Compact perturbative expressions for neutrino oscillations in matter
We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by neutrino energy plane. This extension also gives the exact oscillation probabilities in vacuum for all values of baseline divided by neutrino energy. The expansion parameter used is related to the ratio of the solar to the atmospheric $$\Delta m^2$$ scales but with a unique choice of the atmospheric $$\Delta m^2$$ such that certain firstorder effects are taken into account in the zerothorder Hamiltonian. Using a mixing matrix formulation, this framework has the exceptional feature that the neutrino oscillation probability in matter has the same structure as in vacuum, to all orders in the expansion parameter. It also contains all orders in the matter potential and $$\sin\theta_{13}$$. It facilitates immediate physical interpretation of the analytic results, and makes the expressions for the neutrino oscillation probabilities extremely compact and very accurate even at zeroth order in our perturbative expansion. Furthermore, the first and second order results are also given which improve the precision by approximately two or more orders of magnitude per perturbative order.
 Authors:

^{[1]}
;
^{[2]};
^{[3]}
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Vanderbilt Univ., Nashville, TN (United States)
 Univ. de Sao Paulo, Sao Paulo (Brazil); Yachay Tech Univ., San Miguel de Urcuqui (Ecuador)
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Publication Date:
 OSTI Identifier:
 1256704
 Report Number(s):
 FERMILABPUB16126T; YACHAYPUB1601PN; arXiv:1604.08167
Journal ID: ISSN 10298479; 1452689
 Grant/Contract Number:
 AC0207CH11359
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS CP violation; neutrino physics