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.
Highlights
Many extensions of the Standard Model (SM) include a new Uð1Þ gauge group that is broken spontaneously, important examples being the minimal Uð1ÞB−L model [1,2,3], the left-right symmetric model [4,5] and Pati-Salam model [6]
If the breaking scale is beyond the reach of new gauge boson searches at colliders, observation of stochastic gravitational waves generated from a Uð1Þ-breaking phase transition is the key to testing such models [7]
This is because the nucleation temperature of the phase transition is encoded by the peak position of gravitational wave spectrum, and ground-based detectors such as Advanced LIGO [8], Advanced Virgo [9], KAGRA [10], planned Einstein Telescope [11,12] and planned Cosmic Explorer [13] cover the region of 10–100 Hz, which corresponds to nucleation temperature of Oð100Þ–Oð1000Þ TeV if the speed of phase transition over the Hubble rate is 1000
Summary
Many extensions of the Standard Model (SM) include a new Uð1Þ gauge group that is broken spontaneously, important examples being the minimal Uð1ÞB−L model [1,2,3], the left-right symmetric model [4,5] and Pati-Salam model [6]. We study the phase transition of a Uð1Þ gauge symmetry breaking in a SUSY model and gravitational waves generated from it. We comment in passing that SUSY models are more predictive than non-SUSY models about high-scale Uð1Þbreaking phase transitions This is because in non-SUSY models where scalar field φ breaks an extra Uð1Þ, no symmetry forbids the Higgs portal term (H denotes the SM Higgs field), 1In a different context, gravitational waves in a SUSY Uð1ÞB−L model has been discussed in Ref. To achieve the correct electroweak symmetry breaking, one has two options; one fine-tunes the portal coupling λφH so that the emergent mass term λφHjhφij2H†H is negligible compared to genuine Higgs mass term m2HH†H; or one assumes that the genuine Higgs mass term nearly cancels the emergent mass term In the latter case, the study of the Uð1Þ-breaking phase transition involves the SM Higgs field and depends on unknown genuine Higgs mass term m2H, in addition to the Uð1Þ-breaking scale.
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