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1. Measurement of CP asymmetry in $$ {\textrm{B}}_{\textrm{s}}^0\to {\textrm{D}}_{\textrm{s}}^{\mp }{\textrm{K}}^{\pm } $$ decays

   https://doi.org/10.1007/JHEP03(2025)139  

   Aaij, R; Abdelmotteleb, A_S W; Abellan_Beteta, C; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> A measurement of theCP-violating parameters in$$ {B}_s^0\boldsymbol{\to}{D}_s^{\mp }{K}^{\pm} $$ $B_s^0\to D_s^{\mp }{K}^{\pm }$decays is reported, based on the analysis of proton-proton collision data collected by the LHCb experiment corresponding to an integrated luminosity of 6 fb⁻¹at a centre-of-mass energy of 13 TeV. The measured parameters are obtained with a decay-time dependent analysis yieldingC_f= 0.791 ± 0.061 ± 0.022,$$ {A}_f^{\Delta \Gamma} $$ $A_f^{\text{∆}\Gamma }$= −0.051 ± 0.134 ± 0.058,$$ {A}_{\overline{f}}^{\Delta \Gamma} $$ $A_{\overline{f}}^{\text{∆}\Gamma }$= −0.303 ± 0.125 ± 0.055,S_f= −0.571 ± 0.084 ± 0.023 and$$ {S}_{\overline{f}} $$ $S_{\overline{f}}$= −0.503 ± 0.084 ± 0.025, where the first uncertainty is statistical and the second systematic. This corresponds to CP violation in the interference between mixing and decay of about 8.6σ. Together with the value of the$$ {B}_s^0 $$ $B_s^0$mixing phase −2β_s, these parameters are used to obtain a measurement of the CKM angleγequal to (74 ± 12)° modulo 180°, where the uncertainty contains both statistical and systematic contributions. This result is combined with the previous LHCb measurement in this channel using 3 fb⁻¹resulting in a determination of$$ \gamma ={\left({81}_{-11}^{+12}\right)}^{\circ } $$ $\gamma ={\left({81}_{-11}^{+12}\right)}^{\circ }$. 

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2. Spin density matrix elements in exclusive $$\rho ^0$$ meson muoproduction

   https://doi.org/10.1140/epjc/s10052-023-11359-4  

   Alexeev, G D; Alexeev, M G; Alice, C; Amoroso, A; Andrieux, V; Anosov, V; Augsten, K; Augustyniak, W; Azevedo, C_D R; Badelek, B; et al (October 2023, The European Physical Journal C)

   Abstract We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive$$\rho ^0$$ ${\rho }^0$meson muoproduction at COMPASS using 160 GeV/cpolarised$$ \mu ^{+}$$ ${\mu }^{+}$and$$ \mu ^{-}$$ ${\mu }^{-}$beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/$$c^2$$ $c^2$$$< W<$$ $<W<$17.0 GeV/$$c^2$$ $c^2$, 1.0 (GeV/c)$$^2$$ ${}^2$$$< Q^2<$$ $<Q^2<$10.0 (GeV/c)$$^2$$ ${}^2$and 0.01 (GeV/c)$$^2$$ ${}^2$$$< p_{\textrm{T}}^2<$$ $<p_{\text{T}}^2<$0.5 (GeV/c)$$^2$$ ${}^2$. Here,Wdenotes the mass of the final hadronic system,$$Q^2$$ $Q^2$the virtuality of the exchanged photon, and$$p_{\textrm{T}}$$ $p_{\text{T}}$the transverse momentum of the$$\rho ^0$$ ${\rho }^0$meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($$\gamma ^*_T \rightarrow V^{ }_L$$ ${\gamma }_T^{\ast }\to V_L^{}$) indicate a violation ofs-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive$$\rho ^0$$ ${\rho }^0$production. 

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3. Measurement of the e+e− → $$ {B}_s^0{\overline{B}}_s^0X $$ cross section in the energy range from 10.63 to 11.02 GeV using inclusive $$ {D}_s^{+} $$ and D0 production

   https://doi.org/10.1007/JHEP08(2023)131  

   Zhukova, V; Mizuk, R; Adachi, I; Aihara, H; Al_Said, S; Asner, D M; Atmacan, H; Aulchenko, V; Aushev, T; Ayad, R; et al (August 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We report the first measurement of the inclusivee⁺e⁻→$$ b\overline{b} $$ $b\overline{b}$→$$ {D}_s^{\pm } $$ $D_s^{\pm }$Xande⁺e⁻→$$ b\overline{b} $$ $b\overline{b}$→ D⁰/$$ {\overline{D}}^0 $$ ${\overline{D}}^0$Xcross sections in the energy range from 10.63 to 11.02 GeV. Based on these results, we determineσ(e⁺e⁻→$$ {B}_s^0{\overline{B}}_s^0 $$ $B_s^0{\overline{B}}_s^0$X) andσ(e⁺e⁻→$$ B\overline{B} $$ $B\overline{B}$X) in the same energy range. We measure the fraction of$$ {B}_s^0 $$ $B_s^0$events at Υ(10860) to bef_s= ($$ {22.0}_{-2.1}^{+2.0} $$ ${22.0}_{-2.1}^{+2.0}$)%. We determine also the ratio of the$$ {B}_s^0 $$ $B_s^0$inclusive branching fractions$$ \mathcal{B} $$ $B$($$ {B}_s^0 $$ $B_s^0$→ D⁰/$$ {\overline{D}}^0 $$ ${\overline{D}}^0$X)/$$ \mathcal{B} $$ $B$($$ {B}_s^0 $$ $B_s^0$→$$ {D}_s^{\pm } $$ $D_s^{\pm }$X) = 0.416 ± 0.018 ± 0.092. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energye⁺e⁻collider. 

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4. Spherical convex hull of random points on a wedge

   https://doi.org/10.1007/s00208-023-02704-9  

   Besau, Florian; Gusakova, Anna; Reitzner, Matthias; Schütt, Carsten; Thäle, Christoph; Werner, Elisabeth_M (August 2023, Mathematische Annalen)

   Abstract Consider two half-spaces$$H_1^+$$ $H_1^{+}$and$$H_2^+$$ $H_2^{+}$in$${\mathbb {R}}^{d+1}$$ $R^{d+1}$whose bounding hyperplanes$$H_1$$ $H_1$and$$H_2$$ $H_2$are orthogonal and pass through the origin. The intersection$${\mathbb {S}}_{2,+}^d:={\mathbb {S}}^d\cap H_1^+\cap H_2^+$$ $S_{2,+}^d:=S^d\cap H_1^{+}\cap H_2^{+}$is a spherical convex subset of thed-dimensional unit sphere$${\mathbb {S}}^d$$ $S^d$, which contains a great subsphere of dimension$$d-2$$ $d-2$and is called a spherical wedge. Choosenindependent random points uniformly at random on$${\mathbb {S}}_{2,+}^d$$ $S_{2,+}^d$and consider the expected facet number of the spherical convex hull of these points. It is shown that, up to terms of lower order, this expectation grows like a constant multiple of$$\log n$$ $logn$. A similar behaviour is obtained for the expected facet number of a homogeneous Poisson point process on$${\mathbb {S}}_{2,+}^d$$ $S_{2,+}^d$. The result is compared to the corresponding behaviour of classical Euclidean random polytopes and of spherical random polytopes on a half-sphere. 

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5. Measurement of CP violation in B0 → D+D− and $$ {\textrm{B}}_{\textrm{s}}^0 $$ → $$ {\textrm{D}}_{\textrm{s}}^{+}{\textrm{D}}_{\textrm{s}}^{-} $$ decays

   https://doi.org/10.1007/JHEP01(2025)061  

   Aaij, R; Abdelmotteleb, A_S W; Abellan_Beteta, C; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (January 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> A time-dependent, flavour-tagged measurement ofCPviolation is performed withB⁰→ D⁺D⁻and$$ {B}_s^0 $$ $B_s^0$→$$ {D}_s^{+}{D}_s^{-} $$ $D_s^{+}{D}_s^{-}$decays, using data collected by the LHCb detector in proton-proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 6 fb⁻¹. InB⁰→ D⁺D⁻decays theCP-violation parameters are measured to be$$ {\displaystyle \begin{array}{c}{S}_{D^{+}{D}^{-}}=-0.552\pm 0.100\left(\textrm{stat}\right)\pm 0.010\left(\textrm{syst}\right),\\ {}{C}_{D^{+}{D}^{-}}=0.128\pm 0.103\left(\textrm{stat}\right)\pm 0.010\left(\textrm{syst}\right).\end{array}} $$ $\begin{array}{c}{S}_{D^{+}{D}^{-}}=-0.552\pm 0.100\left(\text{stat}\right)\pm 0.010\left(\text{syst}\right),\\ C_{D^{+}{D}^{-}}=0.128\pm 0.103\left(\text{stat}\right)\pm 0.010\left(\text{syst}\right).\end{array}$ In$$ {B}_s^0 $$ $B_s^0$→$$ {D}_s^{+}{D}_s^{-} $$ $D_s^{+}{D}_s^{-}$decays theCP-violating parameter formulation in terms ofϕ_sand|λ|results in$$ {\displaystyle \begin{array}{c}{\phi}_s=-0.086\pm 0.106\left(\textrm{stat}\right)\pm 0.028\left(\textrm{syst}\right)\textrm{rad},\\ {}\mid {\lambda}_{D_s^{+}{D}_s^{-}}\mid =1.145\pm 0.126\left(\textrm{stat}\right)\pm 0.031\left(\textrm{syst}\right).\end{array}} $$ $\begin{array}{c}{\varphi }_s=-0.086\pm 0.106\left(\text{stat}\right)\pm 0.028\left(\text{syst}\right)\mathrm{rad},\\ \mid {\lambda }_{D_s^{+}{D}_s^{-}}\mid =1.145\pm 0.126\left(\text{stat}\right)\pm 0.031\left(\text{syst}\right).\end{array}$ These results represent the most precise single measurement of theCP-violation parameters in their respective channels. For the first time in a single measurement,CPsymmetry is observed to be violated inB⁰→ D⁺D⁻decays with a significance exceeding six standard deviations. 

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