2026/02/28 by Anonymous, Vincenzo Cirigliano, Martin Hoferichter +1
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ex #hep-lat #hep-ph #nucl-ex #nucl-th
paper · pdf · doi:10.1103/rg2q-m515
published as Phys. Rev. Lett. 137, 051902 (2026) · 13 pages, 2 figures; journal version
openalex publication_date 2026/06/24 · openalex created_date 2026/06/25 · arxiv created 2026/07/30 · arxiv updated 2026/07/31 · openalex updated_date 2026/07/31
The consistent matching of short-distance contributions and hadronic matrix elements is crucial for precise predictions of weak processes involving hadrons. In this Letter, we address this point for charged-current processes involving two pions—pion <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>β</a:mi> </a:math> decay <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msup> <c:mrow> <c:mi>π</c:mi> </c:mrow> <c:mrow> <c:mo>±</c:mo> </c:mrow> </c:msup> <c:mo stretchy="false">→</c:mo> <c:msup> <c:mrow> <c:mi>π</c:mi> </c:mrow> <c:mrow> <c:mn>0</c:mn> </c:mrow> </c:msup> <c:msup> <c:mrow> <c:mi>e</c:mi> </c:mrow> <c:mrow> <c:mo>±</c:mo> </c:mrow> </c:msup> <c:msub> <c:mrow> <c:mi>ν</c:mi> </c:mrow> <c:mrow> <c:mi>e</c:mi> </c:mrow> </c:msub> </c:mrow> </c:math> and hadronic <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>τ</f:mi> </f:math> decays <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>τ</h:mi> <h:mo>±</h:mo> </h:msup> <h:mo stretchy="false">→</h:mo> <h:msup> <h:mi>π</h:mi> <h:mo>±</h:mo> </h:msup> <h:msup> <h:mi>π</h:mi> <h:mn>0</h:mn> </h:msup> <h:msub> <h:mi>ν</h:mi> <h:mi>τ</h:mi> </h:msub> </h:math> —whose decay rates depend on the so-called <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>γ</k:mi> <k:mi>W</k:mi> </k:math> box correction. Using recent results from lattice QCD, we show how to formulate the matching beyond leading-logarithmic accuracy, in particular, how to cancel the dependence on the scheme choice for evanescent operators. As main results, we obtain a prediction for the decay rate of pion <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>β</m:mi> </m:math> decay with theory uncertainties improved by a factor of 3, which renders theory uncertainties negligible for future determinations of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>V</o:mi> <o:mrow> <o:mi>u</o:mi> <o:mi>d</o:mi> </o:mrow> </o:msub> </o:math> even beyond the reach of the PIONEER experiment, and an evaluation of isospin-breaking corrections to <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>τ</q:mi> <q:mo stretchy="false">→</q:mo> <q:mi>π</q:mi> <q:mi>π</q:mi> <q:msub> <q:mi>ν</q:mi> <q:mi>τ</q:mi> </q:msub> </q:math> with negligible uncertainty from the short-distance matching, as necessary for a future <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>τ</t:mi> </t:math> -based determination of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon.