Prospects of $$|V_{us}|$$ and axial vector form factors in $$\varLambda \rightarrow pe^{-}{\bar{\nu }}_{e}$$ decay at STCF

Abstract We report a feasibility study of the hyperon semileptonic decay $$\varLambda \rightarrow pe^{-} {\bar{\nu }}_{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mo>→</mml:mo> <mml:mi>p</mml:mi> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:math> by using a fast simulation software package at STCF. With an anticipated integrated luminosity of 3.4 trillion $$J/\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> per year at a center-of-mass energy of 3.097 GeV, the statistical sensitivity of the branching fraction is determined to be 0.15%. The statistical sensitivities of form factors $$g_{av}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>av</mml:mi> </mml:mrow> </mml:msub> </mml:math> and $$g_w$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:math> are determined to be 0.4% and 2.15%, respectively. The projected sensitivity of $$|V_{us}|$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>us</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is obtained by combining this result with $$g_1(0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> from Lattice QCD, to be 0.9%, including the systematic uncertainty from the LQCD input and the statistical uncertainties of input branching fraction and form factors. The precise measurement to be obtained at STCF will provide a rigorous test of the Standard Model.