Search Results (65)

Introducing an additional term into the thermodynamic potential density of the quark matter system, as required for thermodynamic consistency, resolves the inconsistency that arises in the conventional perturbative quantum chromodynamics (QCD) model. In this work, we use a revised, thermodynamically consistent perturbative QCD model to compute the stability window and equation of state of up-down ($ud$) quark matter at zero temperature. Our results indicate that the measured tidal deformability for GW170817 places an upper limit on the maximum mass of $ud$ quark stars, but does not rule out the possibility of such stars with a mass of about two solar masses. However, when the maximum mass of $ud$ quark stars significantly exceeds two solar masses, such as the compact object with a mass in the range of 2.50–2.67 $M_{\odot }$ observed in the GW190814 event, it cannot be identified as a $ud$ quark star according to the revised perturbative QCD model. Full article

The introduction of axions gives rise to additional one-loop diagrams for the two-photon decays of neutral pions via axion-pion mixing. We compute this correction that has been overlooked in existing calculations, within the framework of SU(2) chiral perturbation theory. Our analysis shows that the correction is proportional to the axion-photon coupling and the square of the axion mass. In the classical axion parameter space, this correction is strongly suppressed by the axion decay constant. However, for QCD axions in the MeV or higher mass range, the correction may become significant. Furthermore, when combined with experimental measurements of the decay width of the ${\pi }^0\to \gamma \gamma$ process, our results rule out the standard QCD axion as a viable explanation for the observed discrepancy between chiral perturbation theory predictions and experimental data. Full article

Future $e^{+}{e}^{-}$ colliders are expected to play a fundamental role in measuring Standard Model (SM) parameters with unprecedented precision and in probing physics beyond the SM (BSM). This study investigates two-particle angular correlation distributions involving final-state SM charged hadrons. Unexpected correlation structures in these distributions is considered to be a hint for new physics perturbing the QCD partonic cascade and thereby modifying azimuthal and (pseudo)rapidity correlations. Using Pythia8 Monte Carlo generator and fast simulation, including selection cuts and detector effects, we study potential structures in the two-particle angular correlation function. We adopt the QCD-like Hidden Valley (HV) scenario as implemented in Pythia8 generator, with relatively light HV v-quarks (below about 100 GeV), to illustrate the potential of this method. Full article

Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU\left(N\right)$ Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with the lattice results. Good agreement is found at low temperatures, providing a viable scenario for a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures, a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD). Full article

This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC₂D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC₂D, both theoretical and numerical studies derive the presence of the so-called baryon superfluid phase at a sufficiently large chemical potential (${\mu }_q$), where diquark condensates govern the ground state. The hadron mass spectrum simulated in this phase shows that the mass of an iso-singlet ($I=0$) and $0^{-}$ state is remarkably reduced, but such a mode cannot be described by the chiral perturbation theory. Motivated by this fact, I have invented a LSM constructed upon the linear representation of chiral symmetry, more precisely Pauli–Gürsey symmetry. It is shown that my LSM successfully reproduces the low-lying hadron mass spectrum in a broad range of ${\mu }_q$ simulated on the lattice. As applications of the LSM, topological susceptibility and sound velocity in cold and dense QC₂D are evaluated to compare with the lattice results. Additionally, the generalized Gell–Mann–Oakes–Renner relation and hardon mass spectrum in the presence of a diquark source are analyzed. I also introduce an extended version of the LSM incorporating spin-1 hadrons. Full article

We propose a model for the QCD running coupling constant based on the analytical inverse QCD coupling constant concept with an additional regularization in the low momentum region. Analyticity in the $q^2$-complex plane, where q is the four-momentum transfer, is imposed by methods of the Analytic Perturbation Theory. The model incorporates a peculiar low-momentum behavior for ${\alpha }_s(q^2)$ as a divergence at $q^2=0$ to retrieve color confinement, without spoiling its correct high-momentum behavior. This was achieved by means of a two-parameter regularization function, for which we considered three possible analytic expressions. In fact, within the framework of the Analytic Perturbation Theory, ${\alpha }_s(q^2)$ assumes a finite value for $q^2=0$, at all perturbative orders (infrared stability), hence the infrared divergence cannot be implemented. For this reason, we found it more straightforward to work with its reciprocal, namely, ${\epsilon }_s(q^2)=1/{\alpha }_s(q^2)$, imposing its vanishing at the origin of the $q^2$-complex plane via the multiplication of the aforementioned regularizing functions and the spectral density. Once the two free parameters of the regularization functions were settled by fitting to the experimental values of ${\alpha }_s(q^2)$ at the momenta where these data were available and reliable, the model could reproduce the QCD running coupling constant at any other momentum transferred. Full article

QCD with the isospin chemical potential ${\mu }_I$ is a useful laboratory to delineate the microphysics in dense QCD. To study the quark–hadron continuity, we use a quark–meson model that interpolates hadronic and quark matter physics at microscopic level. The equation of state is dominated by mesons at low density but taken over by quarks at high density. We extend our previous studies with two flavors to the three-flavor case to study the impact of the strangeness, which may be brought by kaons $(K_{+},K_0)=(u\overline{s},s\overline{d})$ and the U_A(1) anomaly. In the normal phase, the excitation energies of kaons are reduced by ${\mu }_I$ in the same way as hyperons in nuclear matter at the finite baryon chemical potential. Once pions condense, kaon excitation energies increase as ${\mu }_I$ does. Moreover, strange quarks become more massive through the U_A(1) coupling to the condensed pions. Hence, at zero and low temperature, the strange hadrons and quarks are highly suppressed. The previous findings in two-flavor models, sound speed peak, negative trace anomaly, gaps insensitive to ${\mu }_I$, persist in our three-flavor model and remain consistent with the lattice results to ${\mu }_I\sim$ 1 GeV. We discuss the non-perturbative power corrections and quark saturation effects as important ingredients to understand the crossover equations of state measured on the lattice. Full article

We study in detail the influence of different chemical potentials (baryon, electric charge, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zero-net strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. We find that the inclusion of all quark masses (even the light ones) can produce different results depending on the chemical potential values or constraints assumed. A positive or negative deviation of 10% from the pressure of free massless quarks with the same chemical potential was found to take place as low as ${\mu }_B=77$ to as high as $48,897$ MeV. This illustrates the fact that the “free” or conformal limit is not a unique description. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit. Full article

We study cold strange quark stars employing an enhanced version of the quark-mass density-dependent model, which incorporates excluded volume effects to address non-perturbative QCD repulsive interactions. We provide a comparative analysis of our mass formula parametrization with previous models from the literature. We identify the regions within the parameter space where three-flavor quark matter is more stable than the most tightly bound atomic nucleus (stability window). Specifically, we show that excluded volume effects do not change the Gibbs free energy per baryon at zero pressure, rendering the stability window unaffected. The curves of pressure versus energy density exhibit various shapes—convex upward, concave downward, or nearly linear—depending on the mass parametrization. This behavior results in different patterns of increase, decrease, or constancy in the speed of sound as a function of baryon number density. We analyze the mass–radius relationship of strange quark stars, revealing a significant increase in maximum gravitational mass and a shift in the curves toward larger radii as the excluded volume effect intensifies. Excluded volume effects render our models compatible with all modern astrophysical constraints, including the properties of the recently observed low-mass compact object HESSJ1731. Full article

We review the semi-inclusive hadroproduction of a neutral hidden-flavor tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0 determinations of leading-twist fragmentation functions to describe the formation mechanism of a tetraquark state within the next-to-leading order perturbative QCD. This framework builds on the basis of a spin physics-inspired model, taken as a proxy for the lowest-scale input of the constituent heavy-quark fragmentation channel. Then, all parton-to-tetraquark fragmentation functions are consistently obtained via the above-threshold DGLAP evolution in a variable-flavor number scheme. We provide predictions for a series of differential distributions calculated by the hands of the JETHAD method, well-adapted to $\mathrm{NLL}/{\mathrm{NLO}}^{+}$ hybrid-factorization studies, where the resummation of next-to-leading energy logarithms and beyond is included in the collinear picture. We provide corroborating evidence that high-energy observables sensitive to semi-inclusive tetraquark emissions at the HL-LHC exhibit a fair stability under radiative corrections, as well as MHOU studies. Our analysis constitutes a prime contact point between QCD resummations and the exotic matter. Full article

We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson–Schwinger equations in differential form. In the local case, we obtain closed-form solutions in the simplest case of the scalar field and extend it to the Yang–Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang–Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson–Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive a gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g., for quantum chromodynamics at lower energies. Full article

The precision and predictive power of perturbative QCD (pQCD) prediction depends on both a precise, convergent, fixed-order series and a reliable way of estimating the contributions of unknown higher-order (UHO) terms. It has been shown that by applying the principle of maximum conformality (PMC), which applies the renormalization group equation recursively to set the effective magnitude of ${\alpha }_s$ of the process, the remaining conformal coefficients will be well matched with the corresponding ${\alpha }_s$ at each order, leading to a scheme-and-scale invariant and more convergent perturbative series. The PMC series, being satisfied with the standard renormalization group invariance, has a rigorous foundation. Thus it not only can be widely applied to virtually all high-energy hadronic processes, but also can be a reliable platform for estimating UHO contributions. In this paper, by using the total decay width $\Gamma (H\to \gamma \gamma )$ which has been calculated up to N⁴LO QCD corrections, we first derive its PMC series by using the PMC single-scale setting approach and then estimate its unknown N⁵LO contributions by using a Bayesian analysis. The newly suggested Bayesian-based approach estimates the magnitude of the UHO contributions based on an optimized analysis of the probability density distribution, and the predicted UHO contribution becomes more accurate when more loop terms have been known to tame the probability density function. Using the top-quark pole mass $M_t$ = 172.69 GeV and the Higgs mass $M_H$ = 125.25 GeV as inputs, we obtain $\Gamma (H\to \gamma \gamma )=9.56504\mathrm{keV}$, and the estimated N⁵LO contribution to the total decay width is $\Delta {\Gamma }_H=\pm 1.65\times {10}^{-4}\mathrm{keV}$ for the smallest credible interval of $95.5\%$ degree of belief. Full article

The anomalous dimension ${\gamma }_m=1$ in the infrared region near the conformal edge in the broken phase of the large $N_f$ QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for $N_f=8$ and for $N_c=3$. Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result, ${\gamma }_m=1$, by comparing the pion matrix element of the trace of the energy-momentum tensor $⟨\pi \left(p_2\right)|(1+{\gamma }_m)·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=⟨\pi \left(p_2\right)|{\theta }_{\mu }^{\mu }|\pi \left(p_1\right)⟩=2M_{\pi }^2$ (up to trace anomaly) with the estimate of $⟨\pi \left(p_2\right)|2·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=2M_{\pi }^2$ through the Feynman–Hellmann theorem combined with an assumption $M_{\pi }^2\sim m_f$ characteristic of the broken phase. We show that this is not justified by the explicit evaluation of each matrix element based on the dilaton chiral perturbation theory (dChPT): $⟨\pi \left(p_2\right)|2·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=2M_{\pi }^2+[(1-{\gamma }_m)M_{\pi }^2·2/(1+{\gamma }_m)]=2M_{\pi }^2·2/(1+{\gamma }_m)\ne 2M_{\pi }^2$ in contradiction with his estimate, which is compared with $⟨\pi \left(p_2\right)|(1+{\gamma }_m)·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=(1+{\gamma }_m)M_{\pi }^2+\left[(1-{\gamma }_m)M_{\pi }^2\right]=2M_{\pi }^2$ (both up to trace anomaly), where the terms in $\left[\right]$ are from the $\sigma$ (pseudo-dilaton) pole contribution. Thus, there is no constraint on ${\gamma }_m$ when the $\sigma$ pole contribution is treated consistently for both. We further show that the Feynman–Hellmann theorem is applied to the inside of the conformal window where dChPT is invalid and the $\sigma$ pole contribution is absent, and with $M_{\pi }^2\sim m_f^{2/(1+{\gamma }_m)}$ instead of $M_{\pi }^2\sim m_f$, we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of $f_0\left(500\right)$ to $\pi \pi$ for $N_f=2$. It is shown to be consistent with the reality, when $f_0\left(500\right)$ is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance. Full article

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD-generating functional integral. We expand the perturbative boundary conditions to both perturbative and nonperturbative fields integrated into the QCD-generating functional integral. It allows us to nullify the CP odd term in the QCD Lagrangian and, thus, to solve the strong CP problem. The presently popular solution to the strong CP problem of introducing axions violates the principle of renormalizability of the Quantum Field Theory, which is very successful phenomenologically. Our solution obeys the principle of renormalizability of the Quantum Field Theory and does not involve new exotic particles like axions. Full article

Dynamical chiral symmetry breaking (D$\chi$SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in terms of QCD. It not only highlights one of the most important aspects of D$\chi$SB, the dynamical generation of constituent quark masses, but also makes plausible that D$\chi$SB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher n-point functions are taken into account. In particular, the quark–gluon vertex, i.e., the most elementary n-point function describing the full, non-perturbative quark–gluon interaction, plays a dichotomous role: It is subject to D$\chi$SB as signalled by its scalar and tensor components but it is also a driver of D$\chi$SB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, D$\chi$SB in QCD is located close to the critical point and is thus a delicate effect. In addition, requiring a precise determination of QCD’s three-point functions, D$\chi$SB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon–gluon and the quark–gluon interactions. Full article