Quark States Research Articles

Pure gauge QCD and holography

Holographic models for the pure gauge quantum chromodynamics (QCD) vacuum are explored. The holographic renormalization of these models is considered as required by a phenomenological approach that takes the β-functions of the models as the only input. This approach is done taking the dilaton as the coordinate orthogonal to the border. This choice greatly simplifies the analysis and gives a geometrical interpretation for the fixed points of the renormalization group flow. Examples are constructed that present asymptotic freedom, confinement of static quarks, either with vanishing or nonvanishing gluon condensate G2. The latter models require an extension of the dilaton-gravity models already considered in the literature. This extension is also determined by the only input, i.e. the β-function. In addition, the restrictions imposed by the trace anomaly equation (TAE) are studied. In doing so, a holographic derivation of this equation is presented.

Bounds on dark matter interpretation of Fermi-LAT GeV excess

Annihilation of light dark matter of mDM≈(10–40) GeV into the Standard Model fermions has been suggested as a possible origin of the gamma-ray excess at GeV energies in the Fermi-LAT data. In this paper, we examine possible model-independent signatures of such dark matter models in other experiments such as AMS-02, colliders, and cosmic microwave background (CMB) measurements. We point out that first generation of fermion final states is disfavored by the existing experimental data. Currently AMS-02 positron measurements provide stringent bounds on cross sections of dark matter annihilation into leptonic final states, and e+e− final state is in severe tension with this constraint, if not ruled out. The e+e− channel will be complementarily verified in an early stage of ILC and future CMB measurements. Light quark final states (qq¯) are relatively strongly constrained by the LHC and dark matter direct detection experiments even though these bounds are model-dependent. Dark matter signals from annihilations into qq¯ channels would be constrained by AMS-02 antiproton data which will be released in very near future. In optimistic case, diffuse radio emission from nearby galaxy (clusters) and the galactic center might provide another hint or limit on dark matter annihilation.

Higgs boson as a top-mode pseudo-Nambu-Goldstone boson

In the spirit of the top-quark condensation, we propose a model which has a naturally light composite Higgs boson, ``tHiggs'' (${h}_{t}^{0}$), to be identified with the 126 GeV Higgs discovered at the LHC. The tHiggs, a bound state of the top quark and its flavor (vectorlike) partner, emerges as a pseudo-Nambu--Goldstone boson (NGB), ``top-mode pseudo-Nambu-Goldstone boson,'' together with the exact NGBs to be absorbed into the $W$ and $Z$ bosons as well as another (heavier) top-mode pseudo-Nambu-Goldstone bosons ($CP$-odd composite scalar, ${A}_{t}^{0}$). Those five composite (exact/pseudo-) NGBs are dynamically produced simultaneously by a single supercritical four-fermion interaction having $U(3)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry which includes the electroweak symmetry, where the vacuum is aligned by a small explicit breaking term so as to break the symmetry down to a subgroup, $U(2)\ifmmode\times\else\texttimes\fi{}U(1{)}^{\ensuremath{'}}$, in a way not to retain the electroweak symmetry, in sharp contrast to the little Higgs models. The explicit breaking term for the vacuum alignment gives rise to a mass of the tHiggs, which is protected by the symmetry and hence naturally controlled against radiative corrections. Realistic top-quark mass is easily realized similarly to the top-seesaw mechanism by introducing an extra (subcritical) four-fermion coupling which explicitly breaks the residual $U(2{)}^{\ensuremath{'}}\ifmmode\times\else\texttimes\fi{}U(1{)}^{\ensuremath{'}}$ symmetry with $U(2{)}^{\ensuremath{'}}$ being an extra symmetry besides the above $U(3{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1)$. We present a phenomenological Lagrangian of the top-mode pseudo-Nambu-Goldstone bosons along with the Standard Model particles, which will be useful for the study of the collider phenomenology. The coupling property of the tHiggs is shown to be consistent with the currently available data reported from the LHC. Several phenomenological consequences and constraints from experiments are also addressed.

Jet propagation and medium excitation in a quark–gluon plasma

Abstract We implement the complete set of elastic 2 → 2 parton scattering processes in the Linearized Boltzmann Transport (LBT) model to study the parton propagation inside a hot quark–gluon plasma. We calculate and compare the elastic energy loss and the transverse momentum distribution of quarks and gluons. We further simulate a single jet propagation and the induced medium excitation within a static quark–gluon plasma to study how the jet energy and profiles are modified by the jet-medium interaction and in particular the jet-induced wake. Effects of the recoiled thermal partons and the jet-induced wake on the jet energy loss and profiles are studied in detail.

Matching excluded-volume hadron-resonance gas models and perturbative QCD to lattice calculations

We match three hadronic equations of state at low energy densities to a perturbatively computed equation of state of quarks and gluons at high energy densities. One of them includes all known hadrons treated as point particles, which approximates attractive interactions among hadrons. The other two include, in addition, repulsive interactions in the form of excluded volumes occupied by the hadrons. A switching function is employed to make the crossover transition from one phase to another without introducing a thermodynamic phase transition. A chi-square fit to accurate lattice calculations with temperature $100 < T < 1000$ MeV determines the parameters. These parameters quantify the behavior of the QCD running gauge coupling and the hard core radius of protons and neutrons, which turns out to be $0.62 \pm 0.04$ fm. The most physically reasonable models include the excluded volume effect. Not only do they include the effects of attractive and repulsive interactions among hadrons, but they also achieve better agreement with lattice QCD calculations of the equation of state. The equations of state constructed in this paper do not result in a phase transition, at least not for the temperatures and baryon chemical potentials investigated. It remains to be seen how well these equations of state will represent experimental data on high energy heavy ion collisions when implemented in hydrodynamic simulations.

Global structure of conformal theories in theSU(3)gauge theory

We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions, on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using a new method "local analysis", we conjecture that the "conformal region" exists together with the confining region and the deconfining region in the phase structure parametrized by beta and K, both in the cases of the large Nf QCD within the conformal window (referred as Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the chiral transition temperature (referred as High Temperature QCD). Our numerical simulation on a lattice of the size 16^3 x 64 shows the following evidence of the conjecture. In the conformal region we find the vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative effects and temporal propagators of meson behave at large t as a power-law corrected Yukawa-type decaying form. The transition from the conformal region to the deconfining region or the confining region is a sharp transition between different vacua and therefore it suggests a first order transition both in Conformal QCD and in High Temperature QCD. Within our fixed lattice simulation, we find that there is a precise correspondence between Conformal QCD and High Temperature QCD in the temporal propagators under the change of the parameters Nf and T/Tc respectively. In particular, we find the correspondence between Conformal QCD with Nf = 7 and High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson unparticle model. From this we estimate the anomalous mass dimension gamma* = 1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc --> infty is a free quark state in the Z(3) twisted vacuum.

Selection Rules for Hadronic Transitions ofXYZMesons

Many of the XYZ mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (BO) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet BO potentials, and quarkonium tetraquarks, which are bound states in BO potentials with light-quark+antiquark flavor. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are derived and used to identify XYZ mesons that are candidates for ground-state energy levels in the BO potentials for charmonium hybrids and tetraquarks.

Light-Front Holographic QCD and the Confinement Potential

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time τ=t+z/c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. In fact, the potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. We also show that the holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrödinger equation. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension z of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The predictions of the LF equations of motion include a zero-mass pion in the chiral mq→0 limit, and linear Regge trajectories M2(n,L)∝n+L with the same slope in the radial quantum number n and orbital angular momentum L. The light-front AdS/QCD holographic approach thus gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, and the excitation spectra of relativistic light-quark meson and baryon bound states in QCD in terms of a single mass parameter. We also briefly discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.

Recent developments in the study of deconfinement in nucleus–nucleus collisions

Deconfinement refers to the creation of a state of quasi-free quarks and gluons in strongly interacting matter. Model predictions and experimental evidence for the onset of deconfinement in nucleus–nucleus collisions were discussed in our first review on this subject. These results motivated further experimental and theoretical studies. This review addresses two subjects. First, a summary of the past, present and future experimental programmes related to discovery and study of properties of the onset of deconfinement are presented. Second, recent progress is reviewed on analysis methods and preliminary experimental results for new strongly intensive fluctuation measures are discussed, which are relevant for current and future studies of the onset of deconfinement and searches for the critical point of strongly interacting matter.

Light top squark in precision top quark sample

The uncertainty of $t\bar{t}$ production cross section measurement at LHC is at a-few-percent level which still allows the stop pair production $\tilde{t}\tilde{t}^{*}$ with identical final states $2b+\ell+nj+{E}_{T}$. In this paper, we attempt to use the existing measurement of $W$-polarization in top quark decay to improve the distinction between stop and top quark states. We apply the ATLAS $\chi^2$ method of $W$-polarization measurement in semi-leptonic $t\bar{t}$ final state to semi-leptonic stop pair samples and study its prediction. We find that the faked top events from stop mostly contribute to the left-handed polarized $W$ due to the reconstruction. The benchmark point with maximal contribution to top events only changes $F_{L}$ by 1%. After comparing with the current experiments, we conclude that the current measurement of $W$-polarization in $t$ decay cannot exclude the light stop scenario.

On the metric of the space of states in a modified QCD

The form of the resulting Feynman propagators in a proposed local and gauge invariant QCD for massive fermions suggests the existence of indefinite metric associated to quark states, a property that might relate it with the known Lee-Wick theories. Thus, the nature of the asymptotic free quark states in the theory is investigated here by quantizing the quadratic part of the quark action. As opposite to the case in the standard QCD, the free theory does not show Hamiltonian constraints. The propagation modes include a family of massless waves and a complementary set of massive oscillations. The theory can be quantized in a way that the massive modes show positive metric and the massless ones exhibit negative norms. It is remarked that, since QCD is expected to not exhibit gluon or quark asymptotic states, the presence of negative metric massless modes does not constitute a definite drawback of the theory. In addition, the fact that the positive metric quark states are massive, seems to be a good feature of the model, being consistent with the approximate existence of asymptotically free massive states in high-energy processes.

A hierarchy of the quark masses in a top condensate model with multiple Higgses

We discuss the quark masses in a top condensate model where not only two quark but also four quark composite states may exist. We show that the presence of the top color group SU (3)1× SU (3)2 with the correct quark representations can justify even in the absence of the additional technicolor interactions a hierarchy of the quark masses where the light quarks masses have the same size, the charm and bottom masses are higher and similar and the top is the heaviest.

AdS-sliced flavor branes and adding flavor to the Janus solution

We implement D7 flavor branes in anti-de Sitter-sliced coordinates on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ with the ansatz that the brane fluctuates only in the warped ($\ensuremath{\mu}$) direction in this slicing, which is particularly appropriate for studying the Janus solution. The natural field theory dual in this slicing is $\mathcal{N}=4$ super-Yang--Mills on two copies of ${\mathrm{AdS}}_{4}$. Branes extending from $\ensuremath{\mu}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ can end at different locations, giving rise to quarks with a piecewise constant mass on each ${\mathrm{AdS}}_{4}$ half-space, jumping discontinuously between them. A second class of flavor brane solutions exists in this coordinate system, dubbed ``continuous'' flavor branes, which extend across the entire range of $\ensuremath{\mu}$. We propose that the correct dual interpretation of the ``disconnected'' flavor brane in this ansatz is a quark hypermultiplet with constant mass on one of the ${\mathrm{AdS}}_{4}$ half-spaces with totally reflecting boundary conditions at the boundary of ${\mathrm{AdS}}_{4}$; whereas the dual interpretation of a continuous flavor brane has totally transparent boundary conditions. Numerical studies indicate that AdS-sliced D7 flavor branes of both classes exhibit spontaneous chiral symmetry breaking, as a nonzero vacuum expectation value persists for solutions of the equation of motion down to zero mass. Continuous flavor branes in this ansatz exhibit many other surprising behaviors: their masses seem to be capped at a modest value near $m=0.551$ in units of the inverse AdS radius, and there may be a phase transition between continuous branes of different configurations. We also numerically study quark states in Janus. The behavior of the mass and vacuum expectation value is similar in Janus, including the existence of chiral symmetry breaking at zero mass, though qualitative features of the phase diagram change (sometimes significantly) as the Janus parameter ${c}_{0}$ increases.

On the definition and interpretation of a static quark-antiquark potential in the color-adjoint channel

We study possibilities to define a static quark-antiquark pair in a color-adjoint orientation based on Wilson loops with generator insertions, using both lattice QCD and leading-order perturbation theory in various gauges. Nonperturbatively, the only way to obtain nonzero results while maintaining positivity of the Hamiltonian is by using either temporal gauge or Coulomb gauge with some additional constraint on the temporal links removing the residual gauge symmetry. In this case the correlator is equivalent to a gauge invariant correlation function of a static quark-antiquark pair and a static adjoint quark; the resulting three-point potential is attractive. Saturating open color indices with color magnetic fields instead also leads to a gauge invariant correlator. However, this object is found to couple to the singlet sector only and results in a hybrid potential. None of the considered lattice observables reproduces the repulsive adjoint potential predicted by perturbation theory in Lorenz or Coulomb gauges.

Entropy and Temperature from Entangled Space and Time

Two coupled oscillators provide a mathematical instrument for solving many problems in modern physics, including squeezed states of light and Lorentz transformations of quantum bound states. The concept of entanglement can also be studied within this mathematical framework. For the system of two entangled photons, it is of interest to study what happens to the remaining photon if the other photon is not observed. It is pointed out that this problem is an issue of Feynman’s rest of the universe. For quantum bound-state problems, it is pointed out the longitudinal and time-like coordinates become entangled when the system becomes boosted. Since time-like oscillations are not observed, the problem is exactly like the two-photon system where one of the photons is not observed. While the hadron is a quantum bound state of quarks, it appears quite differently when it moves rapidly than when it moves slowly. For slow hadrons, Gell-Mann’s quark model is applicable, while Feynman’s parton model is applicable to hadrons with their speeds close to that of light. While observing the temperature dependence of the speed, it is possible to explain the quark-to-parton transition as a phase transition.

Physics of Quark Gluon Plasma: An Update and the Status Report

The microsecond old universe was too hot for the nucleons to survive as bound states of quarks. When the temperature of the universe fell below ∼10 K as a result of cooling due to expansion, the quarks got confined inside the nucleons to reside there ever after—making them inaccessible to any direct observation in isolation. Natural objects like the core of the compact astrophysical objects may also contain deconfined quark matter. Therefore, creation of a deconfined phase of thermal quarks and gluons will be very important for understanding the evolution of the early universe and the physics of compact astrophysical objects like neutron star. Calculations based on lattice QCD indicate that hadronic matter at high temperatures and densities undergoes a phase transition to a thermalized system of deconfined quarks and gluons, called quark gluon plasma (QGP). It is expected that such high densities and temperatures may be achieved by colliding two nuclei at RHIC, LHC, or FAIR energies. The present volume addresses some of the experimental and theoretical issues related to quark-hadron phase transition in the relativistic heavy ion collisions by the world experts in the field. On the experimental sides it contains results from CERN’s Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) and Brookhaven National Laboratory’s Relativistic Heavy Ion Collider (RHIC). Comparison of experimental results from RHIC and LHC is extremely useful to gain insights into the properties of the matter formed in these experiments. The present volume offers a review on this subject. On the theoretical side the present volume contains papers on the space-time evolution of the system formed in heavy ion collisions including the effects of viscosities through hydrodynamic equations, issues of equilibration, electromagnetic and heavy quark probes of QGP, quarkonia suppression in QGP, ridge, and transverse correlations. Recent progress in the femtoscopy and particle production in strong electromagnetic fields in heavy ion collisions is also addressed adequately. In summary, the present volume brings out recent developments on almost all the relevant issues of heavy ion collisions like creation, evolution, and signals of QGP. We are sure that the volume will be useful for the current practitioners and young new entrants to this exciting field of research.

Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions

We investigate the chemical-potential ($\ensuremath{\mu}$) dependence of static-quark free energies in both the real and imaginary $\ensuremath{\mu}$ regions, performing lattice QCD simulations at imaginary $\ensuremath{\mu}$ and extrapolating the results to the real-$\ensuremath{\mu}$ region with analytic continuation. Lattice QCD calculations are done on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. Static-quark potentials are evaluated from the Polyakov-loop correlation functions in the deconfinement phase. To perform the analytic continuation, the potential calculated at imaginary $\ensuremath{\mu}=i{\ensuremath{\mu}}_{\mathrm{I}}$ is expanded into a Taylor expansion series of $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ up to fourth order and the pure imaginary variable $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ is replaced by the real one ${\ensuremath{\mu}}_{\mathrm{R}}/T$. At real $\ensuremath{\mu}$, the fourth-order term sizably weakens the $\ensuremath{\mu}$ dependence of the potential. At long distance, all of the color-singlet and -nonsinglet potentials tend to twice the single-quark free energy, indicating that the interactions between static quarks are fully color screened for finite $\ensuremath{\mu}$. For both real and imaginary $\ensuremath{\mu}$, the color-singlet $q\overline{q}$ and the color-antitriplet $qq$ interactions are attractive, whereas the color-octet $q\overline{q}$ and the color-sextet $qq$ interactions are repulsive. The attractive interactions have a stronger $\ensuremath{\mu}/T$ dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary $\ensuremath{\mu}$, and the mass is extrapolated to real $\ensuremath{\mu}$ by analytic continuation. The screening mass thus obtained has a stronger $\ensuremath{\mu}$ dependence than the prediction of hard-thermal-loop perturbation theory at both real and imaginary $\ensuremath{\mu}$.

QCD on the Light-Front

Light-Front Hamiltonian theory provides a rigorous frame-independent framework for solving nonperturbative QCD. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schr\"odinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. The valence LF meson wavefunctions for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable $\zeta^2=b^2_\perp x(1-x)$, which is conjugate to the invariant mass squared. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. The corresponding light-front Dirac equation provides a model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS_5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between amplitudes in the fifth dimension of AdS space and light-front wavefunctions. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting, and the implications of light-front quantization for the value of the cosmological constant.

Energy spectrum of bottom- and charmed-flavored mesons from polarized top quark decayt(↑)→W++B/D+XatO(αs)

We consider the decay of a polarized top quark into a stable $W^+$ boson and charmed-flavored (D) or bottom-flavored (B) hadrons, via $t(\uparrow)\rightarrow W^++D/B+X$. We study the angular distribution of the scaled-energy of B/D-hadrons at next-to-leading order (NLO) considering the contribution of bottom and gluon fragmentations into the heavy mesons B and D. To obtain the energy spectrum of B/D-hadrons we present our analytical expressions for the parton-level differential decay widths of $t(\uparrow)\rightarrow b+W^+(+g)$ at NLO. Comparison of our predictions with data at the LHC enable us to test the universality and scaling violations of the B- and D-hadron fragmentation functions (FFs). These can also be used to determine the polarization states of top quarks and since the energy distributions depend on the ratio $m_W /m_t$ we advocate the use of such angular decay measurements for the determination of the top quark's mass.

Theory of baryon resonances at largeNc

At large number of colors, N_c quarks in baryons are in a mean field of definite space and flavor symmetry. We write down the general Lorentz and flavor structure of the mean field, and derive the Dirac equation for quarks in that field. The resulting baryon resonances exhibit an hierarchy of scales: The crude mass is O(N_c), the intrinsic quark excitations are O(1), and each intrinsic quark state entails a finite band of collective excitations that are split as O(1/N_c). We build a (new) theory of those collective excitations, where full dynamics is represented by only a few constants. In a limiting (but unrealistic) case when the mean field is spherically-and flavor-symmetric, our classification of resonances reduces to the SU(6) classification of the old non-relativistic quark model. Although in the real world N_c is only three, we obtain a good accordance with the observed resonance spectrum up to 2 GeV.