Hadroproduction of t anti-t pair in association with an isolated photon at NLO accuracy matched with parton shower

We simulate the hadroproduction of a t anti-t pair in association with a hard photon at LHC using the PowHel package. These events are almost fully inclusive with respect to the photon, allowing for any physically relevant isolation of the photon. We use the generated events, stored according to the Les-Houches event format, to make predictions for differential distributions formally at the next-to-leading order (NLO) accuracy and we compare these to existing predictions accurate at NLO using the smooth isolation prescription of Frixione. We also make predictions for distributions after full parton shower and hadronization using the standard experimental cone-isolation of the photon.


Introduction
Isolated hard photons are important experimental tools for a variety of processes at the LHC. Most notably, one of the cleanest channels to identify the Standard Model (SM) Higgs particle is its decay into a pair of hard photons. Although this channel has a small (about 0.2 %) branching ratio as compared to the hadronic and leptonic channels, the spectacular resolution of the electromagnetic calorimeters of the ATLAS and CMS detectors and the relatively low background made this as one of the prime discovery channels [1,2].
From the theoretical point of view isolated hard photons are rather cumbersome objects. Unlike leptons, the photons couple directly to quarks. If the quark that emits the photon is a light quark, treated massless in perturbative QCD, then the emission is enhanced at small angles and in fact, becomes singular for strictly collinear emission. The usual experimental definition of an isolated photon allows for small hadronic activity even inside the isolation cone. Due to the divergence of the collinear emission, this isolation cannot be implemented directly in a perturbative computation at leading-order (LO) accuracy because even small hadronic activity inside the cone leads to infinite results.
Of course, one can approximate the experimental definition with complete isolation of the photon from the coloured particles inside a fixed cone and obtain a perturbative prediction at LO. The problem however, comes back with a different face if we want to define the isolated photon in a computation at the next-to-leading order (NLO) accuracy. At NLO there are two kinds of radiative corrections: (i) the virtual one with the same final state as the Born contribution, but including a loop and (ii) the real one that involves the emission of a real parton in the final state. These two contributions are separately divergent, but their sum is finite for infrared (IR) safe observables according to the KLN theorem [3,4]. The IR-safe observables are represented by a jet function J m , where m is the number of partons in the final state: for an n-jet measure m = n at LO and for the virtual corrections, while m = n + 1 in the real correction.
There exist general methods (see e.g. Ref. [5]) to combine the real and virtual corrections for infrared (IR) safe observables J m , for which J n+1 tends to J n smoothly in kinematically degenerate regions of the phase space, namely when two final-state partons become collinear or a final-state gluon becomes soft. The problem with the isolated-photon cross section in perturbative QCD is that the cone-photon isolation is not IR safe beyond LO. The extra gluon in the real radiation may be radiated within the isolation cone in which case the event will be cut even if the gluon energy tends to zero.
There are ways to make predictions for photon production in perturbation theory, but all have drawbacks. In a pioneering work [6] the measurement of the inclusive photon cross section was advocated, but that is not very useful from the experimental point of view. In Ref. [7] an isolation procedure was proposed that is similar in spirit to the case of inclusive cross section, yet provides a smooth isolation prescription that is IR safe at all orders in perturbation theory. However, the implementation of the smooth prescription experimentally is very cumbersome as it requires very fine granularity of the detector, so it has never become popular among experimenters.
There is a precise way of defining the isolated photon theoretically, but that requires the inclusion of the photon fragmentation component as well (see e.g. [8]). The drawback of this approach is the need for non-perturbative input and the extra computational effort for a contribution that is mostly discarded when the experimental isolation is used (cone with small hadronic activity inside that is described by the fragmentation contribution). Thus one would be tempted to neglect the fragmentation contribution completely, which is however, uncontrolled from the theoretical point of view and thus is not a viable option in a fixed-order computation.
In the last decade new approaches were proposed to make predictions that are formally accurate to NLO but include the advantage of event simulations of the shower Monte Carlo (SMC) programs [9,10,11]. By now many processes have been included in the generic frameworks of these NLO+PS approaches, the aMCatNLO [12] and the POWHEG-BOX [13] codes. In a series of papers we combined the POWHEG-BOX with the HELAC-NLO package [14] into PowHel to make predictions for the hadroproduction of a tt-pair in association with a hard boson (scalar [15], pseudoscalar [16], vector [17] or jet [18]). The only missing boson of the SM in this list is the hard photon. In view of the above, the reason is clear: the photon has to be isolated, which makes this computation more involved than for the other cases.
In this paper we use the PowHel framework and propose a computationally cheap way of discarding the fragmentation contribution by returning to the idea of inclusive photon production, but in a different sense as proposed originally in Ref. [6]. The output of the POWHEG-BOX consists of events stored according to the Les Houches accord (LHEs) [19]. We propose to simulate a sufficiently inclusive event sample, which when fed into a SMC, produces events on which the usual experimental cone isolation can be applied. We demonstrate the validity of this approach on the example of tt γ hadroproduction, but the approach is general and can be used to make predictions for any other process that involves isolated hard photons in the final state at NLO accuracy matched with PS.

Details of the implementation
PowHel is a computational framework composed of the POWHEG-BOX [13] and the HELAC-NLO [14] packages to provide predictions at the hadron level with NLO QCD accuracy in the hard process. The essential ingredients needed for a particular process are the matrix elements for the Born, virtual and real-emission contributions, spin-and colour-correlated matrix elements and a suitable phase space for the Born process. The matrix elements are provided by HELAC-NLO while the Born phase space is constructed by us using the relatively simple kinematics at the Born level. The Born phase space is generated with the help of one kinematic invariant and three angles. An overall azimuth is kept fixed and randomly reinstated at the end of the calculation as a common practice in POWHEG-BOX. Matrix elements are generated for the following subprocesses: qq → γ tt, g g → γ tt (tree-level for the Born process and at one-loop for the virtual) and qq → γ tt g, g g → γ tt g for the real emission (q ∈ {u, d, c, s, b}). The ordering among particles follows the convention of POWHEG-BOX: non-QCD particles, massive quarks, massless partons. Matrix elements for all other subprocesses are obtained from these by means of crossing.
All matrix elements, including the crossed ones, are compared to the stand-alone version of HELAC-NLO in several, randomly chosen phase-space points. The internal consistency between the Born, spin-, colour-correlated and real-emission matrix elements is checked by comparing the limit of the real-emission part and the corresponding counter terms in all kinematically degenerate regions of the phase space.
In order to check the whole implementation we compare differential distributions to those in Ref. [20] using the LHC setup in the published paper: the calculation was performed for LHC at centre-of-mass energy √ s = 14 TeV with a CTEQ6L1 and CTEQ6.6M PDF at LO and NLO accuracy and a one-and two-loop running α s , respectively. The mass of the t-quark was m t = 172 GeV, the fine-structure constant, was set to α EM = 1/137. The renormalization and factorization scales were set fixed, equal to m t . In the analysis a photon was required to be hard, p ⊥ ,γ > 20 GeV and the smooth isolation of Frixione [7] was employed with isolation parameters δ 0 = 0.4 and γ = n = 1. The cross sections obtained with PowHel are enlisted on Tab. 1. We found complete agreement with the predictions of [20] both for the cross sections and for the available distributions as well. Two out of these are depicted in Fig. 1.   Table 1: Cross sections obtained with PowHel at LO and NLO accuracy using the setup and cuts of [20]. The renormalization and factorization scales are made equal to µ.   [20] at the central scale with NLO accuracy for the differential cross section as a function of the transverse momentum of the photon and anti-t quark.
Lower panels depict the ratio of predictions in [20] (MSS) to ours. The uncertainties appearing on the lower panels only take into account the statistical uncertainty of our calculation.
Having checked the implementation of the NLO computation, we generated events with the POWHEG-BOX. The final state in the Born contribution, tt γ, is composed of two massive and one massless particles. The cross section when the photon is emitted from a massless (anti)quark can become singular. This can happen when the photon is emitted by one massless (anti)quark from the initial state, or from a final state one in the real-emission contribution. These configurations have to be avoided such that the physical cross sections for isolated photon production do not depend on the actual implementation.
Let us first focus only on the singular radiation present at the Born level. In this case there are two simple solutions to avoid infinite contributions to the cross section. The first is a technical cut [18], which if applied on the transverse momentum of the photon, can avoid the singularity. This cut has to be sufficiently small so that when physical cuts are applied, the prediction becomes independent of this technical cut. Although this method offers an easy way to avoid the singularity, yet we end up generating events mostly with photons having small transverse momentum. Hence the majority of events will be generated in a region of phase space which has no physical importance and the efficiency of the event generation is small.
The other solution is the inclusion of a suppression factor [21] which can be used to enhance event generation in certain regions of the phase space. In our calculation the analytical form of suppression was chosen to be and we found i = 2 a suitable choice and p ⊥ ,supp = 100 GeV was set throughout the whole calculation. It is not necessary, yet we included also the technical cut on the transverse momentum of the photon, by requiring the transverse momentum of the photon in the underlying phase space to be larger than 15 GeV. We checked that this cut does not affect our predictions with physical cuts larger than 15 GeV. Our strategy to handle singularities coming from collinear photon-emission from final state massless (anti)quarks will be covered in the next section.

NLO-LHE comparison
In this and all the upcoming sections predictions are made for proton-proton collisions at √ s = 8 TeV with the following parameters: CT10nlo PDF using LHAPDF [22] with a 2-loop running α s considering 5 massless quark-flavours, m t = 172.5 GeV, α EM = 1/137. For our default scale we decided to use a dynamical one, the half of the sum of transverse masses of all final-state particles: where the hat reminds us that underlying-Born kinematics was used to evaluate the sum. For the NLO-LHE comparison the following set of cuts was employed: • The photon had to be hard enough, p ⊥ ,γ > 30 GeV.
• The photon was constrained into the central region, |y γ | < 2.5.
The cross section at LO and NLO accuracy as a function of the equal renormalization and factorization scale normalized to the default scale µ 0 is shown in Fig. 2. We find significant reduction of the scale dependence and an NLO K-factor K = 1.21 at our default scale choice.
Next we turn to comparisons of predictions at NLO accuracy with those obtained from the pre-showered events. With this comparison our only aim is to demonstrate that our framework can generate meaningful pre-showered events using the Frixione isolation (the standard in fixed-ordered calculations). On Figs. 3-5 six sample distributions are depicted to illustrate the effect of the POWHEG Sudakov. In general we find agreement between the corresponding predictions except for the transverse-momentum distribution for the extra parton (left plot of Fig. 5). The effect of the POWHEG Sudakov suppression is clearly visible in the low p ⊥ region where the radiation activity is highly limited, as expected. The presence of the extra cut in the real-emission part (the Frixione isolation)   dσ/dp y t Figure 4: The same as Fig. 3 for the rapidities of the photon and the t-quark. of the POWHEG Sudakov. It is worth mentioning that the formal accuracy is still NLO, the difference is due to higher order terms.

Photon isolation revisited
When photons are produced with massless partons in the final state the usual soft/collinear divergences coming from parton-parton splittings are accompanied by a new type of collinear splitting, namely the quark-photon one. The singularity produced by a collinear photon emission off a massless (anti)quark can be absorbed into the photon fragmentation function, decomposing the cross section into direct photon production and a fragmentaion contribution.
The only known solution that leads to an IR-safe cross section at all orders in perturbation theory that avoids the fragmentation contribution is offered in Ref. [7] where QCD activity is considered in a continuously shrinking cone around the photon such that the allowed activity decreases with decreasing cone size.
While in a theoretical calculation the shrinking cone size can be easily implemented, in an experiment the finite resolution of the detector does not allow for taking the smooth limit. As a result most of the experiments adopt a different isolation criterium: reduced hadronic activity is allowed around the photon in a cone with finite size such that for the total hadronic transverse energy inside the cone In Eq. (4.1) E ⊥ ,i is the transverse energy of the ith track, R γ is the isolation cone size, R(p γ , p i ) is the separation between the photon and the ith track measured in rapidityazimuthal angle plane, while E max had is the maximal hadronic energy allowed to be deposited in the cone of R γ around the photon. In the following we call this quantity hadronic or partonic leakage depending on whether the process is considered on the hadron or the parton level. In a fixed-order calculation an isolation of the form of Eq. (4.1) does not completely remove the singularity of collinear quark-photon emission and therefore, cannot be applied. Setting E max ⊥ ,had = 0 removes this singularity, but cuts into the phase space of soft gluon emission in the real correction, hence it is not IR-safe. Therefore, it is clear that a close-to-experiment isolation cannot be applied to a fixed-order calculation as it is unless the fragmentation contribution is taken into account.
The factorization of the collinear singularity of quark-photon splitting into the fragmentation contribution requires regularization of this splitting. A simple way of regularization is isolating it in a small cone of radius R γ,q around the photon, which gives an IR-safe cross section if there are no gluons simultaneously with the light quark in the final state. As a result, the direct contribution depends on this isolation radius logarithmically, proportional to ln R γ,q , with some coefficient c γ,q . The fragmentation component is given by a function f γ,q (R γ,q ), to be measured experimentally, which vanishes for vanishing radius R γ,q , f γ,q (0) = 0. Thus the fragmentation contribution can be neglected if R γ,q is sufficiently small.
Employing such a factorization, the photon fragmentation function would have to be measured at a fixed radius and it would be dependent also on R γ,q . The direct photon contribution contains the term c γ,q ln R γ,q and the prediction depends on R γ,q , too. R γ,q is an unphysical parameter, which plays a similar role to that of the factorization scale when the traditional MS factorization is used. In the following we show that when the preferred experimental cone isolation is employed, the dependence on R γ,q is negligible provided it is chosen small enough so that the fragmentation contribution is negligible. The reason for this independence is that the coefficient c γ,q is suppressed both kinematically by the physical isolation criteria and also dynamically because the only subprocess where it can appear is quark-gluon scattering among the real-radiation processes.
In principle we can choose R γ,q arbitrarily small, thus suppressing the fragmentation contribution completely. In practice, choosing a very small value for R γ,q makes the generation of the events inefficient. However, as the direct photon contribution is independent of R γ,q below some threshold value. Thus, in the range where the direct contribu-tion is independent of R γ,q we can choose its value anywhere, so in practice we suggests R γ,q = 0.05 − 0.1 as a good compromise that allows for event generation.
Our proposal is equivalent to a generation (technical) cut on the real-emission phase space when contributions with massless (anti)quarks present in the final state to remove the quark-photon singularity. Such generation cuts have used in the past to simulate LHEs for processes when the final state may become singular already at the Born level [18], as discussed also in the previous section. For this technical cut we suggest a small, minimal separation in the rapidity-azimuthal angle plane, such that real-emission contributions with massless (anti)quark(s) in the final state are only considered if the following criterium is fulfilled: where {γ i } is the set of final-state photons, {q i ,q j } is the set of massless (anti)quarks in the final state and R γ,q is the minimal separation between massless (anti)quarks and photons in the final state. As the value of R γ,q is arbitrary we check that the cross section with experimental selection cuts is independent of R γ,q . This criterium is IR-safe with respect to the emission of a soft-gluon.
Regularization of the quark-photon singularity with a technical cut as described above can be used only if there are no light partons at the LO in the final state such as our present example. Using the idea of technical cut, we can modify our proposal such that it can be used for arbitrary processes with an isolated photon in the final state. We simply employ a smooth technical isolation of the photons according to the formula (Frixione-type isolation with γ = n = 1) for all δ ≤ δ 0 , where δ 0 is a sufficiently small, pre-defined number. It can be chosen arbitrarily as long as the predictions with physical cuts are independent of δ 0 . We shall show that for δ 0 ≤ 0.1 the physical predictions are indeed independent of δ 0 and coincide with the predictions obtained with the cone-type technical cut within 0.5 %. The advantage of the smooth technical cut is that it can also be applied to processes with an arbitrary number of light partons in the final state in the Born computation.
With such a technical cut we can generate sufficiently inclusive LHE sample. On the pre-showered events prepared this way it is easy to apply a close-to-experiment type of cut such as Eq. (4.1), the quark-photon singularity is appropriately screened hence allowing for a small hadronic (or partonic) activity in the cone around the photon and cannot lead to infinite predictions. Photon fragmentation is suppressed and gives negligible contribution to the physical cross section (after the experimental cuts). This procedure of making theoretical predictions is made possible by the generation of LHEs as opposed to producing differential distributions directly, as in the case of computing cross sections at fixed order in perturbation theory beyond LO accuracy.

Independence of the technical cuts
If events are generated with the method outlined in Sec. 4 the technical cut, R γ,q , should be chosen such that the distributions obtained at various stages of event simulation (from LHEs, after parton shower and after full SMC) should be independent of it. In order to see this independence, we generated events with three different technical isolation values: R γ,q ∈ {0.01, 0.05, 0.1}. Then predictions are presented and compared at various stages of the event simulation. These event generations are done with parameters listed in Sec. 3. Although the particle content can be different at different stages, we kept the set of cuts applied to the events the same: • There is a cut on the transverse momentum of the hardest photon: p ⊥ ,γ > 30 GeV.
• The hardest photon should be well-isolated from the jets: ∆R(γ, j) > 0.4 measured on the rapidity-azimuthal angle plane.
• A hadronic (or partonic) leakage is allowed in an R γ = 0.4 cone around the photon according to Eq. (4.1) with E max ⊥ ,had = 3 GeV.

Independence of the technical cuts of distributions from LHEs
The particle content in pre-showered events is the same as in the NLO calculation. The extra parton is generated according to the POWHEG Sudakov. Although the shower history is not complete at this stage, and as a result the fragmentation contribution is also excluded, it is informative to see whether a change in the technical isolation has any effect on the distributions, which has a less complicated final state compared to the further stages. The photon has to be isolated from jets hence a jet algorithm is trivially applied to the only massless parton present in the final state, while the t-quarks are kept stable and not considered as tracks for jet reconstruction.  be present, we expect low partonic leakage into the cone around the photon. From the cross section and the distributions perfect agreement can be seen between the different predictions obtained with different technical isolations.

Independence of the technical cut after parton shower
At the LHE stage agreement was found between predictions made with different technical isolations chosen to be sufficiently small. As already mentioned the pre-showered events can only have a very limited soft-QCD content, when the extra parton becomes soft, so it is naturally interesting whether the independence of the technical isolation can be maintained even if the parton shower is fully carried out. Hence, as the next step, we used PYTHIA to perform the parton shower to see what happens when the final state is rich in soft-QCD activity, but the photon fragmentation is still neglected. These predictions are made with PYTHIA-6.4.25 using the 2010 Perugia tune [26] to turn it into a k ⊥ -ordered shower, hadronization and multiparticle interactions were turned off, only QCD radiation was allowed and t-quarks were kept stable. The cross sections obtained with the cuts listed previously with different technical isolations can be found in the third column of Tab. 2. If we compare these cross sections with those obtained from the LHEs, a 3-4 % decrease is found, although the cuts were kept the same. This decrease can be accounted for the much richer soft-QCD content of the final state, which allows for larger partonic leakage 1 into the cone around the photon vetoing more events thus decreasing the cross section. Indeed, if the allowed partonic leakage is relaxed the difference between the predictions at the LHE and PS stages decreases. The cross sections obtained with different technical isolations are compatible with each other. The same set of distributions are depicted on Figs. 9-11. From the distributions it can be seen that not only the cross section after cuts, but distributions are invariant under a change in the technical isolation.

Independence of the technical cut after full SMC
Our only aim here is to demonstrate that physical results do not depend on a sufficiently chosen technical cut, hence for simplicity, in our hadron-level simulations we turned off multiparticle interactions in PYTHIA. At the previous stages of event simulation it was possible to keep the t-quark stable but in order to present predictions after full SMC it had to be decayed accordingly. As the full SMC is used, te fragmentation contribution is also  : Transverse-momentum distribution for the hardest photon and the t-quark after parton shower done with PYTHIA without hadronization and t-quarks kept stable for three different technical isolations. On the lower panels the ratios are depicted to the prediction with R γ,q = 0.01. On the upper ratio plot the fraction of predictions made with R γ,q = 0.05 and R γ,q = 0.01 is depicted, while on the lower ratio plot the fraction of R γ,q = 0.1 and R γ,q = 0.01 is shown.   Figure 12: Transverse-momentum distribution for the hardest photon and the t-quark after parton shower and hadronization with PYTHIA for three different technical isolations. On the lower panels the ratios are depicted to the prediction with R γ,q = 0.01. On the upper ratio plot the fraction of predictions made with R γ,q = 0.05 and R γ,q = 0.01 is depicted, while on the lower ratio plot the fraction of R γ,q = 0.1 and R γ,q = 0.01 is shown. state caused by the hadronization.

Independence of the smooth technical cut
Finally we demonstrate that the two types of technical cuts, the cone-type defined by Eq. (4.2) and the smooth one defined by Eq.  subscript 's' refers to smooth technical isolation, while 'c' for cone-type one. The same set of differential distributions as in the previous subsections are presented in Figs. 15-17 using the parameter values R γ,q = δ 0 = 0.1. We find agreement within the statistical uncertainty of the integrations. The same conclusions can be drawn if R γ,q = δ 0 = 0.05, which we do not show here.  y t Figure 16: The same as Fig. 15 but for the rapidities of the hardest-photon and the t-quark.

Effect of the parton shower
In the previous section it was demonstrated that predictions obtained at various stages of event simulation (LHE, PS and SMC) do not depend upon the sufficiently small technicalisolation. To quantify the effect of the parton shower and in the next section to present physical predictions after full SMC we decided to use R γ,q = 0.05 as our technical isolation. For this comparison we used the setup of the previous section. Our standard distributions can be found on Figs. 18-20. While for rapidities and separations the difference between the LHE and PS stages only manifest in an overall change in normalization, for the transversemomentum distributions the change is not only a constant factor in normalization, but there is even a change in the shape. As we expect, the shower softens the spectra. This softening added to the difference between the predictions of LHEs and at NLO suggests very small PS effect at high transverse momenta. and in the large-p ⊥ regime saturates around 5%, while for the transverse momentum of the t-quark it reaches even 15% when the p ⊥ approaches 500 GeV. If our default, rather tight, criterium on the allowed hadronic leakage is loosen up (going from 3 GeV to 10 GeV) the difference observed in the photon transverse-momentum distribution remains more-or-less the same, but in the case of the transverse momentum of the t-quark the difference drops from 15% to around 10% in the high-p ⊥ region. The relaxation in the hadronic leakage condition results in a smaller difference, ∼ 1%, for rapidities and separations.

Predictions
We conclude with a simple phenomenological study at the hadron level. To this end PYTHIA-6.4.25 was chosen to decay, shower and finally hadronize the events. The event sample with R γ, q = 0.05 at 8 TeV was selected, PYTHIA was run with the 2010 Perugia tune [26], omitting photon showers, making τ ± and π 0 stable and we turned off multiparticle interactions. The cuts employed in this analysis were the following: y t Figure 19: The same as Fig. 18 but for the rapidities of the photon and t-quark. • The analysis was done in the semileptonic decay-channel by requesting exactly one hard lepton or antilepton in the final state with p ⊥ , > 30 GeV, the (anti)lepton had to be isolated from all the jets with ∆R( , j) > 0.4.
• The final state had to contain one hard photon in the central region, |y γ | < 2.5 with p ⊥ ,γ > 30 GeV, isolated from all the jets by ∆R(γ, j) > 0.4. A minimal hadronic leakage was allowed in a R γ = 0.4 cone around the photon with E max ⊥ ,had = 3 GeV according to Eq. (4.1).
• The (anti)lepton and photon had to be separated from each other, ∆R(γ, ) > 0.4.
• The event had to have significant missing transverse momentum, / p ⊥ > 30 GeV.
In our calculation, throughout, a different scale choice was used than that in the literature [20] for tt γ production. Our default scale choice, the half the sum of transverse massesĤ ⊥ /2 was already motivated in [27]. To see the difference between the two scale  choices a scale-uncertainty study is performed and scale-uncertainty bands are shown for the distributions obtained at the hadron level. The renormalization and factorization scales are defined as µ R = ξ R µ 0 and µ F = ξ F µ 0 , respectively, and the band is formed as the upperand lower-bounding envelopes of distributions taken with The antipodal choices ((1/2, 2) and (2, 1/2)) are left out. When these are included, the uncertainty band for rapidities and separations are unchanged while for transverse momenta in the large transverse-momentum region the band widens by a few percent. In Fig. 21 the transverse momenta of the photon and the t-quark are shown. The momentum of the t-quark is reconstructed just like in the previous cases using MCTRUTH. Taking a look at the transverse momentum of the photon the static scale results in a narrower band with a shrinking width. This hints a cross-over point at a higher p ⊥ value, while in the case of the dynamical scale the band, although wider, keeps the same width all across the whole plotted p ⊥ spectrum. While for the p ⊥ -distribution of the photon the presence of a cross-over point is only hinted by the narrowing uncertainty band, for the transverse momentum of the t-quark it is indeed visible around 350 GeV. Until this point the uncertainty band taken with the static scale decreases in width than after opens up. This is somehow expected since a highly boosted t-quark with a heavy companion anti-t and a photon correspond to a system with a large summed transverse mass hence lying far away from the central scale m t .
In Fig. 22 the spectrum of the transverse momentum of the charged lepton and that of the missing momentum are shown. For both distributions a cross-over can be seen around 250 GeV when static scale is used. The dynamical scale choice appears to give reliable scale dependence over the whole plotted range for these observables.
If we turn our attention to the separations between the photon and the t-quark, as well as between the photon and the charged lepton, measured in the rapidity-azimuthal  angle plane, we do not find significant difference between the two scale choices, as seen in Fig. 23. The static scale gives somewhat higher cross section and a slightly narrower uncertainty band. Similar conclusions can be drawn from the rapidity distributions for the photon and the (anti)lepton shown in Fig. 24. In general, the scale dependence is moderate, below 20 % for both scale choices and all observables, except for the predictions at large transverse momenta with the static scale.

Conclusions
In this paper we presented a new way to make predictions for the hadroproduction of isolated photons which uses event samples that emerge in simulations aimed at matching predictions at NLO accuracy with PS. We demonstrated that the presence of a sufficiently small technical cone-isolation of the photons only from massless quarks does not affect the physical results hence can be used to generate sufficiently inclusive pre-showered event samples. This method of generating inclusive photon samples, yielding distributions at NLO accuracy, can be applied to other processes without light jets in the LO prediction.
We also showed that instead of cone-isolation of the photons only from massless quarks, one can also use a smooth technical isolation of the hard photons and generate LHEs. The event samples genetrated with the two different technical cut lead to physical predictions that agree within statistical uncertainty of the computation if the technical isolation paremeters are sufficiently small. The LHEs obtained this way can be further showered and hadronized to obtain differential distributions at the hadronic stage, which include NLO QCD corrections in the hard process, and standard experimental photon isolation can be applied.
Using the POWHEG method one can make predictions at various stages of the event simulation. In particular, for most of the phenomenologically interesting distributions we estimate fairly small (about 10 %, or less) corrections for the ttγ final state due to the parton shower. We also studied the dependence of our predictions on the renormalization and factorization scales and found small and rather uniform scale dependence for the default scaleĤ ⊥ /2.
We demonstrated the validity of our approach using the example of hadroproduction of a tt-pair in association with a hard isolated photon. The method of smooth technical isolation however, is completely general and can be used to any process with isolated hard photons in the final state.