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1. Convolution identities for divisor sums and modular forms

   https://doi.org/10.1073/pnas.2322320121  

   Fedosova, Ksenia; Klinger-Logan, Kim; Radchenko, Danylo (October 2024, Proceedings of the National Academy of Sciences)

   Ribet, Kenneth (Ed.)

   We consider certain convolution sums that are the subject of a conjecture by Chester, Green, Pufu, Wang, and Wen in string theory. We prove a generalized form of their conjecture, explicitly evaluating absolutely convergent sums $\sum _{n_1\in \mathbb{Z}\setminus \{0,n\}}\phi (n_1,n-n_1){\sigma }_{2m_1}\left(n_1\right){\sigma }_{2m_2}(n-n_1),$ where $\phi (n_1,n_2)$is a Laurent polynomial with logarithms. Contrary to original expectations, such convolution sums, suitably extended to $n_1\in \{0,n\}$, do not vanish, but instead, they carry number theoretic meaning in the form of Fourier coefficients of holomorphic cusp forms. 

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2. Development of broad modulus profile upon polymer–polymer interface formation between immiscible glassy–rubbery domains

   https://doi.org/10.1073/pnas.2312533120  

   Gagnon, Yannic J; Burton, Justin C; Roth, Connie B (January 2024, Proceedings of the National Academy of Sciences)

   Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ( $T_{\text{g}}$) where previous work has demonstrated a long-range (∼200 nm) profile in local $T_{\text{g}}\left(z\right)$is established between immiscible glassy and rubbery polymer domains when the polymer–polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus $\tilde{G}\left(z\right)$is established when the polymer–polymer interface ( $\approx$5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad $T_{\text{g}}\left(z\right)$profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus $\tilde{G}\left(z\right)$spanning $\approx$180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in $T_{\text{g}}\left(z\right)$and $\tilde{G}\left(z\right)$arise from a coupling of the spectrum of vibrational modes across the polymer–polymer interface as a result of acoustic impedance matching of sound waves with $\lambda \sim 5$nm during interface broadening that can then trigger density fluctuations in the neighboring domain. 

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3. Structural phase purification of bulk HfO ₂ :Y through pressure cycling

   https://doi.org/10.1073/pnas.2312571121  

   Musfeldt, J. L.; Singh, Sobhit; Fan, Shiyu; Gu, Yanhong; Xu, Xianghan; Cheong, S.-W.; Liu, Z.; Vanderbilt, David; Rabe, Karin M. (January 2024, Proceedings of the National Academy of Sciences)

   We combine synchrotron-based infrared absorption and Raman scattering spectroscopies with diamond anvil cell techniques and first-principles calculations to explore the properties of hafnia under compression. We find that pressure drives HfO ${}_2$:7%Y from the mixed monoclinic ( $P{2}_1/c$) $+$antipolar orthorhombic ( $\mathit{Pbca}$) phase to pure antipolar orthorhombic ( $\mathit{Pbca}$) phase at approximately 6.3 GPa. This transformation is irreversible, meaning that upon release, the material is kinetically trapped in the $\mathit{Pbca}$metastable state at 300 K. Compression also drives polar orthorhombic ( $Pca{2}_1$) hafnia into the tetragonal ( $P{4}_2/nmc$) phase, although the latter is not metastable upon release. These results are unified by an analysis of the energy landscape. The fact that pressure allows us to stabilize targeted metastable structures with less Y stabilizer is important to preserving the flat phonon band physics of pure HfO ${}_2$. 

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4. Characterizing the fundamental bending vibration of a linear polyatomic molecule for symmetry violation searches

   https://doi.org/10.1088/1367-2630/ace471  

   Jadbabaie, Arian; Takahashi, Yuiki; Pilgram, Nickolas H; Conn, Chandler J; Zeng, Yi; Zhang, Chi; Hutzler, Nicholas R (July 2023, New Journal of Physics)

   Abstract Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize the fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$ $\to \tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state, and accurately model the state’s structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state and fit the molecule-frame dipole moment to $D_{\mathrm{m}\mathrm{o}\mathrm{l}}=2.16\left(1\right)$Dand the effective electrong-factor to $g_S=2.07\left(2\right)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin–orbit and vibronic perturbations in the excited $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules. 

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5. Test of lepton flavor universality in ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$ and ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-}$ decays in proton-proton collisions at $\sqrt{\text{s}}=\text{13}\text{TeV}$

   https://doi.org/10.1088/1361-6633/ad4e65  

   CMS_Collaboration, The (July 2024, Reports on Progress in Physics)

   Abstract A test of lepton flavor universality in ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$and ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-}$decays, as well as a measurement of differential and integrated branching fractions of a nonresonant ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}=13\text{TeV}$recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-})$to $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-})$is determined from the measured double ratio $R\left(\text{K}\right)$of these decays to the respective branching fractions of the ${\text{B}}^{\pm }\to \text{J}/\text{ψ}{\text{K}}^{\pm }$with $\text{J}/\text{ψ}\to {\mu }^{+}{\mu }^{-}$and ${\text{e}}^{+}{\text{e}}^{-}$decays, which allow for significant cancellation of systematic uncertainties. The ratio $R\left(\text{K}\right)$is measured in the range $1.1<q^2<6.0{\text{GeV}}^2$, whereqis the invariant mass of the lepton pair, and is found to be $R\left(\text{K}\right)={0.78}_{-0.23}^{+0.47}$, in agreement with the standard model expectation $R\left(\text{K}\right)\approx 1$. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the sameq²range, $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-})=(12.42\pm 0.68)\times {10}^{-8}$, is consistent with the present world-average value and has a comparable precision. 

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