Photon collider search strategy for sleptons and dark matter at the LHC

We propose a search strategy using the LHC as a photon collider to open sensitivity to scalar lepton (slepton ̃̀) production with masses around 15 to 60 GeV above that of neutralino dark matter χ̃1. This region is favored by relic abundance and muon (g− 2)μ arguments. However, conventional searches are hindered by the irreducible diboson background. We overcome this obstruction by measuring initial state kinematics and the missing momentum four-vector in proton-tagged ultraperipheral collisions using forward detectors. We demonstrate sensitivity beyond LEP for slepton masses of up to 220 GeV for 15 . ∆m( ̃̀, χ̃1) . 60 GeV with 100 fb −1 of 13 TeV proton collisions. We encourage the LHC collaborations to open this forward frontier for discovering new physics.


I. INTRODUCTION
Elucidating the elementary properties of dark matter (DM) is among the most urgent problems in fundamental physics. The lightest neutralinoχ 0 1 in supersymmetric (SUSY) extensions of the Standard Model (SM) is one of the most motivated DM candidates [1][2][3]. A favored scenario involves scalar partners of the charged leptons (sleptons˜ ) being one to tens of GeV above theχ 0 1 mass. This enables interactions that reduce theχ 0 1 cosmological relic abundance to match the observed value [4] via a mechanism called slepton coannihilation [5,6]. Furthermore, partners of the muon (smuonμ) and neutralinos with masses near the weak scale are a leading explanation for 3 − 4σ deviations between measurements of the muon magnetic moment and SM prediction [7][8][9][10].
This Letter proposes a search strategy to resolve these longstanding problems by using the LHC as a photon collider [30]. In a beam crossing, protons can undergo an ultraperipheral collision (UPC), where photons from the electromagnetic fields interact to produce sleptons exclusively pp → p(γγ →˜ ˜ )p. The sleptons decay as˜ → χ 0 1 , resulting in the very clean final state p(2 + p miss )p of our search: two intact protons, two leptons , and missing momentum (Fig. 1). As the beam energy is known, measuring the outgoing proton kinematics determines the colliding photon momenta and thus p miss . This experimental possibility is opened by the ATLAS Forward Proton (AFP) [31] and CMS-TOTEM Precision Proton Spectrometer (CT-PPS) [32,33] forward detectors, which FIG. 1. Exclusive pair production of (left) scalar leptons 'sleptons'˜ decaying to dark matterχ 0 1 and (right) SM diboson W W background using the LHC as a photon collider.
recorded first data in 2017 and 2016 respectively. CMS-TOTEM moreover observed double lepton production in high-luminosity proton-tagged events [34], demonstrating initial state reconstruction is feasible.
Photon collisions at the LHC reach sufficient rates to probe rare processes such as SM light-by-light scattering [35,36], anomalous gauge couplings [37,38], and axion-like particles [39,40]. Nonetheless, it is widely considered that photon fusion production of sleptons is not competitive as a discovery window compared to electroweak production [11][12][13][14]; existing photon collider studies therefore focus on slepton mass measurement for specific benchmark points [41][42][43][44][45]. Our proposal argues the contrary that photon collisions play an essential role in SUSY and DM searches. We emulate AFP/CT-PPS proton tagging, which enables powerful background suppression. We demonstrate a strategy that surpasses LEP sensitivity in the favored 15 ∆m(˜ ,χ 0 1 ) 60 GeV corridor, underscoring the importance of initial state kinematics and p miss for the LHC discovery program.

II. PHOTON COLLIDER SIMULATION
Electromagnetic fields surrounding ultrarelativistic protons can be modeled as a beam of nearly on-shell photons, which is known as the equivalent photon approximation [46]. We consider pair production of electrically charged particles X via photon fusion γγ → XX. Analytic expressions of their QED cross-sections σ γγ→XX arXiv:1811.06465v1 [hep-ph] 15 Nov 2018 may be found in Refs. [41,45,47,48]. The LHC crosssection is then the convolution of σ γγ→XX with the effective photon luminosity L (pp) γγ from the protons where m γγ is the invariant mass of the two-photon system. We use MadGraph v2.6.1 [49,50] to numerically evaluate Eq. (1) and perform Monte Carlo simulation for signal and background processes. We study the resulting events using the pylhe package [51], and parameterize detector effects as follows.
The forward detectors identify both the intact outgoing protons at z ±220 m downstream from the collision point and measure their energies E forward . Protons are steered outside the beam profile by the LHC dipole magnets due to the fractional energy loss ξ = 1 − E forward /E beam relative to the beam energy E beam . The AFP/CT-PPS proton acceptance is close to 100% for 0.015 < ξ < 0.15 [31][32][33]. This translates to emitted photon energies of 100 E γ 1000 GeV for √ s = 13 TeV pp collisions. The survival probability of a proton remaining intact following photon emission is reported to be around 90% in phenomenology studies [52], which we treat as an efficiency. We parameterize the proton acceptance as {0, 0.5, 0.7, 0.9} for E γ ∈ {[0, 100], [100, 120], [120, 150], [150, 400]} GeV respectively, and 0.8 otherwise. We conservatively smear the photon four-vector p smeared γ = p generated γ G γ (1, σ γ ) using a Gaussian G γ with width σ γ = 5%, based on the AFP resolution of 5 GeV at ξ 0.015 [31].
The central detectors reconstruct isolated leptons (electrons e and muons µ throughout). To emulate detector resolution, we smear the lepton momenta p using a Gaussian G with width σ = 5%. We parameterize p Tdependent reconstruction efficiencies in accord with AT-LAS [14], which account for all lepton quality conditions. This requires that leptons satisfy transverse momentum p e(µ) T > 4.5(4) GeV and pseudorapidity |η | < 2.5.
To simulate the simplified model signal γγ →˜ ˜ , we employ the model specified by the SLHA parameter file from the auxiliary material of Ref. [14]. This allows comparisons with existing LHC constraints. Only sleptons˜ and the stable neutralinoχ 0 1 are kinematically accessible, whose masses are free parameters. A fourfold mass degeneracy is assumed such that scalar partners of the left-handed and right-handed electrons and muons (selectronsẽ and smuonsμ) satisfy with 100% branching ratio and are handled by Mad-Graph. All other SUSY states are kinematically inaccessible with masses well above 10 TeV. We sample m(˜ ) in 25 GeV steps, and ∆m(˜ ,χ 0 1 ) in steps of no more than 20 GeV. We simulate 50k events per mass point and normalize to cross-sections calculated in MadGraph, which are consistent with those obtained in Refs. [44,45]. For m(˜ ) = 100 GeV, the cross-section is 2.5 fb and falls to 0.25 fb for m(˜ ) = 200 GeV. Only the first two genera-tions˜ ∈ [ẽ,μ] are considered; study of scalar partners of tau leptons (stausτ ) are deferred to future work.

III. SEARCH STRATEGY
Our search strategy focuses on extracting the signal from the dominant irreducible γγ → W W → ν ν background. The W W cross-section times dileptonic branching fraction B is σ γγ→W W ×B 5 fb, which is comparable in size to the slepton signals. We generate 50k events of this process using MadGraph, which also handles the decays to preserve spin correlations of the leptons. We use dilepton triggers for event selection, which we emulate using a p T > 15 GeV condition. Requiring same flavour leptons (ee or µµ) halves the W W background while preserving signal. We then reconstruct three defining features that characterize the signals and background to optimize search sensitivity: mediator mass (W or˜ ), invisible mass (ν orχ 0 1 ), and mediator spin. At the LHC, proton-tagging enables unambiguous bounds on both the parent mediator and DM masses. The mass of the˜ mediators is bound by the invariant mass of the initial state two-photon system m 2 Here, p miss = i p i − f p f is the vectorial sum of the momenta of the visible final states p f subtracted from the initial states p i . In this search, we have i p i = p γ1 + p γ2 and f p f = p 1 + p 2 . We find the ratio m γγ /W miss to be useful for ∆m(˜ ,χ 0 1 ) 30 GeV signals.
To improve mass reconstruction of the parent mediator and DM states, one can impose hypotheses about the decay topology. Assuming the symmetric pair of semiinvisible decays˜ ˜ → χ 0 1 χ 0 1 , with photon and lepton momenta measured, results in the HKSS variables [45]. These also provide mass bounds on the parent mediator and invisible system (see Ref. [45] for definition) Importantly, these variables have more steeply falling tails than m γγ and W miss respectively, and therefore provide better signal separation from the W W background.
To exploit the mediator spin for sensitivity, we use the Barr-Melia variable [53,54], defined by where the pseudorapiditiesη are evaluated in the dilepton centre-of-mass frame (denoted by overlines). Leptons from spin 0˜ mediators decay more centrally than those from spin 1 W bosons, offering discrimination power. Figure 2 displays distributions of benchmark signals and the W W background for these mass and spin sensitive variables, normalized to 100 fb −1 . From this, we Kinematic distributions of search discriminants reconstructing the mass and spin of benchmark slepton signals (lines) and W W background (filled), normalized to 100 fb −1 . Double proton tag, lepton efficiencies and detector smearing are applied, but no lepton trigger emulation is imposed. The event selection applied, denoted SR-common, requires m max DM > 0 GeV, |η | < 2.5, same flavour leptons, and mT2 > 2 GeV. Masses of the signals are displayed in the legend. The lower panel estimates the statistical significance after integrating the signal S and background B counts with the indicated bound on the variable.
impose | cosθ | < 0.65 and construct three signal region (SR) categories targeting small 'compressed', medium 'corridor', and large mass differences ∆m(˜ ,χ 0 1 ): • SR-compressed: m max parent > 80 GeV, m max DM > 0 GeV, m γγ /W miss < 1.4; • SR-corridor: m max parent > 120 GeV, m max DM > 80 GeV; • SR-large: m max parent > 130 GeV, m max DM > 20 GeV. An improved search strategy would involve a shape analysis across m max parent vs m max DM akin to a bumphunt [26] in two dimensions, but is beyond the scope of this work.
Other potential irreducible processes include τ τ → νν νν, which has a large rate σ × B 74 × 0.35 2 9.1 pb. We reject this process by reconstructing the τ mass endpoint using the stransverse mass m T2 > 2 GeV (see Refs. [55][56][57] for definition). This variable uses the lepton momenta and missing transverse momentum defined by p miss T ≡ −p 1 T − p 2 T . We validate mitigation of this background by generating an event sample in Mad-Graph using the sm-lepton masses model to decay the taus. Top quark pairs γγ → tt → b νb ν contribute a small rate σ × B 0.33 × 0.21 2 0.015 fb and we assume a jet veto renders this background negligible.
Turning to reducible backgrounds induced by detector misreconstruction, these typically require data-driven techniques by the experimental collaborations to estimate reliably. We briefly discuss possible mitigation strategies. First, nonresonant production of lepton pairs γγ → , where ∈ [e, µ], has a large cross-section of 140 pb per flavour. Missing momentum results solely from detector resolution and this background is also rendered negligible by the m T2 requirement. This also suppresses resonant dilepton processes from decays of diquark bound states, such as J/ψ and Υ resonances. Next, leptons from fake and nonprompt sources, such as semileptonic decays of B-hadrons, typically become significant at low lepton p T [14]. We expect these to be well controlled by standard lepton quality requirements in the extremely clean events. Finally, protons from pileup collisions can fake intact UPC protons when occurring in the same event as an exclusive or nonexclusive process that gives two leptons and p miss . A veto in the Zero Degree Calorimeter [58] will suppress nonexclusive processes. Timing with 10 ps resolution can associate protons in the forward detectors to the lepton vertices [59].
The mass reach depends on several factors. As m(˜ ) increases, the γγ →˜ ˜ cross-section decreases and the search becomes statistically limited. However, signals with larger m(˜ ) are easier to distinguish from the W W background as the signal becomes better separated from the W boson mass; higher DM masses are similarly easier to separate. For m(˜ ) 130 GeV, sensitivity is limited by the forward detector acceptance, which drops rapidly for proton energy losses of E γ 100 GeV.
Our strategy has limited sensitivity to the very compressed region ∆m(˜ ,χ 0 1 ) 10 GeV due to the trigger emulation p T > 15 GeV. Recent work proposed strategies using initial state radiation (ISR) and low momentum leptons to probe this challenging region [63,64], which is successfully adopted by the ATLAS 2 ISR search [14]. Our strategy can potentially provide a complementary probe of this region, free from hadronic backgrounds. This is only possible if lepton trigger thresholds are lowered by using forward detector triggering, motivating their development for LHC Run 3.
If the fourfold mass degeneracy scheme is relaxed, the LHC blind corridor widens to 10 ∆m(μ R ,χ 0 1 ) 90 GeV [11][12][13][14], where our strategy will play an important role. In conventional electroweak production, the right-handed states˜ R have order 3 times smaller crosssections than the left-handed˜ L counterparts [66]. By contrast, the photon collider strategy has the advantage of equal QED cross-sections for˜ L and˜ R states.
This proposal is widely extendable to other search channels and electrically charged targets. So-called Rparity violating scenarios where theχ 0 1 decays to higher multiplicity final states can profit from clean events. Charged fermions (charginos) face similar difficulties discriminating against W W backgrounds and may benefit in combination with a hadronic channel. Scalar quarks, charged Higgs bosons, spin 1 mediators, disappearing track signatures are also motivated scenarios.
In summary, we proposed a search strategy using the LHC as a photon collider to open sensitivity beyond LEP in the challenging corridor 15 ∆m(˜ ,χ 0 1 ) 60 GeV favored by DM and (g − 2) µ phenomenology. Proton tagging enables the initial state and missing momentum four-vector p miss to be reconstructed, offering striking background discrimination inaccessible to current LHC searches. We encourage experimental collaborations to include this forward physics frontier in flagship hadron collider searches for DM and their charged mediators.
Acknowledgements-We thank the hospitality of the DM@LHC Workshop at Heidelberg University, where discussions for this work began. We are grateful to Alan Barr for helpful conversations and feedback on the manuscript. LB is supported by St John's College, Oxford. JL is supported by STFC.