A scalar potential from gauge condensation and its implications
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Regular Article - Theoretical Physics
A scalar potential from gauge condensation and its implications Eung Jin Chun1,a , Chengcheng Han1,2,b 1 2
School of Physics, KIAS, 85 Hoegiro, Seoul 02455, Republic of Korea School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
Received: 14 April 2020 / Accepted: 13 October 2020 © The Author(s) 2020
Abstract We consider a scalar field φ whose coupling to the kinetic term of a non-abelian gauge field is set at an UV scale M. Then the confinement of the gauge sector will induce a φ-dependent vacuum energy which generates a dimensionful potential for the scalar. It provides a good example of dynamical generation of a new physics scale below M through the vacuum expectation value φ. This mechanism may shed light on the origin of dark matter, or spontaneous symmetry breaking applicable to the electroweak symmetry.
In this paper, we consider a scalar field φ coupling to a general SU (N ) gauge field which confines at a lower scale. Then, a φ-dependent vacuum energy is induced and generates a new potential for the scalar boson in the confining phase. In this way, a new energy scale can emerge to provide us some insight on understanding various phenomena mentioned above. The paper is organized as follows: we will first briefly overview the mechanism, and then discuss various implications in physics of dark matter and symmetry breaking.
1 Introduction 2 The mechanism The existence of a fundamental scalar has been essential to understand an important phenomenon in the nature. The Higgs boson, responsible for the electroweak symmetry breaking, is the only example confirmed by experiment so far. However, it is well believed that a scalar field (inflaton) drives an early expansion of the universe [1–8] to solve the flatness and horizon problems, seeding the primordial fluctuations in cosmic microwave background [9–12]. A scalar field is also required to break Peccei–Quinn (PQ) symmetry at an intermediate scale through which the Strong CP conservation is enforced dynamically [13]. More recently, scalar particles have been considered extensively as a dark matter candidate for various reasons, which can also be extremely light [14]. Furthermore, a light scalar (dilaton) coupling to the gluon fields could lead a fifthforce between the nucleus, motivating a lot of low energy atomic experiments [15]. Such a scalar field with an initial displaced vacuum could induce time-varying gauge couplings through its coupling to the weak and strong gauge fields, providing an first-order phase transition required by the electroweak baryogengesis [16–19].
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2.1 Confinement potential Let us consider an SU (N ) gauge theory with n f light fermions, and a singlet scalar φ which couples to the gauge field through a high dimension operator, φ β 1 (1) L⊃− 2 1−c G μν G μν . 4g M 2g Note that the pre-factor β/2g is included to keep renormalization scale invariance of the operator, g
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