A Lorentz and gauge symmetry preserving regularization method has been proposed recently in 4 dimension based on Euclidean momentum cutoff. It is shown that the triangle anomaly can be calculated unambiguously with this new improved cutoff. The anticommutator of γ^{5} and γ^μ multiplied by five gamma is proportional to terms that do not vanish under a divergent loop-momentum integral, but cancel otherwise.
The U(1) triangle anomaly is present, as an infra-red divergence, in the six-reggeon triple-regge interaction vertex obtained from a maximally non-planar Feynman diagram in the full triple-regge limit of three-to-three quark scattering.
It is shown that the triangle anomaly is present, as an infra-red divergence, in the six-reggeon triple-regge interaction vertex obtained from a maximally non-planar Feynman diagram in the full triple-regge limit of three-to-three quark scattering. A multi-regge asymptotic dispersion relation formalism can be used to isolate all anomaly contributions and to discuss when and how there is a cancelation.
We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We show that the presence of $I_2$ can induce neutral pion ($π^0$) condensation in the QCD vacuum through the electromagnetic triangle anomaly. Within the frameworks of chiral perturbation theory at leading small-momenta expansion as well as the Nambu--Jona-Lasinio model at leading $1/N_c$ expansion, we quantify the dependence of the $π^0$ condensate on $I_2$. The stability of the $π^0$-condensed vacuum against the Schwinger charged pair producti…
Weyl semimetals possess massless chiral quasi-particles, and are thus affected by the triangle anomalies. We discuss the features of the chiral magnetic and chiral vortical effects specific to Weyl semimetals, and then propose three novel phenomena caused by the triangle anomalies in this material: 1) anomaly cooling; 2) charge transport by soliton waves as described by the Burgers' equation, and 3) the shift of the BKT phase transition of superfluid vortices coupled to Weyl fermions. In addition, we establish the conditions under which the chiral magnetic current exists in real materials.
We revisit the role of the chiral "triangle" anomaly in deeply inelastic scattering (DIS) of electrons off polarized protons employing a powerful worldline formalism. We demonstrate how the triangle anomaly appears at high energies in the DIS box diagram for the polarized proton structure function $g_1(x_B,Q^2)$ in both the Bjorken limit of large $Q^2$ and in the Regge limit of small $x_B$. We show that the operator product expansion is not required to extract the anomaly in either asymptotics though it is sufficient in the Bjorken limit. Likewise, the infrared pole in the anomaly arises in bo…
Hadronic electroweak corrections to the muon anomalous magnetic moment (g-2) are reviewed. Emphasis is on clarification of discrepancies among various published studies. A theorem on non-renormalization of the transversal part of a correlator of two vector currents and an axial current is reviewed and its consequences in the form of superconvergent sum rules are discussed.
Reggeized gluon interactions due to a single quark loop are studied in the full triple-regge limit and in closely related helicity-flip helicity-pole limits. Triangle diagram reggeon interactions are generated that include local axial-vector effective vertices. It is shown that the massless quark triangle anomaly is present as a chirality-violating infra-red divergence in the interactions generated by maximally non-planar Feynman diagrams. An asymptotic dispersion relation formalism is developed which provides a systematic counting of anomaly contributions. The asymptotic amplitude is written …
The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in \cite{LR}. The method is realized in the initial dimension of theory without modifying the original lagrangian, it preserves symmetries under non-Abelian gauge and Poincare transformations in spite of the existence of two intrinsic mass scales $M_c$ and $μ_s$ which actually play the roles of UV- and IR-cut off respectively. The axialvector-vector-vector (AVV) triangle diagrams in massless and massive QED are evaluated explicitly by using the loop …
The QCD anomaly coupling of $η'-g-g$ is treated as the axial vector current triangle anomaly. By assuming the divergent axial vector coupling of the $η'$ meson with the quark line in the triangle diagram, we calculate the QCD anomaly of $η'-g-g$ as well as the QED anomaly of $η'-γ-γ$ with only one common parameter $κ_{η'}$. We obtain consistent results of the branching ratios for $B\toη' X_s, J/ψ\toη'γ$ and $η'\to γγ$ when comparing with experimental data.
The recent BaBar measurements of the $γγ^{*}\to π^{0}$ form factor show spectacular deviation from perturbative QCD computations for large space-like $Q^{2}$. At $34\,\rm GeV^{2}$ the data are more than 50% larger than theoretical predictions. Stimulated by these new experimental results, we revisit our previous paper on triangle loop effects related to chiral anomaly, and apply our method to the $γ+ γ^* \to π^0$ form factor measured in the single tag mode $e^{+} + e^{-}\to e^{+} + e^{-} + π^{0}$ with one highly virtual photon. The resultant form factor $F(Q^{2})$ - which depends on only one p…
The Adler-Bell-Jackiw anomaly for massive particles is studied in an external magnetic field. The contributions of the mean spin and the pseudoscalar are accounted for in the quasiclassical approximation. The equation for the evolution of the magnetic helicity with the new quantum corrections is derived. We show that the quantum contribution to the helicity evolution can overcome the classical one in the dense degenerate matter which can be present in the core of a neutron star. The application of the obtained results for the interpretation of magnetar bursts are discussed.
Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop AVV amplitude is equal to zero. According to the Vainshtein's theorem the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for tha case of finite fermion mass in the triangle loop.
We consider the experimental implications of the axial current triangle diagram anomaly in a hydrodynamic description of high density QCD. We propose a signal of an enhanced production of spin-excited hadrons in the direction of the rotation axis in off-central heavy ion collisions.
We investigate the properties of the amplitude induced by the anomaly. In a relatively high energy region those amplitudes are constructed by the vector meson poles and the anomaly terms, in which the anomaly terms can be essentially evaluated by the triangle quark graph. We pay our attention to the anomaly term and make intensive analysis of the existing experimental data, i.e., the electromagnetic $π^0$ and $ω$ transition form factors. Our result shows that it is essential to use the constituent quark mass instead of the current quark mass in evaluating the anomaly term from the triangle gra…
Within renormalizable theories the triangle diagram correctly reproduces the lifetime of the neutral pion $π^0$. However, effective relativistic quark models which contain a second scale besides the quark mass seem unable to give the correct value for this quantity. In the Instanton Liquid Model this second scale is the mean instanton radius, in the NJL model it is the cutoff. The role of the cutoff within a path integral derivation of the chiral anomaly is clarified and the importance of higher order terms contributing to the $π^0$ decay width and other anomalous processes is pointed out.
In [1], we demonstrated that the structure function $g_1(x_B,Q^2)$ measured in polarized deeply inelastic scattering (DIS) is dominated by the triangle anomaly in both the Bjorken limit of large $Q^2$ and the Regge limit of small $x_B$. In the worldline formulation of quantum field theory, the triangle anomaly arises from the imaginary part of the worldline effective action. We show explicitly how a Wess-Zumino-Witten term coupling the topological charge density to a primordial isosinglet ${\bar η}$ arises in this framework. We demonstrate the fundamental role played by this contribution both …
The Standard Model calculation of $H\rightarrowγγ$ has the curious feature of being finite but regulator-dependent. While dimensional regularization yields a result which respects the electromagnetic Ward identities, additional terms which violate gauge invariance arise if the calculation is done setting $d=4$. This discrepancy between the $d=4-ε$ and $d=4$ results is recognized as a true ambiguity which must be resolved using physics input; as dimensional regularization respects gauge invariance, the $d=4-ε$ calculation is accepted as the correct SM result. However, here we point out another …
A Lorentz and gauge symmetry preserving regularization method is discussed in four dimension based on momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom of shift of the loop momentum to define the evaluation of the terms carrying even number of Lorentz indices, e.g. proportional to $k_μk_ν$. The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are free of ambiguities coming from subtractions in non-trivial cases. Finite parts of the result are equal with the results of dimensional…
The high-temperature plasma above the electroweak scale $\sim 100$ GeV may have contained a primordial hypercharge magnetic field whose anomalous coupling to the fermions induces a transformation of the hypermagnetic energy density into fermionic number. In order to describe this process, we generalize the ordinary magnetohydrodynamical equations to the anomalous case. We show that a not completely homogeneous hypermagnetic background induces fermion number fluctuations, which can be expressed in terms of a generic hypermagnetic field configuration. We argue that, depending upon the various pa…
It is pointed out that in the $331-$like model which uses both fundamental and complex conjugate representations for an assignment of the representations to the left-handed quarks and the scalar representation to their corresponding right-handed counterparts, the nature of the scalar should be taken into account in order to make the fermion triangle anomalies in the theory anomaly-free, i.e. renormalizable in a sense with no anomalies, even after the spontaneous symmetry breaking.
Nambu--Jona-Lasinio (NJL) model with Kobayashi-Maskawa-'t Hooft (KMT) term is one of low energy effective theory of QCD which includes the $U_A(1)$ anomaly. We investigate nonet meson properties in this model with three flavors of quarks. We employ two type of regularizations the dimensional and sharp cutoff ones. The model parameters are fixed phenomenologically for each regularization. Evaluating the kaon decay constant, the $η$ meson mass and the topological susceptibility, we show the regularization dependence of the results and discuss the applicability of the NJL model.
The infrared divergent scalar three-point integrals are evaluated by the loop regularization method. Three kinds of infrared divergent integrals, i.e., massless triangle diagram, triangle diagrams with one and two massive internal lines, are systematically evaluated by loop regularization, analytic results are obtained. According the method, the infrared divergences are regulated by the so-called sliding scale $μ_{s}$ which plays the role of infrared cutoff. The amplitudes obtained through loop regularization depend on $μ_{s}$ such that we may extract different contribution by varying $μ_{s}$.…
We derive a universal relation for the transverse part of triangle anomalies within a class of theories whose gravity dual is described by the Yang-Mills-Chern-Simons theory. This relation provides a set of sum rules involving the masses, decay constants and couplings between resonances, and leads to the formulas for the matrix elements of the vector and axial currents in the presence of the soft electromagnetic field. We also discuss that this relation is valid in real QCD at least approximately. This may be regarded as the anomaly matching for resonances as an analogue of that for the massle…
Infra-red properties of the triangle anomaly and the ``anomaly pole'' are elaborated and applied to the study of high-energy scattering in QCD, when the gauge symmetry is partially broken to SU(2). It is shown that the chiral flavor anomaly provides a wee-gluon component for Goldstone bosons that combines with interactions due to the U(1) anomaly to produce an infra-red transverse momentum scaling divergence in scattering amplitudes. After the divergence is factorized out, as a wee-gluon condensate in the infinite momentum pion, the remaining physical amplitudes have confinement and chiral sym…
The loop momenta of a single Feynman diagram in momentum space can be assigned unambiguously within the 'Dyson scheme' without referring to the other Feynman diagrams in the complete set to some order of coupling constant for the certain process. This fact and the scheme which were provided in Dyson's original paper are applied to a typical relevant problem, i.e., the triangle diagrams of the 'axial vector current anomaly'. The calculation is done in four-dimension Minkowski space-time straightforwardly without the aid of any regularization. The linearly divergent terms are canceled sans incer…
We analyse Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet interacting with a massless Majorana spin-$1/2$ field in the adjoint representation of $SU(2)$. We shed light on a long-standing controversy regarding the perturbative evaluation of the supercurrent anomaly in connection with gauge and superconformal symmetry in different frameworks. We find that only superconformal symmetry is unambiguously broken using an invariant …
We present detailed arguments and calculations in support of our recent proposal to identify the axion arising in the solution of the strong CP problem with the Majoron, the (pseudo-)Goldstone boson of spontaneously broken lepton number symmetry. At low energies, the associated $U(1)_L$ becomes, via electroweak parity violation and neutrino mediation, indistinguishable from an axial Peccei-Quinn symmetry in relation to the strong interactions. The axionic couplings are then fully computable in terms of known SM parameters and the Majorana mass scales. The determination of these couplings invol…
With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion makes an octonion, and the gauge field can be treated as self-dual, we calculate the axial current and two vector currents triangle diagram of Bardeen, which yields the contribution of the axial anomaly. The octonion possesses the triality symmetry, and there are 5 symmetry operations $G_{ij}$ and $G_{ijk}$ ($ijk=123)$, in which mixing of spinors and vectors occur. $G_{23}$ does not mix vectors and spinors, but mismatch of the spinor and vector fields occurs. …
In light of the recent 750 GeV diphoton anomaly observed at the LHC, we study the possibility of accommodating the deviation from the standard model prediction based on the recently proposed Gauged Two Higgs Doublet Model. The model embeds two Higgs doublets into a doublet of a non-abelian gauge group $SU(2)_H$, while the standard model $SU(2)_L$ right-handed fermion singlets are paired up with new heavy fermions to form $SU(2)_H$ doublets, and $SU(2)_L$ left-handed fermion doublets are singlets under $SU(2)_H$. An $SU(2)_H$ scalar doublet, which provides masses to the new heavy fermions as we…
Massive $U(1)$ gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity. We study four-dimensional, chiral $U(1)$ gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions. We show that such theories require to be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled -- a Stückelberg limit does not exist. When the infrared fermion spectrum contains a mixed $U(1)$-gravitational…
A search for supersymmetry anomalies requires an examination of the BRS cohomology of supersymmetric Yang-Mills coupled to chiral matter, and the physically interesting (on-shell) anomalies are those which cannot be eliminated using the equations of motion. An analysis of this cohomology problem shows that the simplest situation where a physically interesting supersymmetry anomaly can arise is when: 1. the anomaly occurs in the renormalization of a composite antichiral spinor superfield operator constructed from the chiral matter in the theory, 2. the anomalous diagrams are one-loop triangle d…
Within a spontaneously broken gauge group we carefully analyse and calculate triple gauge boson vertices dominated by triangle one-loop Feynman diagrams involving heavy fermions compared to external momenta and gauge boson masses. We perform our calculation strictly in four dimensions and derive a general formula for the off-shell, one-particle irreducible (1PI) effective vertex which satisfies the relevant Ward Identities and the Goldstone boson equivalence theorem. Our goal is to search for non-decoupling heavy fermion effects highlighting their synergy with gauge chiral anomalies. Particula…
The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff $Ł$ and the boundary conditions for the relevant couplings. The physical theory is obtained at $Ł=0$. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point $Ł=Ł_0\to\infty$ but at the physical value $Ł=0$. As an illustration, we compute the triangle axial anomalies.
We analyze the role of Lorentz symmetry in the perturbative non-gravitational anomalies for a single family of fermions. The theory is assumed to be translational invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators. We study the conservation of global and gauge currents associate with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are…
Gauge invariant topological interactions, such as the D=5 Chern-Simons terms, are required in models in extra dimensions that split anomaly free representations. The Chern-Simons term is necessary to maintain the overall anomaly cancellations of the theory, but it can have significant, observable, physical effects. The CS-term locks the KK-mode parity to the parity of space-time, leaving a single parity symmetry. It leads to new processes amongst KK-modes, eg, the decay of a KK-mode to a 2-body final state of KK-modes. A formalism for the effective interaction amongst KK-modes is constructed, …
On asymptotically and anomaly-free SU(N) chiral gauge theories for arbitrarily large N
Illinois Center for Advanced Studies of the Universe（伊利诺伊大学宇宙高级研究中心）；Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）
We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter current…
