Quark Energy Research Articles

BCS solutions and effective quark energies of the QCD Hamiltonian in the Coulomb gauge

The search of theoretical approximations adequate to the description of the non-perturbative regime of QCD, that is the low-energy portion of the hadron spectrum, requires the adoption of notions more frequently applied to other, more conventional, quantum many body systems, like the atomic nucleus, solid state systems, etc. The identification and the use of effective degrees of freedom is one of the notions whose limitations we shall explore in this work. To start with the choice of the basis to be adopted to represent effective fermionic degrees of freedom is a crucial first step towards the goal of constructing an effective Hamiltonian from which the low energy portion of the hadronic spectrum may emerge as its solution. Here, we propose the use of the harmonic oscillator basis and emphasize its advantages compared to the basis of free momentum states. The starting Hamiltonian is the effective Coulomb plus linear potential, which we have used in previous calculations. We proceed by pre-diagonalizing the Hamiltonian to build a single particle spectrum, namely: the spectrum of effective quark degrees of freedom, starting from arbitrary chosen quark masses, which are later on re-normalized. Then, quark-pair correlations are described in the context of the well-known Bogoliubov transformations. The resulting quasiparticle states are then used to construct meson-like states. The dependence of the results upon the parameters which enter in the calculations is explored in detail.

Low energy protons as probes of hadronization dynamics

Energetic quarks liberated from hadrons in nuclear deep-inelastic scattering propagate through the nuclear medium, interacting with it via several processes. These include quark energy loss and nuclear interactions of forming hadrons. One manifestation of these interactions is the enhanced emission of low-energy charged particles, referred to as grey tracks. We use the theoretical components of the BeAGLE event generator to interpret grey track signatures of parton transport and hadron formation by comparing its predictions to E665 data. We extend the base version of BeAGLE by adding four different options for describing parton energy loss. The E665 data we used consists of multiplicity ratios for fixed-target scattering of 490 GeV muons on Xe normalized to deuterium as a function of the number of grey tracks. We compare multiplicity ratios for E665 grey tracks to the predictions of BeAGLE, varying the options and parameters to determine which physics phenomena can be identified by these data. We find that grey tracks are unaffected by modifications of the forward production. Thus their production must be dominated by interactions with hadrons in the backward region. This offers the advantage that selecting certain particles in the forward region is unlikely to bias a centrality selection. We see a strong correlation between the number of grey tracks and the in-medium path length. Our energy loss model does not reproduce the suppression observed in the projectile region. We see an underprediction of the proton production rate in backward kinematics, suggesting that a stronger source of interaction with the nuclear medium is needed for accurate modeling. These results lay an important foundation for future spectator tagging studies at both Jefferson Lab and at the Electron-Ion Collider, where neutron and proton grey track studies will be feasible down to very small momenta.

Quarks and triality in a finite volume

In order to understand the puzzle of the free energy of an individual quark in QCD, we explicitly construct ensembles with quark numbers $N_V\neq 0\!\mod 3$, corresponding to non-zero triality in a finite subvolume $V$ on the lattice. We first illustrate the basic idea in an effective Polyakov-loop theory for the heavy-dense limit of QCD, and then extend the construction to full Lattice QCD, where the electric center flux through the surface of $V$ has to be fixed at all times to account for Gauss's law. This requires introducing discrete Fourier transforms over closed center-vortex sheets around the spatial volume $V$ between all subsequent time slices, and generalizes the construction of 't Hooft's electric fluxes in the purge gauge theory. We derive this same result from a dualization of the Wilson fermion action, and from the transfer matrix formulation with a local $\mathbb Z_3$-Gauss law to restrict the dynamics to sectors with the required center charge in $V$.

Extracting the jet transport coefficient from hadron suppressions by confronting current NLO parton fragmentation functions

Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ( $$p_{\mathrm{T}}$$ ) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $$A+A$$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $$\hat{q}$$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $$p_{\mathrm{T}}$$ hadron productions, we extract $$\hat{q}$$ quantitatively via a global fit to data for both single hadron and dihadron suppressions and obtain $$\hat{q}/T^3 = 4.74 - 6.72$$ at $$T = 370$$ MeV in central $$Au+Au$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=200$$ GeV, and $$\hat{q}/T^3 = 3.07 - 3.98$$ at $$T = 480$$ MeV in central $$Pb+Pb$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=2.76$$ TeV. The numerical results show that the uncertainties for $$\hat{q}$$ extraction are brought by the different contributions of gluon-to-hadron in the six sets of FFs due to gluon energy loss being 9/4 times of quark energy loss.

Interface effects of quark matter: Light-quark nuggets and compact stars

The interface effects of quark matter play important roles in the properties of compact stars and small nuggets, such as strangelets and nonstrange quark matter ($ud\mathrm{QM}$) nuggets. By introducing a density derivative term to the Lagrangian density and adopting Thomas-Fermi approximation, we find it is possible to reproduce the results obtained by solving Dirac equations. Adopting certain parameter sets, the energy per baryon of $ud\mathrm{QM}$ nuggets decreases with baryon number $A$ and become more stable than nuclei at $A\ensuremath{\gtrsim}300$. The effects of quark matter symmetry energy are examined, where $ud\mathrm{QM}$ nuggets at $A\ensuremath{\approx}1000$ can be more stable than others if large symmetry energy is adopted. In such cases, larger $ud\mathrm{QM}$ nuggets will decay via fission and the surface of a $ud\mathrm{QM}$ star will fragment into a crust made of $ud\mathrm{QM}$ nuggets and electrons, which resembles the cases of a strange star's crust. The corresponding microscopic structures are then investigated adopting spherical and cylindrical approximations for the Wigner-Seitz cells, where the droplet phase is found to be the most stable configuration with $ud\mathrm{QM}$ stars' crusts and $ud\mathrm{QM}$ dwarfs made of $ud\mathrm{QM}$ nuggets ($A\ensuremath{\approx}1000$) and electrons. For the cases considered here, the crust thickness of $ud\mathrm{QM}$ stars is typically $\ensuremath{\sim}200\text{ }\text{ }\mathrm{m}$, which reaches a few kilometers if we neglect the interface effects and adopt Gibbs construction. The masses and radii of $ud\mathrm{QM}$ dwarfs are smaller than typical white dwarfs, which would increase if the interface effects are neglected.

Probing Charm Quark Dynamics via Multiparticle Correlations in Pb-Pb Collisions at sqrt[s_{NN}]=5.02 TeV.

Multiparticle azimuthal correlations of prompt D^{0} mesons are measured in Pb-Pb collisions at a nucleon-nucleon center-of-mass energy of sqrt[s_{NN}]=5.02 TeV. For the first time, a four-particle cumulant method is used to extract the second Fourier coefficient of the azimuthal distribution (v_{2}) of D^{0} mesons as a function of event centrality and the D^{0} transverse momentum. The ratios of the four-particle v_{2} values to previously measured two-particle cumulant results provide direct experimental access to event-by-event fluctuations of charm quark azimuthal anisotropies. These ratios are also found to be comparable to those of inclusive charged particles in the event. However, hints of deviations are seen in the most central and peripheral collisions. To investigate the origin of flow fluctuations in the charm sector, these measurements are compared to a model implementing fluctuations of charm quark energy loss via collisional or radiative processes in the quark-gluon plasma. These models cannot quantitatively describe the data over the full transverse momentum and centrality ranges, although the calculations with collisional energy loss provide a better description of the data.

Study of two color QCD on large lattices

We study two colors lattice QCD (${\mathrm{QC}}_{2}\mathrm{D}$) with two flavors of staggered fermions on ${40}^{4}$ and ${32}^{4}$ lattices with lattice spacing $a=0.048\text{ }\text{ }\mathrm{fm}$ in the wide range of the quark chemical potential ${\ensuremath{\mu}}_{q}$. Our focus is on the confinement-deconfinement transition in this theory. Thus we compute the string tension from the Wilson loops and the static quark free energy from the Polyakov loops. We find that the deconfinement transition found earlier in the range ${\ensuremath{\mu}}_{q}\ensuremath{\approx}800--1000\text{ }\text{ }\mathrm{MeV}$ is shifted to higher values. This shift is attributed to decreasing of the lattice spacing used in our simulations in comparison with the earlier study.

Study of charm and bottom quark energy loss and associated meson RAA spectra in proton-lead collisions at [formula omitted] TeV

In the present analysis, we compute the energy loss of heavy quarks (charm and bottom) due to elastic collisions and gluon radiation in proton-Lead (p-Pb) collisions at sNN = 5.02 TeV. We calculate the collisional energy loss using Peigne and Peshier formalism and radiative energy loss using the generalised dead cone approach and reaction operator formalism. We also calculate the fluctuations in the resulting medium using the CMT (Chakraborty, Mustafa and Thoma) formalism. The nuclear modification factors RpPb including shadowing, energy loss and fluctuations are calculated for B+,0 and D+,0 mesons in p-Pb collisions at sNN = 5.02 TeV and are compared with the recent measurements by CMS experiment.

Properties of Hot Quark Matter with Neutrino Confinement in the NJL Model

The thermodynamic characteristics of hot $\beta$-equilibrium three-flavor quark matter with neutrino confinement are studied in terms of the local SU(3) Nambu-Jona-Lasinio (NJL) model, which also accounts for the 't Hooft interaction which leads to mixing of quark flavors. For different temperatures $T \in [20 \div 100]$ MeV and baryon number densities $n_B \in [0 \div 1.8]$ fm$^{-3}$ the constituent quark masses, quark condensates, and relative contributions of individual types of particles to the pressure and chemical potentials of the constituent particles are determined. In order to determine the role of neutrinos in the hot quark matter, the pressures and energies in states with and without neutrinos are compared. Keywords: hot quark matter: neutrino confinement: NJL model: equation of state.

Symmetry energy effects on the properties of hybrid stars

Symmetry energy is an important part of the equation of state of isospin asymmetry matter. However, the huge uncertainties of symmetry energy remain at suprasaturation densities, where the phase transitions of strongly interacting matter and the quark matter symmetry energy are likely to be taken into account. In this work, we investigate the properties of symmetry energy by using a hybrid star with the hadron-quark phase transition. The interaction among strange quark matter (SQM) in hybrid stars is based on a 3-flavor NJL model with different vector and isovector channels, while the equation of state (EOS) of the nuclear matter is obtained by considering the ImMDI-ST interaction by varying the parameters x, y, and z. Our results indicate that the various parameters and coupling constants of the interactions from the ImMDI-ST and NJL model can lead to widely different trends for the symmetry energy in the hadron-quark mixed phase and the different onsets of the hadron-quark phase transition. In addition, it has been found that the radii and tidal deformabilities of hybrid stars constrain mostly the density dependence of symmetry energy while the observed maximum masses of hybrid stars constrain mostly the EOS of symmetric nuclear and quark matter.

Measurement of charged-pion production in deep-inelastic scattering off nuclei with the CLAS detector

Background: Energetic quarks in nuclear deep-inelastic scattering propagate through the nuclear medium. Processes that are believed to occur inside nuclei include quark energy loss through medium-stimulated gluon bremsstrahlung and intranuclear interactions of forming hadrons. More data are required to gain a more complete understanding of these effects. Purpose: To test the theoretical models of parton transport and hadron formation, we compared their predictions for the nuclear and kinematic dependence of pion production in nuclei. Methods: We have measured charged-pion production in semi-inclusive deep-inelastic scattering off D, C, Fe, and Pb using the CLAS detector and the CEBAF 5.014-GeV electron beam. We report results on the nuclear-to-deuterium multiplicity ratio for π+ and π− as a function of energy transfer, four-momentum transfer, and pion energy fraction or transverse momentum—the first three-dimensional study of its kind. Results: The π+ multiplicity ratio is found to depend strongly on the pion fractional energy z and reaches minimum values of 0.67±0.03, 0.43±0.02, and 0.27±0.01 for the C, Fe, and Pb targets, respectively. The z dependencies of the multiplicity ratios for π+ and π− are equal within uncertainties for C and Fe targets but show differences at the level of 10% for the Pb-target data. The results are qualitatively described by the GiBUU transport model, as well as with a model based on hadron absorption, but are in tension with calculations based on nuclear fragmentation functions. Conclusions: These precise results will strongly constrain the kinematic and flavor dependence of nuclear effects in hadron production, probing an unexplored kinematic region. They will help to reveal how the nucleus reacts to a fast quark, thereby shedding light on its color structure and transport properties and on the mechanisms of the hadronization process.Received 25 September 2021Accepted 23 December 2021DOI:https://doi.org/10.1103/PhysRevC.105.015201©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasColor confinementDeep inelastic scatteringLepton induced nuclear reactionsParticle interactionsParticle productionQuantum chromodynamicsStrong interactionNuclear PhysicsParticles & Fields

Proto-magnetars within quasiparticle model

We investigate the thermodynamical properties of strange quark matter (SQM) at zero/finite temperature and under constant magnetic field within quasiparticle model. The quark matter symmetry energy, energy per baryon, free energy per baryon, anisotropic pressures are also studied and the result indicates that both the effects of temperature and magnetic field can significantly influence the thermodynamical properties of quark matter and proto-quark stars (PQSs). Our result also indicates that the maximum mass and the core temperature of PQSs not only depends on the heating process at the isentropic stages, but also but also the magnetic field strength and orientation distribution inside the magnetar within quasiparticle model.

Proto-magnetars within quasiparticle model

We investigate the thermodynamical properties of strange quark matter (SQM) at zero/finite temperature and under constant magnetic field within quasiparticle model. The quark matter symmetry energy, energy per baryon, free energy per baryon, anisotropic pressures are also studied and the result indicates that both the effects of temperature and magnetic field can significantly influence the thermodynamical properties of quark matter and proto-quark stars (PQSs). Our result also indicates that the maximum mass and the core temperature of PQSs not only depends on the heating process at the isentropic stages, but also but also the magnetic field strength and orientation distribution inside the magnetar within quasiparticle model.

Dissecting the collinear structure of quark splitting at NNLL

We explore the collinear limit of final-state quark splittings at order {alpha}_s^2 . While at general NLL level, this limit is described simply by a product of leading-order 1 → 2 DGLAP splitting functions, at the NNLL level we need to consider 1 → 3 splitting functions. Here, by performing suitable integrals of the triple-collinear splitting functions, we demonstrate how one may extract {mathrm{mathcal{B}}}_2^q(z) , a differential version of the coefficient {mathrm{mathcal{B}}}_2^q that enters the quark form factor at NNLL and governs the intensity of collinear radiation from a quark. The variable z corresponds to the quark energy fraction after an initial 1 → 2 splitting, and our results yield effective higher-order splitting functions, which may be considered as a step towards the construction of NNLL parton showers. Further, while in the limit z → 1 we recover the standard soft limit results involving the CMW coupling with scale kt, the z dependence we obtain also motivates the extension of the notion of a physical coupling beyond the soft limit.

Isospin effect on quark matter instabilities

We have studied the mechanical and chemical instabilities as well as the liquid-gas-like phase transition in isospin asymmetric quark matter based on the NJL and the pNJL model. Areas of the mechanical instability region and the liquid-gas coexistence region are seen to be enlarged with a larger quark matter symmetry energy or in the presence of strange quarks. Our study shows that the light cluster yield ratio observed in relativistic heavy-ion collisions may not be affected much by the uncertainties of the isospin effect, and favors a smooth hadron-quark phase transition in compact stars as well as their mergers.

Treating divergence in quark matter by using energy projectors

We calculate the gluon self-energy using quark energy projectors in a general quark-gluon plasma. By separating the quark field into positive- and a negative-energy modes, the quark loop constructed with the same mode is always convergent, and the divergence appears only in the mixed loop with different modes and is medium independent. After removing the divergence in vacuum, we obtain the one-loop gluon self-energy at finite temperature, chemical potential, and quark mass without approximation. With the method of quark-loop resummation, we calculate nonperturbatively the gluon Debye mass and thermodynamic potential. In the limit of small gluon momentum in comparison with temperature, chemical potential, and quark mass, our calculation comes back to the known HTL/HDL results in literature.

Heavy quark jet production near threshold

In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1 − z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJR ∼ m and EJR » m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJR/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.

Heavy quark radiation in the quark\u2013gluon plasma in the Moliere theory: angular distribution of the radiation

We study the effects of adding the Coulomb interactions to the harmonic oscillator (HO) approximation of the heavy parton propagating through the quark–gluon plasma (the extension to QCD of the Molliere theory). We explicitly find the expression for the transverse momentum distribution of the gluon radiation of the heavy quark propagating in the quark gluon plasma in the framework of the Moliere theory, taking into account the BDMPSZ radiation in the HO approximation, and the Coulomb logarithms described by the additional logarithmic terms in the effective potential. We show that these Coulomb logarithms significantly influence the HO distribution, derived in the BDMPSZ works, especially for the small transverse momenta, filling the dead cone, and reducing the dead cone suppression of the heavy quark radiation (dead cone effect). In addition we study the effect of the phase space constraints on the heavy quark energy loss, and argue that taking into account of both the phase space constraints and of the Coulomb gluons reduces the dependence of the heavy quark energy loss on its mass in the HO approximation.

Leading jets and energy loss

The formation and evolution of leading jets can be described by jet functions which satisfy non-linear DGLAP-type evolution equations. Different than for inclusive jets, the leading jet functions constitute normalized probability densities for the leading jet to carry a longitudinal momentum fraction relative to the initial fragmenting parton. We present a parton shower algorithm which allows for the calculation of leading-jet cross sections where logarithms of the jet radius and threshold logarithms are resummed to next-to-leading logarithmic (NLL′) accuracy. By calculating the mean of the leading jet distribution, we are able to quantify the average out-of-jet radiation, the so-called jet energy loss. When an additional reference scale is measured, we are able to determine the energy loss of leading jets at the cross section level which is identical to parton energy loss at leading-logarithmic accuracy. We identify several suitable cross sections for an extraction of the jet energy loss and we present numerical results for leading subjets at the LHC. In addition, we consider hemisphere and event-wide leading jets in electron-positron annihilation similar to measurements performed at LEP. Besides the average energy loss, we also consider its variance and other statistical quantities such as the KL divergence which quantifies the difference between quark and gluon jet energy loss. We expect that our results will be particularly relevant for quantifying the energy loss of quark and gluon jets that propagate through hot or cold nuclear matter.

From noninteracting to interacting picture of quark–gluon plasma in the presence of a magnetic field and its fluid property

We have attempted to build a parametric-based simplified and analytical model to map the interaction of quarks and gluons in the presence of magnetic field, which has been constrained by quark condensate and thermodynamical quantities like pressure, energy density, etc., obtained from the calculation of lattice quantum chromodynamics (QCDs). To fulfill that mapping, we have assumed a parametric temperature and magnetic field-dependent degeneracy factor, average energy, momentum and velocity of quarks and gluons. Implementing this QCD interaction in calculation of transport coefficient at finite magnetic field, we have noticed that magnetic field and interaction both are two dominating sources, for which the values of transport coefficients can be reduced. Though the methodology is not so robust, but with the help of its simple parametric expressions, one can get a quick rough estimation of any phenomenological quantity, influenced by temperature and magnetic field-dependent QCD interaction.