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1. Exploring Jahn-Teller distortions: a local vibrational mode perspective

   https://doi.org/10.1007/s00894-024-05882-8  

   Quintano, Mateus ; Moura, Renaldo T ; Kraka, Elfi ( April 2024 , Journal of Molecular Modeling)

   The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$/$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$, as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,$$\mathrm {[Fe{(CN)}_6]^{4-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$/$$\mathrm {[Fe{(CN)}_6]^{3-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$. We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$to$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From$$\mathrm {[Fe{(CN)}_6]^{4-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$to$$\mathrm {[Fe{(CN)}_6]^{3-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$we observed an increase in covalency without altering the bond nature. Distinct$$\pi $$$\pi$back-donation disparity could be confirmed by comparison with the isolated CN$$^-$$${}^{-}$system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.

   The adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies

    

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2. Measurement of non-prompt $${{\textrm{D}}^{0}}$$-meson elliptic flow in Pb–Pb collisions at $$\sqrt{s_{\textrm{NN}}} = 5.02$$ TeV

   https://doi.org/10.1140/epjc/s10052-023-12259-3  

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

   The elliptic flow$$(v_2)$$$\left(v_2\right)$of$${\textrm{D}}^{0}$$${\text{D}}^0$mesons from beauty-hadron decays (non-prompt$${\textrm{D}}^{0})$$${\text{D}}^0)$was measured in midcentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair$$\sqrt{s_{\textrm{NN}}} = 5.02$$$\sqrt{s_{\text{NN}}}=5.02$ TeV with the ALICE detector at the LHC. The$${\textrm{D}}^{0}$$${\text{D}}^0$mesons were reconstructed at midrapidity$$(|y|<0.8)$$$\left(\right|y|<0.8)$from their hadronic decay$$\mathrm {D^0 \rightarrow K^-\uppi ^+}$$$D^0\to K^{-}{\pi }^{+}$, in the transverse momentum interval$$2< p_{\textrm{T}} < 12$$$2<p_{\text{T}}<12$ GeV/c. The result indicates a positive$$v_2$$$v_2$for non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$mesons with a significance of 2.7$$\sigma $$$\sigma$. The non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$-meson$$v_2$$$v_2$is lower than that of prompt non-strange D mesons with 3.2$$\sigma $$$\sigma$significance in$$2< p_\textrm{T} < 8~\textrm{GeV}/c$$$2<p_{\text{T}}<8\text{GeV}/c$, and compatible with the$$v_2$$$v_2$of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.

    

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3. Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path

   https://doi.org/10.1007/s00493-023-00015-w  

   Scott, Alex ; Seymour, Paul ; Spirkl, Sophie ( October 2023 , Combinatorica)

   A graphGisH-freeif it has no induced subgraph isomorphic toH. We prove that a$$P_5$$$P_5$-free graph with clique number$$\omega \ge 3$$$\omega \ge 3$has chromatic number at most$$\omega ^{\log _2(\omega )}$$${\omega }^{{log}_2\left(\omega \right)}$. The best previous result was an exponential upper bound$$(5/27)3^{\omega }$$$(5/27)3^{\omega }$, due to Esperet, Lemoine, Maffray, and Morel. A polynomial bound would imply that the celebrated Erdős-Hajnal conjecture holds for$$P_5$$$P_5$, which is the smallest open case. Thus, there is great interest in whether there is a polynomial bound for$$P_5$$$P_5$-free graphs, and our result is an attempt to approach that.

    

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4. Semileptonic form factors for $$B\rightarrow D^*\ell \nu $$ at nonzero recoil from $$2+1$$-flavor lattice QCD: Fermilab Lattice and MILC Collaborations

   https://doi.org/10.1140/epjc/s10052-022-10984-9  

   Bazavov, A. ; DeTar, C. E. ; Du, D. ; El-Khadra, A. X. ; Gámiz, E. ; Gelzer, Z. ; Gottlieb, S. ; Heller, U. M. ; Kronfeld, A. S. ; Laiho, J. ; et al ( December 2022 , The European Physical Journal C)

   We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu $$$B\to D^{\ast }\ell \nu$at nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$$N_f=2+1$flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$$a\approx 0.15$fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$$|V_{\mathrm{cb}}|$. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$$\left(V_{\mathrm{cb}}\right)=(38.40\pm 0.{68}_{\text{th}}\pm 0.{34}_{\text{exp}}\pm 0.{18}_{\text{EM}})\times {10}^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$${\chi }^2\text{/dof}=126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict$$R(D^*) = 0.265 \pm 0.013$$$R\left(D^{\ast }\right)=0.265\pm 0.013$, which confirms the current tension between theory and experiment.

    

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5. Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces

   https://doi.org/10.1007/s00440-021-01070-4  

   Miller, Jason ; Sheffield, Scott ; Werner, Wendelin ( June 2021 , Probability Theory and Related Fields)

   We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$for$$\kappa '$$${\kappa }^{\prime }$in (4, 8) that is drawn on an independent$$\gamma $$$\gamma$-LQG surface for$$\gamma ^2=16/\kappa '$$${\gamma }^2=16/{\kappa }^{\prime }$. The results are similar in flavor to the ones from our companion paper dealing with$$\hbox {CLE}_{\kappa }$$${\text{CLE}}_{\kappa }$for$$\kappa $$$\kappa$in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$in terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$independently into two colors with respective probabilitiespand$$1-p$$$1-p$. This description was complete up to one missing parameter$$\rho $$$\rho$. The results of the present paper about CLE on LQG allow us to determine its value in terms ofpand$$\kappa '$$${\kappa }^{\prime }$. It shows in particular that$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$and$$\hbox {CLE}_{16/\kappa '}$$${\text{CLE}}_{16/{\kappa }^{\prime }}$are related via a continuum analog of the Edwards-Sokal coupling between$$\hbox {FK}_q$$${\text{FK}}_q$percolation and theq-state Potts model (which makes sense even for non-integerqbetween 1 and 4) if and only if$$q=4\cos ^2(4\pi / \kappa ')$$$q=4{cos}^2(4\pi /{\kappa }^{\prime })$. This provides further evidence for the long-standing belief that$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$and$$\hbox {CLE}_{16/\kappa '}$$${\text{CLE}}_{16/{\kappa }^{\prime }}$represent the scaling limits of$$\hbox {FK}_q$$${\text{FK}}_q$percolation and theq-Potts model whenqand$$\kappa '$$${\kappa }^{\prime }$are related in this way. Another consequence of the formula for$$\rho (p,\kappa ')$$$\rho (p,{\kappa }^{\prime })$is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.

    

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