Title: The effective $\mathrm{\Delta }{m}_{ee}^2$ in matter

Abstract

In this study we generalize the concept of an effective $$\Delta m^2_{ee}$$ for $$\nu_e/\bar{\nu}_e$$ disappearance experiments, which has been extensively used by the short baseline reactor experiments, to include the effects of propagation through matter for longer baseline $$\nu_e/\bar{\nu}_e$$ disappearance experiments. This generalization is a trivial, linear combination of the neutrino mass squared eigenvalues in matter and thus is not a simple extension of the usually vacuum expression, although, as it must, it reduces to the correct expression in the vacuum limit. We also demonstrated that the effective $$\Delta m^2_{ee}$$ in matter is very useful conceptually and numerically for understanding the form of the neutrino mass squared eigenstates in matter and hence for calculating the matter oscillation probabilities. Finally we analytically estimate the precision of this two-flavor approach and numerically verify that it is precise at the sub-percent level.

Authors:

Denton, Peter B.; Parke, Stephen J.

Publication Date:

Mon Nov 05 00:00:00 EST 2018

Research Org.:

Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1480890

Alternate Identifier(s):

OSTI ID: 1471721

Report Number(s):

arXiv:1808.09453; FERMILAB-PUB-18-286-T
Journal ID: ISSN 2470-0010; PRVDAQ; 093001

Grant/Contract Number:  

AC02-07CH11359

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS