Study of the Λ → p ℓ ν ¯ ℓ Semileptonic Decay in Lattice QCD

We present the first lattice QCD determination of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Λ</a:mi> <a:mo stretchy="false">→</a:mo> <a:mi>N</a:mi> </a:math> vector and axial-vector form factors, which are essential inputs for studying the semileptonic decay <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="normal">Λ</e:mi> <e:mo stretchy="false">→</e:mo> <e:mi>p</e:mi> <e:mo>ℓ</e:mo> <e:msub> <e:mover accent="true"> <e:mi>ν</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mo>ℓ</e:mo> </e:msub> </e:math> . This channel provides a clean, theoretically controlled avenue for extracting the Cabibbo-Kobayashi-Maskawa matrix element <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo stretchy="false">|</k:mo> <k:msub> <k:mi>V</k:mi> <k:mrow> <k:mi>u</k:mi> <k:mi>s</k:mi> </k:mrow> </k:msub> <k:mo stretchy="false">|</k:mo> </k:math> from the baryon sector. Our analysis uses a gauge ensemble with physical light, strange, and charm quark masses and yields the most precise determination to date of the full set of transition form factors—including second-class contributions—as well as the associated couplings, radii, and the ratio of muon-to-electron decay rates, an observable sensitive to possible nonstandard scalar and tensor interactions. We compare our nonperturbative results with next-to-next-to-leading order expansions in the small parameter <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mi>δ</o:mi> <o:mo>=</o:mo> <o:mo stretchy="false">(</o:mo> <o:msub> <o:mrow> <o:mi>m</o:mi> </o:mrow> <o:mrow> <o:mi mathvariant="normal">Λ</o:mi> </o:mrow> </o:msub> <o:mo>−</o:mo> <o:msub> <o:mrow> <o:mi>m</o:mi> </o:mrow> <o:mrow> <o:mi>N</o:mi> </o:mrow> </o:msub> <o:mo stretchy="false">)</o:mo> <o:mo>/</o:mo> <o:msub> <o:mrow> <o:mi>m</o:mi> </o:mrow> <o:mrow> <o:mi mathvariant="normal">Λ</o:mi> </o:mrow> </o:msub> <o:mo>≈</o:mo> <o:mn>0.16</o:mn> </o:mrow> </o:math> . We find that the common phenomenological approximation of neglecting the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>q</u:mi> <u:mn>2</u:mn> </u:msup> </u:math> dependence of the form factors leads to a <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mo>∼</w:mo> <w:mn>4</w:mn> <w:mo>%</w:mo> </w:math> deviation in the decay rate. This underscores the critical importance of precise, fully nonperturbative form factor inputs for achieving the subpercent precision targets of upcoming experimental programs.