The renormalization of the chiral np interaction with Delta-excitations in intermediate states is considered at next-to-leading order (NLO) and next-to-next-to-leading order (N2LO) for central waves. The inclusion of the Delta-excitation as an explicit degree of freedom improves the convergence properties of the effective field theory results for np scattering with respect to Delta-less theory, and allows the existence of a deuteron bound state in the infinite cut-off limit. The 1S_0 singlet and 3S_1 triplet phase shifts reproduce data for p ~ m_pi. The role of spectral function regularization is also discussed.
The Delta-Delta component of the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the relativistic field theory model of the deuteron. For the probability of the Delta-Delta component of the deuteron we give P(Delta-Delta) = 0.08 %. This prediction agrees good with the experimental estimate P(Delta-Delta) < 0.4 % at 90 % of CL (D. Allasia et al., Phys. Lett. B174 (1986) 450).
The probability P(Delta-Delta) to find the Delta-Delta component inside the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the Nambu-Jona-Lasinio model of light nuclei. We obtain P(Delta-Delta) = 0.3%. This prediction agrees good with the experimental estimate P(Delta-Delta) < 0.4% at 90% of CL (D. Allasia et al., Phys. Lett. B174 (1986) 450).
Deuteron-proton elastic scattering is studied in the multiple scattering expansion formalism. The four contributions are taken into account: one-nucleon-exchange, single- and double scattering, and $Δ$-isobar excitation. The presented approach was applied to describe the differential cross sections at deuteron energies between 500 and 1300 MeV in a whole angular range. The obtained results are compared with the experimental data.
Photodisintegration of the deuteron above pi-threshold is studied in a coupled channel approach including N-Delta- and pi-d-channels with pion retardation in potentials and exchange currents.
The pi+ d scattering and the d(p,n) charge exchange reaction are used to study the Delta-Nucleon interaction in the Delta resonance energy region. Various observables, such as inclusive and exclusive cross sections, angular distributions, and analyzing powers, are calculated in a coupled channel approach and shown to be influenced by the Delta-Nucleon potential.
Photo disintegration of the deuteron and photo pionproduction on the deuteron are described in the region of the $Δ$-resonance. The two reactions are unitarily coupled. A novel definition of electromagnetic exchange currents in the presence of pionproduction is given. Numerical predictions are done for spin-independent and spin-dependent observables of both reactions. The sensitivity of the results with respect to the nucleon-$Δ$ transition current and with respect to the irreducible nucleon-$Δ$ potential is studied.
The cross section for the dd -> 4He pi pi reaction is estimated near threshold in a two-step model where a pion created in a first interaction produces a second pion in a subsequent interaction. This approach, which describes well the rates of 2pi and eta production in the pd -> 3He pi pi and dd -> 4He eta reactions, leads to predictions that are much too low compared to experiment. Alternatives to this and the double-Delta model will have to be sought to explain these data.
We present a parameter--free calculation of the dispersive and absorptive contributions to the pion--deuteron scattering length based on chiral perturbation theory. We show that once all diagrams contributing to leading order to this process are included, their net effect provides a small correction to the real part of the pion--deuteron scattering length. At the same time the sizable imaginary part of the pion--deuteron scattering length is reproduced accurately.
We discuss convergence issues as well as short distance constraints on the deuteron wave functions based on chiral perturbation theory relevant to pion deuteron scattering. Non-analytical terms arise in the multiple scattering series for the pion-deuteron scattering length limiting the accuracy of the calculations. This result resembles similar findings in the structure of the NN interaction. The effects are found not to be numerically large. The iso-scalar $πN $ scattering length from the iso-vector one and the $πd$ scattering length yields values compatible with the experimental number and w…
We investigate the symptoms of broken rotational invariance, caused by the use of light front dynamics, for deuterons obtained using one- and two-pion-exchange potentials. A large mass splitting between states with m=0 and m=1 is found for the deuteron obtained from the one-pion-exchange (OPE) potential. The size of the splitting is smaller when the chiral two-pion-exchange (TPE) potential is used. When the TPE potential constructed without chiral symmetry is used, the deuteron becomes unbound. These results arise from significant relativistic effects which are much larger than those of the Wi…
The present status of the theoretical description of electromagnetic reactions on the deuteron above pion threshold is reviewed. Three major topics are considered: (i) retardation effects in $π$-meson exchange contributions to $NN$-interaction and meson exchange currents in deuteron photodisintegration above $π$-threshold in the $Δ$-resonance region, (ii) off-shell effects in the one-body current treated in a simple pion cloud model in deuteron photodisintegration in and above the $Δ$-resonance region, and (iii) final state interaction effects in photoproduction of $π$ and $η$ mesons on the de…
Incoherent photoproduction of pions on the deuteron in the Delta(1232) resonance region is studied, where besides the impulse approximation complete two-body rescattering in the nucleon-nucleon and pion-nucleon final state subsystems is included.
We analyze the deuteron bound state through the One Pion Exchange Potential. We pay attention to the short distance peculiar singularity structure of the bound state wave functions in coordinate space and the elimination of short distance ambiguities by selecting the regular solution at the origin. We determine the so far elusive amplitude of the converging exponential solutions at the origin. All bound state deuteron properties can then be uniquely deduced from the deuteron binding energy, the pion-nucleon coupling constant and pion mass. This generates correlations among deuteron properties.…
Spin observables for the three charge states of the pion for the pion photoproduction reaction on the deuteron, $γd\toπNN$, with polarized photon beam and/or oriented deuteron target are predicted. For the beam-target double-spin asymmetries, it is found that only the longitudinal asymmetries $T_{20}^{\ell}$ and $T_{2\pm 2}^{\ell}$ do not vanish, whereas all the circular and the other longitudinal asymmetries do vanish. The sensitivity of spin observables to the model deuteron wave function is investigated. It has been found that only $T_{21}$ and $T_{22}$ are sensitive to the model deuteron w…
The influence of final state $NN$- and pi N-rescattering in incoherent pion photoproduction on the deuteron has been investigated. For the elementary photoproduction operator an effective Lagrangian model is used which describes well the elementary reaction. The interactions in the final two-body subsystems are taken in separable form. While NN-rescattering shows quite a significant effect, particularly strong for neutral pion production, pi N-rescattering is almost negligible. Inclusion of such effects leads to an improved and quite satisfactory agreement with experiment.
Photodisintegration of the deuteron above $π$ threshold is studied in a coupled channel approach including $N Δ$ and $πd$ channels with consideration of pion retardation in potentials and exchange currents. A much improved description of total and differential cross sections in the energy region between $π$ threshold and 400-450 MeV is achieved. With respect to polarization observables, the description of the linear photon asymmetry and the proton polarization remains problematic.
A complete calculation of the corrections to pion-deuteron scattering length up to order $χ^{3/2}$ with $χ=m_π/M_{N}$ is performed. The calculation includes the dispersive contributions and corrections due to the explicit treatment of the $Δ$ resonance. s-wave pion-nucleon scattering parameters are extracted from a combined analysis of modern experimental data.
The production of pions by antiproton-deuteron annihilation at rest is analyzed. Assuming the possible existence of two delta-isobars in a deuteron some enhancement in the distribution over the invariant mass of two negative charged pions is predicted.
The elastic backward proton-deuteron scattering is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Contributions of the one-nucleon and one-pion exchange mechanisms to the cross section and polarization observables are investigated in explicit form. Results of numerical calculations for the cross section, tensor analyzing power and spin transfers are presented. The one-pion exchange contribution is essential for describing the spin averaged cross section, while in polarization observables it is found to be less important.
Coherent pion electroproduction on the deuteron is studied in the $Δ(1232)$ resonance region in the impulse approximation, i.e., neglecting pion rescattering and two-body effects. The elementary reaction on the nucleon is described in the framework of an effective Lagrangian approach including the dominant $P_{33}(1232)$ resonance and the usual background terms of the Born contributions for $π^0$ production. We have studied the influence of these different contributions on the various structure functions which determine the unpolarized exclusive differential cross section in a variety of kinem…
Photoproduction of two pions on nucleon and deuteron is studied for photon energies from threshold up to $E_γ= 1.5$ GeV. For the elementary operator an effective Lagrangean approach is used with resonance and Born contributions. The model parameters are fixed by resonance decay widths and multipole analyses of single pion photoproduction. A satisfactory description of total cross sections of two-pion production on the proton for various charge channels is achieved, except for $π^0π^0$ production for which a significant underestimation is found near threshold. The operator then serves for the e…
Formal expressions are developed for the general five-fold differential cross section of incoherent $π$-photoproduction on the deuteron including beam and target polarization. The polarization observables of the cross section are described by various beam, target and beam-target asymmetries for polarized photons and/or polarized deuterons. They are given as bilinear hermitean forms in the reaction matrix elements divided by the unpolarized cross section. In addition, the corresponding observables for the semi-exclusive reaction $\vec d(\vec γ,π)NN$ are also given.
In this dissertation we apply the pionless effective field theory to low energy neutron deuteron elastic scattering process. We calculated some of the polarization observables in neutron deuteron scattering to next-to-next-to-next-to-leading-order, in particular the transverse asymmetry $A_y$. All of the previous calculations have the same characteristic feature of under-predicting this observable, this is known as the $A_y$-puzzle. At this order of the pionless EFT new two-body $P$-wave interaction terms enter into the Lagrangian. This interaction terms give crucial contributions to the $A_y$…
We study the changes produced by the deuteron on the QCD quark condensate by means the Feynman-Hellmann theorem and find that the pion mass dependence of the pion-nucleon coupling could play an important role. We also discuss the relation between the many body effect of the condensate and the meson exchange currents, as seen by photons and pions. For pion probes, the many-body term in the physical amplitude differs significantly from that of soft pions, the one linked to the condensate. Thus no information about the many-body term of the condensate can be extracted from the pion-deuteron scatt…
Incoherent $η$ photoproduction on the deuteron is studied with the main emphasis on the role of final state interactions. In addition to the previously studied mechanisms of $NN$ and $ηN$ rescatterings, the role of an intermediate pion exchange is considered in detail, where first a pion is photoproduced on one nucleon and then rescatters into an $η$ meson on the other, the spectator nucleon. It is found, that the role of this pion mediated contribution is comparable in size to that of $ηN$ rescattering. Results for total and semi-inclusive differential cross sections and associated polarizati…
The off-shell aspects of the one-pion-exchange potential (OPEP) are discussed. Relativistic Hamiltonians containing relativistic kinetic energy, relativistic OPEP with various off-shell behaviors and Argonne $v_{18}$ short-range parameterization are used to study the deuteron properties. The OPEP off-shell behaviors depend on whether a pseudovector or pseudoscalar pion-nucleon coupling is used and are characterized by a parameter $μ$. We study potentials having $μ$=-1, 0 and +1 and we find that they are nearly unitarily equivalent. We also find that a nonrelativistic Hamiltonian containing loc…
The empirical value of the real part of the pion-deuteron scattering length can be well understood in terms of the dominant isovector $πN$-double scattering contribution. We calculate in chiral perturbation theory all one-pion loop corrections to this double scattering term which in the case of $πN$-scattering close the gap between the current-algebra prediction and the empirical value of the isovector threshold T-matrix $T_{πN}^-$. In addition to closing this gap there is in the $πd$-system a loop-induced off-shell correction for the exchanged virtual pion. Its coordinate space representation…
The contribution of the two-step process gamma + d -> p + n -> pi0 + d to the imaginary part of the amplitude for coherent pion production on the deuteron is calculated exploiting unitarity constraints. The result shows that this absorptive process is not negligible and has to be considered in an extraction of the elementary neutron production amplitude from the gamma + d -> pi0 + d cross section at threshold. In addition, it is argued that a consistent calculation of gamma + d -> pi0 + d in baryon chiral perturbation theory beyond next-to-leading order requires the inclusion of this absorptiv…
Within a dynamical model, rescattering effects are studied in coherent pion photoproduction on the deuteron in the $Δ$(1232) resonance region. The model consists of a system of coupled equations for the N$Δ$, NN$π$ and NN channels. Pion rescattering leads in general to a significant reduction of total and differential cross sections resulting in a better description of experimental data. Only a few polarization observables are sensitive to rescattering effects. In particular $T_{20}$ allows an analysis of the reaction mechanism for specific kinematics. The question how rescattering affects the…
Deuteron Compton scattering below pion photoproduction threshold is considered in the framework of the non-relativistic diagrammatic approach with the Bonn OBE potential. The complete gauge-invariant set of diagrams is taken into account which includes resonance diagrams without and with rescattering and diagrams with one- and two-body seagulls. The obtained results are compared with predictions of other models and with experimental data. A possibility of determining isospin-averaged electromagnetic polarizabilities of the nucleon is discussed.
Photo production of pions on the deuteron is studied in the spectator nucleon model. The Born terms of the elementary production amplitude are determined in pseudovector $π$N coupling and supplied with a form factor. The $Δ$ resonance is considered both in the $s$ and the $u$ channel. The parameters of the $Δ$ resonance and the cutoff of the form factors are fixed on the leading photoproduction multipoles. Results for total and differential cross sections are compared with experimental data. Particular attention is paid to the role of Pauli correlations of the final state nucleons in the quasi…
We present a nonrelativistic coupled-channel calculation of the deuteron structure including Delta Delta and NN^*(1440) channels, besides the standard NN S and D-wave components. All the necessary building blocks to perform the calculation have been obtained from the same underlying quark model. The calculated NN^*(1440) probabilities find support in the explanation given to different deuteron reactions.
The generalized Gerasimov-Drell-Hearn sum rule is evaluated for the contribution of single pion production on the deuteron by explicit integration up to an energy of 1.5 GeV for both coherent and incoherent production. As elementary $γ^* N\toπN$ amplitude the MAID2003 model has been used. For incoherent production final state interaction is included in the final $NN$ and $πN$ subsystems. The resulting contribution to the generalized transverse GDH sum rule is considerably smaller than the negative contribution from the disintegration channel $d(e,e')np$ which dominates the sum rule at low $Q^2…
Mechanisms of the charge exchange reaction $dp\to \{pp\}_{\!s} Nπ$, where $\{pp\}_{\!s}$ is a two-proton system at low excitation energy, are studied at beam energies 1 -- 2 GeV and for invariant masses $M_X$ of the final $Nπ$ system that correspond to the formation of the $Δ(1232)$ isobar. The direct mechanism, where the initial proton is excited into the $Δ(1232)$, dominates and explains the existing data on the unpolarized differential cross section and spherical tensor analyzing power $T_{22}$ for $M_X> 1.2$ GeV/$c^2$. However, this model fails to describe $T_{20}.
Incoherent pion photoproduction on the deuteron is studied for photon energies from threshold up to 1 GeV with special emphasis on polarization observables. The elementary $γN\toπN$ amplitude is taken from the MAID model. The influence of final state interactions on total and semi-exclusive cross sections $\vec d(\vecγ,π)NN$ is investigated by including complete rescattering in the final $NN$- and $πN$-subsystems. For charged pion-production the influence of $NN$-rescattering is moderate whereas $πN$-rescattering is almost negligible. Much stronger influences of $NN$-rescattering are seen in n…
The contribution of incoherent single pion photoproduction to the spin response of the deuteron, i.e., the asymmetry of the total photoabsorption cross section with respect to parallel and antiparallel spins of photon and deuteron, is calculated over the region of the $Δ$-resonance with inclusion of final state $NN$- and $πN$-rescattering. Sizeable effects, mainly from $NN$-rescattering, are found leading to an appreciable reduction of the spin asymmetry. Furthermore, the contribution to the Gerasimov-Drell-Hearn integral is explicitly evaluated by integration up to a photon energy of 550 MeV.…
The isoscalar and isovector scattering lengths (b_0,b_1) are determined using a unitarized coupled channel approach based on chiral Lagrangians. Using experimental values of pionic hydrogen and deuterium as well as low energy pi N scattering data, the free parameters of the model are calculated. Isospin violation is incorporated to a certain extent by working with physical particle masses. For the deuterium scattering length a_{pi-d} new significant corrections concerning real and imaginary parts are evaluated, putting new constraints from pi-d scattering on the values of (b_0,b_1). In particu…
Incoherent pion electroproduction on the deuteron is studied from threshold up to the second resonance region with special emphasis on the influence of final state interaction, in particular on polarization observables. The elementary $γN\toπN$ amplitude is taken from the MAID-2003 model. Final state interaction is included by considering complete rescattering in the final $NN$ and $πN$ subsystems. Their influence on the structure functions governing the semi-exclusive differential cross section, where besides the scattered electron only the produced pion is detected, is investigated in detail…
Positive pion electroproduction from the deuteron near threshold has been considered within an approach based on the unitary transformation method. The gauge independence of the treatment is provided by using an explicitly gauge independent expression for the reaction amplitude. The results of calculations for kinematics of the experiments on forward-angle $π^+$ meson electroproduction accomplished at Saclay and Jefferson Laboratory are discussed and compared with those given by the impulse approximation. It is shown that the observed behaviour of the cross sections is in accordance with the c…
Pion elastic scattering on deuterium is studied in the KMT multiple scattering approach developed in momentum space. Using a Paris wave function and the same methods and approximations as commonly used in pion scattering on heavier nuclei excellent agreement with differential cross section data is obtained for a wide range of pion energies. Only for $T_π>250$ MeV and very backward angles, discrepancies appear that are reminiscent of disagreements in pion scattering on $^3$He, $^3$H, and $^4$He. At low energies the second order corrections have been included. Polarization observables are studie…
We discuss a recent computation of Compton scattering on the deuteron at photon energies of order the pion mass. An interaction kernel is computed in baryon chiral perturbation theory and sewn to phenomenological deuteron wave functions. As an appetizer, we consider a computation of the pion-deuteron scattering length using this method.
The nucleon-deuteron radiative capture process is investigated using the chiral nuclear potentials and the electromagnetic currents developed by the Bochum-Bonn group. While the strong interaction is taken up to the next-to-next-to-leading order, the electromagnetic current consists of a single nucleon current, the leading one-pion exchange one and is supplemented by contributions from the long-range two-pion exchange current at next-to-leading-order. The theoretical predictions for the cross sections as well as analyzing powers show strong dependence on the values of regularization parameters…
We examine elastic Compton scattering off the deuteron for photon energies between 50 MeV and 100 MeV in the framework of chiral effective field theories to next-to-leading order. We compare one theoretical scheme with only pions and nucleons as explicit degrees of freedom to another in which the Delta(1232) resonance is treated as an explicit degree of freedom. Whereas pion degrees of freedom suffice to describe the experimental data measured at about 70 MeV, the explicit Delta(1232) gives important contributions that help to reproduce the angular dependence at higher energies. The static iso…
Deuteron Compton scattering below pion photoproduction threshold is considered in the framework of the nonrelativistic diagrammatic approach with the Bonn OBE potential. A complete gauge-invariant set of diagrams is taken into account which includes resonance diagrams without and with NN-rescattering and diagrams with one- and two-body seagulls. The seagull operators are analyzed in detail, and their relations with free- and bound-nucleon polarizabilities is discussed. It is found that both dipole and higher-order polarizabilities of the nucleon are needed for a quantitative description of rec…
We investigate the role of the delta isobar in the reaction $πd\to πd$ at threshold in chiral effective field theory. We discuss the corresponding power counting and argue that this calculation completes the evaluation of diagrams up to the order (m_pi/M_N)^(3/2), with m_pi (M_N) for the pion (nucleon) mass. The net effect of all delta contributions at this order to the pion-deuteron scattering length is (2.4 +/- 0.4)x 10^(-3) m_pi^{-1}.
We evaluate the deuteron charge, quadrupole, and magnetic form factors using wave functions obtained from chiral effective theory ($χ$ET) when the potential includes one-pion exchange, chiral two-pion exchange, and genuine contact interactions. We study the manner in which the results for form factors behave as the regulator is removed from the $χ$ET calculation, and compare co-ordinate- and momentum-space approaches. We show that, for both the LO and NNLO chiral potential, results obtained by imposing boundary conditions in co-ordinate space at $r=0$ are equivalent to the $Λ\to \infty$ limit …
The fragmentation of deuterons into pions emitted forward in the kinematic region forbidden for free nucleon-nucleon collisions is analyzed. It is shown that the inclusion of the non-nucleon degrees of freedom in a deuteron allows to describe the experimental data about inclusive pion spectrum rather satisfactory and improves the description of data concerning the deuteron analyzing power T_{20}. The experimental data show the positive sign and very small values, less than 0.2, of T_{20} what can't be reproduced by the calculations ignoring these degrees of freedom.
We analyze the renormalization of the NN interaction at low energies and the deuteron bound state through the Chiral Two Pion Exchange Potential assumed to be valid from zero to infinity. The short distance Van der Waals singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines that, after renormalization, in the 1S0 singlet channel and in the 3S1-3D1 triplet channel one can use the deuteron binding energy, the asymptotic D/S ratio and the S-wave scattering lengths as well as the chiral potential parameters as independent var…
We discuss the theoretical and experimental situations for charge symmetry violation (CSV) effects in the elastic scattering of pi+ and pi- on deuterium (D) and 3He/3H. Accurate comparison of data for both types of targets provides evidence for the presence of CSV effects. While there are indications of a CSV effect in deuterium, it is much more pronounced in the case of 3He/3H. We provide a description of the CSV effect on the deuteron in terms of single- and double- scattering amplitudes. The Delta-mass splitting is taken into account. Theoretical predictions are compared with existing exper…
An explicit evaluation of the spin asymmetry of the deuteron and the associated GDH sum rule is presented which includes photodisintegration, single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed whereas for double pion production an effective Lagrangean approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 $μ…
Incoherent pion photoproduction on the deuteron is studied in the first resonance region. The unpolarized cross section, the beam asymmetry, and the vector and tensor target asymmetries are calculated in the framework of a diagrammatic approach. Pole diagrams and one-loop diagrams with $NN$ scattering in the final state are taken into account. An elementary operator for pion photoproduction on the nucleon is taken in various on-shell forms and calculated using the SAID and MAID multipole analyses. Model dependence of the obtained results is discussed in some detail. A comparison with predictio…
Kaon photoproduction on the deuteron is studied with respect to a specific two-body contribution, namely a pion mediated production process, besides other final state interaction contributions from kaon-nucleon and hyperon-nucleon scattering. In this process, a pion is first photoproduced on one nucleon and then interacts with the spectator nucleon in a strangeness exchange reaction leading to a kaon and a hyperon. A sizeable effect from this pion mediated contribution is found, considerably larger than the previously studied hyperon-nucleon rescattering, whereas kaon-nucleon rescattering is m…
The photoproduction of a neutral pion on the deuteron is considered in the energy region around the eta threshold, where a bump-like structure was observed at very backward pion angles. Different dynamical aspects which may be responsible for this phenomenon are analysed within a theoretical frame which includes intermediate eta-NN configurations. The results show in particular, that a three-body treatment of the eta-NN interaction is of special importance.
The S wave pion deuteron scattering length is presented at NLO in the Effective Field Theory formulation of the two nucleon system with perturbative pions. At this order, this observable is determined by the iso-scalar S wave pion nucleon scattering length a^+, by pion re-scattering contributions inside the deuteron and by two nucleon two pion contact interactions that involve two unknown parameters which renormalise the appearing divergences. By choosing their values accordingly and in agreement with their natural sizes predicted by the power counting, we are able to accommodate the available…
Elastic deuteron Compton scattering and the quartet S wave of nd scattering are investigated in the effective field theory of nuclear physics with perturbative pions. Convergence and aggreement with experiment are good.
The deuteron spectrum in n+p -> 2 H(pi pi) at k_n = 1.88 GeV/c and theta_d = 0^o is explained by considering a Delta Delta excitation as the dominant reaction mechanism for the 2 pi production. We present a new theoretical approach based on a coupled channel formalism which allows to include the residual interaction within the intermediate Delta Delta and Delta N systems. The corresponding interaction potentials V_{DeltaDelta} and V_{DeltaN} are adopted from a meson exchange model with pi, rho, omega, and sigma exchange taken into account. The influence of the residual interaction on the deute…
Chiral effective field theory (ChEFT) is a modern framework to analyze the properties of few-nucleon systems at low energies. It is based on the most general effective Lagrangian for pions and nucleons consistent with the chiral symmetry of QCD. For energies below the pion-production threshold it is possible to eliminate the pionic degrees of freedom and derive nuclear potentials and nuclear current operators solely in terms of the nucleonic degrees of freedom. This is very important because, despite a lot of experience gained in the past, the consistency between two-nucleon forces, many-nucle…
We show that processes involving pions that remain very near their mass-shell can be reliably computed in the pionless effective field theory, with the pion integrated in as a heavy field. As an application, we compute the pion-deuteron scattering amplitude near threshold to next-to-leading order in the momentum expansion. This amplitude is formally dominated by an infrared logarithm of the form log(gamma/mpi), where gamma is the deuteron binding momentum, and mpi is the mass of the pion. The coefficient of this logarithm is determined by the S-wave pion-nucleon scattering lengths.
The fragmentation of deuterons into pions emitted forward in the kinematic region forbidden for free nucleon-nucleon collisions is analyzed. It is shown that the inclusion of the non-nucleonic degrees of freedom in a deuteron results in a satisfactory description of the data for the inclusive pion spectrum and improves the description of the data about $T_{20}$. According to the data, $T_{20}$ has very small positive values, less than 0.2, which contradicts the theoretical calculations ignoring these degrees of freedom.
