Abstract
For a discrete symmetry that is anomalous under QCD, the domain walls produced in the early universe from its spontaneous breaking can naturally annihilate due to QCD instanton effects. The gravitational waves generated from wall annihilation have their amplitude and frequency determined by both the discrete symmetry breaking scale and the QCD scale. The evidence of stochastic gravitational waves at nanohertz observed by pulsar timing array experiments suggests that the discrete-symmetry-breaking scale is around 100 TeV, assuming the domain-wall explanation. The annihilation temperature is about 100 MeV, which could naturally be below the QCD phase transition temperature. We point out that the QCD phase transition within some domains with an effective large QCD θ angle could be a first-order one. To derive the phase diagram in θ and temperature, we adopt a phenomenological linear sigma model with three quark flavors. The domain-wall explanation for the NANOGrav, EPTA, PPTA and CPTA results hints at a first-order QCD phase transition, which predicts additional gravitational waves at higher frequencies. If the initial formation of domain walls is also a first-order process, this class of domain-wall models predicts an interesting gravitational wave spectroscopy with frequencies spanning more than ten orders of magnitude, from nanohertz to 100 Hz.
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Acknowledgments
We thank Andrew Long, Pedro Schwaller, Luca Visinelli, Carlos Wagner, Chen Zhang and Ariel Zhitnitsky for useful discussion. The work is supported by the U.S. Department of Energy under the contract DE-SC-0017647. YB is grateful to the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ (Project ID 39083149), where this work was initialized. This work was completed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452.
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Bai, Y., Chen, TK. & Korwar, M. QCD-collapsed domain walls: QCD phase transition and gravitational wave spectroscopy. J. High Energ. Phys. 2023, 194 (2023). https://doi.org/10.1007/JHEP12(2023)194
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DOI: https://doi.org/10.1007/JHEP12(2023)194