arXiv subjects

Koji Harada

Publications and source records attributed to Koji Harada.

At least 19 recordsLinked to original sources

arXiv2024

Saddle-point approximation to the false vacuum decay at finite temperature in one-dimensional quantum mechanics

We calculate the false-vacuum decay rate in one-dimensional quantum mechanics on the basis of the saddle-point approximation in the Euclidean path integral at finite temperature. The saddle points are the finite-T and shifted bounce solutions, which are finite-period analogs of the (zero-temperature) bounce solution, and the shot solutions. We re-examined the zero-temperature result by Callan and Coleman and compare with the zero-temperature limit of our results. We also perform some numerical calculations to illustrate the temperature dependence of the decay rate and compare it with the result by Affleck.

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arXiv2016

Numerical study of renormalization group flows of nuclear effective field theory without pions on a lattice

We formulate the next-to-leading order nuclear effective field theory without pions in the two-nucleon sector on a spatial lattice, and investigate nonperturbative renormalization group flows in the strong coupling region by diagonalizing the Hamiltonian numerically. The cutoff (proportional to the inverse of the lattice constant) dependence of the coupling constants is obtained by changing the lattice constant with the binding energy and the asymptotic normalization constant for the groundstate being fixed. We argue that the critical line can be obtained by looking at the finite-size dependence of the groundstate energy. We determine the relevant operator and locate the nontrivial fixed point, as well as the physical flow line corresponding to the deuteron in the two-dimensional plane of dimensionless coupling constants. It turns out that the location of the nontrivial fixed point is very close to the one obtained by the corresponding analytic calculation, but the relevant operator is quite different.

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arXiv2013

Convergent perturbative nuclear effective field theory

We consider the nuclear effective field theory including pions in the two-nucleon sector in the S waves up to including the next-to-next-to-leading order (NNLO) terms according to the power counting suggested by the Wilsonian renormalization group analysis done in a previous paper. We treat only the leading contact interaction nonperturbatively, and the rest, including the long-distance part of pion exchange, are treated as perturbations. To define the long-distance part, it is important to introduce a separation scale, or a cutoff. We employ a hybrid regularization, in which the loops with only contact interactions are regularized with Power Divergence Subtraction (PDS), while the loops with (long-distance part of) pion exchange are regularized with a Gaussian damping factor (GDF), to simplify the (nonperturbative) leading-order amplitudes. The scale introduced by PDS is identified with the cutoff of GDF up to a numerical factor. We emphasize that the introduction of the GDF requires a careful definition of the coupling constant for the pion exchange. We obtain the analytic expressions for the phase shifts for the $^1S_0$ and $^3S_1$-$^3D_1$ channels. By fitting them to the Nijmegen partial wave analysis data, it is shown that the effective theory expansion with perturbative long-distance part of pion exchange is converging.

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arXiv2012

Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons

Low-energy effective field theory describing a nonrelativistic three-body system is analyzed in the Wilsonian renormalization group (RG) method. No effective auxiliary field (dimeron) that corresponds to two-body propagation is introduced. The Efimov effect is expected in the case of an infinite two-body scattering length, and is believed to be related to the limit cycle behavior in the three-body renormalization group equations (RGEs). If the one-loop property of the RGEs for the nonrelativistic system without the dimeron field, which is essential in deriving RGEs in the two-body sector, persists in the three-body sector, it appears to prevent the emergence of limit cycle behavior. We explain how the multi-loop diagrams contribute in the three-body sector without contradicting the one-loop property of the RGEs, and derive the correct RGEs, which lead to the limit cycle behavior. The Efimov parameter, $s_{0}$, is obtained within a few percent error in the leading orders. We also remark on the correct use of the dimeron formulation. We find rich RG-flow structure in the three-body sector. In particular, a novel nontrivial fixed point of the three-body couplings is found when the two-body interactions are absent. We also find, on the two-body nontrivial fixed point, the limit cycle is realized as a loop of finite size in the space of three-body coupling constants when terms with derivatives are included.

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arXiv2011

Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions

Pionful nuclear effective field theory (NEFT) in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, $Λ$, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space including up to $\mathcal{O}(p^2)$ and find the nontrivial fixed points in the $^1S_0$ and $^3S_1$--$^3D_1$ channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative.

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arXiv2009

Apparently noninvariant terms of $U(N)\times U(N)$ nonlinear sigma model in the one-loop approximation

We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an inhomogeneous Zinn-Justin equation). In the literature the discussions on ANTs are confined to the SU(2) case. We generalize them to the U(N) case and demonstrate explicitly at the one-loop level that despite the presence of divergent ANTs in the effective action of the "pions", the symmetry is preserved.

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arXiv2009

More about the Wilsonian analysis on the pionless NEFT

We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective theory (NEFT) in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of $\mathcal{O}(p^4)$ in the $S$ waves, and, on the other hand, (2) we consider the RG flows in higher partial waves ($P$ and $D$ waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two ``fixed lines'' and a ``fixed surface'' which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the $S$ waves, but there are \textit{two} relevant directions in the $P$ waves at the nontrivial fixed points and \textit{three} in the $D$ waves. We explain the physical meaning of the $P$-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern, and Richardson, and possible implementation of Power Divergence Subtraction (PDS) in higher partial waves.

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arXiv2009

Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory

Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.

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arXiv2008

Problems in the derivations of the renormalization group equation for the low momentum nucleon interactions

We carefully examine all the four derivations of the renormalization group equation (RGE) for the so-called $\Vlk$ potential, given by Bogner, \textit{et. al.}[nucl-th/0111042]. Two derivations based on the ``semi-group composition law'' are shown to be unjustified, while the other two based on the completeness relation of the model space must be modified if there are bound states. It is however shown that the RGE is unchanged if the bound state wavefunctions in the reduced theory are required to have the same low-momentum components as those in the original theory. Several aspects of the $\Vlk$ approach are also discussed.

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arXiv2006

Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --

The Legendre flow equation, a version of exact Wilsonian renormalization group (WRG) equation, is employed to consider the power counting issues in Nuclear Effective Field Theory. A WRG approach is an ideal framework because it is nonperturbative and does not require any prescribed power counting rule. The power counting is determined systematically from the scaling dimensions of the operators at the nontrivial fixed point. The phase structure is emphasized and the inverse of the scattering length, which is identified as a relevant coupling, is shown to play a role of the order parameter. The relations to the work done by Birse, McGovern, and Richardson and to the Kaplan-Savage-Wise scheme are explained.

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arXiv2006

Wilsonian RG and Redundant Operators in Nonrelativistic Effective Field Theory

In a Wilsonian renormalization group (RG) analysis, redundant operators, which may be eliminated by using field redefinitions, emerge naturally. It is therefore important to include them. We consider a nonrelativisitic effective theory (the so-called ``pionless'' Nuclear Effective Field Theory) as a concrete example and show that the off-shell amplitudes cannot be renormalized if the redundant operators are not included. The relation between the theories with and without such redundant operators is established in the low-energy expansion. We perform a Wilsonian RG analysis for the \textit{off-shell} scattering amplitude in the theory with the redundant operator.

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arXiv2005

Effective Theory Approach to the Skyrme model and Application to Pentaquarks

The Skyrme model is reconsidered from an effective theory point of view. From the most general chiral Lagrangian up to including terms of order $p^4$, $N_c$ and $δm^2$ ($δm\equiv m_s-m$), new interactions, which have never been considered before, appear upon collective coordinate quantization. We obtain the parameter set best fitted to the observed low-lying baryon masses, by performing the second order perturbative calculations with respect to $δm$. We calculate the masses and the decay widths of the other members of (mainly) anti-decuplet pentaquark states. The formula for the decay widths is reconsidered and its baryon mass dependence is clarified.

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arXiv2004

The Skyrme Model Revisited: An Effective Theory Approach and Application to the Pentaquarks

The Skyrme model is reconsidered from an effective theory point of view. Starting with the most general Lagrangian up to including terms of order $p^4$, $N_c$ and $δm^2$ ($δm\equiv m_s-m$), we obtain new interactions, which have never been discussed in the literature. We obtain the parameter set best fitted to the low-lying baryon masses by taking into account the representation mixing up to $\bm{27}$. A prediction for the mainly anti-decuplet excited nucleon $N'$ and $Σ'$ is given.

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arXiv1999

RPA for Light-Front Hamiltonian Field Theory

A self-consistent random phase approximation (RPA) is proposed as an effective Hamiltonian method in Light-Front Field Theory (LFFT). We apply the general idea to the light-front massive Schwinger model to obtain a new bound state equation and solve it numerically.

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arXiv1997

Variational Mass Perturbation Theory for Light-Front Bound-State Equations

We investigate the mesonic light-front bound-state equations of the 't Hooft and Schwinger model in the two-particle, i.e. valence sector, for small fermion mass. We perform a high precision determination of the mass and light-cone wave function of the lowest lying meson by combining fermion mass perturbation theory with a variational approach. All calculations are done entirely in the fermionic representation without using any bosonization scheme. In a step-by-step procedure we enlarge the space of variational parameters. For the first two steps, the results are obtained analytically. Beyond that we use computer algebraic and numerical methods. We achieve good convergence so that the calculation of the meson mass squared can be extended to third order in the fermion mass. Within the numerical treatment we include higher Fock states up to six particles. Our results are consistent with all previous numerical investigations, in particular lattice calculations. For the massive Schwinger model, we find a small discrepancy (less than 2 percent) in comparison with known bosonization results. Possible resolutions of this discrepancy are discussed.

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arXiv1996

Perturbative Tamm-Dancoff Renormalization

A new two-step renormalization procedure is proposed. In the first step, the effects of high-energy states are considered in the conventional (Feynman) perturbation theory. In the second step, the coupling to many-body states is eliminated by a similarity transformation. The resultant effective Hamiltonian contains only interactions which do not change particle number. It is subject to numerical diagonalization. We apply the general procedure to a simple example for the purpose of illustration.

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arXiv1996

Dynamics of the Light-Cone Zero Modes: Theta Vacuum of the Massive Schwinger Model

The massive Schwinger model is quantized on the light cone with great care on the bosonic zero modes by putting the system in a finite (light-cone) spatial box. The zero mode of $A_{-}$ survives Dirac's procedure for the constrained system as a dynamical degree of freedom. After regularization and quantization, we show that the physical space condition is consistently imposed and relates the fermion Fock states to the zero mode of the gauge field. The vacuum is obtained by solving a Schrödinger equation in a periodic potential, so that the theta is understood as the Bloch momentum. We also construct a one-meson state in the fermion-antifermion sector and obtained the Schrödinger equation for it.

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arXiv1995

Six-body Light-Front Tamm-Dancoff approximation and wave functions for the massive Schwinger model

The spectrum of the massive Schwinger model in the strong coupling region is obtained by using the light-front Tamm-Dancoff (LFTD) approximation up to including six-body states. We numerically confirm that the two-meson bound state has a negligibly small six-body component. Emphasis is on the usefulness of the information about states (wave functions). It is used for identifying the three-meson bound state among the states below the three-meson threshold. We also show that the two-meson bound state is well described by the wave function of the relative motion.

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