Earth-density effects in long-baseline neutrino experiments in a four-flavor (3+1) sterile-neutrino framework
Earth matter effects are a leading systematic in long-baseline (LBL) determinations of the CP-violating phase delta13, and eV scale sterile neutrinos remain a phenomenologically open extension of the three-flavor paradigm motivated by short-baseline anomalies. We extend the constant density versus realistic Earth profile analysis of Ref. 1 to a four-flavor (3+1) framework, in which a fourth, mostly sterile mass eigenstate with deltam2 41 = 0.30 eV2 and active-sterile mixing angles theta14 = 8.13degree, theta24 = 5.40degree couples to the active sector both through its mixing and through an additional neutral current (NC) matter potential that acts on the active flavors but not on the sterile state. We derive an analytical, leading-order account of how the NC potential ANC enters the reconstructed delta13 bias through an effective non standard interaction like term generated by adiabatically integrating out the fast deltam241 oscillation; replace the four-shell Earth density model with the continuous, polynomial PREM profile of Dziewonski & Anderson (1981) for the layered true trajectory; and extend the baseline scan to four representative values of the sterile CP phase delta14 is 0, pi/2, pi, 3pi/2 and to a non-zero mixing angle theta34 = 5degree. Within this benchmark, the bias remains below our scan resolution for L <= 5000 km. It grows once the trajectory samples the lower mantle and core, with the sterile sector redistributing rather than uniformly amplifying or suppressing the bias across baseline, in agreement with our original finding and now traced to a specific interference mechanism identified analytically below.