Chiral perturbation theory with Wilson-type fermions including a2a^2 effects: Nf=2N_f=2 degenerate case

We have derived the quark mass dependence of $m_{\pi}^2$, $m_{\rm AWI}$ and $f_{\pi}$, using the chiral perturbation theory which includes the $a^2$ effect associated with the explicit chiral symmetry breaking of the Wilson-type fermions, in the case of the $N_f=2$ degenerate quarks. Distinct features of the results are (1) the additive renormalization for the mass parameter $m_q$ in the Lagrangian, (2) $O(a)$ corrections to the chiral log ($m_q\log m_q$) term, (3) the existence of more singular term, $\log m_q$, generated by $a^2$ contributions, and (4) the existence of both $m_q\log m_q$ and $\log m_q$ terms in the quark mass from the axial Ward-Takahashi identity, $m_{\rm AWI}$. By fitting the mass dependence of $m_\pi^2$ and $m_{\rm AWI}$, obtained by the CP-PACS collaboration for $N_f=2$ full QCD simulations, we have found that the data are consistently described by the derived formulae. Resumming the most singular terms $\log m_q$, we have also derived the modified formulae, which show a better control over the next-to-leading order correction.Comment: 21 pages, 4 figures (10 eps files), Revtex4, some discussions and references added, the final version to appear in PR

Two-dimensional Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Density

We analytically investigate the 2-dimensional Gross-Neveu model at finite temperature and density using Wilson fermion action. The relation between the phase structure on the lattice and that in the continuum is clarified.Comment: LATTICE98(hightemp), 3 pages, 3 eps figure

Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Chemical Potential

We investigate the phase structure of the two-dimensional lattice Gross-Neveu model formulated with the Wilson fermion action to leading order of 1/N expansion. Structural change of the parity-broken phase under the influence of finite temperature and chemical potential is studied. The connection between the lattice phase structure and the chiral phase transition of the continuum theory is clarified.Comment: 42 pages, 20 EPS figures, using REVTe

Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory

The calculation of the finite lattice spacing corrections for I=2 pi-pi scattering is carried out for isotropic and anisotropic Wilson lattice actions. Pion masses and decay constants are also determined in this context. These results correct the phase shift calculated from the lattice, which is connected to the scattering length and effective range in this low energy scattering process. When in terms of the lattice-physical parameters for either Wilson action, these lattice spacing effects first appear at the next-to-leading order counter-terms.Comment: 15 pages, additional discussion of pion decay constant, version published in PR

Oscillation Frequency Dependence of Non-Classical Rotation Inertia of Solid 4^4He

The non-classical rotational inertia fraction of the identical cylindrical solid $^4$He below 300 mK is studied at 496 and 1173 Hz by a double resonance torsional oscillator. Below 35 mK, the fraction is the same at sufficiently low rim velocities. Above 35 mK, the fraction is greater for the higher than the lower mode. The dissipation peak of the lower mode occurs at a temperature $\sim$ 4 mK lower than that of the higher mode. The drive dependence of the two modes shows that the reduction of the fraction is characterized by critical velocity, \textit{not} amplitude nor acceleration.Comment: 4 pages, 4 figure

Product Development and the Timing of Information Disclosure under U.S.and Japanese Patent Systems

This paper examines the consequences of the differences in the timing of information disclosure between the U.S. and Japanese patent systems. Under the Japanese system it is possible for a firm to apply for a patent knowing the exact specifications of a rival's patent application. In contrast, in the U.S. the only way a firm learns about a rival's innovation is upon the actual granting of the rival's patent. We argue that this difference enables Japanese firms to coordinate their R&D efforts better than their U.S. counterparts and that this, in turn, leads to smaller quality improvements under the Japanese system. We show that the creation/diffusion tradeoff of patents can be influenced not only by the scope and length of patent protection but also by other features of the patenting process.

Enhancement of field renormalization in scalar theories via functional renormalization group

The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the field in the broken phase. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.Comment: 20 pages, 7 figures. To appear in Physical Review

Markov bases and subbases for bounded contingency tables

In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. In general a Markov basis for unbounded contingency table under a certain model differs from a Markov basis for bounded tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for contingency tables whose cell entries are bounded. However, in the process, one has to compute the universal Gr\"obner basis of the ideal associated with the design matrix for a model which is, in general, larger than any reduced Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized problems. In this paper we focus on bounded two-way contingency tables under independence model and show that if these bounds on cells are positive, i.e., they are not structural zeros, the set of basic moves of all $2 \times 2$ minors connects all tables with given margins. We end this paper with an open problem that if we know the given margins are positive, we want to find the necessary and sufficient condition on the set of structural zeros so that the set of basic moves of all $2 \times 2$ minors connects all incomplete contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of Statistical Mathematic

The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur