Polarisation studies in H-t production

0.23 MB·English

by  R. M. Godbole

Polarisation studies in H−t production
R. M. Godbole
3
CenterforHighEnergyPhysics,IndianInstituteofScience,Bangalore
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0 E-mail: [email protected]
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L. Hartgring
n
a Nikhef,Amsterdam
J E-mail: [email protected]

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2 I. Niessen
UniversityofNijmegen
]
h E-mail: [email protected]
p
- C. D. White∗
p
e SchoolofPhysicsandAstronomy,UniversityofGlasgow
h
E-mail: [email protected]
[

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v We summarise a recent study looking at top quark polarisation effects in charged Higgs boson
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production. Labframeangularandenergyobservablesrelatingtoleptonicdecaysoftopquarks
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8 areanalysed,andcorrespondingasymmetryparametersobtained.Theseareshowntobesensitive
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totoppolarisationandrobustwithrespecttohigherordercorrections. Thus,theyareanefficient
.
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probeofchargedHiggsparameterspace.
0
3
1
:
v
i
X
r
a
ProspectsforChargedHiggsDiscoveryatColliders-Charged2012,
October8-11,2012
UppsalaUniversity,Sweden
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
PolarisationstudiesinH−t production C.D.White
t t
− −
H H
Figure1: LeadingorderdiagramsforH−t production.
1. Introduction
ManyextensionsoftheStandardModelinvolvemorethanHiggsdoublet,animmediatecon-
sequenceofwhichisthepresenceofachargedHiggsboson. Observationofthelatterwouldthus
beaspectacularconfirmationofBSMphysics, andthehuntforsuchparticlesisongoing. Anim-
portantproductionmode(particularlywhenthechargedHiggsbosonmassexceedsthatofthetop
quark) is that of associated production with a (single) top quark. This is analagous toWt produc-
tionintheStandardModel,andtheleadingorderFeynmandiagramsareshowninfigure1. Inthis
contribution, we assume that the coupling of the Higgs to the top quark is given by a type-II two
Higgsdoubletmodelcoupling:
i
G =− √ V [m tanβ(1−γ )+m cotβ(1+γ )], (1.1)
H−tb¯ tb b 5 t 5
v 2
where,asusual,tanβ istheratioofHiggsVEVs(withoverallnormalisationv);m andm arethe
t b
topandbottomquarkmasses,andV theappropriateCKMmatrixelement. However,ourconclu-
tb
sionsaremoregeneralthanthis,andmayapplyinotherscenarios.
Given that the above coupling involves a superposition of left- and right-handed projectors,
the top quark will be produced with a net polarisation on average. The degree of longitudinal
polarisationisdefinedby
σ(+,+)−σ(−,−)
P = , (1.2)
t
σ(+,+)+σ(−,−)
whereσ(±,±)isthecross-sectionforproducingapositivelyornegativelypolarisedtopquark. In
SMpairproduction,eachtoporantitopisunpolarisedonaverage,sothatP =0. InH±tproduction,
t
P will be nonzero, and will depend on the parameter space (m ,tanβ). If the top quark decays
t H−
accordingtot →Wb→ f f¯bforsomefermionicdecayproduct f,thelatterisdistributedinthetop
quarkrestframe
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∼ (1+κ Pcosθ ).
f t f,rest
2
Here θ is the angle between f and the top quark spin vector, and κ the analysing power,
f,rest f
whose value depends on the identity of f, and potentially receives higher order corrections from
both SM and BSM sources. For a positively charged lepton (f =l), the analysing power κ (cid:39)1,
l
and turns out to be insensitive to BSM corrections to the decay of the top quark, up to quadratic
correctionsintheinversescaleofnewphysics[1]. Thus,leptonicdecayproductsoftopquarksare
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PolarisationstudiesinH−t production C.D.White
highlyefficientpolarisationanalysers.
ConsideranewphysicsparticleX producedinassociationwithatopquark. Thecouplingof
X to the top will produce a non-zero polarisation P (cid:54)=0 in general. If the top decays leptonically,
t
theangulardistributionoftheproducedleptonwillbegovernedbyP andκ . BSMcorrectionsto
t l
thedecayareirrelevanttoagoodapproximation,asstatedabove,andthusitfollowsthatleptonic
decayproductsoftopquarkscanbeusedtodirectlyprobethecouplingofX tothetopquark. Here
X isachargedHiggsboson,butourargumentiseasilygeneralisedtoothernewphysicsscenarios.
Above we considered the top quark rest frame. Given the difficulty of fully reconstructing
topquarkmomenta,itiseasierandmoreusefultoconsiderquantitiesinthelabframe. Assuming
thatthetopquarkdirectioncanbereconstructed,onemaydefinetheazimuthal(φ )andpolar(θ )
l l
anglesbetweenthedecayleptonandthedirectionofitsparenttop. Thesewerefirstdefinedin[1],
and analysed within a charged Higgs context in [2, 3] (see also [4]). Both carry an imprint of top
polarisation: apurelypolarcorrelationinthelabframeappearsasamixtureofpolarandazimuthal
informationinthelabframe,duetothenon-zeroboostofthetopquarkinthelatter.
2. ResultsinH−t production
In [3], we examined the above angular distributions using the recently developed MC@NLO
softwareforH−t production[5]. ThiscombinesNLOmatrixelementsforthisproductionprocess
withpartonshowerandhadronisationalgorithms,andalsoincludesspincorrelations[6]. Bycom-
paring these results with LO ones obtained using MadGraph [7], one may evaluate the robustness
ofpolarisationobservableswithrespecttohigherordercorrections. Allresultsherewereobtained
withtopandbottomquarkmassesofm =172GeVandm =4.95GeVrespectively,atopwidth
t b
of Γ =1.4 GeV, and a common renormalisation and factorisation scale µ = µ =m . We use
t r f t
MSTW2008LOandNLOpartons[8],asappropriate.
In figure 2 we show the distribution of the azimuthal angle φ , as a function of tanβ and for
l
two different charged Higgs boson masses. It is strongly peaked at φ =0 and φ =2π, due to
l l
the boost fromthe top quark restframe. Polarisation information modifies this shape, and wecan
efficiently distil this information into a single number: noting the crossing points in figure 2, we
candefinetheasymmetryparameter
σ(cosφ >0)−σ(cosφ <0)
l l
A = . (2.1)
φ
σ(cosφ >0)+σ(cosφ <0)
l l
EachpointinparameterspacecorrespondstoadifferentvalueofA ,asshowninfigure3(a). Thus,
φ
this quantity can be used to pin down the coupling of a charged Higgs boson to the top quark, as
wellastoenhancethesignaltobackgroundratio.
Results for the polar angle are shown in figure 4. This is strongly peaked near θ =0, again
l
due to the boost from the top quark rest frame. Polarisation information also modifies the overall
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PolarisationstudiesinH−t production C.D.White
dφl0.8 dφl0.6
/ d1/σσ0.7 mH=200 GeV / d1/σσ0.5 mH=200 GeV tan β=40
0.6
m=1500 GeV m=1500 GeV
0.5 H tan β=5 0.4 H
0.4 0.3
0.3
0.2
0.2
0.1
0.1
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
φ φ
l l
Figure2: Azimuthalangleφ betweenthetopquarkanditsdecayleptoninH−t production,obtainedusing
l
MC@NLO[5].
AAφφ00..7755 AAθθ
00..5555
00..77
00..55
00..6655
00..4455
00..66
00..44
00..5555
00..3355
00..55
00..33
00..4455
00..2255
00..44
00..22
00 55 1100 1155 2200 2255 3300 3355 4400 00 55 1100 1155 2200 2255 3300 3355 4400
ttaann ββ ttaann ββ
Figure3: Behaviourof(a)theazimuthalasymmetryparameterA ;(b)thepolarasymmetryparameterA ,
φ θ
atbothLO(blue)andMC@NLO(black)levels.UpperandlowercurvescorrespondtochargedHiggsboson
massesof1500and200GeV.AlsoshownaretheresultsobtainedforSMWt production(lowerbands).
shapeinthiscase,ascanbeencapsulatedbythepolarasymmetryparameter
σ(θ <π/4)−σ(θ >π/4)
l l
A = , (2.2)
θ
σ(θ <π/4)+σ(θ >π/4)
l l
whosebehaviourisshowninfigure3(b)fordifferentparameterspacevalues. Weseeinparticular
thatthepolarasymmetryisabletodistinguishdifferentchargedHiggsbosonmassesathightanβ,
thusprovidesusefulcomplementaryinformationwhencombinedwiththeazimuthalasymmetry.
Further information can be gained by considering observables based on ratios of energies of
thetopquarkanditsdecayproducts,whichwereshownin[9]tocarrypolarisationinformation:
E E
b l
z= , u= , (2.3)
E E +E
t l b
Here E , E and E are the energies of the top quark, and its decay b quark and lepton. The
t b l
observables of eq. (2.3) were defined for boosted top quarks, such that it is easier to construct
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PolarisationstudiesinH−t production C.D.White
/ddθσl1.4 /ddθσl1.4
1/σ1.2 mH=200 GeV 1/σ1.2 mH=200 GeV
m=1500 GeV m=1500 GeV
1 H 1 H
0.8 0.8
tan β=5
0.6 0.6 tan β=40
0.4 0.4
0.2 0.2
0 0
0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3
θl θl
Figure 4: Polar angle θ between the top quark and its decay lepton in H−t production, obtained using
l
MC@NLO[5].
σσ/du d2.5 No cut σσ/dz d2.5 No cut
1/ 2 1/ 2
B>0.8 B>0.8
B>0.9 B>0.9
1.5 1.5
1 1
0.5 0.5
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
u z
Figure5: ThezanduparametersinH−t production,obtainedusingMC@NLO[5],andfordifferentcuts
ontheboostparameter.
them. Herewecharacterisetheboostofthetopquarkusingtheparameter
|(cid:126)p |
top
B= , (2.4)
E
t
i.e. theratioofthree-momentumandenergy. UponimposinganincreasingcutontheBparameter,
the shape of the distributions of the z and u parameters converge to a shape which carries polar-
isation information, as shown in figure 5. Again there are crossing points for curves obtained at
differentvaluesoftanβ andm . Analogouslytotheangulardistributionsconsideredearlier,one
H−t
maydefineasymmetryparameters(see[3]formoredetails)
σ(u>0.215)−σ(u<0.215) σ(0.1≤z≤0.4)−σ(0.4≤z≤0.7)
A = ; A = . (2.5)
u z
σ(u>0.215)+σ(u<0.215) σ(0.1≤z≤0.4)+σ(0.4≤z≤0.7)
Thebehaviouroftheseasymmetriesatdifferentpointsinparameterspaceisshowninfigure6. One
sees more sensitivity to additional radiation than for angular observables, although the results are
stillreasonablyrobust. Furthermore,theenergyasymmetriesprovidecomplementaryinformation
totheangularobservables: theyaresensitivetonewphysicscorrectionsinboththeproductionand
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PolarisationstudiesinH−t production C.D.White
AAuu00..5566 AAzz00..0033
00..5544 00..0022
00..5522 00..0011 B>0.8
B>0.8
00..55 00
00..4488 00..0011
00..4466 00..0022
00..4444 00..0033
00..4422 00..0044
00 55 1100 1155 2200 2255 3300 3355 4400 00 55 1100 1155 2200 2255 3300 3355 4400
ttaann ββ ttaann ββ
Figure6: Energyasymmetryparameters,atbothLO(blue)andMC@NLO(black)levels. Upperandlower
curvescorrespondtochargedHiggsbosonmassesof1500and200GeV.Alsoshownaretheresultsobtained
forSMWt production(flatbands).
decay of the top quark, rather than just the production stage. A recent paper analysed the z and u
parameters in a different new physics context, and also concluded that these observables remain
usefulevenwhendetectoreffectsandreconstructionambiguitiesareaccountedfor[10].
To summarise, polarisation observables are an efficient way of probing the parameter space
of new physics models. We have here focused on the case of H−t production. As stressed in [3],
similarmethodscanalsobeusedinapurelySMcontexte.g. enhancingasignalofWt production
againstthetoppairbackground.
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