2016/12/05 by Meng-Lin Du, Feng-Kun Guo, Ulf-G Meißner
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.1088/0954-3899/44/1/014001
openalex created_date 2016/07/22 · openalex publication_date 2016/12/05 · openalex updated_date 2026/07/30
Abstract We perform the leading one-loop renormalization of the chiral Lagrangian for spinless matter fields living in the fundamental representation of SU( N ). The Lagrangian can also be applied to any theory with a spontaneous symmetry breaking of SU( N ) L × SU( N ) R to SU <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> </mml:math> and spinless matter fields in the fundamental representation. For QCD, the matter fields can be kaons or pseudoscalar heavy mesons. Using the background field method and heat kernel expansion techniques, the divergences of the one-loop effective generating functional for correlation functions of single matter fields are calculated up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , where p denotes a small momentum or Goldstone boson mass. The divergences are absorbed by counterterms not only from the third order but also from the second order chiral Lagrangian.