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${\frac {{\rm {d}}^{3}N}{{\rm {d}}p_{t}^{2}{\rm {d}}\phi {\rm {d}}y}}={\frac {{\rm {d}}^{2}N}{2\pi {\rm {d}}p_{t}^{2}{\rm {d}}y}}[1+2\sum _{n}{v_{n}{\rm {cos}}(n(\phi -\Psi _{R}))}]$

A further analysis focuses on an exclusive $b$-decay mode, namely $B_{d}\rightarrow J/\psi K_{S}^{0}$, which is one of a number of decays that are interesting for studies of CP violation in the B system.

In the Standard Model $B_{d}^{0}-{\overline {B_{d}^{0}}}$ mixing is a direct consequence of second order weak interactions. Starting with a $B_{d}^{0}$ meson produced at time $t$=0, the probability, ${\mathcal {P}}$, to observe a ${\overline {B_{d}^{0}}}$ decaying at the proper time Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} can be written, neglecting effects from ${\mathcal {CP}}$ violation: ${\mathcal {P}}(B_{d}^{0}\rightarrow {\overline {B_{d}^{0}}})~=~{\frac {\Gamma _{d}}{2}}e^{-\Gamma _{d}t}[\cosh({\frac {\Delta \Gamma _{d}}{2}}t)~+~\cos(\Delta m_{d}t)]$. Here Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma_d~=~\frac{\Gamma_d^H~+~\Gamma_d^L}{2}} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta \Gamma_d~=~\Gamma_d^H -\Gamma_d^L} , and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta m_d~=~m^H_d~-~m^L_d} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L} denote respectively the heavy and light physical states.

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