A search for the analogue to Cherenkov radiation by high energy neutrinos at superluminal speeds in ICARUS

The OPERA collaboration has claimed evidence of superluminal {\nu}{_\mu} propagation between CERN and the LNGS. Cohen and Glashow argued that such neutrinos should lose energy by producing photons and e+e- pairs, through Z0 mediated processes analogous to Cherenkov radiation. In terms of the parameter delta=(v^2_nu-v^2_c)/v^2_c, the OPERA result implies delta = 5 x 10^-5. For this value of \delta a very significant deformation of the neutrino energy spectrum and an abundant production of photons and e+e- pairs should be observed at LNGS. We present an analysis based on the 2010 and part of the 2011 data sets from the ICARUS experiment, located at Gran Sasso National Laboratory and using the same neutrino beam from CERN. We find that the rates and deposited energy distributions of neutrino events in ICARUS agree with the expectations for an unperturbed spectrum of the CERN neutrino beam. Our results therefore refute a superluminal interpretation of the OPERA result according to the Cohen and Glashow prediction for a weak current analog to Cherenkov radiation. In particular no superluminal Cherenkov like e+e- pair or gamma emission event has been directly observed inside the fiducial volume of the"bubble chamber like"ICARUS TPC-LAr detector, setting the much stricter limit of delta<2.5 10^-8 at the 90% confidence level, comparable with the one due to the observations from the SN1987A.


Abstract
The OPERA collaboration [1] has reported evidence of superluminal ν µ propagation between CERN and the LNGS. Cohen and Glashow [2] argued that such neutrinos should lose energy by producing photons and e + e − pairs, through Z 0 mediated processes analogous to Cherenkov radiation. In terms of the parameter δ ≡ (v 2 ν −v 2 c )/v 2 c , the OPERA result corresponds to δ ≈ 5·10 −5 .
For this value a of δ a very significant deformation of the neutrino energy spectrum and an abundant production of photons and e + e − pairs should be observed at LNGS. We present an analysis based on the 2010 and part of the 2011 data sets from the ICARUS experiment, located at Gran Sasso National Laboratory and using the same neutrino beam from CERN. We find that the rates and deposited energy distributions of neutrino events in ICARUS agree with the expectations for an unperturbed spectrum of the CERN neutrino beam. Our results therefore refute a superluminal interpretation of the OPERA result according to the Cohen and Glashow prediction [2] for a weak current analog to Cherenkov radiation. In particular no superluminal Cherenkov like e + e − pair or γ emission event has been directly observed inside the fiducial volume of the bubble chamber like ICARUS TPC-LAr detector, setting the much stricter limit of δ < 2.5 · 10 −8 at the 90% confidence level, comparable with the one due to the observations from the SN1987a [4].

I. INTRODUCTION
The OPERA collaboration has presented evidence of superluminal neutrino propagation [1], reporting a travel time between CERN and the LNGS laboratory some 60 ns shorter than expected for travel at light speed. The OPERA result corresponds to δ ≡ (v 2 ν −v 2 c )/v 2 c ≈ 5 · 10 −5 with only small variations over the energy domain of the detected neutrinos. Observations of neutrinos from Supernova SN1987a at much lower energies around 10 MeV yield a strong constraint [4] δ < 4 · 10 −9 implying a rapid increase with energy of the hereby alleged anomaly.
As is well known, charged particles travelling at speeds exceeding that of light emit characteristic electromagnetic radiation known as Cherenkov radiation. Because neutrinos are electrically neutral, conventional Cherenkov radiation of superluminal neutrinos does not arise or is otherwise weakened. However neutrinos do carry electroweak charge and, as pointed out by Cohen and Glashow [2], may emit Cherenkov-like radiation via weak interactions when traveling at superluminal speeds. Cohen and Glashow argue that, under the assumptions of the usual linear conservation of energy and momentum and only slow variation of δ over the OPERA-relevant energy domain, superluminal neutrinos would radiate and lose energy via the three following processes The emission rate and energy loss is dominated by the third process, which is kinematically allowed under the stated assumptions. The process 3, from now on referred to as pair bremsstrahlung [2], proceeds through the neutral current weak interaction and has a threshold energy E thr ≈ 2m e / √ δ corresponding to about 140 MeV for the OPERA value of δ. In the high energy limit the electron and neutrino masses may be neglected, and Cohen and Glashow [2] compute 1 the rate of pair emission Γ, and the associated neutrino energy loss rate dE/dx to leading order in δ: Note that the average fractional energy loss per pair emission event is dE/dx ΓE ≈ 0.78; that is, about 3 4 of the neutrino energy is lost on average with each emission. Furthermore, under the approximation of a continuous energy loss, the integration of dE/dx over a distance L provides the following result for the final neutrino energy, E νf , as a function of the initial energy, E νi : Folding the initial neutrino spectrum of the CERN to Gran Sasso neutrino beam with the energy at Gran Sasso predicted with the above formula, the expected neutrino interaction rates and pair bremsstrahlung rates as a function of δ may be estimated. In particular, for

II. SIMULATION RESULTS
A full 3-dimensional simulation of the generation and transport of CNGS neutrinos from CERN to Gran Sasso while undergoing pair bremsstrahlung has been performed using the official CNGS simulation setup [9,10], based on the fluka [11,12] Monte Carlo transport code.
Accounting for the threshold, and under the hypothesis that δ does not vary significantly in the range of energies of interest, the pair bremsstrahlung interaction rate differential in the neutrino energy loss, w, and in the pair invariant mass s e + e − ≡ sδ, can be expressed as: The kinematical limits are given by: The neutrino deflection angle Ψ with respect to the incident neutrino direction can be expressed as: and the e + e − pair angle as: The resulting mean free path for a 19 GeV neutrino (the fluence-averaged energy of CNGS neutrinos) is ≈ 490 km for δ = 5 · 10 −5 , and the deflection angle is of the order of √ δ, comparable with the angular width of the neutrino beam. Hence the need for a full Monte Carlo simulation of the neutrino propagation to Gran Sasso.
All results presented in this section are for 10 19 protons on target (pot) and, for rates, for a detector (Argon) mass of 1 kt. In this way they can be easily rescaled to whichever Gran Sasso detector mass and exposure, neglecting the minor differences in neutrino cross sections total rates, total fluence, etc) is less than one percent in all cases. The systematic error on the computed neutrino (and hence e + e − pairs) rates is mostly due to the uncertainties in the hadron production model of fluka, and can be conservatively estimated to be lower than 10% (see for example [11,13]).
The unperturbed (δ = 0) fluence spectra of CNGS ν µ at Gran Sasso, and the one com- puted corresponding to δ = 5 · 10 −5 are shown in Fig. 1: the lack in the latter spectrum of the sharp 12.5 GeV ridge predicted by formula 6 can be easily appreciated.
The computed (anti)neutrino charged and neutral current rates (all flavours included), the charged current rates for ν µ andν µ with energy above 60 GeV, and the pair bremsstrahlung rates at Gran Sasso are presented in Fig. 3. The expected rates are summarized in Table I for a few representative values of δ. only the correction for the signal quenching in LAr has been applied to both the experimental and Monte Carlo results.
A dedicated search for e + e − events has been also carried out using the same exposure. This analysis constrains δ to values a few order of magnitude smaller than the one claimed by OPERA. In order to identify ν µ andν µ charged current (CC) as well as neutral curent (NC) events, further cuts have been applied to the fiducial volume: in particular events with the vertex in the last 2.5 metres of the detector have not been considered for this analysis in order to identify cleanly possible muon tracks. The total number of identified ν µ andν µ CC events, and of neutral current events, are compared in Table II: 21 events cannot be safely assigned despite the reduced fiducial volume. The resulting reference exposure for NC and CC events is 5.05 · 10 21 t·pot.
The measured raw energy deposition E dep for ν µ andν µ CC events as obtained from a calorimetric measurements corrected only for signal quenching is presented in Fig. 5 The strong constraints of Cohen and Glashow [2] predict that a superluminal high energy neutrino spectrum will be heavily depleted and distorted after L = 732 km from CERN to LNGS: in particular for δ in the range indicated by OPERA the charged current rate would be reduced to roughly 32% of the expected one, the average ν µ energy would be 12.1 GeV (against 19 GeV), the average energy of ν µ undergoing charged current interactions would be 12.5 GeV (against 28.7 GeV), and no neutrino interactions should be observed above 30 GeV.
Indeed at δ = 5 · 10 5 essentially no E ν > 30 GeV should arrive from CERN to LNGS, while our results are indicating no visible deviation of the incoming neutrino beam with respect to the expected rate and energy distribution. This result confirms the inconsistence between the OPERA δ value and the observed neutrino rate and spectrum already reported in ref. [2].
In addition, with ICARUS a bubble chamber like detector a much more stringent limit to δ may be set from the direct observation inside the ICARUS detector volume of Cherenkov like events (eq. 1,3) generated by the passing superluminal neutrinos. These events would be characterized either by a single gamma ray converting into an e + e − pair (eq. 1) and/or two single electrons (eq. 3) both with no hadronic recoils in the incoming neutrino direction. The transverse momenta of the particles in the events (1) and (3), as determined by the centre of mass system, are however far too small to be experimentally observable. Therefore events of both types (1) and (3) would appear as narrow e + e − pairs pointing directly to the beam direction, with no detectable hadronic activity. The rate of such events for the ICARUS detector exposure under consideration (6.70 · 10 21 t·pot) can be derived from those presented in Fig. 3. With the OPERA result (δ ≈ 5 · 10 −5 ) more than 7 · 10 6 electron positron pairs should have been observed for this exposure, each with an energy spectrum peaked around 10 GeV (see Fig. 2 expected), we can set the limit δ < 2.5 · 10 −8 at 90% CL for CNGS neutrinos 2 , comparable to the limit δ < 1.4 · 10 −8 established by SuperKamiokande [3] from the lack of depletion of atmospheric neutrinos, and somewhat larger than the lower energy velocity constraint δ < 4 · 10 −9 from SN1987a [4]. The ICARUS events already collected during 2011 represent conservatively a factor three higher statistics and should provide more accurate information on the indicated process. A similar increase in statistics is expected from the 2012 CNGS run. However, due to the δ 3 dependence of the pair bremsstrahlung cross section, no major change of the δ limit can be expected if no e + e − event will be found in the final data sample.

CONCLUSIONS
The spectra and rates at Gran Sasso of neutrino and e + e − for the CNGS beam have been computed in the theoretical framework presented in [2,14]. In particular, pair bremsstrahlung events have been accounted for during the propagation of neutrinos from CERN to Gran Sasso National Laboratory. The resulting neutrino spectra and rates for δ ≈ 5 · 10 −5 as suggested by OPERA are significantly different from the unaffected ones.
Preliminary results from the ICARUS experiment do not support any statistically significant deviation from the unperturbed spectrum and therefore exclude δ values comparable to the one claimed by OPERA.
Furthermore ICARUS did not detect any e + e − event, despite a few millions were expected for δ = 5 · 10 −5 . The lack of e + e − -like event translate into a 90% CL limit of δ < 2.5 · 10 −8 for multi-GeV neutrinos. and grant number N N202 064936. The work of A. Cohen was supported by the U.S.
Department of Energy Office of Science. Finally we thank CERN, in particular the CNGS staff, for the successful operation of the neutrino beam facility