Construction of the $$a_4$$ family

Abstract The COMPASS Collaboration recently reported a new broad $$J^{PC}=4^{++}$$ J PC = 4 + + structure, denoted as $$a_4(2610)$$ a 4 ( 2610 ) , which has sparked our interest in studying the $$a_4$$ a 4 family with $$I^GJ^{PC}=1^{-}4^{++}$$ I G J PC = 1 - 4 + + . In this work, we investigate the mass spectra and Okubo–Zweig–Iizuka-allowed two-body strong decays of the $$a_4$$ a 4 family using the modified Godfrey–Isgur quark model and the quark-pair creation model. We also explore the possibility of identifying $$a_4(2610)$$ a 4 ( 2610 ) as a 4 F or 2 H state, and our numerical results suggest that it could be a promising candidate for the $$a_4(2H)$$ a 4 ( 2 H ) state. In addition, we predict the masses and the widths of the $$a_4(1H)$$ a 4 ( 1 H ) and $$a_4(3F)$$ a 4 ( 3 F ) states.