# Effects of Variations of SUSY Breaking Scale on Neutrino Parameters At Low Scale Under Radiative Corrections

DOI : 10.17577/IJERTCONV10IS07005

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#### Effects of Variations of SUSY Breaking Scale on Neutrino Parameters At Low Scale Under Radiative Corrections

Khumanthem Helensana Devi1 , K. Sashikanta Singh 2 , N.Nimai Singp

Department of Physics , Manipur University, Imphal, 795003, India

Abstract:- Radiative stability of neutrino parameters for inverted hierarchy is studied using renormalisation group analysis for different seesaw scales and varying susy breasking scale. We adopt the top-down approach starting from the grand unified scale which leads to the electroweak scale values of the neutrino parameters. We proposed the possibility of a Self-Complementary relation among three mixing angles, 23 13 + 12 , and also its radiative evolution under the same framework.

Keywords IH , SS scale, ms scale, RGE, neutrino parameters

1. INTRODUCTION

Neutrino is evident when considering the fact that neutrino masses require physics beyond the standard theory

. Till date we do not have a clear picture of such new physics and its energy scale. Hence we need more studies regarding these. The phenomenology of SUSY [1] is to a large extent determined by the SUSY breaking mechanism and the SUSY breaking scale ( m s ) which determined the SUSY particle masses , the field contents of physical particles , the mass hierarchy and their particle contents.

Supersymmetry (SUSY) is a transformation relating fermions to bosons and vice-versa. It ensures the stability of hierarchy between the weak and Planck scales. It can provide a natural mechanism for understanding electroweak symmetry breaking (EWSB)[2] and Higgs Physics . SUSY at TeV scale is not a necessary consequence but is motivated by the possible cancellation of quadratic divergences [3] in radiative correction to the Higgs boson mass. Minimal Supersymmetric Standard Model (MSSM)[4] is a straight-forward symmetrization of the SM with minimal number of new parameters . Due to lack of evidence for superpartners in Large Hadron Collider [1, 5] simplest SUSY scenarios is forced towards region of parameter space unnatured for the Higgs sector. Supersymmetric particles are ruled out upto 2.4TeV (Gluinos)[3]. The discovery of Higgs boson with a mass around 125 GeV imposes constraints on SUSY models[6].

LHC has reached almost its maximum energy of about 14TeV.

The tightest 95 % confidence level upper bound [7] for sum of neutrino masses , m is m < 0.146 eV (NH) , m < 0.172 eV (IH) and m <

0.121 eV (degenerate) . Running of RGE [9, 10, 11] can be divided into two regions governed by different RG eqns as:

(a)from GU T down to the seesaw scale (b)from seesaw scale down to EW .

From Model building point of view , we can observe that neutrino oscillation experiments hint not only for neutrino masses but the study of individual parameters and how they evolve carry physical insight.

In his paper, section 2 includes inputs of top-down approach . Section 3 includes tables and graphs. Section 4 includes results and analysis.

2. INPUTS FOR TOP DOWN APPROACH

In this paper, we try to confine SUSY and ms scales . We used values of yukawa and guage couplings as initial inputs by studying the radiative evolution of the three gauge, yukawa and Higgs couplings using bottom-up approach with the change of ms scale which is not mentioned here . Using all necessary mathematical frameworks, we analyzed the radiative nature of neutrino parameters using top-down approach. We proposed a phenomenological motivated relation known as Self Complementarity relation (SC) , 23=q( 13 + 12 ) , q=1.1. It is like QLC relation which connects the quark and lepton sectors. It bears signature of certain hidden symmetry. In order to check the stability of SC relation against radiative evolution we have to vary SS and ms scales.

 Input GUT scale Seesaw Scale (tan 40) parameters 1016 GeV 1015 GeV 1014 GeV 1013GeV m1 (eV) 0.0512 0.0517 0.0508 0.0502 m2 (eV) 0.0513 0.0518 0.0509 0.0503 m3 (eV) 0 0 0 0 12 /0 33.77 33.55 33.20 33.95 13 /0 8.32 8. 40 8.44 8.22 180 180 180 180 240 240 240 240

3. Tables and graphs

Table 1 : Input set for IH case (m3=0) at tan40. 23 is used from SC relation

 ms scale m2 31 m2 21 13 12 23 (TeV) (10-3 eV2) (10-5 eV2) (/0) (/0) (/0) (/0) 2 2.526 5.875 8.40 33.59 46.21 240.00 4 2.501 6.452 8.40 33.60 46.23 240.00 6 2.482 6.914 8.40 33.60 46.24 240.00 8 2.473 7.111 8.40 33.61 46.25 240.00 10 2.464 7.300 8.40 33.61 46.25 240.00 12 2.454 7.555 8.40 33.61 46.26 240.00 14 2.451 7.634 8.40 33.61 46.26 240.00

Table 2 : Variation of neutrino parameters on changing ms for IH case (m3=0) at SS scale of 1015 GeV for tan40 .

Fig1. Variation of 12 with increasing ms scale at tan40.

Fig2. Variation of 13 with increasing ms scale at tan40.

Fig3. Variation of 23 with increasing ms scale at tan40.

Fig4. Variation of m2 31 with increasing ms scale at tan40.

Fig5. Variation of m2 21 with increasing ms scale at tan40.

Fig6. Variation of with increasing ms scale at tan40.

4. RESULT AND ANALYSIS

In this work, stability of neutrino parameters for inverted hierarchy case(m3 = 0) is studied on changing ms scale for different SS scale at tan 40

using top-down approach. With increasing ms scale , m2

31 decreases while other neutrino parameters increases except 13 which is stable throughout . We observed from the output data that neutrino parameters were affected on changing ms scale from 2TeV to 14TeV with SS scale of values between 1013 GeV to 1015 GeV. Higher m s scales (12 TeV and 14 TeV) are preferred . SS scale of 1015 GeV is preferred among other SS scales . Outputs of neutrino parameters are within 2 range. SC relation is invariant against radiative evolution.

The evolutions of the leptonic mixing angles are insignificant because of small Yukawa couplings of charged leptons in the SM.

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