Systematic analysis of $$B_s \rightarrow SP$$ decays in perturbative QCD approach

Abstract Within the perturbative QCD (PQCD) framework, we present a systematic investigation of charmless $$B_s \rightarrow SP$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>S</mml:mi> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> decays, where S and P denote scalar and pseudoscalar mesons, respectively. By employing two distinct structural scenarios for scalar mesons, we calculate the branching fractions and direct CP asymmetries for these processes. Our results reveal branching fractions ranging from $$10^{-7}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:msup> </mml:math> to $$10^{-5},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> values that are well within the measurable range of current experiments. A striking contrast emerges between penguin- and tree-dominated decays: while penguin-dominated processes yield larger branching fractions, tree-dominated decays exhibit significantly enhanced direct CP asymmetries. In particular, the decays $$B_s \rightarrow f_0(1370) \eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1370</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>η</mml:mi> </mml:mrow> </mml:math> and $$B_s \rightarrow a_0(1450) K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1450</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> </mml:math> demonstrate marked sensitivity to the choice of scalar meson scenario, offering critical constraints for identifying the optimal model once experimental data are available. Furthermore, we calculate the branching fractions of $$B_s \rightarrow f_0(980)(\sigma )P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>980</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> decays in two distinct ranges of the mixing angle of $$f_0(980)-\sigma .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>980</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>-</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> The dependencies of both branching fractions and CP asymmetries on this mixing angle are rigorously analyzed, establishing a framework essential for determining its value with future experimental results. These findings provide a robust theoretical foundation for advancing the understanding of nonleptonic $$B_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> decays in QCD-based formalisms, as well as the nature of scalar mesons.