Resolving the Bethe–Salpeter Kernel

doi:10.1088/0256-307X/38/7/071201

Chin. Phys. Lett.

2021, Vol. 38

Issue (7): 071201 DOI: 10.1088/0256-307X/38/7/071201

THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Resolving the Bethe–Salpeter Kernel

Si-Xue Qin^1* and Craig D. Roberts^2,3*

¹Department of Physics, Chongqing University, Chongqing 401331, China
²School of Physics, Nanjing University, Nanjing 210093, China
³Institute for Nonperturbative Physics, Nanjing University, Nanjing 210093, China

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Si-Xue Qin and Craig D. Roberts 2021 Chin. Phys. Lett. 38 071201

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Abstract A novel method for constructing a kernel for the meson bound-state problem is described. It produces a closed form that is symmetry-consistent (discrete and continuous) with the gap equation defined by any admissible gluon-quark vertex, $\varGamma$. Applicable even when the diagrammatic content of $\varGamma$ is unknown, the scheme can foster new synergies between continuum and lattice approaches to strong interactions. The framework is illustrated by showing that the presence of a dressed-quark anomalous magnetic moment in $\varGamma$, an emergent feature of strong interactions, can remedy many defects of widely used meson bound-state kernels, including the mass splittings between vector and axial-vector mesons and the level ordering of pseudoscalar and vector meson radial excitations.

Received: 18 May 2021 Published: 07 June 2021

PACS:	11.10.St	(Bound and unstable states; Bethe-Salpeter equations)
	11.30.Rd	(Chiral symmetries)
	12.38.Lg	(Other nonperturbative calculations)
	24.85.+p	(Quarks, gluons, and QCD in nuclear reactions)

Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11805024 and 11947406).

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https://cpl.iphy.ac.cn/10.1088/0256-307X/38/7/071201 OR https://cpl.iphy.ac.cn/Y2021/V38/I7/071201

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	Si-Xue Qin and Craig D. Roberts

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