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Abstract <p>The masses of pure gauge glueballs are calculated with the use of relativistic string Hamiltonian without fitting parameters. The string tension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma_{f}=0.184\)</EquationSource> <!--NuclPhys2660005Badalian-m1--> </InlineEquation> GeV<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({}^{2}\)</EquationSource> <!--NuclPhys2660005Badalian-m2--> </InlineEquation> in fundamental representation is fixed, using the Necco–Sommer lattice data, and to calculate the vector coupling <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha_{V}(r)\)</EquationSource> <!--NuclPhys2660005Badalian-m3--> </InlineEquation> the value of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\Lambda}_{\overline{MS}}^{0}=238\)</EquationSource> <!--NuclPhys2660005Badalian-m4--> </InlineEquation> MeV (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(N_{f}=0\)</EquationSource> <!--NuclPhys2660005Badalian-m5--> </InlineEquation>) is taken. The spin–spin potential, defined via the vacuum correlation function, is shown to produce a screening effect and decrease a hyperfine splittings between tensor and scalar glueballs. The masses of first and second <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(0^{++}\)</EquationSource> <!--NuclPhys2660005Badalian-m6--> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(2^{++}\)</EquationSource> <!--NuclPhys2660005Badalian-m7--> </InlineEquation> excitations are predicted. For the ground states the masses <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(M(0^{++})=1508\)</EquationSource> <!--NuclPhys2660005Badalian-m8--> </InlineEquation> MeV, <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(M(2^{++})=2292\)</EquationSource> <!--NuclPhys2660005Badalian-m9--> </InlineEquation> MeV (case A), in agreement with those of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(f_{0}\)</EquationSource> <!--NuclPhys2660005Badalian-m10--> </InlineEquation>(1500), <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(f_{2}\)</EquationSource> <!--NuclPhys2660005Badalian-m11--> </InlineEquation>(2300) are obtained, and the first excitation mass <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(M(0^{++})=2613\)</EquationSource> <!--NuclPhys2660005Badalian-m12--> </InlineEquation> MeV is predicted. In case B <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(M(0^{++})=1.669\)</EquationSource> <!--NuclPhys2660005Badalian-m13--> </InlineEquation> MeV, <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(M(2^{++})=2212\)</EquationSource> <!--NuclPhys2660005Badalian-m14--> </InlineEquation> MeV are obtained.</p>

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The Spin–Spin Dynamics of Glueballs

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. M. Badalian,
  • M. S. Lukashov

摘要

Abstract

The masses of pure gauge glueballs are calculated with the use of relativistic string Hamiltonian without fitting parameters. The string tension \(\sigma_{f}=0.184\) GeV \({}^{2}\) in fundamental representation is fixed, using the Necco–Sommer lattice data, and to calculate the vector coupling \(\alpha_{V}(r)\) the value of \({\Lambda}_{\overline{MS}}^{0}=238\) MeV ( \(N_{f}=0\) ) is taken. The spin–spin potential, defined via the vacuum correlation function, is shown to produce a screening effect and decrease a hyperfine splittings between tensor and scalar glueballs. The masses of first and second \(0^{++}\) , \(2^{++}\) excitations are predicted. For the ground states the masses \(M(0^{++})=1508\) MeV, \(M(2^{++})=2292\) MeV (case A), in agreement with those of \(f_{0}\) (1500), \(f_{2}\) (2300) are obtained, and the first excitation mass \(M(0^{++})=2613\) MeV is predicted. In case B \(M(0^{++})=1.669\) MeV, \(M(2^{++})=2212\) MeV are obtained.