Anomaly In QCD Research Articles

Anomaly-Induced Quenching of gA in Nuclear Matter and Impact on Search for Neutrinoless ββ Decay

How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is accomplished by matching the Fermi-liquid fixed point theory to the “Extreme Single Particle (shell) Model” (acronym ESPM) in superallowed Gamow–Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for (1−qssb)≠0—that one might identify as “fundamental quenching (FQ)”—in certain experiments seems to be alarmingly significant. I present arguments for how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to confirm or refute this observation is discussed in terms of the superallowed Gamow–Teller transition in the doubly-magic nucleus 100Sn and in the spectral shape in the multifold forbidden β decay of 115In.

Semiclassics with ’t Hooft flux background for QCD with 2-index quarks

We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ2× T2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the ’t Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-N orientifold equivalence between QCD(Sym/ASym) and mathcal{N} = 1 supersymmetric SU(N) Yang-Mills theory.

Mass radius of the proton

The mass radius is a fundamental property of the proton that so far has not been determined from experiment. Here we show that the mass radius of the proton can be rigorously defined through the formfactor of the trace of the energy-momentum tensor (EMT) of QCD in the weak gravitational field approximation, as appropriate for this problem. We then demonstrate that the scale anomaly of QCD enables the extraction of the formfactor of the trace of the EMT from the data on threshold photoproduction of $J/\psi$ and $\Upsilon$ quarkonia, and use the recent GlueX Collaboration data to extract the r.m.s. mass radius of the proton ${\rm R_m = 0.55 \pm 0.03 \ fm}$. The extracted mass radius is significantly smaller than the charge radius of the proton ${\rm R_C = 0.8409 \pm 0.0004 \ fm}$. We attribute this difference to the interplay of asymptotic freedom and spontaneous breaking of chiral symmetry in QCD, and outline future measurements needed to determine the mass radius more precisely.

Central exclusive diffractive production of axial-vector f1(1285) and f1(1420) mesons in proton-proton collisions

We present a study of the central exclusive diffractive production of the $f_{1}(1285)$ and $f_{1}(1420)$ resonances in proton-proton collisions. The theoretical results are calculated within the tensor-pomeron approach. Two pomeron-pomeron-$f_{1}$ tensorial couplings labeled by $(l,S) = (2,2)$ and $(4,4)$ are derived. We adjust the model parameters (coupling constants, cutoff constant) to the WA102 experimental data taking into account absorption effects. Both the $(l,S) = (2,2)$ and $(4,4)$ couplings separately allow one to describe the WA102 differential distributions. We compare these predictions with those of the Sakai-Sugimoto model, where the pomeron-pomeron-$f_{1}$ couplings are determined by the mixed axial-gravitational anomaly of QCD. We derive an approximate relation between the pomeron-pomeron-$f_{1}$ coupling constants of this approach and the $(l,S) = (2,2)$ and $(4,4)$ couplings. Then we present our predictions for the energies available at the RHIC and LHC. The total cross sections and several differential distributions are presented. Analysis of the distributions in the azimuthal angle $\phi_{pp}$ between the transverse momenta of the outgoing protons may be used to disentangle $f_{1}$- and $\eta$-type resonances contributing to the same final channel. We find for the $f_{1}(1285)$ a total cross section $\sim 38$ $\mu$b for $\sqrt{s} = 13$ TeV and a rapidity cut on the $f_{1}$ of $|{\rm y_{M}}| < 2.5$. We predict a much larger cross section for production of $f_{1}(1285)$ than for production of $f_{2}(1270)$ in the $\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ decay channel for the LHC energies. This opens a possibility to study the $f_{1}(1285)$ meson in experiments planned at the LHC.

Topological term, QCD anomaly, and the \u03b7\u2032 chiral soliton lattice in rotating baryonic matter

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η′ meson and the QCD anomaly leads to an inhomogeneous condensate of the η′ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η′ CSL is much smaller than that for the π0 CSL found previously. We also argue that the η′ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.

Effects of a parallel electromagnetic field in the three-flavor Nambu–Jona-Lasinio model

In this work, we explore the ground state of QCD system and the relevant collective modes in a parallel electromagnetic (EM) field within the effective three-flavor Nambu--Jona-Lasinio model. From the features of neutral chiral condensates, three critical EM fields are identified in our study: $e\bar{I}_2^{c_i}~(i=1,2,3)$. Moreover, competition between QCD and QED anomalies is found: the negativeness of $\pi_{\rm d}^*$ and $\pi_{\rm s}^*$ is a signal of QCD anomaly dominance for all the flavors, and the positiveness of $\pi_{\rm s}^*$ beyond $e\bar{I}_2^{c_1}$ indicates QED anomaly dominance for strange quark. For the lowest-lying neutral collective modes, the masses of $\Pi$ and $H$ modes reduce to zero around the critical EM fields and the scalar-pseudoscalar components are exchanged between $\Sigma$ and $H$ modes, as can be seen in the crossing structure.

Gauge mediation without gravitino problem by virtue of the QCD anomaly

We consider the possibility that the Peccei-Quinn charged dynamical supersymmetry breaking (DSB) mechanism readily accommodates gauge mediation without the gravitino problem. Given a gravitino of ${m}_{3/2}=\mathcal{O}(\mathrm{eV})$ for the Intriligator-Seiberg-Shih model, an axion, converted from a Nambu-Goldstone boson, could become a dark matter candidate, while the QCD anomaly and a sizable $\ensuremath{\mu}$ value are naturally generated. We also stress that rather minimal DSB content is sufficient to yield the observed mass of the lightest Higgs boson, other than the acceptable soft mass of sparticles in the observable sector.

η′ and η mesons at high T when the UA(1) and chiral symmetry breaking are tied

The approach to the eta'-eta complex employing chirally well-behaved quark-antiquark bound states and incorporating the non-Abelian axial anomaly of QCD through the generalization of the Witten-Veneziano relation, is extended to finite temperatures. Employing the chiral condensate has led to a sharp chiral and U_A(1) symmetry restoration, but with the condensates of quarks with realistic explicit chiral symmetry breaking, which exhibit a smooth, crossover chiral symmetry restoration in qualitative agreement with lattice QCD results, we get a crossover U_A(1) transition, with smooth and gradual melting of anomalous mass contributions. This way we obtain a substantial drop of the eta' mass around the chiral transition temperature, but no eta mass drop. This is consistent with the present empirical evidence.

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.

Chern-Simons five-form and holographic baryons

In the top-down holographic model of QCD based on D4/D8-branes in type IIA string theory and some of the bottom up models, the low energy effective theory of mesons is described by a 5 dimensional Yang-Mills-Chern-Simons theory in a certain curved background with two boundaries. The 5 dimensional Chern-Simons term plays a crucial role to reproduce the correct chiral anomaly in 4 dimensional massless QCD. However, there are some subtle ambiguities in the definition of the Chern-Simons term for the cases with topologically non-trivial gauge bundles, which include the configurations with baryons. In particular, for the cases with three flavors, it was pointed out by Hata and Murata that the naive Chern-Simons term does not lead to an important constraint on the baryon spectrum, which is needed to pick out the correct baryon spectrum observed in nature. In this paper, we propose a formulation of well-defined Chern-Simons term which can be used for the cases with baryons, and show that it recovers the correct baryon constraint as well as the chiral anomaly in QCD.

Chiral effective theories from holographic QCD with scalars

We develop a method for integrating out the heavy Kaluza-Klein modes of scalar type as well as those of vector and axial-vector types, in a class of hard-wall bottom-up approaches of holographic QCD models, including the Dirac-Born-Infeld and Chern-Simons parts. By keeping only the lowest-lying vector mesons, we first obtain an effective chiral Lagrangian of the vector mesons based on the hidden local symmetry, and all the low-energy constants in the HLS Lagrangian are expressed in terms of holographic integrals and, consequently, are fully determined by the holographic geometry and a few constants of mesons. We find that the Gell-Mann--Oakes--Renner relation is manifestly reproduced at the lowest order of derivative expansion. We also explicitly show that a naive inclusion of the Chern-Simons term cannot reproduce the desired chiral anomaly in QCD, and hence, some counterterms should be provided: This implies that the holographic QCD models of hard-wall type cannot give definite predictions for the intrinsic parity-odd vertices involving vector and axial-vector mesons. After integrating out the vector mesons from the HLS Lagrangian, we further obtain the Lagrangian of chiral perturbation theory for pseudoscalar mesons with all the low-energy constants fully determined.

Realistic implementation of chiral magnetic wave in heavy ion collisions

A chiral magnetic wave (CMW) is a gapless collective excitation of chiral charges along the direction of magnetic field in the quark-gluon plasma that arises from the triangle anomaly of QCD. We perform a reliable study of the CMW in a realistic simulation of heavy ion collisions, and find that the CMW contributions to the charge-dependent elliptic flow of pions, $\ensuremath{\Delta}{v}_{2}\ensuremath{\equiv}{v}_{2}({\ensuremath{\pi}}^{\ensuremath{-}})\ensuremath{-}{v}_{2}({\ensuremath{\pi}}^{+})$, linearly depending on the net charge asymmetry ${A}_{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\equiv}({N}_{+}\ensuremath{-}{N}_{\ensuremath{-}})/({N}_{+}+{N}_{\ensuremath{-}})$ with a positive slope $r$, is comparable to the recent experimental results from the Relativistic Heavy Ion Collider (RHIC). We identify a ``freeze-out hole effect,'' which is a direct consequence of the propagation of the CMW during the realistic evolution of the fireball, as the dominant physics effect responsible for a sizable contribution from the CMW to the slope parameter $r$, and emphasize that a proper treatment of the freeze-out condition is crucial in any reliable computation of the CMW contribution to the slope parameter $r$. We also implement a chiral phase transition effect in our study, which illustrates the sensitivity of the results to chiral phase transition temperature, and suggest that the CMW can be an important probe of the QCD chiral phase transition. Our results on the impact parameter dependence compare well with the RHIC experiments. We also give predictions for the Large Hadron Collider (LHC) energy.

Inverse magnetic catalysis induced by sphalerons

The recently discovered inverse magnetic catalysis around the critical temperature indicates that some important information is missing in our current understanding of conventional chiral dynamics of QCD, which is enhanced by the magnetic field. In this work, we provide a mechanism to explain that the inverse magnetic catalysis around the critical temperature is induced by sphalerons. At high temperatures, sphaleron transitions between distinct classical vacua cause an asymmetry between the number of right- and left-handed quarks due to the axial anomaly of QCD. In the presence of a strong magnetic field, the chiral imbalance is enhanced and destroys the right- and left-handed pairings, which naturally induces a decreasing critical temperature of the chiral phase transition for increasing magnetic field. The inverse magnetic catalysis at finite baryon density, and the critical end point in the presence of a strong magnetic field is also explored in this work.

Anomaly-induced charges in baryons

We show that quantum chiral anomaly of QCD in magnetic backgrounds induces a novel structure of electric charge inside baryons. To illustrate the anomaly effect, we employ the Skyrme model for baryons, with the anomaly-induced gauged Wess-Zumino term (\pi_0 + (multi-pion)) E_i B_i. Due to this term, the Skyrmions giving a local pion condensation ((\pi_0 + (multi-pion)) \neq 0) necessarily become a local charge source, in the background magnetic field B_i. We present detailed evaluation of the anomaly effects, and calculate the total induced charge, for various baryons in the magnetic field.

Nuclear Matter Properties from a Chiral Soliton Model

We present a recent investigation on properties of nuclear matter within a chrial soliton approach which includes the explicit scalar dilaton-quarkonium meson saturating the quark loop contribution to the scale anomaly of QCD. We discuss the binding energy per nucleon, the compressibility of nuclear matter and the behavior of meson–nucleon coupling constants according to the density variations in the system.

Anomaly-induced quadrupole moment of the neutron in magnetic field

The neutrons cannot possess a quadrupole moment in the vacuum. Nevertheless, we show that in the presence of an external magnetic field the neutrons acquire a new type of quadrupole moment $Q^{ij}= \chi\,\sigma^i B^j$ involving the components of spin and magnetic field. This "chiral magnetic" quadrupole moment arises from the interplay of the chiral anomaly and the magnetic field; we estimate its value for the neutron in the static limit, and find $\chi \simeq 1.35\cdot10^{-2}\,{\rm fm}^4$. The detection of the quadrupole moment of the neutron would provide a novel test of the role of the chiral anomaly in low-energy QCD and can be possible in the presence of both magnetic and inhomogeneous electric fields. The quadrupole moment of the neutron may affect e.g. the properties of neutron stars and magnetars.

Effect of r averaging on chiral anomaly in lattice QCD with Wilson fermion: finite volume and cutoff effects

We demonstrate the effectiveness of averaging over the Wilson parameter r (which has been proposed earlier) in removing the cutoff effects of naive Wilson fermions in both the anomaly term and the pseudoscalar density term in the flavor singlet axial Ward identity at O(g^2) involving slowly varying background gauge fields. We show that it is the physical fermion contribution which is largely influenced by the r averaging. We have studied the possible interplay between finite size and cutoff effects by investigating in detail naive, O(a) improved and OStm Wilson fermion cases for a range of volumes and lattice fermion mass (am). For naive Wilson fermions r averaging is shown to remove the effects of the interplay. We have shown that for the pseudoscalar density term to O (g^2) the lattice result differs from the continuum result by exhibiting considerable am dependence which appears to be a manifestation of cutoff effects with naive Wilson fermion. The pseudoscalar density term to O(g^2) is shown to be almost independent of am when r-averaging is performed.

Massive pions, anomalies and baryons in holographic QCD

We consider a holographic model of QCD, obtained by a very simple modification of the original construction, which describes at the same time the pion mass, the QCD anomalies and the baryons as topological solitons. We study in detail its phenomenological implications in both the mesonic and baryonic sectors and compare with the observations.

Chiral anomaly in lattice QCD with twisted mass Wilson fermion

The flavour singlet axial Ward identity with Osterwalder–Seiler twisted mass Wilson fermion action is studied on a finite lattice, with finite fermion mass and the Wilson parameter r up to 1. Approach to the infinite volume chiral limit and emergence of the anomaly is significantly better than that obtained with O(a) and O(a2) improved fermion actions. We have shown explicitly that up to O(g2), parity violating terms cancel in the Ward identity even at finite volume and finite lattice spacing.

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.