Boaz Keren-Zur, Yaron Oz
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.
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We show that a chiral nonlinear sigma model coupled to degenerate neutrons exhibits a ferromagnetic phase at high density. The magnetization is due to the axial anomaly acting on the parallel layers of neutral pion domain walls spontaneously formed at high density. The emergent magnetic field would reach the QCD scale ~ 10^19 [G], which suggests that the quantum anomaly can be a microscopic origin of the magnetars (highly magnetized neutron stars).
The important role played by chiral symmetry and axial anomaly in QCD in nuclear physics is reviewed. Some recent topics on possible chiral restoration in hot and/or dense matter are picked up. We also discuss so called {\em effective} restoration of chiral anomaly hot and/or dense matter, as may be seen in a character change of $η'$ meson.
Gribov viewed the axial anomaly as a manifestation of the collective motion of charged fermions with arbitrarily high momenta in the vacuum. In the presence of an external magnetic field and a chirality imbalance, this collective motion becomes directly observable in the form of the electric current - this is the chiral magnetic effect (CME). I give an elementary introduction into the physics of CME, and discuss some recent developments.
New hidden particles could potentially be emitted and discovered in rare nuclear transitions. In this work we investigate the production of hidden vector bosons with primarily axial couplings to light quarks in nuclear transitions, and we apply our results to the recent anomaly seen in $^8$Be decays. The relevant matrix elements for $^8{\rm Be}^*(1^+) \rightarrow ^8{\rm Be} (0^+)$ transitions are calculated using ${\it ab \, initio}$ methods with inter-nucleon forces derived from chiral effective field theory and the in-medium similarity renormalization group. We find that the emission of a li…
The generation of a chiral shift parameter in the normal ground state of magnetized relativistic matter is discussed. The chiral shift contributes to the axial current density, but does not modify the conventional axial anomaly relation. The analysis based on gauge invariant regularization schemes suggests that this finding is also valid in gauge theories. We argue that the chiral shift parameter can affect observable properties of compact stars. In the regime of heavy ion collisions, the chiral shift parameter can modify the key features of the chiral magnetic effect.
Nucleon matrix elements of axial anomaly, axial currents and pseudoscalar currents in the QCD sum rule
利用QCD求和规则，分析核子与轴反常、轴流及赝标量流耦合常数，表达为夸克、胶子及部分子分布矩的矩阵元，并考虑非对角贡献。
We investigate the phase structure of massless three-flavor QCD by extending the Nambu-Jona- Lasinio model to include the effects of confinement and the axial anomaly. We study the interplay between the chiral and diquark condensates induced by the axial anomaly, as well as their relationship with the Polyakov loop, which parameterizes confinement. By minimizing the thermodynamic potential we construct the QCD phase diagram and investigate the possibility of realizing a recently discovered low temperature critical point and an associated BEC-BCS crossover. We also perform a Ginzburg-Landau exp…
The $γ^* π^0 \rightarrow γ$ form factor, including the extension off the pion mass-shell, is obtained from a generalized impulse approximation within a QCD-based model field theory known to provide an excellent description of the pion charge form factor. This approach implements dressing of the vertex functions and propagators consistent with dynamical chiral symmetry breaking, gauge invariance, quark confinement and perturbative QCD. Soft nonperturbative behavior, dictated by the axial anomaly, is found to evolve to the perturbative QCD limit only for \mbox{$Q^2 \geq 20~{\rm GeV}^2$}.
We study the QCD phase structure in the three-flavor Nambu-Jona-Lasinio model, incorporating the interplay between the chiral and diquark condensates induced by the axial anomaly. We demonstrate that for an appropriate range of parameters of the model, the interplay leads to the low temperature critical point in the phase structure predicted by a previous Ginzburg-Landau analysis. We also show that a Bose-Einstein condensate (BEC) of diquark molecules emerges in the intermediate density region, and as a result, a BEC-BCS crossover is realized with increasing quark chemical potential.
Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from non-conservation of the flavor-singlet current. Similar non-conservation also leads to the axial ano…
The axial anomaly is responsible for the masses and mixing of the mesons $η$ and $η'$. An open question is if (and to what extent) it affects also other hadrons. We show that anomalous terms can be important to understand the spectroscopy of the pseudotensor mesons $η_2 (1645)$ and $η_2 (1870)$. In fact, pseudotensor mesons belong to a so-called heterochiral multiplet, for which a quadratic mixing term between nonstrange and strange isoscalar members arises. On the contrary, for so-called homochiral multiplets, such as the ground-state (axial-)vector and tensor mesons, this mixing is not possi…
The contribution of axial anomaly to charge symmetry breaking in pion-nucleon coupling constants is calculated within instanton model for QCD vacuum. It has been demonstrated that the contribution is large and allows to explain Nolen-Schiffer anomaly.
Motivated by an apparent puzzle of the light-front vacua incompatible with the axial anomaly, we have considered the two-dimensional massless Schwinger model for an arbitrary interpolating angle of the quantization surface. By examining spectral deformation of the Dirac sea under an external electric field semiclassically, we have found that the axial anomaly is quantization angle independent. This indicates an intricate nontrivial vacuum structure present even in the light-front limit.
The $SU(2)_A \times U(2)_V$-symmetric chiral linear sigma model in the presence of the axial anomaly is studied in the local-potential approximation of the Functional Renormalization Group (FRG). The renormalization group (RG) flow is investigated in a truncation which reproduces recent results for the $U(2)_A \times U(2)_V$-symmetric model in the limit of vanishing axial anomaly strength. We search for the conjectured O(4) fixed point in the presence of the $U(1)_A$ anomaly and analyze its stability properties.
This paper has been withdrawn by authors for significant modification.
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 study flavor mixing and the axial anomaly in QCD at zero and finite temperature. Using the instanton liquid model, we show that the strength of the anomaly is essentially unchanged near the critical temperature for chiral symmetry restoration. We demonstrate that nevertheless, chiral symmetry restoration has important consequences for the eta and eta prime. In particular, the strange and non-strange components of the eta unmix near T_c. The anomaly does not affect the strange eta, so we expect a light purely strange pseudoscalar meson near the phase transition.
The phase diagram of strongly interacting matter is studied within a three-flavor Nambu--Jona-Lasinio model, which contains the coupling between chiral and diquark condensates through the axial anomaly. Our results show that it is essential to include the 2SC phase in the analysis. While this is expected for realistic strange quark masses, we find that even for equal up, down, and strange bare quark masses, 2SC pairing can be favored due to spontaneous flavor-symmetry breaking by the axial anomaly. This can lead to a rich phase structure, including BCS- and BEC-like 2SC and CFL phases and new …
Perturbative results of matrix elements of the axial current and their relation with the axial anomaly
本文用微扰QCD计算胶子靶的局域与非局域轴矢流矩阵元，揭示轴反常与夸克质量贡献间的抵消机制及其与角动量守恒的关系。
The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: 1) by splitting of coordinates in the expression for the axial current and 2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advanta…
We investigate meson and nucleon dynamics at finite baryon density and temperature by coupling the nucleon field and the omega meson to the three-flavor linear sigma model and calculate hadronic properties around the nuclear liquid-gas transition. We apply the functional renormalization group method, and find that mesonic fluctuations increase the strength of the coefficient of the $U_A(1)$ breaking determinant operator as a function of the chiral condensate. As a consequence, we find that the actual value of the anomaly increases discontinuously at the first order nuclear liquid-gas transitio…
We discuss a connection between axial anomaly and polarized radiative processes. By comparison with the corresponding unpolarized cases, we consider some physical outputs for the $π^+$ and $Z^0$ polarized radiative decays. We analyse in detail the pattern of mass singularity cancellation.
Manifestations of strong and electromagnetic axial anomalies in two-photon decays of $η$ and $η'$ mesons are studied. Applying dispersive approach to axial anomaly in the singlet current, we obtain an anomaly sum rule containing strong and electromagnetic anomaly contributions. The relevant low energy theorem was generalized to the case of mixed states and used to evaluate the subtraction constant of the strong anomaly-related form factor $\langle 0 |G\tilde{G} |γγ\rangle$. We made a numerical estimation of the contributions of gluon and electromagnetic anomalies to the two-photon decays of $η…
The induced axial current and the chiral anomaly are studied in the normal phase of magnetized relativistic matter. A special attention is paid to the role of the chiral shift parameter Delta, leading to a relative shift of the longitudinal momenta in the dispersion relations of opposite chirality fermions. In the Nambu-Jona-Lasinio model, it is shown directly from the form of the gap equation that Delta necessarily exists in the normal phase in a magnetic field. By making use of the gauge invariant point-splitting regularization, we then show that the presence of Delta essentially modifies th…
Motivated by the ongoing measurements of the Primakoff process pi- gamma* --> pi- pi0 by COMPASS collaboration at CERN, the transition form factor for the canonical anomalous process gamma* --> pi+ pi0 pi- is calculated in a constituent quark loop model. The simplest contribution to this process is the quark "box" amplitude. In the present paper we also explicitly include the vector meson degrees of freedom, i.e., the rho and the omega, thus giving rise to additional, resonant contributions. We find that in order to satisfy the axial anomaly result, a further subtraction in the resonant part i…
The prescription for the $γ_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.
Many meson processes are related to the U_A(1) axial anomaly, present in the Feynman graphs where fermion loops connect axial vertices with vector vertices. However, the coupling of pseudoscalar mesons to quarks does not have to be formulated via axial vertices. The pseudoscalar coupling is also possible, and this approach is especially natural on the level of the quark substructure of hadrons. In this paper we point out the advantages of calculating these processes using (instead of the anomalous graphs) the graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate espec…
In this paper, we consider finite isospin chiral perturbation theory including the effects of the axial anomaly (through the Wess-Zumino-Witten term) in a strong magnetic field. We firstly prove that in a strong external magnetic field ($H_{\rm ext}$) or more precisely the Schwinger limit, where photon back-reactions are suppressed, only neutral pions can condense and the condensation of charged pions is forbidden. Secondly, we find that the $π^{0}$ domain wall is an example of a phase that can exist in a strong magnetic field and suggest the existence of a new phase transition line from the n…
The axial anomaly contribution to generalized longitudinal-transverse polarizability $δ_{LT}^{}$ is calculated within Regge approach. It is shown that the contribution from the exchange of the $a_1^{}(1260)$ Regge trajectory is nontrivial and might have the key role to explain the large difference between the predictions of chiral perturbation theory and the experimental data for the neutron $δ_{LT}^{}$. We also present the prediction for the proton $δ_{LT}^{}$, which will be measured at the Thomas Jefferson National Accelerator Facility in near future.
Effects of a flavor singlet vector interaction in the Polyakov - Nambu - Jona-Lasinio (PNJL) model are studied in combination with the axial U(1) breaking Kobayashi - Maskawa - 't Hooft interaction. Using a consistent cutoff scheme we investigate the QCD phase diagram and its dependence on the vector coupling strength $g_v$. We find that the first order chiral phase transition at moderate baryon chemical potentials and its critical point, a generic feature of most NJL-type models without vector coupling, disappear for sufficiently large values of $g_v$ that are consistent with lattice QCD resu…
Zero temperature properties of an (axial-) vector meson extended linear sigma model are discussed, concerning on the possible different realizations of the axial anomaly term. The different anomaly terms are compared with each other on the basis of a chi^2 minimalization process. It is found that there is no essential difference among the different realizations. This means that any of them can be equally used from phenomenological point of view.
We study the interplay between chiral and diquark condensates within the framework of the Ginzburg-Landau free energy, and classify possible phase structures of two and three-flavor massless QCD. The QCD axial anomaly acts as an external field applied to the chiral condensate in a color superconductor and leads to a crossover between the broken chiral symmetry and the color superconducting phase, and, in particular, to a new critical point in the QCD phase diagram.
We extend the approach of Dolgov and Zakharov to the axial anomaly to study polarized radiative decays. We analyse the pattern of mass singularity cancellation in the corresponding decay rates. We compare polarized and unpolarized cases. The cancellation of the infrared and collinear singularities is verified to all powers of the lepton mass for the $π^+$ and $Z^0$ polarized radiative decays.
The generalization of the axial anomaly is considered. It is shown that bilocal axial quark operators on the light cone possess, beside the point-like anomaly, also a light-like anomaly. The consequences for the definition of anomaly-free quark distribution functions and the effect of both gluon coefficient function and splitting kernels in polarized deep inelastic scattering are discussed.
We study the QCD phase structure in the three-flavor Nambu--Jona-Lasinio model, incorporating the chiral-diquark interplay due to the axial anomaly. We demonstrate that for a certain range of model parameters, the low temperature critical point predicted by a Ginzburg-Landau analysis appears in the phase diagram. In addition, we show that the axial anomaly presents a new scenario for a possible BEC-BCS crossover in the color-flavor locked phase of QCD.
A low energy theorem concerning a matrix element of the QCD axial anomaly between vacuum and two-photons states is tested against different instanton models. In the chiral limit the theorem is fulfilled by the Diakonov&Petrov model, whereas it is violated by single-instanton approximations. Beyond the chiral limit the theorem, and two relations established for other matrix elements of the QCD axial anomaly between vacuum and meson states, result to be violated also by the Diakonov&Petrov model.
We generalize the dispersive approach to axial anomaly by A.D. Dolgov and V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the $π^0,η,η'\rightarrowγγ^*$ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element $\langle 0 |G\tilde{G} |γγ^*(q^2) \rangle$ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The dua…
We report on effects of the q-$\bar{\rm q}$ vector interaction and/or the U(1)$_A$-anomaly-induced chiral-diquark coupling on the charge-neutral quark matter in $β$-equilibrium. We show that when the vector coupling is absent, there can appear a cross-over region sandwiched by two critical points in the intermediate temperature ($T$) region, while the phase transition in the low-$T$ region including zero temperature keeps being first order until the strength of the anomaly term is increased to have a critical value. On the other hand, when the vector coupling is also present, there appears a c…
Renormalization of the axial vector currents due to Goldstone loops is studied in a simple extension of Manohar - Georgi chiral quark model which incorporates $U(1)_A$ anomaly effects. The polarized strage quark sea in the polarized nucleon results from different renormalization of the flavor singlet and octet currents and is in reasonable agreement with the experiment.
The gluonic contributions to the conventional PCAC formulas due to flavor singlet axial anomaly have been instrumental in explaining the mass of the $η^{\prime}$ and providing a plausible explanation for solving the spin crisis. We show that they also play an important role in the description of photo- and electroproduction of vector mesons at low energy and high momentum transfers. We calculate the contributions of this type to $ϕ$ meson electromagnetic production in a model, which contains also a soft pomeron, and find agreement with recent CLAS data.
Whilst the prospect of new $Z'$ gauge bosons with only axial couplings to the Standard Model (SM) fermions is widely discussed, examples of anomaly-free renormalisable models are lacking in the literature. We look to remedy this by constructing several motivated examples. Specifically, we consider axial vectors which couple universally to all SM fermions, as well as those which are generation-specific, leptophilic, and leptophobic. Anomaly cancellation typically requires the presence of new coloured and charged chiral fermions, and we argue that in a large class of models masses of these new s…
Axial anomaly leads to exact sum rules for transition form factors providing the important constraints to respective distribution amplitudes. This rigorous NPQCD approach is valid even if QCD factorization is broken. The status of possible small non-OPE corrections to continuum in comparison to BABAR and BELLE data is discussed.
We investigate the interplay between the chiral and diquark condensates on the basis of the Ginzburg-Landau potential with QCD symmetry. We demonstrate that the axial anomaly drives a new critical point at low temperature in the QCD phase diagram and leads to a smooth crossover between the hadronic and color superconducting phases.
In vacuum, in the chiral limit the coupling of a pion to two on-shell photons is directly related to the coefficient of the axial anomaly in QED. This relationship is lost at any nonzero temperature. Explicit calculations show that the coupling decreases with temperature and vanishes at Tc, the temperature of chiral symmetry restoration.
The axial anomaly in the divergence of the singlet axial current in QCD $+$ QED leads to low-energy theorems for the matrix element of this operator equation over vacuum and two--photon states and for the matrix element over vacuum and two--gluon states. The solution of these theorems is related only to the nonperturbative phenomena. These matrix elements are calculated in instanton vacuum generated N-JL type quark model for arbitrary $N_f .$ It is shown that this model does satisfy the low-energy theorems.
We discuss the role of the U(1) axial anomaly in the spin structure functions of the nucleon, with particular emphasis on how one might determine its x dependence in present and future deep inelastic scattering experiments. We focus on the C-odd spin structure function g3 and also the deuteron structure function g1^d.
We revisit the QCD+QED axial anomaly low-energy theorems which give an exact relation between the matrix elements of the gluon and photon parts of the axial anomaly operator equation within the framework of the {\em effective action} derived from the instanton vacuum. The matrix elements between the vacuum and two photon states and between the vacuum and two gluon states are investigated for arbitrary $N_f $ in the chiral limit. Having gauged the effective action properly, we show that the model does exactly satisfy the low-energy theorems.
We investigate what can be learnt about the $η$ -$η'$ mixing by means of dispersive representation of axial anomaly. We show that our method leads to the strong bounds for the $η-η'$ mixing angle: $θ= -15.3^o \pm 1^o$. Moreover, our result manifests also a dramatic dependence of the width $Γ_{η\to 2γ}$ on the mixing angle $θ$. This property explains how the relatively small mixing strongly effects the decay width.
In this report, I discuss the current state of the problem of the axial anomaly in quantum electrodynamics (QED) and quantum chromodynamics (QCD) and how the axial anomaly is related to the structure of the vacuum in QCD. In QCD, the vacuum average of the axial anomaly is proportional to a new quantum number n, the winding number. The axial anomaly condition implies that there are zero modes of the Dirac equation for a massless quark and that there is spontaneous breaking of chiral symmetry in QCD, which leads to the formation of a quark condensate. The axial anomaly can be represented in the …
$Z \to γγ$ decay amplitude is considered and proven to be zero due to properties of polarization vectors and Bose statistics. Triangular diagrams for a pseudoscalar $\to γγ$ and $Z \to γγ$ processes with massive fermions in the loop are explicitely calculated. In the Standard Model axial anomaly vanishes in the sum of these diagrams as Z boson is mixed with one of the Goldstone bosons.
It is shown that the rates of the decays Upsilon(1^3D_1) -> eta Upsilon(1S) and Upsilon(1^3D_2) -> eta Upsilon(1S) should be comparable to and likely exceed that of the recently discussed in the literature two-pion transition Upsilon(1D) -> pi pi Upsilon(1S). The reason for this behavior is that the discussed eta transitions are enhanced by the contribution of the anomaly in the flavor singlet axial current in QCD.
Interplay between axial anomaly and quark-hadron duality in the presence of strong mixing is considered. The anomaly sum rule for meson transition form factors based on the dispersive representation of axial anomaly and quark-hadron duality in octet channel is analyzed. The comparison of this sum rule to the experimental data on $η$ and $η'$ mesons transition form factors shows that the interval of duality in this channel is rather small, contradicting the usual understanding of quark-hadron duality. The same values of interval of duality are supported by considering the two-point correlator i…
We consider the response of the QCD ground state at finite baryon density to a strong magnetic field B. We point out the dominant role played by the coupling of neutral Goldstone bosons, such as pi^0, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of B ~ m_pi^2/e, a metastable object appears - the pi^0 domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to B. As a result, for B ~ 10^{19} G a stack of parallel pi^0 domain walls is energetically more favorable than nuclear matter at the same densit…
The role of the axial anomaly in the chiral phase transition at finite temperature and quark chemical potential is investigated within a non-perturbative functional renormalization group approach. The flow equation for the grand potential is solved to leading-order in a derivative expansion of a three flavor quark-meson model truncation. The results are compared with a standard and an extended mean-field analysis, which facilitates the exploration of the influence of bosonic and fermionic fluctuations, respectively, on the phase transition. The influence of U(1)_A-symmetry breaking on the chir…
The relation for transition form factors of eta and eta' mesons is obtained by combining the exact nonperturbative QCD sum rule, following from the dispersive representation of axial anomaly, and quark-hadron duality. It is valid at all virtual photon momenta and allows one to express the transition form factors entirely in terms of meson decay constants. This relation is in a good agreement with experimental data.
The dispersive representation of axial anomaly leads to the anomaly sum rules (ASRs), exact nonperturbative relations in QCD. The analytical continuation of the ASRs to the time-like region is performed. The transition form factors of $π^0$, $η$ and $η'$ mesons in this region are calculated. A good agreement with the available experimental data is found. Based on the ASRs, we have provided the foundations for the vector meson dominance model in these processes.
Axial Anomaly, entanglement and polarization
研究轴向异常引发的光子纠缠及介子衰变，揭示时间分离与极化现象的关联。
Axial anomaly and nesting is elucidated in the context of the inhomogeneous chiral phase. Using the Gross-Neveu models in 1+1 dimensions, we shall discuss axial anomaly and nesting from two different points of view: one is homogeneous chiral transition and the other is the Ferrel-Fulde-Larkin-Ovchinnikov (FFLO) state in superconductivity, which are closely related to each other by way of duality. It is shown that axial anomaly leads to a particular kind of the FFLO state within the two dimensional Nambu-Jona Lasinio model, where axial anomaly is manifested in a different mode. Nesting is a dri…
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…
The QCD + QED axial anomaly low-energy theorems are applied to estimate the accuracy of an instanton vacuum - based chiral quark model. The low-energy theorems give an exact relation between the matrix elements of the gluon and photon parts of the QCD + QED axial anomaly operator equation. The matrix elements between vacuum and two photon states and between vacuum and two gluon states are calculated for arbitrary N_f. It is shown that this model does satisfy the low-energy theorems with an accuracy of $\sim 17%$. We estimate also the contribution of the nonperturbative conversion of gluons int…
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