Papers

We test the system-size dependence of bottomonium suppression using the same open-quantum-system transport framework for Pb-Pb, O-O, and Ne-Ne collisions. The microscopic transport coefficients are retained from previous Pb-Pb analyses. Using QTraj, we solve the next-to-leading-order pNRQCD Lindblad equation in anisotropic hydrodynamic backgrounds and calculate integrated $\Upsilon$ double ratios. The QGP-induced evolution reproduces the observed sequential hierarchy and overall magnitude of the O-O suppression measured by CMS and LHCb. We quantify the sensitivity to both transport coefficients and to the termination temperature of the in-medium evolution. The Ne-Ne measurement favors somewhat stronger suppression than predicted, although the present experimental uncertainty is large. The extension from Pb-Pb to light ions supports, at least for observables less sensitive to cold nuclear matter effects, a common microscopic origin of bottomonium suppression in deconfined matter, characterized by the same temperature-dependent transport coefficients despite the large change in collision-system size.

We introduce a new method for extracting resonance pole positions that does not require non-Hermitian extensions of a Hamiltonian. The complex resonance poles are extracted from unitary time evolution of a persistent state, a compact trial state chosen such that its survival amplitude is governed by a single exponential over an extended time window. We solve several two- and three-body systems interacting via short- and long-range forces on a lattice and show that the pole positions obtained using the persistent state method converge approximately exponentially with the linear size of the system. We also consider a gate-based quantum implementation of our method using the Rodeo algorithm and a Hamiltonian variational ansatz, and outline an extension to two-cluster scattering.

The LUX-ZEPLIN (LZ) Collaboration has reported a nuclear-recoil candidate with reconstructed energy $248\pm23_{\rm stat}\pm23_{\rm sys}\,\mathrm{keV}$. We investigate an interpretation in terms of composite inelastic dark matter, in which a dimension-ten operator splits the lightest baryon of a confining $SU(3)_{\rm D}$ theory into two Majorana states. Endothermic scattering is mediated by a leptophobic vector coupled to baryon number. For a dark-baryon mass of $1\,\mathrm{TeV}$ and a splitting of $300\,\mathrm{keV}$, a reference nucleon cross section of $6.5\times10^{-43}\,\mathrm{cm^2}$ lies within LZ's published two-sided 90% confidence interval. This benchmark fixes $M_V/g_B\simeq9.9\,\mathrm{TeV}$, where $M_V$ and $g_B$ are the mediator mass and baryon-number gauge coupling, and is compatible with solar neutrino and dijet constraints.

We study the spectroscopy and decays of the $B_c$ meson in a nonrelativistic quark model in which all observables follow from a single set of wave functions, with spin-dependent effects included directly in the bound-state equation. With parameters calibrated to the measured $B_c(1S)$ and $B_c(2S)$ masses, we predict the $S$-, $P$-, and $D$-wave spectrum up to $n=5$, the pseudoscalar and vector decay constants with one-loop QCD corrections, the E1 and M1 radiative widths, and the radial Regge trajectories of ten spin-parity families. The $1P$ multiplet is predicted at 6692–6746~MeV with the normal fine-structure ordering, compatible with lattice QCD and located in the region of the two structures observed by LHCb in the $B_c^+\gamma$ spectrum. The $1D$ states lie near 7008~MeV, below the $BD$ threshold, and all four $D$-wave families are provided. The decay constant $f_{B_c}=507.1$~MeV is consistent with recent QCD sum-rule results and corresponds to $\mathcal{B}(B_c\to\tau\nu_\tau)\approx3\%$. The E1 widths follow the expected angular weights, while their magnitudes are governed mainly by the radial overlap. The $1P\to1S$ (81–112~keV) and $1D\to1P$ (71–93~keV) widths suggest the $1D\to1P\to1S$ cascade as a promising route toward the first $D$-wave $B_c$ state. The Regge trajectories are nearly linear, with slopes decreasing from about 5.8~GeV$^2$ for the $S$-wave to 4.7–4.8~GeV$^2$ for the $D$-wave states. These results may guide forthcoming measurements at the LHC and future $e^+e^-$ facilities.

We present a non-perturbative Ward-identity prescription for determining the flowed quark field renormalization factor $Z_\chi$, avoiding the computational difficulties of the conventional ringed prescription. The method is based on vector-current normalization and ratios of flowed and unflowed meson two-point functions. We determine the resulting $\mathring{Z}_{\chi}^{V}(t_f,a)$ on five $2+1$-flavor clover ensembles and validate it in the pseudoscalar, scalar, axial-vector, and tensor channels. Renormalized matrix elements obtained through sequential continuum and zero-flow-time extrapolations agree with independent RI/MOM and RI/SMOM determinations. The finite-lattice-spacing bilinear renormalization factors show differences that decrease toward finer lattices, reflecting the different discretization effects of the renormalization methods. The cross-channel agreement demonstrates the viability of the proposed prescription; together, the method and its systematic validation establish a robust foundation for the non-perturbative renormalization of flowed fermionic operators in future lattice calculations.

We apply the gradient-flow framework to determine the nonperturbative medium contribution to the jet transport coefficient $\hat q$ using quenched lattice QCD in the temperature range $0.76T_c \leq T \leq 2.25T_c$. The calculation focuses on the leading-twist contribution at leading order for an asymptotically energetic quark propagating through a thermal pure-gluon plasma. In the infinite-energy limit, the operator-product expansion expresses $\hat q/T^3$ in pure gauge theory as the product of a perturbative short-distance coefficient and the entropy density $s/T^3$. The latter is determined from the gradient-flow energy-momentum tensor at three lattice spacings for each temperature and the former is estimated perturbatively at one-loop order. We find that $\hat q/T^3$ is strongly suppressed below $T_c$, rises rapidly across the deconfinement transition, and remains approximately constant at $\hat q/T^3\simeq1.1$ throughout the deconfined temperature range studied. This is statistically consistent with the previous quenched lattice determination based on a different renormalization procedure, providing a nontrivial validation of the gradient-flow framework for the jet transport coefficient. The systematic treatment of operator renormalization and matching provided by gradient flow becomes particularly important in full QCD, because the need to renormalize quark operators and account for their mixing with the gluonic sector can likewise be addressed within the same framework.

In this work, we study the noisy truncated Hausdorff moment problem in the context of recovering parton distribution functions (PDFs) from their moments. We start by reviewing basics of the Hausdorff moment problem and analyze how the relation between the amount of moment data provided and the ability for $f(x)$ to be reconstructed varies across different classes of parton distribution functions; we then turn to using Bayesian methods centered around Gaussian Processes (GPs) to solve the moment problems. Standard aspects of Bayesian regression such as covariance kernel choice, analytical characterization of the posterior, hyperparameter sampling with Monte Carlo methods, and validation metrics are detailed. In addition to this, powerful novel tools, such as a method to correct for mean bias in posterior distributions, and a simple class of covariance kernels whose $x$ correlation length is learned during sampling are introduced. Finally, we test our framework on 5 datasets from valence, gluon, and sea quark phenomenological pion and nucleon PDF datasets, selected to reflect diversity in PDF behavior. We find that our GP framework robustly reconstructs PDFs given a moderate number of moments. Additionally, the novel tools developed in this work resolve persistent issues that would be difficult to address via conventional means. The presented framework can be readily applied to moments obtained via lattice Quantum Chromodynamics (LQCD) to reconstruct PDFs from theoretical first principles.

The axion-photon coupling, crucial for experimental axion searches and tests of the strong CP solution, receives a substantial model-independent contribution $\mathcal C_{\rm QCD}$ from QCD dynamics. Next-to-leading-order chiral perturbation theory (NLO ChPT) in different frameworks has yielded puzzling discrepancies of up to $8\%$, motivating precise first-principles calculations. We present an independent lattice QCD determination using a method complementary to the recent background-field calculation. Computing pseudoscalar-to-two-photon three-point functions and exploiting anomalous Ward identities, we separate $\mathcal C_{\rm QCD}$ into an exact anomaly contribution and a light-quark-mass-suppressed correction. The latter is computed using domain-wall fermions, whose excellent chiral symmetry strongly suppresses discretization effects. Working on two near-physical $N_f=2+1$ ensembles with continuum extrapolation, we obtain $\mathcal C_{\rm QCD}^{\rm IS}=1.619(30)$ (isospin-symmetric), $\mathcal C_{\rm QCD}^{\rm IB}=0.347(22)$ (isospin-breaking), and $\mathcal C_{\rm QCD}=1.965(35)$ in total. While direct comparisons with published NLO ChPT predictions reveal apparent tensions, we identify their sources and show that the ChPT results can be reconciled with our lattice determination. Our result provides a first-principles benchmark for the QCD contribution to the axion-photon coupling and a quantitative test of competing ChPT descriptions.

Heating matter can restore symmetries spontaneously broken at low temperature. The axial $U(1)$ symmetry of quantum chromodynamics (QCD) is different: it is present in the classical theory with massless quarks but is broken upon quantization by the axial anomaly. The anomaly persists at every temperature, yet its observable effects can weaken. Can hot matter nevertheless behave as though this symmetry were restored at long distances? Whether such effective axial $U(1)$ restoration occurs depends on how microscopic quark and gluon dynamics governs the strength and spatial range of axial breaking. This review brings together theoretical developments and first-principles lattice QCD calculations. We examine how gluon-field topology shapes the low-lying Dirac modes and their correlations, how these modes contribute to axial breaking at different spatial scales, and what this implies for the order and critical behavior of the chiral phase transition as quark masses approach zero.

We study interacting relativistic charged bosons at finite temperature and isospin density in a thermodynamically consistent mean-field approach with repulsive phi-4 and phi-6 interactions. The thermodynamics is formulated in an Extended Canonical Ensemble, in which the conserved isospin density, not the chemical potential, is the independent variable. This is essential in the condensed phase, where mu_I is fixed by condensation. With one constant fitted to the lattice pressure at T=120 MeV, the model reproduces the lattice isospin density, energy density, and trace anomaly, phi-6 being more accurate.

We investigate the electromagnetic form factors of the $\rho$ meson family within a holographic QCD framework based on Einstein-dilaton gravity with confining backgrounds. We obtain the elastic and transition form factors using a spectral decomposition of the three-point isospin current correlator and an independent approach based on the Kaluza-Klein expansion. Furthermore, we establish a holographic dictionary of the current matrix element. The elastic form factors are in agreement with available lattice QCD results, whereas the transition form factors, not yet determined within lattice QCD, are predictions of the model. For the elastic case, the electric form factor for the $\rho$ meson family exhibits a zero at $q^{2} = 6\, m_{\rho^{n}}^{2}$ and in particular for the ground state $q^{2} = 3.61\,\text{GeV}^{2}$, consistent with light-front and Dyson-Schwinger calculations. We also compute strong couplings between vector meson states and find some approximate selection rules. In the elastic case and low-$q^{2}$ regime, we calculate dimensionless electric radius, magnetic and quadrupole moments and compare with other approaches. In the high-$q^{2}$ regime, the form factors follow the expected scaling behavior, and the model predicts their asymptotic normalization. The results in the high-$q^{2}$ regime lead to superconvergence relations and establish a new sum rule involving masses, decay constants and couplings.

We present a real time formalism to numerically describe the gravitational collapse of a scalar quantum field in the spherically symmetric case. We employ a Pauli-Villars regulator that is specifically designed to cancel the ultraviolet divergences in the energy-momentum tensor identified by covariant point splitting, including the logarithmic ones. Using this regulator, we find that the leading term of the entanglement entropy, which is proportional to the surface area, vanishes for a spherical region of flat spacetime. First numerical results for the dynamical case indicate that for a collapsing shell of a massless scalar field, the area normalized entropy is concentrated on the shell and has an approximately constant maximum value during time evolution. This maximum value appears to be finite in the continuum limit and only mildly dependent on the regulator mass.

In lattice QCD computations of generalized parton distributions (GPDs), the large momentum expansion generally requires all hard scales, $2|x\pm\xi|P^z$ and $2|1\pm x|P^z$, to be much larger than $\Lambda_{\rm QCD}$. We show that this condition can be relaxed for $2|x\pm\xi|P^z$ at large $\xi$, making the important $x\sim\pm\xi$ regions accessible to lattice calculations and considerably expanding the region of computability. Revisiting previous lattice results with complete one-loop matching, we obtain the expected partonic threshold behavior—GPDs continuous at $x=\pm\xi$ but with discontinuous derivatives—which has not previously been observed on the lattice. We thus obtain, for the first time, important prediction for GPDs in the distribution-amplitude-like region, which smoothly connects the quark and antiquark PDF-like behaviors.

The study of phase transitions plays an important role in understanding qualitative changes in the behaviour of physical systems at criticality. Despite decades of progress, there is still a strong demand for high-precision numerical tools capable of resolving subtle critical phenomena. Motivated by this need, in this thesis, we present two complementary numerical investigations of phase transitions in lattice systems. The first uses GPU-accelerated higher-order tensor renormalization group (HOTRG) techniques to study the two-dimensional generalized XY model, characterizing its ferromagnetic, nematic, and paramagnetic phases and mapping their phase boundaries using thermodynamic observables in the thermodynamic limit. The second develops and benchmarks a configurational temperature estimator, constructed from gradients and Hessians of the Euclidean lattice action, in compact U(1) lattice gauge theories. On one hand, tensor network methods capture rich phase structures when truncation and finite-bond effects are adequately controlled. On the other hand, the configurational temperature estimator provides an independent, low-overhead means of validating thermal sampling across different algorithms and models, and can also be used as a runtime diagnostic to identify sampling pathologies before large-scale production runs.

Gauge theoretic descriptions of 2D quantum magnets are defined on a restricted physical Hilbert space by imposing Gauss's law. In this work, we study an unconstrained compact lattice QED$_{2+1}$ coupled to bond phonons, in which local Gauss operators are conserved, but their eigenvalues are not a priori fixed. Using exact auxiliary-field quantum Monte Carlo simulations at $N_f = 2$, we investigate how the physical Gauss sector becomes energetically favourable, and how this process is connected to confinement and symmetry breaking. We identify an orthogonal semimetallic (OSM) phase, in which fermions striped off their gauge charge and form a Dirac liquid. This phase mixes various Gauss sectors, and becomes unstable when Gauss's law is explicitly enforced. Upon the imposition of Gauss's law, compactness allows for monopole excitations carrying antiferromagnetic (AFM) and valence-bond-solid (VBS) quantum numbers. Gauge field fluctuations and spinon-phonon coupling tune between the competition of such monopoles and generate a phase diagram with OSM, AFM and VBS orders. The transitions out of the OSM phase coincide with the dynamical generation of Gauss's law, while the competition between AFM and VBS charged monopoles produces a transition consistent with deconfined quantum criticality. Thus our results establish that upon the projection to the physical Hilbert space, deconfinement in compact lattice QED$_{2+1}$ is always unstable towards either AFM or VBS order.

We review recent advances in particle physics enabled and motivated by the rapid progress of quantum technologies. The continued development of quantum computing toward large-scale, fault-tolerant systems has the potential to address dynamical problems that remain extremely challenging for classical computational approaches, opening new avenues for studying nonperturbative dynamical processes. Tabletop detectors and quantum-enhanced technologies have reached unprecedented sensitivities, enabling novel searches for ultralight particles, gravitational waves, and other physics beyond the Standard Model in parameter regimes previously inaccessible to conventional instrumentation. Taken together, these developments highlight a rapidly evolving landscape in which quantum technologies are beginning to reshape fundamental physics. We aim to synthesize recent progress and illuminate the opportunities they present for advancing particle physics in the coming years.

We report the results of the first numerical lattice study using domain-wall fermions in the Sp(4) gauge theory coupled to two flavours of (Dirac) fermions, transforming in the fundamental representation of the gauge group. This theory plays a prominent role in the literature on extensions of the Standard Model with composite dynamics. It provides a short-distance completion for a class of composite Higgs models, or, alternatively, of dark matter models based on the strongly interacting massive particle paradigm. We adopt the Möbius formulation of domain-wall fermions (MDWF), implemented within the Grid software environment. We report the results of extensive tests of the algorithm implementation, and of the optimisation of the choices of algorithmic parameters appearing in the MDWF action. We then measure masses and decay constants of the lightest flavoured mesons in ensembles with moderately large fermion masses and several choices of lattice coupling, and perform an extrapolation to the continuum. We compare our results for the physical observables to published measurements obtained in the same field theory, but derived on the lattice by employing Wilson fermions. We demonstrate that, with the deployment of moderate computational resources, the MDWF formulation can yield order-of-magnitude gains in the approach to the continuum limit, in regions of physical parameter space relevant to phenomenological applications of this theory.

We investigate the structure of the $K^+$ meson through calculating its valence-quark (anti quark) generalized parton distribution functions (GPDs) and form factors (FFs). For this purpose, we use a theoretical framework which is based on the exponential representation scheme (ERS). In this scheme the valence-quark GPDs of the light mesons, including the kaon, are considered as the valence quark distribution function crossed by the exponential of a profile function, at zero skewness. We apply the modified chiral quark model ($\chi QM$ ) to obtain the input valence distribution functions of the kaon in above scheme and calculate its valence GPDs. The kaon's electromagnetic and gravitational form factors are also determined and compared with existing experimental data and the results of some theoretical and phenomenological models.

This work describes a variational technique to solve non-Hermitian quantum systems, in particular those with negative coupling quartic self-interaction. Differences of applying variational methods from standard quantum mechanics to non-Hermitian quantum mechanics – including potential pitfalls – are highlighted. A successful implementation of the variational approach for the non-Hermitian case is presented. The technique is used to analyze scalar quantum field theory in d=2 with negative quartic self-interaction in the Hamiltonian formulation in lattice discretization.

Over the past three decades, generalized parton distributions (GPDs) have emerged as one of the most active and important areas of research in nucleon structure and quantum chromodynamics (QCD). Since the last comprehensive review two decades ago, substantial progress has been made in experimental measurements of hard exclusive processes, such as deeply virtual Compton scattering and near-threshold $J/\psi$ production, as well as in increasingly sophisticated phenomenological analyses of GPDs that enable three-dimensional nucleon tomography. Theoretical advances in perturbative coefficient functions, scale evolutions, and kinematic and power corrections have considerably improved the precision of GPD phenomenology, while new hard exclusive processes for probing GPDs have been explored. More interestingly, lattice QCD can now directly access GPDs at fixed parton momentum fractions $x$ and skewness $\xi$ through large-momentum expansions, in addition to the traditional calculations of their moments, or generalized form factors. Significant progress has also been made in exploring the QCD energy-momentum tensor that encodes fundamental information on the nucleon's mass distribution, complete spin structure, and spatial distributions of momentum current and color-Lorentz forces acting on quarks and gluons.

Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales. We develop a sign-free path-integral framework for Kitaev quantum doubles $\mathcal D(G)$ by organizing single-link perturbations in terms of non-invertible electric and magnetic 1-form symmetries that proliferate distinct anyon species. For any finite group $G$, an exact $\textit{matterization}$ isometry introduces vertex degrees of freedom and maps the link-only model onto a $G$ gauge–Higgs theory. Furthermore, the 1-form symmetries of the fixed point allow us to define generalized Fredenhagen–Marcu order parameters that become finite when the corresponding anyons condense. For $G = S_3$, quantum Monte Carlo simulations show that proliferating a non-Abelian electric anyon drives a first-order transition in which all nontrivial electric anyons condense. In the purely magnetic limit, the model reduces to a $(2+1)$D pure $G$ gauge theory; for $G=S_3$, it exhibits a first-order confinement transition, diagnosed by the onset of a Wilson-loop area law and the restoration of an emergent magnetic 1-form symmetry. These results provide a unified numerical framework for non-Abelian anyon condensation, confinement, and generalized symmetry breaking.

Motivated by the recent CMS data on a family of $2^{++}$ states from $J/\psi J/\psi$ mass spectrum, we determine the masses of the $2^{++}$ $J/\psi J/\psi$ molecule and $cc\bar c\bar c$ states, by using (for the first time) the two lowest QCD Laplace Sum Rules (LSR) moment-ratios within the standard optimization criteria with respect to the LSR variable $\tau$ and to the QCD continuum threshold $t_c$ implemented by the $R_{P/C}$ requirement that the lowest ground state (Pole) contribution to the LSR is larger than the QCD continuum one. Including factorized NLO perturbative and LO $G^4$ gluon condensates in the OPE, we obtain the the lowest ground state masses: $M^{2^{++}}_{J/\psi J/\psi}=6521(69)$ MeV and $M^{2^{++}}_{cc\bar c \bar c}=6347(99)$ MeV with the couplings\,: $f^{2^{++}}_{J/\psi J/\psi}=96(14)$ keV and $f^{2^{++}}_{cc\bar c \bar c}= 151(29)$ keV normalized as $f_\pi=93$ MeV. The masses of the first radial excitations are :$M^{2^{++}{rad}}_{J/\psi J/\psi}=7987(251 )$ MeV and $M^{2^{++}{rad}}_{cc\bar c \bar c}=7739(221)$ MeV indicating a mass-splitting about $2.5 (M_{\psi(2S)}-M_{J/\psi})$. The decay constants are $f^{2^{++}{rad}}_{J/\psi J/\psi}=248(70)$ keV and: $f^{2^{++}{\rm rad}}_{cc\bar c\bar c}=453(96) $ keV which are (unexpectedly) larger than the lowest ground state ones. These features may indicate some new dynamics compared to ordinary $\bar cc$ states. We extend the analysis to the $0^{++}$ states and to the $\Upsilon\Upsilon$ family where the results are compiled in Tables 2 and 3. We critically review some other QCD spectral sum rules (QSSR) results. We suggest that the X(6600) might be a molecule ground state. Using a two-component mass mixing scheme, the X(6900) and X(7100) might be interpreted as a mixture of the $cc\bar c\bar c$ lowest ground state with its 1st radial excitation via an angle $\theta=5^0$.

This work reports on the computation of the ghost-gluon vertex for the pure Yang-Mills SU(3) gauge group, using lattice simulations and the Landau gauge. The simulations access only one of the form factors that describes the vertex. The form factor is estimated using large statistical ensembles of gauge configurations, with two different lattice spacings and two different volumes to check for finite size effects. Moreover, the calculation shows the importance of using lattice perturbation theory, instead of its continuum version, to correct for the breaking of rotational symmetry. The measured bare lattice form factors are compatible, within errors, for all the ensembles. The form factor has a maximum at momentum $\sim 1$ GeV, is suppressed in the infrared and is compatible with a constant behaviour at high momenta, in good agreement with the corresponding lattice estimations for the SU(2) gauge group.

It has been over fifty years since Kenneth Wilson had his Nobel-prize-winning ideas on the renormalization group. In this time frame, despite many attempts, no mathematical results have implemented Wilson's vision to a satisfactory degree. Although a number of predictions stemming from the renormalization group framework have been proven to date, these proofs usually rely on alternative ideas and do not cover the full predictive power of Wilson's renormalization group. The discovery of pathologies within rigorous implementations of renormalization group transformations have further reduced the enthusiasm of the mathematics community for this subject. This paper presents a novel framework to implement Wilson's original idea in a rigorous manner based on inverse limits of finite systems. Doing so, one avoids these pathologies and hence obtains a mathematically sound framework for Wilson's renormalization group. This opens up a completely new path to tackle some of the existing problems in rigorous renormalization group theory like the existence of non-trivial fixed points.

High-energy hadron reactions could be appropriate to find exotic evidences in exotic hadron candidates instead of global observables such as masses, spins, parities, and decay widths, because quarks and gluons are explicit degrees of freedom. One of possible methods is to use fragmentation functions (FFs) by taking advantage of properties on favored and disfavored functions, which corresponds to valence-quark and sea-quark distributions in parton distribution functions. Looking at these FFs, we should be able to find the exotic nature as the valence-quark distributions reflect the nature of valence constituents as shown in the pion and the proton. Recent accurate measurements of the $f_0$(980) FFs by the Belle collaboration made it possible to find its internal configuration by looking at their second moments and functional forms. Global analysis results of the $f_0$(980) FFs indicate that its internal configuration looks like $s\bar s$, which is different from a tetraquark or $K\bar K$-molecule like configuration suggested from low-energy studies. This fact indicates that the internal configuration looks different depending on the energy. At low energies, it looks like a tetraquark ($K\bar K$ molecule) hadron, but it looks like a $q\bar q$ hadron at high energies. In the similar way, some exotic hadron candidates could become ordinary $q\bar q$ or $qqq$ hadrons at high energies, although they are interpreted as exotic at low energies. This kind of new idea should be tested by future experiments especially by looking at energy or momentum dependencies in high energy hadron reactions.

In lepton scattering from nuclei, it has been taken for granted that nuclear modifications do not exist for the longitudinal-transverse structure-function ratio $R$, although nuclear effects in $F_2$ have been investigated for a long time. In fact, experimental data of lepton-nucleus scattering have been analyzed with this assumption. It is obviously not appropriate because nuclear modifications exist in the function $R$ theoretically as shown in this work. In this work, we explain nucleon's Fermi motion's effects by using a convolution description for nuclear structure functions, especially on the deuteron. The longitudinal and transverse structure functions are defined by taking the virtual photon momentum direction along the $z$ axis. However, nucleons in a nucleus could move in any direction, so that nucleon's longitudinal and transverse structure functions could mix with each other in the nuclear medium. Such mixing effects could be of the order of $\vec p_\perp^{\,2}/Q^2$, where $\vec p_\perp$ is the nucleon's transverse momentum and $Q^2$ is given by $Q^2=-q^2$ with the virtual-photon momentum $q$, because the transverse Fermi-motion is the source of such a mixture. In addition, nuclear effects are different between the longitudinal and transverse structure functions in the convolution model because their $x$-dependent functional forms are different. Convolution integrals have different results between the longitudinal and transverse structure functions for nuclei. Because the experiment is in progress at the Thomas Jefferson National Accelerator Facility to measure the function $R$ for the deuteron, the numerical results are shown on the nuclear effects of $R$ in the deuteron. Hopefully, such nuclear effects are found experimentally by future experiments including heavy nuclear targets.

(Suzuki-)Trotter decompositions, splitting methods, (Lie) product formulae... The most common numerical methods for the time evolution of quantum systems come with many names. And they are used practically everywhere with applications ranging from the solution of classical equations of motion and various Monte Carlo simulations to the real and imaginary time evolution on classical as well as quantum computers. Here we review the state of the art of said methods, focussing especially on the progress made over the last few years. We highlight recently discovered efficient time evolution algorithms and explain how best to use them in practice. A central part of this work is the estimation of error bounds that has improved greatly within the past decade. The relevance of time evolution methods for quantum computing is discussed with a focus on noisy hardware. Finally, a comprehensive overview of generalisations, related methods and alternatives to Trotterization is provided. This includes time-dependent Hamiltonian dynamics, processed methods, multi-product formulae, symplectic integrators, TDVP for tensor networks, quantum signal processing, Crouch-Grossman methods and more. The overall perspective in this work is that of a theoretical physicist. All mathematical proofs as well as some technical details are omitted for easier readability. Instead, this review serves as a hands-on guide and, of course, as a starting point for references that provide further details.

Most modern lattice QCD calculations take the masses of the light quarks to be degenerate, setting $m_u=m_d$, a choice that, while not physical, increases computational efficiency and lowers the complexity of simulations and analysis. For many observables, the systematic error associated with this simplification is expected to be negligible, as $\Delta m_{ud}=m_d-m_u$ is significantly below the QCD scale. So far lattice studies have examined the role of strong isospin breaking (SIB) in hadron mass splittings, but SIB effects in thermodynamic observables have only been studied in terms of the crossover temperature with unphysically heavy quarks. Motivated by the recent observation of an unexpectedly large ratio between the abundances of charged versus neutral kaons in heavy-ion collision experiments, we investigate the effects of SIB in QCD thermodynamics by computing observables for three non-degenerate flavors ($N_f=1+1+1$) with physical quark masses using dynamical improved staggered fermions. In particular, we investigate the difference between the $u$- and $d$-quark condensates and extract the pseudocritical temperature, the equation of state, and conserved-charge fluctuations, comparing results to standard $N_f=2+1$ simulations.

Detector observables pose a fundamental challenge for nonperturbative lattice methods due to their intrinsically real-time and asymptotic nature. We propose quantum simulation platforms as an ideal setting for studying these observables. Using quantum spin systems as a demonstration, we construct lattice detector operators and establish their connection to continuum energy-flow observables. We demonstrate this framework in the $1+1$-dimensional quantum Ising model, where finite lattice calculations show quantitative agreement with conformal field theory expectations at criticality. These results support the interpretation of the lattice flow operators as regulated counterparts of continuum detectors in the scaling and asymptotic limits, providing a concrete route toward realizing high-energy collider physics on table-top quantum platforms.

Because it offers exactly-integer topological quantities, the modified Villain discretization offers a route to correct anomaly structure at finite lattice spacing. I will present a 4-dimensional purely-bosonic modified Villain model with an ABJ-type vector-vector-axial anomaly. The model may have a direct continuous phase transition from one SSB phase to another, giving hope of yielding 4D CFT with a VVA anomaly.