Physical Nucleon Research Articles

Nucleon Self-Energy Including Two-Loop Contributions

The nucleon self-energy is calculated in SU(2) covariant chiral perturbation theory to study the pion mass dependence of the nucleon mass up to chiral order O(q6), i.e., including two-loop diagrams. The contributions of the diagrams are expressed by a small set of (scalar) master integrals. The extended-on-mass-shell (EOMS) renormalization scheme is applied by systematically subtracting infrared regular parts of the integrals (besides the divergences) to ensure that the renormalized results are consistent with the power counting. The master integrals are evaluated in two ways: Firstly, they are calculated by means of the chiral expansion in d dimensions, using the strategy of regions to differentiate between the infrared singular and regular part. This yields the physical nucleon mass in a 1/m-expansion and is in agreement with the infrared-renormalized result. Secondly, the master integrals are solved numerically without relying on the 1/m-expansion using the sector decomposition method.

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

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.

Kaon-Nucleon systems and their interactions in the Skyrme model

We study kaon-nucleon systems in the Skyrme model in a method based on the bound state approach of Callan-Klebanov but with the kaon around the physical nucleon of the rotating hedgehog. This corresponds to the variation after projection, reversing the order of semiclassical quantization of $1/N_c$ expansion. The method, however, is considered to be suited to the study of weakly interacting kaon-nucleon systems including loosely $\bar{K}N$ bound states such as $\Lambda(1405)$. We have found a bound state with binding energy of order ten MeV, consistent with the observed state. We also discuss the $\bar{K}N$ interaction and find that it consists of an attraction in the middle range and a repulsion in the short range.

PROBING THE PARTON CONTENT OF THE NUCLEON

The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.

Neutron charge density from simple pion cloud models

The physical nucleon is modeled as a bare nucleon surrounded by a pion cloud using a psuedoscalar pion-nucleon coupling to examine its implications for the neutron form factor, F{sub 1}(Q{sup 2}), and the corresponding transverse charge density, {rho}(b), in the infinite momentum frame. Two versions, one with a tunable Pauli-Villars parameter and another with light-front cloudy-bag pion-nucleon form factors, are examined. A qualitative agreement with the experimental form factor (F{sub 1}<0 for all Q{sup 2}) and transverse charge density is achieved when the nucleon is treated as having a finite extent. The bare nucleon must have a finite extent if this model is to account for a negative definite F{sub 1} and consequently a negative transverse charge density of the neutron at its center.

Contributions of radiative gluons and vector mesons to theF2structure function

We calculate unpolarized quark distribution functions and ${F}_{2}$ structure functions for the proton and the neutron. The calculation is preformed in the light-cone frame. For the bare nucleon three different distributions---namely, spin-0 diquark, spin-0 plus spin-1 diquark, and no diquark models---have been used. Using perturbative QCD an initial gluon distribution is generated inside the core nucleon. The physical nucleon is assumed to be a superposition of the bare nucleon plus virtual light-cone Fock states of baryon octets and baryon decuplets along with the corresponding pseudoscalar mesons and vector mesons. The initial distributions are evolved. The ${F}_{2}$ structure functions are calculated from the evolved distributions and it is shown that they are in reasonable agreement with the NMC and ZEUS results along with a CTEQ6M fit. Also, it is shown that the meson cloud is a major contributing factor to the sea quark asymmetry and one needs both pseudoscalar mesons and vector mesons to account fully for Gottfried sum rule violation.

Generalized parton distributions in a meson cloud model

We present a model calculation of the generalized parton distributions where the nucleon is described by a quark core surrounded by a mesonic cloud. In the one-meson approximation, we expand the Fock state of the physical nucleon in a series involving a bare nucleon and two-particle, meson-baryon, states. We discuss the role of the different Fock-state components of the nucleon by deriving a convolution formalism for the unpolarized generalized parton distributions, and showing predictions at different kinematics.

Contribution of radiative gluons and spin-one diquarks to theF2structure function

We calculate unpolarized quark distribution functions and the ${F}_{2}$ structure functions for the proton and the neutron. The calculations are preformed in the light-cone frame. For the bare nucleon we have used three different distributions, namely, the spin-0 diquark, the spin-0 plus spin-1 diquark, and the no diquark models. By using perturbative QCD an initial gluon distribution is generated inside the core nucleon. The physical nucleon is assumed to be a superposition of the bare nucleon plus the virtual light-cone Fock states of baryon octets and decuplets and pseudoscalar meson pairs. The initial distributions are evolved. The ${F}_{2}$ structure functions calculated from the evolved distributions are compared with NMC and ZEUS results along with a CTEQ6M fit. Also, it is shown that the meson cloud is a contributing factor to sea-quark asymmetry and to Gottfried sum-rule violation.

General Relativistic Bound States of a Fermion and a Scalar Interacting via a Massive Scalar

A complete set of numerical solutions is obtained, in the ladder approximation, to the Bethe-Salpeter equation describing bound states of a spin-\(\frac{1}{2}\) fermion and spin-0 boson with arbitrary masses that interact via the exchange of a massive, spin-0 boson. The equation has been used previously, without solutions actually being calculated, to derive some properties of nucleons by treating the physical nucleon as a bound state of a “bare” nucleon and a “bare” meson. It is likely that most, if not all, two-body, bound-state Bethe-Salpeter equations can be solved in the ladder approximation using the method discussed here.

Virtual meson cloud of the nucleon and generalized parton distributions

We present the general formalism required to derive generalized parton distributions within a convolution model where the bare nucleon is dressed by its virtual meson cloud. In the one-meson approximation the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The baryon is assumed here to be either a nucleon or a {delta} described within the constituent-quark model in terms of three-valence quarks; correspondingly, the meson, assumed to be a pion, is described as a quark-antiquark pair. Explicit expressions for the unpolarized generalized parton distributions are obtained and evaluated in different kinematics.

Physical nucleon properties from lattice QCD.

We investigate various resummations of the chiral expansion and fit to the extremely accurate lattice QCD data for the mass of the nucleon recently obtained by the CP-PACS group. Using a variety of finite-range regulators, we demonstrate a remarkably robust chiral extrapolation of the nucleon mass. The systematic error associated with the chiral extrapolation alone is estimated to be less than 1%.

NEUTRON CHARGE RADIUS: RELATIVISTIC EFFECTS AND THE FOLDY TERM

The neutron charge radius is studied within a light-front model with different spin coupling schemes and wave functions. The cancellation of the contributions from the Foldy term and Dirac form factor to the neutron charge form factor is verified for large nucleon sizes and it is independent of the detailed form of quark spin coupling and wave function. For the physical nucleon our results for the contribution of the Dirac form factor to the neutron radius are insensitive to the form of the wave function while they strongly depend on the quark spin coupling scheme.

Extended model for monopole catalysis of nucleon decay

A new model for monopole catalysis of nucleon decay is proposed. Unlike in the earlier one, the only light fields in this model are the photon and Skyrme (pion) field. The model admits the 't Hooft--Polyakov monopole and Skyrmion as classical solutions, while baryon number nonconservation occurs through an anomaly involving an intermediate mass axial vector field resembling W and Z bosons. By considering spherically symmetric monopole-Skyrmion configurations, we find that the Skyrmion loses essentially all its mass when interacting with the monopole, which is phenomenologically identical to the monopole catalysis of nucleon decay. Short-distance monopole-Skyrmion physics in this model is interesting too, as there exist almost degenerate metastable monopole-Skyrmion bound states separated by substantial energy barriers. Yet the height of the latter is much smaller than the physical nucleon mass, so the complete disappearance of the normal undeformed Skyrmion remains perfectly possible in Skyrmion-monopole scattering.

Convergence of chiral effective field theory

We formulate the expansion for the mass of the nucleon as a function of pion mass within chiral perturbation theory using a number of different ultra-violet regularisation schemes; including dimensional regularisation and various finite-ranged regulators. Leading and next-to-leading order non-analytic contributions are included through the standard one-loop Feynman graphs. In addition to the physical nucleon mass, the expansion is constrained by recent, extremely accurate, lattice QCD data obtained with two flavors of dynamical quarks. The extent to which different regulators can describe the chiral expansion is examined, while varying the range of quark mass over which the expansions are matched. Renormalised chiral expansion parameters are recovered from each regularisation prescription and compared. We find that the finite-range regulators produce consistent, model-independent results over a wide range of quark mass sufficient to solve the chiral extrapolation problem in lattice QCD.

One-nucleon effective generators of the Poincaré group derived from a field theory: Mass renormalization

We start from a Lagrangian describing scalar "nucleons" and mesons which interact through a simple vertex. Okubo's method of unitary transformation is used to describe a single nucleon dressed by its meson cloud. We find an expression for the physical mass of the nucleon being correct up to second order in the coupling constant. It is then verified that this result is the same as the corresponding expression found by Feynman techniques. Finally we also express the three boost operators in terms of the physical nucleon mass. Doing so we find expressions for all the ten generators of Poincar\'e transformations for the system of one single dressed nucleon.

Pionic Corrections to Nucleon Electromagnetic Properties in a Light-Cone Framework

Relativistic calculations of the effects of the pion cloud on the electromagnetic properties of the nucleon are presented. Light-cone formalism is used to construct the physical nucleon wave function that contains two components: a bare nucleon and a pion associated by recoil baryon with the nucleon or delta quantum numbers. Both sectors are coupled by a relativistic light-cone interaction Hamiltonian. A perturbative treatment is used to solve for the physical nucleon state. The elastic electromagnetic nucleon form factorsGp,nE(Q2) andGp,nM(Q2) are computed in terms of matrix elements of current operator and the nucleon wave function. TheQ2-dependence of contributions to the nucleon form factor from the various sectors of the model space is calculated and compared. The nature of the observed deviations from form- factor scaling and dipole parametrization is discussed.

Transition from meson to quark dynamics in the nucleon form factors

Even in the few GeV 2 region, there is already a pronounced deviation of the nucleon form factors from dipole parametrization and scaling. With the pion cloud model of nucleon structure formulated in the light-cone Fock approach, the Q 2 dependence of all four elastic nucleon form factors G E p,n(Q 2) and G M p,n( Q 2) is examined. Two different mesonic are included: the coupling through intermediate vector mesons to bare nucleons and the direct photon-pion interaction with pion-nucleon and pion-delta components in the nucleon. Contributions to the physical nucleon form factors from various sectors of the model space are calculated and compared. The model predicts scaling violation of roughly 10% which is consistent with perturbative treatment of the π- N and π-Δ. The observed deviations from dipole parametrization are attributed to pion cloud at small Q 2 and perturbative quark-gluon dynamics at large Q 2.

The role of the pion cloud in electroproduction of the Δ(1232)

We calculate the ratios E2 M1 and C2 M1 of the multipole amplitudes for electroproduction of the Δ(1232) in the range of photon virtuality 0 < − K 2 < 1 GeV 2 in a chiral chromodielectric model and a linear σ-model. We find that relatively large experimental values can be explained in terms of the pion contribution alone; the contribution arising from d-state quark admixture remains below 10%. We describe the pion cloud as a coherent state and use spin and isospin projection to obtain the physical nucleon and the Δ. The A 1 2 and A 3 2 amplitudes are reasonably well reproduced in the σ-model; in the chromodielectric model, however, they are a factor of two too small.

Nuclear many-body theory for the study of QCD sum rules in matter.

We discuss the calculation of QCD sum rules for hadrons in matter from the point of view of nuclear many-body theory and treat the sum rule for the rho meson as an example. We describe the factorization approximation that is used to calculate four-quark condensates in vacuum and in matter and discuss the corrections to that approximation in some detail. In the case of the rho meson, we find that corrections to the factorization approximation in matter can vary from about 10 to 40 percent depending upon the model used to describe the nucleon. If the nucleon is considered to be composed of a quark coupled to a scalar (T=0) diquark, the corrections are significant, while, if the quark is coupled to an axial-vector (T=1) diquark, the corrections are small. The physical nucleon may be taken to have equal scalar and axial-vector diquark components. In that case, corrections of about 20 percent are found for the density-dependent part of the vector-isovector polarization tensor. More precise estimates require a more detailed picture of nucleon structure than that considered here. In a previous work we discussed the corrections to the factorization approximate for the nucleon-nucleon correlator evaluated in nuclear matter. The corrections we calculated served to eliminate a problematic density dependence of the four-quark condensates that arose when using the factorization approximation in matter. However, our study provided a successful analysis only when the interpolating field advocated by Ioffe was used. The situation in the case of sum rules for the vector-isovector polarization tensor is subject to fewer uncertainties, since the choice of the current is unique. We find that, while the corrections we calculate for the density dependence of the four-quark condensates are not small, they lead to only very small modifications in the predicted density dependence of the rho mass.

Exclusive high- Q2 electroproduction: light-cone wave functions and electromagnetic form factors of mesons

In the light-cone technique, one can describe exclusive electroproduction treating mesons and baryons as (non-pointlike) partons of the nucleon. In this technique, the non-perturbative light-cone wave function of the meson-baryon Fock state of the physical nucleon defines the universal, projectile independent, density (flux) of on-mass-shell mesons in the proton. We apply the light-cone technique to electroproduction reaction ep → eπ + n long considered as a means of measuring the electromagnetic form factor of the pion. We show that the interpretation of the long-standing puzzle of large transverse cross section ( σ T ) in terms of the γ ∗ ϱ → π transition on the ϱ mesons in the light-cone proton is possible, but requires quite a slow decrease of the F ϱπ ( Q 2) form factor. This interpretation can be tested in the related ep → eπ 0 p reaction. Corrections which are due to the final-state meson-baryon interactions (FSI) are evaluated and are shown to amount to a 25% effect at moderately large Q 2. Vanishing FSI with increasing Q 2 — the color transparency phenomenon — is shown to be very strong.