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1. 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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2. New LHCb pentaquarks as hadrocharmonium states

   https://doi.org/10.1142/S0217732320501515  

   Eides, Michael I.; Petrov, Victor Yu.; Polyakov, Maxim V. (June 2020, Modern Physics Letters A)

   New LHCb Collaboration results on pentaquarks with hidden charm 1 are discussed. These results fit nicely in the hadrocharmonium pentaquark scenario.[Formula: see text] In the new data the old LHCb pentaquark [Formula: see text] splits into two states [Formula: see text] and [Formula: see text]. We interpret these two almost degenerated hadrocharmonium states with [Formula: see text] and [Formula: see text], as a result of hyperfine splitting between hadrocharmonium states predicted in Ref. 2. It arises due to QCD multipole interaction between color-singlet hadrocharmonium constituents. We improve the theoretical estimate of hyperfine splitting[Formula: see text] that is compatible with the experimental data. The new [Formula: see text] state finds a natural explanation as a bound state of [Formula: see text] and a nucleon, with [Formula: see text], [Formula: see text] and binding energy 42 MeV. As a bound state of a spin-[Formula: see text] meson and a nucleon, hadrocharmonium pentaquark [Formula: see text] does not experience hyperfine splitting. We find a series of hadrocharmonium states in the vicinity of the wide [Formula: see text] pentaquark that can explain its apparently large decay width. We compare the hadrocharmonium and molecular pentaquark scenarios and discuss their relative advantages and drawbacks. 

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3. Misiurewicz polynomials and dynamical units, part I

   https://doi.org/10.1142/S1793042123500616  

   Benedetto, Robert L; Goksel, Vefa (July 2023, International Journal of Number Theory)

   We study the dynamics of the unicritical polynomial family [Formula: see text]. The [Formula: see text]-values for which [Formula: see text] has a strictly preperiodic postcritical orbit are called Misiurewicz parameters, and they are the roots of Misiurewicz polynomials. The arithmetic properties of these special parameters have found applications in both arithmetic and complex dynamics. In this paper, we investigate some new such properties. In particular, when [Formula: see text] is a prime power and [Formula: see text] is a Misiurewicz parameter, we prove certain arithmetic relations between the points in the postcritical orbit of [Formula: see text]. We also consider the algebraic integers obtained by evaluating a Misiurewicz polynomial at a different Misiurewicz parameter, and we ask when these algebraic integers are algebraic units. This question naturally arises from some results recently proven by Buff, Epstein, and Koch and by the second author. We propose a conjectural answer to this question, which we prove in many cases. 

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4. Marchenko–Pastur law with relaxed independence conditions

   https://doi.org/10.1142/s2010326321500404  

   Bryson, Jennifer; Vershynin, Roman; Zhao, Hongkai (January 2021, Random Matrices: Theory and Applications)

   null (Ed.)

   We prove the Marchenko–Pastur law for the eigenvalues of [Formula: see text] sample covariance matrices in two new situations where the data does not have independent coordinates. In the first scenario — the block-independent model — the [Formula: see text] coordinates of the data are partitioned into blocks in such a way that the entries in different blocks are independent, but the entries from the same block may be dependent. In the second scenario — the random tensor model — the data is the homogeneous random tensor of order [Formula: see text], i.e. the coordinates of the data are all [Formula: see text] different products of [Formula: see text] variables chosen from a set of [Formula: see text] independent random variables. We show that Marchenko–Pastur law holds for the block-independent model as long as the size of the largest block is [Formula: see text], and for the random tensor model as long as [Formula: see text]. Our main technical tools are new concentration inequalities for quadratic forms in random variables with block-independent coordinates, and for random tensors. 

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5. A trace inequality of Ando, Hiai, and Okubo and a monotonicity property of the Golden–Thompson inequality

   https://doi.org/10.1063/5.0091111  

   Carlen, Eric A.; Lieb, Elliott H. (June 2022, Journal of Mathematical Physics)

   The Golden–Thompson trace inequality, which states that Tr  e H+ K ≤ Tr  e H e K , has proved to be very useful in quantum statistical mechanics. Golden used it to show that the classical free energy is less than the quantum one. Here, we make this G–T inequality more explicit by proving that for some operators, notably the operators of interest in quantum mechanics, H = Δ or [Formula: see text] and K = potential, Tr  e H+(1− u) K e uK is a monotone increasing function of the parameter u for 0 ≤ u ≤ 1. Our proof utilizes an inequality of Ando, Hiai, and Okubo (AHO): Tr  X s Y t X 1− s Y 1− t ≤ Tr  XY for positive operators X, Y and for [Formula: see text], and [Formula: see text]. The obvious conjecture that this inequality should hold up to s + t ≤ 1 was proved false by Plevnik [Indian J. Pure Appl. Math. 47, 491–500 (2016)]. We give a different proof of AHO and also give more counterexamples in the [Formula: see text] range. More importantly, we show that the inequality conjectured in AHO does indeed hold in the full range if X, Y have a certain positivity property—one that does hold for quantum mechanical operators, thus enabling us to prove our G–T monotonicity theorem. 

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