The Delta-Delta Intermediate State in 1S0 Nucleon-Nucleon Scattering From Effective Field Theory

We examine the role of the Delta-Delta intermediate state in low energy NN scattering using effective field theory. Theories both with and without pions are discussed. They are regulated with dimensional regularization and MSbar subtraction. We find that the leading effects of the Delta-Delta state can be absorbed by a redefinition of the contact terms in a theory with nucleons only. It does not remove the requirement of a higher dimension operator to reproduce data out to moderate momentum. The explicit decoupling of the Delta-Delta state is shown for the theory without pions.Comment: 16 pages, 3 figures, uses harvma

Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory

Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the $S$ matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.Comment: 7 page

The Long and Short of Nuclear Effective Field Theory Expansions

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.Comment: 22 pages, 9 figures, references corrected, minor modification

Low Energy Theorems For Nucleon-Nucleon Scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_\pi$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_\pi$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in chiral limit; minor revisions including revised figure reference to recent work adde

Time-reversal symmetric resolution of unity without background integrals in open quantum systems

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green's function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schroedinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly the exponential decays due to the resonance poles.Comment: 62 pages, 13 figure

The NN scattering 3S1-3D1 mixing angle at NNLO

The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is calculated to next-to-next-to-leading order in an effective field theory with perturbative pions. Without pions, the low energy theory fits the observed epsilon_1 well for momenta less than $\sim 50$ MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to $\sim 150$ MeV with one less parameter. Furthermore, for these momenta the accuracy of our calculation is similar to an effective field theory calculation in which the pion is treated non-perturbatively. This gives phenomenological support for a perturbative treatment of pions in low energy two-nucleon processes. We explain why it is necessary to perform spin and isospin traces in d dimensions when regulating divergences with dimensional regularization in higher partial wave amplitudes.Comment: 17 pages, journal versio

Exact Markovian kinetic equation for a quantum Brownian oscillator

We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast for non-integrable systems, the invariant subspaces follow a dynamics with broken-time symmetry, involving generalized functions. This result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces. We comment on the relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte

Star-unitary transformations. From dynamics to irreversibility and stochastic behavior

We consider a simple model of a classical harmonic oscillator coupled to a field. In standard approaches Langevin-type equations for {\it bare} particles are derived from Hamiltonian dynamics. These equations contain memory terms and are time-reversal invariant. In contrast the phenomenological Langevin equations have no memory terms (they are Markovian equations) and give a time evolution split in two branches (semigroups), each of which breaks time symmetry. A standard approach to bridge dynamics with phenomenology is to consider the Markovian approximation of the former. In this paper we present a formulation in terms of {\it dressed} particles, which gives exact Markovian equations. We formulate dressed particles for Poincar\'e nonintegrable systems, through an invertible transformation operator \Lam introduced by Prigogine and collaborators. \Lam is obtained by an extension of the canonical (unitary) transformation operator $U$ that eliminates interactions for integrable systems. Our extension is based on the removal of divergences due to Poincar\'e resonances, which breaks time-symmetry. The unitarity of $U$ is extended to ``star-unitarity'' for \Lam. We show that \Lam-transformed variables have the same time evolution as stochastic variables obeying Langevin equations, and that \Lam-transformed distribution functions satisfy exact Fokker-Planck equations. The effects of Gaussian white noise are obtained by the non-distributive property of \Lam with respect to products of dynamical variables. Therefore our method leads to a direct link between dynamics of Poincar\'e nonintegrable systems, probability and stochasticity.Comment: 24 pages, no figures. Made more connections with other work. Clarified ideas on irreversibilit

Near-Earth asteroids spectroscopic survey at Isaac Newton Telescope

The population of near-Earth asteroids (NEAs) shows a large variety of objects in terms of physical and dynamical properties. They are subject to planetary encounters and to strong solar wind and radiation effects. Their study is also motivated by practical reasons regarding space exploration and long-term probability of impact with the Earth. We aim to spectrally characterize a significant sample of NEAs with sizes in the range of $\sim$0.25 - 5.5 km (categorized as large), and search for connections between their spectral types and the orbital parameters. Optical spectra of NEAs were obtained using the Isaac Newton Telescope (INT) equipped with the IDS spectrograph. These observations are analyzed using taxonomic classification and by comparison with laboratory spectra of meteorites. A total number of 76 NEAs were observed. We classified 44 of them as Q/S-complex, 16 as B/C-complex, eight as V-types, and another eight belong to the remaining taxonomic classes. Our sample contains 27 asteroids categorized as potentially hazardous and 31 possible targets for space missions including (459872) 2014 EK24, (436724) 2011 UW158, and (67367) 2000 LY27. The spectral data corresponding to (276049) 2002 CE26 and (385186) 1994 AW1 shows the 0.7 $\mu$m feature which indicates the presence of hydrated minerals on their surface. We report that Q-types have the lowest perihelia (a median value and absolute deviation of $0.797\pm0.244$ AU) and are systematically larger than the S-type asteroids observed in our sample. We explain these observational evidences by thermal fatigue fragmentation as the main process for the rejuvenation of NEA surfaces. In general terms, the taxonomic distribution of our sample is similar to the previous studies and matches the broad groups of the inner main belt asteroids. Nevertheless, we found a wide diversity of spectra compared to the standard taxonomic types.Comment: Accepted in Astronomy & Astrophysics (A&A

Charge-Dependence of the Nucleon-Nucleon Interaction

Based upon the Bonn meson-exchange-model for the nucleon-nucleon ($NN$) interaction, we calculate the charge-independence breaking (CIB) of the $NN$ interaction due to pion-mass splitting. Besides the one-pion-exchange (OPE), we take into account the $2\pi$-exchange model and contributions from three and four irreducible pion exchanges. We calculate the CIB differences in the $^1S_0$ effective range parameters as well as phase shift differences for partial waves up to total angular momentum J=4 and laboratory energies below 300 MeV. We find that the CIB effect from OPE dominates in all partial waves. However, the CIB effects from the $2\pi$ model are noticable up to D-waves and amount to about 40% of the OPE CIB-contribution in some partial waves, at 300 MeV. The effects from 3$\pi$ and 4$\pi$ contributions are negligible except in $^1S_0$ and $^3P_2$.Comment: 12 pages, RevTex, 14 figure