Low-Energy Constants of Chiral Perturbation Theory from Pion Scalar Form Factors in $N_f=2+1$-Flavor Lattice QCD with Controlled Errors
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2025
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| author | von Hippel, Georg Ottnad, Konstantin |
| author_facet | von Hippel, Georg Ottnad, Konstantin |
| contents | We determine the low-energy constants (LECs) $f_0$, $L_4^r$ and $L_5^r$ of SU(3) Chiral Perturbation Theory ($χ$PT) from a lattice QCD calculation of the scalar form factors of the pion with fully controlled systematics. Lattice results are computed on a large set of $N_f=2+1$ gauge ensembles covering four lattice spacings $a\in[0.049,0.086]\mathrm{fm}$, pion masses $M_π\in[130,350]\mathrm{MeV}$, and various large physical volumes. By determining the notorious quark-disconnected contributions with unprecedented precision and using a large range of source-sink separations $t_\mathrm{sep}\in[1.0,3.25]\mathrm{fm}$, we are able for the first time to obtain the scalar radii from a $z$-expansion parameterization of the form factors rather than a simple linear approximation at small momentum transfer. The LECs are obtained from the physical extrapolation of the radii using NLO SU(3) NLO $χ$PT to parameterize the quark mass dependence. Systematic uncertainties are estimated via model averages based on the Akaike Information Criterion. Our determination of $L_4^r$ is the first lattice determination to obtain a result not compatible with zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_20689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-Energy Constants of Chiral Perturbation Theory from Pion Scalar Form Factors in $N_f=2+1$-Flavor Lattice QCD with Controlled Errors von Hippel, Georg Ottnad, Konstantin High Energy Physics - Lattice High Energy Physics - Phenomenology We determine the low-energy constants (LECs) $f_0$, $L_4^r$ and $L_5^r$ of SU(3) Chiral Perturbation Theory ($χ$PT) from a lattice QCD calculation of the scalar form factors of the pion with fully controlled systematics. Lattice results are computed on a large set of $N_f=2+1$ gauge ensembles covering four lattice spacings $a\in[0.049,0.086]\mathrm{fm}$, pion masses $M_π\in[130,350]\mathrm{MeV}$, and various large physical volumes. By determining the notorious quark-disconnected contributions with unprecedented precision and using a large range of source-sink separations $t_\mathrm{sep}\in[1.0,3.25]\mathrm{fm}$, we are able for the first time to obtain the scalar radii from a $z$-expansion parameterization of the form factors rather than a simple linear approximation at small momentum transfer. The LECs are obtained from the physical extrapolation of the radii using NLO SU(3) NLO $χ$PT to parameterize the quark mass dependence. Systematic uncertainties are estimated via model averages based on the Akaike Information Criterion. Our determination of $L_4^r$ is the first lattice determination to obtain a result not compatible with zero. |
| title | Low-Energy Constants of Chiral Perturbation Theory from Pion Scalar Form Factors in $N_f=2+1$-Flavor Lattice QCD with Controlled Errors |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2503.20689 |