Exclusive LHC physics with heavy ions: SuperChic 3
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Abstract
We present results of the updated SuperChic 3 Monte Carlo event generator for central exclusive production. This extends the previous treatment of proton–proton collisions to include heavy ion (pA and AA) beams, for both photon and QCD-initiated production, the first time such a unified treatment of exclusive processes has been presented in a single generator. To achieve this we have developed a theory of the gap survival factor in heavy ion collisions, which allows us to derive some straightforward results about the A scaling of the corresponding cross sections. We compare against the recent ATLAS and CMS measurements of light-by-light scattering at the LHC, in lead-lead collisions. We find that the background from QCD-initiated production is expected to be very small, in contrast to some earlier estimates. We also present results from new photon-initiated processes that can now be generated, namely the production of axion-like particles, monopole pairs and monopolium, top quark pair production, and the inclusion of W loops in light-by-light scattering.
1 Introduction
CEP may proceed via either QCD or photon-induced interactions, see Fig. 1, as well as through a combination of both, namely via photoproduction. Although producing the same basic exclusive signal, each mechanism is distinct in terms of the theoretical framework underpinning it and the phenomenology resulting from it. The QCD-initiated mechanism benefits from a ‘\(J^{PC}=0^{++}\)’ selection rule, permitting the production of a range of strongly interacting states in a precisely defined gluon-rich environment, while also providing a non-trivial test of QCD in a distinct regime from standard inclusive production. The framework for describing photon-initiated production is under very good theoretical control, such that one can in effect use the LHC as a photon–photon collider; this well understood QED initial state provides unique sensitivity to beyond the Standard Model (BSM) effects. Photoproduction can for example provide a probe of low x QCD effects such as gluon saturation in both proton and nuclear targets. For further information and reviews, see [2, 3, 4, 5, 9].
As mentioned above, a range of measurements have been made and are ongoing at the LHC. To support this experimental programme, it is essential to provide Monte Carlo (MC) tools to connect the theoretical predictions for CEP with the experimental measurements. For this reason the authors have previously produced the publicly available SuperChic MC [10, 11], subsequently upgraded to version 2 in [12]. This generates a wide range of QCD and photon-initiated processes in pp collisions, with the former calculated using the perturbative ‘Durham’ approach. In addition, this includes a fully differential treatment of the soft survival factor, that is the probability of no additional soft particle production, which would spoil the exclusivity of the event.
Other available MC implementations include: FPMC [13], which generates a smaller selection of final-states and does not include a differential treatment of survival effects, although it also generates more inclusive diffractive processes, beyond pure CEP; an implementation of CEP in Pythia described in [14], which provides a full treatment of initial-state showering effects for a small selection of processes, allowing both pure CEP and semi-exclusive production to be treated on the same footing, while the survival factor is included via the standard Pythia treatment of multi-particle interactions (MPI); the Starlight MC [15] generates a range of photon-initiated and photoproduction processes in heavy ion collisions; ExHuME [16], for QCD-initiated production of a small selection of processes; CepGen [17], which considers photon-initiated production but aims to allow the user to add in arbitrary processes; for lower mass QCD-initiated production, the Dime [18], ExDiff [19] and GenEx [20] MCs.
As discussed above, the SuperChic MC aims to provide a treatment of all mechanisms for CEP, both QCD and photon initiated, within a unified framework. However, so far it has only considered the case of proton–proton (or proton–antiproton) collisions; CEP with heavy ion (pA and AA) beams, so-called ‘ultra-peripheral’ collisions (UPCs), have not been included at all. Such processes are of much interest, with in particular the large photon flux \(\sim Z^2\) per ion enhancing the signal for various photon-initiated processes. In this paper we therefore extend the MC framework to include both proton–ion and ion–ion collisions, for arbitrary beams and in both QCD and photon-initiated production.
Indeed, a particularly topical example of this is the case of light-by-light (LbyL) scattering, \(\gamma \gamma \rightarrow \gamma \gamma \), evidence for which was found by ATLAS [21] and more recently CMS [22]. These represent the first direct observations of this process, and these data already show sensitivity to various BSM scenarios [23, 24]. However, one so-far unresolved question is the size of the potential background from QCD-initiated production, \(gg \rightarrow \gamma \gamma \), which in both analyses was simply taken from the SuperChic prediction in pp collisions and scaled by \(A^2 R^4\), where the factor \(R\sim 0.7\) accounted for gluon shadowing effects, that is assuming that all A nucleons in each ion can undergo CEP. While the normalization of this baseline prediction was in fact left free and set by data-driven methods, it is nonetheless important to address whether such a prediction is indeed reliable, by performing for the first time a full calculation of QCD-initiated production in heavy ion collisions. We achieve this here, and as we will see, predict that this background is much lower than previously anticipated.
A further topical CEP application is the case of high mass production of electroweakly coupled BSM states, for which photon-initiated production will be dominant at sufficiently high mass [9]. Events may be selected with tagged protons in association with central production observed by ATLAS and CMS, during nominal LHC running. There are possibilities, for example, to probe anomalous gauge couplings (see [25] and references therein) and search for high mass pseudoscalar states [26] in these channels, accessing regions of parameters space that are difficult or impossible to reach using standard inclusive methods. With this in mind, we also present various updates to the photon-initiated production channels. Namely, we provide a refined calculated of Standard Model (SM) LbyL scattering, including the W loops that are particularly important at high mass, as well as generating axion-like particle (ALP), monopole pair and monopolium production. We also include photon-initiated top quark pair production. We label the MC including these updates SuperChic 3.
The outline of this paper is as follows. In Sect. 2 we present details of the implementation of CEP in pA and AA collisions, for both photon and QCD-initiated cases. In Sect. 3 we discuss the new photon-initiated processes that are included in the MC. In Sect. 4 we take a closer look at LbyL scattering, comparing in detail to the ATLAS and CMS data, and considering both the photon-initiated signal and QCD-initiated background. In Sect. 5 we summarise the processes generated by SuperChic 3 and provide information on its availability. In Sect. 6 we conclude, and in Appendix A we present some analytic estimates of the expected scaling with A of the QCD-initiated production process in pA and AA collisions, supporting our numerical findings.
2 Heavy ion collisions
We first consider the photon-initiated production, before moving on to consider the QCD-initiated case.
2.1 \(\gamma \gamma \) collisions: unscreened case
2.2 \(\gamma \gamma \) collisions: screened case
2.3 The ion–ion opacity
The parameters of the one channel eikonal description of nucleon–nucleon amplitude, described in the text
\(\sqrt{s}\) [TeV] | \(\sigma _0\) [mb] | a [GeV\(^2\) ] | b [GeV\(^{-2}\)] | c |
---|---|---|---|---|
5.02 | 146 | 0.180 | 20.8 | 0.414 |
8.16 | 159 | 0.190 | 26.3 | 0.402 |
39 | 228 | 0.144 | 23.3 | 0.397 |
63 | 245 | 0.150 | 28.0 | 0.390 |
2.4 QCD-induced production
We can also apply the above formalism to the case of QCD-initiated diffractive production in heavy ions. We will discuss two categories for this, namely semi-exclusive and fully exclusive production, below.
2.4.1 Semi-exclusive production
We first consider the case of incoherent QCD-induced CEP. Here, while the individual nucleons remain intact due to the diffractive nature of the interaction, the ion will in general break up. This can therefore lead to an exclusive-like signal in the central detector, with large rapidity gaps between the produced state and ion decay products. If zero degree calorimeter (ZDC) detectors are not used to veto on events where additional forward neutrons are produced, this will contribute to the overall signal.
2.4.2 Exclusive production
2.4.3 Including the participating nucleons
However, the survival factor due to this active pair would be better treated separately and included explicitly, as its precise value will depend on the underlying CEP process. More significantly, the exclusive production process must take place close to the periphery of the ions, where the corresponding nucleon density is low and the average number of nucleon–nucleon interactions contained in the above expression can be below one. Applying the above factor alone will therefore overestimate the corresponding survival factor, giving a value higher than that due to the active pair, and so such a separate treatment is essential.
However, this is not the end of the story. In particular the position of the nucleons in the ion shell are not completely independent, and we can expect some repulsion between them due to \(\omega \) meson exchange [39]. In the ion periphery the nucleon density is rather small, and hence it is reasonable to describe this repulsion in the same way as the repulsive ‘core’ in the deuteron wave function [39]. Here, the separation between the nearest nucleons cannot be less than \(r_{\mathrm{core}}=0.6-0.8\) fm. To account for this, we can subtract an interval of length \(2r_{\mathrm{core}}\) in the z direction from the nucleon density (25) which enters the calculation of the opacity.^{3}
2.4.4 Numerical results
In Fig. 5 (left) we show numerical predictions for the ratio of QCD-initiated cross sections at \(\sqrt{s}=5.02\) TeV in proton–ion (pA) and ion–ion (AA) collisions to the proton–proton result. In all cases we include the survival factor due to the active nucleon pair, but in the solid curves we include the effect due to the additional nucleons present in the ion(s) as well. To be concrete, we show results for \(\gamma \gamma \) production within the ATLAS event selection [21]. We take (12) for the dependence of the ion radius on A, while we show results for \(d=0.5, 0.55\) and 0.6 fm (dotted, solid and dashed lines, respectively), including survival effects, in Fig. 6 to give an indication of the sensitivity of the cross section to the value of the ion skin thickness. This also provides a clearer demonstration of the trends for the full cross section (i.e. including survival effects): the solids curves in the two plots correspond to the same results.
In all cases, the impact of survival effects is found to be sizeable. Already for proton–ion collisions these reduce the corresponding cross sections by up to two order of magnitude, while in ion–ion collisions the effect is larger still, leading to a reduction of up to four and six orders of magnitude in the semi-exclusive and exclusive cases, respectively. As discussed earlier, this is to be expected: as the range of the QCD-initiated CEP interaction is much smaller than the ion radius, the majority of potential nucleon–nucleon CEP interactions (in the absence of survival effects due to the non-interacting nucleons) would take place in a region of high nucleon density, where additional particle production is essentially inevitable. This is in strong contrast to the case of photon-initiated production, where the long range QED interaction allows all protons in the ion to contribute coherently in an ultra-peripheral process.
Considering in more detail the cross sections including survival effects, in the proton–ion case, the relatively gentle scaling of the exclusive and semi-exclusive cross sections with A is clear, which upon inspection are indeed found to follow a rough \(\sim A^{1/3}\) trend, consistent with (39) and (46). As expected from the discussion in Sect. 2.4.2, the exclusive and semi-exclusive cross sections are of similar sizes. Interestingly, we can see that the precise calculation predicts that the exclusive cross section is in fact somewhat enhanced relative to the semi-exclusive. For the ion–ion case we can see that the semi-exclusive cross section again increases only very gently with A, again as expected. Upon inspection, we observe that the trend is consistent with a flatter A dependence then the simple \(\sim A^{1/3}\) scaling predicted using the analytic calculation of Appendix A; on closer investigation, we find that this is due to the correct inclusion of the impact parameter dependence of the elastic nucleon–nucleon scattering amplitude in the definition of the opacity (24), which is omitted in the simplified analytic approach. In the exclusive case, interestingly the cross section in fact decreases with A, albeit with a relatively flat behaviour at larger A. This is again found to be due to the full calculation of the opacity. Again, numerically the exclusive and semi-exclusive cross sections enter at roughly the same order, with some suppression in the former case, as expected from the discussion in Sect. 2.4.2.
3 New processes
In this section we briefly describe the new processes and refinements that have been included in SuperChic since the version described in [12].
3.1 Light-by-light scattering: W loop contributions
In previous versions of SuperChic, expressions for the fermion loop contributions to the \(\gamma \gamma \rightarrow \gamma \gamma \) light-by-light scattering process in the \(\hat{s} \gg m_f^2\) limit were applied. We now move beyond this approximation, applying the SANC implementation [41] of this process, which includes the full dependence on the fermion mass in the loop. This in addition includes the contribution from W bosons, which was not included previously, again with the full mass dependence. We also implement a modified version of the SANC implementation for the \(gg \rightarrow \gamma \gamma \) process, which has the same form as the quark-loop contributions to the light-by-light scattering process, after accounting for the different colour factors and charge weighting.
In Fig. 7 (left) we show the diphoton invariant mass distribution due to QCD and photon-initiated CEP in pp collisions at \(\sqrt{s}=14\) TeV. The photons are required to have transverse momentum \(p_\perp ^\gamma > 10\) GeV and pseudorapidity \(|\eta ^\gamma |<2.4\). We can see that while the former dominates for \(M_{\gamma \gamma } \lesssim 150\) GeV, above this the latter is more significant. This is due to the well-known impact of the Sudakov factor in the QCD-initiated cross section [9] which suppresses higher mass production, due to the increasing phase space for additional gluon radiation, so that at high enough mass this compensates the suppression in the photon-initiated cross section due to the additional powers of the QED coupling \(\alpha \). We also show the relative contributions of fermion and W boson loops to the photon-initiated cross section. While for \(M_{\gamma \gamma } \lesssim 2 M_W\) the latter is as expected negligible, at sufficiently high invariant mass it comes to dominate. In Fig. 7 (right) we show the impact of excluding the fermion masses for the QCD-initiated case. The photons are required to have transverse momentum \(p_\perp ^\gamma > 16\) GeV and pseudorapidity \(|\eta ^\gamma |<2.4\). We can see that at lower \(M_X\) the difference is at the \(\sim 30\%\) level, decreasing to below \(10\%\) at higher mass, in the considered region. Thus the previous SuperChic predictions will have overestimated the cross section by this amount. It should be noted however, that for the \(gg\rightarrow \gamma \gamma \) case this is below the level of other theoretical uncertainties, due in particular to the gluon PDF and soft survival factor. Moreover, this is a purely LO result, and we may expect higher order corrections to increase the cross section by a correction of this order.
Finally, we note that the MC prediction for QCD-initiated CEP processes such as diphoton production does not include the impact of so-called ‘enhanced’ screening effects. These may be expected to reduce the corresponding cross section by as much as a factor of \(\sim 2\) [42, 43], but we leave a detailed study of this to future work. Note that such effects are entirely absent in the case of photon-initiated CEP.
3.2 ALP production
3.3 Monopole and monopolium production
Magnetic monopoles complete the symmetry of Maxwell’s equations and explain charge quantization [45]. As such states would be expected to have large electromagnetic couplings, one possibility is to search for the production of monopole pairs, or bound states of monopole pairs (so called ‘monopolium’) through exclusive photon-initiated production at the LHC [46]. In the MC we have implemented the CEP of both monopoles pairs, and monopolium, in the latter case followed by the decay to two photons.
3.4 \(\gamma \gamma \rightarrow t\overline{t}\)
We include photon-initiated top quark production. This is implemented using the same matrix elements as the lepton pair production process, with the mass, electric charge and colour factors suitably modified. We find a total photon-initiated cross section of 0.25 fb in pp collisions at \(\sqrt{s}=14\) TeV, and 36 fb in Pb–Pb collisions at \(\sqrt{s}=5.02\) TeV. Note that the QCD-initiated cross section in pp collisions is about 0.02 fb, and so is an order of magnitude smaller, while in Pb–Pb this will be smaller still.
4 Light-by-light scattering: a closer look
Predicted cross sections, in nb, for diphoton final states within the ATLAS [21] and CMS [22] event selections, in Pb–Pb collisions at \(\sqrt{s}=5.02\) TeV. That is, the photons are required to have transverse energy \(E_\perp ^\gamma >2\) (3) GeV and pseudorapidity \(|\eta ^\gamma |<2.4\), while in the CMS case an additional cut of \(m_{\gamma \gamma } > 5\) GeV is imposed. Results with and without an additional acoplanarity cut aco < 0.01, and cut on the combined transverse momentum \(p_\perp ^{\gamma \gamma }<1\) (2) GeV in the CMS (ATLAS) case are shown. The cross sections for the light-by-light scattering (LbyL) and QCD-initiated photon pair production, in both the coherent and incoherent cases, are given. The result of simply scaling the pp cross section (including the pp survival factor) by \(A^2 R^4\) with \(R=0.7\) is also shown
LbyL | QCD (coh.) | QCD (incoh.) | \(A^2 R^4\) | |
---|---|---|---|---|
ATLAS | 50 | 0.008 | 0.05 | 50 |
ATLAS (aco < 0.01, \(p_\perp ^{\gamma \gamma }<2\) GeV) | 50 | 0.007 | 0.01 | 10 |
CMS | 103 | 0.03 | 0.2 | 180 |
CMS (aco < 0.01, \(p_\perp ^{\gamma \gamma }<1\) GeV) | 102 | 0.02 | 0.03 | 30 |
However, in addition to the desired photon-initiated signal, there is the possibility that QCD-initiated diphoton production may contribute as a background. We are now in a position for the first time to calculate this, using the results of Sect. 2.4. The results for the QCD-initiated background (both coherent and incoherent), as well as the prediction for the light-by-light signal, are shown in Table 2. We consider both the ATLAS and CMS event selection in the central detectors. Namely, the produced photons are required to have transverse energy \(E_\perp ^\gamma >2\) (3) GeV and pseudorapidity \(|\eta ^\gamma |<2.4\) in the case of CMS (ATLAS), while for CMS an addition cut of \(m_{\gamma \gamma } > 5\) GeV is imposed. We show results before and after further cuts on the diphoton system \(p_\perp ^{\gamma \gamma }<1 (2) \) GeV for CMS (ATLAS) and acoplanarity (\(1-\Delta \phi _{\gamma \gamma }/\pi <0.01\)) are imposed, which are designed to suppress the non-exclusive background.
We can see that incoherent background, which we recall corresponds to the case that the colliding ions do not remain intact, is further suppressed by the additional acoplanarity and \(p_\perp ^{\gamma \gamma }\) cuts; as we would expect, due to the broader \(p_\perp \) spectrum of the incoherent cross section. This is seen more clearly in Fig. 9, which shows the (normalized) acoplanarity distributions in the three cases. We can see that the QED-initiated process is strongly peaked at low acoplanarity (< 0.01), as is the coherent QCD-initiated process, albeit with a somewhat broader distribution due to the broader QCD form factor in this case. On the other hand, for incoherent QCD-initiated production we can see that the spectrum is spread quite evenly over the considered acoplanarity region.
It should be emphasised that in both the ATLAS and CMS analyses the normalization of the QCD-initiated background is in fact determined by the data. In particular, the predicted QCD background from this \(A^2 R^4\) scaling is allowed to be shifted by a free parameter \(f^\mathrm{norm}\), which is fit to the observed cross section in the aco \(>0.01\) region, where the LbyL signal is very low. Interestingly in both analyses a value of \(f^\mathrm{norm} \approx 1\) is preferred, which is significantly larger than our prediction; from Table 2 we can roughly expect \(f^\mathrm{norm} \sim \sigma ^\mathrm{incoh}/\sigma ^{A^2 R^4} \sim 10^{-3}\). However, great care is needed in interpreting these results: as is discussed in [22] this normalization effectively account for all backgrounds that result in large acoplanarity photons, not just those due to QCD-initiated production. Indeed, in this analysis it is explicitly demonstrated that the MC for the background for \(e^+ e^-\) production significantly undershoots the data in the large acoplanarity region, and it is suggested that this could be due to events where extra soft photons are radiated. Our results clearly predict that the contribution to the observed events in the large acoplanarity region should not be due to QCD-initiated production, suggesting that a closer investigation of other backgrounds, such as the case of \(e^+ e^- + \gamma \) discussed in [22], would be worthwhile.
Finally, we note that in the ATLAS analysis [21] the number of events in the region with diphoton acoplanarity \(> 0.01\), where the QED-initiated CEP signal will be strongly suppressed, with and without neutrons detected in the ZDCs is observed. They find 4 events with a ZDC signal, that is with ion dissociation, and 4 without, which roughly corresponds to a \(O(10\,\mathrm{fb})\) cross section in both cases. However from Table 2 we predict a much smaller cross sections of roughly 0.04 (0.01) fb with (without) ZDC signals, i.e. 0 events in both cases. While some care is needed, in particular as the predictions in Table 2 have not been corrected for detector effects, this predicted QCD contribution is clearly far too low to explain these observed events. We note that the probability of excitation of a GDR in each ion can be rather large (in [38] a probability of \(\sim 30\%\) for the related vector meson photoproduction process is predicted), however these should generally lead to events in the acoplanarity \(<0.01\) region. Inelastic photon emission can lead to ion break up at larger acoplanarity, but is predicted in [49] to be at the % level. Again, clearly further investigation of these issues is required.
5 SuperChic 3: generated processes and availability
SuperChic 3 is a Fortran based Monte Carlo that can generate the processes described above and in [12], with and without soft survival effects. User-defined distributions may be output, as well as unweighted events in the HEPEVT, Les Houches and HEPMC formats. The code and a user manual can be found at http://projects.hepforge.org/superchic.
Here we briefly summarise the processes that are currently generated, referring the reader to the user manual for further details. The QCD-initiated production processes are: SM Higgs boson via the \(b\overline{b}\) decay, \(\gamma \gamma \), 2 and 3-jets, light meson pairs (\(\pi ,K,\rho ,\eta ('),\phi \)), quarkonium pairs (\(J/\psi \) and \(\psi (2S)\)) and single quarkonium (\(\chi _{c,b}\) and \(\eta _{c,b}\)). Photoproduction processes are: \(\rho \), \(\phi \), \(J/\psi \), \(\psi (2S)\) and \(\Upsilon (1S)\). Photon-initiated processes are: W pairs, lepton pairs, \(\gamma \gamma \), SM Higgs boson via the \(b\overline{b}\) decay, ALPs, monopole pairs and monopolium. pp, pA and AA collisions are available for arbitrary ion beams, for QCD and photon-initiated processes. For photoproduction, currently only pp and pA beams are included. Electron beams are also included for photon-initiated production.
6 Conclusions and outlook
In this paper we have presented the updated SuperChic 3 Monte Carlo generator for central exclusive production. In such a CEP process, an object X is produced, separated by two large rapidity gaps from intact outgoing protons, with no additional hadronic activity. This simple signal is associated with a broad and varied phenomenology, from low energy QCD to high energy BSM physics, and is the basis of an extensive experimental programme that is planned and ongoing at the LHC.
SuperChic 3 generates a wide range of final-states, via QCD and photon-initiated production and with pp, pA and AA beams. The addition of heavy ion beams is a completely new update, and we have included a complete description of both photon and QCD-initiated production. In the latter case this is to the best of our knowledge the first time such a calculation has been attempted. We have accounted for the probability that the ions do not interact inelastically, and spoil the exclusivity of the final state. While this is known to be a relatively small effect in the photon-initiated case, in the less peripheral QCD-initiated case the impact has been found to be dramatic.
These issues are particularly topical in light of the recent ATLAS and CMS observations of exclusive light-by-light scattering in heavy ion collisions. We have presented a detailed comparison to these results, and have shown that the signal cross section can be well produced by our SM predictions, and any background from QCD-initiated production is expected to be essentially negligible, in contrast to some estimates presented elsewhere in the literature. We find that the presence of additional events outside the signal region, with and without neutrons observed in the ZDCs (indicating ion break up) cannot be explained by the predicted QCD-initiated background. Addressing this open question therefore remains an experimental and/or theoretical challenge for the future.
Finally, there are very promising possibilities to use the CEP channel at high system masses to probe electroweakly coupled BSM states with tagged protons during nominal LHC running, accessing regions of parameters space that are difficult or impossible to reach using standard inclusive search channels. With this in mind, we have presented updates for photon-initiated production in pp collisions, including axion-like particle, monopole pairs and monopolium, as well as an updated calculation of SM light-by-light scattering including W boson loops. These represent only a small selection of possible additions to the MC, and indeed as the programme of CEP measurements at the LHC continues to progress, we can expect further updates to come.
Footnotes
- 1.
Correspondingly, we have \(s= A_1 A_2 s_{nn}\), where \(s_{nn}\) is the squared c.m.s. energy per nucleon and \(A_i\) is the ion mass number.
- 2.
Strictly speaking this is only true for the contribution proportional to the electric form factors, see [12] for further discussion; however here we indeed take \(F_M=0\).
- 3.
To be precise, we omit the region \((-r_{\mathrm{core}},r_{\mathrm{core}})\), that is we take mean value of \(z=0\) for the active nucleon. In the case of the ion–ion opacity, for which additional nucleon–nucleon interactions can take place at different impact parameters to the active nucleon, such a simple replacement will in general overestimate the cross section, but for peripheral collisions this remains a good approximation.
Notes
Acknowledgements
We thank David d’Enterria and Marek Tasevsky for useful discussions, Vadim Isakov for useful clarifications on questions related to nuclear structure, and Radek Žlebčák for identifying various bugs and mistakes in the previous MC version. LHL thanks the Science and Technology Facilities Council (STFC) for support via Grant awards ST/P004547/1. MGR thanks the IPPP at the University of Durham for hospitality. VAK acknowledges support from a Royal Society of Edinburgh Auber award.
References
- 1.FP420 R & D, M. G. Albrow et al., JINST 4, T10001 (2009). arXiv:0806.0302
- 2.M.G. Albrow, T.D. Coughlin, J.R. Forshaw, Prog. Part. Nucl. Phys. 65, 149 (2010). arXiv:1006.1289 ADSCrossRefGoogle Scholar
- 3.M. Tasevsky, Int. J. Mod. Phys. A 29, 1446012 (2014). arXiv:1407.8332 ADSCrossRefGoogle Scholar
- 4.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W. Stirling, Int. J. Mod. Phys. A 29, 1430031 (2014). arXiv:1405.0018 ADSCrossRefGoogle Scholar
- 5.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, Int. J. Mod. Phys. A 29, 1446004 (2014)ADSCrossRefGoogle Scholar
- 6.LHC Forward Physics Working Group, K. Akiba et al., J. Phys. G 43, 110201 (2016). arXiv:1611.05079
- 7.ATLAS Collaboration, Technical Design Report for the ATLAS Forward Proton Detector, CERN-LHCC-2015-009; ATLAS-TDR-024; M. Tasevsky, Conf. Proc. 1654, 090001 (2015)Google Scholar
- 8.M. Albrow et al., CERN Report No. CERN-LHCC-2014-021. TOTEM-TDR-003. CMS-TDR-13 (2014) (unpublished) Google Scholar
- 9.V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C 23, 311 (2002). arXiv:hep-ph/0111078 ADSCrossRefGoogle Scholar
- 10.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C 65, 433 (2010). arXiv:0909.4748 ADSCrossRefGoogle Scholar
- 11.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling, Eur. Phys. J. C 69, 179 (2010). arXiv:1005.0695 ADSCrossRefGoogle Scholar
- 12.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, Eur. Phys. J. C 76, 9 (2016). arXiv:1508.02718 ADSCrossRefGoogle Scholar
- 13.M. Boonekamp et al., (2011). arXiv:1102.2531
- 14.L. Lönnblad, R. Žlebčák, Eur. Phys. J. C 76, 668 (2016). arXiv:1608.03765 ADSCrossRefGoogle Scholar
- 15.S.R. Klein, J. Nystrand, J. Seger, Y. Gorbunov, J. Butterworth, Comput. Phys. Commun. 212, 258 (2017). arXiv:1607.03838 ADSCrossRefGoogle Scholar
- 16.J. Monk, A. Pilkington, Comput. Phys. Commun. 175, 232 (2006). arXiv:hep-ph/0502077 ADSCrossRefGoogle Scholar
- 17.L. Forthomme, (2018). arXiv:1808.06059
- 18.L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, Eur. Phys. J. C 74, 2848 (2014). arXiv:1312.4553 ADSCrossRefGoogle Scholar
- 19.R.A. Ryutin, V.A. Petrov, (2017). arXiv:1704.04387
- 20.R.A. Kycia, J. Turnau, J.J. Chwastowski, R. Staszewski, M. Trzebiski, (2017). arXiv:1711.06087
- 21.ATLAS Collaboration, M. Aaboud et al., Nat. Phys. 13, 852 (2017). arXiv:1702.01625
- 22.CMS Collaboration, A.M. Sirunyan et al., (2018). arXiv:1810.04602
- 23.S. Knapen, T. Lin, H.K. Lou, T. Melia, Phys. Rev. Lett. 118, 171801 (2017). arXiv:1607.06083 ADSCrossRefGoogle Scholar
- 24.J. Ellis, N.E. Mavromatos, T. You, Phys. Rev. Lett. 118, 261802 (2017). arXiv:1703.08450 ADSMathSciNetCrossRefGoogle Scholar
- 25.C. Baldenegro, S. Fichet, G. von Gersdorff, C. Royon, JHEP 06, 142 (2017). arXiv:1703.10600 ADSCrossRefGoogle Scholar
- 26.C. Baldenegro, S. Fichet, G. Von Gersdorff, C. Royon, JHEP 06, 131 (2018). arXiv:1803.10835 ADSCrossRefGoogle Scholar
- 27.V.M. Budnev, I.F. Ginzburg, G.V. Meledin, V.G. Serbo, Phys. Rep. 15, 181 (1975)ADSCrossRefGoogle Scholar
- 28.R.D. Woods, D.S. Saxon, Phys. Rev. 95, 577 (1954)ADSCrossRefGoogle Scholar
- 29.L.C. Chamon et al., Phys. Rev. C 66, 014610 (2002). arXiv:nucl-th/0202015 ADSCrossRefGoogle Scholar
- 30.E. Gotsman, E. Levin, U. Maor, Int. J. Mod. Phys. A 30, 1542005 (2015). arXiv:1403.4531 ADSCrossRefGoogle Scholar
- 31.V.A. Khoze, A.D. Martin, M.G. Ryskin, J. Phys. G 45, 053002 (2018). arXiv:1710.11505 ADSCrossRefGoogle Scholar
- 32.V.A. Khoze, A.D. Martin, M.G. Ryskin, (2018). arXiv:1806.05970
- 33.M.G. Ryskin, A.D. Martin, V.A. Khoze, Eur. Phys. J. C 60, 249 (2009). arXiv:0812.2407 ADSCrossRefGoogle Scholar
- 34.V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C 74, 2756 (2014). arXiv:1312.3851 ADSCrossRefGoogle Scholar
- 35.V.A. Khoze, A.D. Martin, M.G. Ryskin, Int. J. Mod. Phys. A 30, 1542004 (2015). arXiv:1402.2778 ADSCrossRefGoogle Scholar
- 36.M.L. Good, W.D. Walker, Phys. Rev. 120, 1857 (1960)ADSCrossRefGoogle Scholar
- 37.C.M. Tarbert et al., Phys. Rev. Lett. 112, 242502 (2014). arXiv:1311.0168 ADSCrossRefGoogle Scholar
- 38.A.J. Baltz, S.R. Klein, J. Nystrand, Phys. Rev. Lett. 89, 012301 (2002). arXiv:nucl-th/0205031 ADSCrossRefGoogle Scholar
- 39.R.V. Reid Jr., Ann. Phys. 50, 411 (1968)ADSCrossRefGoogle Scholar
- 40.C.F.V. Weizsacker, Z. Phys. 96, 431 (1935)ADSCrossRefGoogle Scholar
- 41.D. Bardin, L. Kalinovskaya, E. Uglov, Phys. Atom. Nucl. 73, 1878 (2010). arXiv:0911.5634 ADSCrossRefGoogle Scholar
- 42.M.G. Ryskin, A.D. Martin, V.A. Khoze, Eur. Phys. J. C 60, 265 (2009). arXiv:0812.2413 ADSCrossRefGoogle Scholar
- 43.S. Ostapchenko, M. Bleicher, Eur. Phys. J. C 78, 67 (2018). arXiv:1712.09695 ADSCrossRefGoogle Scholar
- 44.S. Knapen, T. Lin, H.K. Lou, T. Melia, (2017). arXiv:1709.07110
- 45.P.A.M. Dirac, Proc. R. Soc. Lond. A 133, 60 (1931)ADSCrossRefGoogle Scholar
- 46.L.N. Epele, H. Fanchiotti, C.A.G. Canal, V.A. Mitsou, V. Vento, Eur. Phys. J. Plus 127, 60 (2012). arXiv:1205.6120 CrossRefGoogle Scholar
- 47.L.N. Epele, H. Fanchiotti, C.A. Garcia Canal, V. Vento, Eur. Phys. J. C 56, 87 (2008). arXiv:hep-ph/0701133 ADSCrossRefGoogle Scholar
- 48.D. d’Enterria, G.G. da Silveira, Phys. Rev. Lett. 111, 080405 (2013). arXiv:1305.7142 ADSCrossRefGoogle Scholar
- 49.K. Hencken, D. Trautmann, G. Baur, Z. Phys. C 68, 473 (1995). arXiv:nucl-th/9503004 ADSCrossRefGoogle Scholar
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