Reassessing the sensitivity to leptonic CP violation

Journal of High Energy Physics, Mar 2015

We address the validity of the usual procedure to determine the sensitivity of neutrino oscillation experiments to CP violation. An explicit calibration of the test statistic is performed through Monte Carlo simulations for several experimental setups. We find that significant deviations from a χ 2 distribution with one degree of freedom occur for experimental setups with low sensitivity to δ. In particular, when the allowed region to which δ is constrained at a given confidence level is comparable to the whole allowed range, the cyclic nature of the variable manifests and the premises of Wilk’s theorem are violated. This leads to values of the test statistic significantly lower than a χ 2 distribution at that confidence level. On the other hand, for facilities which can place better constraints on δ the cyclic nature of the variable is hidden and, as the potential of the facility improves, the values of the test statistics first become slightly higher than and then approach asymptotically a χ 2 distribution. The role of sign degeneracies is also discussed.

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Reassessing the sensitivity to leptonic CP violation

Received: August Reassessing the sensitivity to leptonic CP violation Mattias Blennow 0 1 3 6 7 8 Pilar Coloma 0 1 3 4 7 8 Enrique Fernandez-Martinez 0 1 2 3 5 7 8 Open Access 0 1 3 7 8 c The Authors. 0 1 3 7 8 0 850 West Campus Dr , Blacksburg, VA, 24061 U.S.A 1 Stockholm , 106 91 Sweden 2 Instituto de F sica Te orica UAM/CSIC 3 KTH Royal Institute of Technology, AlbaNova University Center 4 Center for Neutrino Physics, Physics Department , Virginia Tech 5 Departamento de F sica Te orica, Universidad Aut onoma de Madrid 6 Department of Theoretical Physics, School of Engineering Sciences 7 Calle Nicol as Cabrera 13-15, Cantoblanco , Madrid, E-28049 Spain 8 Calle Francisco Tom as y Valiente , Cantoblanco, Madrid, E-28049 Spain We address the validity of the usual procedure to determine the sensitivity of neutrino oscillation experiments to CP violation. An explicit calibration of the test statistic is performed through Monte Carlo simulations for several experimental setups. We find that significant deviations from a 2 distribution with one degree of freedom occur for experimental setups with low sensitivity to . In particular, when the allowed region to which is constrained at a given confidence level is comparable to the whole allowed range, the cyclic nature of the variable manifests and the premises of Wilk's theorem are violated. This leads to values of the test statistic significantly lower than a bution at that confidence level. On the other hand, for facilities which can place better constraints on the cyclic nature of the variable is hidden and, as the potential of the facility improves, the values of the test statistics first become slightly higher than and then approach asymptotically a 2 distribution. The role of sign degeneracies is also discussed. violation; Neutrino Physics; CP violation; Statistical Methods 1 Introduction 2 3 4 Summary and outlook Distribution of the test statistic for the null hypothesis Mixing in the lepton sector of the Standard Model is described by the unitary PontecorvoMaki-Nakagawa-Sakata (PMNS) matrix [15]. In the standard three family scenario, it can and, if neutrinos are Majorana particles, two additional Majorana CP phases. Neutrino i mj2). Unlike for the CKM matrix, the mixing angles of the PMNS matrix Electroweak Baryogenesis, JCKM is not large enough to account for the observed Baryon asymmetry of the Universe [13, 14], the discovery of an additional source of CP violation Given the current knowledge on the neutrino oscillation parameters, the focus for the next generation of neutrino oscillation experiments will be to determine the neutrino determination of the mass ordering, there has been a lively discussion in the literature on whether or not the common way of assessing the sensitivity of a future experiment is applicable [1518]. As shown in ref. [17], the common approach does give a reasonable approximation of the median sensitivity, although not for the reasons typically used in the argumentation for it. The small correction was mainly based on the one-sided nature of the hypothesis test and only to a minor degree on the non-gaussianity of the statistical 2 distribution of the test statistic should be common approach when making sensitivity analyses is that the change in number of events events unchanged. In addition, there is no guarantee that the predicted data without statistical fluctuations, as used in the common approach, will be representative. In the present work, these assumptions are tested by explicit Monte Carlo simulations in order to find out exactly how much the sensitivity analyses are affected by these assumptions. To do so, we start from the basic frequentist definitions and apply the Feldman-Cousins approach [19] in order to determine the sensitivity of several experimental setups. Statistical approach The most common way of quantifying the experimental sensitivity to leptonic CP violation rejected. In the literature, this is typically computed by constructing the test statistic where 2 = 2 log L, and L is the likelihood of observing the data given a particular set of oscillation parameters. It is worth noting that this involves minimizing over all nuisance parameters, which may be subject to external constraints (we will discuss how such external one degree of freedom, based on the implications of Wilks theorem [20]. In addition, the Asimov data set1 [21], i.e., the event rates without statistical fluctuations, is assumed to be representative for the experimental outcome and is thus used to estimate the expected confidence level (CL) at which the CP conservation hypothesis would be rejected. However, as for the case of the neutrino mass ordering [15, 17], it is not clear to what degree the assumptions underlying Wilks theorem are violated when testing CP conservation in this fashion, resulting in a need to explicitly test this framework. The procedure to test the CP conservation hypothesis at a given CL can be summariz (...truncated)


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Mattias Blennow, Pilar Coloma, Enrique Fernandez-Martinez. Reassessing the sensitivity to leptonic CP violation, Journal of High Energy Physics, 2015, pp. 5, Volume 2015, Issue 3, DOI: 10.1007/JHEP03(2015)005