Higgs boson production: A comparison of parton showers and … · 2005-03-31 · Higgs boson production: A comparison of parton showers and resummation C. Bala´zs* Department of

PHYSICAL REVIEW D, VOLUME 63, 014021

Higgs boson production: A comparison of parton showers and resummation

C. Balazs*Department of Physics & Astronomy, University of Hawaii, Honolulu, Hawaii 96822

J. Huston†

Department of Physics & Astronomy, Michigan State University, East Lansing, Michigan 48824

I. Puljak‡

Laboratoire de Physique Nucle´aire et des Hautes Energies, Ecole Polytechnique, 91128 Palaiseau, Franceand University of Split, 21000 Split, Croatia

~Received 29 August 2000; published 12 December 2000!

The search for the Higgs boson~s! is one of the major priorities at the upgraded Fermilab Tevatron and at theCERN Large Hadron Collider~LHC!. Monte Carlo~MC! event generators are heavily utilized to extract andinterpret the Higgs signal, which depends on the details of the soft-gluon emission from the initial state partonsin hadronic collisions. Thus, it is crucial to establish the reliability of the MC event generators used by theexperimentalists. In this paper, the MC based parton shower formalism is compared to that of an analyticresummation calculation. Theoretical input, predictions and, where they exist, data for the transverse momen-tum distribution of Higgs bosons,Z0 bosons, and photon pairs are compared for the Tevatron and the LHC.This comparison is useful in understanding the strengths and the weaknesses of the different theoreticalapproaches, and in testing their reliability.

DOI: 10.1103/PhysRevD.63.014021 PACS number~s!: 12.38.Cy, 12.20.Fv, 13.85.Qk, 14.80.Bn

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I. INTRODUCTION

To reveal the dynamics of electroweak symmetry breing, a new generation of hadron colliders will search for tHiggs boson~s!. The potential of the upgraded FermilaTevatron, the 2 TeV center of mass energy proton-antiprocollider starting operation within a year, was analyzedRef. @1#. Later in this decade, two experimental collabotions ~ATLAS and CMS! will join the search at the CERNLarge Hadron Collider~LHC! with 14 TeV proton-protoncollisions. An extraction of the Higgs signal at the LHC rquires not only precise knowledge of the signal and baground invariant mass distributions, but also an accuratediction of the corresponding transverse momentum (pT)distributions. In general, the determination of the signalquires a detailed event modeling, an understanding ofdetector resolution, kinematical acceptance and efficienall of which depend on thepT distribution. The shape of thisdistribution in the low to moderatepT region can dictate thedetails of both the experimental triggering and the analystrategies for the Higgs boson search. It can also be usedevise an improved search strategy and to enhance thetistical significance of the signal over the background@2,3#.In the gg→HX→ggX mode at the LHC, for example, thshape of the signal and the backgroundpT distribution of thephoton pairs is different~cf. Refs. @4,5#!, with the signalbeing harder. This difference can be utilized to increasesignal to background ratio. Furthermore, since vertex poing with the photons is not possible in the CMS barrel, t

*Email address: [email protected]†Email address: [email protected]‡Email address: [email protected]

0556-2821/2000/63~1!/014021~12!/$15.00 63 0140

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shape of thepT distribution affects the precision of the determination of the event vertex from which the Higgs bos~decaying into two photons! originated.1 Thus, for a successful, high precision extraction of the Higgs signal, the theretical calculation must be capable of reproducing thepected transverse momentum distribution.

To reliably predict thepT distribution of Higgs bosons athe LHC, especially for the low to mediumpT region wherethe bulk of the rate is, the effects of the multiple soft-gluemission have to be included. One approach which achiethis is parton showering@6#. Parton shower Monte Carlo programs such asPYTHIA @7#, HERWIG @8# and ISAJET @9# arecommonly used by experimentalists, both as a way of coparing experimental data to theoretical predictions and aas a means of simulating experimental signatures in kmatic regimes for which there are no experimental data~such as for the LHC!. The final output of these Monte Carlprograms consists of the 4-momenta of a set of final sparticles. This output can either be compared to recstructed experimental quantities or, when coupled withsimulation of a detector response, can be directly compato raw data taken by the experiment and/or passed throthe same reconstruction procedures as the raw data. Inway, the parton shower programs can be more useful toperimentalists than analytic calculations. Indeed, almostof the physics plots by the ATLAS Collaboration@10# in-volve comparisons toPYTHIA version 5.7.

Predictions of the Higgs bosonpT can also be obtained

1The vertex with the most activity is chosen as the vertex frwhich the Higgs particle has originated. If the Higgs boson is tycally produced at a relatively high value ofpT , then this choice iscorrect a large fraction of the time.

©2000 The American Physical Society21-1

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C. BALAZS, J. HUSTON, AND I. PULJAK PHYSICAL REVIEW D63 014021

utilizing an analytic resummation formalism, which sumcontributions ofaS

nlnm(mH /pT) ~wheremH is the Higgs bosonmass andm<2n21) up to all orders in the strong couplinaS . In the recent literature, most calculations of this kind aeither based on, or originate from, the lowpT factorizationformalism @11# ~for the latest review see Ref.@12#!. Thisformalism resums the effects of the multiple soft-gluon emsion while also systematically including the fixed order QCcorrections. It is possible to smoothly match the resummresult to the fixed order one in the intermediate to highpT

region, thus obtaining a prediction for the fullpT distribution@13#. In this paper, we use this formalism as an analy‘‘benchmark’’ to calculate thepT distributions of Higgsbosons at the LHC and ofZ0 bosons and photon pairs produced in hadron collisions.

For many physical quantities, the predictions from parshower Monte Carlo programs should be nearly as precisthose from analytic theoretical calculations. It is expecthat both Monte Carlo and analytic calculations should acrately describe the effects of the emission of multiple sgluons from the incoming partons, an all orders problemQCD. The initial state solf-gluon emission affects the kinmatics of the final state partons. This may have an impacthe signatures of physics processes at both the triggeranalysis levels and thus it is important to understandreliability of such predictions. The best method for testithe reliability is a direct comparison of the predictionsexperimental data. If no experimental data are availablecertain predictions, then some understanding of the reliaity may be gained from a comparison of the predictions frthe two different methods.

In the absence of experimental data for Higgs boson pduction, we can gauge the reliability of calculations for thprocess by comparing them to each other. We also compredictions from the different formalisms to data for prcesses which are similar to Higgs boson production atLHC. In this way we can perform a genuine ‘‘reality checkof the various theoretical predictions. Production of a ligneutral Higgs boson at the LHC in the standard model~SM!and its supersymmetric extensions proceeds via the partsubprocessgg ~through heavy fermion loop!→HX. One ofthe major backgrounds for a light Higgs boson, in the mrange of 100 GeV&mH&150 GeV, is diphoton productiona sizable contribution to which comes from the same,gginitial state. Since the major part of the soft-gluon radiatiis initiated from the incoming partons, the structures ofresummed corrections are similar for Higgs boson adiphoton production. Because the latter is measurable aFermilab Tevatron, diphoton production provides an exctional opportunity to test the different theoretical models.Z0

boson production can also be a good testing ground forsoft-gluon corrections to Higgs boson production. The trement of the fixed order and resummed QCD correctionsZ0 boson production is theoretically well understood aimplemented at next-to-next-to-leading order@13#. Further-more, just as in the diphoton case, predictions can alsotested against Tevatron data. TheZ0 data have the advantagthat sufficient statistics exist in the run 1 data from Collid

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Detector at Fermilab~CDF! and D0 to allow for detailedcomparisons to the theoretical predictions.

II. LOW pT FACTORIZATION

In this section the low transverse momentum factorizatformalism and its matching to the usual factorization areviewed. The problem arises as follows. When calculatfixed order QCD corrections to thepT distribution of theHiggs boson produced in the inclusive processpp→HX, thestandard QCD factorization theorem is invoked:

ds

dpT2

5 f j 1 /p~mH! ^

ds j 1 j 2

dpT2 ~mH ,pT! ^ f j 2 /p~mH!, ~1!

which is a convolution in the partonic momentum fractionand is derived under the usual assumptionpT@mH .2 WhenpT!mH occurs, as a result of soft and soft1collinear emis-sion of gluons from the initial state, the theorem fails. Tratio of the two very different physical scales in the partoncross sections j 1 j 2

produces large logarithms of the form

ln(mH /pT), which are not absorbed by the parton distributifunctions f j /p , unlike the ones originating from purely colinear parton emission. These logarithms are enhanced1/pT

2 pre-factor at lowpT . ~The same factor suppresses thefor large pT .) As a result, the HiggspT distribution calcu-lated using the conventional hadronic factorization theoris un-physical in the lowpT region.

To resolve this problem, the differential cross sectionsplit into a part which contains all the logarithmic terms (W)and into a regular term (Y):

ds

dpT2

5W~mH ,pT!1Y~mH ,pT!. ~2!

SinceY does not contain logarithms ofpT , it can be calcu-lated using the usual factorization. TheW term has to beevaluated differently, keeping in mind that failure of thstandard factorization occurs because it neglects the trverse motion of the incoming partons in the hard scatteriAs has been proved@11#, W has a simple form in the Fourieconjugate, that is the transverse position (bW ) space,

W~mH ,b!5Cj 1 /h1~mH ,b!e2S(mH ,b

*)Cj 2 /h2

~mH ,b!, ~3!

with the Sudakov exponent defined as

2Here and henceforth, summation on double partonic indices~e.g.j i) is implied. Also, since we are focusing on the transverse mmentum, longitudinal partonic momentum fractions are either kimplicit or, when applicable, integrated over.

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HIGGS BOSON PRODUCTION: A COMPARISON OF . . . PHYSICAL REVIEW D 63 014021

S~mH ,b* !5EC0

2/b*2

mH2 dm2

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m2 D 1B„aS~m!…G ,

~4!

which resums the large logarithmic terms.3 The partonic re-coil against soft gluons, as well as the intrinsic partotransverse momentum, is included in the generalized padistributions

Cj /h~mH ,b,x!5@Cja~mH ,b* ! ^ f a/h~mH!#~x!

3Fa/h~mH ,b,x!, ~5!

where the convolution is evaluated over the partonic momtum fractionx. TheA andB functions, and the Wilson coefficientsCja , are free of logarithms and safely calculable pturbatively as expansions in the strong coupling:

A~aS!5 (n51

` S aS

p D n

A(n), etc. ~6!

The process independent non-perturbative functionsFa/h ,describing long distance transverse physics, are extrafrom low-energy experiments@14#.

The matching of the low and the highpT regions isachieved via theY piece. To correct the behavior of the rsummed piece in the intermediate and highpT regions, it isdefined as the difference of the cross section calculatedthe standard factorization formula at a fixed ordern of per-turbation theory and itspT!mH asymptote.4 The resummedcross section, to orderaS

n , then reads as

ds

dpT2

5W~mH ,pT!1ds (n)

dpT2

2ds (n)

dpT2 U

pT!mH

. ~7!

At low pT , the logarithms are large and the asymptotic pdominates the fixed orderpT distribution. The last two termsin Eq. ~7! nearly cancel, andW is a good approximation tothe cross section. At highpT the logarithms are small, anthe expansion of the resummed term cancels thepT singularterms~up to higher orders inaS), and the cross section reduces to the fixed order perturbative result. After matchthe resummed and fixed order cross sections in such a mner, it is expected that the normalization of the resummcross section reproduces the fixed order total rate, since wexpanded and integrated overpT it deviates from the fixedorder result only in higher order terms. For further detailsthe low pT factorization formalism and its application tHiggs boson production we refer to the recent literat@5,16#.

3To prevent evaluation of the Sudakov exponent in the n

perturbative region, the impact parameterb5ubW u is replaced byb* 5b/A11(b/bmax)2. The choice ofC052e2gE, wheregE is theEuler constant, is customary.

4The expression for theY term for Higgs boson production can bfound elsewhere@15#.

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III. PARTON SHOWERING AND RESUMMATION

For technical reasons, the initial state parton shower pceeds by abackwardsevolution, starting at the large~nega-tive! Q2 scale of the hard scatter and then considering emsions at lower and lower ~negative! virtualities,corresponding to earlier points on the cascade~and earlierpoints in time!, until a scale corresponding to the factoriztion scale is reached. The transverse momentum of the instate is built up from the whole series of splittings aboosts. The showering process is independent of the hscattering process being considered~as long as one does nointroduce any matrix element corrections!, and depends onlyon the initial state partons and the hard scale of the proc

Parton showering utilizes the fact that the leading orsingularities of cross sections factorize in the collinear limThis is expressed as

limpbuupg

uMn11u252paS

pb•pgPa→bg~z!uM nu2, ~8!

whereMn11 is the invariant amplitude for the process prducingn partons and a gluon,aS is the strong coupling constant,pb andpg are the 4-momenta of the daughters of pton a, and Pa→bg(z) is the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi ~DGLAP! evolution kernel associated witthe a→bg splitting. These leading order collinear singulaties can be factorized into a Sudakov form factor

Sshower~Q!5EQ0

2

Q2dm2

m2

aS~m!

2p E0

1

dz Pa→bg~z!, ~9!

which is interpreted as the probabilityP5exp(2Sshower) ofthe partonic evolution from scaleQ0 to Q with no resolvablebranchings. This probability can be used to determinescale for the first emission and hence for the whole cascThe formalism can be extended to soft singularities as wby using angular ordering. In this approach, the choice ofhard scattering is based on the use of evolved parton dibutions, which means that the inclusive effects of initial-stradiation are already included. What remains is, thereforeconstruct the exclusive showers.

Parton showering resums primarily the leading logarithwhich are universal, that is process independent, and deponly on the given initial state. In this lies one of the strengof Monte Carlo programs, since parton showering canincorporated into a wide variety of physical processes.analytic calculation, in comparison, can resum all logrithms. For example, the lowpT factorization formalismsums all of the logarithms withmH /pT in their arguments.As discussed earlier, all of the ‘‘dangerous logarithms’’ aincluded in the Sudakov exponent~4!. TheA andB functionsin Eq. ~4! contain an infinite number of coefficients, with thA(n) coefficients being universal, while theB(n)’s are processdependent, with the exception ofB(1). In practice, the num-ber of towers of logarithms included in the analytic Sudakexponent depends on the level to which a fixed order calation was performed for a given process. Generally, inext-to-next-to-leading order calculation is available, th

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B(2) can be extracted and incorporated. Extraction of higcoefficients requires knowledge of even higher order Qcorrections. So far, only theA(1), A(2) andB(1) coefficientsare known for Higgs boson production but the calculationB(2) is in progress@17#. If we try to interpret parton showering in the same language, then we can say that the MoCarlo Sudakov exponent always contains a term analogto A(1). It was shown in Ref.@18# that a term equivalent toB(1) is also included in the~HERWIG! shower algorithm, anda suitable modification of the Altarelli-Parisi splitting function, or equivalently the strong coupling constantaS , alsoeffectively approximates theA(2) coefficient.5

In contrast with the shower Monte Carlo programs alytic resummation calculations integrate over the kinemaof the soft-gluon emission, with the result that they are liited in their predictive power to inclusive final states. Whthe Monte Carlo program maintains an exact treatment ofbranching kinematics, in the original lowpT factorizationformalism no kinematic penalty is paid for the emissionthe soft gluons, although an approximate treatment ofcan be incorporated into its numerical implementations, sas ResBos@5,13#. Neither the parton showering process nthe analytic resummation translate smoothly into kinemaconfigurations where one hard parton is emitted at largepT .In the Monte Carlo matrix element corrections and in tanalytic resummation calculation, matching is necessThis matching is standard procedure for resummed calctions, and matrix element corrections are becoming increingly common in Monte Carlo programs@19–21#.

With the appropriate input from higher order cross s

5This is rigorously true only for the highx or At region.

FIG. 1. TheZ0 pT distribution~at low pT) from CDF for run 1compared to predictions from ResBos~curve! and from PYTHIA

~histograms!. The two PYTHIA predictions use the default~rms!value for the non-perturbativekT ~0.44 GeV! and the value thatgives the best agreement with the shape of the data~2.15 GeV!. Thenormalization of the resummed prediction was rescaled upward8.4%. ThePYTHIA prediction was rescaled by a factor of 1.4 for thshape comparison.~Including only soft-gluon QCD correctionsPYTHIA does not contain the QCDK factor.!

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tions, a resummation calculation has the correspondhigher order normalization and scale dependence. Themalization and scale dependence for the Monte Carlo pgram, though, remains that of a leading order calculatiThe parton showering process redistributes the eventphase space, but does not change the total cross section~forexample, for the production of a Higgs boson!.6

One quantity which is expected to be well describedboth calculations is the transverse momentum of the fistate electroweak boson in a subprocess such asqq→W6X, Z0X or gg→HX, where most of thepT is providedby initial state parton emission. The parton showering splies the same sort of transverse kick as the resummedgluon emission in the analytic calculation. Indeed, simiSudakov form factors appear in both approaches. The cospondence between the Sudakov form factors of resumtion and Monte Carlo approaches embodies many subtlerelating to both the arguments of the Sudakov factors as was the impact of sub-leading logarithms@22#.

At a point in its evolution, typically corresponding to thvirtuality of a few GeV2, the parton shower is cut off and theffects of gluon emission at softer scales must be paretrized and inserted by hand. This is similar to the somewarbitrary division between perturbative and non-perturbatregions in the resummation calculation. The parametrizais typically expressed in a Gaussian form, similar to that ufor the non-perturbativekT in a resummation program@14#.In general, the value for the non-perturbative^kT& needed ina Monte Carlo program will depend on the particular kinmatics and initial state being investigated. A value of t

6Technically, one could add the branching forq→q1Higgs bo-son in the shower, which would somewhat increase the Higgs bocross section. However, the main contribution to the higher ordeKfactor comes from the virtual corrections and the ‘‘Higgs bremstrahlung’’ contribution is negligible.

by

FIG. 2. TheZ0 pT distribution ~for the full range ofpT) fromCDF for run 1 compared to predictions from ResBos~curve! andfrom PYTHIA ~histogram!. The normalization of the resummed prediction was rescaled upwards by 8.4%. ThePYTHIA prediction wasrescaled by a factor of 1.4 for the shape comparison.

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average non-perturbativekT of greater than 1 GeV, for example, does not imply that there is an anomalous intrinsickTassociated with the parton size. Rather, this amount of^kT&needs to be supplied to provide what is missing in the trcated parton shower. If the shower is cut off at a highvirtuality, more of the ‘‘non-perturbative’’kT will be needed.

IV. Z0 BOSON PRODUCTION AT THE TEVATRON

From a theoretical viewpoint,Z0 boson production at theTevatron is one of the highest precision testing groundsthe effects of multiple soft-gluon emission. The fully diffeential fixed order cross section has been calculated uO(aS

2), and theA(1,2), B(1,2), and C(1) resummed coeffi-cients are known for this process, and have been numericimplemented@13#. Since theO(aS

2) corrections are relativelysmall ~the order of a percent!, the contribution ofB(2) isalmost negligible. Thus, nominally the same perturbatphysics is implemented in the shower Monte Carlo prograas in the resummation calculation. Any differences betwtheir predictions can be ascribed to the small differencethe implementation of the perturbative physics and todifferent non-perturbative physics they contain. Experimtally, the 4-momentum of aZ0 boson, and thus itspT , can bemeasured with great precision in thee1e2 decay mode.Resolution effects are relatively minor and are easily crected. Thus, theZ0 pT distribution is an excellent probe othe effects of the soft-gluon emission.

The resolution correctedpT distribution ~in the low pTregion! for Z0 bosons from the CDF experiment@23# isshown in Fig. 1, compared to both the resummed predic

FIG. 3. A comparison of thePYTHIA predictions for diphoton

production at the Tevatron for the two different subprocesses,qqandgg. The same cuts are applied toPYTHIA as in the CDF dipho-ton analysis.

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of ResBos and to two predictions fromPYTHIA version6.125. OnePYTHIA prediction uses the default value of intrinsic kT

rms50.44 GeV~dashed histogram!7, and the seconda value of 2.15 GeV~solid histogram!, per incoming parton.8

The latter value was found to give the best agreementPYTHIA with the data, and a similar conclusion has bereached in comparisons of the CDFZ0 pT data withHERWIG

@24#. All of the predictions use the CTEQ4M parton distrbutions@25#. The shift between the twoPYTHIA predictions atlow pT is clearly evident. As might have been expected,high pT region~above 10 GeV! is unaffected by the value othe non-perturbativekT . Much of the kT ‘‘given’’ to theincoming partons at their lowest virtuality,Q0, is reduced atthe hard scatter due to the number of gluon branchingsceding the collision. The emitted gluons carry off a sizabfraction of the original non-perturbativekT @26#. This pointwill be investigated in more detail later for the case of Higboson production.

In the resummed calculation it has been shown thataddition to the perturbative physics~Sudakov-Wilson coeffi-cients,Cja), the choice of the non-perturbative parameteaffects the shape of the distribution in the lowestpT region

7For a Gaussian distribution,kTrms51.13 kT&.

8A previous publication@19# indicated the need for a substantiallarger non-perturbativekT&, of the order of 4 GeV, for the case oW6 production at the Tevatron. The data used in the comparishowever, were not corrected for resolution smearing, a fairly laeffect for the case ofW→en production and decay.

FIG. 4. A comparison of thePYTHIA predictions for diphotonproduction at the Tevatron for the two different subprocesses,gg

~top! andqq ~bottom!, for two recent versions ofPYTHIA. The samecuts are applied toPYTHIA as in the CDF diphoton analysis.

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and the location of the peak@13#. In order to qualitativelycompare this effect to the smearing applied in the MoCarlo programs, it is possible to bring the resummation fmula to a form where the non-perturbative function acts aGaussian type smearing term. This, using the Ladinsky-Yparametrization@27# of the non-perturbative function, leadto an rms value of 2.5 GeV for the effectivekT smearingparameter forZ0 production at the Tevatron. This is in agrement with thePYTHIA and HERWIG results: to describe welthe Z0 production data at the Tevatron, 2–2.5 GeV noperturbativekT is needed in these implementations. Thesummed curve agrees with the shape of the data well, wis a non-trivial result, since the resummation calculation dnot contain any free parameters which are fitted to theZ0 pT

distribution. Even with the optimal non-perturbativekTrms

52.15 GeV, there is slight shape difference betweenshower Monte Carlo program and the data. This mightpartially due to the lack of theB(2) coefficient in the showerMonte Carlo programs. This is supported by the fact thathe B(2) coefficient was not included in the resummed pdiction, the result would be an increase in the height ofpeak and a decrease in the rate between 10 and 20 Gleading to a better agreement with the bestPYTHIA prediction@12#.

TheZ0 pT distribution is shown over a widerpT range inFig. 2. ThePYTHIA and ResBos predictions both describe tdata well. Note especially the agreement ofPYTHIA with thedata at highpT , made possible by explicit matrix eleme

FIG. 5. A comparison of thePYTHIA and ResBos predictions fodiphoton production at the Tevatron for the two different subp

cesses,gg ~left! andqq ~right!. The same cuts are applied toPYTHIA

and ResBos as in the CDF diphoton analysis. The bottom figshow the same in logarithmic scale.

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corrections ~from the subprocessesqq→Z0g and gq→Z0q) to theZ0 production process.9

V. DIPHOTON PRODUCTION

Most of the experience that we have for comparisonsdata to resummation calculations or Monte Carlo programbased on Drell-Yan pair production, that is mostly onqqinitial states. It is important then to examine diphoton prduction at the Tevatron, where a large fraction of the conbution at low mass is due togg scattering. The prediction fothe diphotonpT distribution at the Tevatron, fromPYTHIA

~version 6.122!, is shown in Fig. 3, using the experimentcuts applied in the CDF analysis@28#. About half of thediphoton cross section at the Tevatron is due to thegg sub-process, and the diphotonpT distribution is noticeablybroader for thegg subprocess than for theqq subprocess.

A comparison of thepT distributions for the two diphoton

9Slightly different techniques are used for the matrix element crections byPYTHIA @19# and byHERWIG @20#. In PYTHIA, the partonshower probability distribution is applied over the whole phaspace and the exact matrix element corrections are applied onthe branching closest to the hard scatter. InHERWIG, the correctionsare generated separately for the regions of phase space unpopby HERWIG ~the ‘‘dead zone’’! and the populated region. In the deazone, the radiation is generated according to a distribution usingfirst order matrix element calculation, while the algorithm for talready populated region applies matrix element corrections whever a branching is capable of being ‘‘the hardest so far.’’

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FIG. 6. A comparison of thePYTHIA predictions for diphoton

production at the LHC for the two different subprocesses,qq andgg. Similar cuts are applied to the diphoton kinematics as thused by ATLAS and CMS.

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subprocesses (qq,gg) in two recent versions ofPYTHIA, 5.7and 6.1, is shown in Fig. 4. There seems to be little diffence in thepT distributions between the two versions fboth subprocesses. As will be shown later, this is not truethe case of Higgs boson production. In Fig. 5 are shownResBos predictions for diphoton production at the Tevatfrom qq and gg scattering compared to thePYTHIA predic-tions. Thegg subprocess predictions in ResBos agree wwith those fromPYTHIA while theqq pT distribution is no-ticeably broader in ResBos. The latter behavior is due topresence of theY piece in ResBos at moderatepT , that is thematching of theqq cross section to the fixed orderqq→ggg at high pT . The corresponding matrix element corection is not implemented inPYTHIA. ThePYTHIA and Res-Bos predictions forgg→gg agree in the moderatepT re-gion, even though the ResBos prediction has theY piecepresent and is matched to the matrix element piecegg→ggg at high pT , while there is no such matrix elemencorrection forPYTHIA. This demonstrates the smallnesstheY piece for thegg subprocess, which is the same concsion that was reached in Ref.@3#. One way to understand thiis recalling that thegg parton-parton luminosity falls very

steeply with increasing partonic center of mass energy,As.This falloff tends to suppress the size of theY piece since theproduction of the diphoton pair at higherpT requires largervalues of the longitudinal momentum fractions.

Comparisons of the diphoton data measured by bothCDF @28# and D0@29# experiments indicate a disagreemeof the observed diphotonpT distribution with the NLO QCDpredictions@30#. In particular, thepT distribution in the data

FIG. 7. A comparison of thePYTHIA predictions for diphotonproduction at the LHC for the two different subprocesses,gg ~top!

andqq ~bottom!, for two recent versions ofPYTHIA. Similar cuts areapplied to the diphoton kinematics as are used by ATLAS aCMS.

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is noticeably broader than that predicted by fixed order Qcalculations, but in agreement with the predictions of ResB@31#. The transverse distributions of the diphoton pair aparticularly sensitive to the effects of soft-gluon radiatioThe pT distribution, for example, is a delta function calclated at leading order, and is strongly smeared by theorders Sudakov factor. Given the small size of the diphocross section at the Tevatron, the comparisons for run 1statistically limited. A more precise comparison betwetheory and experiment will be possible with the 2 fb21 orgreater data sample that is expected for CDF and D0 in ruand at the LHC. The Monte Carlo prediction for the diphotproduction cross section, as a function of the diphotonpTand using cuts appropriate to ATLAS and CMS, is shownFig. 6. As at the Tevatron, about half of the cross sectiondue togg scattering and the diphotonpT distribution fromgg scattering is noticeably broader than that fromqq pro-duction.

In Fig. 7 is shown a comparison of the diphotonpT dis-tribution at the LHC for two different versions ofPYTHIA,for the two different subprocesses. Note that thepT distribu-tion in PYTHIA version 5.7 is somewhat broader than thatversion 6.122 for the case ofgg scattering. The effectivediphoton mass range being considered here is lower than150 GeV Higgs boson mass that will be considered innext section. As will be seen, the differences in soft-gluemission between the two versions ofPYTHIA are larger inthat case. In Fig. 8 are shown the ResBos predictionsdiphoton production at the LHC fromqq andgg scatteringcompared to thePYTHIA predictions. Again, thegg subpro-cess in ResBos agrees well withPYTHIA, while the qq pT

d

FIG. 8. A comparison of thePYTHIA and ResBos predictions fodiphoton production at the LHC for the two different subprocess

gg ~left! and qq ~right!. Similar cuts are applied toPYTHIA andResBos as in the ATLAS and CMS diphoton analyses. The botfigures show the same in logarithmic scale.

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distribution is noticeably broader in ResBos, for the reascited previously.

VI. HIGGS BOSON PRODUCTION

A comparison of the SM HiggspT distribution at theLHC, for a Higgs boson mass of 150 GeV, is shown in F9, for ResBos and the two recent versions ofPYTHIA. Asbefore,PYTHIA has been rescaled by a factor of 1.7, to agwith the normalization of ResBos to allow for a better shacomparison. There are a number of features of interest. Fthe peak of the resummed distribution has moved topT'11 GeV~compared to about 3 GeV forZ0 boson produc-tion at the Tevatron!. This is partially due to the larger mas~150 GeV compared to 90 GeV!, but is primarily because othe larger color factors associated with initial state gluo(CA53) rather than quarks (CF54/3), and also because othe larger phase space for initial state gluon emission atLHC. Second, and more importantly, there is a substandisagreement for the shape of the HiggspT distribution be-tween ResBos andPYTHIA 5.7, and between the two versionof PYTHIA. An understanding of the reasons for these diffences is critical, as the shape of the transverse momendistribution for the Higgs boson in the low to moderatepTregion can dictate the details of both the experimental tgering and the analysis strategies for the Higgs boson seaAs noted before, most of the studies for Higgs boson prodtion by CMS and ATLAS have been based onPYTHIA 5.7.For the CMS detector, the higherpT activity associated withHiggs boson production in version 5.7 allows for a moprecise determination of the event vertex from whichHiggs boson~decaying into two photons! originates. Vertex

FIG. 9. A comparison of predictions for the HiggspT distribu-tion at the LHC from ResBos and from two recent versionsPYTHIA. The ResBos andPYTHIA predictions have been normalizeto the same area. The bottom figure shows the same in logarithscale.

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pointing with the photons is not possible in the CMS barand the large number of interactions occurring with hiintensity running will mean a substantial probability thatleast one of the interactions will have more activity than tHiggs vertex, thus leading to the assignment of the Higboson decay to the wrong vertex, and therefore a noticedegradation of thegg effective mass resolution.

In comparison to ResBos, the older version ofPYTHIA

produces too many Higgs events at moderatepT . Twochanges have been implemented in the newer versionThe first change is that a cut is placed on the combinationz ~longitudinal momentum fraction! and Q2 ~partonic virtu-ality! values in a branching:u5Q22 s(12z),0, wheresrefers to the squared invariant mass of the subsystem ohard scattering plus the shower partons considered topoint. The association withu is relevant if the branching isinterpreted in terms of a 2→2 hard scattering. The corner oemissions that do not respect this requirement occurs wthe Q2 value of the space-like emitting parton is littlchanged and thez value of the branching is close to unityThis effect is mainly for the hardest emission~largestQ2).The net result of this requirement is a substantial reductiothe total amount of gluon radiation@32#.10 In the secondchange, the parameter for the minimum gluon energy emi

10Such branchings are kinematically allowed, but since matrixement corrections would assume initial state partons to haveQ2

50, a non-physicalu results ~and thus no possibility to imposematrix element corrections!. The correct behavior is beyond thpredictive power of leading logarithm Monte Carlo programs.

f

ic

FIG. 10. A comparison of predictions for the HiggspT distribu-tion at the Tevatron from ResBos and from two recent versionsPYTHIA. The ResBos andPYTHIA predictions have been normalizeto the same area. The bottom figure shows the same in logarithscale.

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in space-like showers is modified by an extra factor rougcorresponding to the 1/g factor for the boost to the harsubprocess frame@32#. The effect of this change is to increase the amount of gluon radiation. Thus, the two effeare in opposite directions but with the first effect being domnant. In principle, this problem could affect thepT distribu-tion for all PYTHIA processes. In practice, it affects onlygginitial states, due to the enhanced probability for branchin such an initial state.

The newer version ofPYTHIA agrees well with ResBos alow to moderatepT , but falls below the resummed prediction at highpT . The agreement of the predictions ofPYTHIA

6.1 with those of ResBos, in the low to moderatepT region,gives some credence that the changes made inPYTHIA movein the right direction. The disagreement at highpT can beeasily understood: ResBos switches to the next-to-leadorder Higgs boson1jet matrix element at highpT , while thedefault PYTHIA can generate the HiggspT distribution onlyby initial state gluon radiation, using the Higgs boson msquared as the maximum virtuality. HighpT Higgs bosonproduction is another example where a 2→1 Monte Carlocalculation with parton showering cannot completely repduce the exact matrix element calculation, without the usematrix element corrections. The highpT region is better re-produced if the maximum virtualityQmax

2 is set equal to thesquared partonic center of mass energy,s, rather thanmH

2 .This is equivalent to applying the parton shower to allphase space. However, this has the consequence of depthe low pT region, as ‘‘too much’’ showering causes evento migrate out of the peak. The appropriate scale to usPYTHIA ~or any Monte Carlo program! depends on thepTrange to be probed. If matrix element information is used

FIG. 11. A comparison of predictions for the HiggspT distribu-tion at the LHC from ResBos, a recent version ofPYTHIA, andHERWIG. All predictions have been normalized to the same arThe bottom figure shows the same in logarithmic scale.

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constrain the behavior, the correct highpT cross section canbe obtained while still using the lower scale for showerinThus, the incorporation of matrix element correctionsHiggs boson production~involving the processesgq

→qH,qq→gH, gg→gH) is the next logical project for theMonte Carlo experts, in order to accurately describe the hpT region, and is already in progress@26,33#.

A comparison of the two versions ofPYTHIA and of Res-Bos is also shown in Fig. 10 for the case of Higgs bosproduction at the Tevatron with center-of-mass energy ofTeV ~for a hypothetical SM Higgs boson mass of 10GeV!.11 The same qualitative features are observed as atLHC: the newer version ofPYTHIA agrees better with ResBoin describing the lowpT shape, and there is a falloff at higpT unless the larger virtuality is used for the parton showeThe default ~rms! value of the non-perturbativekT ~0.44GeV! was used for thePYTHIA predictions for Higgs bosonproduction.

VII. COMPARISON WITH HERWIG

The variation between versions 5.7 and 6.1 ofPYTHIA

gives an indication of the uncertainties due to the types

11As an exercise, events for an 80 GeVW boson and an 80 GeVHiggs boson were generated at the Tevatron usingPYTHIA 5.7 @34#.

A comparison of the distribution of values ofu and the virtualityQfor the two processes indicates a greater tendency for the Hvirtuality to be near the maximum value and for there to be a lar

number of Higgs events with positiveu.

.

FIG. 12. A comparison of predictions for the HiggspT distribu-tion at the LHC from ResBos, two recent versions ofPYTHIA, andHERWIG. All predictions have their absolute normalizations. Tbottom figure shows the same in logarithmic scale.

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choices that can be made in Monte Carlo programs.

prescription thatu be negative for all branchings is a choicrather than an absolute requirement. Perhaps the better ament of version 6.1 with ResBos is an indication that t

adoption of theu restrictions was correct. Of course, themay be other changes toPYTHIA which would also lead tobetter agreement with ResBos for this variable.

Since there are a variety of choices that can be madMonte Carlo implementations, it is instructive to compathe predictions for thepT distribution for Higgs boson production from ResBos andPYTHIA with that from HERWIG

version 5.6. TheHERWIG prediction, for the HiggspT distri-bution at the LHC, is shown in Fig. 11, along with thPYTHIA and ResBos predictions, all normalized to the RBos prediction.12 ~In all cases, the CTEQ4M parton distribution was used.! The predictions fromHERWIG andPYTHIA 6.1are very similar, with theHERWIG prediction matching theResBos shape somewhat better at lowpT . It is interestingthat HERWIG matches the ResBos prediction so closely wiout the implementation of any kinematic cuts as inPYTHIA

6.1. Perhaps the reason is related to the treatment of ccoherence in theHERWIG parton showering algorithm. Foreference, absolutely normalized predictions from ResB

12The normalization factors~ResBos and Monte Carlo! are 1.68for both versions ofPYTHIA and 1.84 forHERWIG.

FIG. 13. Top: a comparison of thePYTHIA predictions for thepT

distribution of a 100 GeV Higgs boson at the Tevatron usingdefault~rms! non-perturbativekT ~0.44 GeV! and a larger value~4GeV!, at the initial scaleQ0 and at the hard scatter scale. Alsshown is the ResBos prediction. Bottom: the vector sum ofintrinsic kT (kT11kT2) for the two initial state partons at the initiascaleQ0 and at the hard scattering scale, for the two valuesprimordial kT .

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PYTHIA, andHERWIG for the pT distribution of a 150 GeVHiggs boson at the LHC are shown in Fig. 12.

VIII. NON-PERTURBATIVE kT

A question still remains as to the appropriate input vaof non-perturbativekT in the Monte Carlo programs toachieve a better agreement in shape, both at the Tevatronat the LHC.13 In Figs. 13 and 14 are shown comparisonsResBos andPYTHIA predictions for the HiggspT distributionat the Tevatron and the LHC. ThePYTHIA prediction~version6.1 alone! is shown with several values of non-perturbatikT . Surprisingly, no difference is observed between the pdictions with the different values ofkT , with the peak inPYTHIA always being somewhat below that of ResBos. Tinsensitivity can be understood from the plots at the bottof the two figures, which show the sum of the noperturbative partonic initial statekT’s (kT11kT2) at Q0 andat the hard scatter scaleQ. Most of thekT is radiated away,with this effect being larger~as expected! at the LHC. Thelarge gluon radiation probability from agg initial state andthe greater phase space available at the LHC lead to a sger degradation of the non-perturbativekT than was observedwith Z0 production at the Tevatron.

For completeness, a comparison ofPYTHIA and ResBos is

13This has also been explored for direct photon production in R@35#.

e

e

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FIG. 14. Top: a comparison of thePYTHIA predictions for thepT

distribution of a 150 GeV Higgs boson at the LHC using the defa~rms! non-perturbativekT ~0.44 GeV! and a larger value~4 GeV!, atthe initial scaleQ0 and at the hard scatter scale. Also shown isResBos prediction. Bottom: The vector sum of the intrinskT (kT11kT2) for the two initial state partons at the initial scaleQ0

and at the hard scattering scale, for the two values of primordialkT .

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shown in Fig. 15 forZ0 boson production at the LHC. Therare two points that are somewhat surprising. First, therstill a very strong sensitivity to the value of the noperturbativekT used in the smearing. Second, the best agment with ResBos is obtained with the default value~0.44GeV!, in contrast to the 2.15 GeV needed at the Tevatron~cf.Fig. 1!. Note again the agreement ofPYTHIA with ResBos atthe highest values ofZ0 pT due to the explicit matrix ele-ment corrections applied. The sum of the incoming partonkTdistributions, both at the scaleQ0 and at the hard scatterinscale, are shown in Fig. 16 for several different starting~rms!values of primordialkT ~per parton!. There is substantiallyless radiation for aqq initial state than for agg initial state~as in the case of the Higgs boson!, leading to a noticeabledependence of theZ0 pT distribution on the primordialkTdistribution.

IX. CONCLUSIONS

An understanding of the signature for Higgs boson pduction at either the Tevatron or the LHC depends uponunderstanding of the details of the multiple soft-gluon emsion from the initial state partons. This soft-gluon radiati

FIG. 15. A comparison of the predictions for thepT distributionfor Z0 production at the LHC fromPYTHIA and ResBos, whereseveral values ofkT have been used to make thePYTHIA predictions.

m8.

ys

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can be modeled either in a Monte Carlo program or byanalytic resummation calculation, with various choices psible in both implementations. A comparison of the two aproaches helps in understanding their strengths and wnesses, and their reliability. The data from the Tevatron teither exist now, or will exist in run 2, and from the LHCwill be extremely useful to test both methods.

Note added. At the final stage of preparing this manuscript, we became aware of a new paper@36#, which studiedthe A and B functions for Higgs boson production up tO(aS

4), and presented an expression for the coefficientB(2).

ACKNOWLEDGMENTS

We would like to thank Stefano Catani, Claude CharlGennaro Corcella, Steve Mrenna, and Torbjo¨rn Sjostrand foruseful conversations. We thank Willis Sakumoto for proving the figures for CDFZ0 production and Valeria Tano fothe HERWIG curves. C.B. and J.H. thank C.-P. Yuan for nmerous discussions and blackboard lectures. This worksupported in part by the DOE under grant DE-FG-094ER40833 and by the NSF under grant PHY-9901946.

FIG. 16. A comparison of the total initial statekT (kT11kT2)distributions forZ0 production at the LHC fromPYTHIA, both at theinitial scaleQ0 and at the hard scattering scale, for several~rms!values of the initial statekT . The mean and rms numbers referthe values at the hard scattering scale.

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Higgs boson production: A comparison of parton showers and … · 2005-03-31 · Higgs boson production: A comparison of parton showers and resummation C. Bala´zs* Department of