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Gravitational form factors of the pion and meson dominance
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abstract
We show that the recent MIT lattice QCD data for the pion's gravitational form factors are, in the covered momentum transfer range, fully consistent with the meson dominance principle. In particular, the $2^{++}$ component can be accurately saturated with the $f_2(1270)$ meson, whereas the $0^{++}$ component with the $\sigma$ meson. To incorporate the large width of the $\sigma$, we use the dispersion relation with the spectral density obtained from analyses of the physical pion scattering data. Effects of the pion mass are estimated within Chiral Perturbation Theory and are found to be small between the lattice and the physical point. We also discuss the implications of the perturbative QCD constraints at high momentum transfers, leading to specific sum rules for the spectral densities of the gravitational form factors, and argue that these densities cannot be of definite sign.
Forward citations
Cited by 4 Pith papers
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Transverse densities of the energy-momentum tensor and the gravitational form factors the pion
The scalar gravitational transverse density of the pion, related to the trace anomaly, must change sign with transverse distance, while the tensor density is positive definite.
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Dispersive Determination of Nucleon Gravitational Form Factors
Using unitarity and dispersion relations, the paper extracts a nucleon D-term of -3.38 and a scalar trace density radius of 0.97 fm at the physical pion mass.
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Gluon Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton Confronted with Lattice Data II
σ-pole residues in gluon D-form factors for π, N, ρ and Δ are consistent with dilaton effective theory predictions within large uncertainties.
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Scalar and tensor meson dominance and gravitational form factors of the pion
Monopole fits to lattice pion gravitational form factors support scalar f0(600) and tensor f2(1270) meson dominance, yield chiral LECs and D(0)=-0.95(3), and expose sum-rule violations needing negative spectral strength.
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