We investigate the interactions of weakly interacting massive particles (WIMPS) with nucleons in nuclear medium by taking into account the effect of nuclear dynamics. We derive the nonrelativistic effective operators starting from the relativistic mean-field approximation. Certain interactions receive non-negligible corrections, which may significantly change the sensitivities of WIMP-nucleus scattering cross section to these effective operators.
Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of th…
We derive the short-range contributions and the leading relativistic corrections to the three-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion.
We utilize a light-front relativistic quark model (LF RQM) to predict the 3q core contribution to the electroexcitation amplitudes for the Delta(1232)P33, N(1440)P11, N(1520)D13, and N(1535)S11 up to Q2= 12GeV2. The parameters of the model have been specified via description of the nucleon electromagnetic form factors in the approach that combines 3q and pion-cloud contributions in the LF dynamics.
We present a simple calculation of the nucleon self-energy in nuclear matter at finite temperature in a relativistic framework, using the real time thermal field theory. The imaginary parts of one-loop graphs are identified with discontinuities across the unitary and the Landau cuts. We find that in general both the cuts contribute significantly to the spectral function in the region of (virtual) nucleon mass usually considered, even though the unitary cut is ignored in the literature. Also our relativistic spectral function differs from the one in non-relativistic approximation, used in some …
Recently, a relativistic chiral nucleon-nucleon interaction is formulated up to leading order which provides a good description of the phase shifts of $J\leq1$ partial waves [Chin. Phys. C 42 (2018) 014103]. Nevertheless, a separable regulator function that is not manifestily covariant was used in solving the relativistic scattering equation. In the present work, we first propose a covariant and separable form factor to regularize the kernel potential and then apply it to study the simplest but most challenging $^1S_0$ channel which features several low-energy scales. In addition to being self…
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.
We present a relativistic formulation of pion loop corrections to the coupling of photons with nucleons on the light-front. Vertex and wave function renormalization constants are computed to lowest order in the pion field, including their nonanalytic behavior in the chiral limit, and studied numerically as a function of the ultraviolet cutoff. Particular care is taken to explicitly verify gauge invariance and Ward-Takahashi identity constraints to all orders in the m_pi expansion. The results are used to compute the chiral corrections to matrix elements of local operators, related to moments o…
We report on the construction of an accurate relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading (NNLO) order. We compare the so-obtained neutron-proton phaseshifts with the next-to-next-to-next-to-leading order (N$^3$LO) nonrelativistic ones and we show that up to $T_\mathrm{lab.}=200$ MeV, the relativistic chiral nuclear force can describe the PWA93 phaseshifts and inelasticities as well as its N$^3$LO nonrelativistic counterparts. As a result, the relativistic chiral nuclear force can be readily used for relativistic ab initio nuclear structure, reaction, as we…
Nucleon generalized polarizabilities are investigated within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the amplitude for virtual Compton scattering. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-energy-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, $β_{para}(q)$, as a function of the virtual-photon three-momentum transfer $ q,$ is explicitly …
A finite-dimensional matrix model for the nucleon-nucleon cross section operator is used to calculate the dispersive correction to nucleon-nucleus total cross sections, and the leading terms in its expansion in the number of inelastic transitions in the high-energy limit where the longitudnal momentum transfers can be ignored.
We apply a recently proposed covariant power counting in nucleon-nucleon interactions to study strangeness $S=-1$ $ΛN-ΣN$ interactions in chiral effective field theory. At leading order, Lorentz invariance introduces 12 low energy constants, in contrast to the heavy baryon approach, where only five appear. The Kadyshevsky equation is adopted to resum the potential in order to account for the non-perturbative nature of hyperon-nucleon interactions. A fit to the $36$ hyperon-nucleon scattering data points yields $χ^2\simeq 16$, which is comparable with the sophisticated phenomenological models a…
We briefly describe our relativistic quark-diquark model, developed within the framework of point form dynamics, which is the relativistic extension of the interacting quark-diquark model. In order to do that we have to show the main properties and quantum numbers of the effective degree of freedom of constituent diquark. Our results for the nonstrange baryon spectrum and for the nucleon electromagnetic form factors are discussed.
In this talk, we report on two recent studies of relativistic nucleon-nucleon and hyperon-nucleon interactions in covariant chiral perturbation theory, where they are constructed up to leading order. The relevant unknown low energy constants are fixed by fitting to the nucleon-nucleon and hyperon-nucleon scattering data. It is shown that these interactions can describe the scattering data with a quality similar to their next-to-leading order non-relativistic counterparts. These studies show that it is technically feasible to construct relativist baryon-baryon interactions, and in addition, aft…
A transport theory is developed on the quark level to describe nucleon--nucleon collisions. We treat the strong interaction effectively by the Friedberg-Lee model both in its original and in its modified confining version. First we study the stability of the static three-dimensional semiclassical configuration, then we present results of the time evolution given by a Vlasov equation for the quarks coupled to a Klein-Gordon equation for the mean field. We find at higher energies that the nucleons are almost transparent, whereas at lower energies we observe a substantial interaction. At very low…
We demonstrate that a relativistic constituent-quark model can give nucleon form factors in agreement with data for both low and high momentum transfer. The relativistic features of the model and the specific form of the wave function are essential for the result.
We utilize a light-front relativistic quark model to predict the 3q core contribution to the electroexcitation of nucleon resonances of the [70,1-] multiplet on the proton and neutron at Q2 < 5GeV2. The investigation is stimulated in large degree by expected progress in the studies of the electroexcitation of nucleon resonances in the third resonance region in the CLAS experiment. For the resonances N(1520)3/2-, N(1535)1/2-, and N(1675)5/2-, experimental data on electroexcitation amplitudes on the proton are available in a wide range of Q2. This allowed us to quantify the expected meson-baryon…
We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the $np$ phase shifts up to $T_\mathrm{lab}=200$ MeV and even higher can be achieved with a $\tildeχ^2/\mathrm{d.o.f.}$ less than 1. Both the next-to-leading order results and the next-to-next-to-leading order results describe the phase shifts equally well up to $T_\mathrm{lab}=200$ MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provi…
We study the effects of the | qqq q\bar{q} > component of the hadronic wave function on the description of the electromagnetic structure of the nucleon. Starting with a qqq baryonic wave function which describes the baryonic and mesonic low energy spectrum, the extra q\bar{q} pair is generated through a relativistic version of the 3P_0 model. It is shown that this model leads to a renormalization of the quark mass that allows one to construct a conserved electromagnetic current. We conclude that these dynamical relativistic corrections play an important role in reproducing the Q2 dependence of…
The deep inelastic scattering of leptons off nuclei is considered within the the Bethe-Salpeter formalism. It is shown that nuclear short-range structure can be expressed in terms of the nucleon structure functions and four-dimensional Fermi motion of the nucleons. The four-dimensional Fermi motion broadens the bound nucleon localization area, what lead to the observation of the nucleon structure change in nuclei -- EMC effect. The $\rm ^4He$ to deuteron structure functions ratio is found in good agreement with experimental data. It is shown that the pattern of the ratio is defined by dynamica…
We investigate the influence of the central two-body NN correlations on several quantities observed in relativistic heavy-ion collisions. It is demonstrated with explicit Monte Carlo simulations, that the basic correlation measures, such as the fluctuations of participant eccentricity, initial size fluctuations, or the fluctuations of the number of sources producing particles, are all sensitive to the inclusion of the two-body correlations. The effect is at the level of about 10-20%. Moreover, the realistic (Gaussian) correlation function gives indistinguishable results from the hard-core repu…
In the diquark-quark model of the nucleon including scalar and axialvector diquarks we compare solutions of the ladder Bethe-Salpeter equation in the instantaneous Salpeter approximation and in the fully covariant (i.e. four-dimensional) treatment. We obtain that the binding energy is severly underestimated in the Salpeter approximation. For the electromagnetic form factors of the nucleon we find that in both approaches the overall shapes of the respective form factors are reasonably similar up to $Q^2 \approx 0.4$ GeV^2. However, the magnetic moments differ substantially as well as results fo…
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…
A nonrelativistic decomposition for the quark energy by the ratio of the dispersion of quark momentum squared and the effective quark mass is investigated in the framework of the relativistic oscillator constituent quark model as bound systems of three valence quarks. It is shown that relativistic corrections are defined by dispersion of the squared absolute value of the quark momentum. The variations of the quark mass and oscillator parameter are studied in detail both in the spectrum and in the nucleon magnetic moments.
We investigate the electromagnetic properties of the deuteron such as the charge and magnetic form factors by solving the Bethe-Salpeter equation (BSE) with the separable ansatz. In solving the deuteron bound state solution to the BSE, we include negative energy components of $P$-wave in addition to the $^3S_1$ and $^3D_1$ states of positive energy, employing a rank IV separable ansatz. We found that the inclusion of the negative energy components improves systematically the electromagnetic properties which are not described in the conventional non-relativistic impulse approximation.
We study the chiral behavior of the nucleon and $Δ$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $πN$ and $πΔ$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $πN…
We calculate the corrections to the strange matrix elements of the nucleon resulting from the breaking of rotational invariance on the light-cone. In the meson cloud model, the strange magnetic moment mu_S is seen to change sign once the spurious form factors arising from this violation are subtracted. The resulting mu_S is small and slightly positive, in agreement with the trend of the recent data from the SAMPLE experiment. The value of the strange magnetic form factor is predicted to be largely Q^2 independent over the range accessible in upcoming experiments.
Deuteron electrodisintegration is described in a relativistic PWIA framework. The reduction to the factorized PWIA, and the effect thereof on the observables accessible in parity-violating scattering, is discussed. The extent to which such relativistic effects may affect the extraction of strangeness nucleon form factors from measurements of the PV asymmetry, is investigated.
The non-relativistic effective theory of dark matter-nucleon interactions depends on 28 coupling strengths for dark matter spin up to 1/2. Due to the vast parameter space of the effective theory, most experiments searching for dark matter interpret the results assuming that only one of the coupling strengths is non-zero. On the other hand, dark matter models generically lead in the non-relativistic limit to several interactions which interfere with one another, therefore the published limits cannot be straightforwardly applied to model predictions. We present a method to determine a rigorous u…
We examine isospin breaking in the nucleon wave functions due to the $u - d$ quark mass difference and the Coulomb interaction among the quarks, and their consequences on the nucleon electroweak form factors in a nonrelativistic constituent quark model. The mechanically induced isospin breaking in the nucleon wave functions and electroweak form factors are exactly evaluated in this model. We calculate the electromagnetically induced isospin admixtures by using first-order perturbation theory, including the lowest-lying resonance with nucleon quantum numbers but isospin 3/2. We find a small ($\…
Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts with $2\leq L\leq 6$ and mixing angles with $2\leq J\leq6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic co…
Considering the magnetic moment and polarizabilities of the nucleon we emphasize the need for relativistic chiral EFT calculations. Our relativistic calculations are done via the forward-Compton-scattering sum rules, thus ensuring the correct analytic properties. The results obtained in this way are equivalent to the usual loop calculations, provided no heavy-baryon expansion or any other manipulations which lead to a different analytic structure (e.g., infrared regularization) are made. The Baldin sum rule can directly be applied to calculate the sum of nucleon polarizabilities. In contrast, …
A covariant formulation of spin-dependent deep-inelastic scattering from nuclei is presented. In the relativistic impulse approximation the inclusive nuclear cross section is described in terms of the amplitude for forward, virtual-photon scattering from an off-mass-shell nucleon. The general structure of the off-shell nucleon hadronic tensor is derived, and the leading behavior of the off-shell nucleon structure functions computed in the Bjorken limit. The formalism, which is valid for nucleons bound inside nuclei with spin 1/2 or 1, is applied to the case of the deuteron.
Calculations of form factors in different forms of relativistic kinematics are presented. They involve the instant, front and point forms. In the two first cases, different kinematical conditions are considered while in the latter case, both a Dirac-inspired approach and a hyperplane-based one are incorporated in our study. Numerical results are presented for the pion form factors with emphasis on both the low and high Q**2 range. A new argument is presented, explaining why some approaches do considerably much better than other ones whenonly a single-particle current is considered.
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory. The so-called triangle relation is found to be violated by about 1.5 %. We encounter a substantial isospin-breaking correction to neutral-pion-nucleon scattering beyond Weinberg's prediction due to a cusp effect. Finally, the application to hadronic atoms is briefly discussed.
The relativistic three-body problem is approached via the extension of the SL(2,C) group to the Sp(4,C) one. In terms of Sp(4,C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates interaction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E^2,J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.
Within the pion-nucleon chiral perturbation theory we derive the leading chiral correction to the nucleon GPD at $ξ=0$. We discuss the difficulties of consideration of nonlocal light-cone operators within the theory with a heavy particle and the methods to solve the difficulties. The consideration of the chiral corrections directly for nonlocal operators allows to resolve the ambiguity of the inverse Mellin transformation. In particular, we show that the mixing between axial and vector GPDs are of order $m_π^2/M_N^2$, which is two orders of magnitude less that it follows from the Mellin moment…
Using heavy baryon chiral perturbation theory we study the leading chiral corrections to the complete set of nucleon generalized parton distributions (GPDs). We compute the leading quark mass and momentum transfer dependence of the moments of nucleon GPDs through the nucleon off-forward twist-2 matrix elements. These results are then applied to get insight on the GPDs and their impact parameter space distributions.
We report the calculation of electromagnetic form factors of nucleons within a relativistic three-quark model with Gaussian shape for the nucleon-quark vertex. The allowed region for two adjustable parameters, the range parameter $Λ_N$ in the Gaussian and the constituent quark mass $m_q$, is obtained from fitting the data for magnetic moments and electromagnetic radii of nucleons. The shapes of electric and magnetic nucleon form factors calculated in this approach with the central parameters $m_q$=420 MeV and $Λ_N$=1.25 GeV are close to the data for momentum transfers $0\le Q^2\le 1$ GeV$^2$
Elastic electron-3He scattering is studied in the relativistic impulse approximation. The amplitudes for the three-nucleon system - 3He - are obtained by solving the relativistic generalization of the Faddeev equation. The charge and magnetic form factor are calculated and compared with the experimental data for the momentum transfer squared up to 100 fm-2. The influence of the various nucleon form factors is investigated.
The Drell-Hearn-Gerasimov sum rule for the nucleon is investigated within a relativistic constituent quark model formulated on the light-front. The contribution of the N - Delta(1232) transition is explicitly evaluated using different forms for the baryon wave functions and adopting a one-body relativistic current for the constituent quarks. It is shown that the N - Delta(1232) contribution to the sum rule is sharply sensitive to the introduction of anomalous magnetic moments for the constituent quarks, at variance with the findings of non-relativistic and relativized quark models. The experim…
We report the predictions for the 3q core contributions to the electroexcitation of the resonances Delta(1232)3/2+, N(1440)1/2+, N(1520)3/2-, N(1535)1/2-, and N(1675)5/2- on the proton obtained in the light-front relativistic quark model (LF RQM). For these states, experimental data on the electroexcitation transition amplitudes allow us to make comparison between the experiment and LF RQM predictions in wide range of Q2 and also to quantify the expected meson-baryon contributions as a function of Q2.
It is shown that accounting for the relativistic structure of the deuteron allows to explain the ratio of the Drell-Yan pair production cross-section at the low Bjorken $x$ off the deuteron and the proton. Thus, the sea quark distributions in the nucleon should be studied with accounting for the effects of the relativistic structure of the deuteron. The suggested approach reduces theoretical uncertainty in extracting the ratio $\bar u/\bar d$ from the data and it is important for the clarification of the nature of the sea quark asymmetry in the nucleon.
We present results for the isotriplet and isosinglet tensor form factors of the nucleon in the relativistic confined quark model. The model allows us to calculate not only their normalizations at $Q^2=0$ and the related tensor charges, but also the full $Q^2$-dependence. Our results are compared to existing data and predictions of other theoretical approaches. We stress the importance of these form factors for the phenomenology of physics beyond the Standard Model.
A new analysis of baryon sum rules is done with modern values of parameters and known perturbative corrections. The restriction for gluon and quark condensates and the new value of nucleon coupling constant are found.
Significant differences between transverse and longitudinal polarized parton distributions are found at low energies within a light-front covariant quark model of the nucleon. These differences are due to relativistic spin effects introduced by the Melosh rotations and survive evolution to higher $Q^2$ scales. A specific observable related to double-spin asymmetries in lepton pair production in polarized hadron-hadron collisions is defined. The possibility of assessing the relevance of these relativistic spin effects in future experiments at RHIC and HERA--$\vec{N}$ is discussed.
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.
A procedure is proposed which accounts for final state interaction corrections for near threshold meson production in nucleon-nucleon scattering. In analogy with the Watson-Migdal approximation, it is shown that in the limit of extremely strong final state effects, the amplitude factorizes into a primary production amplitude and an elastic scattering amplitude describing a $3 \to 3$ transition. This amplitude determines the energy dependence of the reaction cross section near the reaction threshold almost solely. The approximation proposed satisfies the Fermi-Watson theorem and the coherence f…
The strangeness contribution to the nucleon magnetic moment is calculated at the one-loop level in a relativistic SU(3) chiral potential model and is found to be {\em positive}, that is, with an {\em opposite} sign to the nucleon strangeness polarization. It is the ``Z'' diagram that violates the usual relation between spin and magnetic moment. The positive value is due to the contribution from the intermediate excited quark states, while the intermediate ground state gives a negative contribution. Our numerical results agree quite well with the new measurement of the SAMPLE Collaboration.
The long range structure of the nucleon is discussed starting from the old model of a quark bag with a pion cloud (``cloudy bag'') carrying on to the more recent ideas of the parton model of the nucleon. On the basis of the most recent measurements of the form factors at MAMI, JLab and MIT quantitative results for nucleon charge densities are presented within both non-relativistic and relativistic frameworks.
We report the calculation of electromagnetic form factors of nucleons within a relativistic three-quark model with Gaussian shape for the nucleon-quark vertex. The allowed region for two adjustable parameters, the range parameter $Λ_N$ in the Gaussian and the constituent quark mass $m_q$, is obtained from fitting the data for magnetic moments and electromagnetic radii of nucleons. It is found that their values calculated with $m_q$=420 MeV and $Λ_N$=1.25 GeV agree very well with the experimental data. It is turned out that the electric proton and magnetic nucleon form factors fall faster than …
We use the field theoretical model to perform relativistic calculations of neutrino energy losses caused by the direct Urca processes on nucleons in the degenerate baryon matter. By our analysis, the direct neutron decay in the superdense nuclear matter under beta equilibrium is open only due to the isovector meson fields, which create a large energy gap between protons and neutrons in the medium. Our expression for the neutrino energy losses, obtained in the mean field approximation, incorporates the effects of nucleon recoil, parity violation, weak magnetism, and pseudoscalar interaction. Fo…
Results for the proton and neutron electric and magnetic form factors as well as the nucleon axial form factor are presented for constituent quark models, based on either one-gluon-exchange and Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The only input to the calculations is the nucleon wave function of the corresponding constituent quark model. A comparison is given to results of the instanton-induced constituent quark model treated with the Bethe-Salpeter equation.
Form factors of the energy-momentum tensor (EMT) can be interpreted in certain frames in terms of spatial distributions of energy, stress, linear and angular momentum, based on 2D or 3D Fourier transforms. This interpretation is in general subject to "relativistic recoil corrections", except when the nucleon moves at the speed of light like e.g. in the infinite-momentum frame. We show that it is possible to formulate a large-$N_c$ limit in which the probabilistic interpretation of the nucleon EMT distributions holds also in other frames. We use the bag model formulated in the large-$N_c$ limit…
The Nachtmann moment is employed to study the contribution of twist-3 operator to the nucleon spin structure functions. Target mass corrections to the Cornwall-Norton moments of the spin structure functions $g_{1,2}$ are discussed. It is found that the corrections play a sizeable role to the contribution of the twist-3 $\tilde d_2$ extracted from the Cornwall-Norton moments.
The $O(α)$ leptonic QED corrections to neutral current polarized deep inelastic lepton-nucleon scattering are calculated in leptonic variables both for the case of longitudinal and transverse nucleon polarization. The results of the complete calculation are compared with the corresponding leading log expressions. Numerical results are presented for the corrections in the kinematic range of the HERMES experiment and possible future polarized proton beam experiments at HERA.
We compute corrections to both the isovector anomalous magnetic moment and the isovector electromagnetic current of the nucleon to $O(p^3)$ in the framework of covariant two-flavor Baryon Chiral Perturbation Theory. We then apply these corrections to lattice data for the anomalous magnetic moment from the LHPC, RBC & UKQCD and QCDSF collaborations.
