Accessing Nucleon Transversity with One-Point Energy Correlators

We propose a novel probe of the nucleon’s transversity distribution <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msubsup> <a:mrow> <a:mi>h</a:mi> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> <a:mrow> <a:mi>q</a:mi> </a:mrow> </a:msubsup> </a:mrow> </a:math> using the one-point energy correlator (OPEC), an infrared-and-collinear safe jet substructure observable. We demonstrate that in transversely polarized <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msup> <c:mrow> <c:mi>p</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">↑</c:mo> </c:mrow> </c:msup> <c:mi>p</c:mi> </c:mrow> </c:math> collisions, the OPEC exhibits a single-spin asymmetry (SSA) with a clean <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mi>sin</f:mi> <f:mo stretchy="false">(</f:mo> <f:msub> <f:mrow> <f:mi>ϕ</f:mi> </f:mrow> <f:mrow> <f:mi>s</f:mi> </f:mrow> </f:msub> <f:mo>−</f:mo> <f:msub> <f:mrow> <f:mi>ϕ</f:mi> </f:mrow> <f:mrow> <f:mi>n</f:mi> </f:mrow> </f:msub> <f:mo stretchy="false">)</f:mo> </f:mrow> </f:math> angular dependence. This method probes SSA over a much wider kinematic range in the angular scale <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:msub> <j:mrow> <j:mi>θ</j:mi> </j:mrow> <j:mrow> <j:mi>n</j:mi> </j:mrow> </j:msub> </j:mrow> </j:math> compared to traditional measurements of hadron transverse momentum <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mrow> <l:msub> <l:mrow> <l:mi>j</l:mi> </l:mrow> <l:mrow> <l:mo>⊥</l:mo> </l:mrow> </l:msub> </l:mrow> </l:math> , establishing a complementary and systematically distinct channel to study the nucleon’s three-dimensional structure at the RHIC and the future electron-ion collider.