ofheavygluinoeffects,andpresenttheeffectiveLagrangianfordecoupledgluinos.
r
a
RADCOR2009-9thInternationalSymposiumonRadiativeCorrections(ApplicationsofQuantumField
TheorytoPhenomenology),
October25-302009
Ascona,Switzerland
Speaker.
∗
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
SUSY-QCDcorrectionstoMSSMHiggsbosonproductionviagluonfusion MargareteMühlleitner
1. Introduction
One of the major goals at the LHC is the production of Higgs boson(s) [1]. In the Minimal
SupersymmetricExtensionoftheStandardModel(MSSM)twocomplexHiggsdoubletsareintro-
duced to give masses to up- and down-type fermions [2]. After electroweak symmetry breaking
there are five physcial Higgs states, two CP-even neutral Higgs bosons h,H, one neutral CP-odd
Higgs state A and two charged Higgs bosons H . At tree level, the Higgs sector can be param-
±
eterized by two independent parameters, the pseudoscalar Higgs boson mass M and the ratio of
A
thetwovacuumexpectation values(VEV)ofthetwocomplexHiggsdoublets, tanb =v /v . The
2 1
Higgscouplings toquarksandgaugebosons aremodifiedwithsinandcosofthemixinganglesa
andb withrespecttotheStandardModel(SM)couplings, wherea denotestheh,H mixingangle.
Thebottom(top)Yukawacouplingsareenhanced(suppressed)forlargevaluesoftanb ,sothattop
Yukawacouplings playadominant roleatsmallandmoderatevaluesoftanb .
AttheLHCandTevatronneutralHiggsbosonsarecopiouslyproducedviagluonfusiongg
→
h,H,A, which is mediated in the case of h,H by (s)top and (s)bottom loops [3]. The pure QCD
corrections to the (s)quark loops have been obtained including the full Higgs and (s)quark mass
dependences and increase the cross sections by 100% [4]. This result can be approximated
∼
byveryheavy top(s)quarks with 20 30% accuracy fortanb <5[5]. Inthislimitthenext-to-
∼ −
∼
leadingorder(NLO)QCD[6]andlaterthenext-to-next-to-leadingorder(NNLO)QCDcorrections
[7] have been obtained, the latter leading to a moderate increase of 20-30%. Finite top mass
effects at NNLO have been discussed in [8]. Finally, the estimate of the next-to-next-to-next-to-
leading order effects [9] indicates improved perturbative convergence. The full supersymmetric
(SUSY)QCDcorrections havebeenobtainedinthelimitofheavySUSYparticle masses[10]and
more recently including the full mass dependence [11]. The electroweak loop effects have been
calculated in [12]. In this article we will describe in Section 2 the calculation of the full SUSY-
QCD corrections in gluon fusion to h,H, and we will present for the first time numerical results
for the total cross section. In Section 3 we will discuss the consistent derivation of the effective
Lagrangian forthescalarHiggscouplings togluonsafterthegluinodecoupling.
2. GluonFusion
Atleadingorder(LO)thegluonfusionprocessesgg h/H aremediatedbyheavyquarkand
→
squark triangleloops, cf. Fig.1,thelattercontributing significantly forsquarkmasses <400GeV.
∼
The LO cross section in the narrow-width approximation can be obtained from the h/H gluonic
decaywidths,[3,13]
dLgg
s (pp h/H) = s h/Ht (2.1)
LO → 0 h/Hdt
h/H
p 2
s h/H = G (h/H gg)
0 8M3 LO →
h/H
2
s h/H = GFa s2(m R) (cid:229) gh/HAh/H(t )+(cid:229) gh/HAh/H(t ) , (2.2)
0 288√2p (cid:12) Q Q Q Q Q Q (cid:12)
(cid:12)Q Q (cid:12)
(cid:12) (cid:12)
(cid:12) e e e (cid:12)
(cid:12) e (cid:12)
(cid:12) (cid:12)
2
SUSY-QCDcorrectionstoMSSMHiggsbosonproductionviagluonfusion MargareteMühlleitner
˜
Q
g Q g Q˜ g
h,H h,H h,H
g g g
Figure1: Diagramscontributingtogg h,H atleadingorder.
→
where t =M2 /s with s being the squared hadronic c.m. energy and t =4m2 /M2 .
h/H h/H Q/Q˜ Q/Q˜ h/H
TheLOformfactorsaregivenby
3
Ah/H(t ) = t [1+(1 t )f(t )]
Q 2 −
3
Ah/H(t ) = t [1 t f(t )] (2.3)
Q˜ −4 −
1
arcsin2 t 1
√t ≥
f(t ) =  1 1+√1 t 2 .
−4 log1 √1−t −ip t <1
(cid:20) − − (cid:21)

Andthegluonluminosity atthefactorization scale m isdefinedas
F
dLgg 1dx
= g(x,m 2)g(t /x,m 2),
dt t x F F
Z
where g(x,m 2) denotes the gluon parton density of the proton. The NLOSUSY-QCDcorrections
F
consist of the virtual two-loop corrections, cf. Fig.2, and the real corrections due to the radiation
processesgg gh/H,gq qh/H andqq¯ gh/H,cf. Fig.3. Thefinalresultforthetotalhadronic
→ → →
g g g t˜,˜b
t˜,˜b g h/H t˜,˜b g˜ h/H g h/H
g g g
Figure2: SomegenericdiagramsforthevirtualNLOSUSY-QCDcorrectionstothesquarkcontributions
tothegluonicHiggscouplings.
crosssections canbesplitaccordingly intofiveparts,
a dLgg
s (pp h/H+X)=s h/H 1+Ch/H s t +D s h/H+D s h/H+D s h/H. (2.4)
→ 0 p h/Hdt gg gq qq¯
h/H
h i
The strong coupling constant is renormalized in the MS scheme, with the top quark and squark
contributionsdecoupledfromthescaledependence. Thequarkandsquarkmassesarerenormalized
on-shell. The parton densities are defined in the MS scheme with five active flavors, i.e. the top
quarkandthesquarksarenotincludedinthefactorizationscaledependence. Afterrenormalization
we are left with collinear divergences in the sum of the virtual and real corrections which are
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SUSY-QCDcorrectionstoMSSMHiggsbosonproductionviagluonfusion MargareteMühlleitner
absorbed intherenormalization ofthepartondensity functions, sothattheresultEq.(2.4)isfinite
and depends on the renormalization and factorization scales m and m , respectively. The natural
R F
scalechoicesturnouttobem =m M . Thenumericalresultsarepresentedforthemodified
R F h/H
∼
q
g
g q q
g
t˜,˜b t˜,˜b t˜,˜b
h,H h,H
g g q¯ h,H
Figure 3: Typical diagrams for the real NLO QCD corrections to the squark contributions to the gluon
fusionprocesses.
smalla scenario[14],definedbythefollowingchoicesofMSSMparameters[m =172.6GeV],
eff t
M = 800GeV tanb = 30
Q˜
M = 1000GeV m = 2TeV (2.5)
g˜
M = 500GeV A =A = 1.133TeV.
2 b t
−
Inthisscenario thesquark massesamountto
m = 679GeV m = 935GeV
t˜1 t˜2 (2.6)
m = 601GeV m = 961GeV.
b˜1 b˜2
Fig. 4displaysthegenuineSUSYQCDcorrectionsnormalizedtotheLObottomquarkformfactor,
140
C b (gg → H) Preliminary
120 SUSY
small a
eff
100 tgb = 30
real part
80
imaginary part
60 D approximation
b
40
20
0
-20
-40
100 150 200 250 300 350 400 450 500
M [GeV]
H
Figure 4: The genuine SUSY QCD corrections normalized to the LO bottom quark form factor. Real
corrections:red(lightgray),virtualcorrections:blue(darkgray),comparedtotheD approximation(dashed
b
lines). A hasbeenrenormalizedintheMSscheme.
b
i.e. Ah/H(t ) Ah/H(t )(1+Cb a s). The corrections can be sizeable, but can be described
b b → b b SUSY p
reasonably withtheusualD approximation [15],ifA isrenormalized intheMSscheme.
b b
3. Decoupling oftheGluinos
In this section we will address the limit of heavy quark, squark and gluino masses, where
in addition the gluinos are much heavier than the quarks and squarks. For the derivation of the
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SUSY-QCDcorrectionstoMSSMHiggsbosonproductionviagluonfusion MargareteMühlleitner
effective Lagrangian for the scalar Higgs couplings to gluons weanalyze the relation between the
quarkYukawacouplingl andtheHiggscouplingtosquarksl inthelimitoflargegluinomasses.
Q Q˜
Wedefinethesecouplings atleading orderinthecaseofvanishing mixing,
m m2 v
l =gH Q , l =2gH Q =kl 2 , withk =2 , (3.1)
Q Q v Q˜ Q v Q gH
Q
H
where g denotes the normalization factor ofthe MSSMHiggs couplings to quark pairs withre-
Q
specttotheSM.Inthefollowingwewillsketchhowthemodifiedrelationbetweenthesecouplings
forscalesbelowthegluino massM isderived. Fordetails, seeRef.[16]. Westartwiththeunbro-
g˜
kenrelationbetweentherunningMScouplingsofEq.(3.1)andthecorresponding renormalization
group equations (RGE)forscales above M . Ifthescales decrease below M thegluino decouples
g˜ g˜
from the RGEs leading to modified RGEs which are different for the two couplings l and kl 2
Q˜ Q
so that the two couplings deviate for scales below M . The proper matching at the gluino mass
g˜
scale yields a finite threshold contribution for the evolution from the gluino mass scale to smaller
scales,whilethelogarithmicstructureofthematchingrelationisgivenbythesolutionoftheRGEs
below M . Inorder todecouple consistently thegluino from theRGEforgluino massscales large
g˜
comparedtothechosenrenormalizationscale,amomentumsubstractionofthegluinocontribution
for vanishing momentum transfer hastobe performed [17]. Werefer thereader to[16]for details
and giveheredirectly theresult forthe modifiedrelation between thequark Yukawacoupling and
theeffectiveHiggscoupling tosquarks takingintoaccountthepropergluinodecoupling:
2gH m2Q =l¯ (m ) 1+C a s logMg2˜ +3logm2Q˜ +1 , (3.2)
Q v Q˜,MO Q˜ F p m2 2 m2 2
( Q˜ Q !)
wherem isthepolemassandMOdenotesthemomentumsubstracted coupling,whichistakenat
Q
the squark massscale, which is the proper scale choice of the effective Higgs coupling tosquarks
andwhichisrelevantforanadditional largegapbetweenthequarkandsquarkmasses.
Takingintoaccounttheradiativecorrectionstotherelationbetweentheeffectivecouplingsaf-
terdecoupling thegluinosleadstothefollowingeffectiveLagrangianinthelimitofheavysquarks
andquarks,
H
Leff = 1a2sp Gamn Gamn Hv (cid:229) gHQ 1+141ap s +(cid:229) g4Q˜ 1+CSQCDap s +O(a s2) , (3.3)
(Q (cid:20) (cid:21) Q˜ h i )
wheregH =vl¯ (m )/m2. ThecofficientC isgivenby
Q˜ Q˜,MO Q˜ Q˜ SQCD
37
C = . (3.4)
SQCD
6
Itiswell-definedinthelimitoflargegluinomassesandthusfulfillstheconstraintoftheAppelquist–
Carazzone decoupling theorem[18].
4. Conclusions
We have presented first results for the NLO SUSY QCD corrections to gluon fusion into
CP-even MSSM Higgs bosons, including the full mass dependence of the loop particles. The
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SUSY-QCDcorrectionstoMSSMHiggsbosonproductionviagluonfusion MargareteMühlleitner
genuine SUSY-QCD corrections can be sizeable. We furthermore demonstrated, that the gluino
contributions canbedecoupled inthelargeM limitinaccordance withtheAppelquist-Carazzone
g˜
theorem.
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