Partially quenched chiral perturbation theory without Φ0\Phi_0

This paper completes the argument that lattice simulations of partially quenched QCD can provide quantitative information about QCD itself, with the aid of partially quenched chiral perturbation theory. A barrier to doing this has been the inclusion of $\Phi_0$, the partially quenched generalization of the $\eta'$, in previous calculations in the partially quenched effective theory. This invalidates the low energy perturbative expansion, gives rise to many new unknown parameters, and makes it impossible to reliably calculate the relation between the partially quenched theory and low energy QCD. We show that it is straightforward and natural to formulate partially quenched chiral perturbation theory without $\Phi_0$, and that the resulting theory contains the effective theory for QCD without the $\eta'$. We also show that previous results, obtained including $\Phi_0$, can be reinterpreted as applying to the theory without $\Phi_0$. We contrast the situation with that in the quenched effective theory, where we explain why it is necessary to include $\Phi_0$. We also compare the derivation of chiral perturbation theory in partially quenched QCD with the standard derivation in unquenched QCD. We find that the former cannot be justified as rigorously as the latter, because of the absence of a physical Hilbert space. Finally, we present an encouraging result: unphysical double poles in certain correlation functions in partially quenched chiral perturbation theory can be shown to be a property of the underlying theory, given only the symmetries and some plausible assumptions.Comment: 45 pages, no figure

Simulations with different lattice Dirac operators for valence and sea quarks

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a "mixed" action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.Comment: 17 pages, 1 ps figure (2 clarification paragraphs added

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

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

Finite temperature effects in Coulomb blockade quantum dots and signatures of spectral scrambling

The conductance in Coulomb blockade quantum dots exhibits sharp peaks whose spacings fluctuate with the number of electrons. We derive the temperature-dependence of these fluctuations in the statistical regime and compare with recent experimental results. The scrambling due to Coulomb interactions of the single-particle spectrum with the addition of an electron to the dot is shown to affect the temperature-dependence of the peak spacing fluctuations. Spectral scrambling also leads to saturation in the temperature dependence of the peak-to-peak correlator, in agreement with recent experimental results. The signatures of scrambling are derived using discrete Gaussian processes, which generalize the Gaussian ensembles of random matrices to systems that depend on a discrete parameter -- in this case, the number of electrons in the dot.Comment: 14 pages, 4 eps figures included, RevTe

Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields

We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.Comment: 40 pages, JHEP styl

The potential of effective field theory in NN scattering

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

A comparison of limited-stretch models of rubber elasticity

In this paper we describe various limited-stretch models of non-linear rubber elasticity, each dependent on only the first invariant of the left Cauchy-Green strain tensor and having only two independent material constants. The models are described as limited-stretch, or restricted elastic, because the strain energy and stress response become infinite at a finite value of the first invariant. These models describe well the limited stretch of the polymer chains of which rubber is composed. We discuss Gent's model which is the simplest limited-stretch model and agrees well with experiment. Various statistical models are then described: the one-chain, three-chain, four-chain and Arruda-Boyce eight-chain models, all of which involve the inverse Langevin function. A numerical comparison between the three-chain and eight-chain models is provided. Next, we compare various models which involve approximations to the inverse Langevin function with the exact inverse Langevin function of the eight-chain model. A new approximate model is proposed that is as simple as Cohen's original model but significantly more accurate. We show that effectively the eight-chain model may be regarded as a linear combination of the neo-Hookean and Gent models. Treloar's model is shown to have about half the percentage error of our new model but it is much more complicated. For completeness a modified Treloar model is introduced but this is only slightly more accurate than Treloar's original model. For the deformations of uniaxial tension, biaxial tension, pure shear and simple shear we compare the accuracy of these models, and that of Puso, with the eight-chain model by means of graphs and a table. Our approximations compare extremely well with models frequently used and described in the literature, having the smallest mean percentage error over most of the range of the argument

Where Does the Alignment Score Distribution Shape Come from?

Alignment algorithms are powerful tools for searching for homologous proteins in databases, providing a score for each sequence present in the database. It has been well known for 20 years that the shape of the score distribution looks like an extreme value distribution. The extremely large number of times biologists face this class of distributions raises the question of the evolutionary origin of this probability law

Deconstructing 1S0 nucleon-nucleon scattering

A distorted-wave method is used to analyse nucleon-nucleon scattering in the 1S0 channel. Effects of one-pion exchange are removed from the empirical phase shift to all orders by using a modified effective-range expansion. Two-pion exchange is then subtracted in the distorted-wave Born approximation, with matrix elements taken between scattering waves for the one-pion exchange potential. The residual short-range interaction shows a very rapid energy dependence for kinetic energies above about 100 MeV, suggesting that the breakdown scale of the corresponding effective theory is only 270MeV. This may signal the need to include the Delta resonance as an explicit degree of freedom in order to describe scattering at these energies. An alternative strategy of keeping the cutoff finite to reduce large, but finite, contributions from the long-range forces is also discussed.Comment: 10 pages, 2 figures (introduction revised, references added; version to appear in EPJA

Spin and interaction effects in quantum dots: a Hartree-Fock-Koopmans approach

We use a Hartree-Fock-Koopmans approach to study spin and interaction effects in a diffusive or chaotic quantum dot. In particular, we derive the statistics of the spacings between successive Coulomb-blockade peaks. We include fluctuations of the matrix elements of the two-body screened interaction, surface-charge potential, and confining potential to leading order in the inverse Thouless conductance. The calculated peak-spacing distribution is compared with experimental results.Comment: 5 pages, 4 eps figures, revise