Two-dimensional Quantum Chromodynamics Research Articles

Heavy quark fragmentation function in two-dimensional QCD in Nc→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c\\rightarrow \\infty $$\\end{document} limit

We carry out a comprehensive study of the quark-to-meson fragmentation function in the ’t Hooft model, i.e., the two-dimensional quantum chromodynamics (QCD) in Nc→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c\\rightarrow \\infty $$\\end{document} limit, following the operator definition pioneered by Collins and Soper. We apply the Hamiltonian approach as well as the diagrammatic approach to construct the functional form of the quark-to-meson fragmentation function in terms of the meson’s light-cone wave function. For the sake of comparison, we also investigate the heavy quark fragmentation into quarkonium in two-dimensional QCD within the framework of the nonrelativistic QCD (NRQCD) factorization, at the lowest order in quark velocity. In the heavy quark limit, the quark fragmentation function obtained from the ab initio method agrees well, both analytically and numerically, with that obtained from the NRQCD approach. This agreement might be regarded as a nontrivial justification for the validity of both field-theoretical approaches to compute the heavy quark fragmentation function.

Mass decomposition of the pion in the ’t Hooft model

We obtain the energy-momentum tensor (EMT) in the 't Hooft model of two-dimensional quantum chromodynamics. The EMT is decomposed into contributions from quark and gluon fields, with all of the (plus component of) the light front momentum being carried by the quark field. The energy is split between quark and gluon fields, with the gluon field carrying the self-energy of the dressed quarks. We consider the pion in the limit of small but non-zero quark masses -- which has previously withstood numerical treatment -- as as a concrete example. We solve for the pion wave function using a variational method and obtain numerical results for its energy breakdown into quark and gluon contributions.

Detection of particles of dark matter from the spectrum of secondary particles in high-energy proton-proton collisions in a thermodynamic model

In a simple hydrodynamic model, the transverse momentum distributions are found for A hyperons formed in pp collisions at ultrarelativistic energies. The calculated spectra are compared with the experimental data obtained for various colliders in a wide range of proton collision energies, including the data from experiments at the Large Hadron Collider. An interpretation of the transverse momentum spectra of soft photons in pp collisions is proposed, taking into account the X17 boson with a mass of 17 MeV - a new particle, a possible candidate for the role of dark matter particles. A tube model is proposed on the basis of combining two-dimensional quantum chromodynamics and quantum electrodynamics. An interpretation is proposed for the detection of a 38 MeV boson in the spectra of photons emitted in the reactions of protons with carbon nuclei at an incident proton momentum of 5.5 GeV/c. The X38 boson with a mass of 38 MeV has a mass close to the boson mass obtained by us, equal to 35 MeV for an electromagnetic tube. This new particle was discovered in experiments carried out recently in Dubna for the reactionp p + C→2γ + X. To interpret the obtained experimental data on the spectra of emitted photons depending on their mass, it is proposed to use the formulas obtained for massive particles, setting the mass of a boson decaying into two photons equal to 38 MeV. It was proposed to consider bosons X17 and X38 as particles of dark matter.

Interpolating ’t Hooft model between instant and front forms

The 't Hooft model, i.e., the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $\ensuremath{\delta}$ between $\ensuremath{\delta}=0$ for the instant form dynamics (IFD) and $\ensuremath{\delta}=\ensuremath{\pi}/4$ for the light-front dynamics (LFD). With this parameter $\ensuremath{\delta}$, we formulate the interpolating mass gap equation which takes into account the nontrivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions not only reproduce the previous IFD result at $\ensuremath{\delta}=0$ as well as the previous LFD result at $\ensuremath{\delta}=\ensuremath{\pi}/4$ but also link them together between the IFD and LFD results with the $\ensuremath{\delta}$ parameter. We find the interpolation angle independent characteristic energy function which satisfies the energy-momentum dispersion relation of the dressed fermion, identifying the renormalized fermion mass function and the wave function renormalization factor. The renormalized fermion condensate is also found independent of $\ensuremath{\delta}$, indicating the persistence of the nontrivial vacuum structure even in the LFD. Using the dressed fermion propagator interpolating between IFD and LFD, we derive the corresponding quark-antiquark bound-state equation in the interpolating formulation verifying its agreement with the previous bound-state equations in the IFD and LFD at $\ensuremath{\delta}=0$ and $\ensuremath{\delta}=\ensuremath{\pi}/4$, respectively. The mass spectra of mesons bearing the feature of the Regge trajectories are found independent of the $\ensuremath{\delta}$-parameter reproducing the previous results in LFD and IFD for the equal mass quark and antiquark bound states. The Gell-Mann-Oakes-Renner relation for the pionic ground-state in the zero fermion mass limit is confirmed indicating that the spontaneous breaking of the chiral symmetry occurs in the 't Hooft model regardless of the quantization for $0\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}\ensuremath{\pi}/4$. We obtain the corresponding bound-state wave functions and discuss their reference frame dependence with respect to the frame independent LFD result. Applying them for the computation of the so-called quasi-parton distribution functions now in the interpolating formulation between IFD and LFD, we note a possibility of utilizing not only the reference frame dependence but also the interpolation angle dependence to get an alternative effective approach to the LFD-like results.

Mass structure of hadrons and light-front sum rules in the t′ Hooft model

We study the mass/energy structure of the bound state of hadrons in two-dimensional quantum chromodynamics in the large number of color limit (t' Hooft model). We analyze separately the contributions from the traceless and trace part of the energy-momentum tensor, and show that the masses are related to the matrix elements of the scalar charge and Coulomb energy. We derive the light-front sum rules for the scalar charge and Coulomb energy, expressed in terms of the light-front wave functions, and find that they are regular at $x=0$ without the delta function contribution. We also consider the result for the massless Goldstone boson, as well as the structure of the gravitational form factors of the bound meson states.

Quantum simulation of quantum field theories as quantum chemistry

Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing those computations using quantum devices, with the help of near-term and future quantum algorithms. We show that this construction is very similar to quantum simulation problems appearing in quantum chemistry (which are widely investigated in quantum information science), and the renormalization group theory provides a field theory interpretation of conformal truncation simulation. Taking two-dimensional Quantum Chromodynamics (QCD) as an example, we give various explicit calculations of variational and digital quantum simulations in the level of theories, classical trials, or quantum simulators from IBM, including adiabatic state preparation, variational quantum eigensolver, imaginary time evolution, and quantum Lanczos algorithm. Our work shows that quantum computation could not only help us understand fundamental physics in the lattice approximation, but also simulate quantum field theory methods directly, which are widely used in particle and nuclear physics, sharpening the statement of the quantum Church-Turing Thesis.

Model of quark–antiquark interaction in quantum chromodynamics on the light front

We formulate a model of quark–antiquark interaction related to the limit transition to the light-front Hamiltonian in quantum chromodynamics. As ultraviolet regularization, we use a lattice in the space of transverse coordinates, and we additionally introduce a longitudinal light-front coordinate cutoff and also corresponding periodic boundary conditions. We regard the zero mode with respect to this coordinate as an independent dynamical variable. The state space of the model is limited to a quark and an antiquark that interact only via the zero mode of the gluon field on the light front. In this framework, we obtain a discrete mass spectrum of bound states. This spectrum is determined by an equation that with respect to the longitudinal coordinate turns out to be analogous to the’ t Hooft equation in two-dimensional quantum chromodynamics. The equation also contains a quark–antiquark potential that ensures confinement in the transverse space.

Exact solution of the’ t Hooft equation in the limit of heavy quarks with unequal masses

We consider the’ t Hooft equation for bound states in the two-dimensional quantum chromodynamics in the limit of an infinite number of colors. In the case of quarks with unequal masses tending to infinity, we obtain an approximation to the low-energy part of the spectrum and the corresponding wave functions. We show that as in the case of equal masses, the’ t Hooft equation in the first approximation reduces to the Schrodinger equation with a linear potential, i.e., to the equation for a particle in a “triangular” potential well. We also discuss the possibility of obtaining corrections to this approximation.

Entanglement entropy in ’t Hooft model

We use the replica trick approach to calculate, in the large-$N$ limit, the entanglement $c$-function in two-dimensional quantum chromodynamics with the gauge group $U(N)$ and quark in the fundamental representation ('t Hooft model). We show explicitly that the result is equal to a sum (with certain numerical coefficients) of entanglement $c$-functions of free massive scalars, which represent mesons in the spectrum of the 't Hooft model. Interestingly, each meson contributes as a pointlike particle. We provide an explanation for why this is the case.

PT symmetry in classical and quantum statistical mechanics

-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. -symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with -symmetry include Z( N ) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural -symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate -symmetric Hamiltonian.

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

The solitons and kinks of the SU(3) generalized sine-Gordon model (GSG) are shown to describe the baryonic spectrum of two-dimensional quantum chromodynamics (QCD2). The GSG model arises in the low-energy effective action of bosonized QCD2 with unequal quark mass parameters. The GSG potential for Nf = 3 flavors resembles the potential of the effective chiral lagrangian proposed by Witten to describe low-energy behavior of four dimensional QCD. Among the attractive features of the GSG model are the variety of soliton and kink type solutions for QCD2 unequal quark mass parameters [JHEP(0701)(2007)(027)]. Exotic baryons in QCD2 [J. Ellis et al JHEP0508(2005)081] are discussed in the context of the GSG model. Various semi-classical computations are performed improving the results of this reference and clarifying the role of unequal quark masses. The remarkable double sine Gordon model also arises as a reduced GSG model bearing a kink(K) type solution describing a multi-baryon; so, the description of some resonances in QCD2 may take advantage of the properties of the K system.

TOPOLOGICAL CONTRIBUTIONS TO FERMIONIC CORRELATORS AND NONPERTURBATIVE ASPECTS OF QCD IN TWO DIMENSIONS

We analyze the formation of fermionic condensates in two-dimensional quantum chromodynamics for matter in the fundamental representation of the gauge group. We show that a topological regular instanton background is crucial in order to obtain nontrivial correlators. We discuss both massless and massive cases.

Screening in Two-Dimensional QCD

We discuss the issue of screening and confinement of external color charges in bosonized two-dimensional quantum chromodynamics. Our computation relies on the static solutions of the semiclassical equations of motion. We consider the problem with fermions in the fundamental representation, as well as arbitrary products thereof, from which the case of adjoint representation may be obtained by suitable constraints in the massless case. The mass term is treated perturbatively. Under these assumptions, we arrive at the conclusion that, in the cases considered so far (fermions in the fundamental representation or arbitrary numbers of copies thereof) screening seems to prevail. Indeed, we found no solution compatible to confinement. To confirm this result further, we outline the construction of operators corresponding to screened quarks.

Multiflavor correlation functions in non-Abelian gauge theories at finite fermion density in two dimensions

We compute vacuum expectation values of products of fermion bilinears for two-dimensional quantum chromodynamics at finite flavored-fermion densities. We introduce the chemical potential as an external charge distribution within the path-integral approach and carefully analyze the contribution of different topological sectors to fermion correlators. We show the existence of chiral condensates exhibiting an oscillatory inhomogeneous behavior as a function of a chemical potential matrix. This result is exact and goes in the same direction as the behavior found in four-dimensional QCD within the large $N$ approximation.

TWO-DIMENSIONAL QUANTUM CHROMODYNAMICS ON A CYLINDER

We study two-dimensional quantum chromodynamics with massive quarks on a cylinder in a light-cone formalism. We eliminate the non-dynamical degrees of freedom and express the theory in terms of the quark and Wilson loop variables. It is possible to perform this reduction without gauge fixing. The fermionic Fock space can be defined independent of the gauge field in this light-cone formalism.

QCD 2 in a box

Box quantization of two-dimensional quantumchromodynamics is discussed. It provides a solution to severe infrared problems, a new interpretation of discretized light-cone quantization and - in the large N limit - a simple model for chiral symmetry restoration.

Infrared regularization in two-dimensional quantum chromodynamics

Using 2-dimensional quantum chromodynamics as an example, it is shown that the gauge-invariant fields formalism allows one to avoid the difficulties related to the choice of an infrared regularization, and leads to confinement of both single quarks and quark-antiquark pairs.

Explicit expressions for masses and bindings of multibaryons in QCD(2)

We derive explicit expressions for the masses and the binding energies of k-baryon states in two-dimensional (one space and one time) quantum chromodynamics (QCD(2)). The expressions are given using the parameters n 1, n 2, …, n N f−1 which characterize the representation of SU( N f), where N f is the number of flavours, in terms of its Young tableau description. We find that the difference between the mass of the k-baryon state and the sum of masses of any combination of its constituents is independent of the value N f (i.e. the number of flavours)(up to the overall mass scale M). These results hold within a certain bosonized form of QCD(2) and within the strong coupling limit of ( G/ m) → ∞, where G is the gauge coupling constant and m the quark mass.

Multi-baryons in QCD(2)

We find multi-baryon states in two-dimensional quantum chromodynamics. We show that to bind two baryons the model must involve at least seven flavours. All calculations are performed in the strong coupling limit and the semiclassical approximation is employed in the derivation of the results. We briefly comment on the properties of the derived states.

QCD2 AS THE THEORY OF MATTER FIELDS IN A CHIRAL BACKGROUND

On the physical states, two-dimensional quantum chromodynamics ( QCD 2) is shown to reduce to the theory of fermions in a chiral background.