Search

The pyrochlore lattice magnet has been one of the most fruitful platforms for the experimental and theoretical search for spin liquids. Besides the canonical case of spin ice, works in recent years have identified a variety of new quantum and classical spin liquids from the generic nearest-neighbor anisotropic spin Hamiltonian on the pyrochlore lattice. However, a general framework for the thorough classification and characterization of these exotic states of matter has been lacking, and so is an exhaustive list of all possible spin liquids that this model can support and what is the corresponding structure of their emergent field theory. In this work, we develop such a theoretical framework to allocate interaction parameters stabilizing different classical spin liquids and derive their corresponding effective generalized emerging Gauss's laws at low temperatures. Combining this with Monte Carlo simulations, we systematically identify all classical spin liquids for the general nearest-neighbor anisotropic spin Hamiltonian on the pyrochlore lattice. We uncover new spin liquid models with exotic forms of generalized Gauss's law and multipole conservation laws. Furthermore, we present an atlas of all spin liquid regimes in the phase diagram, which illuminates the global picture of how different classical spin liquids are connected in parameter space and transition into each other. Our work serves as a treasure map for the theoretical study of classical and quantum spin liquids, as well as for the experimental search and rationalization of exotic pyrochlore lattice magnets., Comment: 25 pages, 10 figures, 5 tables

The high-luminosity upgrade of the LHC (HL-LHC) brings unprecedented requirements for precision bunch-by-bunch luminosity measurement and beam-induced background monitoring in real time. A key component of the CMS Beam Radiation Instrumentation and Luminosity detector system is a stand-alone luminometer, the Fast Beam Condition Monitor (FBCM), which is able to operate independently at all times with a triggerless asynchronous readout. FBCM utilizes a dedicated front-end ASIC to amplify the signals from CO$_2$-cooled silicon-pad sensors with 1 ns timing resolution. Front-end (FE) electronics are subject to high-radiation conditions, thus all components are radiation hardened: sensors, ASICs, transceivers, etc. The FBCM ASIC contains 6 channels, each outputting a high-speed binary signal carrying the time-of-arrival and time-over-threshold information. This signal is sent via a gigabit optical link to the back-end electronics for analysis. A dedicated test system is designed for the FBCM FE electronics with a modular setup for all testing needs of the project from initial ASIC validation test to system-level testing with the full read-out chain. The paper reports on the design, read-out architecture, and testing program for the FBCM electronics., Comment: 6 pages, 5 figures. Presented at 6th International Conference on Technology and Instrumentation in Particle Physics (TIPP2023), 4-8 Sep 2023, Cape Town, Western Cape, South Africa. Submitted to PoS(TIPP2023)

In this study, a novel material from the rare-earth based breathing pyrochlore family, Ba3Tm2Zn5O11, was successfully synthesized. Powder X-ray diffraction and high-resolution powder neutron diffraction confirmed phase purity and crystal structure, while thermogravimetric analysis revealed incongruent melting behavior compared to its counterpart, Ba3Yb2Zn5O11. High-quality single crystals of Ba3Tm2Zn5O11 were grown using the traveling solvent floating zone technique and assessed using Laue diffractometer and single crystal X-ray diffraction. Thermodynamic characterization indicated paramagnetic behavior down to 0.05 K, and inelastic neutron scattering measurements identified distinct crystal electric field bands. Additional low-energy excitation studies on single crystals revealed dispersionless bands at 0.8 and 1 meV. Computed phonon dispersions from first principles calculations ruled out phonons as the source of these modes, further illustrating the puzzling and unique properties of Ba3Tm2Zn5O11.

We compute differential distributions for Drell-Yan processes at the LHC and the Tevatron colliders at next-to-next-to-leading order in perturbative QCD, including fiducial cuts on the decay leptons in the final state. The comparison of predictions obtained with four different codes shows excellent agreement, once linear power corrections from the fiducial cuts are included in those codes that rely on phase-space slicing subtraction schemes. For $Z$-boson production we perform a detailed study of the symmetric cuts on the transverse momenta of the decay leptons. Predictions at fixed order in perturbative QCD for those symmetric cuts, typically imposed in experiments, suffer from an instability. We show how this can be remedied by an all-order resummation of the fiducial transverse momentum spectrum, and we comment on the choice of cuts for future experimental analyses., Comment: 31 pages LaTeX, 13 figures

Compass models provide insights into the properties of Mott-insulating materials that host bond-dependent anisotropic interactions between their pseudospin degrees of freedom. In this article, we explore the classical and quantum ground state properties of one such model relevant to certain layered perovskite materials akin to Ba$_2$IrO$_4$ - namely, the Heisenberg-compass model on the square lattice. We first investigate the ground state phase diagram of this model using classical Monte Carlo simulations. These reveal that the low temperature classical phase diagram is divided into six different classes of long-range ordered phases, including four phases that exhibit an order by disorder selection and two phases that are stabilized energetically. This model admits a special duality transformation, known as the Klein duality, conveniently allowing to map one region of coupling parameters onto another and constraining the phase diagram, and which we exploit in our study. From the analysis of the zero-point energy and the free energy of the spin waves, we find that order by quantum disorder at zero temperature and order by thermal disorder select the same orderings as those found from classical Monte Carlo simulations. We further investigate the quantum ground states of this model using numerical exact diagonalization on small clusters by exploiting the translational symmetry of the square lattice. We obtain a ground state phase diagram bearing close resemblance to that found from the classical analysis., Comment: 18 pages, 6 figures

Order-by-disorder, whereby fluctuations lift an accidental classical ground state degeneracy to stabilize a subset of ordered states, is a recurrent and prominent theme in the field of frustrated magnetism where magnetic moments, or spins, are subject to competing interactions. Thus far, such a phenomenon has been discussed in systems where the quantum ground state is not a product state. In this circumstance, both thermal and quantum fluctuations act to lift the accidental classical degeneracy, begging the question whether one mechanism of order-by-disorder is possible without the other. In this paper, we present results exposing a novel route to order-by-disorder, without quantum zero-point fluctuations, in a family of ferromagnetic Heisenberg materials with the Dzyaloshinskii-Moriya (DM) interaction as the leading perturbation. We prove that any colinear ferromagnetic state is an exact eigenstate, even in the presence of the anisotropic DM interaction, while thermal fluctuations give rise to a preference in the magnetization direction. Here, we present in detail an example of the pyrochlore Heisenberg ferromagnet with DM interactions. Using both linear spin-wave theory and classical Monte Carlo simulations, we find that the magnetization can spontaneously rotate at intermediate temperature(s) within the colinear ferromagnetic phase when the DM interaction is large. Additionally, we find that in the large DM regime, the ferromagnetic ground state becomes unstable within the framework of non-linear spin-wave theory. Our results show that thermal order-by-disorder is possible even in the absence of quantum zero-point fluctuations., Comment: 15 pages, 8 figures

The high-luminosity upgrade of the LHC brings unprecedented requirements for real-time and precision bunch-by-bunch online luminosity measurement and beam-induced background monitoring. A key component of the CMS Beam Radiation, Instrumentation and Luminosity system is a stand-alone luminometer, the Fast Beam Condition Monitor (FBCM), which is fully independent from the CMS central trigger and data acquisition services and able to operate at all times with a triggerless readout. FBCM utilizes a dedicated front-end application-specific integrated circuit (ASIC) to amplify the signals from CO$_2$-cooled silicon-pad sensors with a timing resolution of a few nanoseconds, which enables the measurement of the beam-induced background. FBCM uses a modular design with two half-disks of twelve modules at each end of CMS, with four service modules placed close to the outer edge to reduce radiation-induced aging. The electronics system design adapts several components from the CMS Tracker for power, control and read-out functionalities. The dedicated FBCM23 ASIC contains six channels and adjustable shaping time to optimize the noise with regards to sensor leakage current. Each ASIC channel outputs a single binary high-speed asynchronous signal carrying time-of-arrival and time-over-threshold information. The chip output signal is digitized, encoded and sent via a radiation-hard gigabit transceiver and an optical link to the back-end electronics for analysis. This paper reports on the updated design of the FBCM detector and the ongoing testing program., Comment: 16th Topical Seminar on Innovative Particle and Radiation Detectors (IPRD23) 2023 Sept 25-29 Siena, Italy

We introduce a novel geometrically frustrated classical Ising model, dubbed the "spin vorticity model", whose ground state manifold is a novel classical spin liquid, a "2-form Coulomb phase". We study the thermodynamics of this model both analytically and numerically, exposing the presence of algebraically decaying correlations and demonstrating an extensive ground state entropy, and give a comprehensive account of its ground state properties and excitations. Each classical ground state may be decomposed into collections of closed 2-dimensional membranes, supporting fractionalized string excitations attached to the boundaries of open membranes. At finite temperature, the model can then be described as a gas of closed strings in a background of fluctuating membranes. We demonstrate that the emergent gauge structure of the low-temperature phase is naturally captured in the formalism of 2-form electrodynamics, which describes 1-dimensional charged strings coupled to a rank-2 anti-symmetric gauge field. After establishing the classical spin vorticity model, we consider perturbing it with quantum exchange interactions, from which we derive an effective membrane exchange model of the quantum dynamics of these membranes, which maps to a frustrated 2-form U(1) lattice gauge theory. We show the existence of a fine-tuned Rokhsar-Kivelson point where the quantum ground state is an equal weight superposition of all classical ground state configurations. We further demonstrate how to quantize the string excitations, by coupling a 1-form string field to the emergent 2-form U(1) gauge field, thus mapping a quantum spin model to a 2-form gauge-Higgs model. We discuss the stability of the gapless deconfined phase of this gauge theory and the possibility of realizing a novel class of phases of quantum matter: 2-form U(1) quantum spin liquids., Comment: 42 pages, 18 figures, 1 table

Gauge theories are powerful tools in theoretical physics, allowing complex phenomena to be reduced to simple principles, and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behaviour at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and matrix gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the matrix gauge field, rendering the system spin ice like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and matrix gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers pyrochlore materials., Comment: 13 pages, 5 figures

In this paper we study the divisibility and primality properties of the Bernoulli random walk. We improve or extend some of our divisibility results to wide classes of iid or independent non iid random walks. We also obtain new primality results for the Rademacher random walk. We study the value distribution of divisors of the random walk in the Cram\'er model, and obtain a general estimate of a similar kind to that of the Bernouilli model. Earlier results on divisors and quasi-prime numbers in the Bernoulli model are recorded, as well as some other recent for the Cram\'er random model, based on an estimate due to Selberg., Comment: 53 pages

Inclusive e$^+$e$^-$ production has been studied with HADES in $\pi^-$ + p, $\pi^-$ + C and $\pi^- + \mathrm{CH}_2$ reactions, using the GSI pion beam at $\sqrt{s_{\pi p}}$ = 1.49 GeV. Invariant mass and transverse momentum distributions have been measured and reveal contributions from Dalitz decays of $\pi^0$, $\eta$ mesons and baryon resonances. The transverse momentum distributions are very sensitive to the underlying kinematics of the various processes. The baryon contribution exhibits a deviation up to a factor seven from the QED reference expected for the dielectron decay of a hypothetical point-like baryon with the production cross section constrained from the inverse $\gamma$ n$\rightarrow \pi^-$ p reaction. The enhancement is attributed to a strong four-momentum squared dependence of the time-like electromagnetic transition form factors as suggested by Vector Meson Dominance (VMD). Two versions of the VMD, that differ in the photon-baryon coupling, have been applied in simulations and compared to data. VMD1 (or two-component VMD) assumes a coupling via the $\rho$ meson and a direct coupling of the photon, while in VMD2 (or strict VMD) the coupling is only mediated via the $\rho$ meson. The VMD2 model, frequently used in transport calculations for dilepton decays, is found to overestimate the measured dielectron yields, while a good description of the data can be obtained with the VMD1 model assuming no phase difference between the two amplitudes. Similar descriptions have also been obtained using a time-like baryon transition form factor model where the pion cloud plays the major role., Comment: (HADES collaboration)

Let $X=\{X_j , j\ge 1\}$ be a sequence of independent, square integrable variables taking values in a common lattice $\mathcal L(v_{ 0},D )= \{v_{ k}=v_{ 0}+D k , k\in \Z\}$. Let $S_n=X_1+\ldots +X_n$, $a_n= {\mathbb E\,} S_n$, and $\s_n^2={\rm Var}(S_n)\to \infty$ with $n$. Assume that for each $j$, $\t_{X_j} =\sum_{k\in \Z}{\mathbb P}\{X_j=v_k\}\wedge{\mathbb P}\{X_j=v_{k+1}\}>0$. Using the Bernoulli part, we prove a general sharp correlation inequality extending the one we obtained in the i.i.d.\,case in \cite{W3}: Let $0<\t_j\le \t_{X_j}$ and assume that $ \nu_n =\sum_{j=1}^n \t_j \, \uparrow \infty$, $n\to \infty$. Let $\k_j\in \mathcal L(jv_0,D)$, $j=1,2,\ldots$ be a sequence of integers such that \begin{equation*} {\rm(1)}\qquad\frac{\kappa_j-a_j}{\s_j}=\mathcal O(1 ), \qq\quad {\rm(2)}\qquad \s_j \,{\mathbb P}\{S_j=\kappa_j\} ={\mathcal O}(1). \end{equation*} Then there exists a constant $C $ such that for all $1\le m

This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research., Comment: QCD Town Meeting White Paper, as submitted to 2023 NSAC LRP committee on Feb. 28, 2023

Accidental ground state degeneracies -- those not a consequence of global symmetries of the Hamiltonian -- are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order-by-thermal-disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, $\Delta $, and show that at low temperatures it scales as the square root of temperature, $\sqrt{T} $. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy., Comment: Main text: 7 pages and 3 figures. Supplemental material: 8 pages and 3 figures

The production of $\Sigma^0$ hyperons in proton proton collisions at a beam kinetic energy of 3.5 GeV impinging on a liquid hydrogen target was investigated using data collected with the HADES setup. The total production cross section is found to be $\mathrm{\sigma (pK^{+}\Sigma^{0}) [\mu b] = 17.7 \pm 1.7 (stat) \pm 1.6 (syst)}$. Differential cross section distributions of the exclusive channel $\mathrm{pp \rightarrow pK^{+}\Sigma^{0}}$ were analyzed in the center-of-mass, Gottfried-Jackson and helicity reference frames for the first time at the excess energy of 556 MeV. The data support the interplay between pion and kaon exchange mechanisms and clearly demonstrate the contribution of interfering nucleon resonances decaying to $\mathrm{K^{+}\Sigma^{0}}$. The Bonn-Gatchina partial wave analysis was employed to analyse the data. Due to the limited statistics, it was not possible to obtain an unambiguous determination of the relative contribution of intermediate nucleon resonances to the final state. However nucleon resonances with masses around 1.710 $\mathrm{GeV/c^{2}}$ ($\mathrm{N^{*}(1710)}$) and 1.900 $\mathrm{GeV/c^{2}}$ ($\mathrm{N^{*}(1900)}$ or $\mathrm{\Delta^{*}(1900)}$) are preferred by the fit.

The double differential production cross sections, $d^2\sigma/d\Omega dE$, for hydrogen isotopes and charged pions in the reaction of p + Nb at 3.5 GeV proton beam energy have been measured by the High Acceptance DiElectron Spectrometer (HADES). Thanks to the high acceptance of HADES at forward emission angles and usage of its magnetic field, the measured energy range of hydrogen isotopes could be significantly extended in comparison to the relatively scarce experimental data available in the literature. The data provide information about the development of the intranuclear cascade in the proton-nucleus collisions. They can as well be utilized to study the rate of energy/momentum dissipation in the nuclear systems and the mechanism of elementary and composite particle production in excited nuclear matter at normal density. Data of this type are important also for technological and medical applications. Our results are compared to models developed to describe the processes relevant to nuclear spallation (INCL++) or oriented to probe either the elementary hadronic processes in nuclear matter or the behavior of compressed nuclear matter (GiBUU).

Hadron production ($\pi^\pm$, proton, $\Lambda$, $K_S^0$, $K^\pm$) in $\pi^- + \mathrm{C}$ and $\pi^- + \mathrm{W}$ collisions is investigated at an incident pion beam momentum of $1.7~\mathrm{GeV}/c$. This comprehensive set of data measured with HADES at SIS18/GSI significantly extends the existing world data on hadron production in pion induced reactions and provides a new reference for models that are commonly used for the interpretation of heavy-ion collisions. The measured inclusive differential production cross-sections are compared with state-of-the-art transport model (GiBUU, SMASH) calculations. The (semi-) exclusive channel $\pi^- + A \rightarrow \Lambda + K_S^0 +X$, in which the kinematics of the strange hadrons are correlated, is also investigated and compared to a model calculation. Agreement and remaining tensions between data and the current version of the considered transport models are discussed.

The Reactions with Relativistic Radioactive Beams (R$^3$B) collaboration of the Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany, has constructed an experimental setup to perform fundamental studies of nuclear matter, using as a probe reactions with exotic nuclei at relativistic energies. Among the various detection systems, one of the most recent upgrades consisted on the installation of a large area, around 2 m$^2$, multi-gap Resistive Plate Chamber (RPC), equipped with twelve 0.3 mm gaps and readout by 30 mm pitch strips, exhibiting a timing precision down to 50 ps and efficiencies above 98% for MIPs in a previous characterization of the detector. The RPC was part of the setup of the FAIR Phase 0 experiment that focused on measuring, for the first time, nucleon-nucleon short-range correlations (SRC) inside an exotic nucleus ($^{16}$C) that occurred in Spring 2022. The excellent timing precision of this detector will allow the measurement of the forward emitted proton momentum with a resolution of around 1%. In beam measurements show an RPC efficiency above 95% and a time precision better than 100 ps (including the contribution of a reference scintillator and the momentum spread of the particles) for forward emitted particles.

We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as $\Gamma_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the $\psi_3$ state in most parts of the $\Gamma_5$ regime. Likewise, thermal fluctuations treated classically, select the $\psi_3$ state at $T=0^+$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the $\psi_2$ state of $\Gamma_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from $\psi_2$ to $\psi_3$ at a temperature $T_{\Gamma_5}

For sums $S_n=\sum_{k=1}^n X_k$, $n\ge 1$ of independent random variables $ X_k $ taking values in $\Z$ we prove, as a consequence of a more general result, that if (i) For some function $1\le \phi(t)\uparrow \infty $ as $t\to \infty$, and some constant $C$, we have for all $n$ and $\nu\in \Z$, \begin{equation*}\label{abstract1} \big|B_n\P\big\{ S_n=\nu\big\}- {1\over \sqrt{ 2\pi } }\ e^{- {(\nu-M_n)^2\over 2 B_n^2} }\big|\,\le \, {C\over \,\phi(B_n)}, \end{equation*} then (ii) There exists a numerical constant $C_1$, such that for all $n $ such that $B_n\ge 6$, all $h\ge 2$, and $\m=0,1,\ldots, h-1$, \begin{align*}\label{abstract1} \Big|{\mathbb P}\big\{ S_n\equiv\, \m\ \hbox{\rm{ (mod $h$)}}\big\}- \frac{1}{h}\Big| \le {1\over \sqrt{2\pi}\, B_n }+\frac{1+ 2 {C}/{h} }{ \phi(B_n)^{2/3} } + C_1 \,e^{-(1/ 16 )\phi(B_n)^{2/3}}. \end{align*} Assumption (i) holds if a local limit theorem in the usual form is applicable, and (ii) yields a strenghtening of Rozanov's necessary condition. Assume in place of (i) that $\t_j =\sum_{k\in \Z}{\mathbb P}\{X_j= k\}\wedge{\mathbb P}\{X_j= k+1 \} >0$, for each $j$ and that $\nu_n =\sum_{j=1}^n \t_j\uparrow \infty$. We prove also strenghtened forms of the asymptotic uniform distribution property., Comment: 18 pages. arXiv admin note: text overlap with arXiv:2208.02700

Let $X $ be a square integrable random variable with basic probability space $(\O, \A, \P)$, taking values in a lattice $\mathcal L(v_0,1)=\big\{v_k=v_0+ k,k\in \Z\big\}$ and such that $\t_X =\sum_{k\in \Z}\P\{X=v_k\}\wedge \P\{X=v_{k+1}\}>0$. Let $ X_i$, $i\ge 1 $ be independent, identically distributed random variables having same law than $X$, and let $S_n=\sum_{j=1}^nX_j$, for each $n$. Let $\m_k\ge 0$ be such that $ \m= \sum_{k\in \Z}\m_k $ verifies $1- \t_X<\m<1$, noting that $\t_X< 1$ always. Further let $\t=1-\m$, $s(t) =\sum_{k\in \Z} \m_k\, e^{ 2i \pi v_kt}$ and $\rho$ be such that $1-\t<\rho<1$. We prove the following uniform semi-local theorems for the class $\mathcal F=\{F_{d}, d\ge 2\}$, where $F_{d}= d\N$. \noi(i) There exists $\theta=\theta(\rho,\t)$ with $ 0< \theta <\t$, $C$ and $N$ such that for $ n \ge N$, \begin{align*} \sup_{u\ge 0}\,\sup_{d\ge 2} \Big| \P \{ S_n+u\in F_{d} \} - {1\over d}- {1\over d}\sum_{ 0< |\ell|

This report summarizes the work of the Energy Frontier Topical Group on EW Physics: Heavy flavor and top quark physics (EF03) of the 2021 Community Summer Study (Snowmass). It aims to highlight the physics potential of top-quark studies and heavy-flavor production processes (bottom and charm) at the HL-LHC and possible future hadron and lepton colliders and running scenarios.

Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short Note., Comment: 4 pages. arXiv admin note: substantial text overlap with arXiv:2208.02700

High precision measurements of flow coefficients $v_{n}$ ($n = 1 - 4$) for protons, deuterons and tritons relative to the first-order spectator plane have been performed in Au+Au collisions at $\sqrt{s_{NN}} = 2.4$ GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at the SIS18/GSI. Flow coefficients are studied as a function of transverse momentum $p_{t}$ and rapidity $y_{cm}$ over a large region of phase space and for several classes of collision centrality. A clear mass hierarchy is found for the slope of $v_{1}$, $d v_{1}/d y^{\prime}|_{y^{\prime} = 0}$ where $y^{\prime}$ is the scaled rapidity, and for $v_{2}$ at mid-rapidity. Scaling with the number of nucleons is observed for the $p_{t}$ dependence of $v_{2}$ and $v_{4}$ at mid-rapidity, which is indicative for nuclear coalescence as the main process responsible for light nuclei formation. $v_{2}$ is found to scale with the initial eccentricity $\langle \epsilon_{2} \rangle$, while $v_{4}$ scales with $\langle \epsilon_{2} \rangle^{2}$ and $\langle \epsilon_{4} \rangle$. The multi-differential high-precision data on $v_{1}$, $v_{2}$, $v_{3}$, and $v_{4}$ provides important constraints on the equation-of-state of compressed baryonic matter., Comment: 21 pages, 18 figures, 4 tables; Figs. 11 updated; The manuscript has associated data in the HEPData repository: https://doi.org/10.17182/hepdata.152804

The global polarization of {\Lambda} hyperons along the total orbital angular momentum of a relativistic heavy-ion collision is presented based on the high statistics data samples collected in Au+Au collisions at \sqrt{s_{NN}} = 2.4 GeV and Ag+Ag at 2.55 GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at GSI, Darmstadt. This is the first measurement below the strangeness production threshold in nucleon-nucleon collisions. Results are reported as a function of the collision centrality as well as a function of the hyperon transverse momentum (p_T) and rapidity (y_{CM}) for the range of centrality 0--40%. We observe a strong centrality dependence of the polarization with an increasing signal towards peripheral collisions. For mid-central (20--40%) collisions the polarization magnitudes are (%) = 6.8 \pm 1.3 (stat.) \pm 2.1 (syst.) for Au+Au and (%) = 6.2 \pm 0.4 (stat.) \pm 0.6 (syst.) for Ag+Ag, which are the largest values observed so far. This observation thus provides a continuation of the increasing trend previously observed by STAR and contrasts expectations from recent theoretical calculations predicting a maximum in the region of collision energies about 3 GeV. The observed polarization is of a similar magnitude as predicted by 3D fluid dynamics and the UrQMD plus thermal vorticity model and significantly above results from the AMPT model., Comment: 8 pages, 4 figures

Pinch point singularities, associated with flat band magnetic excitations, are tell-tale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features -- shaped as half-moons and stars -- arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns., Comment: 7 pages, 5 figures. Supplemental Material appended