Gravitational waves from phase transition in minimal SUSY <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>−</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:math> model
Naoyuki Haba, Toshifumi Yamada
Abstract
Many extensions of the Standard Model include a new $U(1)$ gauge group that is broken spontaneously at a scale much above TeV. If a $U(1)$-breaking phase transition occurs at nucleation temperature of $O(100)--O(1000)\text{ }\text{ }\mathrm{TeV}$, it can generate stochastic gravitational waves in $O(10)--O(100)\text{ }\text{ }\mathrm{Hz}$ range if ${\ensuremath{\beta}}_{\mathrm{n}}/{H}_{\mathrm{n}}=1000$, which can be detected by ground-based detectors. Meanwhile, supersymmetry (SUSY) may play a crucial role in the dynamics of such high-scale $U(1)$ gauge symmetry breaking, because SUSY breaking scale is expected to be at TeV to solve the hierarchy problem. In this paper, we study the phase transition of $U(1)$ gauge symmetry breaking in a SUSY model in the SUSY limit. We consider a particular example, the minimal SUSY $U(1{)}_{B\ensuremath{-}L}$ model. We derive the finite temperature effective potential of the model in the SUSY limit, study a $U(1{)}_{B\ensuremath{-}L}$-breaking phase transition, and estimate gravitational waves generated from it.