Matter vs. vacuum oscillations at long-baseline accelerator neutrino experiments arXiv:2001.08676 Suman Bharti1, Ushak Rahaman2, S. Uma Sankar1 1Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India, 2Centre for Astro-Particle Physics (CAPP) and Department of Physics, University of Johannesburg, South Africa Abstract We search for evidence of modiﬁcation of neutrino oscillation by matter eﬀect in the data of T2K and NOνA. We ﬁnd that vacuum oscillations provide as good a ﬁt to the data as matter modiﬁed oscillations. Even an extended run of these experiments, with 5 years each in neutrino and anti-neutrino modes, can not make a 3 σ distinction between vacuum and matter modiﬁed oscillations. A 5 σ discrimination against vacuum oscillations requires the combination of (5ν + 5¯ν) runs of T2K, NOνA and DUNE. Introduction Due to the propagation of the neutrinos through earth matter, it is expected that the oscillation probabilities would be modiﬁed by matter eﬀects. These matter eﬀects are sensitive to the sign of ∆31 and their observation can lead to a determination of this sign. For baselines less than 1000 km, the matter eﬀects lead to negligibly small changes in νµ/¯νµ survival probabilities [1]. In the case of atmospheric neutrinos, the survival probabilities Pµµ and P¯ µ¯ µ are expected to undergo signiﬁcant changes due to matter eﬀects. However, at present Super-Kamiokande is able to make only a small distinction between them [2]. In the long- baseline accelerator experiment, the νe/¯νe appearance data is sensitive to matter eﬀects [3, 4]. But they are also sensitive to the unknown CP violating phase δCP. Given a set of data, three solutions are likely to occur [5, 6]: • matter modiﬁed oscillations with NH and δ1 CP, • vacuum oscillations with δ2 CP and • matter modiﬁed oscillations with IH and δ3 CP. Unless the question of vacuum vs matter modiﬁed oscillations is resolved, it may not be possible to measure δCP. Establishing CP violation in neutrino oscillations is one of the most impor- tant goals of both current and future long-baseline accelerator neutrino experiments. To achieve this goal, it becomes impor- tant to establish a distinction between vacuum oscillations and matter modiﬁed oscillations. Analysis procedure We calculated the theoretical event spectra with three ﬂavour oscillations using GLoBES [7, 8], for the appearance and disap- pearance channels in both neutrino and anti-neutrino modes for T2K and for NOνA. These rates are calculated with the mat- ter potential parametrized as q ∗A, where A is the standard Wolfenstein matter term [9] and q is a multiplicative factor. In this analysis, we consider the possibility of non-standard matter term, as was done in ref. [2]. ∆21 and sin2 θ12 were held ﬁxed to their best-ﬁt values [10]. Other oscillation parameters were varied in their 3 sigma ranges given in ref. [10]. q has been varied in the range [0, 2]. For each data set of each experiment, the Poissonian χ2 is calculated with χ2 = X i 2[(Nth i −Nexp i ) + Nexp i × ln(Nexp i /Nth i )] + X j [2 × Nth j ] + χ2(sys), (1) where i stands for bins for which Nexp i ̸= 0 and j stands for bins for which Nexp j = 0. The term χ2(sys) arise due to systematic uncertainties. For each of the two experiments, we included sys- tematic uncertainty of 10%, using the pull method. We varied the pull parameter in 3σ range and marginalized over it to de- termine χ2 as a function of test values of oscillation parameters, mass hierarchies and q. We calculated the total χ2 for both NH test and IH test by adding up χ2 m from all experiments and all channels, but for same parameter values. We added priors on sin2 θ13, sin2 θ23 and |∆31| (|∆32|) for NH (IH). We found the minimum of χ2(tot) and subtracted it from all other val- ues of χ2(tot) to obtain ∆χ2 and marginalised ∆χ2 over all the oscillations parameters except hierarchy and q. Analysis and expectations of NOνA and T2K present T2K and NOνA data for the POT