Measurement of the CKM angle γ and $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ mixing frequency with $$ {B}_s^0\to {D}_s^{\mp }{h}^{\pm }{\pi}^{\pm }{\pi}^{\mp } $$ decays

Abstract

The CKM angle γ is measured for the first time from mixing-induced CP violation between $$ {B}_s^0\to {D}_s^{\mp }{K}^{\pm }{\pi}^{\pm }{\pi}^{\mp } $$ B s 0 → D s ∓ K ± π ± π ∓ and $$ {\overline{B}}_s^0\to {D}_s^{\pm }{K}^{\mp }{\pi}^{\mp }{\pi}^{\pm } $$ B ¯ s 0 → D s ± K ∓ π ∓ π ± decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 fb−1 recorded with the LHCb detector. A time-dependent amplitude analysis is performed to extract the CP-violating weak phase γ − 2βs and, subsequently, γ by taking the $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ B s 0 ‐ B ¯ s 0 mixing phase βs as an external input. The measurement yields γ = (44 ± 12)° modulo 180°, where statistical and systematic uncertainties are combined. An alternative model-independent measurement, integrating over the five-dimensional phase space of the decay, yields $$ \gamma =\left({44}_{-13}^{+20}\right){}^{\circ} $$ γ = 44 − 13 + 20 ° modulo 180°. Moreover, the $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ B s 0 ‐ B ¯ s 0 oscillation frequency is measured from the flavour-specific control channel $$ {B}_s^0\to {D}_s^{-}{\pi}^{+}{\pi}^{+}{\pi}^{-} $$ B s 0 → D s − π + π + π − to be ∆ms = (17.757 ± 0.007(stat) ± 0.008(syst)) ps−1, consistent with and more precise than the current world-average value.

Simultaneous determination of the charm mixing and CP-violating parameters together with the CKM angle $\gamma$

“…Besides the cascade decays, we considered also measurements of the time-dependent rates of the neutral 𝐵 meson decays to charmed mesons, such as 𝐷 − 𝜋 + and 𝐷 − 𝑠 𝐾 + (𝜋 + 𝜋 − ) [17][18][19]. These decays depend on the CP-violating phase between 𝐵 𝑑,𝑠 mixing (𝜙 𝑑,𝑠 ) and decay (𝛾), as depicted in…”

Two-loop QCD penguin contribution to the width difference in Bs − $$ {\overline{B}}_s $$ mixing

“…B q H and B q L , respectively, and have masses M H,L and widths Γ H,L . The oscillation phenomena involve the three quantities |M q 12 |, |Γ q 12 | and arg(−M q 12 /Γ q 12 ) which are related to the experimentally accessible quantities∆M q = M q H − M q L , ∆Γ q = Γ qL .757 ± 0.007 (stat) ± 0.008 (syst) ) ps −1[4] …”

CP violation in beauty with the LHCb experiment

“…Also the decay mode 0 → − + + − can be similary used for a Δ measurement. The LHCb measurement in this case [3] uses the full statistics available in Run 1 and Run 2, 9 fb −1 . The signal yield, 148,000 events, is smaller but comparable to the 0 → − + analysis.…”

“…ps −1 . A LHCb Δ combination can be performed using 5 statistically independent measurement using the − + [1, 2], − + + − [3] and the / + − [4,5] final states. The corresponding Δ values are shown by the bottom plot in Fig.…”