Showing papers on "Chiral anomaly published in 2001"
TL;DR: In this article, a relativistic chiral unitary approach based on coupled channels was proposed to perform the necessary resummation of the lowest order chiral Lagrangian.
693 citations
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TL;DR: In this article, a number of examples of conical singularities that give chiral fermions are described; the physics can be determined but the metric is not known explicitly, while in others the metric can be described explicitly but the physics is more challenging to understand.
Abstract: M-theory compactification on a manifold X of $G_2$ holonomy can give chiral fermions in four dimensions only if X is singular. A number of examples of conical singularities that give chiral fermions are known; the present paper is devoted to describing some additional examples. In some of them, the physics can be determined but the metric is not known explicitly, while in others the metric can be described explicitly but the physics is more challenging to understand.
285 citations
TL;DR: In this article, the form of the chiral anomaly on an S1/Z2 orbifold with chiral boundary conditions was discussed and it was shown that the 4-divergence of the higher-dimensional current evaluated at a given point in the extra dimension is proportional to the probability of finding the Chiral zero mode there.
135 citations
TL;DR: In this paper, the chiral symmetry aspects of positive and negative parity baryons were studied by identifying them with linear representations of SU (N f ) ⊗ SU(N f ).
Abstract: We study chiral symmetry aspects of the positive and negative parity baryons by identifying them with linear representations of the chiral group SU (N f ) ⊗ SU (N f ). It is shown that there are two distinct schemes: those possessing naive and mirror assignments. We construct linear sigma models for baryons in the two assignments and examine their physical implications. Then we investigate properties of the naive and mirror nucleons microscopically by using QCD interpolating fields. Finally, we propose experiments to distinguish the two chiral assignments for the nucleon.
122 citations
TL;DR: In this article, a discrete quantum field theory on fuzzy manifolds using non-commutative geometry is developed, based on previous treatments of instantons and chiral fermions on fuzzy spaces and especially fuzzy spheres.
Abstract: In continuum physics, there are important topological aspects like instantons, θ-terms and the axial anomaly. Conventional lattice discretizations often have difficulties in treating one or the other of these aspects. In this paper, we develop discrete quantum field theories on fuzzy manifolds using noncommutative geometry. Basing ourselves on previous treatments of instantons and chiral fermions (without fermion doubling) on fuzzy spaces and especially fuzzy spheres, we present discrete representations of θ-terms and topological susceptibility for gauge theories and derive axial anomaly on the fuzzy sphere. Our gauge field action for four dimensions is bounded by a constant times the modulus of the instanton number as in the continuum.
95 citations
TL;DR: In this paper, a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry is presented, along with a scheme for exploring this physics on the lattice.
Abstract: This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, the author discusses how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP-violating parameter \ensuremath{\Theta}. One particularly elegant scheme for exploring this physics on the lattice is presented in some detail. This uses an auxiliary extra space-time dimension, with the physical world being a four-dimensional interface.
92 citations
TL;DR: In this article, a momentum space framework is proposed to treat field-theoretical infinities in perturbative calculations when parity-violating objects occur. But the framework does not handle the subtleties involved when a radiative correction is finite.
Abstract: This is the second in a series of two contributions in which we set out to establish a novel momentum space framework to treat field-theoretical infinities in perturbative calculations when parity-violating objects occur Since no analytic continuation on the space-time dimension is effected, this framework can be particularly useful to treat dimension-specific theories Moreover, arbitrary local terms stemming from the underlying infinities of the model can be properly parametrized We (re)analyze the indeterminacy of the radiatively generated $\mathrm{CPT}$ violating Chern-Simons term within an extended version of ${\mathrm{QED}}_{4}$ and calculate the Adler-Bardeen-Bell-Jackiw triangle anomaly to show that our framework is consistent and general enough to handle the subtleties involved when a radiative correction is finite
88 citations
TL;DR: In this article, the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes were derived for two-pion exchange diagrams at two-loop order.
Abstract: We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3 $MeV at $r=1.0 $fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $\pi N$-scattering amplitude. We also evaluate the one-loop $2\pi$-exchange diagram with two second order chiral $\pi \pi NN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2\pi$-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.
74 citations
TL;DR: The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD as mentioned in this paper, and it may work in nature as well in the future.
Abstract: ▪ Abstract Developments during the past eight years have refuted the folklore that chiral symmetries cannot be preserved on the lattice. The mechanism that permits chiral symmetry to coexist with the lattice is quite general and may work in nature as well. The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD.
71 citations
TL;DR: In this paper, a vector manifestation of the Wigner realization of chiral symmetry is proposed, in which the symmetry is restored at the critical point by the massless degenerate pion and its flavor partners.
Abstract: We propose ``vector manifestation'' (VM) of the Wigner realization of chiral symmetry in which the symmetry is restored at the critical point by the massless degenerate pion (and its flavor partners) and the $\ensuremath{\rho}$ meson (and its flavor partners) as the chiral partner, in sharp contrast to the traditional manifestation \'a la the linear sigma model where the symmetry is restored by the degenerate pion and the scalar meson. The application to the chiral phase transition of large ${N}_{f}$ QCD is performed using the hidden local symmetry Lagrangian. Combined with the Wilsonian matching proposed recently, VM determines the critical number of massless flavors ${N}_{f}\ensuremath{\simeq}5$ without much ambiguity.
66 citations
TL;DR: In the first order chiral perturbation theory, the corrections to Fπ0 and Mπ0 in a magnetic field at finite temperature have been found as mentioned in this paper, and it was shown that they are shifted in such a manner that Gell-Mann--Oakes--Renner relation remains valid under these conditions.
Abstract: In the first order of chiral perturbation theory the corrections to Fπ0 and Mπ0 in a magnetic field at finite temperature have been found. It was shown that they are shifted in such a manner that Gell-Mann--Oakes--Renner relation remains valid under these conditions.
Book•
06 Jul 2001
TL;DR: The Sigma Model Chiral Bag Model Nucleon Properties Large-Nc Baryons Excited Baryon as mentioned in this paper The Sigma Model Symmetries and Wave Functions Chiral Symmetry
Abstract: Ingredients of the Standard Model Symmetries and Wave Functions Chiral Symmetry The Sigma Model Chiral Bag Model Nucleon Properties Large-Nc Baryons Excited Baryons.
TL;DR: In this article, the regularization problem of Weyl fermions from 4+1 dimensions was studied. But the results were limited to the case of 4 + 1 dimensions.
Abstract: Contents: 1. Introduction, 2. Chiral gauge theories & the gauge anomaly, 3. The regularization problem, 4. Weyl fermions from 4+1 dimensions, 5. The Ginsparg-Wilson relation, 6. Gauge-invariant lattice regularization of anomaly-free theories.
TL;DR: In this article, the relativistic corrections to the leading order two-pion exchange diagrams were calculated in baryon chiral perturbation theory and the resulting isovector central and isoscalar spin-spin and tensor amplitudes involve nonstatic terms proportional to the squared nucleon center-of-mass momentum.
Abstract: We calculate in baryon chiral perturbation theory the relativistic ${1/M}^{2}$ corrections to the leading order two-pion exchange diagrams. We give explicit expressions for the corresponding one-loop $\mathrm{NN}$ amplitudes in momentum space. The resulting isovector central and isoscalar spin-spin and tensor $\mathrm{NN}$ amplitudes involve nonstatic terms proportional to the squared nucleon center-of-mass momentum ${p}^{2}.$ From the two-pion exchange box diagrams we obtain an isoscalar quadratic spin-orbit $\mathrm{NN}$ amplitude. We give also analytical expressions for the corresponding $\mathrm{NN}$ potentials in coordinate space. The diagrammatic results presented here make the chiral $\mathrm{NN}$ potential complete at next-to-next-to-next-to-leading order.
TL;DR: In this article, it was shown that in Riemann-cartan spacetimes with torsion, only the Pontrjagin type four-form π-nieh-Yan term arises additionally in the chiral anomaly, but not the NiehYan term as has been claimed in a recent paper.
Abstract: In Riemann-Cartan spacetimes with torsion only its axial covector piece A couples to massive Dirac fields. Using renormalization group arguments, we show that in addition to the familiar Riemannian term only the Pontrjagin type four-form $\mathrm{dA}\ensuremath{\wedge}\mathrm{dA}$ arises additionally in the chiral anomaly, but not the Nieh-Yan term ${d}^{*}A,$ as has been claimed in a recent paper [Phys. Rev. D. 55, 7580 (1997)].
TL;DR: In this paper, conditions for achieving optical asymmetric synthesis using the electric-dipole light-field interaction are derived, where parity requirements are used to show that any optical scenario in which the dynamics of the molecule depends on the overall sign of the electric field allows for control over the production of one chiral species in preference to its mirror image.
Abstract: Conditions for achieving ‘‘optical asymmetric synthesis,’’ an example of controlled chiral symmetry breaking, using the electric-dipole light-field interaction are derived. These include scenarios in which neither the medium nor the light is chiral by itself. Specifically, parity requirements are used to show that any optical scenario in which the dynamics of the molecule depends on the overall sign of the electric field allows for control over the production of one chiral species in preference to its mirror image. A sample laser-molecule scenario is used to demonstrate these conditions.
TL;DR: It is shown that both the apparent success of the constituent quark model in reproducing the ratio of the proton to neutron magnetic moments and the apparentsuccess of the Foldy term in reproduces the observed charge radius of the neutron are coincidental.
Abstract: Understanding hadron structure within the framework of QCD is an extremely challenging problem. In order to solve it, it is vital that our thinking should be guided by the best available insight. Our purpose here is to explain the model-independent consequences of the approximate chiral symmetry of QCD for two famous results concerning the structure of the nucleon. We show that both the apparent success of the constituent quark model in reproducing the ratio of the proton to neutron magnetic moments and the apparent success of the Foldy term in reproducing the observed charge radius of the neutron are coincidental. That is, a relatively small change of the current quark mass would spoil both results.
TL;DR: In this paper, it was shown that noncommutative U(r) gauge theories with a chiral fermion in the adjoint representation can be constructed on the lattice with manifest star-gauge invariance in arbitrary even dimensions.
Abstract: We show that noncommutative U(r) gauge theories with a chiral fermion in the adjoint representation can be constructed on the lattice with manifest star-gauge invariance in arbitrary even dimensions. Chiral fermions are implemented using a Dirac operator which satisfies the Ginsparg-Wilson relation. A gauge-invariant integration measure for the fermion fields can be given explicitly, which simplifies the construction as compared with lattice chiral gauge theories in ordinary (commutative) space-time. Our construction includes the cases where continuum calculations yield a gauge anomaly. This reveals a certain regularization dependence, which is reminiscent of parity anomaly in commutative space-time with odd dimensions. We speculate that the gauge anomaly obtained in the continuum calculations in the present cases can be cancelled by an appropriate counterterm.
01 Jan 2001
TL;DR: In this paper, the covariant coupled-channel Bethe-Salpeter equation with the interaction kernel truncated at chiral order Q 3 is solved, where only those terms which are leading in the large Nc limit of QCD are included.
Abstract: The relativistic chiral SU(3) Lagrangian is used to describe kaonnucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel Bethe-Salpeter equation with the interaction kernel truncated at chiral order Q 3 where we include only those terms which are leading in the large Nc limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large Nc baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU(3) symmetry-breaking eects are well controlled by the combined chiral and large Nc expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of plab ’ 500 MeV.
TL;DR: In this article, a domain wall formulation of lattice fermions is used to simulate two-flavor, finite temperature QCD near the chiral phase transition, and the desired chiral properties are seen for the condensate, suggesting that the domain wall fermion formulation may be an effective approach for numerical study of QCD at finite temperature.
Abstract: The domain wall formulation of lattice fermions is expected to support accurate chiral symmetry, even at finite lattice spacing. Here we attempt to use this new fermion formulation to simulate two-flavor, finite temperature QCD near the chiral phase transition. In this initial study, a variety of quark masses, domain wall heights and domain wall separations are explored using an 8^3 x 4 lattice. Both the expectation value of the Wilson line and the chiral condensate show the temperature dependence expected for the QCD phase transition. Further, the desired chiral properties are seen for the chiral condensate, suggesting that the domain wall fermion formulation may be an effective approach for the numerical study of QCD at finite temperature.
TL;DR: In this paper, it was shown that colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop, and this effect sets in at chiral symmetry restoration temperature $T_{\chi}$.
Abstract: We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature $T_{\chi}$
and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at $T_{\chi}$
is shown to be supported by finite temperature lattice calculations.
TL;DR: In this article, the standard scalar and spinor actions on a d-dimensional manifold are recovered from such actions in the limit of large matrices if their normalizations are correctly scaled as the limit is taken.
Abstract: Previously matrix model actions for "fuzzy" fields have been proposed using noncommutative geometry. They retained "topological" properties extremely well, being capable of describing instantons, θ-states, the chiral anomaly, and even chiral fermions with no "doubling." Here, we demonstrate that the standard scalar and spinor actions on a d-dimensional manifold are recovered from such actions in the limit of large matrices if their normalizations are correctly scaled as the limit is taken.
TL;DR: In this article, the authors studied the dependence of the size of the corresponding eigenvalue of the lattice Dirac operator on the number of SU(3) configurations, which is a systematic expansion in path length of a solution of the Ginsparg-Wilson equation.
TL;DR: In this paper, both the UV and IR origins of the one-loop triangle gauge anomalies for non-Abelian chiral gauge theories with fundamental, adjoint and bi-fundamental fermions for U(N) groups were discussed.
Abstract: We discuss both the UV and IR origins of the one-loop triangle gauge anomalies for noncommutative non-Abelian chiral gauge theories with fundamental, adjoint and bi-fundamental fermions for U(N) groups We find that gauge anomalies only originate from planar triangle diagrams, the nonplanar triangle contributions giving rise to no breaking of the Ward identities Generally speaking, theories with fundamental and bi-fundamental chiral matter are anomalous Theories with only adjoint chiral fermions are anomaly free
TL;DR: In this paper, a non-perturbative calculation of the cross-section of vertices involving pions using a Lagrangian is presented. But their results differ from those of previous calculations.
Abstract: We perform a non-perturbative calculation of the $J/\Psi-\pi$ cross section using a $SU(2)\times SU(2)$ effective Lagrangian. Our results differ from those of previous calculations, specially in the description of vertices involving pions.
CERN1
TL;DR: In this paper, a finite volume correction to the chiral condensate with dynamical quarks was proposed, which diverges logarithmically with the four-volume $V$.
Abstract: Quenched chiral perturbation theory is used to compute the first finite volume correction to the chiral condensate. The correction diverges logarithmically with the four-volume $V$. We point out that with dynamical quarks one can obtain both the chiral condensate and the pion decay constant from the distributions of the lowest Dirac operator eigenvalues.
TL;DR: In this article, the Nieh-Yan topological invariant cannot contribute to the chiral anomaly in spaces with torsion, and the authors respond to the claim by Kreimer and Mielke.
Abstract: We respond to the claim by Kreimer and Mielke to the effect that the Nieh-Yan topological invariant cannot contribute to the chiral anomaly in spaces with torsion.
TL;DR: In this article, the authors present results from numerical simulations of the Gross-Neveu model with a U (1) chiral symmetry and N f = 4 fermion species at nonzero temperature.
TL;DR: In this article, a derivation of the low-energy effective meson Lagrangian of the Nambu-Jona-Lasinio (NJL) model on the basis of Schwinger's proper-time regularization of the one-loop fermion determinant is presented.
Abstract: We present a derivation of the low-energy effective meson Lagrangian of the Nambu -- Jona-Lasinio (NJL) model on the basis of Schwinger's proper-time regularization of the one-loop fermion determinant. We consider the case in which the $SU(2)\times SU(2)$ chiral symmetry of the NJL Lagrangian is broken by the current quark mass matrix with $\hat{m}_u
e\hat{m}_d$. The non-degeneracy of $d$ and $u$ masses destroys one of the most crucial features of the proper-time expansion -- the chiral-invariant structure of Seeley -- DeWitt coefficients. We show however that systematic resummations inside the proper-time expansion are still possible and derive a result which is in full agreement with the chiral Ward -- Takahashi identities.