arXiv subjects

M. Wakamatsu

Publications and source records attributed to M. Wakamatsu.

At least 19 recordsLinked to original sources

arXiv2020

The physics of helical electron beam in a uniform magnetic field as a testing ground of gauge principle

According to Bliokh et al., allowing free propagation along the direction of a uniform magnetic field, the familiar Landau electron state can be regarded as a non-diffracting version of the helical electron beam propagating along the magnetic field. Based on this observation, they argued that, while propagating along the magnetic field, the Landau electrons receive characteristic rotation with three different angular velocities, depending on the eigen-value $m$ of the canonical OAM operator, which is generally gauge-variant, and this splitting was in fact experimentally confirmed. Through complete analyses of highly mysterious $m$-dependent rotational dynamics of the quantum Landau states, we try to make clear how and why their observation does not contradict the widely-believed gauge principle.

quant-ph↗

arXiv2018

The issue of gauge choice in the Landau problem and the physics of canonical and mechanical orbital angular momenta

One intriguing issue in the nucleon spin decomposition problem is the existence of two types of decompositions, which are representably characterized by two different orbital angular momenta (OAMs) of quarks. The one is the manifestly gauge-invariant mechanical OAM, while the other is the so-called gauge-invariant canonical (g.i.c.) OAM, the concept of which was introduced by Chen et al. To get a deep insight into the difference of these two decompositions, it is therefore vitally important to understand the the physical meanings of the above two OAMs correctly. Also to be clarified is the implication of the gauge symmetry that is immanent in the concept of g.i.c. OAM. We find that the famous Landau problem provides us with an ideal tool to answer these questions owing to its analytically solvable nature. After deriving a complete relation between the standard eigen-functions of the Landau Hamiltonian in the Landau gauge and in the symmetric gauge, we try to unravel the physics of the the canonical OAM and the mechanical OAM, by paying special attention to their gauge-dependence. We also argue that, different from the mechanical OAM of the electron, the canonical OAM or its gauge-invariant version would not correspond to any direct observables at least in the Landau problem. Also briefly discussed is the uniqueness or non-uniqueness problem of the nucleon spin decomposition, which arises from the arbitrariness in the definition of the so-called physical component of the gauge field.

hep-ph↗

arXiv2010

Gauge- and frame-independent decomposition of nucleon spin

In a recent paper, we have shown that the way of gauge-invariant decomposition of the nucleon spin is not necessarily unique, but there still exists a preferable decomposition from the observational viewpoint. What was not complete in this argument is a fully satisfactory answer to the following questions. Does the proposed gauge-invariant decomposition, especially the decomposition of the gluon total angular momentum into its spin and orbital parts, correspond to observables which can be extracted from high-energy deep-inelastic-scattering measurements ? Is this decomposition not only gauge-invariant but also Lorentz frame-independent, so that it is legitimately thought to reflect an intrinsic property of the nucleon ? We show that we can answer both of these questions affirmatively, by making full use of a gauge-invariant decomposition of covariant angular momentum tensor of QCD in an arbitrary Lorentz frame.

hep-ph↗

arXiv2010

On Gauge-Invariant Decomposition of Nucleon Spin

We investigate the relation between the known decompositions of the nucleon spin into its constituents, thereby clarifying in what respect they are common and in what respect they are different essentially. The decomposition recently proposed by Chen et al. can be thought of as a nontrivial generalization of the gauge-variant Jaffe-Manohar decomposition so as to meet the gauge-invariance requirement of each term of the decomposition. We however point out that there is another gauge-invariant decomposition of the nucleon spin, which is closer to the Ji decomposition, while allowing the decomposition of the gluon total angular momentum into the spin and orbital parts. After clarifying the reason why the gauge-invariant decomposition of the nucleon spin is not unique, we discuss which decomposition is more preferable from the experimental viewpoint.

hep-ph↗

arXiv2010

The role of orbital angular momentum in the proton spin

The orbital angular momenta $L^u$ and $L^d$ of up and down quarks in the proton are estimated as functions of the energy scale as model-independently as possible, on the basis of Ji's angular momentum sum rule. This analysis indicates that $L^u - L^d$ is large and negative even at low energy scale of nonperturbative QCD, in contrast to Thomas' similar analysis based on the refined cloudy bag model. We pursuit the origin of this apparent discrepancy and suggest that it may have a connection with the fundamental question of how to define quark orbital angular momenta in QCD.

hep-ph↗

arXiv2010

Flavor asymmetry of the polarized sea-quark distributions in the proton

The recent global analysis of helicity parton distributions, which takes into account available data from inclusive and semi-inclusive polarized deep inelastic scattering, as well as from polarized proton-proton scattering at RHIC, appears to offer the first strong evidence that polarized sea-quark distributions are flavor asymmetric, i.e. $Δ\bar{u}(x) \ne Δ\bar{d}(x)$. We point out that the flavor symmetry breaking pattern indicated by their analysis, i.e. $Δ\bar{u}(x) > 0$ and $Δ\bar{d}(x) < 0$ with the magnitude correlation $|Δ\bar{u}(x)| < |Δ\bar{d}(x)|$, is just consistent with our theoretical predictions given several years ago on the basis of the chiral quark soliton model. We also address ourselves to understanding the physics behind this observation.

hep-ph↗

arXiv2009

Can the Feynman-Hellmann theorem be used to separate the connected- and disconnected-diagram contributions to the nucleon sigma term ?

In recent lattice QCD studies, the Feynman-Hellmann theorem is often used to estimate separate contributions of the connected and disconnected diagrams to the nucleon sigma term. We demonstrate through a simple analysis within an effective model of QCD why this could be dangerous although the theorem is naturally expected to hold for the sum of the two contributions, i.e. the net nucleon sigma term.

hep-ph↗

arXiv2009

Chiral Quark Soliton Model and Nucleon Spin Structure Functions

The chiral quark soliton model (CQSM) is one of the most successful models of baryons at quark level, which maximally incorporates the most important feature of low energy QCD, i.e. the chiral symmetry and its spontaneous breakdown. Basically, it is a relativistic mean-field theory with full account of infinitely many Dirac-sea quarks in a rotational-symmetry-breaking mean field of hedgehog shape. The numerical technique established so far enables us to make a nonperturbative evaluation of Casimir effects (i.e. effects of vacuum-polarized Dirac sea) on a variety of baryon observables. This incompatible feature of the model manifests most clearly in its predictions for parton distribution functions of the nucleon. In this talk, after briefly reviewing several basic features of the CQSM, we plan to demonstrate in various ways that this unique model of baryons provides us with an ideal tool for disentangling nonperturbative aspect of the internal partonic structure of the nucleon, especially the underlying spin structure function of the nucleon.

hep-ph↗

arXiv2009

Transverse momentum distributions of quarks in the nucleon from the Chiral Quark Soliton Model

We report the first calculation of the simplest but most fundamental transverse momentum dependent (TMD) distribution of quarks in the nucleon, i.e. the time-reversal-even unpolarized TMD quark and antiquark distribution with isoscalar combination, within the framework of the chiral quark soliton model. The nonperturbative account of the deformed Dirac-sea quarks within the theoretical scheme enables us to make a reliable predictions not only for the quark distribution but also for the antiquark distribution. We found that the predicted average transverse momentum square $ $ of quarks and antiquarks depends strongly on their longitudinal momentum fraction $x$, which means that the frequently used assumption of factorization in $x$ and $k_\perp$ is significantly violated. It is also found, somewhat unexpectedly, that the average transverse momentum square of antiquarks is considerably larger than that of quarks.

hep-ph↗

arXiv2009

Chiral-odd generalized parton distributions, transversity decomposition of angular momentum, and tensor charges of the nucleon

The forward limit of the chiral-odd generalized parton distributions (GPDs) and their lower moments are investigated within the framework of the chiral quark soliton model (CQSM), with particular emphasis upon the transversity decomposition of nucleon angular momentum proposed by Burkardt. A strong correlation between quark spin and orbital angular momentum inside the nucleon is manifest itself in the derived second moment sum rule within the CQSM, thereby providing with an additional support to the qualitative connection between chiral-odd GPDs and the Boer-Mulders effects. We further confirm isoscalar dominance of the corresponding first moment sum rule, which indicates that the Boer-Mulders functions for the $u$- and $d$-quarks have roughly equal magnitude with the same sign. Also made are some comments on the recent empirical extraction of the tensor charges of the nucleon by Anselmino et al. We demonstrate that a comparison of their result with any theoretical predictions must be done with great care, in consideration of fairly strong scale dependence of tensor charges, especially at lower renormalization scale.

hep-ph↗

arXiv2008

On the physics behind the form factor ratio $μ_p G_E^p (Q^2) / G_M^p (Q^2)$

We point out that there exist two natural definitions of the nucleon magnetization densities : the density $ρ_M^K (r)$ introduced in Kelly's phenomenological analysis and theoretically more standard one $ρ_M (r)$. We can derive an explicit analytical relation between them, although Kelly's density is more useful to disentangle the physical origin of the different $Q^2$ dependence of the Sachs electric and magnetic form factors of the nucleon. We evaluate both of $ρ_M (r)$ and $ρ_M^K (r)$ as well as the charge density $ρ_{ch}(r)$ of the proton within the framework of the chiral quark soliton model, to find a noticeable qualitative difference between $ρ_{ch}(r)$ and $ρ_M^K (r)$, which is just consistent with Kelly's result obtained from the empirical information on the Sachs electric and magnetic form factors of the proton.

nucl-th↗

arXiv2008

Phenomenological analysis of the nucleon spin contents and their scale dependence

In the past few years, a lot of evidences have been accumulated, which indicate that the gluon polarization inside the nucleon is likely to be small at least at the low renormalization scales. On the other hand, the recent lattice QCD analyses suggest that the net orbital angular momentum carried by the quarks is nearly zero. There is also some indication noticed by Brodsky and Gardner based on the COMPASS observation of small single-spin asymmetry on the isoscalar deuteron target, that the gluon orbital angular momentum inside the nucleon is likely to be small. Naively combining all these observations, we are led to a rather embarrassing conclusion that the nucleon constituents altogether do not carry enough amount of angular momentum saturating the total nucleon spin. We show that this somewhat confused state of affairs can be cleared up only by paying careful attention to the scale dependencies of the nucleon spin decomposition.

hep-ph↗

arXiv2007

Photoproduction of neutral kaons on the liquid deuterium target in the threshold region

The photoproduction process of neutral kaons on a liquid deuterium target is investigated near the threshold region, Egamma = 0.8-1.1 GeV. K0 events are reconstructed from positive and negative pions, and differential cross sections are derived. Experimental momentum spectra are compared with those calculated in the spectator model using a realistic deuteron wave function. Elementary amplitudes as given by recent isobar models and a simple phenomenological model are used to study the effect of the new data on the angular behavior of the elementary cross section. The data favor a backward-peaked angular distribution of the elementary n(gamma,K0)Lambda process, which provides additional constraints on current models of kaon photoproduction. The present study demonstrates that the n(gamma,K0)Lambda reaction can provide key information on the mechanism of the photoproduction of strangeness.

nucl-ex↗

arXiv2007

Comparative Analysis of Transversities and Longitudinally Polarized Distributions of the Nucleon

We carry out a comparative analysis of the transversities and the longitudinally polarized parton distribution functions in light of the first empirical extraction of the transversity distributions recently done by Anselmino et al. It is shown that the precise determination of the isoscalar tensor charge, which is defined as the 1st moment of the isoscalar combination of the transversity distributions, is of fundamental importance for clarifying the internal spin structure function of the nucleon.

hep-ph↗

arXiv2007

Comparative analysis of the transversities and the longitudinally polarized distribution functions of the nucleon

A first empirical extraction of the transversity distributions for the $u$- and $d$-quarks has been done by Anselmino {\it et al.} based on the combined global analysis of the measured azimuthal asymmetries in semi-inclusive deep inelastic scatterings and those in $e^+ e^- \to h_1 h_2 X$ processes. Although with large uncertainties, the determined transversity distributions already appear to reveal a remarkable qualitative difference with the corresponding longitudinally polarized distributions. We point out that this difference contains very important information on internal spin structure of the nucleon.

hep-ph↗

arXiv2007

On the D-term of the nucleon generalized parton distributions

It is known that some of the deeply-virtual-Compton-scattering observables, for instance, the beam-charge asymmetry in the hard electroproduction of real photons on the nucleon, are extremely sensitive to the magnitude of D-term appearing in the parameterization of the generalized parton distributions. We report a theoretical analysis of both the isoscalar and isovector parts of the nucleon D-term within the framework of the chiral quark soliton model, without recourse to the derivative expansion type approximation used in previous works.

hep-ph↗

arXiv2007

On the new COMPASS measurement of the deuteron spin-dependent structure function $g_1^d$

Very recently, a new measurement of the deuteron spin-dependent structure function $g_1^d (x)$ was reported by the COMPASS group. A main change from the old SMC measurement is a considerable improvement of the statistical accuracy in the low $x$ region $0.004 < x < 0.03$. We point out that the new COMPASS data for $g_1^d (x)$ as well as their QCD fits for $ΔΣ$ and $Δs + Δ\bar{s}$ are all remarkably close to our theoretical predictions given several years ago based on the chiral quark soliton model.

hep-ph↗

arXiv2006

Photo-production of neutral kaons on 12C in the threshold region

Kaon photo-production process on $^{12}$C has been studied by measuring neutral kaons in a photon energy range of 0.8$-$1.1 GeV. Neutral kaons were identified by the invariant mass constructed from two charged pions emitted in the $K^{0}_{S}\toπ^{+}π^{-}$ decay channel. The differential cross sections as well as the integrated ones in the threshold photon energy region were obtained. The obtained momentum spectra were compared with a Spectator model calculation using elementary amplitudes of kaon photo-production given by recent isobar models. Present result provides, for the first time, the information on $n(γ,K^{0})Λ$ reaction which is expected to play an important role to construct models for strangeness production by the electromagnetic interaction. Experimental results show that cross section of $^{12}{\rm C}(γ,K^0)$ is of the same order to that of $^{12}{\rm C}(γ,K^+)$ and suggest that slightly backward $K^0$ angular distribution is favored in the $γn\to K^0Λ$ process.

nucl-ex↗