New physics vs new paradigms: distinguishing CPT violation from NSI
Abstract
Our way of describing Nature is based on local relativistic quantum field theories, and then CPT symmetry, a natural consequence of Lorentz invariance, locality and hermiticity of the Hamiltonian, is one of the few if not the only prediction that all of them share. Therefore, testing CPT invariance does not test a particular model but the whole paradigm. Current and future long baseline experiments will assess the status of CPT in the neutrino sector at an unprecedented level and thus its distinction from similar experimental signatures arising from nonstandard interactions is imperative. Whether the whole paradigm is at stake or just the standard model of neutrinos crucially depends on that.
1 Introduction

Locality.

Lorentz invariance.

Hermiticity of the Hamiltonian.
If CPT is not conserved, one of the assumptions above has to be violated. Quantum gravity, for example, is expected to be nonlocal. However its effects are suppressed by the Planck mass! But this is exactly the right ballpark for neutrinos to show it. In fact, neutrinos are not only an ideal system to accommodate CPT violation [2] but also the most accurate tool to test it as well. In Ref. [3] we have shown that the most stringent limits on CPT violation arise not from the kaon system but from neutrino oscillation experiments. And contrary to the kaon case, these limits will improve in the next years significantly. Given the impact such a result would have, it is crucial to distinguish a true, genuine CPT violation from just a new, unknown interaction, no matter how sophisticated. After all, “outstanding claims require outstanding evidence”.
In this work we will confront the presence of intrinsic CPT violation with new neutrino interactions with matter usually known as neutrino nonstandard interactions (NSI).^{1} NSIs are an agnostic way to parametrize all the CPT preserving possibilities economically and therefore provide the ideal tool to discriminate between a legitimate CPT violation, a phenomenon that challenges our description of Nature in terms of local relativistic quantum fields and a more or less complicated interaction that can be accommodated in the current paradigm. Here we will explore how such a distinction can be made if a different mass and/or mixing pattern is extracted from the experiments when analyzing neutrino and antineutrino data sets separately, as it happens in the case of T2K, where different best fit points are obtained for neutrino and antineutrino oscillation parameters [10].
Our paper is structured as follows: in Sects. 2 and 3 we develop an analytic approach using the twoneutrino approximation for illustration purposes, showing how CPT violation can mimic NSI. Next, in Sect. 4 we present the details of the full simulation of DUNE using the the complete 3neutrino picture. Our results are also presented and discussed in this section. Finally, we conclude in Sect. 5 with a summary.
2 Theoretical background
3 Analytical results at the probability level
The allowed deviations between the neutrino and antineutrino mass splitting as a function of the NSI coupling \(\epsilon ^m_{\tau \tau }\) (\(\epsilon ^m_{\mu \tau }\)) are shown in the left (right) panel of Fig. 1. There we have chosen \(\theta =41^{\circ }\), inspired by the best fit value for the atmospheric angle of the global fit of neutrino oscillation parameters in Ref. [23], and the energies \(E=1.0,2.5,10\) GeV, being 2.5 GeV the peak energy for \(\nu _e\) appearance at DUNE, see Ref. [24]. From this figure one can read to which amount a measurement of \(\Delta (\Delta m^2)\) different from zero could be induced by NSI instead of being a signal of intrinsic CPT violation. The vertical dashed black lines indicate the current (1–4)\(\sigma \) bounds on \(\epsilon ^m_{\tau \tau }\) and \(\epsilon ^m_{\mu \tau }\). The difference in the slope of the two graphs can be understood from two facts: first, the bound on \(\epsilon _{\mu \tau }^m\) is stronger than the one for \(\epsilon _{\tau \tau }^m\) and second, for the mixing angle of choice, we have \(\cos 2\theta \approx 0.14\) and \(\sin 2\theta \approx 0.99\), so the deviation potentially induced by \(\epsilon _{\tau \tau }^m\) can be much larger. Note that in this section we have assumed equal mixing angles, so that the situation could be even more confusing if one allows for different mixing angles in the neutrino and antineutrino sector. Notice also that these results have been derived at the probability level and, in principle, one can expect the picture to be somehow blurred when the complete analysis of a neutrino experiment is carried out taking into account the full simulated neutrino spectrum and the associated statistical and systematical errors.
4 Results from the simulation of DUNE
In Ref. [3] we have shown that, if the results from the separate neutrino and antineutrino analysis of the T2K collaboration [10] turn out to be true, DUNE could measure CPT violation at more than 3\(\sigma \) confidence level. In this section we will analyze if indeed these results could be confused with NSI.
Oscillation parameters considered in the simulation and analysis of DUNE expected data. In terms of the two neutrino parameterization of Sect. 2, the notation used in this table is equivalent to \(\Delta m_{31}^2 = \Delta m^2_\nu \), \(\Delta \overline{m}^2_{31} = \Delta m^2_{\overline{\nu }}\) and \(\theta _{23} = \theta _\nu \), \(\overline{\theta }_{23} = \theta _{\overline{\nu }}\)
Parameter  Value 

\(\Delta m_{31}^2\)  2.60\(\times 10^{3} \,\text {eV}^2\) 
\(\Delta \overline{m}_{31}^2\)  2.62\(\times 10^{3} \,\text {eV}^2\) 
\(\sin ^2\theta _{23}\)  0.51 
\(\sin ^2\overline{\theta }_{23}\)  0.42 
\(\Delta m^2_{21}\), \(\Delta \overline{m}^2_{21}\)  \(7.56\times 10^{5} \,\text {eV}^2\) 
\(\sin ^2\theta _{12}\), \(\sin ^2\overline{\theta }_{12}\)  0.321 
\(\sin ^2\theta _{13}\), \(\sin ^2\overline{\theta }_{13}\)  0.02155 
\(\delta \), \(\overline{\delta }\)  1.50\(\pi \) 
Our strategy is as follows: we perform two simulations of DUNE running 3.5 years only in neutrino mode and 3.5 years only in antineutrino mode. To generate the future data, we consider the parameters presented in Table 1, assuming different atmospheric mixing angle and mass splitting for neutrinos and antineutrinos (using the best fit points from T2K, see Table 1), but no NSI. Then, in the statistical analysis, we scan over the standard oscillation parameters \(\delta \), \(\theta _{13}\), \(\theta _{23}\), \(\Delta m_{31}^2\) and their antineutrino counterparts.^{3} Additionally, we scan over the two NSI parameters relevant for our channel of interest, \(\epsilon ^m_{\tau \tau }\) and \(\epsilon ^m_{\mu \tau }\), see Eq. (2). The remaining parameters are set to zero, since they only contribute to \(P_{\mu \mu }\) and \(\overline{P}_{\mu \mu }\) at subleading orders. The same argument applies to the phase of \(\epsilon _{\mu \tau }^m\), which is therefore set to zero, too. Summarizing, we simulate DUNE fake data under the assumption of CPT violation and then we perform the reconstruction of the neutrino signal assuming CPT conservation and the presence of NSI with matter along the neutrino propagation.
Nevertheless, it should be noted that the best fit value we have obtained in this NSI case for the flavor diagonal coupling, \(\epsilon ^m_{\tau \tau }=0.33\), is highly excluded from current experimental data^{6}. To visualize this, together with the results obtained in our analysis, we have plotted in Fig. 2 the profile for both NSI parameters from current data assuming gaussian errors (see black lines in both panels). In the right graph one can see that our preferred value for \(\epsilon ^m_{\tau \tau }\) is actually excluded at close to 5\(\sigma \). Therefore, if the results from T2K (that we take as input parameters for the simulation of the CPTviolating data sample in DUNE) turn out to be true, they would rather hint towards CPT violation than to NSI.
5 Summary
The impact of a potential CPT violation is such that it is imperative to distinguish it from any other unknown physics that can lead to similar experimental signatures. The need for such a distinction is more urgent in the neutrino sector where the future long baseline neutrino experiments will push the CPT invariance frontier to a new level and where neutrinos, due to its uncommon mass generation mechanism, can open unique windows to new physics and new mass scales.
On the other side, NSIs are a simple way to parametrize any unknown physics which may be relevant to neutrino oscillations. In this work we have shown that, although NSIs can mimic fake CPT violation, its experimental signature can be distinguished from a genuine CPT violation due to the bounds on the strength of the NSI arising from other experiments. Indeed, we have found that the different results for the neutrino and antineutrino parameters measured by the T2K Collaboration may be interpreted in terms of a CPT–conserving scenario in combination with neutrino NSI with matter. The match between the prediction of both scenarios is astonishing, as shown in Fig. 3. However, this equivalence has a caveat, since the size of the diagonal NSI coupling required, \(\epsilon _{\tau \tau }^m \simeq 0.3\), is excluded by current neutrino oscillation data. Therefore, the future cannot be more exciting. If the slight indications of CPT violation in the mixing angles offered by the separate analysis of the neutrino and antineutrino data sets by T2K are confirmed by the DUNE experiment, genuine CPT violation i.e. the one that challenges our understanding of Nature in terms of local relativistic quantum field theory will be the only answer. If this were not the case, we explain how the discrimination has to be performed in case a difference is ever found.
Footnotes
 1.
 2.
Note that this is an approximation and, indeed, the effective mixing angles for neutrinos and antineutrinos are not equal, as shown in Eqs. (10)–(13). This simplification has been introduced to pedagogically illustrate the analogous role of the mass splittings and the NSI couplings in the CPT–violating and NSI scenario, respectively. An equivalent discussion can be done in terms of the mixing angles, assuming equal mass splittings for neutrinos and antineutrinos.
 3.
 4.
In our simulation we have assumed 71 energy bins between 0 and 20 GeV.
 5.
We had already discussed this type of imposter solutions in Ref. [3].
 6.
Note that most bounds in the literature are calculated by taking one or two NSI parameters at the time. Obviously, if one allows for several of them to be nonzero, much weaker bounds can be obtained, see for example Ref. [33].
Notes
Acknowledgements
GB acknowledges support from the MEC and FEDER (EC) Grants SEV20140398, FIS201572245EXP, and FPA201784543P and the Generalitat Valenciana under grant PROMETEOII/2017/033. GB acknowledges partial support from the European Union FP7 ITN INVISIBLES MSCA PITNGA2011289442 and InvisiblesPlus (RISE) H2020MSCARISE2015690575. CAT and MT are supported by the Spanish grants FPA201785216P and SEV20140398 (MINECO) and PROMETEO/2018/165 and GV2016142 grants from Generalitat Valenciana. CAT is supported by the FPI fellowship BES2015073593 (MINECO). MT acknowledges financial support from MINECO through the Ramón y Cajal contract RYC201312438 as well as from the L’OréalUNESCO For Women in Science initiative.
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