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Masashi Wakamatsu

Publications and source records attributed to Masashi Wakamatsu.

At least 19 recordsLinked to original sources
arXiv2026

Chiral Quark Soliton Model And Nucleon Parton Distribution Functions

The chiral quark soliton model (CQSM) is an effective quark model of baryons maximally taking account of the most important feature of low-energy QCD, i.e., the spontaneous chiral symmetry breaking of the QCD vacuum and the associated appearance of Nambu--Goldstone pions. It shares many common features with the famous Skyrme model in that the baryons are viewed as rotating hedgehog objects in both models. Despite many similarities, it turned out that the CQSM can give more realistic predictions on most baryon observables. Above all, a decisive advantage of the CQSM over the Skyrme-like models is that it can handle non-local quark--quark correlations in baryons, which is absolutely impossible within the framework of effective meson theories. This feature is decisively important for making theoretical predictions on the quark distribution functions inside the nucleon, which are defined as nucleon matrix elements of bilinear quark operators with light-cone separation. In the present paper, we try to elucidate why and how the CQSM can give successful predictions for a variety of types of nucleon quark distribution functions, especially for the flavor asymmetry of the unpolarized and longitudinally polarized sea-quark (anti-quark) distribution functions in the nucleon.

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arXiv2025

On the role of induced electric field in the time-dependent Aharonov-Bohm effect

Whether the time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate. There are two factors complicating the problem. First, in the closed spacetime line integral of the vector potential that is thought to give the AB-phase shift, how to treat the time-varying vector potential is highly nontrivial. Second, the time-varying magnetic flux generates induced electric field even outside the solenoid. In the present paper, motivated by a recent work by Gao, we re-investigate the role of the induced electric field with the utmost care. This analysis reveals a highly nontrivial effect of the induced electric field, which turns out to be useful for verifying the very existence of the time-dependent AB-effect.

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arXiv2025

Unveiling the role of vector potential in the Aharonov-Bohm effect

The most popular interpretation of the Aharonov-Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle's wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, not a few researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-locality. This frustrating situation is shortly summarized by the statement of Aharonov et al. that the AB effect may be due to a local gauge potential or due to non-local gauge-invariant fields. In the present paper, we shall give several convincing arguments, which support the viewpoint that the vector potential is not just a convenient mathematical tool with little physical entity. Despite its gauge arbitrariness, the vector potential certainly contains a gauge-invariant piece, which solely explains the observed AB phase shift. Importantly, this component has a property such that it is basically unique and cannot be eliminated by any regular gauge transformations. To make the discussion complete, we also discuss the role of remaining gauge arbitrariness still contained in the entire vector potential.

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arXiv2025

Is gauge symmetry vacuous or physical ? : Lessons from the Landau problem as a solvable quantum gauge theoretical system

The gauge symmetry is one of the most important concepts in modern physics, but there are two conflicting views on its meaning or interpretation. The standard view is that local gauge symmetry is the basis of the pursue of fundamental particles and forces in nature. Another view is that the gauge symmetry is not a symmetry of nature but just a redundancy in description. Naturally, both statements are nothing wrong, but one might feel that there is a slight conceptual conflict between the two points of view. Due to the subtlety of the subject, however, little literature exists that discusses the root of such an anxiety. In the present paper, by making full use of the analytically solvable nature of the quantum Landau problem, we argue that the familiar gauge principle plays a critical role in unraveling a subtle mismatch between the two viewpoints above. We reveal that there exist two types of quantities in gauge theories, which should clearly be discriminated. The first are quantities, which look seemingly gauge-invariant but actually not, whereas the second are genuinely gauge-invariant quantities, which correspond to direct experimental observables.

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arXiv2025

On the time-dependent Aharonov-Bohm effect and the 4-dimensional Stokes theorem

The time-dependent Aharonov-Bohm (AB) effect considers the situation in which the magnetic flux inside the solenoid changes time-dependently. Different from the standard AB-effect, the problem is unexpectedly subtle and not easy to solve without any doubt, which is the reason why it is still in a state of unsettlement even theoretically. The difficulty originates from the fact that its theoretical analysis requires line-integrals of the time-dependent vector potential along paths in the 4-dimensional Minkowski space. Owing to the 4-dimensional Stokes theorem, this closed line-integral of the vector potential can be related to the integral of the electric and magnetic fields over the 2-dimensional area, the boundary of which is given by the above-mentioned closed path. The central controversy concerns the success or failure of the claim by Singleton and collaborators based on the 4-dimensional Stokes theorem, which states that the time-dependent part of the AB-phase shift due to the magnetic vector potential is precisely cancelled by the effect of induced electric field generated by the time-variation of the magnetic flux. In the present paper, we carefully reanalyze their cancellation argument by going back to the basic quantum mechanical analysis of the charged particle motion under the presence of the time-dependent external electromagnetic potential combined with more careful treatment of the 4-dimensional Stokes theorem. Careful analysis of the 4-dimensional Stokes theorem shows that the cancellation argument by Singleton et al. is partially correct but their central claim that only the time-independent part of the magnetic field contributes to the AB-phase shift so that there is no time-dependent AB-effect is not justified, thereby supporting likely existence of the time-dependent AB-effect.

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arXiv2025

Extraordinary nature of the nucleon scalar charge and its densities as a signal of nontrivial vacuum structure of QCD

It is widely known that the nucleon scalar charge is proportional to the pion-nucleon sigma term as one of the important low energy observables of QCD. Especially interesting to us is the physics of the nucleon scalar charge densities. This comes from the fact that the corresponding operator has the same quantum number as the physical vacuum. It indicates unusual behavior of the the nucleon scalar density as a function of the distance $r$ from the nucleon center. Namely, it would not be reduced down to zero at the spatial infinity but rather approaches some nonzero constant corresponding to the vacuum quark condensate. Naturally, this unique nature of the nucleon scalar density in the position space also affects the corresponding density in the momentum space, i.e. the corresponding parton distribution function (PDF) as a function of the Bjorken variable $x$. This PDF is known as the chiral-odd twist-3 PDF $e (x)$. We argue that $e(x)$ is likely to have a delta-function type singularity at $x=0$, and that the appearance of this singularity can be interpreted as a signal of the nontrivial vacuum structure of the QCD.

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arXiv2024

Is the Aharonov-Bohm phase shift for a non-closed path a measurable quantity ?

There recently appear some interesting attempts to explain the AB-effect through the interaction between the charged particle and the solenoid current mediated by the exchange of a virtual photon. A vital assumption of this approach is that AB-phase shift is proportional to the change of the interaction energy between the charged particle and solenoid along the path of the moving charge. Accordingly, they insist that the AB-phase change along a path does not depend on the gauge choice so that the AB-phase shift for a non-closed path is in principle measurable. We however notice the existence of two fairly different discussions on the interaction energy between the solenoid and a charge particle, the one is due to Boyer and the other is due to Saldanha and others. In the present paper, based on a self-contained quantum mechanical treatment of the combined system of a solenoid, a charged particle, and the quantized electromagnetic fields, we show that both interaction energies of Boyer and of Saldanha are in fact gauge invariant at least for non-singular gauge transformations but they are destined to cancel each other. Our analysis rather shows that the origin of the AB-phase can be traced back to other part of our effective Hamiltonian. Furthermore, based on the path-integral formalism with our effective Lagrangian, we explicitly demonstrate that the AB-phase shift for a non-closed path is not a gauge-variant quantity, which means that it would not correspond to direct experimental observables.

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arXiv2022

Physical symmetries and gauge choices in the Landau problem

Due to a special nature of the Landau problem, in which the magnetic field is uniformly spreading over the whole two-dimensional plane, there necessarily exist three conserved quantities, i.e. two conserved momenta and one conserved orbital angular momentum for the electron, independently of the choice of the gauge potential. Accordingly, the quantum eigen-functions of the Landau problem can be obtained by diagonalizing the Landau Hamiltonian together with one of the above three conserved operators with the result that the quantum mechanical eigen-functions of the Landau problem can be written down for arbitrary gauge potential. The purpose of the present paper is to clarify the meaning of gauge choice in the Landau problem based on this gauge-potential-independent formulation, with a particular intention of unraveling the physical significance of the concept of gauge-invariant-extension of the canonical orbital angular momentum advocated in recent literature on the nucleon spin decomposition problem. At the end, our analysis is shown to disclose a physically vacuous side face of the gauge symmetry.

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arXiv2021

Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem

As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron. The eigen-energies of the system depend only on the first quantum number $n$, and the second quantum number $m$ does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a {\it gauge-variant} quantity, and observation of a gauge-variant quantity would contradict a fundamental principle of physics called the {\it gauge principle}. In recent researches, however, Bliohk et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly non-trivial $m$-dependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number $m$ in the Landau eigen-states corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number $m$ in the Landau eigen-states was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the {\it particle-like} aspect but also to the {\it wave-like} aspect of the Landau electron.

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arXiv2020

Role of guiding center in Landau level system and mechanical and pseudo orbital angular momenta

There is an interesting but not so popular quantity called pseudo orbital angular momentum (OAM) in the Landau-level system, besides the well-known canonical and mechanical OAMs. The pseudo OAM can be regarded as a gauge-invariant extension of the canonical OAM, which is formally gauge invariant and reduces to the canonical OAM in a certain gauge. Since both of the pseudo OAM and the mechanical OAM are gauge invariant, it is impossible to judge which of those is superior to the other solely from the gauge principle. However, these two OAMs have totally different physical meanings. The mechanical OAM shows manifest observability and clear correspondence with the classical OAM of the cyclotron motion. On the other hand, we demonstrate that the standard canonical OAM as well as the pseudo OAM in the Landau problem are the concepts which crucially depend on the choice of the origin of the coordinate system. We try to reveal the relation between the pseudo OAM and the mechanical OAM as well as their observability by paying special attention to the role of guiding-center operator in the Landau problem.

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arXiv2019

A still unsettled issue in the nucleon spin decomposition problem : On the role of surface terms and gluon topology

In almost all the past analyses of the decomposition of the nucleon spin into its constituents, surface terms are simply assumed to vanish and not to affect the integrated sum rule of the nucleon spin. However, several authors claim that neglect of surface terms is not necessarily justified, especially owing to possible nontrivial topological configuration of the gluon field in the QCD vacuum. There also exist some arguments indicating that the nontrivial gluon topology would bring about a delta-function type singularity at zero Bjorken variable into the longitudinally polarized gluon distribution function, thereby invalidating a naive partonic sum rule for the total nucleon spin. In the present paper, we carefully examine the role of surface terms in the nucleon spin decomposition problem. We shall argue that surface terms do not prevent us from obtaining a physically meaningful decomposition of the nucleon spin. In particular, we demonstrate that nontrivial topology of the gluon field would not bring about a delta-function type singularity into the longitudinally polarized gluon distribution functions. We also make some critical comments on the recent analyses of the role of surface terms in the density level decomposition of the total nucleon angular momentum as well as that of the total photon angular momentum.

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arXiv2018

The role of electron orbital angular momentum in the Aharonov-Bohm effect revisited

This is a brief review on the theoretical interpretation of the Aharonov-Bohm effect, which also contains our new insight into the problem. A particular emphasis is put on the unique role of electron orbital angular momentum, especially viewed from the novel concept of the physical component of the gauge field, which has been extensively discussed in the context of the nucleon spin decomposition problem as well as the photon angular momentum decomposition problem. Practically, we concentrate on the frequently discussed idealized setting of the Aharonov-Bohm effect, i.e. the interference phenomenon of the electron beam passing around the infinitely-long solenoid. One of the most puzzling observations in this Aharonov-Bohm solenoid effect is that the pure-gauge potential outside the solenoid appears to carry non-zero orbital angular momentum. Through the process of tracing its dynamical origin, we try to answer several fundamental questions of the Aharonov-Bohm effect, which includes the question about the reality of the electromagnetic potential, the gauge-invariance issue, and the non-locality interpretation, etc.

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arXiv2016

Unravelling the physical meaning of the Jaffe-Manohar decomposition of the nucleon spin

A general consensus now is that there are two physically inequivalent complete decompositions of the nucleon spin, i.e. the decomposition of the canonical type and that of mechanical type. The well-known Jaffe-Manohar decomposition is of the former type. Unfortunately, there is a wide-spread misbelief that this decomposition matches the partonic picture, which states that motion of quarks in the nucleon is approximately free. In the present monograph, we reveal that this understanding is not necessarily correct and that the Jaffe-Manohar decomposition is not such a decomposition, which natively reflects the intrinsic (or static) orbital angular momentum structure of the nucleon.

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arXiv2015

On the two remaning issues in the gauge-invariant decomposition problem of the nucleon spin

The question whether the total gluon angular momentum in the nucleon can be decomposed into its spin and orbital parts without conflict with the gauge-invariance principle has been an object of long-lasting debate. Despite a remarkable progress achieved through the recent intensive researches, the following two issues still remains to be clarified more transparently. The first issue is to resolve the apparent conflict between the proposed gauge-invariant decomposition of the total gluon angular momentum and the textbook statement that the total angular momentum of the photon cannot be gauge-invariantly decomposed into its spin and orbital parts. We show that this problem is also inseparably connected with the uniqueness or non-uniqueness problem of the nucleon spin decomposition. The second practically more important issue is that, among the two physically inequivalent decompositions of the nucleon spin, i.e. the "canonical" type decomposition and the "mechanical" type decomposition, which can we say is more physical or closer to direct observation ? In the present paper, we try to answer both these questions as clearly as possible.

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arXiv2014

Flavor structure of the unpolarized and longitudinally-polarized sea-quark distributions in the nucleon

It is now widely recognized that a key to unravel the nonperturbative chiral-dynamics of QCD hidden in the deep-inelastic-scattering observables is the flavor structure of sea-quark distributions in the nucleon. We analyze the flavor structure of the nucleon sea in both of the unpolarized and longitudinally polarized parton distribution functions (PDFs) within a single theoretical framework of the flavor SU(3) chiral quark soliton model (CQSM), which contains only one adjustable parameter $Δm_s$, the effective mass difference between the strange and nonstrange quarks. A particular attention is paid to a nontrivial correlation between the flavor asymmetry of the unpolarized and longitudinally polarized sea-quark distributions and also to a possible particle-antiparticle asymmetry of the strange quark distributions in the nucleon. We also investigate the charge-symmetry-violation (CSV) effects in the parton distribution functions exactly within the same theretical framework, which is expected to provide us with valuable information on the relative importance of the asymmetry of the strange and antistrange distributions and the CSV effects in the valence-quark distributions inside the nucleon in the resolution scenario of the so-called NuTeV anomaly in the extraction of the Weinberg angle.

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arXiv2014

Is gauge-invariant complete decomposition of the nucleon spin possible ?

Is gauge-invariant complete decomposition of the nucleon spin possible? Although it is a difficult theoretical question which has not reached a complete consensus yet, a general agreement now is that there are at least two physically inequivalent gauge-invariant decompositions (I) and (II) of the nucleon. %The one is a nontrivial gauge-invariant %generalization of the Jaffe-Manohar decomposition. %The other is an extension of the Ji decomposition, which allows %a gauge-invariant decomposition of the total gluon angular %momentum into the intrinsic spin and orbital parts. In these two decompositions, the intrinsic spin parts of quarks and gluons are just common. What discriminate these two decompositions are the orbital angular momentum parts. The orbital angular momenta of quarks and gluons appearing in the decomposition (I) are the so-called "mechanical" orbital angular momenta, while those appearing in the decomposition (II) are the generalized (gauge-invariant) "canonical" ones. By this reason, these decompositions are also called the "mechanical" and "canonical" decompositions of the nucleon spin, respectively. A crucially important question is which decomposition is more favorable from the observational viewpoint. The main objective of this concise review is to try to answer this question with careful consideration of recent intensive researches on this problem.

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arXiv2013

Are there infinitely many decompositions of the nucleon spin ?

We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. It is crucialy important to recognize the fact that the standard gauge fixing procedure is essentially a process of projecting out the physical components of the massless gauge field. A complexity of the nonabelian gauge theory as compared with the abelian case is that a closed expression for the physical component can be given only with use of the non-local Wilson line, which is generally path-dependent. It is known that, by choosing an infinitely long straight-line path in space and time, the direction of which is characterized by a constant 4-vector $n^μ$, one can cover a class of gauge called the general axial gauge, containing three popular gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within this general axial gauge, we have calculated the 1-loop evolution matrix for the quark and gluon longitudinal spins in the nucleon. We found that the final answer is exactly the same independently of the choices of $n^μ$, which amounts to proving the gauge-independence and path-independence simultaneously, although within a restricted class of gauges and paths. By drawing on all of these findings together with well-established knowledge from gauge theories, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.

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