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We consider the Glauber dynamics of a ferromagnetic Ising-Kac model on a three-dimensional periodic lattice of size$$(2 N + 1)^3$$${(2N+1)}^3$, in which the flipping rate of each spin depends on an average field in a large neighborhood of radius$$\gamma ^{-1}<\!\!< N$$${\gamma }^{-1}<<N$. We study the random fluctuations of a suitably rescaled coarse-grained spin field as$$N \rightarrow \infty $$$N\to \infty$and$$\gamma \rightarrow 0$$$\gamma \to 0$; we show that near the mean-field value of the critical temperature, the process converges in distribution to the solution of the dynamical$$\Phi ^4_3$$${\Phi }_3^4$model on a torus. Our result settles a conjecture from Giacomin et al. (1999). The dynamical$$\Phi ^4_3$$${\Phi }_3^4$model is given by a non-linear stochastic partial differential equation (SPDE) which is driven by an additive space-time white noise and which requires renormalisation of the non-linearity. A rigorous notion of solution for this SPDE and its renormalisation is provided by the framework of regularity structures (Hairer in Invent Math 198(2):269–504, 2014.https://doi.org/10.1007/s00222-014-0505-4). As in the two-dimensional case (Mourrat and Weber in Commun Pure Appl Math 70(4):717–812, 2017), the renormalisation corresponds to a small shift of the inverse temperature of the discrete system away from its mean-field value.

A multi-TeV muon collider offers a spectacular opportunity in the direct exploration of the energy frontier. Offering a combination of unprecedented energy collisions in a comparatively clean leptonic environment, a high energy muon collider has the unique potential to provide both precision measurements and the highest energy reach in one machine that cannot be paralleled by any currently available technology. The topic generated a lot of excitement in Snowmass meetings and continues to attract a large number of supporters, including many from the early career community. In light of this very strong interest within the US particle physics community, Snowmass Energy, Theory and Accelerator Frontiers created a cross-frontier Muon Collider Forum in November of 2020. The Forum has been meeting on a monthly basis and organized several topical workshops dedicated to physics, accelerator technology, and detector R&D. Findings of the Forum are summarized in this report.

A search for the nonresonant production of Higgs boson pairs in the$HH\to b\overline{b}{\tau }^{+}{\tau }^{-}$channel is performed using$140{\mathrm{fb}}^{-1}$of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The analysis strategy is optimized to probe anomalous values of the Higgs boson self-coupling modifier${\kappa }_{\lambda }$and of the quartic$HHVV$($V=W,Z$) coupling modifier${\kappa }_{2V}$. No significant excess above the expected background from Standard Model processes is observed. An observed (expected) upper limit${\mu }_{HH}<5.9(3.3)$is set at 95% confidence-level on the Higgs boson pair production cross section normalized to its Standard Model prediction. The coupling modifiers are constrained to an observed (expected) 95% confidence interval of$-3.1<{\kappa }_{\lambda }<9.0$($-2.5<{\kappa }_{\lambda }<9.3$) and$-0.5<{\kappa }_{2V}<2.7$($-0.2<{\kappa }_{2V}<2.4$), assuming all other Higgs boson couplings are fixed to the Standard Model prediction. The results are also interpreted in the context of effective field theories via constraints on anomalous Higgs boson couplings and Higgs boson pair production cross sections assuming different kinematic benchmark scenarios.

A search for leptoquark pair production decaying into$$te^- \bar{t}e^+$$$t{e}^{-}\overline{t}{e}^{+}$or$$t\mu ^- \bar{t}\mu ^+$$$t{\mu }^{-}\overline{t}{\mu }^{+}$in final states with multiple leptons is presented. The search is based on a dataset ofppcollisions at$$\sqrt{s}=13~\text {TeV} $$$\sqrt{s}=13\text{TeV}$recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb$$^{-1}$$$_{}^{-1}$. Four signal regions, with the requirement of at least three light leptons (electron or muon) and at least two jets out of which at least one jet is identified as coming from ab-hadron, are considered based on the number of leptons of a given flavour. The main background processes are estimated using dedicated control regions in a simultaneous fit with the signal regions to data. No excess above the Standard Model background prediction is observed and 95% confidence level limits on the production cross section times branching ratio are derived as a function of the leptoquark mass. Under the assumption of exclusive decays into$$te^{-}$$$t{e}^{-}$($$t\mu ^{-}$$$t{\mu }^{-}$), the corresponding lower limit on the scalar mixed-generation leptoquark mass$$m_{\textrm{LQ}_{\textrm{mix}}^{\textrm{d}}}$$$m_{{\text{LQ}}_{\text{mix}}^{\text{d}}}$is at 1.58 (1.59) TeV and on the vector leptoquark mass$$m_{{\tilde{U}}_1}$$$m_{{\tilde{U}}_1}$at 1.67 (1.67) TeV in the minimal coupling scenario and at 1.95 (1.95) TeV in the Yang–Mills scenario.

The production of$\mathrm{\Upsilon }(2S)$and$\mathrm{\Upsilon }(3S)$mesons in lead-lead (Pb-Pb) and proton-proton ($pp$) collisions is studied in their dimuon decay channel using the CMS detector at the LHC. The$\mathrm{\Upsilon }(3S)$meson is observed for the first time in Pb-Pb collisions, with a significance above 5 standard deviations. The ratios of yields measured in Pb-Pb and$pp$collisions are reported for both the$\mathrm{\Upsilon }(2S)$and$\mathrm{\Upsilon }(3S)$mesons, as functions of transverse momentum and Pb-Pb collision centrality. These ratios, when appropriately scaled, are significantly less than unity, indicating a suppression of$\mathrm{\Upsilon }$yields in Pb-Pb collisions. This suppression increases from peripheral to central Pb-Pb collisions. Furthermore, the suppression is stronger for$\mathrm{\Upsilon }(3S)$mesons compared to$\mathrm{\Upsilon }(2S)$mesons, extending the pattern of sequential suppression of quarkonium states in nuclear collisions previously seen for the$J/\psi$,$\psi (2S)$,$\mathrm{\Upsilon }(1S)$, and$\mathrm{\Upsilon }(2S)$mesons.

This paper presents a search for pair production of higgsinos, the supersymmetric partners of the Higgs bosons, in scenarios with gauge-mediated supersymmetry breaking. Each higgsino is assumed to decay into a Higgs boson and a nearly massless gravitino. The search targets events where each Higgs boson decays into$b\overline{b}$, leading to a reconstructed final state with at least three energetic$b$-jets and missing transverse momentum. Two complementary analysis channels are used, with each channel specifically targeting either low or high values of the higgsino mass. The low-mass (high-mass) channel exploits$126(139){\mathrm{fb}}^{-1}$of$\sqrt{s}=13\mathrm{TeV}$data collected by the ATLAS detector during Run 2 of the Large Hadron Collider. No significant excess above the Standard Model prediction is found. At 95% confidence level, masses between 130 GeV and 940 GeV are excluded for higgsinos decaying exclusively into Higgs bosons and gravitinos. Exclusion limits as a function of the higgsino decay branching ratio to a Higgs boson are also reported.

A combination of fifteen top quark mass measurements performed by the ATLAS and CMS experiments at the LHC is presented. The datasets used correspond to an integrated luminosity of up to 5 and$20{\mathrm{fb}}^{-1}$of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, respectively. The combination includes measurements in top quark pair events that exploit both the semileptonic and hadronic decays of the top quark, and a measurement using events enriched in single top quark production via the electroweak$t$channel. The combination accounts for the correlations between measurements and achieves an improvement in the total uncertainty of 31% relative to the most precise input measurement. The result is$m_t=172.52\pm 0.14(\mathrm{stat})\pm 0.30(\mathrm{syst})\mathrm{GeV}$, with a total uncertainty of 0.33 GeV.

A combination of searches for new heavy spin-1 resonances decaying into different pairings ofW,Z, or Higgs bosons, as well as directly into leptons or quarks, is presented. The data sample used corresponds to 139 fb⁻¹of proton-proton collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV collected during 2015–2018 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting quark pairs (qq,bb,$$ t\overline{t} $$$t\overline{t}$, andtb) or third-generation leptons (τνandττ) are included in this kind of combination for the first time. A simplified model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confidence level and are compared with predictions for the benchmark model. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The complementarity of the various analyses increases the sensitivity to new physics, and the resulting constraints are stronger than those from any individual analysis considered. The data exclude a heavy vector-boson triplet with mass below 5.8 TeV in a weakly coupled scenario, below 4.4 TeV in a strongly coupled scenario, and up to 1.5 TeV in the case of production via vector-boson fusion.