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1. Measurement of branching-fraction ratios and CP asymmetries in B± → DCP±K± decays at Belle and Belle II

   https://doi.org/10.1007/JHEP05(2024)212  

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

   A<sc>bstract</sc> We report results from a study ofB^±→ DK^±decays followed byDdecaying to theCP-even final stateK⁺K⁻and CP-odd final state$$ {K}_S^0{\pi}^0 $$ $K_S^0{\pi }^0$, whereDis an admixture ofD⁰and$$ {\overline{D}}^0 $$ ${\overline{D}}^0$states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angleϕ₃. The results are based on a combined analysis of the final data set of 772×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle experiment and a data set of 198×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be$$ \mathcal{A} $$ $A$_CP+= (+12.5±5.8±1.4)% and$$ \mathcal{A} $$ $A$_CP−= (−16.7±5.7±0.6)%, and the ratios of branching fractions to be$$ \mathcal{R} $$ $R$_CP+= 1.164±0.081±0.036 and$$ \mathcal{R} $$ $R$_CP−= 1.151±0.074±0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries$$ \mathcal{A} $$ $A$_CP+and$$ \mathcal{A} $$ $A$_CP−have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5^°<ϕ₃< 16.5^°) or (84.5^°<ϕ₃< 95.5^°) or (163.3^°<ϕ₃< 171.5^°) and 0.321 <r_B< 0.465. 

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2. When left and right disagree: entropy and von Neumann algebras in quantum gravity with general AlAdS boundary conditions

   https://doi.org/10.1007/JHEP08(2024)010  

   Marolf, Donald; Zhang, Daiming (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Euclidean path integrals for UV-completions ofd-dimensional bulk quantum gravity were recently studied in [1] by assuming that they satisfy axioms of finiteness, reality, continuity, reflection-positivity, and factorization. Sectors$$ {\mathcal{H}}_{\mathcal{B}} $$ $H_B$of the resulting Hilbert space were then defined for any (d− 2)-dimensional surface$$ \mathcal{B} $$ $B$, where$$ \mathcal{B} $$ $B$may be thought of as the boundary ∂Σ of a bulk Cauchy surface in a corresponding Lorentzian description, and where$$ \mathcal{B} $$ $B$includes the specification of appropriate boundary conditions for bulk fields. Cases where$$ \mathcal{B} $$ $B$was the disjoint unionB⊔Bof two identical (d− 2)-dimensional surfacesBwere studied in detail and, after the inclusion of finite-dimensional ‘hidden sectors,’ were shown to provide a Hilbert space interpretation of the associated Ryu-Takayanagi entropy. The analysis was performed by constructing type-I von Neumann algebras$$ {\mathcal{A}}_L^B $$ $A_L^B$,$$ {\mathcal{A}}_R^B $$ $A_R^B$that act respectively at the left and right copy ofBinB⊔B. Below, we consider the case of general$$ \mathcal{B} $$ $B$, and in particular for$$ \mathcal{B} $$ $B$=B_L⊔B_RwithB_L,B_Rdistinct. For anyB_R, we find that the von Neumann algebra atB_Lacting on the off-diagonal Hilbert space sector$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$ $H_{B_L\bigsqcup B_R}$is a central projection of the corresponding type-I von Neumann algebra on the ‘diagonal’ Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$ $H_{B_L\bigsqcup B_L}$. As a result, the von Neumann algebras$$ {\mathcal{A}}_L^{B_L} $$ $A_L^{B_L}$,$$ {\mathcal{A}}_R^{B_L} $$ $A_R^{B_L}$defined in [1] using the diagonal Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$ $H_{B_L\bigsqcup B_L}$turn out to coincide precisely with the analogous algebras defined using the full Hilbert space of the theory (including all sectors$$ {\mathcal{H}}_{\mathcal{B}} $$ $H_B$). A second implication is that, for any$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$ $H_{B_L\bigsqcup B_R}$, including the same hidden sectors as in the diagonal case again provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. We also show the above central projections to satisfy consistency conditions that lead to a universal central algebra relevant to all choices ofB_LandB_R. 

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3. Comprehensive analysis of local and nonlocal amplitudes in the B0 → K*0μ+μ− decay

   https://doi.org/10.1007/JHEP09(2024)026  

   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 (September 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> A comprehensive study of the local and nonlocal amplitudes contributing to the decayB⁰→K^*0(→K⁺π⁻)μ⁺μ⁻is performed by analysing the phase-space distribution of the decay products. The analysis is based onppcollision data corresponding to an integrated luminosity of 8.4 fb⁻¹collected by the LHCb experiment. This measurement employs for the first time a model of both one-particle and two-particle nonlocal amplitudes, and utilises the complete dimuon mass spectrum without any veto regions around the narrow charmonium resonances. In this way it is possible to explicitly isolate the local and nonlocal contributions and capture the interference between them. The results show that interference with nonlocal contributions, although larger than predicted, only has a minor impact on the Wilson Coefficients determined from the fit to the data. For the local contributions, the Wilson Coefficient$$ {\mathcal{C}}_9 $$ $C_9$, responsible for vector dimuon currents, exhibits a 2.1σdeviation from the Standard Model expectation. The Wilson Coefficients$$ {\mathcal{C}}_{10} $$ $C_{10}$,$$ {\mathcal{C}}_9^{\prime } $$ $C_9^{\prime }$and$$ {\mathcal{C}}_{10}^{\prime } $$ $C_{10}^{\prime }$are all in better agreement than$$ {\mathcal{C}}_9 $$ $C_9$with the Standard Model and the global significance is at the level of 1.5σ. The model used also accounts for nonlocal contributions fromB⁰→ K^*0[τ⁺τ⁻→ μ⁺μ⁻] rescattering, resulting in the first direct measurement of thebsττvector effective-coupling$$ {\mathcal{C}}_{9\tau } $$ $C_{9\tau }$. 

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4. Construction of a Dirichlet form on Metric Measure Spaces of Controlled Geometry

   https://doi.org/10.1007/s11118-024-10144-6  

   Butaev, Almaz; Luo, Liangbing; Shanmugalingam, Nageswari (June 2024, Potential Analysis)

   Abstract Given a compact doubling metric measure spaceXthat supports a 2-Poincaré inequality, we construct a Dirichlet form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$that is comparable to the upper gradient energy form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$. Our approach is based on the approximation ofXby a family of graphs that is doubling and supports a 2-Poincaré inequality (see [20]). We construct a bilinear form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$using the Dirichlet form on the graph. We show that the$$\Gamma $$ $\Gamma$-limit$$\mathcal {E}$$ $E$of this family of bilinear forms (by taking a subsequence) exists and that$$\mathcal {E}$$ $E$is a Dirichlet form onX. Properties of$$\mathcal {E}$$ $E$are established. Moreover, we prove that$$\mathcal {E}$$ $E$has the property of matching boundary values on a domain$$\Omega \subseteq X$$ $\Omega \subseteq X$. This construction makes it possible to approximate harmonic functions (with respect to the Dirichlet form$$\mathcal {E}$$ $E$) on a domain inXwith a prescribed Lipschitz boundary data via a numerical scheme dictated by the approximating Dirichlet forms, which are discrete objects. 

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5. Lower Bounds Against Sparse Symmetric Functions of ACC Circuits: Expanding the Reach of #SAT Algorithms

   https://doi.org/10.1007/s00224-022-10106-8  

   Vyas, Nikhil; Williams, R_Ryan (November 2022, Theory of Computing Systems)

   Abstract We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$ $\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[n^{{\left(\log n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$$\mathcal { C}$$ $C$, by showing that$$\mathcal { C}$$ $C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class$${\mathcal C}$$ $C$. Say that a symmetric Boolean functionf(x₁,…,x_n) issparseif it outputs 1 onO(1) values of$${\sum }_{i} x_{i}$$ ${\sum }_i{x}_i$. We show that for every sparsef, and for all “typical”$$\mathcal { C}$$ $C$, faster#SAT algorithms for$$\mathcal { C}$$ $C$circuits imply lower bounds against the circuit class$$f \circ \mathcal { C}$$ $f\circ C$, which may bestrongerthan$$\mathcal { C}$$ $C$itself. In particular:#SAT algorithms forn^k-size$$\mathcal { C}$$ $C$-circuits running in 2ⁿ/n^ktime (for allk) implyNEXPdoes not have$$(f \circ \mathcal { C})$$ $(f\circ C)$-circuits of polynomial size.#SAT algorithms for$$2^{n^{{\varepsilon }}}$$ $2^{n^{\epsilon }}$-size$$\mathcal { C}$$ $C$-circuits running in$$2^{n-n^{{\varepsilon }}}$$ $2^{n-n^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$$(f \circ \mathcal { C})$$ $(f\circ C)$-circuits of polynomial size. Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJ∘ACC⁰∘THRcircuits of polynomial size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC⁰[Williams JACM’14] andACC⁰∘THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class. 

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