Advances in High Energy Physics

Volume 2015, Article ID 652029, 8 pages

http://dx.doi.org/10.1155/2015/652029

## Effects of the Variation of SUSY Breaking Scale on Yukawa and Gauge Couplings Unification

^{1}Department of Physics, Gauhati University, Guwahati 781014, India^{2}Department of Physics, Manipur University, Canchipur, Imphal 795003, India

Received 28 February 2015; Accepted 6 May 2015

Academic Editor: Emil Bjerrum-Bohr

Copyright © 2015 Konsam Sashikanta Singh and N. Nimai Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The present analysis addresses an interesting primary question on how do the gauge and Yukawa couplings unification scales vary with varying SUSY breaking scales , assuming a single scale for all supersymmetric particles. It is observed that the gauge coupling unification scale increases with whereas third-generation Yukawa couplings unification scale decreases with . The rising of the unification scale and also the mass of the color triplet multiplets is necessary to increase the proton decay lifetime; the analysis is carried out with two-loop RGEs for the gauge and Yukawa couplings within the minimal supersymmetric SU(5) model, while ignoring for simplicity the threshold effects of the heavy particles, which could be as large as a few percentages.

#### 1. Introduction

The most natural extension of the minimal SU(5) GUT [1] is the supersymmetric SU(5) GUT [2] which has wide predictive power [3, 4]. The most important features are the prediction for weak mixing angle and the unification of the three gauge couplings at very large scale which is called the unification scale [3]. It also predicts the unification of the third-generation Yukawa couplings at or below the unification scale and provides a natural solution for the hierarchy problem and an alternative explanation of the electroweak symmetry breaking by the so-called radiative breaking scenario [5–8]. This theory also provides the prediction of proton decay [4] which is caused mainly by operator [9–12]. Since the most stringent limit on proton lifetime is provided by the Super Kamiokande experiment [13, 14], with the current lower experimental bound [15] years, such restrictive value may serve as a criteria to discriminate certain GUT models. This may serve as a direct experimental support to GUT theories.

There are certain arguments against [16, 17] the validity of the SUSY SU(5) GUT model. However there are specific regions in parameter space in minimal renormalizable supersymmetric SU(5) model [18–20] that is consistent with all experimental constraints including gauge couplings unification and the experimental limit on proton lifetime. In the literature there are still some arguments in support of SUSY SU(5) GUT model [21]. In order to suppress the fast operator proton decay, we have to rise both the scale of unification and the mass of the color triplet multiplets [18]. Within the SU(5) SUSY GUT, attempts have also been made to suppress proton decay operator [22]. In such context there is still enough scope for further investigation in this direction.

In this paper our focus is on the unification of the gauge couplings as well as on the Yukawa couplings in two-loops RGEs within the framework of minimal supersymmetric SU(5) GUT using updated data consistent with the LHC result. We numerically solve the unification scale for three* gauge couplings* (, , and ) as well as the three* Yukawa couplings* (, , and ) with varying input values of SUSY breaking scale [18], assuming a single scale for all supersymmetric particles for simplicity of the calculation [23, 24]. There are hints that SUSY particles have a wide spectrum and are not confined to a single energy scale. This kind of assumption is valid as long as the or [25]. We assume the scale to be somewhere in between 500 GeV and 7 TeV. In the present calculation we also ignore the threshold effects of heavy particles which could be as large as a few percentages [19, 20], and latter would affect the unification scale to some extent.

The paper is organized as follows. In Section 2 we collect the necessary input parameters from [26], which are all given at scale in scheme. We then make it evolve up to top quark mass scale () and then converted it into scheme. In Section 3, using the values obtained in Section 2, we calculate the Yukawa couplings for top quark, bottom quark, and tau lepton and also the three gauge couplings at . Using these as the input values and choosing the SUSY breaking scale to be , we then extrapolate them to very high energy scale and study the unification scenarios. In Section 4 we follow a similar procedure as in Section 3 but instead of we choose different (). Here, we divide the running process into two parts, non-SUSY part (from to ) and the SUSY part (from to ). In Section 5 we summarize our results and we conclude.

#### 2. Evolution of Gauge and Yukawa Couplings with Energy Scales

The most recent experimental data from low energy experiment [26], which would be used for generation of the initial input values at low scales, are given in Table 1.