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1. Generalizations of the quadratic bound optimization principle

   https://doi.org/10.1073/pnas.2525320123  

   Li, Xun-Jian; Tian, Guo-Liang; Zhou, Hua; Lange, Kenneth (January 2026, Proceedings of the National Academy of Sciences)

   The quadratic bound (QB) principle proposed by Böhning and Lindsay in 1988 is an important special case of the majorization–minimization or minorization-maximization optimization principle. The quadratic upper-bound (QUB) principle is pertinent to minimization; the analogous quadratic lower-bound principle is pertinent to maximization. Unfortunately, in minimizing a loss $f\left(\mathit{\theta }\right)$ , the QUB principle is limited by the difficulty of finding a constant positive definite matrix $\mathit{B}$ such that $\mathit{B}-d^{2}f\left(\mathit{\theta }\right)$ is positive semidefinite for all $\mathit{\theta }$ . This paper proposes a generalization of the QB principle that avoids this limitation. In particular, we construct QUB algorithms by replacing the matrix $\mathit{B}$ by a continuous matrix-valued function $B_n\left(\mathit{\theta }\right)$ that dominates the Hessian $d^{2}f\left(\mathit{\theta }\right)$ and depends on the both the current iterate ${\mathit{\theta }}_n$ and the next potential iterate $\mathit{\theta }$ . In practice, we require $B_n\left(\mathit{\theta }\right)$ to be diagonal with its diagonal entries separated in $\mathit{\theta }$ . In other words, the $i$ th diagonal entry of $B_n\left(\mathit{\theta }\right)$ depends on $\mathit{\theta }$ only through its $i$ th entry ${\theta }_i$ . Theoretical analysis confirms that this class of generalized QB algorithms enjoys global convergence in favorable circumstances. For the scalar case, the tangency condition that the second derivative equals the bound function at the current point promotes superlinear convergence. Several numerical experiments implemented in Julia illustrate the power of the generalized QB principle. 

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2. Test of lepton flavor universality with a measurement of $R\left(D^{*}\right)$ using hadronic $B$ tagging at the Belle II experiment

   https://doi.org/10.1103/PhysRevD.110.072020  

   Adachi, I; Adamczyk, K; Aggarwal, L; Ahmed, H; Aihara, H; Akopov, N; Aloisio, A; Anh_Ky, N; Asner, D M; Atmacan, H; et al (October 2024, Physical Review D)

   The ratio of branching fractions $R\left(D^{*}\right)=\mathcal{B}(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })$ , where $\ell$ is an electron or muon, is measured using a Belle II data sample with an integrated luminosity of $189{\mathrm{fb}}^{-1}$ at the SuperKEKB asymmetric-energy $e^{+}{e}^{-}$ collider. Data is collected at the $\mathrm{\Upsilon }\left(4\mathrm{S}\right)$ resonance, and one $B$ meson in the $\mathrm{\Upsilon }\left(4\mathrm{S}\right)\to B\overline{B}$ decay is fully reconstructed in hadronic decay modes. The accompanying signal $B$ meson is reconstructed as $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ using leptonic $\tau$ decays. The normalization decay, $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$ , produces the same observable final-state particles. The ratio of branching fractions is extracted in a simultaneous fit to two signal-discriminating variables in both channels and yields $R\left(D^{*}\right)={0.262}_{-0.039}^{+0.041}\left(\mathrm{stat}{)}_{-0.032}^{+0.035}\right(\mathrm{syst})$ . This result is consistent with the current world average and with Standard Model predictions. Published by the American Physical Society2024 

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3. 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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4. Observation and investigation of the $T_{c\overline{c}1}(4430{)}^{+}$ structure in $B^{+}\to \psi \left(2S\right)K_{\mathrm{S}}^0{\pi }^{+}$ decays

   https://doi.org/10.1103/rcfs-ynh2  

   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 (April 2026, Physical Review D)

   The first four-dimensional amplitude analysis of the $B^{+}\to \psi \left(2S\right)K_{\mathrm{S}}^0{\pi }^{+}$ decay is performed with proton-proton collision data collected by the LHCb experiment at $\sqrt{s}=13\mathrm{TeV}$ , corresponding to an integrated luminosity of $5.4\mathrm{f}{\mathrm{b}}^{-1}$ . The data cannot be fully explained by $B^{+}\to \psi \left(2S\right)K^{*+}$ contributions alone. A significantly better description of the data is obtained by adding a $T_{c\overline{c}}^{+}$ contribution decaying to $\psi \left(2S\right){\pi }^{+}$ . The properties of the $T_{c\overline{c}}^{+}$ structure are consistent with the exotic state $T_{c\overline{c}1}(4430{)}^{+}$ reported in the isospin-related ${\overline{B}}^0\to \psi \left(2S\right)K^{-}{\pi }^{+}$ decay. Effects of a possible $T_{c\overline{c}1}(4430{)}^{+}\to {\overline{D}}_1^{*}(2600{)}^0{D}^{+}$ decay mode on the $T_{c\overline{c}1}(4430{)}^{+}\to \psi (2S){\pi }^{+}$ mass distribution are investigated through a Flatté parametrization, providing constraints on the relative decay strength. A description of the $T_{c\overline{c}1}(4430{)}^{+}$ structure using the triangle singularity mechanism is studied and also found to be consistent with the data. 

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5. Evidence for the Rare Decay $B^{+}\to \overline{\mathrm{\Lambda }}p{\mu }^{+}{\mu }^{-}$

   https://doi.org/10.1103/pl88-4435  

   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 (July 2026, Physical Review Letters)

   A search for the rare decay $B^{+}\to \overline{\mathrm{\Lambda }}p{\mu }^{+}{\mu }^{-}$ is performed using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of $\sqrt{s}=13\mathrm{TeV}$ , corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$ . An excess of events is found with respect to the background-only expectation, with a signal significance of 3.5 standard deviations, in the low invariant-mass region of $m\left(\overline{\mathrm{\Lambda }}p\right)<2.8\mathrm{GeV}/c^2$ . The branching fraction is measured to be ${\mathcal{B}}_{\mathrm{low}}(B^{+}\to \overline{\mathrm{\Lambda }}p{\mu }^{+}{\mu }^{-})=\left(1.70_{-0.56}^{+0.65}\right(\mathrm{stat})\pm 0.17(\mathrm{syst})\pm 0.14(\mathrm{ext}\left)\right)\times {10}^{-8}$ , where the last uncertainty is due to external inputs on $\mathcal{B}(B^{+}\to J/\psi \overline{\mathrm{\Lambda }}p)\times \mathcal{B}(J/\psi \to {\mu }^{+}{\mu }^{-})$ . With no significant signal observed in the high $m\left(\overline{\mathrm{\Lambda }}p\right)$ region above $2.8\mathrm{GeV}/c^2$ , an upper limit is set to be ${\mathcal{B}}_{\mathrm{high}}(B^{+}\to \overline{\mathrm{\Lambda }}p{\mu }^{+}{\mu }^{-})<2.8\left(3.7\right)\times {10}^{-9}$ at the 90% (95%) confidence level. 

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