Anomalous quartic WW\gamma\gamma, ZZ\gamma\gamma, and trilinear WW\gamma couplings in two-photon processes at high luminosity at the LHC

Anomalous quartic WW, Zz, and trilinear WW couplings in two-photon processes at high luminosity at the LHC

E. Chapon CEA/IRFU/Service de physique des particules, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France    O. Kepka CEA/IRFU/Service de physique des particules, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France IPNP, Faculty of Mathematics and Physics, Charles University, Prague Center for Particle Physics, Institute of Physics, Academy of Science, Prague    C. Royon CEA/IRFU/Service de physique des particules, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France

We study the pair production via two-photon exchange at the LHC and give the sensitivities on trilinear and quartic gauge anomalous couplings between photons and bosons for an integrated luminosity of 30 and 200 fb. For simplicity and to obtain lower backgrounds, only the leptonic decays of the electroweak bosons are considered.

In the Standard Model (SM) of particle physics, the couplings of fermions and gauge bosons are constrained by the gauge symmetries of the Lagrangian. The measurement of and boson pair productions via the exchange of two photons allows to provide directly stringent tests of one of the most important and least understood mechanism in particle physics, namely the electroweak symmetry breaking stirling . The non-abelian gauge nature of the SM predicts the existence of quartic couplings between the bosons and the photons which can be probed directly at the Large Hadron Collider (LHC) at CERN. The quartic coupling is not present in the SM.

The quartic couplings test more generally new physics which couples to electroweak bosons. Exchange of heavy particles beyond the SM might manifest itself as a modification of the quartic couplings appearing in contact interactions higgsless . It is also worth noticing that in the limit of infinite Higgs masses, or in Higgs-less models higgsless , new structures not present in the tree level Lagrangian appear in the quartic coupling. For example, if the electroweak breaking mechanism does not manifest itself in the discovery of the Higgs boson at the LHC or supersymmetry, the presence of anomalous couplings might be the first evidence of new physics in the electroweak sector of the SM.

Two-photon physics is thus a significant enhancement of the LHC physics program piotr . It allows to study the Standard Model in a unique way at an hadron collider through exchange of photons. This paper focuses on two applications of the diboson production in two-photon events. First we propose a measurement of the cross section with the use of forward detectors to tag the intact protons, that leave the interaction intact at small angles. Second, we explore the sensitivities to anomalous quartic , (QGC) and triple (TGC) gauge couplings. Benefiting from the enhancement of the cross section when anomalous couplings are considered, the study of QGC sensitivities is performed for two values of integrated luminosity, namely 30 and 200 fb at the LHC at the nominal center-of-mass energy of 14 TeV. To simplify the study and reduce the amount of background, we restrict ourselves to consider only the leptonic decays of the and bosons.

The plan of this paper is as follows. The first section is dedicated to the theoretical framework of the photon induced processes. The second section describes the effective Lagrangians of the anomalous triple and quartic couplings which we are intending to study. In the third section, we discuss the implementation of the two-photon and diffractive processes inside the Forward Physics Monte Carlo (FPMC) which we used to generate all our signal and background. In section four, we describe the methods to extract the diffractive and two-photon events with forward detectors at the LHC. The possibility to observe SM -pair production via two-photon exchange is discussed in the fifth section and the section six is dedicated to the derivation of the sensitivity to or anomalous quartic couplings at the LHC. In the last section, we discuss the sensitivity to triple gauge anomalous couplings.

I Two-photon Exchange in the Standard Model

In this section, we first describe the theoretical framework of photon induced processes before focusing on the -pair production through two-photon exchange which we intend to study.

i.1 Two-photon production cross section

Figure 1: Sketch diagram showing the two-photon production of a central system. Unaltered protons leave the interaction at very small angles rad and the central system is produced alone in the central detector without any proton remnants.

Two-photon production in collision is described in the framework of the Equivalent Photon Approximation (EPA) Budnev . The almost real photons (low photon virtuality ) are emitted by the incoming protons producing an object , , through two-photon exchange , see Figure 1. The photon spectrum of virtuality and energy is proportional to the Sommerfeld fine-structure constant and reads


where is the energy of the incoming proton of mass , the photon minimum virtuality allowed by kinematics and and are functions of the electric and magnetic form factors. They read in the dipole approximation Budnev


The magnetic moment of the proton is and the fitted scale . Electromagnetic form factors are steeply falling as a function of . That is the reason why the two-photon cross section can be factorized into the sub-matrix element and two photon fluxes. To obtain the production cross section, the photon fluxes are first integrated over


up to a sufficiently large value of . The result can be written as


where the function is defined as




Note that the formula for the -integrated photon flux was quoted incorrectly several times in the literature. There is a sign error in the original paper in Ref. Budnev in the second term of in Equation 5. Moreover, in Boonekamp:2007iu there is another typesetting error leading to wrong second and last terms.

Figure 2: Relative effective luminosity in collisions at as a function of the two-photon invariant mass. The maximal virtualities of the emitted photons are set to . The dashed curve shows the photon spectrum within the ATLAS or CMS forward detector acceptance (discussed in section IV).

The contribution to the integral above is very small. The -integrated photon flux also falls rapidly as a function of the photon energy which implies that the two-photon production is dominant at small masses . Integrating the product of the photon fluxes from both protons over the photon energies while keeping the two-photon invariant mass fixed to , one obtains the two-photon effective luminosity spectrum .

The effective luminosity is shown in Figure 2 as a function of the mass in full line. The production of heavy objects is particularly interesting at the LHC where new particles could be produced in a very clean environment. The production rate of massive objects is however limited by the photon luminosity at high invariant mass. The integrated two-photon luminosity above for , and is respectively , and of the luminosity integrated over the whole mass spectrum. The luminosity spectrum was calculated using the upper virtuality bound using numerical integration. The luminosity spectrum within the proposed forward detector acceptance to detect the intact protons is also shown in the figure (it is calculated in the limit of low , thus setting ).

Using the effective relative photon luminosity , the total cross section reads


where denotes the differential cross section of the sub-process , dependent on the invariant mass of the two-photon system.

i.2 pair production via photon exchanges




Figure 3: Feynman diagrams of SM processes that contribute to the scattering amplitude in the lowest order perturbation series with a coupling . The trilinear couplings of strength are involved in diagrams a) and b) and the direct quartic coupling of strength in diagram c).

The process that we intend to study is the pair production induced by the exchange of two photons as shown in Figure 3. It is a pure QED process in which the decay products of the bosons are measured in the central detector and the scattered protons leave intact in the beam pipe at very small angles, contrary to inelastic collisions. Since there is no proton remnant the process is purely exclusive; only decay products populate the central detector, and the intact protons can be detected in dedicated detectors located along the beam line far away from the interaction point.

Considering the interactions with at least one photon, three-boson , and four-boson interactions read


where the asymmetric derivative has the form .

The production of bosons via two-photon exchange is forbidden in the lowest order perturbation theory because neither the boson nor the photon carries an electric or weak charge. On the other hand, the boson can be produced in pairs. In this case, both the triple gauge (with and channel exchange) and the quartic gauge boson interactions must be included as shown in Figure 3.

In the process, the fundamental property of divergence cancellations in the SM at high energy is directly effective. A necessary condition for the renormalizibility of the Standard Model at all orders is the so called “tree unitarity” demanding that the unitarity is only minimally (logarithmically) violated in any fixed order of the perturbation series TreelevUnit1 ; TreelevUnit2 . For the binary process of pair production in particular, the tree level unitarity implies that the scattering amplitude should be a constant or vanish in the high energy limit. In the SM, this condition is indeed satisfied due to the cancellation between -, -channel and direct quartic diagrams.

The cross section is constant in the high energy limit. The leading order differential formula for the process is a function of the Mandelstam variables and the mass of the vector boson electroweakCorrections


where is the velocity of the bosons. For the total cross section is .

Measuring the scattering process at the LHC is therefore interesting not only because we can use the hadron-hadron machine as the photon-photon collider with a clean collision environment without beam remnants, but also because it provides a very clear test of the Standard Model consistency in a rather textbook process.

The cross section of the process which proceeds through two-photon exchange is effectively calculated as a convolution (7) of the two-photon luminosity and the total cross section (10). The total two-photon cross section is 95.6 fb.

Since the virtuality of the photon is very close to zero, the electromagnetic coupling appearing in the interaction Lagrangians in Equations (8) and (9) is evaluated at the scale ; the electromagnetic fine-structure constant therefore takes the value . Note that the above mentioned total cross section is different from the usually presented value of 108 fb (see Pierzchala:2008xc for example) by about 10%. This is due to the fact that the authors considered the fixed value of the electromagnetic coupling of 1/129 at the scale of the mass. In fact, the photon virtuality should be taken as the scale and not the mass of the . In the Landau gauge, the invariant charge is driven by the self-energy insertion into the photon propagator only (and not by the vertex correction) misha . In the propagator we have to take the photon virtuality as the scale, which is very small. The total two-photon cross section is therefore . This value has to be corrected for the survival probability factor 0.9.

Ii and photon quartic and trilinear anomalous couplings

The two-photon production of dibosons is very suitable to test the electroweak theory because it allows to probe trilinear and quartic boson couplings. The test is based on deriving the sensitivities with a counting experiment to parameters (coupling strengths) of new auxiliary interaction Lagrangians added to the SM, to simulate low energetic effects of some Beyond Standard Model (BSM) theories whose typical scales (e.g the typical new particle masses) are beyond the reach of the LHC energies. In this section, we give the theoretical implementation of quartic and trilinear anomalous couplings between the or boson and the photon in the FPMC generator.

ii.1 Effective quartic anomalous Lagrangian

ii.1.1 Construction of new quartic anomalous operators

The boson self-interaction in the SM is completely derived from the underlying local symmetry. New vector boson fields are added to the Lagrangian to guarantee the invariance under this symmetry and their self-interactions emerge from the vector boson kinetic terms.

The vector boson masses are, however, more deeply linked with the Higgs field and the vacuum symmetries. The symmetry O(4) of the Higgs potential is in fact larger than the required . It is known that the symmetry O(4) is locally isomorphic to . When the symmetry is spontaneously broken and one particular vacuum is chosen, the vacuum symmetry is reduced. The vacuum is invariant under only. The weak isospin generators corresponding to the broken symmetry constitute a triplet with respect to the vacuum symmetry sub-group. Very interestingly, this vacuum symmetry controls the value of the parameter


and is usually called the custodial symmetry. The SM value of the parameter is and it was very well confirmed experimentally (taking , , and as in Amsler:2008zzb , we obtain so it is known with a precision better than 1%). In models with higher Higgs multiplets, can significantly differ from 1. We will assume that this symmetry holds also in more general theories which we are about to parameterize and construct new effective Lagrangian terms in such a way to obey the deeper symmetry which is tightly linked with the precisely measured value of the parameter.

The boson self-interactions in the SM (including their kinetic terms) can be conveniently represented by where the vector


is a triplet of the custodial symmetry. The field tensor for bosons appearing in the product is .

In the following, the parameterization of the quartic couplings based on Belanger:1992qh is adopted. We concentrate on the lowest order dimension operators which have the correct Lorentz invariant structure and obey the custodial symmetry in order to fulfill the stringent experimental bound on the parameter. Also, the gauge symmetry for those operators which involve photons, is required.

There are only two four-dimension operators:


They are parameterized by the corresponding couplings and . Using the explicit form of the triplet we see that these Lagrangians do not involve photons. Clearly, it is not possible to construct any operator of dimension 5 since an even number of Lorentz indices is needed to contract the field indices. Thus the lowest order interaction Lagrangians which involve two photons are dim-6 operators. There are two of them:


parameterized with new coupling constants , , and the fine-structure constant . The new scale is introduced so that the Lagrangian density has the correct dimension four and is interpreted as the typical mass scale of new physics. Expanding the above formula using the definition of the triplet and expressing the product


we arrive at the following expression for the effective quartic Lagrangian


In the above formula, we allowed the and parts of the Lagrangian to have specific couplings, i.e. , ) and similarly , ). From the structure of in which the indices of photons and are decoupled, we see that this Lagrangian can be interpreted as the exchange of a neutral scalar particle whose propagator does not have any Lorentz index. A such Lagrangian density conserves , , and parities separately and hence represents the most natural extension of the SM.

The current best experimental 95% CL limits on the above anomalous parameters come from the OPAL Collaboration where the quartic couplings were measured in , (for anomalous couplings), and (for couplings) at center-of-mass energies up to 209 GeV. The corresponding confidence level limits on the anomalous coupling parameters were found LEPlimitsQGC


On the other hand, there has not been any direct constraint on the anomalous quartic couplings reported from the Tevatron so far.

Figure 4: Enhancement of the and cross section at with quartic-boson anomalous couplings , , and , from the SM values 95.6 fb and 0, respectively. The survival probability factor is not included.
Figure 5: Missing mass distribution showing the effect of the form factor (19) on the cross section. The signal due to the anomalous coupling appears for masses . Both leptons are in the detector acceptance and above .

ii.1.2 Coupling form factors

Figure 6: The unitarity condition (22) for quartic anomalous couplings and as a function of two-photon invariant mass. The unitarity is violated above the horizontal line at 1. The form of the form factor (24) is used for the two bottom curves.

The and two-photon cross sections rise quickly at high energies when any of the anomalous parameters are non-zero, as illustrated in Figure 4. As it was already mentioned, the tree-level unitarity uniquely restricts the coupling to the SM values at asymptotically high energies. This implies that any deviation of the anomalous parameters , , , from the SM zero value will eventually violate unitarity. Therefore, the cross section rise have to be regulated by a form factor which vanishes in the high energy limit to construct a realistic physical model of the BSM theory. At LEP where the center-of-mass energy was rather low, the wrong high-energy behavior did not violate unitarity; however, it must be reconsidered at the LHC. We therefore modify the couplings as introduced in (17) by form factors that have the desired behavior, i.e. they modify the coupling at small energies only slightly but suppress it when the center-of-mass energy increases. The form of the form factor that we consider


The exact form of the form factor is not imposed but rather only conventional and the same holds for the value of the exponent . corresponds to the scale where new physics should appear and where the new type of production would regularize the divergent high energy behavior of the Lagrangians (17).

The unitarity of the scattering -matrix imposes a condition on the partial waves amplitudes defined as


where are the Legendre polynomials depending on the polar angle in the center-of-mass. The unitarity condition of the scattering amplitude in the process reads


where is the velocity of a boson in the center-of-mass frame and the indices denote the polarization states.

For the anomalous interaction (17), the most restrictive bounds come from the partial wave, which can be easily understood since s with longitudinal polarizations without any spin flip are dominantly produced in this case. For , the unitarity bounds read Eboli:2000ad


where or and for .

The unitarity violation in process was investigated in the Ref. Pierzchala:2008xc . For relevant values of which are to be probed at the LHC using forward detectors, it was found that the unitarity is violated around for the form factor exponent . We therefore adopt this type of form factor for the following study, i.e. the form factor


is introduced for all quartic couplings . The unitarity condition (22) for couplings and is illustrated in Figure 6. First we see that couplings without the form factors violate unitarity already at TeV energies. On the other hand, employing the form factors as described above justifies the non-violation of the unitarity of events inside the AFP acceptance () if the resulting limits on neutral couplings are of the order of . For the charged couplings the unitarity condition is less strict due to in Equations (22) and (23).

ii.2 Anomalous triple gauge couplings

In this section, we discuss the implementation of the triple gauge couplings (TGC). The TGC have already been quite well constrained at LEP. The effective Lagrangian involving trilinear boson couplings with a photon will be introduced and used to study the sensitivities to the coupling parameters in two-photon events. Note that the lowest dimensional triple gauge boson operator is of dimension six, the effect of this coupling in two-photon events will be the subject of a further study. First, the effective Lagrangians describing the triple gauge couplings are introduced before evaluating the anomalous cross section.

ii.2.1 Effective triple gauge boson operators

The most general form of an effective Lagrangian involving two charged vector bosons and one neutral vector boson has only seven terms which have the correct Lorentz structure (see Hagiwara:1986vm ; Kepka:2008yx for details). This is because only seven out of the nine helicity states of the pair production can be reached with the spin-1 vector boson exchange. The other two states have both spins pointing in the same direction with an overall spin 2.

Further more, only three out of the seven operators preserve the and discrete symmetries separately. We restrict ourselves to study this subset of operators. They are the following


where the tensor is , is the trilinear coupling in the SM model whose strength is fixed by the charge of the , and and are the anomalous parameters, and their values are 1 and 0 in the SM, respectively. They can be related to the magnetic and electric moments of the by


where describes the deviation of the parameter from the SM value. (it is straightforward to verify that (25) gives the SM trilinear Lagrangian (8) for and . Our convention differs from the one in Hagiwara:1986vm by a factor of -1).

The current best 95% CL limits on anomalous couplings come from the combined fits of all LEP experiments LEPlimits .


The CDF collaboration presented the most stringent constraints on coupling measured at hadron colliders TEVlimits


analyzing the events in parton-parton interactions. Even though the LEP results are more precise than the results from the hadron collider, there is always a mixture of and exchanges present in the process from which the couplings are extracted. The two-photon production at the LHC has the advantage that pure couplings are tested and no SM exchange is present.

ii.2.2 Anomalous cross section

The effect of the two anomalous couplings is different. The total cross section is much more sensitive to the anomalous coupling . As shown in Figure 7, the SM cross section is a global minimum with respect to the parameter. For the minimum also exists but for large negative values which have already been excluded by experiments. The last term proportional to in (25) does not have a dimensionless coupling. With simple dimensional consideration we see that the scattering amplitude which has to be dimensionless will have the form and will therefore be quickly rising as a function of the two-photon mass . This is seen in Figure 8 where the cross section is shown as a function of the momentum fraction loss of the proton. enhances the overall normalization of the distribution (left) whereas gives rise to the tail (right) as anticipated.

Figure 7: Enhancement of the total cross section with the triple-boson anomalous couplings , . The rise of the cross section due to is well pronounced whereas the dependence on is modest (the tail for large negative where cross section increases is not shown).
Figure 8: dependence of the two-photon cross section for different values of (left) and (right) (SM values are 0). For , the cross section is enhanced at high which is at the edge of the forward detector acceptance (). On the contrary, varying in the interesting range changes mainly the normalization and not the shape of the distribution.

ii.3 Coupling form factors

The rise of the cross section for anomalous TGC at high energy leads again to the violation of unitarity. The enhancement of the cross section has to be again regulated by appropriate from factors. We apply the same form factors as already mentioned for the quartic couplings (24).

Iii The Forward Physics Monte Carlo

In this section, we briefly describe the Forward Physics Monte Carlo (FPMC) generator fpmc used extensively in this paper to produce all signal and background events. FPMC aims to accommodate all relevant models for forward physics which could be studied at the LHC and contains in particular the two-photon and double pomeron exchange processes which are relevant for this study since we focus on events in which both protons are detected. The generation of the forward processes is embedded inside HERWIG herwig . The advantage of the program is that all the processes with leading protons can be studied in the same framework, using the same hadronization model. It is dedicated to generate the following exchanges:

  • two-photon exchange

  • single diffraction

  • double pomeron exchange

  • central exclusive production

In FPMC, the diffractive and exclusive processes are implemented by modifying the HERWIG routine for the process. In case of the two-photon events, as we mentioned in Section I, the Weizsäcker-Williams (WWA) formula describing the photon emission off point-like electrons is substituted by the Budnev flux Budnev which describes properly the coupling of the photon to the proton, taking into account the proton electromagnetic structure.

The effective Lagrangians parametrizing new interactions of electroweak bosons mentioned explicitly in Equations 17 and 25 are functions of six anomalous parameters: , for the triple gauge couplings and for the quartic ones. The corresponding matrix elements squared were obtained with the CompHEP program comphep whose output was interfaced with FPMC.

The single diffractive and double pomeron exchange events are produced in FPMC using the diffractive parton densities measured at HERA herapdf . The outcome of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-Parisi dglap fits to the proton diffractive structure functions are the values of the pomeron and reggeon trajectories , governing the corresponding flux energy and dependences, and the pomeron parton distribution functions.

In addition, due to the factorization breaking between LHC and HERA, an additional survival probability survival is introduced and it is assumed to be 0.03 for DPE and 0.9 for photon exchanges in the following. Technically, in FPMC, for processes in which the partonic structure of the pomeron is probed, the existing HERWIG matrix elements of non-diffractive production are used to calculate the production cross sections. The list of particles is corrected at the end of each event to change the type of particles from the initial state electrons to hadrons and from the exchanged photons to pomerons/reggeons, or gluons, depending on the process.

The output of the FPMC generator was interfaced with the fast simulation of the ATLAS detector in the standalone ATLFast++ package for ROOT atlfast . The fast simulation of ATLAS is performed for all signal and background processes.

Iv Selection of diffractive and photon exchange events at high luminosity at the LHC

In this section, we detail briefly the methods used to select diffractive and two-photon exchange events at the LHC in the ATLAS detector. The same study could be made using the CMS detector which would lead to similar results. At high instantaneous luminosity at the LHC, it is not possible to use the so-called standard rapidity gap method since up to 30 interactions — one hard interaction and many minimum bias events — occur in the same bunch crossing. The exclusive production overlaps with soft interactions which fill the gap devoid of any energy and the gap selection does not work any longer.

At high luminosity, the only method to select the diffractive and photon exchange events is to detect the intact protons in the final state. We thus assume the existence of forward proton detectors in the ATLAS (or CMS) detectors. A project called AFP (ATLAS Forward Physics) is under evaluation in the ATLAS collaboration and corresponds to the installation of forward detectors at 220 and 420 m allowing to detect intact protons in the final state afp . The acceptance of such detectors is about 0.0015 0.15 where is the proton momentum fraction carried by the pomeron or the photon.

V Measuring the process in the Standard Model

Before discussing the possibility of observing anomalous couplings, we will mention how to discover the SM process at the LHC.

v.1 The signal

Figure 9: Diboson production through the two-photon exchange. Intact protons leave the interaction scattered at small angles .

The total cross section of the exclusive process where the interaction proceeds through the exchange of two quasi-real photons shown in Figure 9 is 95.6 fb and this value has to be corrected for the survival probability factor 0.9.

The cross section is rather modest in comparison to the inelastic production which is about three orders of magnitude higher (at , the NLO cross section is 111.6 pb, produced via quark-anti-quark annihilation () and also via gluon-gluon fusion ()). A substantial amount of luminosity has therefore to be collected to have a significant sample. It can only be accumulated when running at high LHC instantaneous luminosities . Under such running conditions, the two-photon events must be selected with the forward proton tagging detectors.

The boson decays hadronically () or leptonically (). The hadronic or semi-leptonic decays in which at least one jet is present could be mimicked by the QCD dijets or non-diffractive production, overlaid with other minimum bias interactions leading to a proton hit in the forward detectors. For simplicity, we focus on the decays only into electrons or muons in the final state. This in turn means that also only the leptonic decays of the lepton () are considered. Semi-leptonic decays of the s will be considered in a further study. About of the total cross section is retained for the analysis. About 1800 events are produced with two leptons in the final states for 30, an integrated luminosity which corresponds approximately to the 3 first years of running. We will see further that taking into account the forward detector acceptance, and the electron/muon reconstruction efficiencies, the expected number of events drops down to 50 events.

v.2 Diffractive and dilepton background

Figure 10: Transverse momentum of the leading or (left) and the momentum fraction loss (right) distributions for processes which have two leptons as well as two forward intact protons in the final state. The signal is outraged by the two-photon and DPE production.

The clean two-leptonic signature of the two boson signal process can be mimicked by several background processes which all have two intact protons in the final state. They are the following:

  1. - two-photon dilepton production

  2. DPE - dilepton production through double pomeron exchange

  3. DPE - diboson production through double pomeron exchange

The Double Pomeron Exchange (DPE) production of dileptons and dibosons is described within the factorized Ingelman-Schlein model where the hard diffractive scattering is interpreted in terms of the colorless pomeron with a partonic structure. Cross sections are obtained as a convolution of the hard matrix elements with the diffractive parton density functions measured at HERA herapdf . Dileptons in DPE are produced as Drell-Yan pairs, probing the quark structure of the pomerons. The exchange is carried out through or . Contrary to the two-photon exclusive case where only scattered protons and leptons in the central detector are present, in DPE events, pomeron remnants accompany the interacting partons. They give a significant boost to the lepton pair in the transverse plane resulting in a non-negligible azimuthal decorrelation between the leptons. Finally, the diboson production in DPE is very similar to the actual signal except that the mass distribution of the system is not as strongly peaked towards small values. The DPE dilepton and diboson total production cross sections at generator level are respectively 743 pb (all lepton families) and 211 fb (all decay modes).

As we already mentioned, the experimental signature of the two-photon or DPE interaction in which two scattered protons go intact in the beam pipe and can be tracked in forward detectors can be lost by additional soft interactions between the outgoing protons. The survival probabilities for the QED two-photon processes and QCD diffractive and central exclusive processes are respectively taken to be 0.9 and 0.03 survival . The mentioned cross sections have to be therefore multiplied by these survival probability factors yielding cross sections of the signal and background shown in Table 1. The dilepton production is the largest background, three orders of magnitude higher than the desired signal.

process total cross section
96.5 fb
39.4 pb
DPE 7.4 pb
DPE 8.1 fb
Table 1: Total cross sections for SM signal and background processes at 14 TeV including the gap survival probability factor (0.9 for QED and 0.03 for DPE processes).

The characteristic properties of the two-photon and DPE productions are visible in Figure 10. The leptons () are required to be within the generic central detector acceptance , . The distributions (left) are peaked towards 0. Since the leptons are predominantly produced at central pseudo-rapidity this reflects the steepness of the two-photon luminosity dependence as a function of . In the DPE dilepton spectrum one can identify the resonance around . The diboson spectrum on the other hand slowly increases until the channel is totally kinematically opened and then decreases due to the drop of the effective photon-photon or pomeron-pomeron luminosity. On the right side of Figure 10, the momentum fraction loss distribution shows again that the two-photon production is dominant at low mass. The momentum fraction tail of the DPE is truncated at which is about the limit of the validity of the factorized pomeron model. The acceptance of the AFP detectors is shown as well. It provides us an access of two-photon masses up to .

The most natural distinction of the diboson signal is the missing transverse energy () in the event due to the undetected two neutrinos, see Figure 11 (left). It provides a very effective suppression not only of the two-photon dileptons where leptons are produced back-to-back in the central detector with no intrinsic , but suppresses also the DPE dilepton background, even though some of the energy is lost due to the pomeron remnants is not seen in the calorimeter. It can be due to either a limited coverage of the calorimeter or due to a minimum energy readout threshold in the system which the pomeron remnants do not pass. Both cases mimic .

Another way to distinguish the diboson signal is to use the missing mass reconstructed in forward detectors which is shown in Figure 11 (right). The dilepton production is dominant at low mass in both two-photon and DPE exchanges, but has also a non-negligible contribution at high mass. The azimuthal angle between the two leading leptons is depicted in Figure 12. Dilepton events are more back-to-back than the diboson ones.

As mentioned before, all signal and background processes are generated using FPMC, interfaced with the fast simulation of the ATLAS detector in the standalone ATLFast++ package. The aim was to examine the general properties of all backgrounds in a fast way to define the strategies for early data measurements with the emphasis on the two-photon dilepton and anomalous coupling studies. Effects of the charge or jet mis-identifications cannot be considered in this study using a fast simulation of the ATLAS detector but will be evaluated with real data.

We will now discuss how to select the signal events from the mentioned background.

Figure 11: Missing transverse energy (left) and reconstructed missing mass in the forward detectors (right) for the two-photon signal and background processes. The signal has a production threshold at and has a large due to the undetected neutrinos.
Figure 12: between two leading leptons. Dilepton events are more back-to-back than diboson events. DPE dileptons is less peaked because of the presence of the pomeron remnants which gives a transverse boost to the Drell-Yan system.

v.3 Strategy to measure the process

It is necessary to use forward detectors to search for production at high luminosity. After tagging the protons with a momentum fraction , the signal is selected with measured in the central detector and a missing mass measured in forward proton detectors (computed as where and are the proton momentum fraction loss and the center-of-mass energy, respectively). Both cuts are natural for diboson production. The production where leptons are produced back-to-back is completely removed requesting the azimuthal angle between the two observed leptons .

Let us note in addition that triggering on those events is quite easy since we have two s in the central ATLAS detectors decaying into leptons. The trigger menus of ATLAS are designed in a way to have the least possible prescales on leptons produced in electroweak bosons decays. The L1 and High Level Triggers (HLT) can be operated without prescales up to luminosities with thresholds of 20 GeV for single muons, and 18 GeV at L1 and 22 GeV at the HLT for single electrons Aad:2009wy . For higher luminosities, the trigger menus will have to be studied and tuned. In addition, most of the protons will be detected in the forward proton detectors located at 220 m which can give an additional L1 trigger.

The remaining background is composed of the DPE () and DPE (20%). We handle it by requesting the transverse momentum of the leading lepton and the missing mass smaller than , see Figure 13. This leaves us with the cross section for the total background (the shown uncertainty reflects the statistical uncertainty of the calculation). In summary, the following requirements are used:

Figure 13: Signal and background before the cut on the leading lepton transverse momentum 25 GeV (left) and before the cut on the missing mass (right). Both constraints are aimed to suppress the DPE production which is the most important background for the measurement.
cut / process DPE DPE
gen. 364500 364500 337500 295200 530 1198
24896 25547 177 17931 8.8 95
10398 10535 126 11487 5.9 89
0.86 14 33 4.7 78
0 0.86 8.3 33 4.7 78
0 0 0 14 3.8 61
0 0 0 7.5 3.5 58
0 0 0 1.0 0.67 51
0 0 0 0.85 0.54 47
0 0 0 0.40 0.25 32
Table 2: Background rejection to select events for =30. The overall final signal is 51, 47, 32 signal events for the upper limit of the forward detector acceptance , 0.1, and 0.05, respectively, whereas the background is as low as 1.7, 1.4, 0.65 events. The statistical uncertainty on the expected number of events is at most 15% and is the largest for DPE.

The successive effects of all mentioned constraints are given in Table 2 where the number of events is shown for 30. In three years, one expects about signal events and background events. It is interesting to notice that this measurement can be successfully carried out even if the AFP acceptance does not reach its design maximum acceptance range . The number of expected events for , and are , for 30. The corresponding total backgrounds are and , respectively.

v.4 Results

The discovery of the process could be achieved with about 5 of data in the leptonic mode only. The signal significance is calculated as the -value , i.e. as the probability to find the number of observed events or more from the background alone. For 5, the confidence expressed in the number of standard deviations for the Gaussian distribution reads 5.3, 5.8, 6.2 for , respectively. The number of signal and background events for 5 and 10 together with the value of the confidence level, is given in Table 3.

It should be noted that the process can be discovered even with lower luminosity if one takes the full-leptonic and semi-leptonic decays of the two final states into account. In Kepka:2008yx we considered a simplified analysis studying the two-photon production and the DPE background only assuming that the overlaid background due to multiple interactions is removed with timing detectors. Events with at least one lepton above in addition to both proton tags in forward detectors were selected. The full-hadronic decays were rejected in order to remove the high QCD dijet background. It turned out that the process can be discovered already with of integrated luminosity by observing 11 signal events and 0.9 background yielding a confidence 5.8. The higher sensitivity to the two-photon production is of course due to the higher cross section when one takes into account the semi-leptonic decays. In this case, however, a new background arises from the central exclusive production of two quarks which was not studied. If one of the quarks radiates a boson, the +jet+jet final state mimics the semi-leptonic decays in two-photon production. This background process is planned to be included in future releases of FPMC to allow a complete study of the two-photon production even in the semi-leptonic decay mode khozeJames .

signal [fb] background [fb] =5 =10
0.05 1.69 0.06 7.5 14
0.1 1.57 0.05 7.1 13
0.15 1.07 0.02 5.1 9.1
Table 3: Signal and total background cross sections for , and the ratio for luminosities 5 and 10 as a function of the forward detector acceptance 0.0015 after all cuts mentioned in the text.

Vi Sensitivity to quartic anomalous coupling of and to photon

vi.1 Signal cross section for quartic couplings

In this section, we study the phenomenological consequences of the new anomalous terms in the Lagrangian. The implementation in the FPMC generator allowed us to compare the studied signal due to anomalous couplings directly with all backgrounds that leave the proton intact and create two leptons, electrons or muons, in the central detector.

As shown in Figure 4, we recall that the anomalous couplings in and processes augment the cross section from their SM values 95.6 fb and 0. The suppression of the cross section due to the form factors is shown in Figure 5. It is important to stress that this effect is large and it has to be taken into account when deriving the sensitivities to the anomalous couplings.

vi.2 Background rejection at high luminosity for signal

In Figure 14, the distributions of the signal due to quartic couplings and the background are superimposed. As expected, the signal due to anomalous coupling appears at high transverse momentum, or at high masses. The first cut used in the analysis is therefore to select high leptons together with intact protons in the final state detected in the forward detectors to identify the exclusive two-photon events. At high luminosity, the forward detector acceptance (high cut on ) removes the highest mass events and part of the signal due to anomalous coupling which appears at high masses is not observed.

Figure 14: Contributions of various background processes to the signal with anomalous coupling with the coupling form factors taken into account at generator level. The signal due to the anomalous coupling manifest itself at high transverse lepton momenta.
Figure 15: Missing transverse energy distribution in the AFP detector acceptance cut (left) and proton missing mass (right) in the AFP acceptance and after the cut on cut for signal and all backgrounds with =30.
Figure 16: Angle between detected leptons (left) and distribution of the leading lepton (right) after all cuts as mentioned in the text for signal and background. The events are normalized for =30.
events for 30
cut / process DPE DPE
gen. 364500 364500 337500 1198 295200 530
24895 25547 177 99 18464 8.8
10398 10534 126 89 11712 6.0
0 0.86 14 77 36 4.7
0 0.27 0.15 3.2 16 2.5
0 0.27 0.15 3.2 13 2.5
0 0 0.10 3.2 12 2.5
0 0 0 0.69 0.20 0.024
Table 4: Rejection of the background by the successive application of the selection cuts. The number of events is normalized to of integrated luminosity. The lepton index corresponds to electrons or muons. The DPE was generated with a minimum Drell-Yan mass 10 GeV. The largest statistical uncertainty is 7% for DPE after all cuts.
events for 30
cut / couplings (with f.f.)
202 200
116 119
104 107
24 23
24 23
24 22
17 16
Table 5: Selection of the signal by the successive application of the cuts. The number of events is given for integrated luminosity of . The lepton index corresponds to electrons or muons.

The events which give a hit in both forward detectors are first selected with . The dependence is depicted in Figure 15 (left) for the signal and the background. Note that the signal is barely distinguishable from the SM process. On the other hand, processes in which lepton pairs are created directly through or DPE exchange are greatly suppressed. The next cut focuses on the high diphoton mass where the signal is preferably enhanced. In Figure 15 (right) we see that the signal due to anomalous coupling is well selected if the reconstructed missing mass in the forward detectors is . It was verified that such selection applies for all anomalous parameters in question in a very similar way, i.e. that the retains the interesting signal for a wide range of anomalous parameters.

The most dominant background which remains is the DPE production. A large part of this background is removed by requesting the angle between reconstructed leptons as illustrated in Figure 16 (left). This removes also the potential two-photon dileptons. However, the cut cannot be arbitrarily relaxed because we would remove part of the signal also. We also require the dilepton mass to be far from the </