Papers

We formulate an S-matrix bootstrap in an exactly flat half-space, where boundary reflection provides geometric infrared control for four-dimensional gravity. Under the channel positivity conditions, we obtain an infrared-finite positivity bound on local four-scalar Wilson coefficients that includes a finite gravitational correction of order $G_N$ and is derived from the full UV absorptive spectrum without specifying a UV theory, imposing a spectral ansatz, requiring weak coupling or expanding the spectrum perturbatively. At fixed dimensionless external state parameters, the coefficient of the leading gravitational correction is independent of the EFT scale and requires neither an arbitrary soft resolution scale nor a model-dependent UV scale. Gaussian wave-packet scattering localizes interactions within the flat region and directly probes bulk Wilson coefficients while exponentially suppressing sensitivity to the boundary. Long-range gravitons remain sensitive to the boundary and give a finite contribution. The smearing functional passes numerical positivity tests with general half-space absorptive kernels in both crossed channels. An explicit string example shows how boundary reflection suppresses the collective contribution of string resonances to the absorptive part of the amplitude, connecting infrared control of low-energy scattering to the UV spectrum of quantum gravity in the same dispersion relation. The framework opens a route to infrared-finite constraints on effective interactions across particle physics and gravity.

We study the tree-level fermion-photon effective vertex for on-shell particles in a relativistic environment undergoing rigid rotation at zero temperature. The rotational background breaks translational invariance in the transverse plane and introduces a preferred direction, leading to a distinct decomposition of the vertex into longitudinal and transverse structures with respect to the rotation axis. Using fermion and photon modes constructed in the rotating frame, we derive the corresponding selection rules and show that the energy and the longitudinal component of the momentum are conserved, whereas no independent transverse momentum-conservation condition arises. Instead, the transverse dependence is governed by radial integrals involving three Bessel functions, whose support constrains the magnitudes of the transverse momentum projections. The vertex can be organized in a circular basis for the transverse components and a Cartesian basis along the rotation axis, and expressed in terms of six Dirac structures. Their coefficients define 24 form-factor components associated with the photon-mode components, physical photon states, and spin-dependent structures induced by the rotating background. We also verify current conservation and gauge invariance of the resulting tree-level matrix element under the boundary conditions considered. These results provide the tree-level structure of the fermion-photon interaction in rotating relativistic matter and establish the basis for the study of radiative corrections in vortical backgrounds.

Pythia is a general-purpose Monte Carlo event generator used in particle, astroparticle, and nuclear physics, by theorists and experimentalists, to simulate particle collisions. Because of the size and diversity of the user community, it is challenging to address all of the needs for new and varied physics models. This paper describes the Pythia-Contrib system, which allows for third-party developers to contribute code to Pythia without introducing external software dependencies to the Pythia code base.

We examine spin-polarized Strange Quark Matter and the complex structure of Strange Quark Stars in the existence of a strong magnetic field. Our framework uses a quasiparticle model, en hanced by a QCD-informed effective quark mass dependent on both chemical potential value and magnetic field strength. The resulting Equation of State yields an energy per baryon below the iron limit, supporting the hypothesis that the actual ground state of matter is strange matter. The Tolman-Oppenheimer-Volkoff expressions are solved and find that the maximum stellar mass decreases with the degree of spin polarization, reaching as high as 2.35 Mo with a related radius 12.33 km. Furthermore, the model predictions for mass, radius, and surface redshift are in excel lent conformance to observational limitations for the massive pulsar PSR J0952-0607. These results highlight the crucial role of quasiparticle medium effects and strong magnetic fields in describing dense matter.

Following the discovery of the exotic state $X(3872)$ in the charmonium spectrum, the possible existence of an analogous state, $X_b$, in the bottomonium sector has attracted considerable attention of the hadronic physics community. In this work, we lay the ground for the development of Born-Oppenheimer chiral effective field theory (BO$\chi$EFT), that allows us to include both quark and hadron degrees of freedom as well as the full complexity of the meson-exchange potential in a systematic way. For illustration, the formalism to leading order (LO) is applied to the system of $\chi_{b1}$ states and in particular the $X_b$. The two parameters that are present at this order are constrained using experimental information on the bottomonium spectrum together with lattice input on static quark-antiquark potentials, including string breaking effects. The framework identifies the observed $1^{++}$ state at 10.513 GeV with a predominantly molecular $X_b$, the bottom counterpart of the $X(3872)$, and predicts an additional predominantly compact bottomonium state at 10.544 GeV, about 60 MeV below the $B\bar{B}^*$ threshold.

The two-loop amplitudes for pseudoscalar pair production in gluon fusion, $gg\to AA$, with each pseudoscalar emitted from its own effective gluon vertex, are known in closed form, but large cancellations near threshold obscure their analytic structure. We expand the IR-finite amplitudes in the pseudoscalar velocity $\beta_A$ through $\beta_A^6$ at fixed scattering angle. All inverse powers of $\beta_A$ and the odd powers through $\beta_A^5$ cancel, and at leading power the angular dependence enters only through $\ln(2p_T/m_A)$. We identify this logarithm with the double parton scattering (DPS) singularity: with the overall constant fixed at threshold, the factorisation formula of Gaunt and Stirling reproduces the velocity dependence of its one-loop coefficient in the forward limit to $3\times10^{-15}$, and a one-loop $gg\to HH$ analysis confirms the corresponding CP-even weight. At two loops the equal-helicity amplitude grows as $\ln^3p_T$, with the leading logarithmic ratio of planar $\mathcal N=4$ super Yang-Mills theory, while the opposite helicity amplitude, which has no one-loop DPS logarithm, grows as $\ln^2p_T$. In the finite virtual correction, relative to the squared tree amplitude, the highest logarithm at order $\alpha_s^2$ is $-\tfrac{7}{64}\alpha_s^2N_c^2\ln^2(2p_T/m_A)$. For $\beta_A\leq0.2$ the series reproduce the unexpanded amplitudes with relative errors of at most $6.77\times10^{-5}$ at the tested points; they provide this two-loop contribution to the hard function for soft-gluon resummation of the pair invariant-mass distribution near $m_{AA}=2m_A$ and are released with code for their numerical evaluation.

Recent work on the two-Higgs-doublet model (2HDM) has uncovered basis-invariant relations among the parameters in the scalar potential that are stable under renormalization group (RG) evolution but do not coincide with any of the standard Higgs-family or Generalized-$\mathrm{CP}$ symmetry classes of the scalar sector. These relations have subsequently been reformulated in terms of so-called GOOFy transformations. In this paper, we show that the same fixed surface admits a conventional interpretation in terms of spurions. The gauge-covariant kinetic terms of the 2HDM possess a Higgs-family $\mathrm{U}(2)_H$ symmetry, and the couplings in the potential may be organized into irreducible spurions under its nontrivial $\mathrm{SU}(2)_H$ subgroup. We first explain the one-loop closure in the spurion language and then establish stability to all orders in the scalar and gauge couplings in any mass-independent scheme. General Yukawa couplings introduce additional Higgs-family covariants and can spoil the scalar-sector selection rule. We therefore consider the six conventional Higgs-family and Generalized-$\mathrm{CP}$ symmetries of the 2HDM, imposed as exact symmetries of the full Lagrangian, and show that closure is controlled by whether the relevant Higgs-family triplet contains an invariant direction. The spurion formulation thus provides a basis-covariant and conventional group-theoretic explanation of the RG stability of the 2HDM parameter relations.

We propose a post-inflationary first-order phase transition modulated by a light spectator field as the origin of primordial large-scale curvature perturbations. Spectator fluctuations acquired during inflation modulate the bubble nucleation history, generating curvature perturbations together with correlated intrinsic gravitational-wave (GW) anisotropies. We show that this mechanism can reproduce the observed amplitude of curvature perturbations while producing a loud stochastic GW background in the frequency bands of space-based detectors such as LISA, Taiji, and TianQin. A concrete benchmark yields strongly enhanced intrinsic GW anisotropies and a local primordial non-Gaussianity signal within reach of future large-scale-structure surveys.

An excited dark-matter state can produce a high-energy nuclear recoil by releasing its mass splitting in a collision. Motivated by the $248$~keV LUX–ZEPLIN candidate, we study freeze-in of a $45$~GeV pseudo-Dirac particle with a $1$~MeV splitting and a $1$~GeV dark photon during non-instantaneous reheating. We choose a recoil normalization compatible with the published INTEGRAL/SPI three-photon decay limit. It predicts $0.43$ events in the LZ window and retains the reference recoil shape. Including both dark-photon and $Z$ exchange, we calculate production and entropy dilution for backgrounds with $T\propto a^{-\alpha}$ and $\rho_\phi\propto a^{-3(1+\omega)}$. For $\Tmax=m_\chi$, the observed abundance requires $\Trh=1.32$~GeV for matter-like constant-width reheating, $3.09$~GeV for quartic oscillations with scalar decay, and $0.588$~GeV for quartic oscillations with constant width, compared with $4.10$~GeV for instantaneous reheating. These finite-reheating solutions are insensitive to increasing $\Tmax$ above $m_\chi$. For $\Tmax\geq m_\chi$, adiabatic kination has no solution with $\Trh>5.96$~MeV, the BBN-motivated cutoff adopted for our scans. At $\alpha_D=10^{-10}$, the estimated thermal-mediator source is below $0.2\%$ of the Standard Model source, and self-conversion does not appreciably deplete the excited population. The calculation relates an exothermic recoil benchmark to the production and dilution history before radiation domination.

Long-baseline (LBL) accelerator experiments are sensitive not only to the standard neutrino oscillation parameters but also to new physics. Currently, there exists a tension between NOvA and T2K data that can be explained by vector non-standard neutrino interactions (NSI) with complex couplings, which in turn introduce degeneracies in LBL measurements. We demonstrate that dark matter direct detection experiments can use their measurements of solar neutrinos to test the NSI resolution of this tension and to break these degeneracies. Using recent solar neutrino data from LZ, XENONnT, and PandaX-4T, we show that dark matter direct detection experiments already constrain part of the NSI solution of the NOvA-T2K tension. These experiments can also probe parts of the NSI parameter space that even DUNE will be blind to. Our analysis combines nuclear recoils from $^8$B neutrinos and electron recoils from $pp$ neutrinos. A future xenon experiment, such as XLZD or PandaX-xT, will be able to cover a significant fraction of the NSI solution of the NOvA-T2K tension.

We study the prospects for an independent determination of $V_{cb}$ from bottom-tagged charged-current deep-inelastic scattering at future electron-proton colliders: the EIC, LHeC, and FCC-eh. The transition $e^- c \to \nu_e b$ probes $|V_{cb}|^2$ through a process with different theoretical and experimental uncertainties from semileptonic $B$ decays. We fit ratios of $b$-tagged charged-current event counts over flavour-inclusive ones in kinematic bins, including correlated parton-distribution and flavour-tag calibration uncertainties, and floating the other CKM parameters. With projected parton distributions and tagging performance motivated by existing studies, we find a potential relative sensitivity in $|V_{cb}|$ of about $0.8\%$ at the LHeC with $1\,\rm{ab}^{-1}$ of integrated luminosity and $0.7\%$ at FCC-eh with $2\,\rm{ab}^{-1}$. The corresponding EIC sensitivity is instead at the level of $20 - 30 \%$, depending on the configuration. The LHeC could thus provide a high-energy determination competitive with low-energy ones, but with substantially different dominant systematic uncertainties, on the timescale of its proposed operation between the HL-LHC and FCC-ee. We identify precise flavour-tag calibration and control of the kinematic response as the main requirements for realising this potential sensitivity.

Stabilizer Rényi entropy quantifies magic relative to a complete Pauli frame. In settings such as helicity states of massless particles, unsynchronized qubit registers, energy eigenbases, and systems under superselection rules, the computational basis may be fixed while the transverse Pauli axes remain unspecified. The stabilizer Rényi entropy then depends on the choice of those axes. We define a phase-averaged stabilizer Rényi entropy by averaging the Pauli moments before taking the logarithm. It is exactly invariant under independent local rephasings. For pure states, it vanishes precisely when the state is a stabilizer state in every phase convention. For a broad class of sparse supports, it reduces to a closed-form function of the basis-state probabilities alone. Within this class, the ceiling for $n$ channels is $\ln[n^{3}/(6n-5)]$ for $n\geq3$ and $\ln\frac{7}{5}$ for two channels. We apply the invariant to tree-level gluon scattering at four and five points, where the helicity-basis phases are unspecified. It saturates the two- and three-channel ceilings: $\ln\frac{7}{5}$ at four points and $\ln\frac{27}{13}$ in $3\to2$ scattering. In same-helicity $2\to3$ scattering, it lies between a floor of $\ln\frac{8}{7}$ and a ceiling of $\ln\frac{184}{125}$, reached in the resolved soft limit and particular collinear limits, respectively. In every configuration studied, the invariant is independent of the fixed external colors.

Inferring the possible existence and location of a critical point on the QCD phase diagram through experimental observations requires equations of state that include both lattice QCD constraints and critical behavior. In this manuscript, we present the first four-dimensional equation of state in the $(T,\mu_B,\mu_Q,\mu_S)$ space combining the lattice 4D $T^\prime$-Expansion Scheme with a critical contribution mapped from the 3D Ising model. We extend the earlier two-dimensional construction, the so-called Ising 2D-TExS in the $(T, \mu_B)$ plane, promoting the critical point to a parametrizable critical surface in the full four-dimensional thermodynamic space. Our framework provides a family of equations of state to systematically study the effects of criticality in realistic hydrodynamic simulations with $BQS$ conserved charges, going beyond the case of strangeness neutrality, by varying the geometry of the critical surface and the strength of criticality at finite $\mu_B$, $\mu_Q$ and $\mu_S$ separately.

Gravitational tail-of-tail corrections arise when radiation scatters twice from the mass-monopole field of its source. In the multipolar effective field theory, one of the two-loop topologies contributing to this process involves genuinely coupled loop momenta, preventing its evaluation through nested one-loop integrations. After tensor reduction, this nonfactorizing structure leads to a particularly challenging family of scalar integrals with unbounded numerator powers as the multipole rank increases. We derive exact closed-form expressions for the entire relevant integer numerator domain, valid in generic dimension and accommodating Feynman, retarded, and advanced prescriptions through consistent analytic continuation. Near $d=3+\epsilon$, we also obtain explicit Laurent expansions through $O(\epsilon)$, retaining the subleading information needed in higher-order radiative calculations. While these expansions determine the dimensional poles, identifying their ultraviolet (UV) or infrared (IR) origin requires a separate analysis of momentum regions. We carry out this analysis throughout the integral domain and apply it directly to the coupled tail-of-tail emission diagram for arbitrary electric and magnetic multipoles. In this way, we independently determine the UV and IR residues, and explicitly verify that the complete infrared pole structure, including both double and simple poles, agrees with the exponentiation of the one-loop gravitational tail. The UV residues, calculated directly from hard-momentum regions, reproduce the established multipole anomalous dimensions when combined with the known contributions of the remaining diagrams.

We investigate dilepton production via virtual quark bremsstrahlung in a hot, magnetized quark-gluon plasma (QGP), extending the Landau-Pomeranchuk-Migdal (LPM) framework to account for a background magnetic field and for Fermi-Dirac quark statistics. An external electromagnetic field drives the quark distribution out of equilibrium, and this off-equilibrium correction, obtained from the Boltzmann equation in the relaxation-time approximation, is in principle explicit in the electric and magnetic field strengths. We argue that this correction, being linear in the electric field, vanishes identically upon integration over the full dilepton solid angle and therefore does not contribute to the dilepton production rate (DPR). The leading magnetic-field signature in the rate instead enters entirely through the equilibrium sector: the medium density and Debye screening mass, computed from the Landau-level structure of the magnetized QGP, modifying the LPM suppression parameter. Working in the regime relevant to the hydrodynamic phase of heavy-ion collisions, we present the LPM-induced DPR for quark scatterers and establish, for the first time, a nonzero magnetic-field imprint on this observable through the LPM mechanism.

We study the potential of very high-energy lepton colliders to probe effective operators affecting the loop-induced Higgs boson decays $h\to \gamma\gamma$ and $h\to Z\gamma$, providing constraints complementary to Higgs coupling measurements at the Large Hadron Collider. In particular, we consider processes with two and three bosons in the final state and analyze their individual and combined impact on the effective field theory parameter space. We demonstrate that these processes at a multi-TeV lepton collider can improve the bounds from rare Higgs decays and electroweak precision observables, surpassing the projections for High-Luminosity LHC and FCC-ee. This is especially true for triboson processes, whose sensitivity is enhanced by the growth with energy of the new physics cross-sections, making them the dominant constraint at very high energies, potentially competitive with FCC-hh.

This paper presents two methods for probing the proton structure and the number of partonic interactions in proton-proton collisions using dimuon production and minimum bias events. At the LHC these targeted measurements can provide information on the average number of partonic scatters in different event classes, their dependence on the partonic momentum fraction, x, and potentially partonic flavour. Within a simple mostly geometric model of multiparton interactions as quasi-independent scatters, the measurements can be used to make inference about the proton-proton overlap dependence on impact parameter and its partonic-x dependence.

High-energy neutrinos from Seyfert galaxies probe particle acceleration near supermassive black holes, but the accelerated nuclear composition remains uncertain. We connect stochastic acceleration to nuclear and radiative cascades to assess nuclear contributions. Acceleration and losses limit the energy per nucleon available to nuclear cascades; without secondary reacceleration, fragmentation cannot raise this scale. For NGC~1068, joint neutrino and gamma-ray constraints depend on the nuclear mixture: helium-dominated injection permits larger nuclear power fractions than the heavier mixtures considered. For the harder candidate {neutrino} spectrum of NGC~7469, the adopted model yields more energetic nuclear cascades, while the source-specific flux selections allow larger nuclear fractions for the heavier mixtures than in NGC~1068. These results show that composition constraints depend on nuclear yields as well as acceleration conditions and available power.

In this work we incorporate thermal fluctuations into fluid-dynamic simulations with the vHLLE code, in linear approximation. The fluctuations are built in following the fluctuation-dissipation theorem. The effect of space discretization into cells in numerical hydrodynamics on the spatial correlation of fluctuations is studied with the help of static structure factor. A difference from the continuum result is pointed out and systematically investigated. Time evolution of the ensuing fluctuations is examined and the Green-Kubo formula is used for the extraction of shear viscosity from the fluctuations. The extracted value is demonstrated to be the same as the input value of the shear viscosity for the simulations using Israel-Stewart equations. It is also shown that numerical regulators commonly used in the codes to ensure stability of the calculation severely spoil the fluctuations and break the fluctuation-dissipation theorem.

Cobimaximal mixing remains a viable approximate pattern since the predicted atmospheric angle ($\pi/4$) and Dirac CP phase ($-\pi/2$) are compatible with current experimental data at the $3\sigma$ level. In this work, we investigate how an additional sterile neutrino state breaks the cobimaximal mixing and the underlying $\mu-\tau$ reflection symmetry in a $3+1$ neutrino scenario. Given the strong constraints already imposed on active-sterile mixings, we examine the resulting restrictions on the model parameter space, assuming a small symmetry breaking induced by the sterile state. We derive predictions for the relevant model parameters, active-sterile mixing angles, and Dirac CP-violating phases, by considering small deviations from the symmetric limit. We also analyze the allowed combinations of Majorana phases through their impact on the effective Majorana mass governing neutrinoless double beta decay. Current experimental limits on this process impose severe constraints on the inverted ordering realization of the $3+1$ scenario, excluding the small breaking regime within the parameter ranges considered. In contrast, the normal ordering case remains viable and predicts values of the effective Majorana mass that lie within the sensitivity reach of upcoming neutrinoless double beta decay experiments.

Quantifying the capability and reliability of agentic systems in high-energy physics (HEP) requires repeated evaluations under controlled configurations. Establishing whether changes to models, tools, or harnesses improve performance also requires these components to be varied independently. We present the High Energy Physics Tool-and-Agent Benchmarking (HEPTABench) framework for portable and controlled evaluations of agentic systems, with separately configurable tasks, scaffolding, models, providers, harnesses, and domain capabilities. The framework combines HEP benchmark tasks and scientific rubrics with experiment execution and versioned tool interfaces. To support inspection, reproducibility, and post-hoc grading, the framework prioritizes recording and reporting complete experiment specifications, agent trajectories, and experiment artifacts. We demonstrate the framework in two benchmark campaigns. The first campaign evaluates a forward long-lived-particle reach calculation across four frontier coding-agent systems, comparing their built-in coding tools with the same tools supplemented by HEP domain tools. We show that including these HEP domain tools improves numerical accuracy and reduces trial-to-trial dispersion for every tested system. In a complementary campaign covering eight symbolic two-body decay tasks, we show that adding symbolic domain tools increases the fraction of successful trials for Claude Haiku 4.5 from $8\%$ to $79\%$, while GPT-5.5 succeeds in every trial with built-in tools alone. Through systematic evaluation of agentic systems, HEPTABench enables the identification of factors that improve the accuracy and reliability of their scientific work.

In the minimal type-I seesaw, one right-handed neutrino (RHN) can decouple from neutrino mass generation. Such a state is usually neglected, yet its feeble couplings make it long-lived, and it can dominate the energy density of the Universe before decaying. We study this in a minimal $U(1)_{B-L}$ model, where the RHNs are produced through $B-L$ gauge interactions, for the cases of a decoupled lightest RHN $N_1$ and a decoupled heaviest RHN $N_3$. The resulting early matter-dominated era dilutes the baryon asymmetry, and for decoupled $N_3$ it also delays the equilibration of the charged-lepton Yukawa interactions, allowing a lighter $N_1$ to generate the asymmetry in the unflavoured regime. Breaking $U(1)_{B-L}$ forms cosmic strings whose gravitational-wave background acquires a spectral break from the early matter-dominated era, with a frequency set by the decoupled RHN mass and the lightest neutrino mass, within reach of future detectors such as SKA, THEIA, LISA, $\mu$ARES, DECIGO and ET.

Three-dimensional femtoscopy probes the space-time structure of particle-emitting sources in relativistic heavy-ion collisions. The collision-energy dependence of Lévy source parameters may reveal the evolution of strongly interacting matter and possible signatures of the QCD phase diagram. We previously studied the excitation function of three-dimensional Lévy source parameters for pion pairs in Au+Au collisions with EPOS4, analyzing the pair-distance distribution \(D(\rho)\) through one-dimensional projections. Here, we analyze the full three-dimensional source distribution and correlation function directly. We construct \(D(\rho_{\rm out},\rho_{\rm side},\rho_{\rm long})\) as a 3D histogram, transform it into \(C(q_{\rm out},q_{\rm side},q_{\rm long})\) using a Fast Fourier Transform, and fit the correlation function with the analytic Lévy formula. This approach can reduce biases arising when one-dimensional projections are used to describe a non-elliptical source. We apply the method across the RHIC Beam Energy Scan range and compare the extracted energy dependence with results from the projection-based method and recent UrQMD calculations. We focus on the out-side observables \(R_{\rm diff}^{2}=R_{\rm out}^{2}-R_{\rm side}^{2}\) and \(R_{\rm out}/R_{\rm side}\), whose different energy dependences in EPOS4 and UrQMD may illuminate the roles of emission duration and source dynamics. This work establishes a direct three-dimensional framework for comparison with future femtoscopic measurements and for exploring possible non-monotonic structures associated with the QCD phase diagram.

The LZ collaboration has recently reported a single nuclear-recoil event at $E_R=248\pm23_\text{stat}\pm23_\text{sys}$ keV, observed in a 2.84 tonne-year exposure with a local significance of $3.4\sigma$, pointing towards an inelastic dark matter (DM) interpretation. We explain this event within a gauged $U(1)_X$ hidden-sector model, spontaneously broken by a singlet scalar whose vacuum expectation value (VEV) gives rise to: (i) gauge boson mass, (ii) a small Majorana mass for the vector-like singlet fermion, the DM candidate, charged under the new symmetry, which splits the fermion into two pseudo-Dirac states (mass splitting proportional to the scalar VEV) thus resulting in a purely off-diagonal vector current, (iii) the frequency and the amplitude of the GW signal arising from the hidden sector symmetry breaking via first-order phase transition (FOPT). The symmetry-breaking scale thus provides a multi-messenger probe connecting terrestrial direct-detection kinematics at the LZ and early-universe FOPT thermodynamics while obtaining thermal DM relic abundance. We delineate the viable parameter space compatible with the LZ event, correct relic density, and detectable GW signals in the low frequency regimes at future interferometers like $\mu {\rm ARES}$ and THEIA while satisfying existing cosmological, astrophysical, and terrestrial bounds.

We extend the quark mean-field (QMF) model to finite temperature and systematically investigate the thermodynamic properties of uniform nuclear matter, using the relativistic mean-field (RMF) model as a reference. For each model, we consider two parameter sets calibrated to the same selected nuclear-matter saturation properties but with different nucleon Dirac effective-mass ratios at saturation. We examine the effective nucleon mass and the composition of $\beta$-equilibrium matter, together with the free energy, energy density, pressure, entropy, and heat capacities of symmetric nuclear matter, pure neutron matter, and $\beta$-equilibrium matter. The QMF and RMF models exhibit similar qualitative trends, but their predictions increasingly differ at high density, where the effective masses have distinct density dependences. These differences are particularly evident in the thermal pressure and thermal index. For the two parameter sets considered in this work, we further provide compact analytical representations of the thermal index, $\Gamma_{\rm th}(\rho_{\rm b},T,\beta)$ over baryon densities of 0.08-1.0 $\rm fm^{-3}$, temperatures of 5-100 MeV, and isospin asymmetries of 0-1. The fits reproduce the numerical results with an accuracy better than $2\%$ and can be directly implemented in binary neutron-star merger simulations. This study establishes a finite-temperature extension of the QMF framework and provides a basis for future assessments of how a quark-structure-based description of nuclear matter affects thermal support and post-merger dynamics in binary neutron-star mergers.

The $x^2$ moment of the genuine twist-3 component of the unpolarized scalar parton distribution function $e(x)$ is related to the average transverse color Lorentz force experienced by a transversely polarized quark in an unpolarized nucleon. This higher-twist quantity probes quark–gluon correlations and provides unique insight into the nonperturbative dynamics of quantum chromodynamics. For the first time, we study the corresponding off-forward matrix element and derive its Lorentz-covariant decomposition in terms of generalized form factors. We calculate these form factors from light-front wave functions obtained by solving the light-front Hamiltonian eigenvalue problem within the Basis Light-Front Quantization framework. Their Fourier transforms provide a spatial picture of the transverse color forces in impact-parameter space. In particular, $\mathscr{F}_2$, whose forward limit is directly related to the twist-3 matrix element $e_2$, can be interpreted as the impact-parameter-space representation of the Boer–Mulders force, providing an intuitive spatial picture of the final-state interaction mechanism underlying the Boer–Mulders effect.

We propose a Lorentz-covariant on-shell formalism for allowed nuclear beta decay. Nuclear matrix elements are organized in a systematic effective field theory expansion in the recoil momentum, with the dependence on nuclear spin and polarization encoded in little-group-covariant structures. In this language, we construct the most general standard and exotic currents for allowed transitions through first recoil order. We then derive the differential decay distribution encoded in a set of Lorentz-invariant form factors. Specializing to the rest frame of the parent nucleus, we relate our parameters to those used in the traditional beta-decay literature and in nucleon- and quark-level effective field theories. The formalism provides a natural framework for extensions to higher recoil orders, radiative corrections, and forbidden transitions.

In this paper, we present the first results for the one-loop decay $A \rightarrow ZZ\gamma$ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. We calculate the one-loop partial decay widths and branching ratios for both unpolarized and polarized final-state $Z$ bosons. The effects of Vector-Like Quarks propagating in the loop are also examined in our phenomenological analysis. We find that the branching ratios can reach $10^{-5}-10^{-4}$ for several benchmark points within the viable parameter space of the considered models. The contributions from Vector-Like Quarks can modify the total rates by approximately $5\%$. With the high luminosities expected at future multi-TeV muon colliders, these effects may be experimentally accessible.

We calculate analytic expression for the cross section up to order $(eB)^2$ for the production of a heavy quark $(Q)$ of mass $m_Q$ through the gluon $(g)$ fusion process $g+g\to Q+\bar{Q}$ in the presence of a constant weak external magnetic field $(B)$ with strength $eB \ll m_Q^2$. This is done using the weak-field expansion of the fermion propagator calculated within Schwinger's proper-time formalism. Owing to the hierarchy of scales ($m_Q^2 \gg eB$), we neglect the effects of the magnetic field on the quark and antiquark spinors in the external lines. Since the magnetic field breaks rotational invariance, the cross section becomes anisotropic and depends on the relative orientation angle $(\theta)$ between the magnetic field and the incoming gluons in the center-of-mass frame. The lowest-order magnetic correction to the vacuum cross section scales as $(eB)^2$ and is found to have $\cos 2\theta$ and $\cos 4\theta$ dependence, reflecting the breaking of rotational symmetry by the magnetic field. The cross section is maximized when the gluons propagate along the field direction ($\theta = 0, \pi$) and minimized in the perpendicular configuration ($\theta = \pi/2$). The resulting asymmetry peaks near the production threshold and falls with increasing center-of-mass energy, scaling as $(eB)^2/m_Q^4$ with the quark mass. These results provide direct, calculable signatures of the initial-stage magnetic field in relativistic heavy-ion collisions which can, in principle, be imprinted on heavy-flavour observables measured in the final state of heavy-ion collisions.

Chiral perturbation theory is a power tool for studying the low-energy strong interactions. In the conventional chiral expansion, according to the power counting rule, the higher-order corrections for physical observables are expected to decrease order by order as the chiral dimension increases. However, most previous study of $\pi K$ scattering lengths by different references showed that the $\mathcal{O}(p^6)$ correction to the scattering lengths is anomalously large and even exceeds the $\mathcal{O}(p^4)$ one. It poses a serious challenge to the convergence of chiral expansion. In order to explore the underlying origin of this phenomenon, the contributions of two-loop diagrams, one-loop diagrams and tree diagrams for the $\pi K$ scattering amplitude are detailed analyzed. The reducible two-loop integrals, sunset integrals and vertex integrals from the $\mathcal{O}(p^6)$ order all violate the power counting rule. The sunset and vertex integrals can be largely canceled numerically, but not enough. Furthermore, $\pi K$ scattering is compared with $\pi\pi$ scattering, which seems not violate the power counting rule. The analysis indicates that $\pi\pi$ scattering contains a higher symmetry, although each $\mathcal{O}(p^6)$-order part also violates the power counting rule, but the violation is much smaller than the one from $\pi K$ scattering. Large kaon mass also makes a contribution to the power-counting breaking, but it is not a major origin. Hence, it needs to pay more attention to the many-loop low-symmetry diagrams in future work. These diagrams may give large contribution and cannot be ignored.