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DOE OSTI2025

Quantum Anomalies in Condensed Matter

Quantum materials provide a fertile ground in which to test and realize unusual phenomena such as quantum anomalies predicted by quantum field theory. There are three important symmetries that are broken when classical field theory is moved into the quantum regime, the scale anomaly, the axial (chiral) anomaly, and the parity anomaly. Several potential device applications may be realized by the discovery of quantum anomalies in condensed matter, enabled by the new physics they embody, including ultra‐sensitive dark matter detectors, far infrared optical modulators, micro‐bolometric detectors, low‐dissipation ballistic transporters, terahertz‐based qubits, terahertz polarization state controls, passive magnetic field sensors, stable topological superconductors that host Majorana fermions, and qubits topologically protected against decoherence. In this perspective article, the definition of these quantum anomalies is laid out, how little is known in the context of condensed matter, and how quantum anomalies are predicted to manifest as anomalous electronic, thermal, and magnetic behavior in experiments on topological quantum materials, including Weyl and Dirac semimetals. Furthermore, the importance that mechanical strain and defects will play in modifying signatures of quantum anomalies is discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Vortical effects in chiral band structures

The chiral vortical effect is a chiral anomaly-induced transport phenomenon characterized by an axial current in a uniformly rotating chiral fluid. It is well understood for Weyl fermions in high energy physics, but its realization in condensed matter band structures, including those of Weyl semimetals, has been controversial. In this work, we develop the Kubo response theory for electrons in a general band structure subject to space- and time-dependent rotation or vorticity relative to the background lattice. For continuum Hamiltonians, we recover the chiral vortical effect in the static limit and the transport or uniform limit when the fluid, strictly, is not a Fermi liquid. In the transport limit of a Fermi liquid, we describe an effect that we dub the gyrotropic vortical effect. The latter is governed by Berry curvature of the occupied bands while the former contains an additional contribution from the magnetic moment of electrons on the Fermi surface. The two vortical effects can be understood as kinematic analogs of the well-known chiral and gyrotropic magnetic effects in chiral band structures. As a result, we address recent controversies in the field and conclude by describing device geometries that exploit Ohmic or Seebeck transport to drive the vortical effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji′s invariant spin decomposition to discuss the spin budget of the nucleon as a quark–diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Path integral approach to quantum anomalies in interacting models

The prediction and subsequent discovery of topological semimetal phases of matter in solid state systems has instigated a surge of activity investigating the exotic properties of these unusual materials. Among these are transport signatures which can be attributed to the chiral anomaly; the breaking of classical chiral symmetry in a quantum theory. This remarkable quantum phenomenon, first discovered in the context of particle physics has now found new life in condensed-matter physics, connecting topological quantum matter and band theory with effective field theoretic models. In this paper we investigate the interplay between interactions and the chiral anomaly in field theories inspired by semimetals using Fujikawa's path integral method. Starting from models in one spatial dimension we discuss how the presence of interactions can affect the consequences of the chiral anomaly leading to renormalization of excitations and their transport properties. This is then generalized to the three-dimensional case where we show that the anomalous response of the system, namely, the chiral magnetic and quantum Hall effects, are modified by the presence of interactions. These properties are investigated further through the identification of anomalous modes which exist within interacting Weyl semimetals. These massive excitations are nonperturbative in nature and are a direct consequence of the chiral anomaly. The effects of interactions on mixed axial-gravitational anomalies are then investigated and the conditions required for interaction effects to be observed are discussed.

Anomalies↗
DOE OSTI2025

Role of the chiral anomaly in polarized deeply inelastic scattering. III. Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass

We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar η ¯ -meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical η ′ mass, with the finite quark mass contribution differing by O ( 10 % ) from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano’s result that the proton’s net quark helicity Δ Σ ∝ χ QCD ′ | m = 0 ( 0 ) , the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percentages. Our prior prediction that the polarized DIS structure function g 1 is quenched by sphaleronlike topological transitions at small x is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion Collider. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Ordinary and exotic mesons in the extended Linear Sigma Model

The extended Linear Sigma Model (eLSM) is a hadronic model based on the global symmetries of QCD and the corresponding explicit, anomalous, and spontaneous breaking patterns. In its basic three-flavor form, its mesonic part contains the dilaton/glueball as well as the nonets of pseudoscalar, scalar, vector, and axial–vector mesons, thus chiral symmetry is linearly realized. In the chiral limit and neglecting the chiral anomaly, only one term – within the dilaton potential – breaks dilatation invariance, and all terms are chirally symmetric. Spontaneous symmetry breaking is implemented by a generalization of the Mexican-hat potential, with explicit symmetry breaking responsible for its tilting. The overall mesonic phenomenology up to ~2 GeV is in agreement with the PDG compilation of masses and partial and total decay widths. The eLSM was enlarged in a straightforward way to include other conventional quark–antiquark nonets (pseudovector and orbitally excited vector mesons, tensor and axial-tensor mesons, radially excited (pseudo)scalar mesons, etc.), as well as two nonets of hybrid mesons, the lightest one with exotic quantum numbers J $\mathscr{PC}$ = 1 -+ not allowed for $\bar{q}q$ objects, such as the resonance π 1 (1600) and the recently discovered η 1 (1855) . In doing so, different types of chiral multiplets are introduced: heterochiral and homochiral multiplets, which differ in the way they transform under chiral transformations. Moreover, besides the scalar glueball that is present from the beginning as dilaton, other glueballs, the tensor, the pseudoscalar and the vector glueballs were coupled to the eLSM: the scalar resonance ƒ 0 (1710) turns out to be mostly gluonic, the tensor glueball couples strongly to vector mesons, and the pseudoscalar glueball couples sizably to $ππη'$ and can be assigned to X (2370) or X (2600). In all cases above, masses and decays can be analyzed allowing for a better understanding of both conventional and non-conventional mesons: whenever data are available, a comparison is performed and, when this is not the case, predictions of decay widths and decay ratios are outlined. The eLSM contains chiral partners on an equal footing and is therefore well suited for studies of chiral symmetry restoration at nonzero temperature and densities: this is done by coupling it to the Polyakov loop. Finally, the QCD phase diagram and the location of the critical endpoint were investigated within this framework.

Chiral symmetry↗
DOE OSTI2026

The X17 with Chiral Couplings

In recent years, the ATOMKI collaboration has performed a series of measurements of excited nuclei, observing a resonant excess of electron-positron pairs at large opening angles compared to the Standard Model prediction. The excess has been hypothesized to be due to the production of a new spin-1 or spin-0 particle, X17, with a mass of about 17 MeV. Recently, the PADME experiment has reported an excess in the $e^+e^-$ cross section at center-of-mass energies near 17 MeV, perhaps further hinting at the existence of a new state. Studies of the spin-1 case have hitherto focused on either vector {\em or} axial-vector couplings to quarks and leptons, whereas UV theories more naturally produce {\em both} vector and axial-vector (\textit{i.e.} chiral) couplings, analogous to the Standard Model weak interactions. We consider the ATOMKI anomalies in the context of an $X$ with chiral couplings to quarks and explore the parameter space that can explain the ATOMKI anomalies, contrasting them with experimental constraints. We find that it is possible to accommodate the reported ATOMKI signals. However, the $99\%$ CL region is in tension with null results from searches for atomic parity violation and direct searches for new low mass physics coupled to electrons. This tension is found to be driven by the magnitude of the reported excess in the transition of $^{12}{\rm C}(17.23)$, which drives the best-fit region towards excluded couplings.

Fieg, Max H. [UC, Irvine; UC, Irvine (main); Fermi↗
DOE OSTI2021

Entropy production far from equilibrium in a chiral charged plasma in the presence of external electromagnetic fields

We report on the time evolution of a charged strongly coupled N = 4 SYM plasma with an axial anomaly subjected to strong electromagnetic fields. The evolution of this plasma corresponds to a fully backreacted asymptotically AdS 5 solution to the Einstein-Maxwell-Chern-Simons theory. We explore the evolution of the axial current and production of axial charges. As an application we show that after a sufficiently long time both the entropy and the holographic entanglement entropy of a strip-like topology (both parallel to and transverse to the flow of axial current) grow linearly in time.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Axion anomalies

We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral symmetry is due to the background axion field. We compute the contributions to this anomalous Ward identity due to the pseudoscalar field alone, which arise in Minkowski space, as well as the effects due to an interaction with an external gravitational field. For the case of massless fermions, these interactions induce terms in the axion effective action that can be removed by the addition of local counterterms. We demonstrate that these counterterms are generated by the transformation of the path integral measure when transforming the theory from a form where the chiral symmetry is manifest to one where the symmetry is only apparent after using the classical equations of motion. We work perturbatively in Minkowski space and include the effects of interactions with a linearized gravitational field. Using the heat kernel method, we study the transformation properties of the path integral measure, and include the effects of non-linear gravity as well as interactions with gauge fields. Finally, we verify our relation by considering derivatively coupled fermions during pseudoscalar-driven inflation and computing the divergence of the axial current in de Sitter spacetime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Exploring self-consistency of the equations of axion electrodynamics in Weyl semimetals

Recent works have provided evidence that an axial anomaly can arise in Weyl semimetals. If this is the case, then the electromagnetic response of Weyl semimetals should be governed by the equations of axion electrodynamics. These equations capture both the chiral magnetic and anomalous Hall effects in the limit of linear response, while at higher orders their solutions can provide detectable electromagnetic signatures of the anomaly. In this work, we consider three versions of axion electrodynamics that have been proposed in the Weyl semimetal literature. These versions differ in the form of the chiral magnetic term and in whether or not the axion is treated as a dynamical field. In each case, we look for solutions to these equations for simple sample geometries subject to applied external fields. We find that in the case of a linear chiral magnetic term generated by a nondynamical axion, self-consistent solutions can generally be obtained. In this case, the magnetic field inside of the Weyl semimetal can be magnified significantly, providing a testable signature for experiments. Self-consistent solutions can also be obtained for dynamical axions, but only in cases where the chiral magnetic term vanishes identically. Finally, for a nonlinear form of the chiral magnetic term frequently considered in the literature, we find that there are no self-consistent solutions aside from a few special cases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Anomalies in string-inspired nonlocal extensions of QED

We investigate anomalies in the class of nonlocal field theories that have been proposed as an ultraviolet completion of four-dimensional quantum field theory with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by the string field theory and ghost-free nonlocal approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired nonlocal extension of QED. We show that the vector anomaly vanishes as required by gauge invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in the scale of nonlocality. We also calculate the nonlocal vector and axial currents explicitly and present an illustrative example by applying our results to the decay of π 0 → γ γ . Published by the American Physical Society 2024

Abu-Ajamieh, Fayez↗
DOE OSTI2024

Flavor-violating ALPs, electron g − 2 , and the Electron-Ion Collider

We revisit the possibility that light axionlike particles (ALPs) with lepton-flavor-violating couplings could give significant contributions to the electron’s anomalous magnetic moment g e − 2 . Unlike flavor diagonal lepton-ALP couplings, which are exclusively axial, lepton-flavor-violating couplings can have arbitrary chirality. Focusing on the e − τ ALP coupling, we find that the size of the contribution to g e − 2 depends strongly on the chirality of the coupling. A significant part of the parameter space for which such a coupling can explain experimental anomalies in g e − 2 can be probed at the Electron-Ion Collider, which is uniquely sensitive to the chirality of the coupling using the polarization of the electron beam. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Magnetic dynamics with Weyl fermions

Transport of charge and valley (axial) degrees of freedom coupled to order-parameter dynamics in magnetic Weyl semimetals is studied in the framework of nonequilibrium thermodynamics. In addition to the established valley-related transport anomalies that are rooted in band-structure topology, we construct dissipative couplings between the three dynamic constituents of the system driven out of equilibrium by electromagnetic perturbations. We show how the valley degree of freedom mediates an effective coupling between the charge and magnetic sectors of the system, through a combination of the chiral anomaly, on the electric side, and the Onsager-paired valley torque and pumping, on the magnetic side. This work complements previous studies of magnetic Weyl semimetals by a more systematic analysis of collective dissipation. We discuss several concrete examples of the valley-mediated current-driven magnetic instabilities and charge pumping, and extend the theory to the antiferromagnetic case.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Precision measurement of the neutral pion lifetime

The explicit breaking of the axial symmetry by quantum fluctuations gives rise to the so-called axial anomaly. This phenomenon is solely responsible for the decay of the neutral pion π0 into two photons (γγ), leading to its unusually short lifetime. Here, we precisely measured the decay width Γ of the π 0 → γγ process. The differential cross sections for π0 photoproduction at forward angles were measured on two targets, carbon-12 and silicon-28, yielding Γ(π 0 → γγ)=7.798±0.056(stat.)±0.109(syst.) eV, where stat. denotes the statistical uncertainty and syst. the systematic uncertainty. We combined the results of this and an earlier experiment to generate a weighted average of Γ(π 0 → γγ)=7.802±0.052(stat.)±0.105(syst.) eV. Our final result has a total uncertainty of 1.50% and confirms the prediction based on the chiral anomaly in quantum chromodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Gluonic Structure from Instantons

The instanton vacuum provides an effective description of chiral symmetry breaking by local topological fluctuations of the gauge fields, as observed in lattice QCD simulations. The resulting effective dynamics at momenta below 1/$\bar{ρ}$ ≈ 0.6 GeV explains the basic features of light-quark correlation functions and is used extensively in studies of hadron structure. The instanton fields also make definite contributions to the gluonic structure of light hadrons, as expressed in the matrix elements of composite quark– gluon or gluon operators. The article reviews the gluonic structure of light hadrons (nucleon, pion) induced by instantons. This includes: (i) twist-2 parton distributions and momentum sum rule; (ii) twist-3 angular momentum and spin-orbit interactions; (iii) twist-3 and twist-4 quark–gluon correlations and power corrections; (iv) trace anomaly and hadron mass decomposition; (v) scalar gluon form factors and mechanical properties; (vi) axial anomaly and pseudoscalar gluon form factors. It also discusses possible further applications of the methods and recent developments including gauge field configurations beyond instantons.

Weiss, C. [Thomas Jefferson National Accelerator F↗
DOE OSTI2020

Tensor supercurrent in QCD

An external Abelian magnetic field excites in the QCD vacuum a tensor super current that represents the tensor polarization of the chiral condensate. This tensor supercurrent can be deduced from the chiral lagrangian in the presence of anoma lies; a similar tensor supercurrent emerges in rotating systems at finite chemical potential. We discuss the microscopic origin of this supercurrent and argue that it screens the instanton-anti-instanton $I\overline I$ molecules in the QCD vacuum, similarly to the vector supercurrent screening Abrikosov vortices in a superconductor. A number of possible experimental manifestations of the tensor supercurrent are discussed: i) spin alignment of axial-vector and vector mesons in heavy ion collisions; ii) tensor charge of the nucleon; iii) transversity of quark distributions in polarized nucleons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗