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arXiv · 2209.13120

Four-quark scatterings in QCD I

Wei-jie Fu·Chuang Huang·Jan M. Pawlowski·Yang-yang Tan
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Abstract

We investigate dynamical chiral symmetry breaking and the emergence of mesonic bound states from the infrared dynamics of four-quark scatterings. Both phenomena originate from the resonant scalar-pseudoscalar channel of the four-quark scatterings, and we compute the functional renormalisation group (fRG) flows of the Fierz-complete four-quark interaction of up and down quarks with its $t$ channel momentum dependence. This is done in the isospin symmetric case, also including the flow of the quark two-point function. This system can be understood as the fRG analogues of the complete Bethe-Salpeter equations and quark gap equation. The pole mass of the pion is determined from both direct calculations of the four-quark flows in the Minkowski regime of momenta and the analytic continuation based on results in the Euclidean regime, which are consistent with each other.

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Wei-jie Fu, Chuang Huang, Jan M. Pawlowski, Yang-yang Tan. 2022-09-27. Four-quark scatterings in QCD I. https://doi.org/10.21468/scipostphys.14.4.069

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