Aad G.Abbott B.Abbott D. C.Abeling K.Abidi S. H.Aboulhorma A.Abramowicz H.Abreu H.Abulaiti Y.Abusleme Hoffman A. C.Acharya B. S.Achkar B.Adam L.Adam Bourdarios C.Adamczyk L.Adamek L.Addepalli S. V.Adelman J.Adiguzel A.Adorni S.Adye T.Affolder A. A.Afik Y.Agaras M. N.Agarwala J.Aggarwal A.Agheorghiesei C.Aguilar-Saavedra J. A.Ahmad A.Ahmadov F.Ahmed W. S.Ai X.Aielli G.Aizenberg I.Akbiyik M.Akesson T. P. A.Akimov A. V.Al Khoury K.Alberghi G. L.Albert J.2025-05-192025-05-192023/09/051434-6044http://dx.doi.org/10.1140/epjc/s10052-023-11869-1https://publicacionesabiertas.userena.cl/handle/123456789/312Searches for the exclusive decays of Higgs and Z bosons into a vector quarkonium state and a photon are performed in the mu(+)mu(-) gamma final state with a proton-proton collision data sample corresponding to an integrated luminosity of 139 fb(-1) collected at root s = 13 TeV with the ATLAS detector at the CERN Large Hadron Collider. The observed data are compatible with the expected backgrounds. The 95% confidence-level upper limits on the branching fractions of the Higgs boson decays into J/psi gamma, psi(2S)gamma, and Upsilon(1S, 2S, 3S)gamma are found to be 2.0 x 10(-4), 10.5x10(-4), and (2.5, 4.2, 3.4) x10(-4), respectively, assuming Standard Model production of the Higgs boson. The corresponding 95% CL upper limits on the branching fractions of the Z boson decays are 1.2 x 10(-6), 2.4 x 10(-6), and (1.1, 1.3, 2.4) x10(-6). An observed 95% CL interval of (-133, 175) is obtained for the kappa(c)/kappa(gamma) ratio of Higgs boson coupling modifiers, and a 95% CL interval of (-37, 40) is obtained for kappa(b)/kappa(gamma).HIERARCHY, MASSArticle