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 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

Electron Trapping in a One-Dimensional Semiconductor Quantum Wire with Multiple Impurities

We demonstrate the trapping of a conduction electron between two identical adatom impurities in a one-dimensional semiconductor quantum-dot array system (quantum wire). Bound steady states arise even when the energy of the adatom impurity is located in the continuous one-dimensional energy miniband. The steady state is a realization of the bound state in continuum (BIC) phenomenon first proposed by von Neuman and Wigner [Phys. Z. 30, 465 (1929)]. We analytically solve the dispersion equation for this localized state, which enables us to reveal the mechanism of the BIC. The appearance of the BIC state is attributed to the quantum interference between the impurities. The Van Hove singularity causes another type of bound state to form above and below the band edges, which may coexist with the BIC

Bound States and Power Counting in Effective Field Theories

The problem of bound states in effective field theories is studied. A rescaled version of nonrelativistic effective field theory is formulated which makes the velocity power counting of operators manifest. Results obtained using the rescaled theory are compared with known results from NRQCD. The same ideas are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to analyze when the Yukawa potential can be replaced by a delta-function potential. The implications of these results for the study of nucleon-nucleon scattering in chiral perturbation theory is discussed.Comment: 23 pages, eps figures, uses revte

The Solar Proton Burning Process Revisited In Chiral Perturbation Theory

The proton burning process p + p -> d + e(+) + \nu(e), important for the stellar evolution of main-sequence stars of mass equal to or less than that of the Sun, is computed in effective field theory using chiral perturbation expansion to the next-to-next-to leading chiral order. This represents a model-independent calculation consistent with low-energy effective theory of QCD comparable in accuracy to the radiative np capture at thermal energy previously calculated by first using very accurate two-nucleon wavefunctions backed up by an effective field theory technique with a finite cut-off. The result obtained thereby is found to support within theoretical uncertainties the previous calculation of the same process by Bahcall and his co-workers.Comment: 30 pages, 2 eps files, aaspp4.sty needed, slightly modified, to be published in Ap.

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

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

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

A direct and sensitive method for screening fructooligosaccharides-digesting microorganisms useful in food and health science

Short-chain fructooligosaccharides (FOS) stimulate selectively the growth and activity of microorganisms in the colon providing positive health effects and well-being in humans and animals. The lack of accurate isolation methods, however, hampers the possibility of getting new potential fructooligosaccharides (FOS)-fermenting yeast or bacterial strains. A valuable screening procedure to visually detect bacterial and yeast strains able to ferment FOS in liquid or solid rich media supplemented with an innocuous pH indicator is described. Using this assay, 15 FOS-consuming strains isolated from different sources were successfully evaluated to prove the utility of the method. This screening procedure is a new and valuable tool in rapid large-scale detection of potential FOS fermenting-strains useful in food and health science.Key words: FOS-fermenting microorganisms, prebiotics, probiotics, symbiotics