Abstract
Non-perturbative results in QCD-like theories can be derived employing positivity of the Euclidean path integral measure, as pioneered by Weingarten, Vafa, and Witten. We show that positivity of the measure can be generalized to parity-invariant theories with Yukawa couplings to fundamental scalars, provided the fermions are Dirac and carry a real representation of the gauge group. This result allows us to demonstrate the conservation of parity and vector-like flavor symmetries in such theories, as well as to derive exact inequalities among hadrons’ masses.
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Acknowledgments
We are grateful to L-X. Xu for collaborating in the early stages of the project and for pointing out a mistake in our original proof of P-conservation. LV would also like to thank D. Cassani, M. Frigerio, M. Knecht, D. Schaich, and A. Wulzer for discussions. This research was partly supported by the Italian MIUR under contract 2017FMJFMW (PRIN2017), the “iniziativa specifica” Physics at the Energy, Intensity, and Astroparticle Frontiers (APINE) of Istituto Nazionale di Fisica Nucleare (INFN), and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 860881-HIDDeN. AV has also received funding from the Swiss National Science Foundation (SNF) through the Eccellenza Professorial Fellowship “Flavor Physics at the High Energy Frontier”, project number 186866.
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Valenti, A., Vecchi, L. Vector-like symmetries and parity conservation in gauge theories with Yukawa couplings. J. High Energ. Phys. 2024, 52 (2024). https://doi.org/10.1007/JHEP02(2024)052
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DOI: https://doi.org/10.1007/JHEP02(2024)052