How to pin down the CP quantum numbers of a Higgs boson in its tau decays at the LHC

0.37 MB·English

by  S. Berge

MZ-TH/11-21
TTK-11-26
How to pin down the CP quantum numbers
of a Higgs boson
in its tau decays at the LHC
2 S. Berge 1, W. Bernreuther†2, B. Niepelt and H. Spiesberger 3
1 ∗ ∗ ∗
0
2 InstitutfürPhysik(WA THEP), Johannes Gutenberg-Universität,55099Mainz,Germany
∗

n † InstitutfürTheoretischePhysik,RWTH Aachen University,52056Aachen, Germany
a
J

9

]
h
p
- Abstract
p
e
h WeinvestigatehowtheCPquantumnumbersofaneutralHiggsbosonorspin-zeroresonance
[
F ,producedattheCERNLargeHadronCollider,canbedeterminedinitst -pairdecaymode
2
v F t t +. Weuseamethod[1]basedonthedistributionsoftwoanglesandapplyittothe
−
0 →
7 major1-prongt decays. Weshowfortheresultingdilepton,lepton-pion,and two-pionfinal
6
statesthatappropriateselectioncutssignificantlyenhancethediscriminatingpowerofthese
0
.
8 observables. From our analysis we conclude that, provided a Higgs boson will be found at
0
the LHC, it appears feasible to collect the event numbers needed to discriminate between a
1
1
CP-even andCP-odd Higgs boson and/or between Higgs boson(s) withCP-conserving and
:
v
CP-violatingcouplingsafterseveralyears ofhigh-luminosityruns.
i
X
r
a
PACSnumbers: 11.30.Er,12.60.Fr, 14.80.Bn,14.80.Cp
Keywords: hadroncolliderphysics,Higgsbosons,tau leptons,parity,CP violation
1 [email protected]
2 [email protected]
3 [email protected]
1
I. INTRODUCTION
If the Large Hadron Collider (LHC) at CERN will reach its major physics goal of discov-
ering a spin-zero resonance, the next step will be to clarify the question whether this is the
standardmodel(SM)Higgs-bosonorsomenonstandardresonance, as predictedby manyof
thepresentlydiscussednewphysicsscenarios. (Forreviews,see[2–6].) Partoftheanswerto
thisquestion will be givenby measuring theCP quantumnumbers of such a particle. There
have been a number of proposals and investigations on how to determine these quantum
numbers for Higgs-likeresonances F , for several production and decay processes at hadron
colliders, including Refs. [1, 7–19]. (For an overview, see [20].) It is the purpose of this ar-
ticleto studya method[1]with whichonecan pindownwhethersuchastateF isCP-even,
CP-odd, or aCP-mixture, namely in its decays into t -lepton pairs with subsequent 1-prong
decays.
Ourinvestigationsbelowareapplicabletoneutralspin-zeroresonancesh ,forinstancetothe
j
Higgs-boson(s)ofthestandardmodelandextensionsthereof,withflavor-diagonalcouplings
toquarks andleptonsas described bytheYukawaLagrangian
L = (√2G )1/2(cid:229) m a f¯f +b f¯ig f h . (1)
Y F f jf jf 5 j
−
j,f
(cid:0) (cid:1)
Here m is the mass of the fermion f and we normalize the coupling constants to the Fermi
f
constantG . Aspecificmodelisselectedbyprescribingthereducedscalarandpseudoscalar
F
Yukawa coupling constants a and b . In the standard model (SM) with its sole Higgs-
jf jf
boson, j=1anda =1,b =0. ManySMextensionspredictmorethanoneneutralspin-
jf jf
zero state and the couplings (1) can have more general values. Two-Higgs doublet models,
for instance, the nonsupersymmetric type-II models and the minimal supersymmetric SM
extension (MSSM, see, e.g., [2–4, 20]) contain three physical neutral Higgs fields h . If
j
the Higgs sector of these models is CP-conserving, or if Higgs-sectorCP violation (CPV)
is negligibly small, then the fields h describe two scalar states, usually denoted by h and
j
H, with b = 0, a = 0, and a pseudoscalar, denoted by A, with a = 0, b = 0. In
jf jf jf jf
6 6
the case of Higgs-sector CPV, the mass eigenstates h are CP mixtures and have nonzero
j
couplingsa =0 and b =0 toscalar and pseudoscalarfermioncurrents. Thiswouldlead
jf jf
6 6
toCP-violatingeffects inthedecays h f f¯already at Born level[9].
j
→
In thefollowing,weuse thegeneric symbolF for anyof theneutral Higgs-bosonsh ofthe
j
models mentioned above or, in more general terms, for a neutral spin-zero resonance. At
theLHC, a F resonance can beproduced, forinstance, in thegluonand gaugebosonfusion
processes gg F and q q F q q , as well as in association with a heavy quark pair, tt¯F
i j ′i ′j
→ →
or bb¯F . Recent studies on Higgs-boson production and decay into t leptons within the SM
and the MSSM include [21, 22]. Our method for determining the CP parity of F can be
appliedtotheseand toanyotherLHCF -productionprocesses.
The spin of a resonance F can be inferred from the polar angle distribution of the F -decay
2
products. In its decays to t leptons, F t t +, which is a promising LHC search channel
−
→
for a number of nonstandard Higgs scenarios (see, e.g. [3, 6] and the recent LHC searches
[23, 24]) t -spin correlations induce specific angular distributions and correlations between
thedirectionsofflightofthechargedt -decayproducts,inparticularanopeningangledistri-
butionandaCP-oddtriplecorrelationandassociatedasymmetries[9,14]. Oncearesonance
F is discovered, these observables can be used to determine whether it is a scalar, a pseu-
doscalar,oraCP mixture.
The discriminating power of these observables can be exploited fully if the t rest frames,
±
i.e.,thet energiesandthree-momentacanbereconstructed. AttheLHCthisispossiblefort
decaysintothreecharged-pions. WiththesedecaymodestheCPpropertiesofaHiggs-boson
resonance can be pinned down efficiently [18]. For t decays into one charged particle the
determination of the t rest frames is, in general, not possible at the LHC. For the 1-prong
±
decays t a the a+a zero-momentum frame can, however, be reconstructed. In [1]
± ± −
→
two observables, to be determined in this frame, were proposed and it was shown, for the
direct decays t +t − p +p −n¯t n t , that the joint measurement of these two observables de-
→
terminestheCPnatureofF . Itwillevenbepossibletodistinguish(nearly)mass-degenerate
scalar and pseudoscalar Higgs-bosons withCP-invariant couplings from one or severalCP
mixtures.
Inthispaperweanalyzethet -pairdecaymodeofF forallmajor1-prongt -decayst a
± ±
→
and investigate how this significantly larger sample can be used for pinning down the CP
quantum numbers of F in an efficient way. As the respective observables originate from
t -spin correlations, the t -spin analyzing power of the charged particle a is crucial for this
determination. The t -spin analyzing power of the charged lepton in the leptonic t decays
and of the charged-pion in the 1-prong hadronic decays t r ,a p is rather poor
± → ± ±1 → ±
whenintegratedovertheenergy spectrumoftherespectivecharged prong. Thus,thecrucial
questionin thiscontext is whetherexperimentallyrealizable cuts can befound such that, on
the one hand, the t -spin analyzing power of the charged prongs is significantly enhanced
and, on the other hand, the data sample is not severely reduced by these cuts. We have
studiedthisquestionindetailand founda positiveanswer.
Thepaperisorganizedasfollows. Inthenextsectionwebrieflydescribethematrixelements
onwhichourMonteCarloeventsimulationisbased,andwerecapitulatethetwoobservables
withwhichtheCPnatureofaHiggs-bosoncanbeunraveled. InSec.IIIweanalyzeindetail
the distribution that discriminates between a scalar and pseudoscalar Higgs-boson, both for
dilepton, lepton-pion, and two-pion final states, for several cuts. We demonstrate for a set
of “realistic”, i.e., experimentally realizable cuts that the objectives formulated above can
actually be met. This is then also shown for the distribution that discriminates between F
bosonswithCP-violatingand -conservingcouplings. We concludein Sec. IV.
3
II. DIFFERENTIALCROSSSECTIONANDOBSERVABLES
Weconsidertheproductionofaspin-zeroresonanceF –inthefollowingcollectivelycalled
aHiggs-boson– attheLHC, and itsdecay to apairoft leptons:
±
pp F +X t t ++X. (2)
−
→ →
Thedecays oft are dominatedby1-prongmodeswithan electron,muon,orcharged-pion
±
inthefinal state. Wetakeintoaccountthefollowingmodes,whichcomprisethemajorityof
the1-prong t decays:
t l+n l+n t ,
→
t a1+n t p +2p 0+n t ,
→ →
t r +n t p +p 0+n t ,
→ →
t p +n t . (3)
→
In thefollowinga =l ,p refer to thecharged prongsinthedecays (3).
∓ ∓ ∓
Thehadronicdifferentialcrosssectionds forthecombinedproductionanddecayprocesses
(2), (3) can be written as a convolution of parton distribution functions and the partonic
differential cross section dsˆ for p p F t +t a+a +X (where p and p are
1 2 − ′− 1 2
→ → →
gluonsor(anti)quarks):
dsˆ = √26G4Fp m2s2t b t dW t (cid:229) |M(p1p2 →F +X)|2 D−1(F ) 2Brt−→a′−Brt+→a+ (4)
dE dW dE dW (cid:12) (cid:12)
a a a+ a+ (cid:12) (cid:12)
′− ′− n(E )n(E )
× 2p 2p a+ a′−
3
(cid:229)
A+b(E )B+ qˆ b(E )B qˆ+ b(E )b(E ) C qˆ qˆ+ .
× a′− · −− a+ −· − a′− a+ ij −i j
i,j=1 !
Here, √s isthepartoniccenter-of-mass energy, b t = 1 4m2t /p2F ,
−
q
(cid:229) M(p1p2 F +X) 2 and D−1(F )= p2F m2F +imF G tFot −1 (5)
| → | −
(cid:0) (cid:1)
isthespinandcoloraveragedsquaredproductionmatrixelementandtheHiggs-bosonprop-
m
agator, respectively, with mF , pF and G tFot denoting the Higgs-bosonmass, its 4-momentum
and its total width4. The squared matrix element T 2 of the decay F t +t X, integrated
−
| | →
overX,isoftheform
|T|2 =√2GFm2t A+B+i sˆ+i +B−i sˆ−i +Cijsˆ+i sˆ−i , (6)
(cid:0) (cid:1)
4 Equation (4) holds as long as nonfactorizableradiative correctionsthat connectthe productionand decay
stageofF areneglected.
4
F A c c c
1 2 3
scalar a2t p2F b t2/2 a2t p2F b t2/2 a2t p2F b t2 0
−
pseudoscalar b2t p2F /2 b2t p2F /2 0 0
−
CPmixture (a2t b t2+bt2)p2F /2 (a2t b t2 bt2)p2F /2 a2t p2F b t2 at bt p2F b t
− − −
Table I: Tree-level coefficients of the squared decay matrix element (6), (7) for F =H, A (scalar,
pseudoscalar) andforaCPmixture.
wheresˆ arethenormalizedt spinvectorsintherespectivet restframes. Thedynamics
± ± ±
ofthedecay is encoded inthecoefficientsA, B andC . Rotationalinvarianceimpliesthat
±i ij
B =B kˆ , C =c d +c kˆ kˆ +c e kˆ , (7)
± ± − ij 1 ij 2 i− −j 3 ijl l−
where k (kˆ ) is the (normalized) t momentum in the t +t zero-momentum frame
− − − −
(ZMF). At tree level, B = 0. (A nonzero absorptive part of the amplitude, induced for
±
instance by the photonic corrections to F tt renders these coefficients nonzero, but the
→
effect is very small [14].) The tree-level coefficients A and c induced by the general
1,2,3
Yukawa couplings (1) are given in Table I (cf. also [14]) for a scalar (bt = 0) and a pseu-
doscalar(at =0)Higgs-boson,F =H, A,and aCP mixture.
Weusethenarrow-widthapproximationfort . Thebranchingratiosofthe1-prongt decays
±
(is3)thaereddifefneoretendtiablysBorlitd±→aan±g=leGoft ±th→ea±t /G ittnot.thMeoHreigogvserr,etshtefmraemaesu,raenddW dtW =d=codscqot sdqj t idnj(4)
− a a a
± ± ±
and E is the differential solid angle and the energy of the charged prong a in the t rest
a ± ±
±
frame. Furthermore, the functions n(E ) and b(E ) encode the decay spectrum of the
a a
∓ ∓
respective1-prong polarizedt decay andare defined in thet rest frames by
∓ ∓
dG (t (sˆ ) a (q )+X)
∓ ∓ ∓ ∓
→ = n(E ) 1 b(E )sˆ qˆ , (8)
G (t a +X)dE dW /(4p ) a∓ ± a∓ ∓· ∓
∓ ∓ a a
→ ∓ ∓
(cid:0) (cid:1)
where qˆ is the normalized momentum vector of the charged prong a in the respective
∓ ∓
frame. The function n(E ) determines the decay rate of t a while b(E ) encodes the
a a
→
t -spin analyzing power of the charged prong a = l,p . We call them spectral functions for
short. They are given for the t -decay modes (3) in Appendix A. Using the spin-density
matrixformalism,thecombinationof(6)and(8)yields,with(5), theformula(4).
Thedecay distribution(6)and thecoefficientsc , c ofTableIimplythat, at thelevelofthe
1 3
t +t intermediatesstates,thespinobservablessˆ+ sˆ andkˆ (sˆ+ sˆ )discriminatebetween
− − −
· · ×
a CP-even and CP-odd Higgs-boson, and between a Higgs-boson with CP-conserving and
CP-violatingcouplings,respectively [9, 14]. A the level of the charged prongs a+a , these
′−
correlationsinduceanontrivialdistributionoftheopeningangle∠(qˆ+,qˆ ) and theCP-odd
−
triplecorrelationkˆ (qˆ+ qˆ ),ascanbereadofffrom(4). Thestrengthofthesecorrelations
−
· ×
depends on the product b(E )b(E ), while n(E )n(E ) is jointly responsible for the
a a+ a a+
′− ′−
5
numberofa+a events5.
′−
A direct analysis of experimental data in terms of the kinematic variables used in the dif-
ferential cross section Eq. (4) is not possiblesince the momentaof the t decay products are
measured in the laboratory frame and the reconstruction of the t and F rest frames is, in
±
general, not possible. In Ref. [1] it was shown that one can, nevertheless, construct exper-
imentally accessible observables with a high sensitivity to the CP quantum numbers of F .
Thecrucial pointis toemploythezero-momentumframeofthea+a pair.
′−
Thedistributionoftheangle
j =arccos(nˆ + nˆ ) (9)
∗ ∗ ∗−
·
⊥ ⊥
discriminatesbetween a JPC =0++ and 0 + state. Here nˆ are normalized impact param-
− ∗±
eter vectors defined in the zero-momentum frame of the a⊥+a pair. These vectors can be
′−
reconstructed[1]fromtheimpactparametervectorsnˆ measuredinthelaboratoryframeby
m ∓
boosting the 4-vectors n =(0,nˆ ) into the a a+ ZMF and decomposing the spatial part
′−
∓ ∓
of the resulting 4-vectors into their components parallel and perpendicular to the respective
p orl momentum. Weemphasizethat j defined inEq. (9)isnotthetrueanglebetween
∓ ∓ ∗
thet decayplanes,butnevertheless,itcarries enoughinformationtodiscriminatebetweena
CP-evenandCP-oddHiggs-boson.
The role of the CP-odd and T-odd triple correlation mentioned above is taken over by the
triplecorrelationO =pˆ (nˆ + nˆ )betweentheimpactparametervectorsjustdefined
andthenormalizedC∗aP mo∗−m·ent∗⊥um×in∗⊥th−ea a+ZMF,whichisdenotedbypˆ . Equivalently,
′− ′− ∗
−
onecan determinethedistributionoftheangle[1]
y = arccos(pˆ (nˆ + nˆ )). (10)
C∗P ∗ ∗ ∗−
· ×
− ⊥ ⊥
In an ideal experiment, where the energies of the t decay products a in the t rest frames
± ±
would be known, one could determine the coefficients A, B , and c by fitting the dif-
± 1,2,3
ferential distribution(4) (using the SM input of the Appendix) to the data. However, due to
missingenergy in the final state, detector resolution effects and limited statistics, one has to
average over energy bins. Moreover, for a = p the function b(E) is not positive (nega-
∓ ∓
6
tive) definite, see below. Therefore, energy averaging can lead to a strong reduction of the
sensitivityto the coefficients of b(E) in the differential cross section. A judicious choice of
bins or cuts is therefore crucial to obtain maximal information on the CP properties of F .
Wewilldiscussthisin detailinthenextsection.
5 The integral n(E )b(E )dE determines the overall t -spin analyzing-power of the particle a. It seems
a a a
worthrecallingthatthephysicsoft decays,i.e.,theV Alaw,hasbeentestedtoalevelofprecisionwhich
R
−
is much higherthan what is neededfor our purposes. Therefore, when comparingpredictionswith future
data,onecanusethefunctionsn(E )andb(E )oftheAppendixasdeterminedwithinthestandardmodel.
a a
6
III. RESULTS
Theobservables(9)and(10)canbeusedforthe1-prongt -pairdecaychannelsofanyHiggs-
bosonproductionprocessat theLHC. Weareinterestedhereinthenormalizeddistributions
of these variables. If no detector cuts are applied, these distributions do not depend on the
momentumof theHiggs-bosonin thelaboratory frame; i.e., thesedistributionsare indepen-
dentofthespecificHiggs-bosonproductionmode. Applyingselectioncuts,wehavechecked
for some production modes (see below)that, for a given Higgs-bosonmass mF &120 GeV,
thenormalizeddistributionsremain essentiallyprocess-independent(see also[1]).
Fordefiniteness,weconsiderinthefollowingtheproductionofonespin-zeroresonanceF at
theLHC(√S=14TeV)inarangeofmassesmF between120and400GeV.Asweemploy
the general Yukawa couplings (1), our analysis below can be applied to a large class of
models,includingthestandardmodel,type-II2-Higgsdoubletmodels,andtheHiggssector
oftheMSSM. Withina wideparameterrangeof type-IImodels,F productionisdominated
by gluon-gluon fusion; for large values of the parameter tanb = v /v (where v are the
2 1 1,2
vacuum expectationvalues of thetwo Higgs doublet fields) the reaction bb¯ F takes over.
→
(Fora recent overviewof variousHiggs-bosonproduction processes and the state-of-the-art
of the theoretical predictions, see, e.g., [25, 26]. Higgs-boson production and decay into
t t + wasanalyzedintheSMandMSSMin[21,22],takingrecentexperimentalconstraints
−
intoaccount.)
For obtaining the results given below we have used the production processes bb¯ F and
→
gg F . The reaction chains (2), (3) were computed using leading-order matrix elements
→
only,butourconclusionswillnotchangewhenhigher-orderQCD correctionsaretakeninto
F
account or other Higgs-boson production channels with large transverse momentum p are
T
considered. Ourmethodcanbeappliedtoallproductionchannels,becausenoreconstruction
of the Higgs-boson momentum or the t momenta is needed for the determination of the
distributions (9) and (10). Therefore, the method is applicable to Higgs-boson production
with small or large transverse momentum, as long as the Higgs resonance can be identified
inthett events. (ForadiscussionofthebackgroundseetheendofSec. IIID.)
If pF issmall,thedistributionscanbemeasuredasdescribedbelow. Ifthet ,t + decayinto
T −
leptonsorviaar ora meson,anapproximatereconstructionoftheHiggs-bosonrestframe,
1
as outlinedin Sec. IIIC, will increase thediscriminatingpowerof thedistributions,because
appropriatecuts inthisframeseparatet -decay particleswithlargeand smallenergies.
F
If p is large, the reconstruction of the Higgs rest frame can be performed, see [27]. With
T
similar cuts as used below, this leads to an even better discriminating power of the j and
∗
y distributions.
C∗P
We have implemented Eq. (4) into a Monte Carlo simulation program which allows us to
studythereconstructionofobservablesinavarietyofreference framesand toimposeselec-
tioncuts onmomentaand energies.
In Sec. IIIA -IIID we analyze, for the various 1-prong final states, the j distributions for
∗
7
HaL Τ®l+Νl+ΝΤ HbL F®Τ-Τ+®l-Π++3Ν
2.5
nodetectorcuts
0.40 H
2.0 mF=400GeV
1.5
0.35
A
*
j
1.0 d
nHElL (cid:144)Σ
d
0.5 bHElL Σ× 0.3 H
(cid:144)1
0(cid:29) .0
0.25
-0.5 A 0.44GeV>El
0.44GeV<E
l
-1.0 0.2
0 mΤ mΤ 0 Π Π 3Π Π
4 2 4 2 4
E j*
l
Figure1: (a)Thespectral functions n(E )andb(E ),Eq.(22),fortheleptonic t decay. Thefunction
l l
n(E ) is given in units of GeV 1. (b) The normalized j distribution for lp final states without
l − ∗
selectioncutsinthelaboratory frameforaHiggsmassofmF =400GeV.Acutontheleptonenergy
in the t rest frame at mt /4 0.44 GeV serves to show the effect of rejecting events where b(El) is
≃
positiveandnegative,respectively.
a scalar and pseudoscalar Higgs-boson, i.e., a spin-zero resonance F with reduced Yukawa
couplings at =0,bt =0 and at =0,bt =0, respectively, to t leptons. For definiteness we
6 6
chooseat =1andbt =1,respectively. ThedistributionoftheCPangley C∗P iscomputedin
Sec. IIIE forHiggs-bosonswithCP-violatingandCP-conservingcouplings.
A. Lepton-pionfinalstate: tt lp +3n
→
We start by discussing the case where the t from F t t + decays leptonically, t
− − −
→ →
l−+n¯l+n t ,andthet + undergoesadirectdecayintoapion,t + p ++n¯t . Thepurposeof
→
this section is to study the shapes of the j distributionsfor scalar and pseudoscalar Higgs-
∗
bosons when cuts are applied to the charged lepton; therefore, no cuts are applied at this
pointto thepion energy andmomentum.
Thechargedleptonenergyspectruminthet l decayisdeterminedbythefunctionsn(E )
l
→
and b(E ) given in the Appendix, Eq. (22). These functions are shown in Fig. 1(a). One
l
seesthatthefunctionb(E ),whichdeterminesthet -spinanalyzingpowerofl,changessign
l
at El = mt /4. Therefore also the slope of the resulting j ∗ distribution for p l final states
changes sign at this energy. The optimal way to separate a CP-even and CP-odd Higgs-
boson would be to separately integrate over the energy ranges El > mt /4 and El < mt /4.
The resulting j distributions for a scalar (H, red lines6) and pseudoscalar (A, black lines)
∗
6 Colorintheelectronicversion.
8
F®Τ-Τ+®l-Π++3Ν
3.5
nocuts
3.0
m =120GeV,cuts
F
1D 2.5 mF=200GeV,cuts
-
V m =400GeV,cuts
e F
G
@ 2.0
El
d
(cid:144)Σ 1.5
d
×
Σ 1(cid:29) .0
(cid:144)1
0.5
0.0
0 mΤ mΤ
4 2
E
l
Figure 2: Normalized lepton energy distribution (in the t rest frame) for different Higgs-boson
masses,withandwithoutselection cuts(11).
Higgs-bosonareshowninFig.1(b). Fortheenergyrange0<El <mt /4,thej ∗ distribution
has a positive(negative)slopefor a scalar (pseudoscalar) Higgs-boson(dashed curves). For
El >mt /4theslopeschangesignandthedifferencebetweenaCP-evenandaCP-oddboson
becomes morepronounced (solidcurves). However, at a LHC experiment,theseparation of
thesetwoenergyrangesisnotpossiblebecausethet momentacannotbereconstructedand,
therefore, theleptonenergy E in thet rest framecan not bedetermined.
l
The difference between the j distributions for a scalar and pseudoscalar Higgs-boson is,
∗
however, not completely washed out by integrating over the full lepton energy range, be-
cause both n(E ) and b(E ) have a significant energy dependence, see Fig. 1(a). The region
l l
0 < El < mt /4 contributes only about 19% to the decay rate G t l; in addition, b(El) is
→
small in this energy range. Therefore, after integration over the full E range, the j distri-
l ∗
bution is already quite close to the solid lines of Fig. 1(b). Moreover, one can suppress the
contribution from the low-energy part of the spectrum by imposing a cut on the transverse
momentumofthechargedleptoninthelaboratoryframe. FortheLHCexperiments,suitable
selection cuts on the transverse momentum and the pseudorapidity of the lepton in the pp
frameare[23, 24]:
pl = (pl)2+(pl)2 20GeV, h 2.5. (11)
T x y l
≥ | |≤
q
The effect of these cuts on the normalized lepton energy distribution in the t rest frame is
−
shown in Fig. 2. Rejecting events with small pl preferentially removes events with small
T
lepton energy in the t rest frame. The effect is more pronounced for light Higgs-boson
masses where the t energy is smaller on average. For mF =120 GeV, only a small fraction
ofp l eventswithEl <mt /4,about3.6%,survivesthecuts(11). FormF =200and400GeV
the corresponding fractions are 9.4% and 14%, respectively. Events with El < mt /4 that
9
HaL F®Τ-Τ+®l-Π++3Ν HbL F®Τ-Τ+®l-Π++3Ν
0.45 0.45
all E all E
H l l
0.40 mΤ <El 0.40 H mΤ <El
2 2
* *
j 0.35 j 0.35
d d
(cid:144)Σ (cid:144)Σ
d d
× ×
Σ 0.3 Σ 0.3
(cid:144)1 (cid:144)1
A
0.25 A m =120GeV 0.25 m =400GeV
F F
p l³20GeV,ÈΗÈ£2.5 p l³20GeV,ÈΗÈ£2.5
T l T l
0.2 0.2
0 Π Π 3Π Π 0 Π Π 3Π Π
4 2 4 4 2 4
j* j*
Figure3: Thenormalized j distributions forlp 3n finalstates. Thesolid (dashed) curvesshow the
∗
distribution with the cuts plT >20 GeV and |h l|<2.5 (without these cuts). (a) mF =120 GeV; (b)
mF =400GeV.
passtheabovecutshaveenergiesclosetomt /4,wherethefunctionb(El)isverysmall. The
resulting j ∗ distribution is almost unaffected by contributions with El < mt /4, for Higgs
massesupto200GeV.Asanexample,thej ∗ distributionsaredisplayedformF =120GeV
inFig.3(a)andformF =400GeVinFig.3(b). Fromtheseresultsweconcludethatonlyfor
very large Higgs-boson masses one can expect to improve the discrimination of scalar and
pseudoscalarbosonsbysuch adetectorcut.
The experimentally relevant case, where in addition also selection cuts on the charged-pion
areapplied,willbediscussedinSection IIID.
B. Hadronicfinalstates: t t + a ,r ,p p +
− →{ −1 − −}
Nextweanalyzethecasewherethet − decaystop − eitherviaar meson,t − r −+n t
→ →
p −+p 0+n t , an a1 meson, t − → a−1 +n t → p −+2p 0+n t , or directly, t − → p −+n t ,
whilet + undergoes a direct 2-body decay, t + p ++n¯t . (The respectivebranching ratios
→
arecollected inTableV).
The spectral functions n(Ep ) and b(Ep ) for the r and a1 modes are given in the Appendix
and shown in Fig. 4. The direct decay mode t − p −+n t is characterized by a constant
→
pionenergy inthet rest frameand hasmaximalt -spinanalyzingpowerb=1.
Asinthecaseofleptonict decay thefunctionsbr (Ep ) andba (Ep )changesign,atapprox-
1
imately 0.55 GeV. In contrast to the leptonic case, however, contributions from small pion
energiesarenotsuppressedbysmalldifferentialrates,asevidencedbythefunctionsnr (Ep )
and na (Ep ). At the LHC one will probably not be able to distinguishbetween the different
1
1-prongdecaymodesintoapion,atleastnotinanefficientway. Thus,onehastocombinein
10