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$2^{++}$ Light Tensor Hybrid Meson from QCD Laplace Sum Rules

Jason Ho, Robin Kleiv, Siyuan Li, Stephan Narison, Tom Steele, Davidson Rabetiarivony

Abstract

We present an analysis of the light tensor ($J^{PC}=2^{++}$) hybrid meson mass and coupling from QCD Laplace Sum Rules where the next-to-leading order (NLO) perturbative (PT) corrections and the contributions of the non-perturbative (NP) condensates up to dimension-six ($D=6$) are included. NLO leading-logarithms corrections due to the condensates which contribute in the chiral limit are considered. We obtain the mass $M_{2^+}= (2038\pm 190)$ MeV and a relatively small coupling $f_{2^+}=(10.5\pm 2.9)$ MeV normalized as $f_π=93$ MeV. Our results suggest that the $f_2(1950)$ or/and the $f'_2(2010)$ may have a sizeable $\bar qqg$ hybrid component. We also compute the tensor hybrid topological charge (value of the two-point function at zero momentum) and find (for the first time) at NLO: $Π_{qg}(0)=(2.41\pm 0.43) \times 10^{-4}{\rm GeV}^6$ which could be checked from some lattice QCD or/and low energy theorems (LET).

$2^{++}$ Light Tensor Hybrid Meson from QCD Laplace Sum Rules

Abstract

We present an analysis of the light tensor () hybrid meson mass and coupling from QCD Laplace Sum Rules where the next-to-leading order (NLO) perturbative (PT) corrections and the contributions of the non-perturbative (NP) condensates up to dimension-six () are included. NLO leading-logarithms corrections due to the condensates which contribute in the chiral limit are considered. We obtain the mass MeV and a relatively small coupling MeV normalized as MeV. Our results suggest that the or/and the may have a sizeable hybrid component. We also compute the tensor hybrid topological charge (value of the two-point function at zero momentum) and find (for the first time) at NLO: which could be checked from some lattice QCD or/and low energy theorems (LET).

Paper Structure

This paper contains 15 sections, 53 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The $2^+$ light hybrid QCD two-point function
  3. The two-point function at LO up to $D=6$ condensates
  4. The lowest Laplace sum rule moments
  5. QCD expression of the Laplace sum rule at LO
  6. QCD input parameters
  7. The lowest Laplace sum rule moment at LO
  8. Higher Laplace sum rule moments at LO
  9. The two-point function at NLO in PT
  10. NLO leading-log contributions of the condensates
  11. Laplace sum rules analysis at NLO
  12. The quest for the $2^{++}$ hybrid topological charge $\Pi_{qg}(0)$
  13. Improved estimate of $\Pi_{qg}(0),\, M_{2^+}$ and $f_{2^+}$
  14. Comments and confrontation with the data
  15. Acknowledgments

Figures (12)

  • Figure 1: QCD expression of the two-point correlator at LO of PT series and including dimension-six condensates contributions. Topologically equivalent permutations of Feynman diagrams are not shown. $\rho$ indicates the deviation from four-quark factorization.
  • Figure 2: $\tau$-behaviour of the hybrid mass for different values of $t_c$ from ${\cal R}^c_{10}$.
  • Figure 3: $\tau$-behaviour of the hybrid coupling for different values of $t_c$ from ${\cal L}_{0}^c$.
  • Figure 4: $\tau$-behaviour of the hybrid mass for different values of $t_c$ from the ratio of moments ${\cal R}^c_{32}$.
  • Figure 5: $\tau$-behaviour of the hybrid coupling for different values of $t_c$ from ${\cal L}^c_{2}$.
  • ...and 7 more figures