Basis light-front quantization for a chiral nucleon-pion Lagrangian

Abstract

We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton. * BLFQ employs the LF formalism [18,19], where physical systems are quantized at fixed LF time x + = t+z [8,20]. The structure and dynamics of the systems are characterized by the Hamiltonian formalism. The LF vacuum has a simple structure since the Fock vacuum is an exact eigenstate of the full normal-ordered Hamiltonian [21,22]. This provides access to the Fock-space expansion of the physical states in the LF field theory and thereby generates physical intuition for their underlying structures [21,22].BLFQ also takes the advantage of the developments in ab initio non-relativistic quantum many-body theories, such as the No-Core Shell Model (NCSM) [23][24][25], and the rapidly developing supercomputing techniques (algorithms and hardwares) (see, e.g., [26] and references therein). In BLFQ, the LF mass-squared operator of a hadron system in the basis representation becomes a sparse matrix whose dimensions are controlled by truncations that respect the relativistic symmetries. By matrix diagonalization, the eigenvalues produce the mass sprectum, while the resulting eigenfunctions are the light-front wave functions (LFWFs) that encode the hadronic properties. The LFWFs can be boosted to a general Lorentz frame for calculating, e.g., form factors and scattering processes [21].The LF quantization approach to treat a chiral model of the nucleon-pion (N π) system was first proposed by Miller [27,28] in investigating the N π scattering and the nucleon-nucleon scattering via perturbation theory. In this work, we will present the first non-perturbative treatment of the same chiral model via the BLFQ method. In particular, we consider a physical proton as the relativistic bound state of the N π system. Via the BLFQ approach, we obtain the LF mass-squared matrix of the N π system within a truncated basis. We compute the proton's mass and the corresponding LFWF by numerical diagonalization of the mass-squared matrix. Based on the LFWF, we evaluate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.The outline of this paper is the following. We begin by introducing our adopted Lagrangian density in Sec. 2. Then, in Sec. 3, we introduce the elements of BLFQ, such as the derivation of the LF Hamiltonian density, our choice of the basis construction and truncation schemes, the derivation of the mass-squared matrix element in the basis representation, and the fo...

Parton distribution functions of heavy mesons on the light front

“…(For the reviews related to BLFQ and its other application, see Refs. [67][68][69][70][71][72][73][74][75]. )…”

Scattering in strong electromagnetic fields: Transverse size effects in time-dependent basis light-front quantization

“…BLFQ has the advantage of being able to solve bound state problems involving positronium [37] and hadron structures [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. In this paper we follow previous work on the physical electron eigenstates in BLFQ [54].…”