Neutrino self-interaction and weak mixing-angle measurements

Neutrino self-interaction with a larger “Fermi constant” is often resorted to for understanding various puzzles of our Universe. We point out that a light, neutrinophilic scalar particle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ϕ</a:mi></a:math> through radiative correction leads to an energy-scale dependence in the neutrino-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>Z</c:mi></c:math>-boson gauge coupling. The driver behind this phenomenon is a large separation between the mass scales of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ϕ</e:mi></e:math> and additional heavy particles needed for gauge invariance. This is a generic effect insensitive to details of the UV completion. We show that the running can change the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>Z</g:mi><g:mi>ν</g:mi><g:mover accent="true"><g:mi>ν</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math> coupling by several percent and affect the measurement of weak mixing angle through neutrino neutral-current processes. We discuss the interplay between the running of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>Z</k:mi><k:mi>ν</k:mi><k:mover accent="true"><k:mi>ν</k:mi><k:mo stretchy="false">¯</k:mo></k:mover></k:math> coupling and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>sin</o:mi><o:mn>2</o:mn></o:msup><o:msub><o:mi>θ</o:mi><o:mi>W</o:mi></o:msub></o:math> in various experimental observables. It is possible to disentangle the two effects with more than one precise measurement.