Prospect for measurement of CP-violating observables in $$ {B}_s^0\to {D}_s^{\mp }{K}^{\pm } $$ decays at a future Z factory

A bstract A precise determination of the CKM angle γ from $$ {B}_s^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math> oscillations in $$ {B}_s^0\to {D}_s^{\mp }{K}^{\pm } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>∓</mml:mo> </mml:msubsup> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math> decays offers a critical test of the Standard Model and probes for new physics. We present a comprehensive study on the prospects of measuring γ at a future Tera- Z factory, utilizing the baseline detector concept of the Circular Electron Positron Collider (CEPC). A two-dimensional simultaneous fit framework, incorporating flavor tagging, decay time resolution modeling, and acceptance corrections, is developed using full Monte Carlo simulations of $$ {B}_s^0\to {D}_s^{\mp}\left(\to {K}^{\mp }{K}^{\pm }{\pi}^{\mp}\right){K}^{\pm } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>∓</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mrow> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>∓</mml:mo> </mml:msup> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>±</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>∓</mml:mo> </mml:msup> </mml:mrow> </mml:mfenced> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math> decays and inclusive background processes. The effective flavor tagging power reaches 23.6%, while the decay time resolution is determined to be 26 fs. Projecting to full statistics of signal events across three dominant $$ {D}_s^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:math> decay channels, we estimate a statistical precision of σ ( γ ) = 0 . 69 ° , which corresponds to 4.1 Tera- Z boson equivalent data. This study has established the feasibility of sub-degree level γ measurements at a Z factory, highlighting its unique advantages in time-dependent CP violation studies through ultra-precise vertexing and background suppression capabilities.