Diphoton + jets at NLO
aa r X i v : . [ h e p - ph ] N ov Diphoton + jets at NLO
Thomas Gehrmann
Institute for Theoretical Physics, University of Zürich, Winterthurerstrasse 190, CH-8057Zürich, SwitzerlandE-mail: [email protected]
Nicolas Greiner ∗ Max Planck Institute for Physics, Föhringer Ring 6, D-80805 München, GermanyE-mail: [email protected]
Gudrun Heinrich
Max Planck Institute for Physics, Föhringer Ring 6, D-80805 München, GermanyE-mail: [email protected]
We present the next-to-leading order QCD corrections to the production of a photon pair in as-sociation with one or two jets. This class of processes constitutes an important background forHiggs physics at the LHC. For the one jet process we include photon fragmentation contributionsand perform a comparison between different photon isolation criteria and various isolation pa-rameters. The two jet calculation has been performed using a smooth cone isolation criterion.We find that the NLO QCD corrections are substantial and can lead to distortions of differentialdistributions. ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ iphoton + jets at NLO
Nicolas Greiner
1. Introduction
The production of a photon pair at the LHC within the Standard Model is an important back-ground for the Higgs boson observed at the LHC [1]. One of the most important decay channels isthe decay into a photon pair [5, 3, 2], due to its clean signature. The Standard Model background,the production of two photons without an intermediate Higgs, is experimentally determined bymeans of sideband subtraction. However, for a more precise determination of the Higgs param-eters, this estimation of the background might not be precise enough. Therefore it is crucial tohave a reliable theoretical prediction for this class of processes. The production of two photons isknown fully differentially at NLO [6], including gluon initiated subprocesses [9] and resummationeffects [10, 11]. Recently also the NNLO result has become available [7].The presence of extra jets allows for a better control of the backgrounds and for a distinction ofdifferent Higgs production processes. In particular, the additional production of two jets allowsto probe the vector boson fusion production mechanism. Therefore the QCD corrections for pro-cesses with the presence of extra jets are an important ingredient for reliable predictions in thediphoton plus jets channel. The production of a photon pair in association with one jet is knownat NLO [8] using a smooth cone isolation criterion [12]. We present an NLO QCD calculation fordiphoton plus one jet where for the first time different photon isolation criteria and different isola-tion parameters are compared, and we present the first NLO calculation of diphoton plus two-jetproduction.
2. Photon isolation and photon fragmentation
A final state photon can either originate from the hard scattering matrix elements which meansit is perturbatively accessible, or it can originate from the fragmentation of hadrons into photons.The latter production mechanism is of non-perturbative nature and therefore can not be describedusing a fixed order calculation. Only the production of photons from the hard interaction canbe computed within perturbation theory from first principles, while the production of photons inhadronization and hadron decays can only be modeled, thereby introducing a dependence on ratherpoorly known fragmentation parameters.The characteristics of the photon typically depend on its origin. Secondary photons, i.e. photonnsstemming from hadronic decays, are usually inside a jet cone formed by the hadrons. Photonscoming from the hard interaction tend to be separated from hadronic jets. In order to distinguishthe two types, one applies photon isolation cuts, which limit the hadronic activity around a photoncandidate. However, a veto on all hadronic activity around the photon direction would result in asuppression of soft gluon radiation in part of the final state phase space, thereby violating infraredsafety of the observables. Consequently, all photon isolation prescriptions must admit some resid-ual amount of hadronic activity around the photon direction. In the following we focus on twotypes of photon isolation. One is the cone-based isolation which is most commonly used at hadroncollider experiments. In this procedure, the photon candidate is identified (prior to the jet clus-tering) from its electromagnetic signature, and its momentum direction (described by transverseenergy E T , g , rapidity h g and polar angle f g ) is determined. Around this momentum direction, acone of radius R g in rapidity h and polar angle f is defined. Inside this cone, the hadronic trans-2 iphoton + jets at NLO Nicolas Greiner verse energy E T , had is measured. The photon is called isolated if E T , had is below a certain threshold,defined either in absolute terms, or as a fraction of E T , g The latter criterion then means that a photoncandidate is considered as isolated if it fulfills the condition E had , cone ≤ e c p g T , (2.1)inside the cone with radius R . The cone-based isolation allows events with a quark being collinearto a photon. The theoretical predictions for cross sections defined with this type of isolation musttherefore take account of photon fragmentation contributions.A different option is the smooth cone isolation [12]. It varies the threshold on the hadronic energyinside the isolation cone with the radial distance from the photon. It is described by the cone size R g , a weight factor n g and an isolation parameter e g . With this criterion, one considers smallercones of radius r g inside the R g -cone and calls the photon isolated if the energy in any sub-conedoes not exceed E had , max ( r g ) = e g p g T (cid:18) − cos r g − cos R g (cid:19) n g . (2.2)By construction, the smooth cone isolation does not admit any hard collinear quark-photon config-urations, thereby allowing a full separation of direct and secondary photon production, and conse-quently eliminating the need for a photon fragmentation contribution in the theoretical description.Despite its theoretical advantages, the smooth cone isolation was up to now used in experimentalstudies of isolated photons only in a discretized approximation. Experimentally, owing to finite de-tector resolution, the implementation of this isolation criterion will always require some minimal,nonzero value of r g , thereby leaving potentially a residual collinear contribution.
3. Diphoton + one jet
A detailed calculation of this process and a comparison between the two photon isolation typescan be found in [13]. The code that has been used to produce the presented results has been madepublic and can be downloaded from https://gosam.hepforge.org/diphoton/ . Both the calculation of diphoton plus one jet as well as with two jets, described in section 4,are performed using the same setup. For the generation of the tree level and real emission matrixelements we use MadGraph [14], the regularization of infrared QCD singularities is handled byMadDipole [15], which makes use of the dipole formalism as developed in Ref. [16]. For inte-gration over the phase space we used MadEvent [17]. The routines for generating histograms anddistributions originate from the MadAnalysis package (see http://madgraph.hep.uiuc.edu). All in-gredients are generated and combined in a fully automated way.The virtual amplitudes have been obtained using GoSam [18], a public package for the automatedgeneration of one-loop amplitudes. It uses Qgraf [19], FORM [20] and Spinney [21] for the gen-eration of the amplitudes, which are optimized and written as a Fortran90 code with the use ofHaggies [22]. For the reduction of the one-loop amplitudes we used Samurai [23], which performs3 iphoton + jets at NLO
Nicolas Greiner a reduction at the integrand level based on the OPP-method [24]. As a rescue for numerically unsta-ble points, the tensor reduction method of the Golem95 library [25] has been used. The remainingmaster integrals are computed with either OneLoop [26], or Golem95 [25].In the case where the fixed cone isolation is used, the real emission contribution contains infraredsingularities related to the collinear emission of the photon off a final-state QCD parton. They needto be regularized by some kind of subtraction terms. The corresponding integrated subtractionterms make this singularity apparent as they contain an explicit pole term when integrating overthe unresolved one-particle phase space in dimensional regularization. This pole is then absorbedinto the fragmentation functions. To regulate these singularities we again make use of the dipoleformalism as developed in Ref.[27] and implemented in the QED extension of MadDipole [28].This extension also offers the framework for a straightforward implementation of fragmentationfunctions.
For the results presented here we assumed as center of mass energy of √ s = p jet T >
40 GeV, p g T > | h g , h j | ≤ .
5, 100 GeV ≤ m gg ≤
140 GeV.For the jet clustering we used an anti- k T algorithm [29] with a cone size of R = . a s atleading order and next-to-leading order are given by a s ( M Z ) = . m r and m F are dynamical scales and set to be equal, and we choose m = ( m gg + (cid:229) j p T , j ) for our central scale. When using cone based isolation, the fragmentation scale m f also enters, andwe set it to be equal to the other scales. To assess the effect of a jet veto, we present results forthe inclusive and the exclusive case, where for the latter we veto on a second jet by demanding p T , jet <
30 GeV. For the photon isolation, we compare the Frixione isolation criterion with thefixed cone criterion for several values of the photon energy fraction z c in the cone, where z c = | ~ p had T , cone || ~ p g T + ~ p had T , cone | , such that in the collinear limit, z c is related to e c in eq. (2.1) by z c = e c + e c . For the Frixione isolationcriterion (see eq. (2.2)), our default values are R = . , n = e = . gg + iphoton + jets at NLO Nicolas Greiner x [ pb ] s Cone isolationLO =0.1 c z=0.05 c z =0.02 c z x [ pb ] s Frixione IsolationLONLO
Figure 1:
Behavior of the exclusive gg +jet cross sections with different isolation prescriptions under scalevariations, m = x m , 0 . ≤ x ≤ m = ( m gg + (cid:229) j p T , j ) . x [ pb ] s Cone isolationLO =0.1 c z=0.05 c z =0.02 c z x [ pb ] s Frixione IsolationLONLO
Figure 2:
Behavior of the inclusive gg +jet+X cross sections with different isolation prescriptions underscale variations, m = x m , 0 . ≤ x ≤ m = ( m gg + (cid:229) j p T , j ) .
4. Diphoton + two jets
For the calculation of a photon pair plus two jets we used the same tools and packages asdescribed in section 3. The calculation has first been described in [33] to which we refer for a moredetailed description.
The numerical results presented in the following have been calculated at a center-of-mass en-ergy of √ s = k T algorithm [29] with a cone size of R j = . N F = p jet T >
30 GeV , p g , T >
40 GeV , p g , T >
25 GeV , | h g | ≤ . , | h j | ≤ . , R g , j > . , R g , g > . . For the photon isolation we restricted ourselves to the Frix-5 iphoton + jets at NLO
Nicolas Greiner s t o t [ pb ] e c inclusive cutsexclusive cuts 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 s t o t [ pb ] e inclusive cutsexclusive cuts Figure 3:
Dependence of the cross sections on the cone isolation parameters e c and e respectively. Thebands correspond to scale variations 0 . ≤ x ≤ ione isolation criterion with R = . , n = e = .
05. A more detailed analysis with differentisolation criteria and various isolation parameters will be presented elsewhere. The scales havebeen chosen as in section 3. Figure 4 shows the scale variation around the central value. A clear re-duction of the scale dependence can be observed by adding the next-to-leading order contributionswith a moderate K-factor of ∼ . m / m x= [ pb ] s LONLO
Figure 4:
Scale dependence of the total cross section at LO and NLO with x = m / m . corrections in differential distributions can be substantial even if the effects on the total cross sec-tion are rather moderate. This is in particular true, if at NLO, regions in phase space open up thatare kinematically not allow at leading order. Figure 5 shows the R -separation between the hardestjet and the hardest photon. The colored bands denote the scale uncertainty when varying aroundthe central scale by a factor of two. For small values of R , the NLO corrections lead to a strongdistortion of the shape. This can be understood in terms of kinematically allowed regions. At LO,the pair of hard photon and hard jet being close in R -space would have to be counterbalanced withthe soft photon and the soft jet. This is kinematically impossible at LO but appears at NLO due tothe additional radiation. 6 iphoton + jets at NLO Nicolas Greiner
Figure 5: R -separation R ( j , g ) between the hardest jet and the hardest photon.
5. Conclusions
We have presented the next-to-leading order QCD corrections to the production of a photonpair in association with one and two jets. This class of processes is important for a reliable pre-diction of the Standard Model background to the H → gg signal. In the one jet case we haveimplemented and compared two types of photon isolation criteria, the fixed cone isolation andFrixione isolation. For both cases we find large NLO corrections and for the inclusive case a strongdependence on the scale. The scale dependence can be effectively reduced by imposing a veto ona second jet. In general we find a strong dependence on isolation types and parameters, howeverit can be observed that for tight isolation parameters, the results obtained with different isolationtypes approach each other. We also calculated the first NLO corrections to the process of diphotonplus two jet production. For the photon isolation we used Frixione isolation and found moderateNLO corrections to the total cross section. The effects on differential distributions depend on theobservable and can lead to strong distortions of the shape. Acknowledgments
We thank the other members of the GoSam collaboration for useful discussions. N.G. andG.H. want to thank the University of Zurich for kind hospitality while parts of this project werecarried out. This work was supported in part by the Schweizer Nationalfonds under grant 200020-138206, and by the Research Executive Agency (REA) of the European Union under the GrantAgreement number PITN-GA-2010-264564 (LHCPhenoNet). We acknowledge use of the com-puting resources of the Rechenzentrum Garching.
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