Higgs boson decays in the Complex MSSM

0.33 MB·

by  K. E. Williams

Higgs boson decays in the Complex MSSM
Karina Williams1 a and Georg Weiglein1 b
8 IPPP, Universityof Durham,Durham DH13LE, UK
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0
2
Abstract. The analysis of the Higgs search results at LEP showed that a part of the MSSM
n
parameter space with non-zero complex phases could not be excluded, where the lightest neutral
a
J Higgs boson, h1, has a mass of only about 45 GeV and the second lightest neutral Higgs boson,
h2, has a sizable branching fraction into a pair of h1 states. Full one-loop results for the Higgs
7 cascade decayh2 →h1h1 arepresentedand combinedwith two-loop Higgspropagator corrections
1
takenfromtheprogramFeynHiggs.Usingtheimprovedtheoreticalpredictiontoanalysethelimits

on topological cross sections obtained at LEP, the existence of an unexcluded region at low Higgs
]
h massisconfirmed.Theeffectofthegenuinevertexcorrections onthesizeandshapeofthisregion
p is discussed.
-
p
PACS. 12.60.Jv Supersymmetricmodels – 14.80.Cp Non-standard-modelHiggs bosons
e
h
[
1 Introduction one-loop results are combined with existing higher-
2
order corrections in the FD approach and will be in-
v
1 Initsgeneralform,theMSSMcontainscomplexphases cludedinthepubliccodeFeynHiggs[5–8].Asanappli-
3 which drive CP-violation. The results of the Higgs- cationofourimprovedresult,weanalysethe coverage
3 boson searches at LEP were analysed in a series of of the LEP exclusion limits on the topological cross
5 MSSM benchmark scenarios [1,2], including one ex- sections for the various Higgs-boson production and
0. plicitly chosen to investigate the effects of these CP- decay cross sections within the Mh1–tanβ parameter
1 violatingphases,calledtheCPXscenario[2].Thissce- plane.
7 nario produced an unexcluded region for light h1 and
0 relativelysmallvaluesoftanβ(theratioofthevacuum
v: expectation values of the two Higgs doublets), so that 2 Calculation of Higgs-boson cascade
i no firm lower bound on the mass of the lightest Higgs decays and decays into SM fermions
X
bosonoftheMSSMcouldbeset[3].Throughoutmuch
r of this region of CPX parameter space, the process
a
h2 → h1h1 dominates the h2 decay width. Therefore, We calculated the full 1PI (one-particle irreducible)
inordertoreliablydeterminewhichparameterregions one-loop vertex contributions to the processes ha →
of the MSSM are unexcluded by the Higgs searches hbhc, taking into account all sectors of the MSSM
so far and which regions will be accessible by Higgs and the complete dependence on the complex phases
searchesin the future, precisepredictions for this pro- of the supersymmetric parameters.These calculations
cess are indispensable. (which make use of the programs FeynArts [9] and
However, the genuine vertex corrections (as op- FormCalc [10]) have been described in more detail in
posed to propagator corrections) to the process h2 → Ref. [4].
h1h1 in the MSSM with complex parameters have so We havederivedalsocomplete one-loopresultsfor
farbeenunavailablewithintheFeynman-diagrammatic the processes ha →ff¯(including SM-type QED and,
(FD) approach.These vertex correctionsareexpected whereappropriate,QCDcorrections)forarbitraryval-
to be sizable as they contain terms depending on the ues of all complex phases of the supersymmetric pa-
fourth power of the top mass. We have obtained com- rameters, as these decays are important over large
plete one-loop results within the FD approach for the parts of the cMSSM parameter space. The partial de-
decays h →h h , including all genuine one-loop ver- caywidthsfortheotherHiggs-bosondecaymodeshave
a b c
tex corrections, in the MSSM with complex phases been taken from the program FeynHiggs.
(cMSSM) [4]. We have furthermore calculated com- In our numerical analysis below, we will compare
plete one-loop results for the decays of neutral Higgs our full result with the contribution from just the t,t˜
bosonsintoSMfermionsinthecMSSM[4].Thesenew sectorintheapproximationwherethegaugecouplings
are neglected and the diagrams are evaluated at zero
a Email: [email protected] externalmomenta,whichwecallthe‘YukawaApprox-
b Email: [email protected] imation’.
Colliders - Higgs Phenomenology Contributed Talk
FortherenormalisationoftheHiggsfieldsitiscon- Mh1=30 GeV
venient to use a DR scheme as in Ref. [5]. Therefore, 0.25
Full
it is necessary to include finite wave-function normal- f,sf
t,st,b,sb
isation factors (Z-factors) to ensure that S-matrix el- 0.2 Yukawa Approx
Tree
ements involving external Higgs fields have the cor- V
e
recton-shellproperties.The form ofthese Z-factorsis h)/G1 0.15
giveninRef. [4].InthecalculationoftheZ-factors,we h+1
incorporate higher-order contributions obtained from →h2 0.1
Γ(
the neutral Higgs-boson self-energies of the program
FeynHiggs. In the analysis below, we will restrict to 0.05
those higher-order contributions for which the phase
0
dependenceatthetwo-loopisexplicitlyknown[6],i.e. 4 5 6 7 8 9 10 15
wedonotincludecontributionsthathavebeenextrap- tanβ
olated from results obtained for the real MSSM.
Fig. 1. Γ(h2 → h1h1) as function of tanβ (MH± is ad-
justed to ensure Mh1 = 30 GeV), for various approxima-
tions.
3 Implementation of exclusion bounds
from the LEP Higgs searches
Inournumericalanalysisbelowweanalysetheimpact Colour: Br(h2→h1+h1)
of our new result on the LEP exclusion bounds in the 40 1
cMSSM. This is done by comparing the cMSSM pre- 30
dictions with the topologicalcrosssectionlimits given 20 0.8
inRefs. [3,11].Thisprocedureisdescribedinmorede-
0.6
tcahialninneRleisf.p[r4e]dainctdedRteof.h[1a2v]e.tIhteinhvioglhveesstcshteactkisitnigcawlhseicnh- βtan 1 7890
6 0.4
sitivity and then comparing the theoretical prediction 5
inthat channelonly with the topologicalcrosssection 4 0.2
3
limit determined at LEP. This ensures a correct sta-
tistical interpretation of the overall exclusion limit at 2 0
the 95% C.L.. However,it should be noted that, since 20 40 60 80 100 120
only one channel can be used at a time, this method Mh1
leads to poorer coverage in areas where two or more Fig. 2. The branching ratio BR(h2 →h1h1) in the Mh1–
tanβ plane of theCPX scenario.
channels have a similar statisticalsensitivity than, for
example,thededicatedanalysescarriedoutinRef. [3].
4.1 Results for the h2 →h1h1 decay width
4 Numerical results
In our numerical analysis we use the parameter val- Fig. 1 shows the relative effect of different contribu-
ues of the CPX benchmark scenario [2], adapted to tions to the h2 →h1h1 decay width in an area of the
the latest experimental central value of the top-quark cMSSM parameter space that is particularly relevant
mass [13] and using an on-shell value for the abso- to the unexcluded region in the LEP Higgs searches.
lute value of the trilinear couplings A and A that is The decay width is plotted against tanβ whilst ad-
t b
somewhat shifted compared to the DR value specified justing MH± such that Mh1 = 30 GeV. All the re-
in Ref. [2]. Specifically, if not indicated differently, we sults plotted include the higher-order corrected wave-
use the parameters function normalisation factors as described in Sect. 3.
The results differ only in the genuine contributions
MSUSY =500 GeV, |At|=|Ab|=900 GeV, to the h2h1h1 vertex. One can see that the full re-
µ=2000 GeV, mg˜ ≡|M3|=1000 GeV, sult(denotedas‘Full’)differsdrasticallyfromthecase
whereonlywave-functionnormalisationfactorsbutno
mt =170.9 GeV, M2 =200 GeV. (1) genuine one-loop vertex contributions are taken into
The lowest-order Higgs sector parameters tanβ and account (‘Tree’). The Yukawa approximation agrees
MH± are varied, with MH± < 1000. The complex muchbetterwiththefullresultandexplainsthequal-
phasesofthe trilinearcouplingsA ,A andthegluino itativebehaviourofthefullresult—inparticular,the
t b
mass parameter M3 are set to region where Γ(h2 → h1h1) ≈ 0 for tanβ ≈ 4.3 is
due to the fact that the Yukawa vertex corrections to
π π π
ϕAt = 2, ϕAb = 2, ϕg˜ = 2. (2) tUhseinmgatthreixfuelllemcoennttricbhuatniognefsriogmn wthheent,t˜t,abn,˜bβsiesctvoarri(e‘dt,.
In Eq. (1) MSUSY denotes the diagonal soft SUSY- st, b, sb’) or using all three generations of fermions
breaking parameters in the sfermion mass matrices, andsfermions(‘f,sf’)yieldsapredictionthatdeviates
which are chosen to be equal to each other. from the full result by up to 15%.
K Williams, G Weiglein Higgs boson decays in the Complex MSSM
40 parameter space. As explained in Sect. 4, this infor-
30 mation is needed for a statistical interpretation of the
topological cross section limits obtained at LEP. One
20
canseeinthefigurethatthechannelse+e− →h2Z →
h1h1Z → b¯bb¯bZ and e+e− → h2h1 → h1h1h1 →
10 b¯bb¯bb¯b have the highest search sensitivity in a region
βan 89 withsmallM andsmallandmoderatevaluesoftanβ
t 67 (the region aht1tanβ ≈ 4 where the channel e+e− →
5 (h2Z) → (b¯bZ) has the highest search sensitivity cor-
4
responds to the drop in the h2 → h1h1 branching ra-
3 tio observed in Fig. 2). For small M and somewhat
h1
2 higher tanβ the channel e+e− →(h2h1)→(b¯bb¯b) has
the highest search sensitivity. It should be noted that
20 40 60 80 100 120
Mh1 all channels involving the decay of the h2 boson in
the regionofsmallM arestronglyinfluenced by the
h1
Γ(h2 →h1h1) decay width, either directly in the case
Fig. 3. The channels predicted to have the highest sta-
of the channels involving the Higgs cascade decay, or
tistical sensitivity for setting an exclusion limit using the
indirectly through the branching ratio of the h2. The
results from the LEP Higgs searches in theCPX scenario.
The colour codings are: red = (h1Z) → (b¯bZ), blue = pcoairnacmideetserwrietghiotnhewrheegrieonΓ(ohf2th→e Ch1PhX1)sicsenimarpioortthanatt
(h2Z) → (b¯bZ), white = (h2Z) → (h1h1Z) → (b¯bb¯bZ),
could not be excluded at the 95% C.L. in the analysis
cyan = (h2h1) → (b¯bb¯b), yellow = (h2h1) → (h1h1h1) →
(b¯bb¯bb¯b), black = otherchannels. of the four LEP collaborations [3].
In Fig. 4 we have compared our new theoretical
40 predictions with the topological cross section limits
30 obtained at LEP for the channels in Fig. 3. We find
anunexcludedregionatM ≈45 GeVandmoderate
20 tanβ where channels involhv1ing the decay h2 → h1h1
play an important role. Thus, our analysis, based on
10 the most up-to-date theory prediction for the h2 →
βan 89 h1h1 channel, confirms the ‘hole’ in the LEP cover-
t 7 age observed in Ref. [3] (see in particular Fig. 19 of
6
5 Ref. [3]).
4
Itshould be noted, onthe other hand,that the re-
3
sultsshowninFig. 4differinseveralrespectsfromthe
2 results presented in Ref. [3]. As discussed above, our
analysishaslessstatisticalsensitivitynearbordersbe-
20 40 60 80 100 120
Mh1 tween areas where different search topologies are pre-
dicted to have the highest exclusion power than the
benchmarkstudiesofRef. [3].Afurtherdifference(be-
Fig. 4. The parameter region in the CPX scenario ex-
sides the improvedtheoreticalprediction) is the input
cluded at the 95% C.L. by the topological cross section
value of the top-quark mass. While we are using the
limits obtained at LEP [3]. The colour codings are: green
latest experimental central value of m = 170.9 [13],
= LEP excluded, white = LEP allowed, grey = theoreti- t
most of the analysis of Ref. [3] was done for m =
cally inaccessible. t
174.3. We have explicitly checked that (as expected)
the unexcluded region is significantly increased if we
In Figs. 2,3 and4 the M –tanβ parameterspace use mt = 174.3 instead. It should also be noted that
h1
the shape and size of the unexcluded region depends
oftheCPXscenarioisanalysed.Fig. 2showsthebranch-
ing ratio of the Higgs cascade decay, BR(h2 →h1h1). sensitively on the value of At used.
Over a large part of the parameter space where the InFig. 5wefocusontheparameterregionatM ≈
h1
decay h2 → h1h1 is kinematically possible it is actu- 45 GeV andmoderate tanβ.While plot(a) showsthe
ally the dominant decay channel. The branching ratio full result (i.e., it is a detailed view of Fig. 4), in plot
is particularly large for low and moderate values of (b) the genuine h2 → h1h1 vertex corrections are ap-
tanβ. In the region where tanβ ≈ 4–5 the Yukawa proximated by the contributions from fermions and
contribution to the matrix element for the h2 →h1h1 sfermions only, and in plot (c) the Yukawa Approxi-
decay changes sign and causes a sharp drop in the mation has been used for the genuine h2 →h1h1 ver-
h2 → h1h1 branching ratio, as was already observed tex corrections. In all three plots the wave function
inFig. 1.Asimilarbehaviouroccursalsointheregion normalisation factors and all other decay widths are
of tanβ ≈35. the same.While allthree graphsshowthe unexcluded
Fig. 3 indicates which channelhas the higheststa- region to be in a similar position in parameter space,
tistical sensitivity and therefore which channel will be the shape of this unexcluded regionchangesquite sig-
usedtosetanexclusionlimitindifferentregionsofthe nificantly.
Colliders - Higgs Phenomenology Contributed Talk
Full Fermion, sfermion Yukawa Approximation
10 10 10
9 9 9
8 8 8
7 7 7
βtan 6 βtan 6 βtan 6
5 5 5
4 4 4
15 20 25 30 35 40 45 50 55 15 20 25 30 35 40 45 50 55 15 20 25 30 35 40 45 50 55
Mh1 Mh1 Mh1
(a) (b) (c)
Fig.5.AcloserlookattheLEPcoverageforMh1 ≈45 GeVandmoderatetanβ.Plot(a)showsthefullresult(detailed
view of plot (b) of Fig. 3). Plot (b) shows the result for the case where only contributions from SM fermions and their
superpartners are taken into account in the genuine vertex corrections. Plot (c) shows the result where the Yukawa
Approximation hasbeen used for thegenuinevertexcorrections. Thecolour codings are: green = LEPexcluded,white
= LEP allowed.
5 Conclusions 4. K.E.WilliamsandG.Weiglein,arXiv:0710.5320[hep-
ph].
Wehaveshownthatournewresultforthedecaywidth 5. M. Frank, T. Hahn, S. Heinemeyer, W. Hollik,
h2 →h1h1, which includes the complete one-loopver- H. Rzehak and G. Weiglein, JHEP 02 (2007) 047,
texcorrections,drasticallyimprovesonresultsobtained hep-ph/0611326.
6. S. Heinemeyer, W. Hollik, H. Rzehak and G. Wei-
usingpropagatorcorrectionsalone.Wehavecombined
glein,Phys. Lett. B 652(2007) 300,arXiv:0705.0746
thiswithnewresultsforneutralHiggsdecaysintotwo
[hep-ph].
fermions in order to re-analyse the CPX parameter
7. S.Heinemeyer,W.HollikandG.Weiglein,Phys.Rev.
spaceusingthelimits ontopologicalcrosssectionsob-
D 58 (1998) 091701, hep-ph/9803277; Phys. Lett. B
tainedfromtheLEPHiggssearches.Wefindthatover
440 (1998) 296, hep-ph/9807423; Eur. Phys. J. C 9
a large part of the parameter space where the decay
(1999) 343. hep-ph/9812472;
h2 →h1h1iskinematicallypossible,itisthedominant M.Frank,S.Heinemeyer,W.HollikandG.Weiglein,
decay channel. We confirm that the parameter space
hep-ph/0212037,intheproceedingsofSUSY02,July
at low Higgs mass can not be completely excluded by
2002, DESY,Hamburg, Germany;
theLEPHiggssearches.Wefurthermoreshowthatthe G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich
sizeandshapeoftheunexcludedregionissignificantly and G. Weiglein, Eur. Phys. J. C 28 (2003) 133,
modified if approximations to the full result are used, hep-ph/0212020.
emphasizing the relevance of the full one-loop result 8. S. Heinemeyer, W. Hollik and G. Weiglein, Com-
fortheh2 →h1h1 decaywidthinthecomplexMSSM. put.Phys.Commun.124(2000)76,hep-ph/9812320;
hep-ph/0002213; see www.feynhiggs.de .
9. J.Ku¨blbeck,M.B¨ohmandA.Denner,Comput.Phys.
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T. Hahn, Comput. Phys. Commun. 140 (2001) 418,
hep-ph/0012260;
We are grateful to P. Bechtle, O. Brein, T. Hahn,
T. Hahn and C. Schappacher, Comput. Phys. Com-
S. Heinemeyer, W. Hollik, S. Palmer, H. Rzehak and
mun. 143 (2002) 54, hep-ph/0105349.
D.St¨ockingerformanyhelpfuldiscussions.Worksup-
The program and the user’s guide are available via
ported in part by the European Community’s Marie-
www.feynarts.de .
CurieResearchTrainingNetworkundercontractMRTN-
10. T.HahnandM.P´erez-Victoria,Comput.Phys.Com-
CT-2006-035505‘Tools and PrecisionCalculations for
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Physics Discoveries at Colliders’.
11. P. Bechtle, privatecommunication.
12. P. Bechtle et al., in preparation.
13. Tevatron Electroweak Working Group,
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