Advances in High Energy Physics

Volume 2016 (2016), Article ID 9496758, 11 pages

http://dx.doi.org/10.1155/2016/9496758

## Octant Degeneracy and Quadrant of Leptonic CPV Phase at Long Baseline Experiments and Baryogenesis

^{1}Department of Physics, Gauhati University, Guwahati 781014, India^{2}Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India

Received 30 May 2016; Revised 22 July 2016; Accepted 8 August 2016

Academic Editor: Abhijit Samanta

Copyright © 2016 Kalpana Bora et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

In a recent work by us, we have studied how CP violation discovery potential can be improved at long baseline neutrino experiments (LBNE/DUNE), by combining with its ND (near detector) and reactor experiments. In this work, we discuss how this study can be further analysed to resolve entanglement of the quadrant of leptonic CPV phase and octant of atmospheric mixing angle , at LBNEs. The study is done for both NH (normal hierarchy) and IH (inverted hierarchy), HO (higher octant), and LO (lower octant). We show how baryogenesis can enhance the effect of resolving this entanglement and how possible values of the leptonic CP violating phase can be predicted in this context. With respect to the latest global fit data of neutrino mixing angles, we predict the values of for different cases. In this context we present favoured values of ( range at ≥2*σ*) constrained by the latest updated BAU range and also confront our predictions of with an up-to-date global analysis of neutrino oscillation data. We find that some region of the favoured parameter space lies within the best fit values around . A detailed analytic and numerical study of baryogenesis through leptogenesis is performed in this framework within the nonsupersymmetric SO models.

#### 1. Introduction

Today, physics is going through precision era; this is more so for neutrino physics. With the measurement of reactor mixing angle [1–7] precisely by reactor experiments, the unknown quantities left to be measured in neutrino sector are leptonic CP violating phase [8–13], octant of atmospheric angle [14–20], mass hierarchy, nature of neutrino, and so forth. Long baseline neutrino experiments (LBNE [21, 22], NOA [23], T2K [24], MINOS [25], LBNO [26], etc.) may be very promising, in measuring many of these sensitive parameters.

Measuring leptonic CP violation (CPV) is one of the most demanding tasks in future neutrino experiments [27]. The relatively large value of the reactor mixing angle measured with a high precision in neutrino experiments [1–5] has opened up a wide range of possibilities to examine CP violation in the lepton sector. The leptonic CPV phase can be induced by the PMNS neutrino mixing matrix [28–30] which holds, in addition to the three mixing angles, a Dirac-type CP violating phase in general as it exists in the quark sector and two extra phases if neutrinos are Majorana particles. Even if we do not yet have significant evidence for leptonic CPV, the current global fit to available neutrino data manifests nontrivial values of the Dirac-type CP phase [31–34]. In this context, possible size of leptonic CP violation detectable through neutrino oscillations can be predicted. Recently, [8], we have explored possibilities of improving CP violation discovery potential of newly planned long baseline neutrino experiments (earlier LBNE, now called DUNE) in USA. In neutrino oscillation probability expression () relevant for LBNEs, the term due to significant matter effect changes sign when oscillation is changed from neutrino to antineutrino mode, or vice versa. Therefore in the presence of matter effects, CPV effect is entangled and hence one has two degenerate solutions, one due to CPV phase and another due to its entangled value. It has been suggested to resolve this issue by combining two experiments with different baselines [35, 36]. But CPV phase measurement depends on value of reactor angle , and hence precise measurement of plays crucial role in its CPV measurements. This fact was utilized recently by us [8], where we have explored different possibilities of improving CPV sensitivity for LBNE (USA). We did so by considering LBNE with(1)its ND (near detector),(2)reactor experiments.

We considered both appearance () and disappearance () channels in both neutrino and antineutrino modes. Some of the observations made in [8] are as follows:(1)CPV discovery potential of LBNE increases significantly when combined with near detector and reactor experiments.(2)CPV violation sensitivity is more in LO (lower octant) of atmospheric angle , for any assumed true hierarchy.(3)CPV sensitivity increases with mass of FD (far detector).(4)When NH is true hierarchy, adding data from reactors to LBNE improves its CPV sensitivity irrespective of octant.

Aim of this work is to critically analyse the results presented in [8], in context of entanglement of quadrant of CPV phase and octant of , and hence study the role of baryogenesis in resolving this entanglement. Though in [8] we studied effect of both ND and reactor experiments on CPV sensitivity of the LBNEs, in this work we have considered only the effect of ND. But similar studies can also be done for the effect of reactor experiments on LBNEs as well. The details of LBNE and ND are same as in [8]. Following the results of [8], either of the two octants is favoured, and the enhancement of CPV sensitivity with respect to its quadrant is utilized here to calculate the values of lepton-antilepton symmetry. This is done considering two cases of the rotation matrix for the fermions, CKM only and CKM + PMNS. Then, this is used to calculate the value of BAU within the nonsupersymmetric SO model [37], characterized by the presence of an intermediate mass scale where both the lepton number conservation and quark-lepton symmetry are broken. In the supersymmetric case, the two effects occur at the unification scale, and no intermediate scale is present.

This is an era of precision measurements in neutrino physics. We therefore consider variation of range at its CL versus range at ≥2*σ* over the corresponding distribution of -minima from Figure 2. We calculate baryon to photon ratio and compare with its experimentally known best fit value. As constrained by the latest updated BAU limits, , we plot range at its CL [6] from its central value versus range at ≥2*σ* over -minima distribution and find that for IH and LO case the allowed has a varied range altering within to in the upper quadrant ( to ) and to in the lower quadrant (0 to ). Similarly to IH and HO case the allowed has a varied range differing within to . As shown in our results in Section 4, in IH and LO case the spectrum of is mostly concentrated in the region for around to , , to , and to . Also exists for around to , to , . survives for around, , to , to in the higher quadrant ( to ). Similarly as shown in our results in Section 4, as allowed by the updated BAU limits in IH and HO case, the parameter space of in the lower quadrant (0 to ) demands to be around , for , , , and . There also exists which constrains to be around , , , , and . In the upper quadrant ( to ) for the present updated BAU constraint, the allowed region of parameter space becomes constrained with , for around , to , , , and . Also the BAU constraint requires to be equal to , for around , to , , , and . Also survives for around , , , , , and . A part of the allowed parameter space is found to lie within the best fit values of . As constrained by the current BAU bounds we present the 3D variation of the favoured range of parameters: range within its C.L, range at its CL, and range at ≥2*σ* varied within in Figure 2.

As can be seen from the results presented in Section 4, from Figures 3(a) and 3(b), we find that BAU can be explained most favourably for the following possible cases: , IH and LO of ; , IH and LO of ; , IH and LO of ; , IH and HO of ; , IH and HO of ; , IH and HO of ; , IH and HO of ; , IH and HO of ; , NH and HO of . It is worth mentioning that the value of and is close to the central value of from the recent global fit result [31, 34, 38–42]. It is fascinating to notice that a nearly maximal CP-violating phase has been reported by the T2K [43], NOA [44], and Super-Kamiokande experiments [45], even if the statistical significance of all these experimental results is below level. This accords with one of our calculated favoured solutions which exactly holds with the current BAU constraints. Moreover, such hints of a nonzero were already present in global analyses of neutrino oscillation data, such as the one in [31–33]. Our main aim in this work is to carry out a detailed analysis of the breaking of the entanglement of the quadrant of leptonic CPV phase and octant of by using the current data of mixing parameters and identify the CPV phase and spectrum required to get the breaking favourable with the current BAU constraint. These results could be important keeping in view that the quadrant of leptonic CPV phase and octant of atmospheric mixing angle are yet not fixed. Also, they are significant in context of precision measurements on neutrino oscillation parameters.

The paper is organized as follows. In Section 2, we discuss entanglement of quadrant of CPV phase and octant of . In Section 3, we present a review on leptogenesis and baryogenesis. In Section 4 we show how the baryon asymmetry (BAU) within the SO model, by using two distinct forms for the lepton CP asymmetry, can be used to break the entanglement. Finally in Section 5, we present our conclusions.

#### 2. CPV Phase and Octant of

As discussed above, from Figure 3 of [8], we find that by combining with ND and reactor experiments, CPV sensitivity of LBNE improves more for LO (lower octant) than HO (higher octant), for any assumed true hierarchy. In Figure 1 we plot CP asymmetry,as a function of leptonic CPV phase , for . CP asymmetry also depends on the mass hierarchy. For NH, CP asymmetry is more in LO than in HO. For IH, CP asymmetry is more in LO than in HO. In this work we have used above information to calculate dependence of leptogenesis on octant of and quadrant of CPV phase. From Figure 1 we see that