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<p>We calculate the scattering amplitude in the two dimensional <i>CP</i> (1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to the <i>O</i>(<i>N</i>) model, for all <i>N</i>. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories.</p>

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Renormalization and running in the 2D CP (1) model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月21日

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  • Diego Buccio,
  • John F. Donoghue,
  • Gabriel Menezes,
  • Roberto Percacci

摘要

We calculate the scattering amplitude in the two dimensional CP (1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to the O(N) model, for all N. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories.