1,157 research outputs found

    Regularization and renormalization in effective field theories of the nucleon-nucleon interaction

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    Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve formally iterating the divergent interaction and then regularizing and renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be introduced, or dimensional regularization can be applied. We show that these two methods yield different results after renormalization. Furthermore, if a cutoff is used, the NN phase shift data cannot be reproduced if the cutoff is taken to infinity. We also argue that the assumptions which allow the use of dimensional regularization in perturbative EFT calculations are violated in this problem. Another possibility is to introduce a regulator into the potential before iteration and then keep the cutoff parameter finite. We argue that this does not lead to a systematically-improvable NN interaction.Comment: 5 pages, LaTeX, uses espcrc1.sty, summary of talk given at the 15th International Conference on Few-Body Problems in Physic

    Electric properties of the Beryllium-11 system in Halo EFT

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    We compute E1 transitions and electric radii in the Beryllium-11 nucleus using an effective field theory that exploits the separation of scales in this halo system. We fix the leading-order parameters of the EFT from measured data on the 1/2+ and 1/2- levels in Be-11 and the B(E1) strength for the transition between them. We then obtain predictions for the B(E1) strength for Coulomb dissociation of the Be-11 nucleus to the continuum. We also compute the charge radii of the 1/2+ and 1/2- states. Agreement with experiment within the expected accuracy of a leading-order computation in this EFT is obtained. We also discuss how next-to-leading-order (NLO) corrections involving both s-wave and p-wave neutron-Be-10 interactions affect our results, and display the NLO predictions for quantities which are free of additional short-distance operators at this order. Information on neutron-Be-10 scattering in the relevant channels is inferred.Comment: 27 pages, 8 figures, final versio

    The potential of effective field theory in NN scattering

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    We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range---which occurs in nature---requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O(m_\pi). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.Comment: 25 pages LaTeX, 3 figures (uses epsf

    Gauge invariant reduction to the light-front

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    The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the electromagnetic current in the light-cone formalism, such that current conservation is satisfied at each order of the perturbation theory.Comment: 12 pages, revtex

    Deuteron Matrix Elements in Chiral Effective Theory at Leading Order

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    We consider matrix elements of two-nucleon operators that arise in chiral effective theories of the two-nucleon system. Generically, the short-distance piece of these operators scales as 1/r^n, with r the relative separation of the two nucleons. We show that, when evaluated between the leading-order wave functions obtained in this effective theory, these two-nucleon operators are independent of the cutoff used to renormalize the two-body problem for n=1 and 2. However, for n greater than or equal to 3 general arguments about the short-distance behavior of the leading-order deuteron wave function show that the matrix element will diverge.Comment: 7 pages, 5 .eps figure

    Relativistic effects and quasipotential equations

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    We compare the scattering amplitude resulting from the several quasipotential equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator, Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved numerically without decomposition into partial waves. We analyze both negative-energy state components of the propagators and retardation effects. We found that the scattering solutions of the Spectator and the Equal-Time equations are very close to the nonrelativistic solution even at high energies. The overall relativistic effect increases with the energy. The width of the band for the relative uncertainty in the real part of the scattering TT matrix, due to different dynamical equations, is largest for backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.

    Unitarity and the Bethe-Salpeter Equation

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    We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the ¤Ľ2¤â\phi^2\sigma interaction Lagrangian and the ¤ÇN\pi N system with ss-, uu-, and tt-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in Phys. Rev.

    Two-body correlations in Bose condensates

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    We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev like decomposition of the wave function. We derive for a fixed hyperradius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The interaction energy is for N~20 five times smaller than that of the Gross-Pitaevskii equation

    Parity-violating asymmetry in ╬│dÔćĺnÔâŚp\gamma d \to \vec{n}p with a pionless effective theory

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    Nuclear parity violation is studied with polarized neutrons in the photodisintegration of the deuteron at low energies. A pionless effective field theory with di-baryon fields is used for the investigation. Hadronic weak interactions are treated by parity-violating di-baryon-nucleon-nucleon vertices, which have undetermined coupling contants. A parity-violating asymmetry in the process is calculated for the incident photon energy up to 30 MeV. If experimental data for the parity-violating asymmetry become available in the future, we will be able to determine the unknown coupling contants in the parity-violating vertices.Comment: 4 pages. A contribution to APFB2011, August 22-26, 2011, Seoul, Kore
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