Alberg and Miller Reply:

Alberg, Mary; Miller, Gerald A.

doi:10.1103/physrevlett.110.179102

Cited by 13 publications

(17 citation statements)

References 5 publications

(5 reference statements)

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“…With the choice of the proton's r 2 p,E to be either 0.879 fm or 0.840 fm, we find that the total probability of a physical proton consisting of a bare nucleon and a single pion is within the range of [0.144, 0.285] (Table 3) or the range [0.206, 0.328] ( Table 6). These results compare well with the studies of the pion cloud effects by the cloudy bag model [54,55]. However, it is also worth noting that the correct size of the pion cloud effects would not be sufficient to obtain the electromagnetic form factors, as will be discussed below.…”

Section: Probabilities Of Fock Sectorssupporting

confidence: 78%

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

Zhao

et al. 2020

Phys. Rev. C

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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...

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Section: Probabilities Of Fock Sectorssupporting

confidence: 78%

“…(47) to the above expression, we obtain the analytic expression of the contribution of a free nucleon to the mass squared operator H LC [Eq. (55)] in terms of the LF basis:…”

Section: Appendices a 2dho Basismentioning

confidence: 99%

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

Zhao

et al. 2020

Phys. Rev. C

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“…The excess ofd in the light-front meson-cloud model at the input scale is responsible for the observed asymmetry, and it is in good agreement with the experimental data after evolution to the relevant experimental scale. More sophisticated meson-cloud models including also the contribution from N → ∆π fluctuations have been discussed in literature [14,26,[53][54][55][56]. Owing to the freedom in the choice of the cutoff in the baryon form factors at the N BM vertices, the contributions of opposite sign from the N π and ∆π fluctuations accommodates to produce very similar results as in our approach.…”

Section: Resultsmentioning

confidence: 51%

Collinear parton distributions and the structure of the nucleon sea in a light-front meson-cloud model

Kofler

Pasquini

2017

Phys. Rev. D

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The unpolarized, helicity and transversity parton distribution functions of the nucleon are studied within a convolution model where the bare nucleon is dressed by its virtual meson cloud. Using light-front time-ordered perturbation theory, the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The bare baryons and mesons are described with light-front wave functions (LFWFs) for the corresponding valence-parton components. Using a representation in terms of overlap of LFWFs, the role of the non-perturbative antiquark degrees of freedom and the valence quark contribution at the input scale of the model is discussed for the leading-twist collinear parton distributions. After introducing perturbative QCD effects through evolution to experimental scales, the results are compared with available data and phenomenological extractions. Predictions for the nucleon tensor charge are also presented, finding a very good agreement with recent phenomenological extractions.

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“…It may be noted that while many high-quality results are available for confined H atom, same for other Coulombic systems are rather scarce. Some notable confinement works along this direction include (a) Hulth en potential [17,28,[70][71][72] (b) Coulomb plus harmonic oscillator [73,74] (c) Morse potential [75] (d) Lennard-Jones potential, [76] and so forth. As maximum work has been done on (a), it is selected here to facilitate easy comparison.…”

Section: Confined Hulth En Potentialmentioning

confidence: 99%

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

Roy

2015

Int J of Quantum Chemistry

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The generalized pseudospectral method is employed to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulthén potential. In both instances, arbitrary cavity size, as well as low and higher states are considered. Apart from bound state eigenvalues, eigenfunctions, expectation values, quite accurate estimates of the critical cage radius for H atom for all the 55 states corresponding to n ≤ 10, are also examined. Some of the latter are better than previously reported values. Degeneracy and energy ordering under the isotropic confinement situation are discussed as well. The method produces consistently high-quality results for both potentials for small as well as large cavity size.For the H atom, present results are comparable to best theoretical values, while for the latter, this work gives considerably better estimates than all existing work so far.

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Alberg and Miller Reply:

Cited by 13 publications

References 5 publications

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

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

Collinear parton distributions and the structure of the nucleon sea in a light-front meson-cloud model

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

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