A consistent event generation for non-resonant diphoton production at hadron collisions
aa r X i v : . [ h e p - ph ] M a y A consistent event generation for non-resonant diphotonproduction at hadron collisions
Shigeru OdakaHigh Energy Accelerator Research Organization (KEK)1-1 Oho, Tsukuba, Ibaraki 305-0801, JapanE-mail: [email protected]
August 6, 2018
Abstract
We have developed a Monte Carlo event generator for non-resonant diphoton ( γγ ) productionat hadron collisions in the framework of GR@PPA, which consistently includes processes havingadditional one jet radiation. The possible double count problem in the generation of radiativeprocesses is avoided by using the LLL subtraction method that we have applied to the weak-boson production processes. The subtraction method has been extended to the final-state QEDdivergence that appears in the qg → γγ + q process. Because a parton shower (PS) whichregularizes the subtracted QED divergence is still under development, we tried to use PYTHIA forthe generation of the fragmentation events to restore the subtracted components. The simulationemploying the ”old” PS of PYTHIA shows a reasonable matching with the GR@PPA events, andthe combined event sample shows a result in reasonable agreement with ResBos. We found thatthe contribution from qg → γγ + q is significant in the LHC condition. This event generator mustbe useful for the background studies in low-mass Higgs boson searches at LHC. Diphoton ( γγ ) production is one of most promising channels for the discovery of the Higgs bosonhaving a relatively small invariant mass ( .
130 GeV/ c ) at LHC. However, the measurement mustsuffer from a large irreducible diphoton background produced via non-resonant QED interactions.It is necessary to understand the properties of this background, not only for the discovery of theHiggs boson but also for detailed studies after the discovery. The identification of photons is rathercomplicated and largely dependent on the detector performance. For instance, a certain isolationcondition has to be required in order to reduce large contamination of π from hadron jets. Theperformance of this selection depends on the details of detector responses and is hard to be evaluatedanalytically. Therefore, it is strongly desired to provide theoretical predictions in the form of MonteCarlo (MC) event generators.The lowest order process for non-resonant diphoton production is very simple as shown in Fig. 1(a). Despite that, the next-to-leading order (NLO) correction to this process is known to be very large[1, 2]. The large correction is predominantly due to the contribution from real radiation processesillustrated in Fig. 1 (b) to (d). While the contribution from gluon radiation processes shown in Fig.1 (b) is not very significant, those from quark radiation processes shown in Fig. 1 (c) and (d) maybecome large due to a very large gluon density inside protons. It must be necessary to include theseprocesses in order to provide a realistic simulation.In this report, we describe the MC event generator for non-resonant diphoton production at hadroncollisions that we have developed. The program has been developed in the framework of the GR@PPAevent generator [3], and supports the generation of radiative processes in Fig. 1 (b) to (d) together withthe lowest-order process in Fig. 1 (a). Though the generator includes radiative processes, it is not fullyincluding NLO corrections. Non-divergent terms in soft/virtual corrections are yet to be included. In1igure 1: Typical Feynman diagrams for non-resonant diphoton production at hadron collisions: (a)the lowest order, (b) a gluon radiation process, (c) a quark radiation process, and (d) another quarkradiation process. The processes (b) and (c) have initial-state QCD divergences, while (d) has afinal-state QED divergence.any case, the radiative processes have various divergences which we need to regularize. The initial-state QCD divergences can be regularized using the method that we have applied to weak-bosonproduction processes, where divergent terms are numerically subtracted from the matrix elementsof radiative processes (the LLL subtraction) [4, 5, 6]. The subtracted contributions are restored bycombining with non-radiative processes to which a parton shower (PS) is applied. We can avoid thedouble count problem by the subtraction and naturally regularize the divergences as a result of themultiple radiation in PS.The quark radiation process illustrated in Fig. 1 (c) and (d) not only has an initial-state QCDdivergence but also has a QED divergence in the final state. We have extended the method appliedto the initial-state QCD to this final-state QED divergence. The extension of the subtraction isstraightforward, while the preparation of an appropriate PS is not trivial since it has to supportQED radiations together with QCD. This PS has to be applied to the quark in the final state of the qg → γ + q process to radiate photons from the final-state quark based on a collinear approximation(the fragmentation process). It is desired to have a capability to force a hard photon radiation inthis PS since we are interested in those events having two hard photons in the final state. Such afinal-state PS is still in development. Instead, we try to use the PYTHIA PS [7] for simulating thefragmentation process in this report. Though the PYTHIA PS is capable of radiating photons, itdoes not have a mechanism to force a hard photon radiation. We need to repeat the generation untilwe observe a sufficiently hard photon in the generated event. We use the so-called ”old” PS in thepresent study. The ”new” PS is not used because we still have some questions on its behavior.We sometimes find reports in which the detection efficiency and acceptance for the diphotonmeasurements are evaluated using event generators for the lowest-order process and fragmentationprocesses. Such evaluations are not self-consistent. Parton showers used in the simulation of fragmen-tation processes have a certain energy scale defining the maximum hardness of the parton radiation.The results depend on this arbitrarily chosen energy scale since those radiations exceeding this scaleare ignored. Non-collinear contributions are also ignored. These ignored contributions may be smallin many processes compared to the contributions taken into consideration. However, as we will showin this report, they become comparable to the lowest-order contribution in the diphoton production.It is necessary to include a simulation based on the exact matrix elements for the qg → γγ + q processin order to make a reliable evaluation.The fragmentation process that we take into consideration in this report is the so-called ”single”fragmentation. The ”double” fragmentation in which two photons are radiated from final-state par-2ons, for instance, from quarks in the gg → q ¯ q process are not supported. We need to introduce ” γγ +2 jets” production processes in order to construct a consistent event generator including the ”double”fragmentation. Besides, gg → γγ and its higher orders are not included at present.We require a typical kinematical condition for the Higgs-boson search at LHC through the presentstudy because we are interested in its background; that is p T ( γ ) ≥
40 GeV/ c, p T ( γ ) ≥
25 GeV/ c, | η ( γ ) | ≤ . , ∆ R ( γγ ) ≥ . ≤ m γγ ≤
140 GeV/ c . (1)We apply an asymmetric requirement to the transverse momenta ( p T ) of photons with respect tothe incident beam direction. The requirement on the pseudorapidity ( η ) is common to the twophotons. In addition, though this is not effective for real diphoton events now we consider, we requirea sufficient ∆ R separation between the two photons, where ∆ R is defined from the differences in thepseudorapidity ( η ) and the azimuthal angle ( φ ) as ∆ R = ∆ η + ∆ φ . Finally, the invariant massof the two photons ( m γγ ) is restricted within the range that we are interested in. These conditionsare required after completing the simulation down to the hadron level. Looser constraints are appliedat the event generation in order to avoid any bias. The simulations are carried out for the designcondition of LHC, proton-proton collisions at a center-of-mass (cm) energy of 14 TeV.This report is organized as follows: the extension of the limited leading-log (LLL) subtractionmethod to the final-state QED divergence is described in Section 2, and the simulation of the frag-mentation process employing the PYTHIA PS is described in Section 3. A typical isolation cut issimulated in Section 4. The results from the combined event simulation is presented in Section 5, andthe discussions are concluded in Section 6. We approximate the final-state QED divergence in the qg → γγ + q process as (cid:12)(cid:12)(cid:12) M ( LLL, fin) qg → γγq (ˆ s, ˆΦ γγq ) (cid:12)(cid:12)(cid:12) = (cid:12)(cid:12)(cid:12) M qg → γq (ˆ s, ˆΦ γq ) (cid:12)(cid:12)(cid:12) f ( LL ) q → qγ ( Q , z ) θ ( µ F SR − Q ) . (2)The leading-log (LL) radiation function can be given as f ( LL ) q → qγ ( Q , z ) = α π π Q P q → qγ ( z ) . (3)The parameter α is the electromagnetic coupling and the splitting function is defined as P q → qγ ( z ) = e q z − z , (4)where e q is equal to 1/3 for down-type quarks and 2/3 for up-type quarks. We evaluate Eq. (2) fortwo possible combinations of the quark and a photon in the final state, and numerically subtractthem from the exact matrix element of qg → γγ + q , together with the LLL term for the initial-stateQCD divergence. The parameters Q and z are defined by using the sum of the energy ( E qγ ) and themomentum ( p qγ ) of the considered q - γ pair. They are defined in the cm frame of the qg → γγ + q event as Q = E qγ − p qγ , (5)and z = p L ( E qγ + p qγ ) + Q / p qγ ( E qγ + p qγ ) + Q , (6)where p L is the momentum component of the q in parallel to the summed momentum. Equation(6) is defined so that z should represent the momentum fraction at the infinite-momentum limit, Q /p qγ →
0. 3quation (3) is slightly different from the radiation function for the initial state [4]; z has vanishedin the denominator. This is because we assume that the cm energy does not change before and afterthe radiation. The mapping to the non-radiative process, qg → γ + q , which is necessary to performin order to evaluate the LLL term in Eq. (2), is also defined according to this assumption. We definethe momentum of the quark in the final state of the mapped qg → γ + q event by the sum of themomenta of the q - γ pair in consideration. Since all particles in the qg → γ + q event are assumed to beon-shell, the invariant mass of the final state evaluated from thus defined momentum becomes smallerthan that of the initial state. In order to compensate for this decrease, we increase the overall scaleof the momenta of the final-state particles. The Q value defined in Eq. (5) is also increased with thesame scaling factor. The z value is independent of this rescaling. These details, the definitions in Eqs.(5) and (6) and the subsequent momentum adjustment, are not universal. They have been chosen inorder to achieve a good matching with the parton shower (PS) that we are developing. Therefore, theapplication of the PYTHIA PS may result in a certain mismatch, though the effect of such detailsmust vanish at the limit where the radiative cross section diverges.An event generator implementing the above subtraction has been developed in the framework ofGR@PPA, and the generation was tried for proton-proton collisions with a cm energy of 14 TeV withCTEQ6L1 [8] used for PDF. The energy scale was defined as µ = | ~p T ( γ ) − ~p T ( γ ) | / , (7)where ~p T ( γ i ) denotes the transverse momentum vector of the two photons. This definition is equivalentto the ordinary definition, µ = p T ( γ ), for q ¯ q → γγ . We used the same definition for the renormalizationand factorization scales. The energy scale for the initial-state PS must be equal to the factorizationscale in our method. Though it is not necessary, we adopted the same definition for the final-statePS. Thus, all the energy scales used in the event generation were identical in this test.The LLL subtraction is limited by the θ function in Eq. (2). This is because the implementationof the PS to be applied to the non-radiative process is limited by a certain energy scale. Thus, theenergy scale used in Eq. (2), µ F SR , must be equal to the one defined for the mapped qg → γ + q eventin order to achieve a good matching. In the present study, we define µ F SR to be equal to the p T ofthe mapped qg → γ + q event.One of the simulation results is shown in Fig. 2. In this figure, we have plotted the distributionof ∆ R between the photon and the quark in the final state of the qg → γγ + q events, where q represents any quark or anti-quark up to the b (¯ b ) quark. We obtain two values since there are twophotons in the final state. We take the smaller one as the ∆ R ( γ - q ). Parton showers are yet to beapplied but the initial-state QCD LLL subtraction is already applied in this simulation. The selectioncondition in Eq. (1) is applied to the generated events. The distribution directly derived from thematrix element before applying the final-state LLL subtraction is shown with a solid histogram inthe figure for comparison. We applied a cut of ∆ R ( γ - q ) > . R ( γ - q ) = 0.Since the LLL subtraction is unphysical, we obtain negative-weight events as well as ordinarypositive-weight events when we apply the subtraction. The event weights are always equal to +1 or − R ( γ - q ) region as expected. The distributionat large ∆ R ( γ - q ) is not altered by the subtraction. We can also see that the distributions after thesubtraction converge to finite values as ∆ R ( γ - q ) →
0; not only the final result converges to zero, butalso the positive and negative weight events converge to a finite value at this limit. These facts showthat the subtraction is done properly at least near the divergent limit. We have applied a small cutoff,∆ R ( γ - q ) > .
01, in the event generation for numerical stability. We can see that the effect of thiscutoff is negligible. 4 -2 -1
110 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ∆ R( γ -q) d σ / d ∆ R ( pb ) positive negative Figure 2: ∆ R ( γ - q ) distribution of the simulated qg → γγ + q events satisfying the kinematical con-dition in Eq. (1). The solid histogram shows the distribution before applying the final-state QEDLLL subtraction, where ∆ R ( γ - q ) > . The subtracted LLL terms must be restored by non-radiative processes to which an appropriate partonshower (PS) is applied. Because our PS is still under development, we try to use the PYTHIA PS [7]in the present study. We used the so-called ”old” PS because this model looks similar to the PS thatwe are developing. We used PYTHIA 6.423 for this study. We generated q ¯ q → gγ and qg → qγ eventsby setting as msel = 0 , msub(14) = 1 , and msub(29) = 1 in the LHC condition at the design energy,14 TeV. The q ¯ q → gγ interaction was turned on for completeness. Though it is very inefficient to findhard photons in the gluon fragmentation, turning on this process is harmless since the productioncross section is small compared to qg → qγ .For PDF, CTEQ6L1 was applied with the help of LHAPDF/LHAGLUE [11] in the LHAPDF5.8.4 distribution by setting as mstp(51) = 10042 and mstp(52) = 2 in PYTHIA. The final-stateparticles were allowed to produce in the region | η | ≤ . p T ≥ c at the on-shell parton level by appropriately setting the ckin parameters. Though this p T cutmay look tight compared to the condition in Eq. (1), it is safe enough because the lower- p T photonsare predominantly produced in the fragmentation. Since we do not want to change the preset energyscales, we set the scale parameters as parp(67) = 1.0 and parp(71) = 1.0 . All the energy scalesmust have been set equal to the p T of the on-shell parton level interaction with this setting. Inaddition, for safety, we explicitly disabled the matrix-element correction by setting as mstp(68) = 0 .The other parameters were left unchanged so that the default ”old” PS and further simulations downto the hadron level should be applied according to the default setting.The event generation with the above setting was repeated and hard photons were looked for in thefragmentation of the final-state partons. The probability to find hard photons in PS is very small.The efficiency to find events satisfying the condition in Eq. (1) was 2 . × − . In order to improvethe efficiency, we enhanced the QED radiation by a factor of 10 by setting as mstj(41) = 10 and5 -2 -1
110 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ∆ R( γ -jet) d σ / d ∆ R ( pb ) no isolation cut Figure 3: ∆ R ( γ -jet) distribution of the simulated γγ + jet events satisfying the kinematical conditionin Eq. (1), where ”jet” represents the quark or gluon in the final state. The solid histogram showsthe distribution of the fragmentation events simulated by PYTHIA. The dashed histogram shows thedistribution of the qg → γγ + q events generated by GR@PPA in which the initial-state and final-state LLL subtractions are fully applied. In both simulations, the event selection has been appliedto those events fully simulated down to the hadron level, while ∆ R ( γ -jet) has been derived from theinformation of the reconstructed or original γγ +jet events at the on-shell parton level. The sum of thetwo distributions is plotted with filled circles. The dotted histogram shows the distribution directlyderived from the qg → γγ + q matrix element before applying the final-state QED LLL subtraction(same as the solid histogram in Fig. 2). The distribution of the q ¯ q → γγ + g events is shown with adot-dashed histogram for comparison. parj(84) = 10.0 . The obtained results were corrected for this enhancement. It is not recommendedin the manual to apply larger enhancement factors because the multiple photon radiation effect maybecome significant. By the way, it should be noted that the efficiency is still at the level of 10 − evenwith this enhancement.In order to investigate the matching with the subtracted GR@PPA simulation results, it is betterto reconstruct the corresponding qg → γγ + q events at the on-shell parton level from full PYTHIAsimulation events in which a hard fragmentation photon is observed. This reconstruction can be doneunambiguously by using the information of the initial-state partons initiated the hard interaction,without using the information of the final-state partons or hadrons. The reconstruction using thefinal-state partons or hadrons is dangerous because their origin is ambiguous. The initial-state partonsinitiated the hard interaction can be found in the documentation lines of the PYTHIA event recordas partons having no child. We first boost the prompt and fragmentation photons to the cm frameof these partons in which the initial-state parton momenta are aligned along the beam direction.We determine the momentum of the remnant on-shell parton from the photon momenta to balancethe total momentum. The flavor of the remnant parton can be determined from the flavor of theinitial-state partons. The total energy of the final state derived from thus determined momenta isusually different from the initial-state cm energy as a result of the application of PS and hadronizationsimulations. We adjust the overall scale of the momenta of the final-state particles to match the totalenergy as is done in the mapping to non-radiative events in the LLL subtraction. We then boost thereconstructed parton and photon momenta to the laboratory frame by using the momentum fractioninformation in pari(33) and pari(34) originally used for the generation of the hard interaction.6he ∆ R ( γ -jet) distribution of the simulated fragmentation events is shown with a solid histogramin Fig. 3, in which the selection condition in Eq. (1) was applied to the simulated hadron-level events,while ∆ R ( γ -jet) was evaluated using the reconstructed on-shell parton level qg → γγ + q information.In order to compare with this result, we applied a full simulation down to the hadron level to theGR@PPA simulation events described in the previous section. The events were generated with alooser kinematical constraint, p T ( γ ) ≥
30 GeV/ c, p T ( γ ) ≥
20 GeV/ c, and | η ( γ ) | ≤ .
0, and theinitial-state and final-state parton showers were applied down to Q = (4 . in [email protected] generated events were passed to PYTHIA in order to simulate parton showers at smaller Q and hadronization/decays. The default setting was unchanged in the PYTHIA simulation, exceptfor the setting of parp(67) = 1.0 and parp(71) = 1.0 . The selection condition in Eq. (1) was thenapplied to the simulated hadron-level events. The γ -jet separation, ∆ R ( γ -jet), was evaluated from theoriginal on-shell parton level information for the selected events. The obtained ∆ R ( γ -jet) distributionis presented with a dashed histogram in Fig. 3.The obtained two distributions seem to be smoothly connected with some overlap around theboundary. We expect that the sum of them should reproduce the spectrum before the final-statesubtraction shown with a dotted histogram around the boundary, since we have chosen the boundary, Q = µ F , in a hard radiation region. The sum should gradually get apart from the prediction withoutthe subtraction to approach the prediction from the fragmentation as ∆ R ( γ -jet) becomes smaller.The sum shown with closed circles in Fig. 3 behaves nearly as expected. However, we can see a smalldip at the boundary. This dip must be due to a certain mismatch in the hard radiation kinematics.Furthermore, the distribution of the fragmentation events seems to be a little bit smaller than weexpect. The distribution looks better if we enhance the fragmentation by a factor of about 20%. Weexpect that we can achieve a better matching with the parton shower that we are developing.People may worry that the drop in the first bin of the fragmentation event distribution in Fig. 3looks unnatural. This drop is caused by a cutoff of the QED PS in PYTHIA. The cutoff is set to 1 GeVin terms of Q by the default, to be equal to that of the QCD PS. Possible QCD phenomena at smaller Q values are simulated otherwise, for instance, by the multiple interaction, while no such simulationsare implemented for QED. Thus, there is no reason to stop the QED PS at Q = 1 GeV. Hardphotons can be radiated from branches having smaller Q values since the momentum determination isindependent of the choice of Q . Actually, if we decrease this cutoff to 0.3 GeV by setting as parj(83)= 0.3 in PYTHIA, the concentration in the first bin increases significantly. Though the concentrationwill further increase if we apply smaller cutoff values, there must be a certain limitation due to non-perturbative effects of QCD. The picture in which a quark branches to a quark and a photon shouldbreak at Q values smaller than the QCD cutoff. The treatment of such small- Q branches is one ofthe subjects in our development.In Fig. 3, the contribution from q ¯ q → γγ + g events is shown with a dot-dashed histogram forcomparison. The initial-state QCD LLL subtraction is applied also to this process. This process doesnot have any final-state divergence. We can see that the contribution from this process is alwayssmaller than qg → γγ + q by nearly a factor of five. It is necessary in real experiments to require a certain isolation condition in the identification ofphotons, in order to reduce the huge background from π in hadron jets. It is difficult to reproducethe cuts applied by experiments with parton-level simulations. This is the main reason why hadron-level event generators are desired. If hadron-level events can be generated consistently, the generatedevents can be passed to detector simulations for more detailed studies including detector responses.In this section we try to simulate a typical isolation condition using the events simulated down tothe hadron level. The condition that we require is defined by using a cone E T defined as E T, cone = X ∆ R 110 0 0.5 1 1.5 2 2.5 3 3.5 4 ∆ R( γ -jet) d σ / d ∆ R ( pb ) Figure 4: ∆ R ( γ -jet) distribution of the simulated γγ + jet events. The isolation cut described in thetext is applied to the events from which the distributions in Fig. 3 are derived. The notation of thehistograms and the plot is the same as Fig. 3.photon under the study and neutrinos. We take as R iso = 0 . E T, cone ≤ 15 GeV.We applied this cut to the events from which the distributions in Fig. 3 were derived. The ∆ R ( γ -jet)distribution after applying the cut is shown in Fig. 4. We can see that the isolation cut stronglysuppresses the fragmentation events in ∆ R ( γ -jet) . . 4, as expected, while it has a very small impactto the LLL subtracted qg → γγ + q and q ¯ q → γγ + g events.Figure 5 shows the p T distribution of the ”jets” in the on-shell parton level γγ + jet events re-constructed for the fragmentation events in the region, ∆ R ( γ -jet) ≤ . 4. The distribution after thecut should sharply drop at 15 GeV/ c if the isolation cut at the on-shell parton level could perfectlyreproduce the cut applied to the hadron-level events. We can see an apparent smearing around theideal cut value. This smearing would result in an inaccuracy of the approximation in analytical eval-uations, such as DIPHOX and ResBos. In any case, the fact that the distribution drops around theideal cut value, as we expect, must imply that the ”reconstruction” of the on-shell parton level eventsis reasonably done. We can obtain a consistent simulation sample by combining the fragmentation events with the LLLsubtracted qg → γγ + q and q ¯ q → γγ + g events, together with the lowest-order q ¯ q → γγ events.The lowest-order events were simultaneously generated by GR@PPA with the LLL subtracted events,to restore the subtracted initial-state divergent components. A loose kinematic condition, p T ( γ ) ≥ 30 GeV/ c, p T ( γ ) ≥ 20 GeV/ c, and | η ( γ ) | ≤ . 0, was commonly applied in the on-shell parton levelevent generation in GR@PPA. The event generation was done for the LHC design condition, pp collisions at 14 TeV, with the energy scale definition in Eq. (7). Built-in parton shower simulationswere applied in GR@PPA down to Q = (4 . . Further small- Q phenomena were simulatedby PYTHIA 6.423, with its default setting but parp(67) = 1.0 and parp(71) = 1.0 . The selectioncondition in Eq. (1) was applied to thus simulated hadron-level events. The fragmentation eventswere separately simulated with PYTHIA as described in previous sections. Finally, the isolation cutdescribed in the previous section was applied to the simulated events.8 p T (jet) (GeV/c) E v e n t s ∆ R( γ -jet) < 0.4 Figure 5: p T distribution the ”jets” in the on-shell parton level γγ + jet events reconstructed forthe fragmentation events in ∆ R ( γ -jet) ≤ . 4. The solid histogram shows the distribution before theisolation cut, and the dashed histogram shows the distribution after the cut, E T, cone ≤ 15 GeV.Figure 6 shows the p T distribution of the diphoton ( γγ ) system in the simulated events. Theobtained distribution is compared with the prediction from ResBos [2]. ResBos provides us with anNLO prediction in which soft QCD radiations are resummed. It is considered to be most reliableat present as far as the p T ( γγ ) distribution is concerned. Unfortunately, since the resummation canpredict inclusive properties only, ResBos cannot provide exclusive event information. It should benoted that the contribution from the gg → γγ process is not included in the ResBos prediction sinceit is yet to be included in our simulation. The ResBos prediction shown in the figure is smaller than theresult presented in the original paper because the m γγ constraint in Eq. (1) is additionally required.We have confirmed that we can obtain a prediction close to the original result if the m γγ constraintis excluded.We can see that the sum (solid histogram) of our simulations is in reasonable agreement withthe ResBos prediction, not only in the p T ( γγ ) dependence but also in the absolute value of the crosssection. The total cross section is 15.5 pb from ResBos and 13.7 pb from our simulation. The differencecan be attributed mainly to the lack of finite terms in the NLO correction in our simulation. Thetechnical difference in the isolation cut may also have resulted in some difference.In our simulation, the contribution from each subprocess is: 4.1 pb (30%) from q ¯ q → γγ , 5.1pb (37%) from the fragmentation, and 3.7 pb (27%) and 0.8 pb (11%) from the LLL subtracted qg → γγ + q and q ¯ q → γγ + g processes, respectively. The contribution from the lowest-order process, q ¯ q → γγ , is smaller than 1/3 of the total sum. Furthermore, as we can see in Fig. 6, the p T ( γγ )spectrum of q ¯ q → γγ is apparently different from the sum. The contribution from the LLL subtracted qg → γγ + q is comparable with the lowest-order contribution. However, it must be noted that thecomposition in the above is not physically meaningful. The above is a result when we separate thesoft and hard radiations at µ = p T of the q ¯ q → γγ or qg → γ + q interaction. The composition changesif we adopt another definition. In any case, we can at least conclude that the contribution from the qg → γγ + q process in which the final-state three particles are well separated is significant in thenon-resonant QED diphoton production. Together with the LL component which is shared betweenthe fragmentation process and the LLL subtracted process, non-LL components remaining after thesubtraction also looks sizable as we can see in Figs. 3 and 4.9 -2 -1 p T ( γγ ) (GeV/c) d σ / dp T ( pb / G e V ) R e s B o ss u m qq – → γγ qg → γγ + q qq – → γγ + g fr a g m e n t a ti on Figure 6: p T distribution of the diphoton ( γγ ) system in the simulated events satisfying the kinematicalcondition in Eq. (1) and the isolation condition. The sum (solid histogram) is presented together withthe distributions of the subprocesses: q ¯ q → γγ , the LLL subtracted qg → γγ + q and q ¯ q → γγ + q and the fragmentation. The ResBos prediction for the same condition is plotted with open circles forcomparison. In conclusion, we have developed an exclusive event generator for non-resonant QED diphoton ( γγ )production at hadron collisions, consistently including additional jet productions. The qg → γγ + q process to be included as a radiative process has a final-state QED divergence as well as an initial-stateQCD divergence. We have developed a subtraction method to regularize the final-state divergence, byextending the method developed for initial-state QCD divergences. The subtraction works well as weexpected. The differential cross section converges to zero after the subtraction at the limit where oneof the pairs of the final-state γ and quark becomes collinear and the original cross section diverges.We tried to use the PYTHIA simulation for the generation of the fragmentation events, with whichthe subtracted component is to be restored without any double count. We generated γ + jet eventsby PYTHIA and picked up another photon produced by the parton shower (PS) in the final state.We have developed a technique to reconstruct on-shell parton level γγ + jet events from those eventsfully simulated down to the hadron level, in order to test the matching with the events generatedby GR@PPA. The fragmentation events generated by using the default ”old” PS show a reasonablematching, though a small mismatch is seen around the boundary and the overall yield seems to be alittle bit smaller. The treatment of small- Q radiations is still an open question in this simulation.A consistent simulation sample was composed by combining the above two generation sampleswith the q ¯ q → γγ and q ¯ q → γγ + g events simultaneously generated with qg → γγ + q in [email protected] event generation was tested for the LHC design condition, pp collisions at 14 TeV, and a typicalHiggs-boson search condition was required to the events simulated down to the hadron level. Atypical isolation cut was also applied to the photons. We observed a reasonable suppression of thefragmentation events in a collinear region, together with a visible smearing of the boundaries due tothe application of PS and hadronization.The combined events show a behavior which reasonably agrees with the prediction from a re-summed NLO calculation by ResBos. The difference in the total cross section at the level of 10%10an be attributed to the lack of finite-term contributions in the NLO correction in our simulation. Inour simulation sample, for which all the energy scales were chosen to be equal to the p T of the basic q ¯ q → γγ or qg → γ + q process, the contribution from the lowest-order q ¯ q → γγ process is smallerthan 1/3. The contribution from qg → γγ + q is comparable with it due to a large density of gluonsinside protons. A consistent inclusion of this process must be necessary for reliable studies.A new PS which implements QED radiations together with QCD is under development. We wantto implement a mechanism to force a hard photon radiation in this PS in order to ensure a reasonablegeneration efficiency for the fragmentation process. Acknowledgments This work has been carried out as an activity of the NLO Working Group, a collaboration betweenthe Japanese ATLAS group and the numerical analysis group (Minami-Tateya group) at KEK. Theauthor wishes to acknowledge useful discussions with the members, especially continuous discussionswith Y. Kurihara. References [1] T. Binoth, J.Ph. Guillet, E. Pilon, M. Werlen, Eur. Phys. J. C , 311 (2000);arXiv:hep-ph/9911340.[2] C. Balazs, E.L. Berger, P. Nadolsky, and C.-P. Yuan, Phys. Rev. D , 013009 (2007);arXiv:0704.0001[hep-ph].[3] S. Tsuno, T. Kaneko, Y. Kurihara, S. Odaka, and K. Kato, Comput. Phys. Commun. , 665(2006); arXiv:hep-ph/0602213.[4] Y. 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