Quark Mass Effects Research Articles

QCD phase diagram in the T–eB plane for varying pion mass

We study the effect of a varying pion mass on the quantum chromodynamics (QCD) phase diagram in the presence of an external magnetic field, aiming to understand it, for the first time, using Nambu–Jona-Lasinio like effective models. We compare results from both its local and nonlocal versions. In both cases, we find that the inverse magnetic catalysis (IMC) near the crossover is eliminated with increasing pion mass, while the decreasing trend of crossover temperature with increasing magnetic field persists for pion mass values at least up to 440 MeV. Thus, the models are capable of capturing qualitatively the results found by lattice QCD (LQCD) for heavy (unphysical) pions. The key feature in the models is the incorporation of the effect of a reduction in the coupling constant with increasing energy. Along with reproducing the IMC effect, it enables models to describe the effects of heavier current quark masses without introducing additional parameters. For the local NJL model, this agreement depends on how the parameters of the model are fit at the physical point. In this respect, the nonlocal version, which, due to its formulation, automatically exhibits the IMC effect around the crossover region, captures the physics more naturally. We further use the nonlocal framework to determine the pion mass beyond which the IMC effect around the transition region does not exist anymore. Published by the American Physical Society 2024

Quark mass effects in Higgs production

We examine the effect of finite top- and bottom-quark masses on the Higgs production cross section in the gluon-gluon fusion channel. We employ both MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} and on-shell renormalisation for the quark masses and provide a thorough comparison. Furthermore, we explore alternative treatments of quark masses, in particular in the four-flavour scheme, and investigate their impact on the cross section. Our work also presents novel predictions for differential cross sections in the Higgs rapidity. The results lead to a significant reduction of scale uncertainties, and our analysis enables us to offer well-grounded recommendations for future research in this area.

Heavy quark mass near the phase transition

Abstract Assuming that the number densities of heavy flavor in hadron gas and in QGP are same at $T_c$, we obtain the effective mass of heavy quark at $T_c$ from the comparison with the hadron resonance gas model which well describes particle yield in heavy-ion collisions. We find that charm quark mass at vanishing baryon chemical potential is around 1.8 GeV which is much heavier than QCD bare mass and close to $D$ meson mass. The mass slightly increases with increasing baryon chemical potential and then decreases.
On the other hand, anticharm quark mass constantly decreases with increasing baryon chemical potential. Bottom quark mass has a similar pattern. Extending the hadron resonance gas model to a bit higher temperature beyond $T_c$, the effective masses of charm and bottom quarks decrease with increasing temperature.

An FONLL prescription with coexisting flavor number PDFs

We present a new prescription to account for heavy quark mass effects in the determination of parton distribution functions (PDFs) based on the FONLL scheme. Our prescription makes explicit use of the freedom to choose the number of active flavors at a given scale and, thus, use coexisting PDFs with different active flavor number. This new prescription is perturbatively equivalent to the former but improves the implementation in two ways. First, it can be naturally generalized to account simultaneously for multiple heavy quark effects, such as charm and bottom effects, which can both be relevant at the same scale due to the small mass difference. Second, it can be trivially generalized to use at any fixed-order or collinear resummed accuracy, while previous prescriptions required ad-hoc expansions of the DGLAP evolution kernels for each coefficient. We supplement the paper with codes for the computation of deep inelastic scattering observables in this new prescription.

Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order

The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-z behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at Oαs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\alpha}_s\\right) $$\\end{document}.

Determination of the Collins-Soper Kernel from Lattice QCD.

This Letter presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice quantum chromodynamics (QCD). This is the first such determination with systematic control of quark mass, operator mixing, and discretization effects. Next-to-next-to-leading logarithmic matching is used to match lattice-calculable distributions to the corresponding TMDs. The continuum-extrapolated lattice QCD results are consistent with several recent phenomenological parametrizations of the Collins-Soper kernel and are precise enough to disfavor other parametrizations.

Heavy quark transverse momentum dependent fragmentation

In this paper, we investigate the heavy quark (HQ) mass effects on the transverse momentum dependent fragmentation function (TMDFF). We first calculate the one-loop TMDFF initiated by a heavy quark. We then investigate the HQ TMDFF in the limit where the transverse momentum, q⊥ is small compared to the heavy quark mass, q⊥ ≪ m and also in the opposite limit where q⊥ ≫ m. As applications of the HQ TMDFF, we study the HQ transverse momentum dependent jet fragmentation function, where the heavy quark fragments into a jet containing a heavy hadron, and we investigate a heavy hadron’s transverse momentum dependent distribution with respect to the thrust axis in e+e− collisions.

Quarkonia dissociation at finite magnetic field in the presence of momentum anisotropy

In this study, we investigate the potential of heavy quarkonia within a magnetized hot QGP medium having finite momentum anisotropy. The phenomenon of inverse magnetic catalysis is introduced into the system, influencing the magnetic field-modified Debye mass and thereby altering the effective quark masses. Concurrently, the impact of momentum anisotropy in the medium is considered that influence the particle distribution in the medium. The thermal decay width and dissociation temperature of quarkonium states, specifically the 1S and 2S states of charmonium and bottomonium, are computed. Our results reveal that both momentum anisotropy and the inverse magnetic catalysis effects play a significant role in modifying the thermal decay width and dissociation temperature of these heavy quarkonia states.

Role of Time-Varying Magnetic Field on QGP Equation of State

The phase diagram of quantum chromodynamics (QCD) and its associated thermodynamic properties of quark-gluon plasma (QGP) are studied in the presence of time-dependent magnetic field. The study plays a pivotal role in the field of cosmology, astrophysics, and heavy-ion collisions. In order to explore the structure of quark-gluon plasma to deal with the dynamics of quarks and gluons, we investigate the equation of state (EoS) not only in the environment of static magnetic field but also in the presence of time-varying magnetic fields. So, for determining the equation of state of QGP at nonzero magnetic fields, we revisited our earlier model where the effect of time-varying magnetic field was not taken into consideration. Using the phenomenological model, some appealing features are noticed depending upon the three different scales: effective mass of quark, temperature, and time-independent and time-dependent magnetic fields. Earlier the effective mass of quark was incorporated in our calculations, and in the current work, it is modified for static and time-varying magnetic fields. Thermodynamic observables including pressure, energy density, and entropy are calculated for a wide range of temperature- and time-dependent as well as time-independent magnetic fields. Finally, we claim that the EoS are highly affected in the presence of a magnetic field. Our results are notable compared to other approaches and found to be advantageous for the measurement of QGP equation of state. These crucial findings with and without time-varying magnetic field could have phenomenological implications in various sectors of high-energy physics.

Artificial first-order phase transition in a magnetized Nambu–Jona-Lasinio model with a quark anomalous magnetic moment

Recently, first-order phase transitions have been predicted as an effect of the inclusion of quark anomalous magnetic moment (AMM) in the hot and magnetized Nambu–Jona-Lasinio model (NJL). These transitions appear in the chiral condensate for different combinations of AMM and magnetic fields and could lead to inverse magnetic catalysis. However, in this work, we show that the predicted first-order phase transitions are related to regularization-dependent issues. To show this, we explore, in the context of the vacuum magnetic regularization (VMR) scheme, two different scenarios: when mass-dependent (MD) and mass-independent (MI) terms are present in the subtraction of the divergences. In the MD case, as we increase the AMM value, it is observed the appearance of a nonmassive minimum in the thermodynamical potential, which induces a first-order phase transition from the massive minimum. We argue that the MD terms must be avoided in order to satisfy the predictions of Lattice QCD, and we propose a MI solution that is valid in the limit which the magnetic fields are smaller than the squared of vacuum effective quark mass. Published by the American Physical Society 2024

QCD vacuum and baryon masses

To study a possible role of the quantum chromodynamics (QCD) vacuum in nuclear and hadron physics, we evaluate a physical quantity in a candidate of the QCD vacuum. In this study, we adopt the Copenhagen (spaghetti) picture of the QCD vacuum and calculate the ground state baryon masses in a constituent quark model. We find that the calculated baryon mass does depend on a parameter that characterizes the Copenhagen picture of the QCD vacuum and satisfies the Gell-Mann–Okubo mass relation for the baryon octet. We also observe that the effective constituent quark mass defined in this study contains a contribution attributed to the Copenhagen vacuum, that is the gluon background field. We then estimate the value of the background gluon field as a function of the up (down) constituent quark mass by using the baryon masses as inputs.

Tetraquark mass relations in quark and diquark models

We present new linear relations among the masses of S-wave tetraquarks with either one flavour (QQQ¯Q¯) or two (QQq¯q¯). Because the relations are sensitive to the hidden-colour, spin, and spatial degrees of freedom, comparison to experimental data can help to reveal the internal structure of tetraquarks, and discriminate among different theoretical models. Depending on the model, the relations are either exact, or valid in perturbation theory, and a thorough comparison with existing literature confirms their validity at the MeV level. Additionally, we explore the connections among tetraquark models, and show how those with effective (quark or diquark) masses are related to dynamical potential models. We also show how the spectrum of diquark models is effectively a limiting case of (more general) quark models, and in particular, that the diquark concept is most relevant in the particular combination QQq¯q¯, where Q is much heavier than q¯.

Quark mass effects in double parton distributions

Double parton distributions can be computed from the perturbative splitting of one parton into two if the distance between the two observed partons is small. We develop schemes to take into account quark mass effects in this computation, and we study these schemes numerically at leading order in the strong coupling. Furthermore, we investigate in detail the structure of the next-to-leading order corrections to the splitting kernels that include quark mass effects.

Inverse magnetic catalysis effect and current quark mass effect on mass spectra and Mott transitions of pions under external magnetic field

Inverse magnetic catalysis effect and current quark mass effect on mass spectra and Mott transitions of pions under external magnetic field

Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants

The quark-antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange. The strange quark effective mass () is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states S 0, S 8, and S 3 are adopted as the most relevant quark-antiquark components, respectively, of the σ(500), f 0(980) and mesons. As a result, the mass hierarchy between states S 0 and S 8, and mesons, can be, respectively, inverted and corrected for quite low values of the strange quark constituent mass. In addition, for some particular values of , the masses of σ(500) and f 0(980) can also be obtained by considering the mixing coupling constant G 08. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the σ(500) − f 0(980) mass difference. Two different estimates for the strengths of the mixings and are proposed, leading to somewhat different behaviors. First by assuming leading transitions to intermediary flavor eigenstates and second by considering a dynamical evolution. The results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.

Heavy quark potential and LQCD based quark condensate at finite magnetic field

In the present work, we have studied heavy quarkonia potential in hot and magnetized quark gluon plasma. Inverse magnetic catalysis (IMC) effect is incorporated within the system through the magnetic field modified Debye mass by modifying the effective quark masses. We have obtained the real and imaginary part of the heavy quark potential in this new scenario. After the evaluation of the binding energy and the decay width we comment about the dissociation temperatures of the heavy quarkonia in presence of magnetic field.

Analytic structure of the Landau gauge quark propagator from Padé analysis

The analytic structure of the two flavorful QCD lattice Landau gauge quark propagator is investigated with Pad\'e approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e., for a Minkowski type of momentum. This pole occurs at Euclidean momenta $p\ensuremath{\sim}\ensuremath{-}300\text{ }\text{ }\mathrm{MeV}$ and it reproduces typical quark mass values used in phenomenological effective quark models. The Pad\'e approximant analysis also gives hints on the presence of a branch cut. Our results also show a clear correlation between the position of this pole, understood as an effective quark mass, and the pion mass that is compatible with partial conservation of the axial current. Slightly differences between the poles for the two quark form factors are observed which can be viewed either as a limitation of the method or as a suggestion that the quark propagator has no spectral representation.

Strange quark mass effect in Bs→γγ, γℓℓ¯ decays

In this paper we investigate the next-to-leading power contribution to the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decays from the strange quark mass effect with the dispersion approach which is QCD inspired and more predictive. We present the analytic expression of the quark mass contribution in the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decays, together with a new term that is missed in the previous study. We also evaluate the resolved photon contribution from the A-type amplitude in ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decay. The numerical results of the strange quark mass contribution to the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decay is about 6% relative to the total branching ratio, while it is relatively small in the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decay due to the large resonance contribution.

Spectroscopy of light baryons: Δ resonances

The spectroscopy of light and strange baryons had been an important aspect with still unknown resonances and intrinsic baryonic properties. This paper focuses on the [Formula: see text] baryons treating [Formula: see text] and [Formula: see text] quarks with different constituent masses. The theoretical framework for calculating the resonance masses is hypercentral Constituent Quark Model (hCQM) with confining potential of the linear form. To account for the spin–orbit splitting in the correct order, first- and second-order corrections of the order [Formula: see text] and [Formula: see text] have been incorporated to the potential and spin-dependent term, respectively. The results obtained have been compared with many varied approaches as well as experimental available states. In addition to mass spectra, Regge trajectories for (n, [Formula: see text]) and ([Formula: see text], [Formula: see text]) have been plotted. The magnetic moment as well as transition magnetic moment have been calculated using effective quark mass. The radiative decay width has been studied for [Formula: see text] and [Formula: see text] channels.

Effects of the quark anomalous magnetic moment in the thermodynamical properties of the magnetized two flavor Nambu–Jona-Lasinio model

The influence of the anomalous magnetic moment (AMM) of quarks in the chiral phase transition is studied in the context of the hot and magnetized two flavor Nambu–Jona-Lasinio model. Making use of the mean field approximation (MFA) and the vacuum magnetic regularization (VMR) scheme, we obtain the effective quark masses as a function of the magnetic field for the two usual different sets of AMM. Basic thermodynamical properties are explored and compared with the zero AMM-case, as the pressure, entropy, energy density, interaction measure and the specific heat. The main differences are present in the thermodynamical quantities when one consider a sizable value of AMM, in which an underestimation over the transition region is observed.