We argue that the recently published CLAS results on the deuteron spin polarizability $γ_0$ [Adhikari {\it et al.}, Phys.\ Rev.\ Lett.\ {\bf 120}, 062501 (2018)], as well as their comparisons with chiral perturbation theory ($χ$PT), are misleading. In reality, the deuteron polarizability is larger by 4 orders of magnitude, as demonstrated here by a novel calculation in pionless EFT. The CLAS paper, on the other hand, presents only a tiny correction to it, based on a partial evaluation of a sum rule for $γ_0$. The sum rule is assumed to have the same form as for the nucleon; we argue it does not. Moreover, their "test of $χ$PT" tacitly involves assumptions which, as we demonstrate, may not be valid at the claimed accuracy.
We establish a simple, explicit relation between the formalisms employed in the treatments of polarization observables in deuteron two-body electrodisintegration published by Arenhövel, Leidemann, and Tomusiak in Few-Body Systems {\bf 15}, 109 (1993) and the results of the present authors published in Phys.~Rev.~C {\bf 40}, 2479 (1989). We comment on the overlap between the two sets of results.
A recent letter [1] investigated the effects of deuteron polarizability in the mu D atom. The importance of understanding this atom has been heightened because of the possible light it could shed on the proton radius puzzle. Here we confirm, clarify, and emphasize the significance of the result [1] that the effects of the third Zemach moment are canceled by part of the deuteron polarizability effects. 1. K. Pachucki, Phys. Rev. Lett. 106, 193007 (2011)
Polarized electron-deuteron deep-inelastic scattering (DIS) with detection of the spectator proton ("tagged DIS") enables measurements of neutron spin structure with maximal control of nuclear effects. We calculate the longitudinal spin asymmetries in polarized tagged DIS using methods of light-front nuclear structure and study their dependence on the measured proton momentum. Asymmetries can be formed with all three deuteron spin states ($\pm 1, 0$) or the two maximum-spin states only ($\pm 1$, involving tensor polarization). The proton momentum dependence can be used to select pure S-wave co…
We demonstrate that a paradigm shift from considering the deuteron as a system of bound proton and neutron to considering it as a pseudo-vector system in which we observe proton and neutron, results in a possibility of probing a new "incomplete" P-state like structure on the light-front (LF), at extremely large internal momenta, which can be achieved in high energy transfer electro-disintegration of the deuteron. Investigating the deuteron on the light-front, where the vacuum-fluctuations are suppressed, we found that this new structure, together with conventional S- and D- states, is a leadin…
We review the recent progress made in studies of deuteron structure at small internucleon distances. This progress is largely facilitated by the new generation of experiments in deuteron electrodisintegration carried out at unprecedentedly high momentum transfer. The theoretical analysis of these data confirms the onset of the high energy eikonal regime in the scattering process which allows one to separate long range nuclear effects from the effects genuinely related to the short distance structure of the deuteron. Our conclusion is that for the first time the deuteron is probed at relative m…
The deuteron magnetic and quadrupole moments are unambiguosly determined within the front-form Hamiltonian dynamics, by using a new current operator which fulfills Poincaré, parity and time reversal covariance, together with hermiticity and the continuity equation. For both quantities the usual disagreement between theoretical and experimental results is largely removed.
Background: DIS on the polarized deuteron with detection of a proton in the nuclear breakup region (spectator tagging) represents a unique method for extracting the neutron spin structure functions and studying nuclear modifications. The tagged proton momentum controls the nuclear configuration during the DIS process and enables a differential analysis of nuclear effects. Such measurements could be performed with the future electron-ion collider (EIC) and forward proton detectors if deuteron beam polarization could be achieved. Purpose: Develop theoretical framework for polarized deuteron DIS …
An extended analysis of the key role of direct interactions, i.e., breakup, stripping and pick-up processes, has been carried out for deuteron-induced reactions. Particular comments concern the deuteron breakup which is the dominant mechanism involved in surrogate reactions on heavy nuclei, around the Coulomb barrier.
We analyze the momentum distributions of constituents in 3He, as well as the spin-dependent observables for (3He,d), (3He,p), and (d,p) breakup reactions. Special attention is paid to the region of small relative momenta of the helium-3 and the deuteron constituents, where a single parameter, D_2, has determining role for the spin-dependent observables. We extract also this parameter for the deuteron, basing on existing data for the tensor analyzing power of this reaction.
We calculate the magnetic quadrupole moment (MQM) of the deuteron at leading order in the systematic expansion provided by chiral effective field theory. We take into account parity and time-reversal violation which, at the quark-gluon level, results from the QCD vacuum angle and dimension-six operators that originate from physics beyond the Standard Model. We show that the deuteron MQM can be expressed in terms of five low-energy constants that appear in the parity- and time-reversal-violating nuclear potential and electromagnetic current, four of which also contribute to the electric dipole …
We calculate the electric dipole moment (EDM) of the deuteron in the standard model with $|ΔS| =1$ interactions by taking into account the $NN - ΛN - ΣN$ channel coupling, which is an important nuclear level systematics. The two-body problem is solved with the Gaussian Expansion Method using the realistic Argonne $v18$ nuclear force and the $YN$ potential which can reproduce the binding energies of $^3_Λ$H, $^3_Λ$He, and $^4_Λ$He. The $|ΔS| =1$ interbaryon potential is modeled by the one-meson exchange process. It is found that the deuteron EDM is modified by less than 10\%, and the main contr…
The two-nucleon contributions to the electric dipole moment (EDM) of the deuteron, induced by the QCD $θ$-term, are calculated in the framework of effective field theory up-to-and-including next-to-next-to-leading order. In particular we find for the difference of the deuteron EDM and the sum of proton and neutron EDM induced by the QCD $θ$-term a value of $(-5.4\pm 3.9)\,\barθ\times 10^{-4}\, e$ fm. The by far dominant uncertainty comes from the CP- and isospin-violating $πNN$ coupling constant.
P odd anapole moment of the deuteron is found in the chiral limit, $m_π \to 0$. The contact current generated by the P odd pion exchange does not contribute to the deuteron anapole. Being combined with usual radiative corrections to the weak electron -- deuteron interaction, our calculation results in a sufficiently accurate theoretical prediction for the corresponding effective constant $C_{2d}$. The experimental measurement of this constant would give valuable information on the P odd $π$NN constant and on the $s$-quark content of nucleons. We calculate also in the same limit $m_π \to 0$ the…
We consider few problems which are related to the deuteron and have simple analytical solution. Relation is found between the deuteron electric quadrupole moment and the $np$-scattering amplitude. The degree of circular polarization of photons is calculated for the radiative capture of longitudinally polarized thermal neutrons. The anapole, electric dipole and magnetic quadrupole moments of the deuteron are calculated.
The deuteron tensor polarization component T_20(Q^2) is calculated by relativistic Hamiltonian dynamics approach. It is shown that in the range of momentum transfers available in to-day experiments, relativistic effects, meson exchange currents and the choice of nucleon electromagnetic form factors almost do not influence the value of T_20(Q^2). At the same time, this value depends strongly on the actual form of the deuteron wave function, that is on the model of NN-interaction in deuteron. So the existing data for T_20(Q^2) provide a crucial test for deuteron wave functions.
We present an analysis of the electric dipole moment (EDM) of the deuteron as induced by CP-violating operators of dimension 4, 5 and 6 including theta QCD, the EDMs and color EDMs of quarks, four-quark interactions and the Weinberg operator. We demonstrate that the precision goal of the EDM Collaboration's proposal to search for the deuteron EDM, (1-3)\times 10^{-27} e cm, will provide an improvement in sensitivity to these sources of one-two orders of magnitude relative to the existing bounds. We consider in detail the level to which CP-odd phases can be probed within the MSSM.
The nuclear physics relevant to the electric dipole moment (EDM) of the deuteron is addressed. The general operator structure of the $P$- and $T$-odd nucleon-nucleon interaction is discussed and applied to the two-body contributions of the deuteron EDM, which can be calculated in terms of $P$- and $T$-odd meson-nucleon coupling constants with only small model dependence. The one-body contributions, the EDMs of the proton and the neutron, are evaluated within the same framework. Although the total theoretical uncertainties are sizable, we conclude that, compared to the neutron, the deuteron EDM…
We evaluate the frame-independent gluon and charm parton-distribution functions (PDFs) of the deuteron utilizing light-front quantization and the impulse approximation. We use a nuclear wave function obtained from solving the nonrelativistic Schroedinger equation with the realistic Argonne v18 nuclear force, which we fold with the proton PDF. The predicted gluon distribution in the deuteron (per nucleon) is a few percent smaller than that of the proton in the domain x_{bj} = Q^2 / (2 p_N \cdot q) \sim 0.4, whereas it is strongly enhanced for x_{bj} larger than 0.6. We discuss the applicability…
The deuteron magnetic moment is calculated using two model wave functions obtained from 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents which are automatically generated by the nuclear force model used in these fits. After normalizing the wave functions, nearly identical predictions are obtained: model WJC-1, with larger relativistic P-state components, gives 0.863(2), while model WJC-2 with very small P-state components gives 0.864(2) These are about 1\% larger than the measured value of the moment, 0.857 n.m…
We substantiate our statement that the deuteron remains bound in the chiral limit. We critically discuss recent claims that effective field theory cannot give a definite answer to this question.
We costruct the relativistic operator of the quadrupole moment of two-particle composite spin one systems with zero orbital moment of the relative motion and derive explicit analytical expression for the quadrupole moment using the approach to relativistic composite systems based on our version of the instant-form relativistic quantum mechanics (RQM). We calculate the quadrupole moments of the rho meson and of the S-wave deuteron without any free parameters, using our unified pi&rho model (Phys. Rev.D 93, 036007 (2016); 97, 033007 (2018)) and our previous results on deuteron. Our calculation g…
We study the effect of the neutrino magnetic moment on the neutrino-deuteron breakup reaction, using a method called the standard nuclear physics approach, which has already been well tested for several electroweak processes involving the deuteron.
We calculate the electric-dipole and magnetic-quadrupole form factors of the deuteron that arise as a low-energy manifestation of parity and time-reversal violation in quark-gluon interactions of effective dimension four and six: the QCD vacuum angle, the quark electric and chromo-electric dipole moments, and the gluon chromo-electric dipole moment. Within the framework of two-flavor chiral perturbation theory, we show that the relative sizes of the corresponding moments allow an identification of the symmetry-breaking source.
The deuteron is considered as a superposition of two-nucleon Fock states with the invariant mass depending on the relative momentum in a proton-neutron pair. The condition of the transversality of the polarization vectors should be imposed at the Fock component level and these vectors depend on the invariant mass of the Fock component. Such "running" longitudinal polarization vector was not used in early estimates of relativistic effects. The technique for the calculation of the average helicity of the proton in the deuteron has been considered in the light-cone variables. A receipt has been p…
In a recent paper Yang and Bodek extracted the free neutron structure function at large x by extrapolating the density dependence of the nuclear EMC ratios to the deuteron. We clarify why this approach is ill-defined for light nuclei, and introduces a large theoretical bias into the extraction of F_2n at large x.
The reaction of the elastic electron-deuteron scattering at high momentum transfer is investigated within the Bethe-Salpeter approach. The relativistic covariant Graz II separable kernel of nucleon-nucleon interactions is used to analyze the deuteron structure functions, form factors and tensor of polarization components. The modern data for the electromagmetic nucleons structure from the double polarization experiments as well as some other models of the nucleon form factors are considered.
The proton-proton momentum correlation function is constructed in three-body photo-disintegration channels from $^{12}$C and $^{16}$O targets in the quasi-deuteron regime within the framework of an extended quantum molecular dynamics model. Using the formula of Lednicky and Lyuboshitz (LL) for the momentum correlation function, we obtain a proton-proton momentum correlation function for the specific three-body photon-disintegration channels of $^{12}$C and $^{16}$O targets, which are assumed to have different initial geometric structures, and extract their respective emission source sizes for …
We calculate the deuteron anapole moment with the wave functions obtained from the Argonne $v18$ nucleon-nucleon interaction model. The anapole moment operators are considered at the leading order. To minimize the uncertainty due to a lack of current conservation, we calculate the matrix element of the anapole moment from the original definition. In virtue of accurate wave functions, we can obtain a more precise value of the deuteron anapole moment which contains less uncertainty than the former works. We obtain a result reduced by more than 25% in the magnitude of the deuteron anapole moment.…
We calculate deuteron positive and negative radial moments involving any bilinear function of the deuteron S and D wave functions for renormalized OPE and TPE chiral potentials. The role played by the strong singularities of the potentials at the origin and the short distance insensitivity of the results when the potentials are fully iterated is emphasized as compared to realistic potentials.
Parity-nonconserving two-body currents due to vector meson exchange are considered with the aim to determine the related contributions to the anapole moment. A particular attention is given to the requirement of current conservation which is essential for a reliable estimate of this quantity. An application is made for the deuteron case.
Effective field theory, including pions, provides a consistent and systematic description of nucleon-nucleon strong interactions up to center-of-mass momentum of order 300 MeV per nucleon. We describe the inclusion of hadronic parity violation into this effective field theory and find an analytic form for the deuteron anapole moment at leading order in the expansion.
Parity violation in low-energy nuclear observables is included in the pionless effective field theory. The model-independent relation between the parity-violating asymmetry in polarized np -> d gamma and the non-nucleon part of the deuteron anapole moment is discussed. The asymmetry in np -> d gamma computed with KSW power-counting, and recently criticized by Desplanques, is discussed.
The calculation of the magnetic moment of the deuteron in the framework of the Bethe--Salpeter approach is performed. The relativistic corrections are calculated analytically and estimated numerically. It is shown that the main contributions are due to partial waves with positive energies and $P$--waves. A comparison with the non-relativistic schemes of calculations including mesonic exchange currents is made.
Production of deuterons by coalescence has an important influence on the moments of the observed proton number distribution. Therefore, this effect must be taken into account when physics conclusions about baryon number fluctuation are drawn from the measurement of proton number fluctuations. We also show that a measurement of the third and fourth moments of the deuteron number distribution would allow to distinguish whether deuterons are produced statistically or by coalescence.
Theoretical models of low-energy (d,p) single-neutron transfer reactions are a crucial link between experimentation, nuclear structure and nuclear astrophysical studies. Whereas reaction models that use local optical potentials are insensitive to short-range physics in the deuteron, we show that including the inherent nonlocality of the nucleon-target interactions and realistic deuteron wave functions generates significant sensitivity to high n-p relative momenta and to the underlying nucleon-nucleon interaction. We quantify this effect upon the deuteron channel distorting potentials within th…
The central tenet of effective theory is that the details of short-distance physics will not have a significant impact on low-energy observables. Here we perform an analysis of electron-deuteron scattering at low momentum transfers which is based on effective field theory. We show that in our approach the deuteron electromagnetic form factors $F_C$ and $F_M$ indeed are largely insensitive to the short-range $NN$ potential at momenta $Q$ up to about 700 MeV. We also find that the effective field theory approach to deuteron electromagnetic structure provides a systematic justification for many f…
The relation between the differential cross section of the charge-exchange breakup of a fast deuteron d+p -> (pp)+n and the differential cross section of the charge transfer process n+p -> p+n is discussed taking into account the effects of the proton identity and of the Coulomb and strong interactions of protons in the final state. The distribution of the relative momenta of the protons is found in the framework of the impulse approach. It is shown that the use of polarized initial deuterons and protons allows one to separate two spin-dependent terms in the amplitude of the charge transfer re…
The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experimental result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better th…
The relativistic light-front dynamics (LFD) method has been shown to give a correct description of the most recent data for the deuteron monopole and quadrupole charge form factors obtained at the Jefferson Laboratory for elastic electron-deuteron scattering for six values of the squared momentum transfer between 0.66 and 1.7 (GeV/c)$^{2}$. The good agreement with the data is in contrast with the results of the existing non-relativistic approaches. In this work we firstly make a complementary test of the LFD applying it to calculate another important characteristic, the nucleon momentum distri…
The process $\overrightarrow{^3{\rm He}}(e,e'\vec{p})d $ (or $\overrightarrow{^3{\rm He}}(e,e'\vec{d})p $) is studied theoretically in a Faddeev treatment with the aim to have access to the spin-dependent momentum distribution of ${\vec p} {\vec d} $ clusters in polarized $^3$He. Final state interactions and meson exchange currents turn out to have a strong influence in the considered kinematical regime (below the pion threshold). This precludes the direct access to the momentum distribution except for small deuteron momenta. Nevertheless, the results for the longitudinal and transverse respon…
What range of momentum components in the deuteron wave function are available e d elastic scattering data sensitive to ? This question is addressed within the context of a model calculation of the deuteron form factors, based on realistic interactions and currents. It is shown that the data on the $A(q)$, $B(q)$, and $T_{20}(q)$ observables at $q \leq 6$ fm$^{-1}$ essentially probe momentum components up to $\simeq 4 m_π$.
We give an overview of a model to describe deep-inelastic scattering (DIS) off the deuteron with a spectator proton, based on the virtual nucleon approximation (VNA). The model accounts for the final-state interactions (FSI) of the DIS debris with the spectator proton. Values of the rescattering cross section are obtained by fits to high-momentum spectator data. By using the so-called "pole extrapolation method", free neutron structure functions can be obtained by extrapolating low-momentum spectator proton data to the on-shell neutron pole. We apply this method to the BONuS data set and find …
Higher-twist effects in the low-order moments of the longitudinal and transverse structure functions of proton and deuteron have been analyzed using available phenomenological fits of existing data in the Q**2 range between 1 and 20 (GeV/c)**2. Both twist-4 and twist-6 contributions have been determined adopting the Natchmann definition of moments, which allows to disentangle properly target-mass effects. The extraction of the matrix elements of the relevant twist-4 operators, describing quark-quark and quark-gluon correlations, is carried out in case of the second moment. The need of transver…
A new method is developed to calculate multiloop Feynman diagrams in non-relativistic field theories. A consistent scheme for regularizing and renormalizing loop integrals is established and shown to reproduce the results of dimensional regularization (DR) and modified minimal subtraction MS^bar or DR and power divergence subtraction (PDS) up to next-to-leading order (NLO). However, significantly less effort is required to evaluate the integrals and the methods are easily generalized to higher order graphs. Thus, even the most complicated multiloop graph can be expressed in terms of analytic f…
The deuteron binding energy is only 2.2 MeV. At the same time, its yield in Pb+Pb collisions at $\sqrt{s_{NN}} = $2.76 TeV corresponds to a thermal yield at the temperature around 155 MeV, which is too hot to keep deuterons bound. This puzzle is not completely resolved yet. In general, the mechanism of light nuclei production in ultra-high energy heavy ion collisions remains under debate. In a previous work [1] we suggest a microscopic explanation of the deuteron production in central ultra-relativistic Pb+Pb collisions, the main mechanism being $πpn \leftrightarrow πd$ reactions in the hadron…
An Electron-Ion Collider (EIC) would enable next-generation measurements of deep-inelastic scattering (DIS) on the deuteron with detection of a forward-moving nucleon (p, n) and measurement of its recoil momentum ("spectator tagging"). Such experiments offer full control of the nuclear configuration during the high-energy process and can be used for precision studies of the neutron's partonic structure and its spin dependence, nuclear modifications of partonic structure, and nuclear shadowing at small x. We review the theoretical description of spectator tagging at EIC energies (light-front nu…
$\textbf{Background:}$ The deuteron shows the essential features of short-range correlations found in all nuclei. Experimental observables related to short-range correlations are connected with the high-momentum components of one- and two-body momentum distributions. An intuitive understanding of short-range correlations is provided by the suppression of the two-body density in coordinate space at small distances. $\textbf{Purpose:}$ The Wigner function provides a quasi-probability distribution in phase-space that allows to investigate short-range correlations as a function of distance and rel…
We present a convenient analytical parametrization of the deuteron wave function calculated within dispersion approach as a discrete superposition of Yukawa-type functions, in both configuration and momentum spaces.
The influence of the magnetic moment interaction of nucleons on nucleon-deuteron elastic scattering and breakup cross sections and on elastic scattering polarization observables has been studied. Among the numerous elastic scattering observables only the vector analyzing powers were found to show a significant effect, and of opposite sign for the proton-deuteron and neutron-deuteron systems. This finding results in an even larger discrepancy than the one previously established between neutron-deuteron data and theoretical calculations. For the breakup reaction the largest effect was found for …
Elastic lepton-deuteron scattering was considered within the limit of zero lepton mass. The deuteron wave function in the coordinate representation for the Reid93 potential was applied to numerical calculations. The angular-momentum dependence of values spin correlation coefficients $C_{xz}^{(0)}$, $C_{zz}^{(0)}$ and tensor asymmetries $A_{xx}^{(0)}$, $A_{xz}^{(0)}$, $A_{zz}^{(0)}$ have been evaluated in 3D format for Reid93 potential. These polarization observables are analyzed for different energies and scattering angles. Application of the obtained values allows better explanation and illus…
We perform the four-body calculation of the hyperfine structure in the first rotational state $J=1$ of the H$_2$, D$_2$, and HD molecules and determine the accurate value for the deuteron electric quadrupole moment $Q_d = 0.285\,699(15)(18)$ fm$^2$ in significant disagreement with former spectroscopic determinations. Our results for the hyperfine parameters agree very well with the currently most accurate molecular-beam magnetic resonance measurement performed several decades ago by N.F. Ramsey and coworkers. They also indicate the significance of previously neglected nonadiabatic effects. Mor…
The $α$-proton Coulomb interaction is included in the description of $α$-deuteron scattering using the screening and renormalization approach in the framework of momentum-space three-particle equations. The technical reliability of the method is demonstrated. Large Coulomb-force effects are found.
