Different origins of running in the 2D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi><mml:mi mathvariant="double-struck">P</mml:mi><mml:mo stretchy="false">(</mml:mo>

We revisit the computation of the beta function in the two-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="double-struck">CP</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum-independent tadpoles or even UV-finite bubble diagrams. We also comment on the relation between the beta functions and the energy dependence of scattering amplitudes. Published by the American Physical Society 2024