Numerical consistency check between two approaches to

radiative corrections for neutrino masses and mixings

MRINAL KUMAR DAS¹, MAHADEV PATGIRI^2,* and N NIMAI SINGH^1,3

¹Department of Physics, Gauhati University, Guwahati 781 014, India

²Department of Physics, Cotton College, Guwahati 781 001, India

³International Centre for Theoretical Physics, Strada Costiera 11, 31014 Trieste, Italy

^*Corresponding author.

E-mail: mahadev@scientist.com; nimai03@yahoo.com

Abstract. We briefly outline the two popular approaches on

radiative corrections to neutrino masses and mixing angles, and then

carry out a detailed numerical analysis for a consistency check

between them in MSSM. We find that the two approaches are nearly

consistent with a discrepancy factor of $4.2\%$ with running

vacuum expectation value (VEV) ($13\%$ for scale-independent VEV) in mass

eigenvalues at low-energy scale but the predictions on mixing angles

are almost consistent. We check the stability of the three types of neutrino models, i.e.,

hierarchical, inverted hierarchical and degenerate models, under radiative corrections, using both approaches, and find consistent conclusions. The neutrino mass models which are found to be stable under radiative corrections in MSSM

are the normal hierarchical model and the inverted hierarchical

model with opposite CP parity. We also carry out numerical analysis

on some important conjectures related to radiative corrections in

the MSSM, viz., radiative magnification of solar and atmospheric

mixings in the case of nearly degenerate model having same CP parity

(MPR conjecture) and radiative generation of solar mass scale in

exactly two-fold degenerate model with opposite CP parity and

non-zero $U_{e3}$ (JM conjecture).

We observe certain exceptions to these conjectures. We find a new result that both solar mass scale and $U_{e3}$ can be

generated through radiative corrections at low energy scale. Finally the effect of

scale-dependent vacuum expectation value in neutrino mass renormalisation is discussed.

Keywords. Radiative correction; renormalisation group equations; neutrino masses and mixing angles; conjecture.

PACS Nos 11.10.Hi; 11.10.Gh