In the anomaly equation for the singlet axial current the chiral limit of the quark mass term does not vanish but comprises contribution from fermion zero modes whose integral exactly cancels the topological charge arising from the Adler-Bell-Jackiw anomaly. This signals chiral symmetry and opens a window for restoring the status of Goldstone boson for the singlet $η^\prime$ without having to invoke the large $N_c$ limit in the underlying QCD. We construct the anomaly term in the effective action that incorporates the chiral symmetry property and yet accounts for the excess mass of $η^\prime$ only when chiral symmetry is broken explicitly by the quark masses. The anomaly term in the present scenario thus plays the role of a catalytic agent that enhances the mass of $η^\prime$ so that the singlet axial current obeys the popular PCAC condition.
The 't Hooft model for the two-dimensional QCD in the limit of infinite number of colours is studied in the axial gauge. The mass-gap and the bound-state equations are derived using the two consequent Bogoliubov-like transformations. Chiral properties of the model are studied in the Hamiltonian and matrix approaches to the latter. Special attention is payed to the explicit pionic solution of the bound-state equation.
We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form …
We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field $b$, in the framework of algebraic renormalization -- a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector $b$.
Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the ``proton spin problem" on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading or…
We re-evaluate our model predictions in Phys. Rev. D 79, 013002 (2009) for different observables in neutrino induced coherent pion production. This comes as a result of the new improved fit to old bubble chamber data of the dominant axial C_5^A nucleon-to-Delta form factor. We find an increase of 20%-30% in the values for the total cross sections. Uncertainties induced by the errors in the determination of C_5^A are computed. Our new results turn out to be compatible within about $1σ$ with the former ones. We also stress the existing tension between the recent experimental determination of the…
We revisit the dynamics of the axial coupling between many N-flatons and an Abelian gauge field, with special attention to its statistically anisotropic signal. The anisotropic power spectrum of curvature perturbations associated to the large wavelength modes of the gauge vector field is generally undetectable, since the anisotropy is confined to small scales. If the gauge field is the electromagnetic field, provided that the number of fields participating in the exponential expansion is large, it could be possible to generate sizable large scale magnetic fields. However, its spectrum is blue,…
In this paper we re-examine how to utilize the previous proposed color-octet axial-vector boson $Z_{\rm C}$ to explain the $3.4σ$ anomaly of $t\bar t$ forward-backward (FB) asymmetry $A_{\rm FB}$ for $m_{t\bar t}> 450$GeV observed by CDF. Our numerical results indicate that the best-fit parameters are $g_A^q=0.07$, $g_A^Q=3$, and $M_{\rm C}=440\text{GeV}$, which are obtained by fitting the mass dependent $A_{\rm FB}$ and total cross section data provided by a recent CDF measurement. Here $g_A^q (g_A^Q)$ and $M_{\rm C}$ are the axial couplings among $Z_{\rm C}$ with the first two (the third) ge…
The concept of effective field theory leads in a natural way to a construction principle for phenomenological sensible models known under the name of the Cheshire Cat Principle. We review its formulation in the chiral bag scenario and discuss its realization for the flavor singlet axial charge. Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. The presence of this surface term allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for th…
An implicit four dimensional regularization is applied to calculate the axial-vector-vector anomalous amplitude. The present technique always complies with results of Dimensional Regularization and can be easily applied to processes involving odd numbers of $γ_5$ matrices. This is illustrated explicitely in the example of this letter.
The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is reanalyzed in the unitary gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the 't Hooft-Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_μ^2/m_Z^2$. The…
We reconsider the DMO sum rule in light of our recent two-loop calculations of isospin and hypercharge vector and axialvector current propagators in chiral perturbation theory. A modified derivation valid to second order in the light quark masses is presented, and a phenomenological analysis yields determination of a combination of finite counterterms occurring in the p^4 and p^6 chiral lagrangians. Suggestions are given for further study.
The SU(3) quark model encounters a great challenge in describing even-parity mesons. Specifically, the $q\bar q$ quark model has difficulties in understanding the light scalar mesons below 1 GeV, scalar and axial-vector charmed mesons and $1^+$ charmonium-like state $X(3872)$. A common wisdom for the resolution of these difficulties lies on the coupled channel effects which will distort the quark model calculations. In this work, we focus on the near mass degeneracy of scalar charmed mesons, $D_{s0}^*$ and $D_0^{*0}$, and its implications. Within the framework of heavy meson chiral perturbatio…
The one-loop QED and electroweak radiative corrections to neutrino-deuteron scattering induced by the neutral current are reexamined, paying a particular attention to the constant term which has never been treated properly in literature. This problem is closely related to the definition of the axial-vector coupling constant $g_{A}$ and requires thorough calculations of the constant terms in the charged current processes, too. We find that the radiative corrections to the neutral current induced reactions amount to 1.7 (1.5) per cent enhancement, if the Higgs boson mass is $m_{H}=1.5 \: m_{Z} (…
The tau -> pi pi pi nu_tau decay is driven by the hadronization of the axial-vector current. Within the resonance chiral theory, and considering the large-Nc expansion, this process has been studied in Ref.[1]. In the light of later developments we revise here this previous work by including a new off-shell width for the lightest a_1 resonance that provides a good description of the tau -> pi pi pi nu_tau spectrum and branching ratio. We also consider the role of the rho(1450) resonance in these observables. Thus we bring in an overall description of the tau -> pi pi pi nu_tau process in excel…
In the calculation of the anomalous magnetic moment of $W^\pm$ bosons, we discuss vector anomalies occuring in the fermion loop that spoil the predictive power of the theory. While the previous analyses were limited to using essentially the manifestly covariant dimensional regularization method, we extend the analysis using both the manifestly covariant formulation and the light-front hamiltonian formulation with several different regularization methods. In the light-front dynamics (LFD), we find that the zero-mode contribution to the helicity zero-to-zero amplitude for the $W^\pm$ gauge boson…
We re-analyse the perturbative radiative corrections to the Higgs mass within the Standard Model in the light of the Taylor-Lagrange renormalization scheme. This scheme naturally leads to completely finite corrections, depending on an arbitrary dimensionless scale. This formulation avoids very large individual corrections to the Higgs mass. In other words, it is a confirmation that the so-called fine-tuning problem in the Standard Model is just an artefact of the regularization scheme and should not lead to any physical interpretation in terms of the energy scale at which new physics should sh…
We study negative modes around the Coleman-de Luccia bounce solution. The conditions for the appearance of an infinite number of the negative modes do not coincide between Lagrangian and Hamiltonian formulations in the literature, and we discuss the origin of this difference in detail. We show how different choices of the variable for the fluctuation around the bounce solution affect the negative mode condition in the Hamiltonian approach, and point out that there exists a choice which gives the same negative mode condition as the Lagrangian approach.
Because of an old quasar APM 08279+5255 at $z=3.91$, some dark energy models face the challenge of the cosmic age problem. It has been shown by Wei and Zhang [Phys. Rev. D {\bf 76}, 063003 (2007)] that the holographic dark energy model is also troubled with such a cosmic age problem. In order to accommodate this old quasar and solve the age problem, we propose in this Letter to consider the interacting holographic dark energy in a non-flat universe. We show that the cosmic age problem can be eliminated when the interaction and spatial curvature are both involved in the holographic dark energy …
A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integral equation is converted into an algebraic eigenvalue problem that can be solved by standard methods. The proposed scheme is very simple to use, is easy in programming and highly accurate.
It is argued that Weinberg's approach to the nucleon-nucleon (NN) interaction problem within effective field theory provides a consistent power counting for renormalized diagrams. Within this scheme the NN potential is organized as an expansion in terms of small quantities like small external momenta and the pion mass (divided by the characteristic large scale of the effective theory). Physical observables to any given order in these small quantities are calculated from the solutions of the Lippmann-Schwinger (or Schr\" odinger) equation.
It is shown that the specific space distribution of the nucleon axial charge may lead to the significant reduction of the cross section of the reaction $p+p\to D+e^++ν$ and may provide the mechanism to explain observed deficit of solar neutrinos.
We emphasise the relation between the spin structure of the proton and the axial U(1) problem. New experiments motivated by the proton spin problem which could shed light on the nature of U(1) symmetry breaking in QCD are discussed.
