Exclusive production of heavy charged Higgs boson pairs
in the reaction at the LHC and a future circular collider
Abstract
We calculate differential cross sections for exclusive production of heavy charged scalar, weakly interacting particles (charged Higgs bosons, charged technipions, etc.) via photonphoton exchanges in the reaction with exact kinematics. We present distributions in rapidities, transverse momenta, and correlations in azimuthal angles between the protons and between the charged Higgs bosons. As an example, the integrated cross section for = 14 TeV (LHC) is about 0.1 fb and about 0.9 fb at the Future Circular Collider (FCC) for = 100 TeV when assuming GeV. The results are compared with results obtained within standard equivalentphoton approximation known from the literature. We discuss the role of the Dirac and Pauli electromagnetic form factors of the proton. We have also performed first calculations of cross sections for the exclusive diffractive KhozeMartinRyskin mechanism. We have estimated limits on the coupling constant within twoHiggs dublet model based on recent experimental data from the LHC. The diffractive contribution is, however, much smaller than the one. The , , and exchanges give even smaller contributions. Absorption corrections are calculated for the first time differentially for various distributions. In general, they lead to a damping of the cross section. The damping depends on the invariant mass and on fourmomentum transfers squared. In contrast to diffractive processes, the larger the collision energy, the smaller the effect of absorption. We discuss a possibility to measure the exclusive production of two charged Higgs bosons with the help of socalled “forward proton detectors” at the LHC experiments.
pacs:
12.60.Fr,13.85.t,14.80.DaI Introduction
There are several reasons why exclusive reactions are interesting Lebiedowicz:thesis ; Albrow:2010yb . One of them is the possibility to search for effects beyond the Standard Model (SM). The main advantage of exclusive reactions is that background contributions are strongly reduced compared to inclusive processes. A good example are searches for exclusive production of supersymmetric Higgs boson Heinemeyer:2007tu ; Tasevsky:2013iea ; Tasevsky:2014cpa , anomalous boson couplings for Pierzchala:2008xc ; Schul:2008sr ; Kepka:2008yx ; Chapon:2009hh or for Fichet:2013gsa ; Fichet:2014uka . So far these processes are usually studied in the socalled equivalentphoton approximation (EPA) (for a description of the method, see e.g. Budnev:1974de ). Within the Standard Model the cross section for the reaction is about 100 fb at TeV Lebiedowicz:2012gg . Gluoninduced processes could also contribute to the exclusive production of Lebiedowicz:2012gg and Enberg:2011qh via quark loops. ^{2}^{2}2An attractive channel is the associated production of a charged Higgs boson with a boson via fusion. Since there is no couplings the associated production process have no treelevel contribution in the 2HDM and in the MSSM and occurs only at oneloop level in the lowest order. The corresponding cross sections are rather small mainly due to suppression of Sudakov form factors and the gap survival factor. The exclusive reactions could be also used in searches for neutral technipion in the diphoton final state Lebiedowicz:2013fta or dilaton Goncalves:2015oua . Here a precise prediction of the cross sections is not possible as the model parameters are still unknown.
Discovery of the heavy Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) Gunion:1989we ; Gunion:1992hs ; Djouadi:2005gj or more generic TwoHiggs Doublet Models (2HDMs) (see e.g. Diaz:2002tp ; Branco:2011iw ) poses a special challenge at future colliders. One of the international projects currently under consideration is the Future Circular Collider (FCC) FCC . The Higgs sector in both the MSSM and 2HDM contains five states: three neutral [two even (, ) and one odd ()] and two charged (, ) Higgs bosons. In general, either or could correspond to the SM Higgs. The charged Higgs boson pair production in the mode was considered in BowserChao:1993ji ; Drees:1994zx ; Moretti:2002sn . In general, the higherorder corrections to the subprocess decrease the treelevel total cross section by about a few percent; see Zhu:1997es ; Lei:2005kr . Also the associated production was discussed in the literature Zhou:2001wp . For a more extensive discussion of charged Higgs boson production at the LHC and ILC, see Kanemura:2014dea .
There are also extensive phenomenological studies on charged Higgs boson(s) production at the LHC in the inclusive reactions via the partonic processes Alves:2005kr ; Heinemeyer:2013tqa . If , the charged Higgs boson can be produced in and decays from the parent production channel , which would compete with the SM process . The dominant decay channels in this mass range are and . In the case of a heavy charged Higgs with , there are three major mechanisms:

Associated production with a top quark via the partonic processes Belyaev:2001qm ; Belyaev:2002eq ; Alwall:2004xw ; Peng:2006wv ; Nhung:2012er ; Cao:2013ud ; Flechl:2014wfa as well as through the gluonbottom fusion Gunion:1986pe ; Zhu:2001nt ; Gao:2002is ; Plehn:2002vy ; Berger:2003sm ; Weydert:2009vr ; Yang:2011jk . The sequential decay is known as a preferred channel. But signals in these processes appear together with large QCD backgrounds. The channels were analyzed in Assamagan:2002ne ; Coleppa:2014cca . In the latter paper, the decay channel was also considered. Recently, the decay channel for a SMlike Higgs was studied in Basso:2012st ; Enberg:2014pua . This decay channel can be particularly important when charged Higgs is produced through the processes.

Associated production with a boson through the subprocesses Dicus:1989vf ; BarrientosBendezu:1998gd ; Moretti:1998xq ; BarrientosBendezu:1999vd ; BarrientosBendezu:2000tu ; Brein:2000cv ; Hollik:2001hy ; Asakawa:2005nx ; Eriksson:2006yt ; Bao:2011sy ; Liu:2013oen and associated production of a charged Higgs boson with a odd Higgs boson, i.e. , was studied in Kanemura:2001hz ; Cao:2003tr .

Charged Higgs boson pair production via Krause:1997rc ; BarrientosBendezu:1999gp ; Brein:1999sy ; Hespel:2014sla , HongSheng:2005uy subprocesses or in association with bottom quark pairs Moretti:2001pp ; Moretti:2003px . For more recent studies, see Aoki:2011wd ; Liu:2015mza .
The cross sections for the inclusive reactions strongly depend on the model parameters, such as , the ratio of the vacuum expectation values of the two Higgs doublets, and others. A program on how to limit the relevant parameters, based on the collider searches and data from factories, was presented, e.g., in Cornell:2009gg . Another important ingredient of the model is the mass of the charged Higgs boson. In the MSSM the relation between the masses of the charged Higgs boson and odd Higgs boson in lowest order is given by ^{3}^{3}3This is particular to the MSSM in lowest order (is modified by oneloop radiative corrections Diaz:1991ki ) and does not hold in 2HDMs or in, e.g., the NexttoMinimal Supersymmetric Standard Model (NMSSM). (for reviews and details, see, e.g. Gunion:1989we ; Djouadi:2005gj ).
Several experimental searches already placed limitations on the mass of the charged Higgs bosons. There is a direct limit of GeV from the LEP searches Searches:2001ac by its decays and . At hadron colliders, the search procedures for a charged Higgs boson differ in term of its mass range. At the Tevatron the searches were mainly focused on the low mass range which can put a constraint to the 2HDM (as an example) on the small and large regions for a charged Higgs boson mass up to GeV Abazov:2009aa . Recent searches at the LHC Chatrchyan:2012vca ; Aad:2012tj ; Aad:2012rjx ; Aad:2013hla ; Aad:2014kga ; CMS:2014pea ; CMS:2014cdp provide new limitations on the model parameters. However, still a possible span of parameters is rather large. For example, in the latest searches ATLAS and CMS put limits on the product of branching fractions ), but there are no modelindependent limits on the mass. The observed limits are reinterpreted in some MSSM scenarios, with mass limits around GeV that depend somewhat on . But in other models such as typeI 2HDM, the limit may be weaker.
Other experimental bounds on the charged Higgs mass come from processes where the charged Higgs boson enters as a virtual particle, i.e. participates in loop diagrams. It is well known that in the typeII 2HDM, where the up and downtype quarks and leptons couple to different doublets, the transitions imposes a strong constraint on the Higgs boson mass GeV. In the typeI 2HDM, instead, all fermions couple to the same doublet and there is no such strong physics constraint (the MSSM is also less sensitive to radiative corrections). The flavor constraints on the Higgs sector are, however, typically model dependent. A detailed analysis of precision and flavor bounds in the 2HDM can be found, e.g., in Coleppa:2013dya .
In the present analysis we wish to concentrate on exclusive production of charged Higgs bosons in protonproton collisions proceeding through exchange of two photons. In Fig. 1 we show basic diagrams contributing to the reaction. The coupling of photons to protons is usually parametrized with the help of proton electromagnetic form factors: (electric), (magnetic) or equivalently (Dirac), (Pauli). We wish to discuss the dependence on the form factors of several differential distributions. In contrast to inclusive processes discussed above, the considered here exclusive reaction is free of the model parameter uncertainties, at least in the leading order, except of the mass of the charged Higgs bosons.
Our paper is organized as follows. In Sec. II we discuss formalism of the reaction both in the equivalentphoton approximation (EPA) in the momentum space commonly used in the literature and in exact kinematics. In Sec. III we present numerical results for total and differential cross sections. In Sec. III.1 we compare results obtained in the exact calculation and those obtained in EPA. We present not only estimation of the total cross section but also several differential distributions important for planning potential future experimental searches. In addition, we discuss the role of absorption corrections commonly neglected for twophoton initiated processes. Finally, we also consider diffractive exclusive production of the bosons through an intermediate recently discovered Higgs boson. Diffractive contribution is discussed in Sec. III.2.
Ii Formalism
We shall study exclusive production of in protonproton collisions at high energies
(1) 
where , and , denote the fourmomenta and helicities of the protons, and denote the fourmomenta of the charged Higgs bosons, respectively. In the following we will calculate the contributions from the diagrams of Fig. 1.
ii.1 Equivalentphoton approximation
Similar processes are treated usually in the equivalentphoton approximation (EPA) in the momentum space, see e.g. Lebiedowicz:2012gg ; Lebiedowicz:2013fta . ^{4}^{4}4An impact parameter EPA was considered recently in Dyndal:2014yea . Only very few differential distributions can be obtained in the EPA approach. In this approximation, when neglecting photon transverse momenta, one can write the differential cross section as
(2) 
where and ’s are an elastic fluxes of the equivalent photons (see e.g.Budnev:1974de ) as a function of longitudinal momentum fraction with respect to the parent proton defined by the kinematical variables of the charged Higgs bosons,
(3) 
with being transverse mass of the boson(s). Above is the amplitude squared averaged over the photon polarization states.
The photon flux is given by the formula Budnev:1974de
(4) 
where the spacelike momentum transfer squared ^{5}^{5}5 Here we discuss the collinear EPA approach, that is, the photon transverse momenta . An approach including transverse momenta of photons was discussed recently in daSilveira:2014jla . and the photon minimal virtuality allowed by kinematics . The coefficient functions and are determined by the electric and magnetic form factors of the proton:
(5) 
where the and form factors are related to Dirac () and Pauli () form factors by
(6) 
Using the standard dipole parametrizations of the Sachs form factors (see, for instance, chapter 2 in Close:2007zzd )
(7)  
(8) 
where is the socalled dipole form factor, , and are the anomalous proton magnetic moment and the nuclear magneton, respectively, we obtain
(9)  
(10) 
We shall use the parametrizations in the following analysis.
ii.2 Exact kinematics
In the present studies we perform, for the first time, exact calculations for the considered exclusive process (1). In general, the cross section can be written as
(11)  
where energy and momentum conservations have been made explicit. The formula is written in the overall centerofmass frame. Above is the amplitude squared averaged over initial and summed over final proton polarization states. The kinematic variables for the reaction (1) are
(12) 
Our calculations have been done using the VEGAS routine Lepage:1980dq and checked on an eightdimensional grid ^{6}^{6}6The details on how to conveniently reduce the number of kinematic integration variables are discussed in Lebiedowicz:2009pj .. The phase space integration variables are taken the same as in Ref.Lebiedowicz:2009pj , except that proton transverse momenta and are replaced by = log and = log, respectively, where = 1 GeV. The main ingredients of the model are the amplitudes for the exclusive process.
The Born amplitudes for the process (1) are calculated as
(13) 
where is the photon propagator. Using the Gordon decomposition the vertex takes the form
(14)  
where is a Dirac spinor and and are initial and final fourmomenta and helicities of the protons, respectively.
In the highenergy approximation, at not too large , ^{7}^{7}7 We show how good the approximation is in Figs. 9, 10, 12, 13. one gets the simple formula
(15) 
which is very convenient for the discussion of the proton spinconserving and the proton spinflipping components separately. It is easy to see that in the approximation [see Eq. (15)] the cross section contains only terms proportional to and no mixed terms proportional to , etc. In exact calculations [with spinors of protons, see Eq. (14)], there is a small contribution of the mixed terms. This will be discussed when presenting our results.
The tensorial vertex in Eq. (13) for the subprocess is a sum of threelevel amplitudes corresponding to , and contact diagrams of Fig. 1, respectively,
(16)  
where and . There are strong cancellations between the three contributions.
A complete calculation for exclusive production in collisions, in addition to the exchange, must take into account more diagrams than those of Fig. 1. We can have the , , and exchanges. The corresponding amplitudes can be obtained by substitution of the photon propagator and the vertex [see (13) and (14)] by the boson propagator and the vertex Alberico:2001sd ,
where we use the shorthand notation , , is the Weinberg mixing angle. The and coupling constants in (16) read:
(18) 
The neutral current form factors appearing in (LABEL:vertex_Zpp) related to the vector part can be related to electromagnetic form factors [see (9) and (10), ],
(19) 
where for small . The form factor related to axialvector neutral current is related to the familiar charge current axialvector form factor:
(20) 
Since the strangeness form factors and are poorly known and small in the following we shall neglect them.
ii.3 Absorption corrections
The absorptive corrections to the Born amplitude (13) are added to give the full physical amplitude for the reaction:
(21) 
Here (and above) we have for simplicity omitted the dependence of the amplitude on kinematic variables.
The amplitude including rescattering corrections between the initial and finalstate protons in the fourbody reaction discussed here can be written as
where and . Here, in the overall centerofmass system, and are the transverse components of the momenta of the finalstate protons and is the transverse momentum carried by additional pomeron exchange. is the elastic scattering amplitude for large and with the momentum transfer . Here we assume channel helicity conservation and the exponential functional form of form factors in the pomeronprotonproton vertices.
We shall show results in the Born approximation as well as include the absorption corrections on the amplitude level. This allows us to study the absorption effects differentially in any kinematical variable chosen, which has, so far, never been done for twophoton induced (sub)processes.
Iii Results
iii.1 Electromagnetic process
In this section we shall present results of our calculations for the reaction (1) calculating from the diagrams of Fig. 1. Let us start our presentation by presenting the total cross section for = 14 TeV (LHC) and = 100 TeV (FCC) and for various charged Higgs mass values. In Table 1 we show cross sections in fb without and with (results in the parentheses) the rescattering corrections. The smaller the values of , the larger are those of cross section ^{8}^{8}8We wish to note on the margin that the cross section for pair production for doubly charged (Higgs) bosons, e.g. , would be 16 times larger Han:2007bk ; Kanemura:2014goa ; Kanemura:2014ipa in the leadingorder approximation considered here. The doubly charged Higgs bosons are expected in models that contain a Higgs boson triplet field.. The values of the gap survival factor for different masses of bosons GeV are, respectively, for TeV (LHC) and for TeV (FCC). In contrast to diffractive processes, the larger the collision energy, the smaller the effect of absorption. We have checked numerically that the cross section contributions with the , , and exchanges are very small compared to the contribution and will be not presented explicitly in this paper.
(GeV)  150  300  500 

(fb)  0.1474 (0.1132)  0.0119 (0.0080)  0.0014 (0.0008) 
(fb)  1.0350 (0.9236)  0.1470 (0.1258)  0.0303 (0.0249) 
In Fig. 2 we show a distribution in an auxiliary integration variable(s) = . If protons are measured, the distributions in Fig. 2 can be measured too. Here and in the following, we discuss the differential distributions for one selected mass of . For example, we shall assume GeV, which is rather a lower limit for the charged Higgs bosons. The general features of the differential distribution for heavier masses are, however, similar. We compare results without (the upper longdashed lines) and with (the lower longdashed lines) absorption corrections due to the interactions.
The rapidity distribution for the charged Higgs bosons is shown in Fig. 3. The larger centerofmass energy the broader the rapidity distributions.
In Fig. 4 we show invariant mass distribution of the subsystem in a broad range of the invariant masses. We compare results for the exact kinematics and for the EPA calculations. Please note that for the EPA, the invariant mass of the diHiggs system is given by .
In Fig. 5 we show decomposition into helicity components of the cross section in the twoHiggs invariant mass and in the rapidity of one of the charged Higgs bosons. Here we use the formula (15) for the vertex which is very convenient for the discussion of the proton spinconserving (the Dirac form factor (9) only) and the proton spinflipping (the Pauli form factor (10) only) components separately.
In Fig. 6 we show the dependence of absorption on . This is quantified by the ratio of full (with the absorption corrections) and Born differential cross sections
(23) 
The absorption effects due to the interaction lead to large damping of the cross section at the LHC and relatively small reduction of the cross section at the FCC. This result must be contrasted with typical diffractive exclusive processes where the role of absorption effects gradually increases with the collision energy.
In Fig. 7 we show the ratio of the cross section for all (, ) terms included in the amplitude to that for terms only both for the exact kinematics and for the EPA calculations. Here for consistency we have neglected the interference effect between the electromagnetic form factors in the EPA approach. At large invariant masses of the ratio for exact calculation is much smaller than that for EPA. This suggests that EPA overestimates the spinflipping contributions.
Let us discuss now a subtle effect of the interference of terms proportional to and . To quantify the effect, let us define the following quantities:
(24)  
(25) 
where means the cross section when, at one proton line, only the term is taken into account and, at the second proton line, only the term is taken into account. represents the cross section where all terms are coherently included. In Fig. 8 we show the relative corrections () coming from the interference effect between different terms in the amplitude. We see from Fig. 8 that for TeV the total cross section from the calculation using exact amplitude (including spinors of protons) is modified by at TeV, while at TeV only by . The smallness of the effect causes the effect of the fluctuations in our Monte Carlo approach. The relative corrections for the EPA approach are somewhat larger.
In Fig. 9 we present distributions in charged Higgs boson transverse momentum , i.e., or . While at low (Higgs) boson transverse momenta the EPA result is very similar to our exact result for all spin components, some deviations can be observed at larger transverse momenta. This is consistent with the similar comparison for the distributions in invariant mass (for the process under consideration large transverse momenta are related to large invariant masses).
If forward/backward protons are measured, then distributions in fourmomentum transfers squared ( = or ) can be obtained and relevant distributions shown in Fig. 10 can be constructed. The absorption effects due to the interactions are stronger for large values of .
In Fig. 11 we show a decomposition of the cross section into helicity components as a function of momentum transfer(s) squared. The proton spinconserving contribution related to the Dirac form factor(s) clearly dominates at very small or . At larger the proton spinflipping contribution related to the Pauli form factor(s) becomes important as well. The double spinflipping contribution (ff) vanish at , while the mixed contributions (fc) and (cf) vanish at and , respectively.
Let us consider now azimuthal correlations between outgoing particles. In Fig. 12 we show correlations between outgoing protons. We emphasize the dip at which is a consequence of the couplings involved in calculating the matrix element(s).
The correlation between outgoing Higgs bosons is shown in Fig. 13. The bosons are produced preferentially backtoback which can be understood given small transverse momenta of virtual photons compared to transverse momenta of the Higgs bosons.
iii.2 Diffractive process
So far we have considered a purely electromagnetic process, the contribution of which is model independent. The corresponding cross section turned out to be rather low. Therefore, one could worry whether other processes might not give a sizeable contribution, comparable to the photonphoton exchanges. One such candidate is the diffractive mechanism discussed, e.g., in the context of exclusive Higgs boson production Khoze:1997dr ; Khoze:2000cy ; Kaidalov:2003ys ; Maciula:2010tv . In the present case the mechanism shown in Fig. 14 seems an important candidate. The hard subprocess amplitude through the loop and channel SM Higgs boson () is given by
(26) 
and enters into invariant amplitude for the diffractive process as in Maciula:2010tv ; Lebiedowicz:2012gg . The tripleHiggs coupling constant is, of course, model dependent. In the MSSM model it depends only on the parameters and . In the general 2HDM it depends also on other parameters such as the Higgs potential parameters or masses of Higgs bosons. How the coupling constant depends on parameters of 2HDM was discussed, e.g., in Gunion:2002zf ; Ginzburg:2004vp ; Ferrera:2007sp ; Baglio:2014nea .
In Fig.15 we show as an example the coupling as a function of and for MSSM (left panel) and 2HDM (right panel). In the latter case we have used a relation given in Ref. Ferrera:2007sp while the formula for the MSSM can be found e.g. Gunion:1989we . The coupling constant in the MSSM case does not exceed 50 GeV (to be compared e.g. to GeV in the Standard Model). The coupling constant in the case of 2HDM can be, in general, very large. Recent data obtained at the LHC in the last three years put stringent constraints on and as well as on masses of the, thus far, unobserved Higgs bosons (some examples of such analyses can be found in Coleppa:2013dya ; Baglio:2014nea ; Broggio:2014mna . The LHC experimental data allow for two regions in the [, ] plane Eberhardt:2013uba ; Baglio:2014nea ; Coleppa:2013dya . One of them is the socalled “alignment limit”. The second one is more difficult to characterize. In the present analysis we focus on the alignment region which means the lightest even Higgs is what has been found at the LHC with GeV Aad:2015zhl . Experimental data allow for some deviations from the . As can be seen from Fig. 15 a small deviation from this limit can modify the coupling constant considerably. The analysis in Coleppa:2013dya suggests that and we keep such a relation throughout our analysis. A deviation from such a relation would increase the discussed coupling constant.
In Fig. 16 we show the dependence of the coupling constant on masses of charged and odd Higgses within 2HDM. ^{9}^{9}9We emphasise again that in the MSSM in the lowest order we have . A minimal value appears when . When we relax this condition the coupling can be even as large as 1000 GeV. This is consistent with the limits of the allowed region in Baglio:2014nea . Summarizing, in the 2HDM is limited to 64 GeV 1000 GeV. The corresponding couplings in the MSSM are smaller than 50 GeV. ^{10}^{10}10 It has been shown, e.g., in Asakawa:2005nx that in some regions of the parameter space of 2HDMs the associated production cross section can be enhanced compared with the MSSM by orders of magnitude. This is a similar process to that discussed in our paper.
In Fig. 17 we show corresponding results for the diffractive contribution for = 14 TeV (left panel) and = 100 TeV (right panel) both the lower and upper limit of the 2HDM tripleHiggs coupling for GeV. In the calculation we have included the “effective” gap survival factor typical for the considered range of energies. The cross section for the exclusive diffractive process is much smaller than that for mechanism both for LHC and FCC. In addition to the result for the 2HDM set of parameters (alignment limit), we also show result with the upper limit GeV. With such a big coupling constant, the contribution with the intermediate neutral Higgs boson dominates over the contribution of boxes for . Therefore, the upper limit also effectively includes the box contributions discussed in the context of inclusive processes Krause:1997rc ; BarrientosBendezu:1999gp ; Brein:1999sy .
iii.3 A comment on possible experimental studies
So far we have calculated the cross section for the reaction. If one wishes to identify the reaction experimentally, one should measure the decay products of bosons. The branching fractions to different channels depend on the model parameters (, , etc.). For low masses of ( GeV) it is expected that the and are the dominant channels. In the case of heavy charged Higgs (with GeV) the or channels are expected to be the relevant ones.
In the first case (light ) could be measured in addition to the forward/backward protons. The emission of neutrinos leads to a strong imbalance between protonproton missing mass and . This should help to eliminate the reaction, but this requires dedicated Monte Carlo studies, including perhaps the process. The and reactions may lead to a similar final state. Although the branching fraction or is only about , it is expected to be a difficult irreducible background because of the relatively large cross section for the . In principle, the (four jets) final channel is also attractive as, in this case, one may check extra conditions GeV and GeV to exclude the contribution. The and processes may lead to similar final channels ( or ) but the corresponding cross sections are expected to be smaller (higherorder processes with loops). Mixed (leptonic quarkish) final states could also be considered.
In the second case (heavy ), in general, both the quark and jet can be measured. In contrast to the previous case we do not know about any sizeable irreducible background. But then the cross sections are rather small as discussed in the previous sections. In the case of the decay channel the actually measured final state can be rather complicated (e.g., ). Therefore, with experimentally limited geometrical acceptance it may be rather difficult to reconstruct the charged Higgs bosons.
A detailed analysis of any of the final states considered here requires separate Monte Carlo studies including experimental geometrical acceptances relevant for a given experiment. This clearly goes beyond the scope of the present paper which aims to attract attention to potentially interesting exclusive processes. The Monte Carlo studies could be done only in close collaboration with relevant experimental groups.
Iv Conclusions
In the present paper we have studied in detail the exclusive production of heavy scalar, weakly interacting, charged bosons in protonproton collisions at the LHC and FCC. In contrast to EPA our exact treatment of the fourbody reaction allows us to calculate any single particle or correlation distribution.
Results of our exact ( kinematics) calculations have been compared with those for the equivalentphoton approximation for observables accessible in EPA. Rather good agreement has been achieved in those cases. However, we wish to emphasize that some correlation observables in EPA are not realistic, or even not accessible, to mention here only correlations in azimuthal angle between the outgoing protons or the charged Higgs bosons. We have predicted an interesting minimum at which is a consequence of the field theoretical couplings involved in the considered reaction.
We have analyzed in detail the role of the Dirac and Pauli form factors. In contrast to light particle production, the Pauli form factor plays an important role especially at large , and related terms in the amplitude cannot be neglected. We see that the double spin preserving contributions are almost identical in both exact and EPA calculations (within ), but the spinflipping contributions are in our calculation somewhat smaller.
In the present paper we have studied, for the first time for the considered twophotoninduced reaction, the absorption effects due to protonproton (both initial and final state) nonperturbative interactions. Any extra interaction may, at the high energies, lead to a production of extra particles destroying exclusivity of the considered reaction. The absorptive effects lead to a reduction of the cross section. The reduction depends on kinematical variables. A good example are distributions in fourmomentum transfers squared. At small and , the absorption is weak and increases when they grow. We have also found interesting dependence of the absorption on .
The relative effect of absorption is growing with growing . A similar tendency has been predicted recently for the in the impact parameter approach Dyndal:2014yea . The impact parameter approach is, however, not useful for many observables studied here. We have predicted that the absorption effects for our twophotoninduced process become weaker at larger collision energy which is in contrast to the typical situation for diffractive exclusive processes. Our study shows that an assumption of no absorption or constant (small) absorption effects, often assumed in the literature for photonphotoninduced processes, is rather incorrect and corresponding results should be corrected.
In addition to calculating differential distributions corresponding to the mechanism we have performed first calculations of the invariant mass for the diffractive KMR mechanism. We have tried to estimate limits on the coupling constant within 2HDM based on recent analyses related to the Higgs boson discovery. The diffractive contribution, even with the overestimated coupling constant, gives a much smaller cross section than the mechanism. We have also made an estimate of the contributions related to , , and exchanges and found that their contributions are completely negligible. This shows that the inclusion of the mechanism should be sufficient, and the corresponding cross sections should be reliable.
Whether the reaction can be identified at the LHC (run 2) or FCC requires further studies including simulations of the decays. Two decay channels seem to be worth studying in the case of light : or . The first decay channel may be difficult due to a competition of the reaction which can also contribute to the channels. The combined branching fraction is about 0.11 = 0.0121 (two independent decays) which is not so small given the fact that the cross section for the production is much bigger than that for production. In the second case (four quark jets), one could measure invariant masses of all dijet systems to reduce the background. In the case of the heavy Higgs boson, the decay can be considered. In principle, both the quark and jet can be measured. In this case we do not know about any sizeable irreducible background.
The reaction considered in this paper is a prototype for any twophotoninduced process. In the future we wish to also consider the reaction where similar effects may occur. This reaction was proposed to search for the anomalous triple or quartic boson coupling. Effects beyond the Standard Model are expected at rather large invariant masses , where we have found strong absorptive corrections. This exclusive reaction is, however, more complicated due to the more complex couplings and spins involved and due to weak decays of the two bosons where strong spinspin correlation effects are expected.
Acknowledgements.
We are indebted to Jan Kalinowski for a discussion and particularly to Maria Krawczyk for help in understanding the present limitations of the 2HDM. The help of Rafał Maciuła in calculating the diffractive component is acknowledged. The work of P.L. was supported by the Polish NCN Grant No. DEC2013/08/T/ST2/00165 (ETIUDA) and by the MNiSW Grant No. IP2014 025173 “Iuventus Plus” as well as by the START fellowship from the Foundation for Polish Science. The work of A.S. was partially supported by the Polish NCN Grant No. DEC2011/01/B/ST2/04535 (OPUS) as well as by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszów.References
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