We present a momentum measurement method based on multiple Coulomb scattering (MCS) in the FASER$ν$ emulsion detector. The measurement of charged-particle momenta is essential for studying neutrino interactions in the TeV energy range at the FASER experiment. This method exploits the sub-micron spatial resolution and long tracking length of the FASER$ν$ detector, enabling momentum determination from a few GeV up to a few TeV. The performance was evaluated using Geant4-based Monte Carlo simulations and validated with muon test beam data in the momentum range 100-300 GeV. As a first probe of the method for higher momentum muons, background muons recorded by the FASER$ν$ detector were examined, showing reconstructed momenta consistent with expectations from their angular spread.
The ForwArd Search ExpeRiment (FASER) [1][2][3][4] at CERN's Large Hadron Collider (LHC) [5] is designed to measure neutrino differential cross-sections in the TeV energy range with the neutrinos produced in the LHC's proton-proton (pp) collisions using the dedicated FASERν emulsion detector [6,7]. In 2021, the FASER Collaboration reported the first evidence of neutrino interaction candidates produced at the LHC [8]. In 2023, the first observation of collider muon neutrinos was achieved using FASER's electronic detector components [9]. This observation was shortly after confirmed by the SND@LHC Collaboration [10]. With the electronic detector, FASER has also made the first measurement of the muon neutrino interaction cross section and flux as a function of energy [11]. In 2024, for the first time, FASER measured the ν e and ν µ interaction cross sections using a 128 kg subset of the FASERν detector after exposure to 9.5 fb -1 of 13.6 TeV pp collisions [12]. The FASERν detector consists of 730 layers of tungsten plates (1.1 mm thick) interleaved with emulsion films, each composed of a 210 µm plastic base coated on both sides with 65 µm emulsion layers. The target volume has dimensions of approximately 25 cm×30 cm×108 cm, corresponding to a target mass of 1.1 metric tons and a total depth of eight interaction lengths.
When a charged particle passes through the emulsion, silver bromide crystals are ionized, and after chemical development, clusters of silver grains are formed along its trajectory [13]. Using the Hyper Track Selector (HTS), a high-speed automated track scanning system [14], these grain sequences can be read out and reconstructed in three dimensions with very high precision, with a typical spatial resolution of 0.2 to 0.3 µm in the transverse plane and a few µm in the z direction. Within a single emulsion layer, the trajectory of a particle is reconstructed as a micro-track, a sequence of aligned silver grains. Two corresponding micro-tracks on each sides of the plastic base are connected to form a base-track, defined as the straight line linking the grains closest to the base surfaces. Base-tracks are connected across multiple films to reconstruct the full threedimensional particle trajectory. In the FASERν detector, the typical transverse position resolution is 0.3 µm [15].
The momentum of charged particles can be measured by the effect of multiple Coulomb scattering (MCS) on the particle trajectory. Two main approaches are used for MCS-based momentum estimation. One is the angular method, which evaluates angular variations of the tracks, previously used in the DONuT [16] and OPERA [17] experiments. The other is the coordinate method, which analyzes positional deviations between successive plates and was used in the DONuT [18] experiment. The choice between the two methods depends on the required momentum range, the achievable spatial and angular resolutions, as well as the detector structure. Although the angular method has the advantage of being insensitive to alignment errors, its applicability was limited to around 8 GeV in OPERA [17]. In contrast, the coordinate method was validated up to 100 GeV through comparison with a spectrometer in DONuT [18], and it can in principle reach a few TeV, albeit requiring large statistics and very precise alignment. Thanks to the excellent position resolution and long tracking length of the FASERν detector, the coordinate method can be effectively applied. By precisely measuring tiny deflections, reliable momentum determination of charged particles can be achieved over a wide range from a few GeV to a few TeV. This range covers the typical momenta of primary muons and secondary hadrons produced in neutrino interactions observed by the FASER experiment, and the method has already been used for the kinematical selection of muon-neutrino interaction candidates requiring at least one track penetrating 100 plates with momentum above 200 GeV [12]. In this paper, we evaluate the performance of the method using Monte Carlo (MC) simulations based on Geant4 [19] from 10 GeV to 3 TeV and validate it with muon test-beam data in the range 100-300 GeV. As a first probe of the method at higher momenta, we further apply it to background muons recorded by the FASERν detector and examine the consistency of the reconstructed momenta with expectations. This paper is organized as follows. Sec. 2 describes the momentum measurement method based on the coordinate method. In Sec. 3, we evaluate its performance using MC simulations. Sec. 4 presents the muon test-beam exposure, the track reconstruction, and the validation of the measurement method using the obtained data. Sec. 5 presents the application of this method to background muons recorded by the FASERν detector and discusses its performance in the TeV momentum range. Finally, Sec. 6 summarizes the conclusions.
Momenta of charged particles are measured by the MCS effect on the trajectory measured in the FASERν detector. A
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