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1. Bounds for ${\mathrm{SL}}_2$ -indecomposables in tensor powers of the natural representation in characteristic $2$

   https://doi.org/10.5802/art.30  

   Larsen, Michael Jeffrey (January 2025, Annals of Representation Theory)

   Elias, Ben (Ed.)

   Let $K$ be an algebraically closed field of characteristic $2$ , $G$ be the algebraic group ${\mathrm{SL}}_2$ over $K$ , and $V$ be the natural representation of $G$ . Let $b_k^{G,V}$ denote the number of $G$ -indecomposable factors of $V^{\otimes k}$ , counted with multiplicity, and let $\delta =\frac{3}{2}-\frac{log3}{2log2}$ . Then there exists a smooth multiplicatively periodic function $\omega \left(x\right)$ such that $b_{2k}^{G,V}=b_{2k+1}^{G,V}$ is asymptotic to $\omega \left(k\right)k^{-\delta }{4}^k$ . We also prove a lower bound of the form $c_W{k}^{-\delta }{(dimW)}^k$ for $b_k^{G,W}$ for any tilting representation $W$ of $G$ . 

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2. Hadronic Vacuum Polarization for the Muon $g-2$ from Lattice QCD: Long-Distance and Full Light-Quark Connected Contribution

   https://doi.org/10.1103/d583-yhfs  

   Bazavov, Alexei; Bernard, Claude W; Clarke, David A; Davies, Christine; DeTar, Carleton; El-Khadra, Aida X; Gámiz, Elvira; Gottlieb, Steven; Grebe, Anthony V; Hostetler, Leon; et al (July 2025, Physical Review Letters)

   We present results for the dominant light-quark connected contribution to the long-distance window of the hadronic vacuum polarization (HVP) contribution to the muon $g-2$ from lattice quantum chromodynamics. Specifically, with a new determination of the lattice scale on MILC’s physical-mass HISQ ensembles, using the ${\mathrm{\Omega }}^{-}$ baryon mass, we obtain a result of $a_{\mu }^{ll,\mathrm{LD}}\left(\mathrm{conn}\right)=400.2\left(2.3{)}_{\mathrm{stat}}\right(3.7{)}_{\mathrm{syst}}[4.3{]}_{\text{total}}\times {10}^{-10}$ . Summing this result with our recent determinations of the light-quark connected contributions to the short- and intermediate-distance windows, we obtain a subpercent precision determination of the light-quark-connected contribution to HVP of $a_{\mu }^{ll}\left(\mathrm{conn}\right)=655.2\left(2.3{)}_{\mathrm{stat}}\right(3.9{)}_{\mathrm{syst}}[4.5{]}_{\text{total}}\times {10}^{-10}$ . Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab $g-2$ experiment. 

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3. Gluon moment and parton distribution function of the pion from $N_f=2+1+1$ lattice QCD

   https://doi.org/10.1103/PhysRevD.109.114509  

   Good, William; Hasan, Kinza; Chevis, Allison; Lin, Huey-Wen (June 2024, Physical Review D)

   We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310 and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm, using ensembles generated by MILC Collaboration with $2+1+1$ flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain $⟨x{⟩}_g=0.394\left(58{)}_{\mathrm{stat}+\mathrm{NPR}}\right(39{)}_{\text{mixing}}$ in the $\overline{\mathrm{MS}}$ scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates. Published by the American Physical Society2024 

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4. Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Complete short and intermediate windows

   https://doi.org/10.1103/PhysRevD.111.094508  

   Bazavov, Alexei; Clarke, David A; Davies, Christine_T H; DeTar, Carleton; El-Khadra, Aida X; Gámiz, Elvira; Gottlieb, Steven; Grebe, Anthony V; Hostetler, Leon; Jay, William I; et al (May 2025, Physical Review D)

   We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_{\mu }$ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_{\mu }$ , respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong-isospin breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark-connected contribution, we obtain $a_{\mu }^{ll,\mathrm{SD}}\left(\mathrm{conn}\right)=48.139\left(11{)}_{\mathrm{stat}}\right(91{)}_{\mathrm{syst}}[92{]}_{\text{total}}\times {10}^{-10}$ and $a_{\mu }^{ll,\mathrm{W}}\left(\mathrm{conn}\right)=206.90\left(14{)}_{\mathrm{stat}}\right(61{)}_{\mathrm{syst}}[63{]}_{\text{total}}\times {10}^{-10}$ . We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a_{\mu }^{\mathrm{SD}}=69.05\left(1{)}_{\mathrm{stat}}\right(21{)}_{\mathrm{syst}}[21{]}_{\text{total}}\times {10}^{-10}$ and $a_{\mu }^{\mathrm{W}}=236.45\left(17{)}_{\mathrm{stat}}\right(83{)}_{\mathrm{syst}}[85{]}_{\text{total}}\times {10}^{-10}$ . This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level. Published by the American Physical Society2025 

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5. Chemical enhancement of superconductivity in ${\mathrm{LaRu}}_3{\mathrm{Si}}_2$ with mode-selective coupling between kagome phonons and flat bands

   https://doi.org/10.1103/rnv1-rbw2  

   Misawa, Ryo; Kriener, Markus; Yamada, Rinsuke; Nakano, Ryota; Jovanovic, Milena; Schoop, Leslie M; Hirschberger, Max (July 2025, Physical Review Research)

   In kagome metals, flat electronic bands induced by frustrated hopping are a platform for strong electron correlations. Here, we investigate the superconductivity in the kagome system ${\mathrm{LaRu}}_3{\left({\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x\right)}_2$ by chemical pressure tuning while preserving the Ru- $4d$ states that constitute the kagome flat bands. We observe a sizable enhancement in the density of states up to $x=0.07$ , as determined by the specific heat, with a concomitant increase in the superconducting transition temperature $T_{\mathrm{c}}$ . Ge dopants induce a uniaxial lattice expansion along the $c$ axis. Our first-principles calculations suggest that this mitigates the detrimental effect of hybridization between kagome layers and reduces the dispersion of the Ru- $d_{x^2-y^2}$ flat band. The calculated chemical potential moves closer to the maximum in the energy-dependent density of states. Our result is consistent with a theoretical prediction of tunable flat-band superconductivity in ${\mathrm{LaRu}}_3{\mathrm{Si}}_2$ by mode-selective coupling between specific kagome phonons and the Ru- $d_{x^2-y^2}$ orbitals. 

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