Physics potential of an experiment using LHC neutrinos

Near the CMS IP, the area surrounding the focusing magnet (Q1) closest to CMS in the LHC tunnel (figure 6) matches the $4\lt | \eta | \lt 5$ acceptance. The CMS forward hadronic calorimeter (HF) (10 nuclear interaction lengths) and the CMS forward shield (composed of steel and borated concrete, with a total of 26 nuclear interaction lengths) provide an excellent shield against all particles emerging from the IP, except for muons and neutrinos. Although the triplet of final focus magnets on both sides of the IP will be rebuilt for HL-LHC, the current geometry was assumed for calculating an approximate rate of neutrino interactions. A hypothetical cylindrical detector placed at 25 m from the IP, around the Q1 magnet, with inner and outer radii of 35 and 90 cm, could cover the $4\lt \left|\eta \right|\lt 5$ range in most of the azimuthal acceptance (320° of 360°) and be stretched in length for over 7 m, up to about 20 m. The detector is placed at one side of the IP only, covering the range $4\lt \eta \lt 5$. The target mass in the detector is taken to be 4.1 × 10²⁷ nucleons cm⁻², corresponding to about 6 m of lead over 15 m, for a weight of about 10 ton m⁻¹. The LHC beam line elements limit extensions of the target length that may be needed for increasing the detector mass and the ν interaction rate. A detailed view of the CMS detector and the Q1 region can be found in [9].

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In the calculation of the neutrino interaction rate, an event by event weight is applied for properly taking into account the νN interaction cross-section dependence on energy and on neutrino type [1]. For the Charged Current cross section of τ neutrinos on nucleons, we can only refer to theoretical expectations [15], that take into account the effect of the F4 and F5 structure functions [16]. As an example, the interaction of a muon neutrino of 30 GeV on nucleons has a cross section of about 20 × 10⁻³⁸ cm², and a τ neutrino of 600 GeV of about 350 × 10⁻³⁸ cm²; for anti-ν the cross section is about a half that of ν. Table 2 summarizes the expected neutrino interactions for 3000 fb⁻¹ of pp collision events, separately for heavy quark production and for W production.

Table 2.  Expected neutrino interactions in the VN (about Q1) location, for 3000 fb⁻¹.

	$4\lt \eta \lt 5$
Neutrinos from c and b production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	2.7 × 105
Neutrino interactions with E > 100 GeV	46000
Neutrino interactions with E > 300 GeV	5500
τ neutrino interactions	8500
Neutrinos from W production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	320
Neutrino interactions with E > 100 GeV	310
Neutrino interactions with E > 300 GeV	300
τ neutrino interactions	110

The bulk of the event sample is from b and c decays, with an energy spectrum quickly decreasing, while leptonic W decays give a small contribution, which is concentrated at very high energies and becomes dominant for energies above 500 GeV. With respect to the experiment targets:

• High energy νN cross section: a measurement of the neutrino interaction cross section on nucleons at energy above 300 GeV can be performed to a few percent accuracy. Thanks to the leptonic W contribution, the accuracy will remain better than 10% at E = 1 TeV. In about hundred neutrino interactions, the charged lepton from leptonic W decays will be observed in CMS.
• $\tau$ neutrino sample: a few thousand τ neutrinos can be observed. A hundred will have energies in the TeV range, thanks to the W contribution.

Hence, a detector placed in this location has an interesting physics potential. A drawback is its interference with the design of the focusing magnets for HL-LHC.

Measurements by LHCb [17] and TOTEM [18] show that in $4\lt | \eta | \lt 5$ there are about 4.5 charged particles on average per pp inelastic interaction at $\sqrt{s}=13$ TeV, mostly pions and kaons. With a pp inelastic cross section of 80 mb and a luminosity of 2 × 10³⁴ cm⁻² s⁻¹, it is estimated that in $4\lt | \eta | \lt 5$ there are 7 × 10⁹ charged particles per second. However, in the location under study the detector would be shielded from charged hadrons emerging from the IP by the CMS hadronic calorimeter (HF) and the CMS forward shield, providing together 36 nuclear interaction lengths, i.e. a damping factor of 2.3 × 10⁻¹⁶, corresponding to almost full absorption for hadrons. Muons from pion and kaon decays will be rare: π and K particles with energies larger than a few GeV will interact before they can decay, and, if not, only energetic muons from the decays will penetrate the forward shield.

The muon rate from pp collisions at $\sqrt{s}=13$ TeV in $4\lt | \eta | \lt 5$ was measured by LHCb [19]: in minimum bias events they observe a rate of 25 kHz of muons with p >10 GeV at a luminosity of 4 × 10³² cm⁻² s⁻¹. This is in excellent agreement with Pythia calculations, assuming that the dominant source is b and c decays: the production cross section is 48 × 10⁵ nb at $\sqrt{s}=13$ TeV and 1.4% of these events have a muon in $4\,\lt | \eta | \lt 5$, which gives an expectation of 27 kHz. The predicted muon rate at 2 × 10³⁴ cm⁻² s⁻¹ luminosity is 1.25 MHz, however, when considering the muon energy spectrum only <10% of those muons are expected to reach the detector in Q1, due to the CMS magnetic field and shielding material. In the proposed location, the detector has a cross section of about 2.2 × 10⁴ cm², so that about 6 muons cm⁻² will impinge on it in a second, i.e. a few ×10⁵/cm²/fb⁻¹.

Machine induced backgrounds vary rapidly while moving along and away from the beam line. An occupancy of a few per cm² per second is estimated for muons in the beam halo moving towards CMS [10]. A sizeable contribution might come from hadronic secondaries emerging from the pp collisions at lower angles and interacting with the machine elements, like the TAS collimators positioned at 18m from the CMS IP [13]: the energy and angular distributions of the debris particles have large uncertainties, but the proposed location should lie in a local minimum. The flux of neutrons and photons in early estimations ranges from 10⁻³ to 1/cm² s⁻¹ [10]. Later simulations [11, 12], validated with local measurements, show a very large contribution of thermal neutrons. Their flux has local fluctuations by several orders of magnitude along the beam line, and can reach 10⁴/cm² s⁻¹, i.e about 10⁹/cm²/fb⁻¹; the uncertainty in the proposed location is very large.

3.3.1. In situ measurement

A measurement was performed to directly evaluate the background environment. A stack of emulsions was installed in the proposed location at the beginning of the 2018 LHC run [20]. It was placed on the concrete underneath Q1, at about 25m from the CMS IP, covering the region of 80–90 cm from the beam axis, i.e. at pseudorapidity η about 4 (figure 6). It was retracted after CMS had collected 1.6 fb⁻¹ of luminosity.

The stack consisted of 10 layers of nuclear emulsions interleaved with 1 mm lead sheets (figure 7).

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The package was protected from neutrons and photons by a 30 mm thick layer of borated polyethylene and 5 mm of lead, on all sides but at the bottom. A 5 mm air gap was left at the bottom so that the inside would not heat up and damage the emulsions. Polyethylene doped with 5% B₂O₃ has an attenuation length for thermal neutrons of 2.4 mm. Simulations with Geant4 v10.4 [21] were performed to check the attenuation length of borated polyethylene for neutrons with energy from 0.025 eV to 1.0 GeV and to study the effect of the thin air gap at the bottom, since neutrons (mainly with thermal energy) come from all directions and can flow through the thin gap; the effective damping factor provided by the B₂O₃ layer was estimated to be about 1% without air gap and 3.5% with a 20 mm air gap. The Physics List (PL) used was FTFP INCLXX HP that relies on the Fritiof + pre-equilibrium model (FTFP) at high energy, the INCL++ [22] model at intermediate energies, and the NeutronHP model for a detailed treatment of neutrons below 20 MeV. This PL has been successfully benchmarked against experimental results in [23].

The package became radioactive during the exposure. An activity of 35 μSv/h was measured immediately after extraction, with a long decay time. When the activity fell below safety threshold, the gamma spectrum from the emulsions was measured. It showed lines characteristics of the decay of Ag-110 m, a metastable state produced when a neutron is captured by a Ag-109 nucleus. The measurement was repeated after a month. From the intensity of the lines, the amount of Ag-110 m could be determined, which, knowing the emulsion composition and the neutron-silver cross section [24], can be turned into an estimate of the integrated neutron flux. However the neutron flux was delivered over an extended time, following the LHC running schedule. Thus the production rate of Ag-110 m had to be weighted over time using the luminosity information provided by CMS, and the integrated fluence of neutrons passing the borated polyethylene layer and impinging on the emulsions was determined to be of the order of 10⁸/cm²/fb⁻¹, comparable to the expectations with no B₂O₃ protection.

The emulsions finally underwent photographic development. The hit density was far above the tolerable limit—about 10⁷/cm² (see section 5.3.1 )—for proceeding to further analysis.

The observed neutron flux, originating mostly from the focusing quadrupoles themselves, and its predicted large variability along the beam line, discourage the use of this location.

The UJ57 and UJ53 halls lie at 90 and 120 m, respectively, from the CMS IP, where the beam line meets the ends of the tunnel that bypasses the CMS experimental cavern, on opposite sides of CMS (figure 8).

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They are open caverns—long and narrow—on a side of the beam line. An iron wall could be built for providing isolation from the beam line and lowering the radiation level if necessary. The available volume for installing a detector is limited, since a 5 m clearance from the beam line is reserved for transport of accelerator elements. It could be 2 m wide, 2 m high, and extend for 15 m. Given the large size iron is preferred to lead. The target mass could consist of 9 m of iron in total, weighting 20 ton m⁻¹ and providing 4.0 × 10²⁷ nucleons cm⁻². The detector would lie at 5 m from the beam, giving a reduced azimuthal coverage (about 1/18 of 2π). The detector in UJ57 can cover the pseudorapidity range $-3.6\lt \eta \lt -3.2$, while the one in UJ53 can cover 3.5 < η < 3.9.

From the studies in section 2, the η acceptance in this location is not optimal. The energy spectrum of neutrinos from b and c decays as well as for leptonic W decays will be softer, the tail at very high neutrino energies will be limited marginally populating the 1 TeV region and beyond. The kinematical acceptance for leptonic W decays with the charged lepton in the CMS acceptance will be enhanced, but that advantage vanishes because of the small angular coverage in azimuth.

It is assumed that both UJ53 and UJ57 would be equipped. Table 3 summarizes the expected neutrino interactions for 3000 fb⁻¹ of pp collision events, separately for heavy quark production and for W production.

Table 3.  Expected neutrino interactions in the near (N) (UJ53+UJ57) location, for 3000 fb⁻¹.

	3.2 < η < 3.9
Neutrinos from c and b production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	2.0 × 103
Neutrino interactions with E > 100 GeV	110
Neutrino interactions with E > 300 GeV	1
τ neutrino interactions	240
Neutrinos from W production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	13
Neutrino interactions with E > 100 GeV	12
Neutrino interactions with E > 300 GeV	10
τ neutrino interactions	4

With respect to the experiment targets:

• High energy νN cross-section: in this location, only a very coarse measurement of the neutrino interaction cross section on nucleon at energy above 300 GeV can be performed, relying on a few leptonic W decays, with accuracy not better than 40%; it is impracticable at 1 TeV.
• $\tau$ neutrino sample: a few hundred τ neutrinos can be observed. Their energies will be low, averaging to about 15 GeV.

Hence, a detector placed in this location has a marginal potential for neutrino physics.

The UJ57 hall is located at the end of the magnet triplet region, of which Q1 (VN location) is the closest to CMS. In [12], expected machine induced backgrounds in UJ57 have been calculated, and found of similar composition and level as in the VN location. The charged hadron fluence will exceed 10⁶/cm²/fb⁻¹ and that of thermal neutrons will be larger than 10⁸/cm²/fb⁻¹. The situation is predicted to improve in the shielded areas farther downstream the beam line, discussed in section 5. The flux of muons, at 90 m from the IP, although it is distributed over a large area, is intense, ∼3 × 10⁵/cm²/fb⁻¹.

Given the low potential that this location has shown for physics, no in situ measurement of the background was planned for confirming the calculations.

Further away from the IP along the beam line, on either side of CMS, are situated the RR53 and RR57 halls, that are classified as LHC 'alcoves' (figure 8). Those are radiation shielded areas that can host electronic equipment made of conventional not radiation tolerant electronics. The radiation environment in those halls is intrinsically mild by construction. The RR53 and RR57 alcoves are located at 237 m from the CMS IP, at a distance of 3 m from the beam line, and shielded from it by a 40 cm thick iron wall. The hall extends for 20 m parallel to the beam, and has transverse dimensions of over 6 m horizontally and 4 m vertically. The iron wall is discontinued at both extremes of the hall for giving access. Slightly upstream of RR53 (RR57) along the beam line are the TOTEM roman pots and the TCL6 collimator; in LHC running conditions they are moved close to the beams and can induce backgrounds which are strongly attenuated by the RR53 shielding.

A detector occupying the RR53 (RR57) hall would subtend the $4\lt | \eta | \lt 5$ pseudorapidity region, the same as for the detector in the VN location (section 3). Its transverse dimensions would need to be large, 5 m horizontally and 3 m vertically. The length is limited to at most 20 m by the hall size. Given the large transverse dimensions, iron is used as target. The target detector could feature 3.0 × 10²⁷ nucleons cm⁻², corresponding to 6.5 m of iron, for a weight of about 40 ton m⁻¹.

Although at a distance of 240 m from the IP, a coincidence with a charged lepton from a leptonic W decay in CMS could still be envisaged. Proof is that the nearby TOTEM roman pots can be operated together with CMS [25].

Event kinematics in this location is as shown for the VN location because it covers the same $4\lt | \eta | \lt 5$ range. However, since the detector lies further away from the beam line, an azimuthal acceptance of only 30° (8% of 2π) can be achieved. The smaller acceptance reduces event statistics that can be partially recovered by equipping both RR53 and RR57.

Table 4 summarizes the expected neutrino interactions for 3000 fb⁻¹ of pp collision events, separately for heavy quark production and for W production.

Table 4.  Expected neutrino interactions in the far (F) (RR53) location, for 3000 fb⁻¹.

	4 < η < 5
Neutrinos from c and b production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	2.5 × 104
Neutrino interactions with E > 100 GeV	4300
Neutrino interactions with E > 300 GeV	520
τ neutrino interactions	880
Neutrinos from W production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	30
Neutrino interactions with E > 100 GeV	29
Neutrino interactions with E > 300 GeV	28
τ neutrino interactions	10

The bulk of the event sample is from b and c decays, with a fast decreasing energy spectrum. Leptonic W decays give a small contribution concentrated at very high energies, that becomes dominant for energies larger than 500 GeV. With respect to the experiment targets:

• High energy νN cross-scion: a measurement of the neutrino interaction cross section on nucleon at energy >300 GeV can be performed to a better than 10% accuracy, and to 20% when E is 1 TeV. In a few events, the charged lepton from leptonic W decays will be observed in CMS.
• $\tau$ neutrino sample: nearly a thousand τ neutrinos can be observed. A few will have TeV energies, thanks to the W contribution.

Hence, a detector placed in this location has physics potential, but the sample of detected neutrinos from leptonic W decays with the charged lepton observed in CMS would be marginal. Another drawback is the size of the detector, which implies a big investment.

Regarding the charged particle flux form the IP, the arguments of section 3.3 apply to this location as well. The flux is still dominated by muons, which distribute over a larger area, resulting in at most 10⁵/cm²/fb⁻¹.

Machine induced backgrounds in RR53 (and similarly in RR57) were simulated in detail and compared to measurements taken with Radiation Monitor devices over long LHC running periods [12]. The radiation field inside the hall, although generally low, is neither uniform in space nor in time. The main component is hadronic secondaries with energies larger than a MeV, that spray out from elements along the beam line. The radiation background is more intense near the entrances where the iron wall is discontinued, it can reach 10⁷–10⁸ hadrons/cm²/fb⁻¹, and its intensity depends on the operation mode of the machine, in particular the TCL6 collimator, located about 20 m upstream the hall. Away from the entrance, at about 6 m from the beam line and in the centre of the hall, the fluence of hadronic secondaries is predicted to be mild (about 10⁴–10⁶/cm²/fb⁻¹); the intensity increases by an order of magnitude at the side closest to the beam line, and drops as much at the opposite side of the hall. Muons can emerge from the decay of hadronic secondaries, and their flux is estimated in the order of 10² /cm²/fb⁻¹ in the centre of the hall. The neutron background is dominated by thermal neutrons: their fluence could reach up 10⁸–10⁹/cm²/fb⁻¹ in the hottest area.

5.3.1. In situ measurement

An emulsion and lead stack similar to the one used in section 3.3.1 was prepared (figure 7). It was installed in RR53 during the LHC Technical Stop 2, in September 2018, and retracted after 5.4 fb⁻¹ of pp collisions collected by CMS.

The thickness of the borated polyethylene container was increased to 90 mm, providing a nominal attenuation factor close to 10⁻¹⁶ for thermal neutrons, but it was open at the bottom of the box in order to prevent overheating. The package was placed in the approximate centre of the RR53 hall, 5.5 m aside of the beam line, and 1 m below it, on a grating false floor to disperse heat from the box. The CERN Engineering team provided Radiation Monitor devices [26, 27] that were placed in critical positions in the hall in order to map the radiation field both inside and in proximity of the hall. In each position two devices were installed, with different thresholds, so to infer both the high energy hadron and the thermal neutron components separately. The monitors were retracted at the same time as the emusion package, and analysed [28]. Those near the centre of the RR53 hall, close to the emulsions, measured mild fluences of both high energy hadrons and of thermal neutrons of a few ×10⁶/cm²/fb⁻¹. The measured values increased closer to the iron wall, or near the forward and backward entrances, by almost an order of magnitude. For comparison, two measurements were performed during the same period outside the hall, along the beam line, and showed values two orders of magnidute larger. These measurements are in average in agreement with the predictions [12] for the LHC machine running configuration used during the time of the measurements, and provide more detailed information.

After extraction, the emulsions were developed at CERN and analysed in the emulsion laboratory in Naples. Clear signals of particle tracks appeared, consistently reproduced in all ten layers. Figures 9 and 10 show distributions of the measured inclinations of the observed particle tracks, horizontally (θ_x) and vertically (θ_y) in two of the ten emulsion films, at different depths in the stack. The stack was aligned with the emulsions orthogonal to the beam line.

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The track density was measured to be large, about 10⁷/cm². The analysis considered only emulsion base-tracks (figure 7) surviving selection criteria which were studied on cosmic ray tracks. The selection is based on the number of Ag grains sensitized in the emulsion layers, which is proportional to the particle ionisation, and on the χ² of the matching between micro-track segments reconstructed in the sensitive layers. Signal tracks are characterised by low χ² and high number of grains, while background due to random coincidences shows high χ² values and a few grains per path length. Each base-track provided two measurements: the θ_x and θ_y directions. The emulsion package was distant 5.5 m in X, and −1.0 m below the beam axis in Y.  Each of the ten emulsions independently showed two peaks in the track angle distribution, on top of a uniform background. One was at about 280 mrad in θ_x and at about −50 mrad in θ_y. Tracks in this peak pointed towards the beam line and indicated a source at a distance of about 5.5 m/280 mrad = 20 m upstream along the beam line, which is confirmed by the orthogonal measurement −1 m/50 mrad = 20 m. Backgrounds depend on the machine configuration; during the emulsion exposure, the dominant contribution was expected to originate in the nearest quadrupole magnet, in agreement with the measurement. The other peak in the distribution of track angles was sharp at  20 mrad in θ_x and at a few mrad below 0 in θ_y. Since the package was at 247 m from the IP, it is expected that muon tracks will have directions 5.5 m/247 m = 22 mrad in X and −1 m/247 m = −4 mrad in Y, which is in good agreement with the observed peak. The size of the Ag clusters along a track in the peak is compatible with that of muons, as determined in cosmic muon measurements. The track population in the 22 mrad peak was measured to be 10⁵/cm²/fb⁻¹, independently in each layer of the package, in good agreement with the expected flux of muons from the IP in the psudorapidity range $4\lt | \eta | \lt 5$ (section 3.3). The track population in the 280 mrad peak was determined to be 10⁶/cm²/fb⁻¹. This is consistent with the charged hadron fluence measured with the Radiation Monitors. A background of 10⁷/cm²/fb⁻¹ tracks at random angles was observed to populate the emulsions uniformly.

Although in the centre of the RR53 hall the neutron flux is measured to be ten times smaller than in the VN location covering the same pseudorapidity range, it is not clear how large the usable area will be. This will tend to reduce the detector acceptance, already penalised because of the small azimuthal coverage. Another disadvantage are localized hadronic sprays that depend on the running configuration of LHC, as observed in our measurement. In summary, this location does not appear convenient for placing a neutrino experiment.

From the discussion in section 2 it appears that a detector covering $| \eta | \gt 6.5$ will have a high flux of energetic neutrinos from b and c decays. In [6, 7] a detector situated at the end of the LHC straight section within a cone with an opening angle of 2 mrad was envisaged. A similar topology was studied also in [29]. This condition is not possible in the CMS intersection region, but it is possible near ATLAS. The cavern of tunnel TI18, used for injection of LEP beams and now in disuse, intercepts the prolongation of the beam axis (PBA), 480 m from the ATLAS IP, at the beginning of the collider's arc, downstream of the first bending dipoles (figure 11).

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The existing space is limited in length to a few meters, and the floor lies a 20–50 cm higher than the PBA. For the sake of site comparison, a small size detector with a half-cylinder shape, only the upper half, with axis at the bottom along the PBA, with a radius of 1.2 m, and a mass of 1.4 × 10²⁷ nucleons cm⁻², 2 m of lead, 10 ton m⁻¹, is considered. The detector would cover the region of $| \eta | \gt 6.7;$ neutrinos have very high energies, as shown in table 1, therefore the νN interaction cross section is large, hence the detector size can be small.

A drawback for a detector in this location is that it will not be possible to exploit the contribution from leptonic W decays (see figure 3).

The energy spectrum of neutrinos in $| \eta | \gt 6.7$ is much harder than in the F location. Moreover, the small size of the detector favours neutrino interactions at higher energy, which have larger interaction cross section on nucleons. The energy spectrum of interacting neutrinos is shown in figure 12. Event weights are applied that take into account the νN interaction cross-section dependence on energy and on neutrino type (section 3). Table 5 summarizes the expected neutrino interactions for 3000 fb⁻¹ of pp collision events, separately for heavy quark production and for W production.

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Table 5.  Expected neutrino interactions in the very far (VF) location, for 3000 fb⁻¹.

	η > 6.7
Neutrinos from c and b production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	2.8 × 105
Neutrino interactions with E > 100 GeV	2.6 × 105
Neutrino interactions with E > 300 GeV	2.2 × 105
τ neutrino interactions	8700
Neutrinos from W production in pp collisions at $\sqrt{s}=14$ TeV
Total neutrino interactions	2
Neutrino interactions with E > 100 GeV	1.7
Neutrino interactions with E > 300 GeV	1.5
τ neutrino interactions	0.4

The contribution from leptonic W decays is negligible. The event sample consists of neutrinos from b and c decays, with a hard energy spectrum ($\langle E\rangle$ = 550 GeV). With respect to the experiment targets:

• High energy νN cross-section: a measurement of the neutrino interaction cross section on nucleon at energy >300 GeV can be performed to a 1% accuracy, and to a few % at 1 TeV.
• $\tau$ neutrino sample: many thousands of τ neutrinos can be observed, with energies reaching into the TeV.

Therefore, a detector placed in this location, although it lies outside the kinematical range of leptonic W decays, has a high potential for neutrino physics.

The backgrounds in the TI18 cavern were carefully investigated in preparation for the FASER experiment [30]. Both simulations and in situ measurements were performed. The equipment was similar to ours: an emulsion-lead package and radiation monitors. The location envisaged for the FASER detector in TI18 was similar to the neutrino detector considered here, placed along the PBA and with a small transverse section. The simulations show that the particles reaching the location are dominantly muons and neutrinos. Muons come from IP but also from secondary particles interacting along the beam line. The charged particle flux was measured to be about 10⁴ /cm²/fb⁻¹. The radiation level was found to be low, a neutron flux of a few ×10⁶/cm²/fb⁻¹ was measured. A track density in the emulsions at the 10⁴/cm²/fb⁻¹ level was observed. These values are a factor of 10, and up to 100, smaller than our measurement in the F location.