The lower excitation spectrum of the nucleon and $Δ$ is calculated in a relativistic chiral quark model. Corrections to the baryon mass spectrum from the second order self-energy and exchange diagrams induced by pion and gluon fields are estimated in the field -theoretical framework. Convergent results for the self-energy terms are obtained when including the intermediate quark and antiquark states with a total momentum up to $j=25/2$. Relativistic one-meson and color-magnetic one-gluon exchange forces are shown to generate spin 0, 1, 2, etc. operators, which couple the lower and the upper components of the two interacting valence quarks and yield reasonable matrix elements for the lower excitation spectrum of the Nucleon and Delta. The only contribution to the ground state nucleon and $Δ$ comes from the spin 1 operators, which correspond to the exchanged pion or gluon in the l=1 orbit, thus indicating, that the both pion exchange and color-magnetic gluon exchange forces can contribute to the spin of baryons. Is is shown also that the contribution of the color-electric component of the gluon fields to the baryon spectrum is enormously large (more than 500 MeV with a value $α_s=0.65$) and one needs to restrict to very small values of the strong coupling constant or to exclude completely the gluon-loop corrections to the baryon spectrum. With this restriction, the calculated spectrum reproduces the main properties of the data, however needs further contribution from the two-pion exchange and instanton induced exchange (for the nucleon sector) forces in consistence with the realistic NN-interaction models.
We examine the role of the Delta-Delta intermediate state in low energy NN scattering using effective field theory. Theories both with and without pions are discussed. They are regulated with dimensional regularization and MSbar subtraction. We find that the leading effects of the Delta-Delta state can be absorbed by a redefinition of the contact terms in a theory with nucleons only. It does not remove the requirement of a higher dimension operator to reproduce data out to moderate momentum. The explicit decoupling of the Delta-Delta state is shown for the theory without pions.
The complete spin structure of the pion-nucleon-loop contribution to the delta self-energy and dressed propagator is calculated in vacuum, with the most general form of the pion-nucleon-delta vertex. The imaginary parts of the ten Lorentz-scalar coefficients are calculated in closed form, while the real parts are obtained numerically from a dispersion relation. The effect of the pion-nucleon-delta coupling constants and form-factor on the pion-nucleon phase-shift in the spin-3/2 isospin-3/2 channel is studied.
We study the strong couplings of the nucleon and delta resonances in a collective model. In the ensuing algebraic treatment we derive closed expressions for decay widths which are used to analyze the experimental data for strong decays into the pion and eta channels.
We investigate the nucleon to Delta(1232) vector and axial vector amplitudes in the non-relativistic quark model of the Isgur-Karl variety. A particular interest is to investigate the SU(6) symmetry breaking, due to color hyperfine interaction. We compare the theoretical estimates to recent experimental investigation of the Adler amplitudes by neutrino scattering.
The gluon condensate as a function of temperature and baryon density in a nucleon medium is obtained from an effective dilaton Lagrangian. It is shown that, at a normal nuclear density of nucleons, n_0 = 0.17 fm^{-3} the gluon condensate decreases by about 10%.
We develop a formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The underlying Bethe-Salpeter equation is transformed into a pair of coupled Salpeter equations. The space- and timelike electromagnetic form factors of the nucleon are calculated in the Mandelstam formalism for squared momentum transfers up to 3 (GeV/c)^2 above threshold. The model is applied also to the Delta(3/2).
The Nucleon-Nucleon interaction in the singlet ($^1 S_0$) and triplet ($^3 S_1$) channels have been studied in the framework of Relativistic Harmonic Model using the Resonating Group Method in Born-Oppenheimer approximation. The full Hamiltonian consists of the kinetic energy, two body confinement potential, confined one gluon exchange potential and one pion exchange potential. Contribution of Confined One Gluon Exchange Potential and One Pion Exchange Potential to the adiabatic nucleon-nucleon interaction potential is discussed.
We investigate the model dependence and the importance of choice of database in extracting the {\it physical} nucleon-Delta(1232) electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
We demonstrate that there exist two kinds of gauge-invariant decompositions of the nucleon spin, which are physically inequivalent. The quark and gluon orbital angular momenta (OAMs) appearing in one decomposition are basically the canonical OAMs, while the quark and gluon OAMs appearing in another decomposition are called the dynamical OAMs. It is shown that the dynamical OAMs of quarks and gluons in the nucleon can be related to definite high-energy deep-inelastic-scattering observables. On the other hand, we conjecture that the canonical OAMs of quarks and gluon in the nucleon are model-dep…
We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory des…
The gluon-exchange contribution to $J/ψ$-nucleon scattering is shown to yield a sizeable scattering length of about -0.25 fm, which is consistent with the sparse available data. Hadronic corrections to gluon exchange which are generated by $ρπ$ and $D\bar D$ intermediate states of the $J/ψ$ are shown to be negligible. We also propose a new method to study $J/ψ$-nucleon elastic scattering in the reaction $π^+ d\to J/ψp p$.
A relativistic quark model and a new set of wave functions of nucleon and Delta have been used to study the electromagnetic propertities of (1/2)^+ baryons and photoelectric production of Delta(1236).
We formulate a new power-counting scheme for a chiral effective field theory of nucleons, pions, and Deltas. This extends chiral perturbation theory into the Delta-resonance region. We calculate nucleon Compton scattering up to next-to-leading order in this theory. The resultant description of existing $γ$p cross section data is very good for photon energies up to about 300 MeV. We also find reasonable numbers for the spin-independent polarizabilities $α_p$ and $β_p$.
In almost all the past analyses of the decomposition of the nucleon spin into its constituents, surface terms are simply assumed to vanish and not to affect the integrated sum rule of the nucleon spin. However, several authors claim that neglect of surface terms is not necessarily justified, especially owing to possible nontrivial topological configuration of the gluon field in the QCD vacuum. There also exist some arguments indicating that the nontrivial gluon topology would bring about a delta-function type singularity at zero Bjorken variable into the longitudinally polarized gluon distribu…
The Sivers mechanism for the single-spin asymmetry in unpolarized lepton scattering from a transversely polarized nucleon is driven by the orbital angular momentum carried by its quark and gluon constituents, combined with QCD final-state interactions. Both quark and gluon mechanisms can generate such a single-spin asymmetry, though only the quark mechanism can explain the small single-spin asymmetry measured by the COMPASS collaboration on the deuteron, suggesting the gluon mechanism is small relative to the quark mechanism. We detail empirical studies through which the gluon and quark orbita…
A covariant quark model, based both on the spectator formalism and on vector meson dominance, and previously calibrated by the physical data, is here extended to the unphysical region of the lattice data by means of one single extra adjustable parameter - the constituent quark mass in the chiral limit. We calculated the Nucleon (N) and the gamma N -> Delta form factors in the universe of values for that parameter described by quenched lattice QCD. A qualitative description of the Nucleon and gamma N -> Delta form factors lattice data is achieved for light pions.
We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing and the quark masses to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We s…
The D(03) dibaryon is generated dynamically as a resonance pole in a pion-nucleon-Delta' three-body model, where Delta' is a stable Delta baryon. Using separable interactions dominated by the Delta(1232) isobar for pion-nucleon and by the D(12) isobar for nucleon-Delta', where D(12) is the nucleon-Delta 2150 MeV dibaryon deduced in and constrained by 1D2 pp scattering, the model reduces to an effective two-body problem for Delta-Delta' which is solved. The mass and width of D(03) are found close to those of the I(JP)=0(3+) resonance peak observed by WASA@COSY in pion-production pn collisions a…
N-Delta and Delta-Delta dibaryon candidates are discussed and related quark-based calculations are reviewed. New hadronic calculations of L=0 nonstrange dibaryon candidates are reported. For N-Delta, I(JP)=1(2+) and 2(1+) S-matrix poles slightly below threshold are found by solving pi-N-N Faddeev equations with relativistic kinematics, and for Delta-Delta several S-matrix poles below threshold are found by solving pi-N-Delta Faddeev equations with relativistic kinematics in which the N-Delta interaction is dominated by the 1(2+) and 2(1+) resonating channels. In particular, the I(JP)=0(3+) Del…
We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework.
In recent papers, we have established the existence of gauge-invariant decomposition of nucleon spin, each term of which can be related to known high-energy deep-inelastic-scattering observables. A subtlety remains, however, for the intrinsic spin part of gluons at the quantum level. In fact, it was sometimes claimed that the evolution of gluon spin depends on the gauge choice and its physical interpretation makes sense only in the light-cone gauge. In the present paper, we will demonstrate explicitly that the gluon spin operator appearing in our decomposition evolves gauge-independently and t…
Three-body hadronic models with separable pairwise interactions are formulated and solved to calculate resonance masses and widths of L=0 N-Delta and Delta-Delta dibaryons using relativistic kinematics. For N-Delta, I(JP)=1(2+) and 2(1+) resonances slightly below threshold are found by solving pi-N-N Faddeev equations. For Delta-Delta, several resonances below threshold are found by solving pi-N-Delta Faddeev equations in which the N-Delta interaction is dominated by the 1(2+) and 2(1+) resonating channels. The lowest Delta-Delta dibaryon resonances found are for I(JP)=0(3+) and 3(0+), the for…
We calculate the form factors of the electromagnetic nucleon-to-$Δ$-resonance transition to third chiral order in manifestly Lorentz-invariant chiral effective field theory. For the purpose of generating a systematic power counting, the complex-mass scheme is applied in combination with the small-scale expansion. We fit the results to available empirical data.
In a world with two quark flavors and a large number of colors (N_c), the polarized and unpolarized quark distributions in the delta are completely determined by those in the nucleon up to {\cal O}(1/N_c). In particular, we find q_Δ(x) =[(1\pm 2T_z)u_N(x)+ (1\mp 2T_z)d_N(x)]/2 and Δq_Δ(x) =[(5\pm 2T_z)Δu_N(x) + (5\mp 2T_z)Δd_N(x)]/10, where q = u, d and $T_z$ the charge state of a delta. The result can be used to estimate the leading chiral-logarithmic corrections to the quark distributions in the nucleon.
The reaction mechanisms for $KΣ(1385)$ photoproduction from the reaction $γp \to K^+Σ^{0}(1385)$ in the resonance energy region are investigated in a hadronic model. Both contributions from $N$ and $Δ$ resonances of masses around 2 GeV as given in the Review of Particle Data Group and by the quark model predictions are included. The Lagrangians for describing the decays of these resonances into $KΣ(1385)$ are constructed with the coupling constants determined from the decay amplitudes predicted by a quark model. Comparing the resulting total cross section for the reaction $γp \to K^+Σ^{0}(1385…
Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We det…
The fundamental program in high energy spin physics focuses on the spin structure of the nucleon. The gluon and orbital angular momentum components of the nucleon spin are virtually unknown. The J_z=1/2 sum rule involves the integrated parton densities and can be used to extract information on the orbital angular momentum and its evolution. To avoid any bias on a model of Delta G, we assume that the gluon asymmetry, A=Delta G/G can be used to extract Delta G over a reasonable kinematic region. Combining the results for Delta G with the evolution equations, we can determine a theoretical expres…
We study a thermodynamically consistent implementation of the nucleon volume in the mean field theory, and find that this volume has large consequences on the properties of hadronic matter under extreme conditions such as in astrophysical objects and high energy heavy-ion collisions. It is shown that we can reproduce the critical temperature $T_{c}\simeq 200$ MeV predicted by lattice QCD calculations for the phase transition from hadronic matter to quark-gluon plasma, by using parameters which are adjusted to fit all empirical data for normal nuclear matter.
We present a calculation of the polarized rho meson cloud in a nucleon using time-ordered perturbation theory in two different variants advocated in the literature. We calculate the induced difference between the distributions Delta d^bar(x) and Delta u^bar(x). We use a recent lattice calculation to motivate an ansatz for the polarized valence quark distribution of the rho meson. Our calculations show that the two theoretical approaches give vastly different results. We conclude that Delta d^bar(x) - Delta u^bar(x) can be of relevant size with important consequences for the combined fits of po…
We study the possible contribution of the nucleon's virtual meson cloud to the sea quark distribution as observed in deep inelastic lepton scattering. We adjust the meson-nucleon cut-offs to the large-x tails of the antiquark distributions, find qualitatively different behavior in the flavor singlet and non-singlet channels and study the scale dependence of our results. We demonstrate that, within convolution models, to reproduce the sea quark distribution the relevant pion momenta should be around 0.8 GeV.
A controversy is raging concerning the most physically meaningful definition of quark and gluon angular momentum, a question of importance in understanding the internal structure of the nucleon. There are, in my, opinion, two principal candidates: the Belinfante version, $\bm{J}_{bel}$, which is gauge invariant, and the Canonical version, $ \bm{J}_{can}$, which is non-gauge invariant, but which has a physically intuitive structure. I demonstrate the wholly unexpected result that for quarks in a spin 1/2 nucleon the expectation value of $\bm{J}_{bel}(\textrm{quark})$ is equal to the expectation…
In this contribution, baryon axial-vector couplings are studied in the framework of the combined 1/Nc and chiral expansions. This framework is implemented on the basis of the emergent spin-flavor symmetry in baryons at large Nc and HBChPT, and linking both expansions (ξ-expansion), where 1/Nc is taken to be a quantity O(p). The study is carried out including one-loop contributions, which corresponds to O(ξ^3) for baryon masses and O(ξ^2) for the axial couplings. An analysis of the Lattice QCD results for the axial couplings of both N and Δis presented.
In analogy to the Altarelli-Parisi equation for the quark and gluon helicity contributions to the nucleon spin, we derive an evolution equation for the quark and gluon orbital angular momenta. The solution of the combined equations yields the asymptotic fractions of the nucleon spin carried by quarks and gluons: $3n_f/(16+3n_f)$ and $16/(16+3n_f)$, respectively, where $n_f$ is the number of active quark flavors. These are identical to the well-known asymptotic partitions of the nucleon momentum between quark and gluon contributions. We show that the axial-anomaly contribution to the quark heli…
The contribution of the anomalous quark-gluon interaction induced by instantons to the polarized and unpolarized gluon distributions in nucleon is estimated. It is shown that this interaction leads to negative gluon polarization in nucleon.
Influence of the effects of the pion-nucleon and nucleon-nucleon re-scattering on the polarization observables of the reaction gamma + d = p + p + pi- in Delta - isobar region is investigated. Pion-nucleon and nucleon-nucleon re-scattering are studied in the diagrammatic approach. Relativistic-invariant forms of the pion photoproduction and pion-nucleon scattering operators are used. The unitarization procedure in K-matrix approach is applied for the resonance partial amplitudes. It is shown a considerable influence of the re-scattering effects on the polarization observables of this reaction …
Previous calculations of the polarizabilities of the nucleon within the framework of heavy baryon chiral perturbation theory have included the contribution of the $Δ$(1232) only its effect on various contact terms or have been performed in chiral SU(3) where systematic errors are difficult to control. Herein we perfrom a corresponding calculation in chiral SU(2) wherein $Δ$(1232) is treated as an explicit degree of freedom and the expansion is taken to third order in soft momenta, the pion mass and the quantity $M_Δ-M_N$, collectively denoted by $ε$. We present the results of a systematic $O(ε…
We perform a relativistic chiral effective-field theory calculation of the pion electroproduction off the nucleon ($e^- N \to e^- N π$) in the Delta(1232)-resonance region. After fixing the three low-energy constants, corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) $γNΔ$ couplings, our calculation provides a prediction for the momentum-transfer and pion-mass dependence of the $γNΔ$ form factors. The prediction for the pion-mass dependence resolves the discrepancy between the recent lattice QCD results and the experimental value for the "C2/M1 ratio" at low $Q^2$.
The inclusive distributions of gluons and pions are calculated with absolute normalization for high-energy nucleon-nucleon collisions. The results for several unintegrated gluon distributions from the literature are compared. The gluon distribution proposed recently by Kharzeev and Levin based on the idea of gluon saturation is tested against DIS data from HERA. We find huge differences in both rapidity and transverse momentum distributions of gluons and pions in nucleon-nucleon collisions for different models of unintegrated gluon distributions. The approximations used recently in the literat…
We calculate the strong couplings of pions to the Delta(1232) resonance using a QCD parameterization method that includes in addition to the usual one-quark also two-quark and previously uncalculated three-quark operators. We find that three-quark operators are necessary to obtain results consistent with the data and other QCD based baryon structure models. Our results are also in quantitative agreement with a model employing large D state admixtures to the nucleon and Delta wave functions indicating that the pion-nucleon and pion-Delta couplings are sensitive to the spatial shape of these bar…
It is shown that the amplitude for the scattering of a heavy quarkonium system from a nucleon near threshold is completely determined by the fraction of angular momentum, as well as linear momentum, carried by gluons in the nucleon. A form for the quarkonium-nucleon non-relativistic potential is derived.
Recent developments in calculations of low energy nucleon properties utilizing effective chiral field theories with explicit spin 3/2 matter fields are presented. In particular, the role of Delta resonances in microscopic calculations of the anomalous magnetic moments of the Nucleon is discussed and a comparison to lattice data is performed. Furthermore, the impact of Deltas on the isovector Pauli form factor of the Nucleon and the problems one faces in calculations of the isovector Nucleon-Delta transition form factors are addressed.
We study the N-Delta-gamma transition in the Dyson-Schwinger approach. The nucleon and Delta baryons are treated as quark-diquark bound states, where the ingredients of the electromagnetic transition current are computed self-consistently from the underlying dynamics in QCD. Although our approach does not include pion-cloud effects, we find that the electric and Coulomb quadrupole form-factor ratios R_EM and R_SM show good agreement with experimental data. This implies that the deformation from a spherical charge distribution inside both baryons can be traced back to the appearance of p waves …
The lower excitation spectrum of the nucleon and $Δ$ is calculated in a relativistic chiral quark model. Contributions of the second order self-energy and exchange diagrams due-to pion fields to the mass spectrum of the SU(2) baryons are estimated. A splitting between N(939) and positive parity nucleon resonance (Roper resonance) $N^*(1440)$ is reproduced with a reasonable accuracy. The obtained structure of one-meson exchange interaction confirms a prediction of the large $N_c$ limit approach stating that the mass splitting between various baryon states receive contributions from operators wh…
Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral distances b = O(M_pi^{-1}) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft-pion-nucleon intermediate states, resulting in a quantum-mechanical picture of the peripheral transverse densi…
We establish relations which express the generalized parton distributions (GPDs) describing the $N\to Δ$ transition in terms of the nucleon GPDs. These relations are based on the known large-$N_c$ relation between the $N\to Δ$ electric quadrupole moment and the neutron charge radius, and a newly derived large-$N_c$ relation between the electric quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Namely, in the large-$N_c$ limit we find $C2=E2$. The resulting relations among the nucleon and $N\toΔ$ GPDs provide predictions for the $N\toΔ$ electromagnetic form factors which are found to…
A feasibility study to extract the polarised gluon density from di-jet events at HERA in next-to-leading order is presented. It is shown that when taking next-to-leading order effects into account the asymmetries at HERA remain measurable and sensitive to the polarised gluon distribution. They can be used to extract the polarised gluon density in the proton in the region 0.005<x_g<0.4.
We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical guidance for chiral extrapolations of lattice QCD results with dynamical fermions.
We calculate the nucleon and the delta mass to fourth order in a covariant formulation of the small scale expansion. We analyze lattice data from the MILC collaboration and demonstrate that the available lattice data combined with our knowledge of the physical values for the nucleon and delta masses lead to consistent chiral extrapolation functions for both observables up to fairly large pion masses. This holds in particular for very recent data on the delta mass from the QCDSF collaboration. The resulting pion-nucleon sigma term is sigma_{piN} = 48.9 MeV. This first quantitative analysis of t…
We study nucleon-to-delta electromagnetic transition form factors and relations between them within the framework of holographic dual model of QCD proposed by Sakai and Sugimoto. In this setup, baryons appear as topological solitons of the five dimensional holographic gauge theory that describes a tower of mesons and their interactions. We find a relativistic extension of the nucleon-delta-vector meson interaction vertices and use these to calculate transition form factors from holographic QCD. We observe that at low momentum transfer, magnetic dipole, electric and Coulomb quadrupole form fact…
We derive exact relations among the polarized gluon and three-gluon distributions in the transversely polarized nucleon which are relevant to single and double spin asymmetries in various hard processes. We also discuss the partonic decomposition of the transverse nucleon spin and point out a potential problem with frame-independence.
The distribution of longitudinal gluons in a nucleon, introduced earlier by Gorsky and Ioffe, is estimated from below by making use of the positivity of density matrix and the analogue of the Wandzura-Wilczek relation for the light-cone distributions of polarized gluons in a transversely polarized nucleon.
We report a theoretical study of the axial Nucleon to Delta(1232) ($N\toΔ$) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the $Δ$ couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble chamber data and in quark models.
We present a coupled system of integral equations for the pi pi --> Nbar N and Kbar K --> Nbar N S-waves derived from Roy-Steiner equations for pion-nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili-Omnes problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including Kbar K intermediate states. In particular, we determine the corrections Delta_sigma and Delta_D, which are needed for the extraction of the pion-nucleon sigma term from pi N scattering, and show that the difference Delta_D - Delta_sigma=(-1.…
