Precision measurement of the mass of the hc(P11) state of charmonium

A precision measurement of the mass of the ${h}_{c}(^{1}P_{1})$ state of charmonium has been made using a sample of $24.5\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{6}$ $\\ensuremath{\\psi}(2S)$ events produced in ${e}^{+}{e}^{\\ensuremath{-}}$ annihilation at the Cornell Electron Storage Ring (CESR). The reaction used was $\\ensuremath{\\psi}(2S)\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{0}{h}_{c}$, ${\\ensuremath{\\pi}}^{0}\\ensuremath{\\rightarrow}\\ensuremath{\\gamma}\\ensuremath{\\gamma}$, ${h}_{c}\\ensuremath{\\rightarrow}\\ensuremath{\\gamma}{\\ensuremath{\\eta}}_{c}$, and the reaction products were detected in the CLEO-c detector. Data have been analyzed both for the inclusive reaction and for the exclusive reactions in which ${\\ensuremath{\\eta}}_{c}$ decays are reconstructed in 15 hadronic decay channels. Consistent results are obtained in the two analyses. The averaged results of the present measurements are $M({h}_{c})=3525.28\\ifmmode\\pm\\else\\textpm\\fi{}\\phantom{\\rule{0ex}{0ex}}0.19(\\mathrm{stat}.)\\ifmmode\\pm\\else\\textpm\\fi{}0.12(\\mathrm{syst}.)\\text{ }\\text{ }\\mathrm{MeV}$, and $\\mathcal{B}\\mathbf{(}\\ensuremath{\\psi}(2S)\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{0}{h}_{c}\\mathbf{)}\\ifmmode\\times\\else\\texttimes\\fi{}\\mathcal{B}({h}_{c}\\ensuremath{\\rightarrow}\\ensuremath{\\gamma}{\\ensuremath{\\eta}}_{c})=(4.19\\ifmmode\\pm\\else\\textpm\\fi{}0.32\\ifmmode\\pm\\else\\textpm\\fi{}0.45)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}4}$. Using the $^{3}P_{J}$ centroid mass, $\\ensuremath{\\Delta}{M}_{hf}(1P)\\ensuremath{\\equiv}⟨M({\\ensuremath{\\chi}}_{cJ})⟩\\ensuremath{-}M({h}_{c})=+0.02\\ifmmode\\pm\\else\\textpm\\fi{}0.19\\ifmmode\\pm\\else\\textpm\\fi{}0.13\\text{ }\\text{ }\\mathrm{MeV}$.