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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)

   AbstractThe 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. Graphical abstractThe 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. Probing light scalars and vector-like quarks at the high-luminosity LHC

   https://doi.org/10.1140/epjc/s10052-025-14085-1  

   Qureshi, U S; Gurrola, A; Flórez, A; Rodriguez, C (April 2025, The European Physical Journal C)

   Abstract A model based on a$$U(1)_{T^3_R}$$ $U{\left(1\right)}_{T_R^3}$extension of the Standard Model can address the mass hierarchy between generations of fermions, explain thermal dark matter abundance, and the muon$$g - 2$$ $g-2$,$$R_{(D)}$$ $R_{\left(D\right)}$, and$$R_{(D^*)}$$ $R_{\left(D^{\ast }\right)}$anomalies. The model contains a light scalar boson$$\phi '$$ ${\varphi }^{\prime }$and a heavy vector-like quark$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$that can be probed at CERN’s large hadron collider (LHC). We perform a phenomenology study on the production of$$\phi '$$ ${\varphi }^{\prime }$and$${\chi }_u$$ ${\chi }_u$particles from proton–proton$$(\textrm{pp})$$ $\left(\text{pp}\right)$collisions at the LHC at$$\sqrt{s}=13.6$$ $\sqrt{s}=13.6$TeV, primarily through$$g{-g}$$ $g-g$and$$t{-\chi _\textrm{u}}$$ $t-{\chi }_{\text{u}}$fusion. We work under a simplified model approach and directly take the$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$and$$\phi '$$ ${\varphi }^{\prime }$masses as free parameters. We perform a phenomenological analysis considering$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$final states to b-quarks, muons, and neutrinos, and$$\phi '$$ ${\varphi }^{\prime }$decays to$$\mu ^+\mu ^-$$ ${\mu }^{+}{\mu }^{-}$. A machine learning algorithm is used to maximize the signal sensitivity, considering an integrated luminosity of 3000$$\text {fb}^{-1}$$ ${\text{fb}}^{-1}$. The proposed methodology can be a key mode for discovery over a large mass range, including low masses, traditionally considered difficult due to experimental constraints. 

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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)

   Abstract 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. 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)

   Abstract 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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5. 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)

   Abstract 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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