Quark Research Articles

Dispersive determination of fourth generation quark masses

We determine the masses of the sequential fourth generation quarks b′ and t′ in the extension of the Standard Model by solving the dispersion relations associated with the mixing between the neutral states Qq¯ and Q¯q, with Q (q) being a heavy (light) quark. The box diagrams responsible for the mixing, which provide the perturbative inputs to the dispersion relations, involve multiple intermediate channels, i.e., the ut and ct channels, u (c, t) being an up (charm, top) quark, in the b′ case, and the db′, sb′, and bb′ ones, d (s, b) being a down (strange, bottom) quark, in the t′ case. The common solutions for the above channels lead to the masses mb′=(2.7±0.1) and mt′≈200 TeV unambiguously. We show that these superheavy quarks, forming bound states in a Yukawa potential, barely contribute to Higgs boson production via gluon fusion and decay to photon pairs and bypass current experimental constraints. The mass of the b¯′b′ ground state is estimated to be about 3.2 TeV. It is thus worthwhile to continue the search for b′ quarks or b¯′b′ resonances at the (high-luminosity) Large Hadron Collider. Published by the American Physical Society 2024

Curvature of the chiral phase transition line from the magnetic equation of state of ( 2+1 )-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge (B, S) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energylike scaling variable that enters the parametrization of the MEoS, allows to explore the variation of Tc(μB,μS)=Tc(1−(κ2Bμ^B2+κ2Sμ^S2+2κ11BSμ^Bμ^S)) along different lines in the (μB,μS) plane. On lattices with fixed cutoff in units of temperature, aT=1/8, we find κ2B=0.015(1), κ2S=0.0124(5) and κ11BS=−0.0050(7). We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10% larger than along the strangeness neutral line. The latter differs only by about 3% from the curvature on a line of vanishing strange quark chemical potential, μs=0. We also show that close to the chiral limit the strange quark mass contributes like an energylike variable in scaling relations for pseudocritical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, Tc(ms)=Tc(msphy)(1−0.097(2)(ms−msphys)/msphy+O((Δms)2). Published by the American Physical Society 2024

Hybrid spectroscopy within the graviton soft-wall model

In this analysis, the so-called holographic graviton soft-wall (GSW) model, first developed to investigate the glueball spectrum, has been adopted to predict the masses of hybrids with different quantum numbers. Results have been compared with other models and lattice calculations. We have extended the GSW model by introducing two modifications based on anomalous dimensions in order to improve our agreement with other calculations and to remove the initial degeneracy not accounted for by lattice predictions. These modifications do not involve new parameters. The next step has been to identify which of our calculated states agree with the PDG data, leading to experimental hybrids. The procedure has been extended to include hybrids made of heavy quarks by incorporating the quark masses into the model. Published by the American Physical Society 2024

QCD sum rules for positive and negative parity heavy baryons at next-to-leading order in αs -expansion

QCD sum rules for positive and negative parity heavy baryons in the heavy quark limit are formulated. We apply the method to Λ and Σ channels. We include the next-to-leading order corrections in αs-expansion to dimension 0 and 3 terms in the operator product expansion. The corrections lead to the considerable reduction of the predicted masses and significantly improves the stability with respect to the Borel parameter, especially for negative parity states. It is also found that, in the heavy quark limit, chiral odd condensates do not contribute to the negative parity states. Published by the American Physical Society 2024

How much strangeness is needed for the axial-vector form factor of the nucleon?

We consider the axial-vector together with its induced pseudoscalar form factor of the nucleon as computed from the chiral Lagrangian with nucleon and isobar degrees of freedom. The form factors are evaluated at the one-loop level, where particular emphasis is put on the use of on-shell masses in the loop expressions. Our results are presented in terms of a novel set of basis functions that generalize the Passarino-Veltman scheme to the case where power-counting violating structures are to be subtracted. The particularly important role of the isobar degrees of freedom is emphasized. We obtain a significant and simultaneous fit to the available lattice QCD results based on flavor SU(2) ensembles for the baryon masses and form factors up to pion masses of about 500 MeV. Our fit includes sizeable finite volume effects that are implied by using in-box values for the hadron masses entering our one-loop expressions. We conclude that from flavor SU(2) ensembles it appears not possible to predict the empirical form factor at the desired precision. Effects from strange quarks are expected to remedy the situation. Published by the American Physical Society 2024

Empirical determination of the energy loss of heavy quarks in nuclear collisions at RHIC and LHC energies

Empirical determination of the energy loss of heavy quarks in nuclear collisions at RHIC and LHC energies

Dynamics of heavy flavor in a weakly magnetized hot QCD medium

We obtain the spatial and momentum-diffusion coefficients (Ds and κ) and the collisional energy loss (dE/dx) of a heavy quark (HQ) traversing through a thermal medium of quarks and gluons in a weak magnetic field (B), for the two cases of the HQ moving either parallel or perpendicular to B. For that purpose, we consider Coulomb scatterings (t-channel) of the HQ with the light quarks, obtained from the imaginary part of the HQ self-energy via the cutting rules. Both the normalized (by T3) κ, and dE/dx, for charm quarks are larger than that for bottom quarks due to the larger mass of the latter. Also, the effect of B is more feeble on the bottom quark, compared to the charm quark. Comparatively, the magnitudes of both κ and dE/dx are significantly smaller for the case of v⊥B. For both the cases, our results show that the momentum transfer between the HQ and the medium takes place preferentially along the direction of HQ velocity, thus leading to a significant increase in the momentum-diffusion anisotropy, compared to B=0. We also calculate the (scaled) spatial diffusion coefficient, which we find to be independent of the heavy flavor mass and is almost unaffected by changes in B. Published by the American Physical Society 2024

Heavy quark fragmentation in e+e− collisions to NNLO+NNLL accuracy in perturbative QCD

Fragmentation of heavy quarks into heavy-flavoured hadrons receives both perturbative and non-perturbative contributions. We consider perturbative QCD corrections to heavy quark production in e+e− collisions to next-to-next-to-leading order accuracy in QCD with next-to-next-to-leading-logarithmic resummation of quasi-collinear and soft emissions. We study multiple matching schemes, and multiple regularisations of the soft resummation, and observe a significant dependence of the perturbative results on these ingredients, suggesting that NNLO+NNLL perturbative accuracy may not lead to real gains unless the interface with non-perturbative physics is properly analysed. We confirm previous evidence that D*+ experimental data from CLEO/BELLE and from LEP are not reconcilable with perturbative predictions employing standard DGLAP evolution. We extract non-perturbative contributions from e+e− experimental data for both D and B meson fragmentation. Such contributions can be used to predict heavy-quark fragmentation in other processes, e.g. DIS and proton-proton collisions.

Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model

Self-polarizing weak decays of Λ-hyperons provide unique insight into the role of entanglement in the fragmentation of QCD strings through measurements of the spin correlations of ΛΛ¯ pairs produced in collider experiments. The simplest quantum field theory representing the underlying parton dynamics is the four-flavor massive Schwinger model plus an effective spin-flip term, where the flavors are mapped to light (up or down) and heavy (strange) quarks and their spins. This construction provides a novel way to explore hyperon spin correlations in 1+1 dimensions. We investigate the evolution of these correlations for different string configurations that are sensitive to the rich structure of the model Hamiltonian. Published by the American Physical Society 2024

Stellar model with non-zero strange quark mass (ms≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_s\ e 0$$\\end{document}) and Mak–Harko density profile admitting observational results

This article describes the configuration of strange quark stars composed of three flavour quarks in hydrostatic equilibrium considering the energy density profile of Mak and Harko and non-zero strange quark mass (ms≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_s\ e {0}$$\\end{document}). A suitable stellar model is proposed assuming equation of state of interior matter as modified MIT equation of state in bag model p=13(ρ-4Bg)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=\\frac{1}{3}(\\rho -4B_g)$$\\end{document}, where Bg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_g$$\\end{document} is known as bag constant, to predict the viability of strange stars. The interior of such compact stars is mainly composed of quarks and electrons to establish charge neutrality condition. We have checked the various stability windows depending on the energy per baryon for different values of bag constant Bg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_g$$\\end{document} and mass of strange quark ms\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_s$$\\end{document}. We have studied the effect of non-zero mass of the strange quark (ms\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_s$$\\end{document}) on the physical properties of the strange star in the context of the modified MIT bag equation of state. We note that the maximum stellar mass decreases with increasing ms\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_s$$\\end{document}. The model is suitable for predicting the radius, central density and other properties of compact stars having mass ≤2.01M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le 2.01M_{\\odot }$$\\end{document}, such as 4U1820-30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4U~1820-30$$\\end{document}, PSRJ1614-2230\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSR~J1614-2230$$\\end{document} etc, which are supposed to be strange stars. The radius of few recently observed compact stars are predicted in our model and they are found to be compatible with the value as predicted from observation. The model is found to be suitable in view of all the necessary criterion along with fulfilment of stability of the stellar configuration as well as stable in view of small radial perturbations.

Gravitational wave emission from close-in strange quark planets around strange stars with magnetic interactions

ABSTRACT According to the strange quark matter hypothesis, strange planets may exist, which are planetary mass objects composed of almost equal numbers of up, down, and strange quarks. A strange planet can revolve around its host strange star in a very close-in orbit. When it finally merges with the host, strong gravitational wave emissions will be generated. Here, the gravitational waveforms are derived for the merging process, taking into account the effects of the strange star’s magnetic field on the dynamics. Effects of the inclination angle are also considered. Templates of the gravitational waveforms are derived. It is found that the magnetic interactions significantly speed up the merging process. Coalescence events of such strange planetary systems occurring in our Galaxy as well as in local galaxies can be effectively detected by current and future gravitational experiments, which may hopefully provide a new method to test the strange quark matter hypothesis and probe the magnetic field of compact stars.

Anomalous diffusion of the heavy quarks through the fractional Langevin equation

The dynamics of heavy quarks within the hot QCD medium have been revisited, considering the influence of anomalous diffusion. This study has been conducted using the framework of the fractional Langevin equation involving the Caputo fractional derivative. We introduce a numerical scheme for the fractional Langevin equation and demonstrate that the mean-squared displacement of the particle exhibits anomalous diffusion, deviating from a linear relationship with time. Our analysis calculates various entities, such as mean-squared momentum, momentum spread, and the nuclear suppression factor RAA. Notably, our findings indicate that superdiffusion strongly suppresses the RAA compared to normal diffusion in the hot QCD medium. The possible impacts on other parameters are also discussed. Published by the American Physical Society 2024

Jet-Origin Identification and Its Application at an Electron-Positron Higgs Factory.

To enhance the scientific discovery power of high-energy collider experiments, we propose and realize the concept of jet-origin identification that categorizes jets into five quark species (b,c,s,u,d), five antiquarks (b[over ¯],c[over ¯],s[over ¯],u[over ¯],d[over ¯]), and the gluon. Using state-of-the-art algorithms and simulated νν[over ¯]H,H→jj events at 240GeV center-of-mass energy at the electron-positron Higgs factory, the jet-origin identification simultaneously reaches jet flavor tagging efficiencies ranging from 67% to 92% for bottom, charm, and strange quarks and jet charge flip rates of 7%-24% for all quark species. We apply the jet-origin identification to Higgs rare and exotic decay measurements at the nominal luminosity of the Circular Electron Positron Collider and conclude that the upper limits on the branching ratios of H→ss[over ¯],uu[over ¯],dd[over ¯] and H→sb,db,uc,ds can be determined to 2×10^{-4} to 1×10^{-3} at 95%confidence level. The derived upper limit for H→ss[over ¯] decay is approximately 3 times the prediction of the standard model.

Semileptonic W Decay to the B Meson with Lepton Pairs in Heavy Quark Effective Theory Factorization up to $\mathcal {O}(\alpha _s)$

Abstract Motivated by the study of heavy–light meson production within the framework of heavy quark effective theory (HQET) factorization, we extend the factorization formalism for a rather complicated process W+ → B+ℓ+ℓ− in the limit of a nonzero invariant squared mass of the dilepton, q2, at the lowest order in 1/mb up to $\mathcal {O}(\alpha _s)$. The purpose of the current study is to extend the HQET factorization formula for the W+ → B+ℓ+ℓ− process and subsequently compute the form factors for this channel up to next-to-leading-order corrections in αs. We explicitly show that the amplitude of the W+ → B+ℓ+ℓ− process can also be factorized into a convolution between the perturbatively calculable hard-scattering kernel and the nonperturbative yet universal light-cone distribution amplitude (LCDA) defined in HQET. The validity of the HQET factorization depends on the assumed scale hierarchy mW ∼ mb ≫ ΛQCD. Within the HQET framework, we evaluate the form factors associated with the W+ → B+ℓ+ℓ− process, providing insights into its phenomenology. In addition, we also perform an exploratory phenomenological study on W+ → B+ℓ+ℓ− by employing an exponential model for the LCDAs for the B+ meson. Our findings reveal that the branching ratio for W+ → B+ℓ+ℓ− is below 10−10. Although the branching ratios are small, this channel in high-luminosity LHC experiments may serve to further constrain the value of λB.

Is the Compact Object Associated with HESS J1731-347 a Strange Quark Star? A Possible Astrophysical Scenario for Its Formation

The analysis of the central compact object within the supernova (SN) remnant HESS J1731-347 suggests that it has a small radius and, even more interestingly, a mass of the order or smaller than 1 M ⊙. This raises the question of which astrophysical process could lead to such a small mass, since the analysis of various types of SN explosions indicate that is it not possible to produce a neutron star with a mass smaller than about 1.17 M ⊙. Here we show that masses of the order or smaller than 1 M ⊙ can be obtained in the case of strange quark stars and that it is possible to build a coherent model explaining not only the mass and the radius of that object, but also its slow cooling suggested in various analyses. We also show that an astrophysical path exists, which leads to the formation of such an object, and we discuss the role played in that scenario by strangelets assumed to constitute the dark matter.

Strange Quark Stars: The Role of Excluded Volume Effects

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.

Unraveling the collisional energy loss of a heavy quark in a quark-gluon plasma

At leading order in the QCD coupling constant, we compute the energy loss per traveling distance of a heavy quark dE/dz from elastic scattering off thermal quarks and gluons at a temperature T, including the thermal perturbative description of soft scatterings (−t<−t*) and a perturbative QCD-based calculation for hard collisions (−t>−t*). Within this soft-hard factorization model, we find that the full results of dE/dz behaves a mild sensitivity to the intermediate cutoff t*, supporting the validity of the soft-hard approach within the temperature region of interest. We rederive the analytic formula for dE/dz in the high-energy approximation, E1≫m12/T, where E1 is the injected heavy quark energy and m1 is its mass. It is realized that the soft logarithmic contribution, dE/dz∝ln(−t*/mD2), arises from the t-channel scattering off thermal partons, while the hard logarithmic term, dE/dz∝ln[E1T/(−t*)], stems from the t-channel scattering off thermal partons, and the one dE/dz∝ln(E1T/m12) comes from the s- and u-channel scattering off gluons. The sum of these contributions cancels the t*-dependence as observed in the full result. The mass hierarchy is observed dE/dz(charm)>dE/dz(bottom). Our full results are crucial for a better description of heavy quark transport in QCD medium, in particular at low and moderate energy. We also calculate the energy loss by imposing the Einstein’s relationship. The related results appear to be systematically larger than that without imposing the Einstein’s relationship. Published by the American Physical Society 2024

QCD Kondo effect for single heavy quark in chiral-symmetry broken phase

We consider the quantum chromodynamics (QCD) Kondo effect for a single heavy quark in quark matter composed of light quarks with chiral symmetry breaking. Introducing several spinor structures in QCD Kondo condensates, i.e., particle-projected condensate, antiparticle-projected condensate, and normal condensate without projection, we calculate the attractive energy gained by the heavy quark within the mean-field approximation in the path-integral formalism. We show that the normal condensate is favored at low density and the particle-projected condensate is favored at high density, when the light quark has a nonzero mass. We interpret such a density-dependent transition between the two condensates in terms of the Kondo resonances. Published by the American Physical Society 2024

Azimuthal Angle Correlations of Muons Produced via Heavy-Flavor Decays in 5.02TeV Pb+Pb and pp Collisions with the ATLAS Detector.

Angular correlations between heavy quarks provide a unique probe of the quark-gluon plasma created in ultrarelativistic heavy-ion collisions. Results are presented of a measurement of the azimuthal angle correlations between muons originating from semileptonic decays of heavy quarks produced in 5.02TeV Pb+Pb and pp collisions at the LHC. The muons are measured with transverse momenta and pseudorapidities satisfying p_{T}^{μ}>4 GeV and |η^{μ}|<2.4, respectively. The distributions of azimuthal angle separation Δϕ for muon pairs having pseudorapidity separation |Δη|>0.8, are measured in different Pb+Pb centrality intervals and compared to the same distribution measured in pp collisions at the same center-of-mass energy. Results are presented separately for muon pairs with opposite-sign charges, same-sign charges, and all pairs. A clear peak is observed in all Δϕ distributions at Δϕ∼π, consistent with the parent heavy-quark pairs being produced via hard-scattering processes. The widths of that peak, characterized using Cauchy-Lorentz fits to the Δϕ distributions, are found to not vary significantly as a function of Pb+Pb collision centrality and are similar for pp and Pb+Pb collisions. This observation will provide important constraints on theoretical descriptions of heavy-quark interactions with the quark-gluon plasma.

Quenching and flow of charm and bottom quarks via semi-leptonic decay of D and B mesons in Pb+Pb collisions at the LHC* *Supported in part by the National Natural Science Foundation of China (12225503, 11935007, 11890710, 11890711, 12175122, 2021-867). W.-J. X. is supported in part by China Postdoctoral Science Foundation (2023M742099). Some of the calculations were performed in the Nuclear

Heavy flavor particles provide important probes of the microscopic structure and thermodynamic properties of the quark-gluon plasma (QGP) produced in high-energy nucleus-nucleus collisions. We studied the energy loss and flow of charm and bottom quarks inside the QGP via the nuclear modification factor ( ) and elliptic flow coefficient ( ) of their decayed leptons in heavy-ion collisions at the LHC. The dynamical evolution of the QGP was performed using the CLVisc (3+1)-dimensional viscous hydrodynamics model; the evolution of heavy quarks inside the QGP was simulated with our improved Langevin model that considers both collisional and radiative energy loss of heavy quarks; the hadronization of heavy quarks was simulated via our hybrid coalescence-fragmentation model; and the semi-leptonic decay of D and B mesons was simulated via PYTHIA. Using the same spatial diffusion coefficient for charm and bottom quarks, we obtained smaller and larger of charm decayed leptons than bottom decayed leptons, indicating stronger energy loss of charm quarks than bottom quarks inside the QGP within our current model setup.