Study of the semileptonic decay Λ → p ℓ ν ¯ ℓ in QCD

We conduct a comprehensive study of the semileptonic decay process <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>p</a:mi> <a:mo>ℓ</a:mo> <a:msub> <a:mover accent="true"> <a:mi>ν</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mo>ℓ</a:mo> </a:msub> </a:math> , focusing on the determination of all six vector and axial-vector form factors that govern the low-energy hadronic matrix elements of the underlying theory. These invariant form factors constitute the essential inputs for describing the decay, and their dependence on the momentum transfer <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>q</g:mi> <g:mn>2</g:mn> </g:msup> </g:math> is analyzed across the entire physical kinematic region. To parametrize the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>q</i:mi> <i:mn>2</i:mn> </i:msup> </i:math> dependence, we adopt both the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>z</k:mi> </k:math> -expansion formalism and a polynomial fitting approach. Utilizing these parametrizations, we compute the exclusive decay widths for both the electron and muon channels and subsequently extract the corresponding branching ratios. Furthermore, we evaluate the ratio of decay widths between the muon and electron channels defined as <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:msup> <m:mrow> <m:mi>R</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mi>e</m:mi> </m:mrow> </m:msup> <m:mo>≡</m:mo> <m:mfrac> <m:mrow> <m:mi mathvariant="normal">Γ</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi mathvariant="normal">Λ</m:mi> <m:mo stretchy="false">→</m:mo> <m:mi>p</m:mi> <m:mi>μ</m:mi> <m:msub> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>ν</m:mi> </m:mrow> <m:mrow> <m:mo stretchy="false">¯</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>μ</m:mi> </m:mrow> </m:msub> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mrow> <m:mi mathvariant="normal">Γ</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi mathvariant="normal">Λ</m:mi> <m:mo stretchy="false">→</m:mo> <m:mi>p</m:mi> <m:mi>e</m:mi> <m:msub> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>ν</m:mi> </m:mrow> <m:mrow> <m:mo stretchy="false">¯</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>e</m:mi> </m:mrow> </m:msub> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mfrac> </m:mrow> </m:math> obtaining <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mrow> <cb:msup> <cb:mrow> <cb:mi>R</cb:mi> </cb:mrow> <cb:mrow> <cb:mi>μ</cb:mi> <cb:mi>e</cb:mi> </cb:mrow> </cb:msup> <cb:mo>=</cb:mo> <cb:mn>0.19</cb:mn> <cb:msubsup> <cb:mrow> <cb:mn>6</cb:mn> </cb:mrow> <cb:mrow> <cb:mo>−</cb:mo> <cb:mn>0.012</cb:mn> </cb:mrow> <cb:mrow> <cb:mo>+</cb:mo> <cb:mn>0.009</cb:mn> </cb:mrow> </cb:msubsup> </cb:mrow> </cb:math> from the polynomial fit and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msup> <eb:mi>R</eb:mi> <eb:mrow> <eb:mi>μ</eb:mi> <eb:mi>e</eb:mi> </eb:mrow> </eb:msup> <eb:mo>=</eb:mo> <eb:mn>0.17</eb:mn> <eb:msubsup> <eb:mn>4</eb:mn> <eb:mrow> <eb:mo>−</eb:mo> <eb:mn>0.005</eb:mn> </eb:mrow> <eb:mrow> <eb:mo>+</eb:mo> <eb:mn>0.002</eb:mn> </eb:mrow> </eb:msubsup> </eb:math> from the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>z</gb:mi> </gb:math> expansion. While both ratios are compatible with previously reported values in the literature, the result from the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>z</ib:mi> </ib:math> expansion exhibits particularly strong agreement with the averages reported by the Particle Data Group.