QCD Axial Anomaly Research Articles

QCD Axial Anomaly Enhances the ηη′ Decay of the Hybrid Candidate η 1(1855)

We study the hybrid mesons with the exotic quantum number I G J PC = 0+1−+ and investigate their decays into the η η′, a 1(1260) π, f 1(1285) η, f 1(1420) η, , , and channels. It is found that the QCD axial anomaly enhances the decay width of the η η′ channel although this mode is strongly suppressed by the small p-wave phase space. Our results support the interpretation of the η 1(1855) recently observed by BESIII as the hybrid meson of I G J PC = 0+1−+. The QCD axial anomaly ensures the η η′ decay mode to be a characteristic signal of the hybrid nature of the η 1(1855).

How the axial anomaly controls flavor mixing among mesons

It is well known that because of the axial anomaly in QCD, mesons with $J^P = 0^-$ are close to $SU(3)_{\mathrm{V}}$ eigenstates: the $eta^\prime(958)$ meson is largely a singlet, and the $\eta$ meson an octet. In contrast, states with $J^P = 1^-$ are flavor diagonal: \textit{e.g.}, the $\phi(1020)$ is almost pure $\bar{s} s$. Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of $G_{\mathrm{fl}} = SU(3)_{\mathrm{L}} \times SU(3)_{\mathrm{R}}$. We construct effective Lagrangians from terms invariant under $G_{\mathrm{fl}}$, and introduce the concept of \textit{hetero-} and \textit{homo}chiral multiplets. Because of the axial anomaly, only terms invariant under the $Z(3)_{\mathrm{A}}$ subgroup of the axial $U(1)_{\mathrm{A}}$ enter. For heterochiral multiplets, which begin with that including the $\eta$ and $\eta^\prime(958)$, there are $Z(3)_{\mathrm{A}}$ invariant terms with low mass dimension which cause states to mix according to $SU(3)_{\mathrm{V}}$ flavor. For homochiral multiplets, which begin with that including the $\phi(1020)$, there are no $Z(3)_{\mathrm{A}}$ invariant terms with low mass dimension, and so states are diagonal in flavor. In this way we predict the flavor mixing for the heterochiral multiplet with spin one, as well as for hetero- and homochiral multiplets with spin two and spin three.

Pion in the holographic model with 5D Yang-Mills fields

We study the pion in the holographic model of Hirn and Sanz which contains two Yang-Mills fields defined in the background of the sliced AdS space. The infrared boundary conditions imposed on these fields generate the spontaneous breaking of the chiral symmetry down to its vector subgroup. Within the framework of this model, we get an analytic expression for the pion form factor and a compact result for its radius. We also extend the holographic model to include the Chern-Simons term which is required to reproduce the appropriate axial anomaly of QCD. As a result, we calculate the anomalous form factor of the pion and predict its ${Q}^{2}$ slope for the kinematics when one of the photons is almost on shell. We also observe that the anomalous form factor with one real and one virtual photon is given by the same analytic expression as the electromagnetic form factor of a charged pion. One of the advantages of the present model is that it does not require an infrared boundary counterterm to correctly reproduce the anomaly of QCD.

ηandη′mesons in the Dyson-Schwinger approach at finite temperature

We study the temperature dependence of the pseudoscalar meson properties in a relativistic bound-state approach exhibiting the chiral behavior mandated by QCD. Concretely, we adopt the Dyson-Schwinger approach with a rank-2 separable model interaction. After extending the model to the strange sector and fixing its parameters at zero temperature, T=0, we study the T-dependence of the masses and decay constants of all ground-state mesons in the pseudoscalar nonet. Of chief interest are $\eta$ and $\eta^\prime$. The influence of the QCD axial anomaly on them is successfully obtained through the Witten-Veneziano relation at T=0. The same approach is then extended to T>0, using lattice QCD results for the topological susceptibility. The most conspicuous finding is an increase of the $\eta^\prime$ mass around the chiral restoration temperature $T_{; ; ; ; \rm Ch}; ; ; ; $, which would suggest a suppression of $\eta^\prime$ production in relativistic heavy-ion collisions. The increase of the $\eta^\prime$ mass may also indicate that the extension of the Witten-Veneziano relation to finite temperatures becomes unreliable around and above $T_{; ; ; ; \rm Ch}; ; ; ; $. Possibilities of an improved treatment are discussed.

Phase structure, collective modes, and the axial anomaly in dense QCD

Using a general Ginzburg-Landau effective Lagrangian, we study the topological structure and low-lying collective modes of dense QCD having both chiral and diquark condensates, for two and three massless flavors. As we found earlier, the QCD axial anomaly acts as an external field applied to the chiral condensate in a color superconductor and, as a new critical point emerges, leads to a crossover between the broken chiral symmetry and color superconducting phases. At intermediate densities where both chiral and diquark condensates are present, we derive a generalized Gell-Mann--Oakes-Renner relation between the masses of pseudoscalar bosons and the magnitude of the chiral and diquark condensates. We show explicitly the continuity of the ordinary pion at low densities to a generalized pion at high densities.

Anomalous Enhancement of a Penguin Hadronic Matrix Element inB→Kη′

We estimate the density matrix element for the pi(0), eta, and eta(') production from the vacuum in the large-N(c) limit. As a consequence, we find that the QCD axial anomaly leads to highly nontrivial corrections to the usual flavor SU(3) relations between B(0)-->K(0)pi(0), B(0)-->K(0) eta, and B(0)-->K(0)eta(') decay amplitudes. These corrections may explain why the B-->Keta(') branching ratio is about 6 times larger than the B-->Kpi one.

New Critical Point Induced By the Axial Anomaly in Dense QCD

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.

BYPASSING THE AXIAL ANOMALIES

Many meson processes are related to the UA(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 Feynman graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate especially the case of the processes related to the Abelian axial anomaly of QED, but we speculate that it seems possible that effects of the non-Abelian axial anomaly of QCD can be accounted for in an analogous way.

Strange and gluonic contributions to the nucleon spin

Inclusive deep inelastic scattering (DIS) experiments lead to a small contribution of the quark spins to the nucleon spin and a negative contribution from strange quarks. Historically this triggered the interest in measuring strange form factors. However, the result of these inclusive experiments has to be reinterpreted taking into account the axial anomaly in QCD, which depends on the gluon contribution to the nucleon spin. The COMPASS experiment at CERN and experiments at RHIC are going to measure this gluonic contribution.

A POSSIBLE GATEWAY TO ηb: χb0(2P)→ηηb

It is argued that the branching ratio for the decay χb0(2P)→ηηb can reach few permil as a result of the enhancement of the η emission by the axial anomaly in QCD. This might make the discussed process practical for an experimental search for the ηb.

The enhancement of the decay ϒ(1D)→ηϒ(1S) by the axial anomaly in QCD

It is shown that the rates of the decays ϒ(13D1)→ηϒ(1S) and ϒ(13D2)→ηϒ(1S) should be comparable to and likely exceed that of the recently discussed in the literature two-pion transition ϒ(1D)→ππϒ(1S). The reason for this behavior is that the discussed η transitions are enhanced by the contribution of the anomaly in the flavor singlet axial current in QCD.

Axial anomaly and low energy tests for instanton vacuum models in 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.

The axial anomaly in QCD at finite temperature

We study flavor mixing and the U(1) A 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 η and η′. In particular, the strange and non-strange components of the η unmix near T c . The anomaly does not affect the strange eta, so we expect a light purely strange pseudoscalar near the phase transition.

Some Phenomenological Aspects of Chiral Symmetry and Axial Anomaly in QCD

Some Phenomenological Aspects of Chiral Symmetry and Axial Anomaly in QCD

Anomalous discrete symmetry.

We examine an interesting scenario to solve the domain wall problem recently suggested by Preskill, Trivedi, Wilczek and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as CP and Z_2 can be anomalous due to a so-called $K$-term induced by instantons. We point out that Z_2 domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the CP-conserving one and the CP-breaking one. In the first case, there exist two Z_2-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of CP violation are discussed and shown to be well within the experimental limits in weak interactions.

The quark—hadron phase transition in an effective meson—glueball theory

The temperature dependence of the gluon and quark condensates is investigated in an effective sigma-type model, incorporating the trace and the axial anomaly of QCD. The restoration of the chiral invariance is accompanied by a small discontiuity in the gluon condensate. The tension and the width of the interface between the coexisting phases at the transition point depend sensitively on the average mass of the glueball—scalar-singlet system.

Heavy quark contributions to ∫ 01d χg1( χ)

Heavy quark contributions to the g 1( χ) structure function are calculable in terms of the light quark contributions. The result is proportional to the axial anomaly in QCD.

QCD axial anomaly and mixing of pseudoscalars

Starting with the QCD axial anomaly we discuss systematically the mixing of light-light and light-heavy pseudoscalar mesons. The π 0− η and π 0− η′ mixing angles are found to be λ πη⋍0.016 and λ πη′⋍0.004 , which are derived without invoking the diagonalization of the mass matrix. For heavy pseudoscalars we assume that the matrix elements of the quark (e.g. the charm quark) operator cγ 5c are saturated by the η c meson and a series of its radial excitations. The π 0− η c and η− η c mixing angles are then found to be λπη c⋍−1×10 −4 and ληη c⋍−5×10 −3 . By use of the mixing of η with c c states the calculated rate for ψ→ γη is in agreement with experimental data and the branching ratio for ψ′→ γη is predicted to be ∼6×10 −5. In addition, the η− η′ mixing is also discussed.