Improved constraints on exotic electron-proton interactions in hydrogen

Atomic spectroscopy provides a sensitive tool for searching for new bosons that mediate exotic forces between elementary fermions. A comparison between a recent high-precision measurement [Bullis , ] of the hyperfine splitting of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>2</a:mn> <a:msub> <a:mi>S</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> electronic level in hydrogen and up-to-date bound-state quantum electrodynamics calculations yields improved constraints on electron-proton exotic interactions. These are expressed in terms of the dimensionless coupling strengths <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>g</b:mi> <b:mi>A</b:mi> </b:msub> <b:msub> <b:mi>g</b:mi> <b:mi>A</b:mi> </b:msub> </b:mrow> <b:mo>,</b:mo> <b:mo> </b:mo> <b:mrow> <b:msub> <b:mi>g</b:mi> <b:mi>p</b:mi> </b:msub> <b:msub> <b:mi>g</b:mi> <b:mi>p</b:mi> </b:msub> </b:mrow> </b:math> , and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>g</c:mi> <c:mi>V</c:mi> </c:msub> <c:msub> <c:mi>g</c:mi> <c:mi>V</c:mi> </c:msub> </c:mrow> </c:math> , corresponding to the exchange of axial-vector, pseudoscalar (axionlike), and vector bosons, respectively. Building on these results, our analysis highlights the importance of examining combinations of spin-dependent potentials that contribute to the same class of exotic interactions. In particular, we employ the combination <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>V</d:mi> <d:mn>2</d:mn> </d:msub> <d:mo>+</d:mo> <d:msub> <d:mi>V</d:mi> <d:mn>3</d:mn> </d:msub> </d:mrow> </d:math> for both axial-vector–axial-vector and vector-vector couplings. These findings motivate further precision measurements toward spin-dependent exotic interactions.