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1. Online Paging with Heterogeneous Cache Slots

   https://doi.org/10.1007/s00453-024-01270-z  

   Chrobak, Marek; Haney, Samuel; Liaee, Mehraneh; Panigrahi, Debmalya; Rajaraman, Rajmohan; Sundaram, Ravi; Young, Neal_E (October 2024, Algorithmica)

   Abstract It is natural to generalize the online$$k$$ $k$-Server problem by allowing each request to specify not only a pointp, but also a subsetSof servers that may serve it. To date, only a few special cases of this problem have been studied. The objective of the work presented in this paper has been to more systematically explore this generalization in the case of uniform and star metrics. For uniform metrics, the problem is equivalent to a generalization of Paging in which each request specifies not only a pagep, but also a subsetSof cache slots, and is satisfied by having a copy ofpin some slot inS. We call this problemSlot-Heterogenous Paging. In realistic settings only certain subsets of cache slots or servers would appear in requests. Therefore we parameterize the problem by specifying a family$${\mathcal {S}}\subseteq 2^{[k]}$$ $S\subseteq 2^{\left[k\right]}$of requestable slot sets, and we establish bounds on the competitive ratio as a function of the cache sizekand family$${\mathcal {S}}$$ $S$:If all request sets are allowed ($${\mathcal {S}}=2^{[k]}\setminus \{\emptyset \}$$ $S=2^{\left[k\right]}\backslash \left\{\varnothing \right\}$), the optimal deterministic and randomized competitive ratios are exponentially worse than for standard Paging ($${\mathcal {S}}=\{[k]\}$$ $S=\left\{\right[k\left]\right\}$).As a function of$$|{\mathcal {S}}|$$ $\left|S\right|$andk, the optimal deterministic ratio is polynomial: at most$$O(k^2|{\mathcal {S}}|)$$ $O\left(k^2\right|S\left|\right)$and at least$$\Omega (\sqrt{|{\mathcal {S}}|})$$ $\Omega \left(\sqrt{\left|S\right|}\right)$.For any laminar family$${\mathcal {S}}$$ $S$of heighth, the optimal ratios areO(hk) (deterministic) and$$O(h^2\log k)$$ $O(h^{2}logk)$(randomized).The special case of laminar$${\mathcal {S}}$$ $S$that we callAll-or-One Pagingextends standard Paging by allowing each request to specify a specific slot to put the requested page in. The optimal deterministic ratio forweightedAll-or-One Paging is$$\Theta (k)$$ $\Theta \left(k\right)$. Offline All-or-One Paging is$$\mathbb{N}\mathbb{P}$$ $NP$-hard.Some results for the laminar case are shown via a reduction to the generalization of Paging in which each request specifies a set$$P$$ $P$ofpages, and is satisfied by fetching any page from$$P$$ $P$into the cache. The optimal ratios for the latter problem (with laminar family of heighth) are at mosthk(deterministic) and$$hH_k$$ $h{H}_k$(randomized). 

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2. Measurement of the branching fractions of $$ \overline{B} $$ → D(*)K−$$ {K}_{(S)}^{\left(\ast \right)0} $$ and $$ \overline{B} $$ → D(*)$$ {D}_s^{-} $$ decays at Belle II

   https://doi.org/10.1007/JHEP08(2024)206  

   Adachi, I; Aggarwal, L; Aihara, H; Akopov, N; Aloisio, A; Althubiti, N; Anh_Ky, N; Asner, D M; Atmacan, H; Aushev, T; et al (August 2024, Journal of High Energy Physics)

   Abstract We present measurements of the branching fractions of eight$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D^(*)+K⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$,B⁻→D^(*)0K⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$decay channels. The results are based on data from SuperKEKB electron-positron collisions at the Υ(4S) resonance collected with the Belle II detector, corresponding to an integrated luminosity of 362 fb⁻¹. The event yields are extracted from fits to the distributions of the difference between expected and observedBmeson energy, and are efficiency-corrected as a function ofm(K⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$) andm(D^(*)$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$) in order to avoid dependence on the decay model. These results include the first observation of$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D⁺K⁻$$ {K}_S^0 $$ $K_S^0$,B⁻→D*⁰K⁻$$ {K}_S^0 $$ $K_S^0$, and$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D*⁺K⁻$$ {K}_S^0 $$ $K_S^0$decays and a significant improvement in the precision of the other channels compared to previous measurements. The helicity-angle distributions and the invariant mass distributions of theK⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$systems are compatible with quasi-two-body decays via a resonant transition with spin-parityJ^P= 1⁻for theK⁻$$ {K}_S^0 $$ $K_S^0$systems andJ^P= 1⁺for theK⁻K*⁰systems. We also present measurements of the branching fractions of four$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D^(*)+$$ {D}_s^{-} $$ $D_s^{-}$,B⁻→D^(*)0$$ {D}_s^{-} $$ $D_s^{-}$decay channels with a precision compatible to the current world averages. 

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3. Search for CP violation in $${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} $$ decays in proton–proton collisions at $$\sqrt{s} = 13\,\text {Te}\hspace{-.08em}\text {V} $$

   https://doi.org/10.1140/epjc/s10052-024-13244-0  

   Hayrapetyan, A; Tumasyan, A; Adam, W; Andrejkovic, J W; Bergauer, T; Chatterjee, S; Damanakis, K; Dragicevic, M; Hussain, P S; Jeitler, M; et al (December 2024, The European Physical Journal C)

   Abstract A search is reported for charge-parity$$CP$$ $\mathrm{CP}$violation in$${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} $$ ${\text{D}}^0\to {\text{K}}_{\text{S}}^0{\text{K}}_{\text{S}}^0$decays, using data collected in proton–proton collisions at$$\sqrt{s} = 13\,\text {Te}\hspace{-.08em}\text {V} $$ $\sqrt{s}=13\text{Te}\text{V}$recorded by the CMS experiment in 2018. The analysis uses a dedicated data set that corresponds to an integrated luminosity of 41.6$$\,\text {fb}^{-1}$$ ${\text{fb}}^{-1}$, which consists of about 10 billion events containing a pair of b hadrons, nearly all of which decay to charm hadrons. The flavor of the neutral D meson is determined by the pion charge in the reconstructed decays$${{{\textrm{D}}}^{{*+}}} \rightarrow {{{\textrm{D}}}^{{0}}} {{{\mathrm{\uppi }}}^{{+}}} $$ $\text{D}_{}^{\ast +}\to {\text{D}}^0{\pi }^{+}$and$${{{\textrm{D}}}^{{*-}}} \rightarrow {\overline{{\textrm{D}}}^{{0}}} {{{\mathrm{\uppi }}}^{{-}}} $$ $\text{D}_{}^{\ast -}\to {\overline{\text{D}}}^0{\pi }^{-}$. The$$CP$$ $\mathrm{CP}$asymmetry in$${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} $$ ${\text{D}}^0\to {\text{K}}_{\text{S}}^0{\text{K}}_{\text{S}}^0$is measured to be$$A_{CP} ({{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} ) = (6.2 \pm 3.0 \pm 0.2 \pm 0.8)\%$$ $A_{\mathrm{CP}}\left({\text{K}}_{\text{S}}^0{\text{K}}_{\text{S}}^0\right)=(6.2\pm 3.0\pm 0.2\pm 0.8)\%$, where the three uncertainties represent the statistical uncertainty, the systematic uncertainty, and the uncertainty in the measurement of the$$CP$$ $\mathrm{CP}$asymmetry in the$${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{{\mathrm{\uppi }}}^{{+}}} {{{\mathrm{\uppi }}}^{{-}}} $$ ${\text{D}}^0\to {\text{K}}_{\text{S}}^0{\pi }^{+}{\pi }^{-}$decay. This is the first$$CP$$ $\mathrm{CP}$asymmetry measurement by CMS in the charm sector as well as the first to utilize a fully hadronic final state. 

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4. Study of the p–p–K$$^{+}$$ and p–p–K$$^{-}$$ dynamics using the femtoscopy technique

   https://doi.org/10.1140/epja/s10050-023-01139-9  

   Acharya, S; Adamová, D; Adler, A; Aglieri_Rinella, G; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, S; Ahn, S U; Ahuja, I; et al (December 2023, The European Physical Journal A)

   Abstract The interactions of kaons (K) and antikaons ($$\mathrm {\overline{K}}$$ $\overline{K}$) with few nucleons (N) were studied so far using kaonic atom data and measurements of kaon production and interaction yields in nuclei. Some details of the three-body KNN and$$\mathrm {\overline{K}}$$ $\overline{K}$NN dynamics are still not well understood, mainly due to the overlap with multi-nucleon interactions in nuclei. An alternative method to probe the dynamics of three-body systems with kaons is to study the final state interaction within triplet of particles emitted in pp collisions at the Large Hadron Collider, which are free from effects due to the presence of bound nucleons. This Letter reports the first femtoscopic study of p–p–K$$^+$$ ${}^{+}$and p–p–K$$^-$$ ${}^{-}$correlations measured in high-multiplicity pp collisions at$$\sqrt{s}$$ $\sqrt{s}$= 13 TeV by the ALICE Collaboration. The analysis shows that the measured p–p–K$$^+$$ ${}^{+}$and p–p–K$$^-$$ ${}^{-}$correlation functions can be interpreted in terms of pairwise interactions in the triplets, indicating that the dynamics of such systems is dominated by the two-body interactions without significant contributions from three-body effects or bound states. 

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5. 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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