Abstract
We demonstrate that the true QCD axion that solves the strong CP problem can be found in all generality outside the customary standard QCD band, with QCD being the sole source of Peccei-Quinn breaking. The essential reason is that the basis of axion-gluon interactions does not need to coincide with the mass basis. Specifically, we consider the case in which the QCD axion field is not the only singlet scalar in Nature but it mixes with other singlet scalars (besides the η′). We determine the exact mathematical condition for an arbitrary N-scalar potential to be Peccei-Quinn invariant. Such potentials provide extra sources of mass for the customary axion without enlarging the Standard Model gauge symmetry. The contribution to the axion mass stemming from the QCD topological susceptibility is shown to be shared then among the N axion eigenstates through a precise sum rule. Their location can only be displaced to the right of the standard QCD band. We demonstrate that the axion closest to this band can be displaced from it by a factor of \( \sqrt{N} \) at most, and this corresponds to the case in which all axion signals are maximally deviated. Conversely, if one axion is found on the standard QCD band, the other eigenstates will be out of experimental reach. Our results imply that any ALP experiment which finds a signal to the right of the standard QCD axion band can be solving the strong CP problem within QCD, with the associated N − 1 excitations to be found in an area of parameter space that we determine. We illustrate the results and phenomenology in some particular cases.
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Acknowledgments
We thank Tony Gherghetta, Benjamin Grinstein, David Kaplan, Aneesh Manohar, Hans Peter Nilles and Steve Parke for interesting discussions. We are also indebted to Daniel Alvarez-Gavela for useful discussions and input, and to Anna Lewis for helping to improve the writing of the manuscript. This project has received funding /support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 860881-HIDDeN, and under the Marie Sklodowska-Curie Staff Exchange grant agreement No 101086085-ASYMMETRY. The work of M. R. is supported by the Marie Sklodowska-Curie grant agreement No 860881-HIDDeN. The work of P.Q. is supported in part by the U.S. Department of Energy Grant No. DE-SC0009919. B. G. acknowledge as well partial financial support from the Spanish Research Agency (Agencia Estatal de Investigación) through the grant IFT Centro de Excelencia Severo Ochoa No CEX2020-001007-S and through the grant PID2019-108892RB-I00 funded by MCIN/AEI/10.13039/501100011033. B.G. thanks very much the Particle Physics group of the University of California San Diego, where part of this work was carried out. Likewise, P. Q. thanks the Galileo-Galilei Institute for theoretical Physics in Florence (GGI) for their warm hospitality, where part of this work was carried out.
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Gavela, B., Quílez, P. & Ramos, M. The QCD axion sum rule. J. High Energ. Phys. 2024, 56 (2024). https://doi.org/10.1007/JHEP04(2024)056
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DOI: https://doi.org/10.1007/JHEP04(2024)056