Predicting isovector charmonium-like states from X(3872) properties

Abstract

Using chiral effective field theory, we predict that there must be isovector charmonium-like DD¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ D{\\overline{D}}^{\\ast } $$\\end{document} hadronic molecules with JPC = 1++ denoted as Wc1. The inputs are the properties of the X(3872), including its mass and the ratio of its branching fractions of decays into J/ψρ0 and J/ψω. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the X(3872) as well as its spin partners. They should show up as either a mild cusp or dip at the DD¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ D{\\overline{D}}^{\\ast } $$\\end{document} thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the X(3872) is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the X(3872) signal dominates over that from the Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document}. The pole positions are 3881.2−0.0+0.8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {3881.2}_{-0.0}^{+0.8} $$\\end{document}−i1.6−0.9+0.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ i{1.6}_{-0.9}^{+0.7} $$\\end{document} MeV for Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document} on the fourth Riemann sheet of the D0D¯∗0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {D}^0{\\overline{D}}^{\\ast 0} $$\\end{document}-D+D∗− coupled-channel system, and 3866.9−7.7+4.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {3866.9}_{-7.7}^{+4.6} $$\\end{document}− i(0.07 ± 0.01) MeV for Wc1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^{\\pm } $$\\end{document} on the second Riemann sheet of the DD¯∗±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left(D{\\overline{D}}^{\\ast}\\right)}^{\\pm } $$\\end{document} single-channel system. The findings imply that the peak in the J/ψπ+π− invariant mass distribution is not purely from the X(3872) but contains contributions from Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document} predicted here. The states should have isovector heavy quark spin partners with JPC = 0++, 2++ and 1+−, with the last one corresponding to Zc. We suggest to search for the charged 0++, 1++ and 2++ states in J/ψπ±π0.