Axial-vector leptophilic fifth force sourced by solar neutrinos

We investigate long-range, purely leptophilic axial-vector interactions mediated by a light gauge boson <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>A</a:mi> <a:mo>′</a:mo> </a:msup> </a:math> that couples to charged leptons and, by weak symmetry, to left-handed neutrinos. We analyze two realizations, a minimal effective model with muon-only couplings and an anomaly-free axial <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>U</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>1</c:mn> <c:msup> <c:mo stretchy="false">)</c:mo> <c:mo>′</c:mo> </c:msup> </c:math> with intergeneration cancelations. In both cases, the solar neutrino flux acts as an extended current that sources a macroscopic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>A</g:mi> <g:mo>′</g:mo> </g:msup> </g:math> field at Earth, with spatial components aligned along the Sun-Earth direction. This field produces a distinctive signature in storage-ring measurements of the muon anomalous magnetic moment, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo stretchy="false">(</i:mo> <i:mi>g</i:mi> <i:mo>−</i:mo> <i:mn>2</i:mn> <i:msub> <i:mo stretchy="false">)</i:mo> <i:mi>μ</i:mi> </i:msub> </i:math> , namely a diurnal, sign-changing contribution that is positive during daytime and negative at night, superimposed on a time-independent positive offset. We obtain bounds <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>g</m:mi> <m:mo>′</m:mo> </m:msup> <m:mo>≲</m:mo> <m:mi mathvariant="script">O</m:mi> <m:mo stretchy="false">(</m:mo> <m:msup> <m:mn>10</m:mn> <m:mrow> <m:mo>−</m:mo> <m:mn>19</m:mn> </m:mrow> </m:msup> <m:mo stretchy="false">)</m:mo> </m:math> in both model frameworks for a light, effectively massless mediator. For completeness, we map the solar-neutrino–sourced potential to electron spin-sensor experiments and find <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msup> <r:mi>g</r:mi> <r:mo>′</r:mo> </r:msup> <r:mo>≲</r:mo> <r:mi mathvariant="script">O</r:mi> <r:mo stretchy="false">(</r:mo> <r:msup> <r:mn>10</r:mn> <r:mrow> <r:mo>−</r:mo> <r:mn>22</r:mn> </r:mrow> </r:msup> <r:mo stretchy="false">)</r:mo> </r:math> in the electron channel.