Quasistable charginos in ultraperipheral proton-proton collisions at the LHC

We propose an approach for the search of charged long-lived particles produced in ultraperipheral collisions at the LHC. The main idea is to improve event reconstruction at ATLAS and CMS with the help of their forward detectors. Detection of both scattered protons in forward detectors allows complete recovery of event kinematics. Though this requirement reduces the number of events, it greatly suppresses the background, including the strong background from the pile-up.


Introduction
The Large Hadron Collider (LHC) can be considered as a photon-photon collider with the photons produced in ultraperipheral collisions of charged particles: protons or heavy ions. In such collisions the colliding particles pass near each other exchanging photons; the particles remain intact after the collision. Enormous collision energy achieved at the LHC permits treatment of the particles' electromagnetic fields as bunches of real photons distributed according to a well-known spectrum. This approximation is known as the equivalent photon approximation (EPA) [1][2][3][4] (see also [5][6][7][8]).
Ultraperipheral collisions are a promising source of New Physics events for the kinds of physics that can appear in photon fusion. They feature clear experimental signature with only the photon fusion result and the two initial particles in the final state. The colliding particles scatter at a very small angle and escape the detector through the beam pipe. They can be registered with forward detectors-ATLAS Forward Proton Detector (AFP) [9] or CMS-TOTEM Precision Proton Spectrometer [10]. These detectors are located at the distance of Table 1: Energy losses required for a particle to be detected in the forward detector placed at different distances from the interaction point (IP).
In the original ATLAS FP420 proposal [11] forward detectors were placed at 420 m from the interaction point, and the corresponding fractional momentum loss range was at smaller values 0.002 < ξ < 0.020. This position at 420 m was not retained in the actual AFP detector, but can be used for estimations of sensitivities. The corresponding energy losses are presented in Table 1. Unfortunately, a heavy ion from lead-lead collisions with the energy of 5.02 TeV/nucleus pair cannot be detected in forward detectors because the production cross section and EPA spectrum are highly suppressed at ξ 0.002. Photon flux in ultraperipheral collisions is proportional to (Z 1 e) 2 (Z 2 e) 2 , where Z 1 e and Z 2 e are electric charges of the colliding particles. In this respect, collisions of heavy ions, e.g. lead ions with Z = 82, look much more promising for the search of New Physics. However, photon energy is limited by the breaking energy of its source particle. In the case of proton, this energy should be at the level of Λ QCD ; calculation based on its electromagnetic form factor results in q = 0.20 GeV [12], whereq is the maximum momentum of a virtual photon in the proton rest frame. In the laboratory reference frame the maximum photon energy isqγ where γ is the Lorentz γ-factor of the proton; for a 6.5 TeV protonqγ = 1.4 TeV. In lead-lead collisions with the energy 5.02 TeV/nucleon pair, maximum photon energy is at the order of 50 GeV. Photons with higher energy are produced as well, but their production is suppressed by the nucleus form factor, thus greatly reducing the benefits from higher photon flux in a collision of heavy ions. Nevertheless, the production cross section for a system with invariant mass about 100 GeV is several orders of magnitude larger in lead-lead collisions than in proton-proton collisions [12].
A good example of New Physics that can be searched in ultraperipheral collisions is supersymmetry (SUSY) [13]. The supersymmetric partners of the electroweak bosons are six particles: four neutralinos and two charginos. Letχ 0 1 be the lightest neutralino andχ ± 1 be the lightest chargino. At present, chargino and neutralino with masses below ∼ 1 TeV are excluded in a large region of SUSY parameters by the LHC results [14, §110.5]. However, the searches are not sensitive to the case when the masses of the lightest chargino and the lightest neutralino are approximately equal. In particular, in the framework of the MSSM, when mχ± 1 − mχ0 1 2 GeV, the strongest bound mχ 1 > 92 GeV comes from the LEP experiments [15]. At this mass scale, the possibility that mχ± 1 < mχ0 1 is excluded, since then the chargino would be stable (assuming R-parity conservation), and the charginos remaining after the Big Bang and/or produced in cosmic rays would form hydrogen-like atoms that would be observed in sea water [16][17][18][19] (see also [20]). 1 Thus, in what follows we consider only the case when the lightest chargino is (slightly) heavier than the lightest neutralino. Such compressed chargino-neutralino spectrum is realized in the following two cases: where M 1 is the bino mass parameter, M 2 is the wino mass parameter, and µ is the higgsino mass parameter. The region of SUSY parameters with mχ0 1 ≈ mχ± 1 ≡ m χ ∼ 100 GeV can be probed at the LHC in ultraperipheral collisions of both protons and heavy ions. Let us consider the cross sections (Section 2), the search strategy (Section 3), and the background (Section 4) for chargino production. Figure 1: Leading order Feynman diagrams for chargino production in an ultraperipheral collision of two protons.

Production cross section
Consider production of a pair of charginos in an ultraperipheral collision of two identical particles with charge Ze. The leading order Feynman diagrams of this process for protons are presented in Fig. 1. Collision is mediated by approximately real photons emitted from the colliding particles. The equivalent photon approximation provides the momentum distribution of these photons [21]: where q is the photon 4-momentum, −q 2 = q 2 ⊥ + (ω/γ) 2 , q ⊥ is the transverse component of the photon momentum, ω is the photon energy, γ is the Lorentz factor of the colliding particle, F (q 2 ) is the form factor originating from the vertices involving the particles which emit photons. For the proton, the Dirac form factor is [22] where is the dipole form factor, µ p = 2.79 is the proton magnetic moment, τ = −q 2 /4m 2 p , m p is the proton mass, and Λ 2 = 0.71 GeV 2 . Since in an ultraperipheral collision |q 2 | Λ 2 QCD 4m 2 p , the magnetic form factor contribution can be neglected. In this case F (q 2 ) ≈ G D (q 2 ), and the equivalent photon spectrum is given by [12] where a = (ω/Λγ) 2 .
Heavy nucleus form factor is more complicated. The most accurate description of nucleus charge distribution appears to be in the form of Bessel decomposition [23]: where j 0 (x) = sin x/x is the spherical Bessel function of order zero, θ(x) is the Heaviside step function, a n and R are parameters of the decomposition. The form factor is the Fourier transform of the charge distribution: Numerical values of a n and R are provided in Ref. [24]. The corresponding equivalent photon spectrum n Pb (ω) is calculated through numerical integration of Eq. (1). Production of charginos in photon fusion is described by the Breit-Wheeler cross section [25], where √ s ≡ √ 4ω 1 ω 2 is the invariant mass of the pair of charginos, ω 1 and ω 2 are photons energies. Cross section for charginos production in ultraperipheral collisions is where N is the colliding particle, n N (ω) is its equivalent photon spectrum. For m χ = 100 GeV, where the proton-proton collision energy is 13 TeV, and lead-lead collision energy is 5.02 TeV/nucleon pair (these parameters correspond to the currently available LHC data).
In order for both colliding particles to be detected in forward detectors (FD), their momentum loss ξ = ∆p/p has to be in the interval ξ min < ξ < ξ max , where ξ min = 0.015 and ξ max = 0.15 for the ATLAS and CMS experiments [9,10] (see Table 1). The corresponding cross section is given by formula (8) with cuts on photon energies: where 2E is the collision energy. For the same parameters as in (9), For lead ions, according to Eq. (9), with the current integrated luminosity 2.5 nb −1 [29,30], there will be 0.053 events. To observe chargino in lead-lead collisions, the integrated luminosity has to be tremendously increased. If the luminosity could be increased by three orders of magnitude, there would be about 50 events. For a lead ion to survive in an ultraperipheral collision, its energy loss should not be much greater than ≈ 100 GeV [12]. The corresponding value of ξ is 1.9 · 10 −4 . Differential cross sections are presented in Fig. 2. Assuming total Run 3 luminosity in proton-proton collisions of 300/fb at the ATLAS and CMS detectors, the number of produced chargino pairs with both protons detected in forward detectors can be of the order of 250 per detector.
In the LHC experiments, some regions of the products phase space are cut off. Common requirements for a particle to be detected in the muon system are p T >p T and |η| <η where p T is the particle transverse momentum, η is its pseudorapidity, andp T andη are experimental cuts on these values. The corresponding (fiducial) cross section for the pp → ppχ + 1χ − 1 reaction is (see [12] for the derivation of this formula with m χ = 0) where x = ω 1 /ω 2 , and The differential with respect to p T cross section is For m χ = 100 GeV, E = 6.5 TeV, ξ min E = 97.5 GeV, ξ max E = 975 GeV,p T = 20 GeV,η = 2.5, we get The differential fiducial cross section is presented in Fig. 3.

Search strategy
Assuming R-parity conservation, with the lightest chargino and the lightest neutralino masses being nearly equal, it is possible thatχ ± 1 lives long enough to escape the detector and decay outside. The experimental signature and, consequently, the background of the chargino production process greatly depend on the stability of chargino. There are three possible scenarios: 1. Chargino decays outside the detector producing a track in the detector.
2. Chargino decays in the body of the detector producing a disappearing track in the detector. This scenario is studied in Ref.
[31], and charginos with the mass 100 GeV and lifetime above 0.02 ns and below 10 ns are excluded.
3. Chargino decays in the beam pipe of the detector. This scenario will not be studied in this paper. See, e.g., [32,33].
Let us consider the case when chargino lives long enough to escape the detector (case 1). Then a track from a charged particle will be observed in the detector. Since in the Standard Model only a muon can go through the detector, the question is whether a chargino can be distinguished from a muon.
For the reaction pp → ppχ + 1χ − 1 , momenta of all four particles in the final state can be measured: momenta of chargino candidates p 1 , p 2 can be reconstructed from their tracks in the detector, and final state protons can be detected by the forward detectors thus providing their energy losses ξ 1 , ξ 2 (protons transverse momentum can be neglected). The observable suitable for the discovery of chargino in ultraperipheral collisions is the mass of the charged particle Eqs. (16) and (17) are equivalent due to momentum conservation law, however experimental uncertainties give different contributions to these formulas, so both of them are useful when dealing with experimental data. Calculating this value for every event with exactly two charged tracks and two protons detected in forward detectors, and plotting the number of such events with respect to m, one should get δ(m − m χ ) smeared with the detector resolution.

Background
A long-lived chargino will produce a signal in the detector very similar to that of a muon. Therefore, the sources of the background will be the reactions producing a pair of muons. We will consider the following processes: Eq. (12) with m χ replaced with m µ also works for the pp → pp µ + µ − reaction. 3 Fiducial cross sections for the pp → pp W + W − → pp µ + ν µ µ −ν µ and pp → pp τ + τ − → pp µ + ν µντ µ −ν µ ν τ reactions were calculated with the help of the Monte Carlo method. Parameters of the calculation were the same as in Eq. (15). Cross section for the γγ → W + W − process is [34] The results are presented in Fig. 3 and Table 2.
Chargino candidate mass distributions according to Eqs. (16), (17) for the signal and background processes were calculated by means of the Monte Carlo method. Finite central detector resolution was taken into account according to [35,Section 4.5]. Finite forward detector resolution was taken into account by replacing in Eqs. (16), (17) ξ i E with a random number normally distributed around ξ i E with the standard variation linearly interpolated with pivot points 5 GeV for ξ i = 0.04 and 10 GeV for ξ i = 0.14, in accordance with [9, Section 3.3.2]. The results are presented in Fig. 4. The peak from muons is well separated from the peak from charginos. The background from W + W − and τ + τ − production and decay is negligible. Note that the background with neutrinos in the final state can be further heavily suppressed by the requirement that p T 1 + p T 2 = 0 where p T i are transverse momenta of the detected particles. 3 The muon mass can be neglected as long as m 2 µ p 2 T .    Figure 4: Monte Carlo simulation of the chargino candidate mass distribution. The integrated luminosity is assumed to be 150/fb.

Conclusions
Simultaneous detection of both protons in forward detectors allows complete reconstruction of kinematics of the charginos produced in ultraperipheral collisions. It allows strong background suppression and discovery of charged heavy quasistable particles. In particular, the case of quasidegenerate chargino and neutralino can be explored in the region previously unavailable.
With the described method, over 100 ofχ + 1χ − 1 pairs per LHC detector could be found in the data collected in Run 2 of the LHC. Application of this method for Run 3 data is very promising.

Aknowledgements
We are grateful to A. D. Stepennov and I. I. Tsukerman for useful discussions. The  [32] The ATLAS Collaboration. Searches for electroweak production of supersymmetric particles with compressed mass spectra in √ s = 13 TeV pp collisions with the ATLAS detector. ATLAS-CONF-2019-014 (2019).
[33] The CMS Collaboration, Search for supersymmetry with a compressed mass spectrum in the vector boson fusion topology with 1-lepton and 0-lepton final states in proton-proton collisions at √ s = 13 TeV. arXiv:1905.13059 (2019).