Pith. sign in

REVIEW 2 major objections 4 minor 79 references

Axial anomalies appear in detectors as beam-collinear spikes whose integrated flux stays fixed by the anomaly.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-10 23:46 UTC pith:AAYH26VE

load-bearing objection Clean LO calculation showing the axial anomaly as collinear deltas in flux detectors; zilch tower and gravity channel are solid kinematics but not yet operator identities. the 2 major comments →

arxiv 2607.06667 v1 pith:AAYH26VE submitted 2026-07-07 hep-ph hep-thnucl-th

Anomaly Realization in Charge-Flux Detector Correlators

Jo\~ao Barata , Ratmir Jumanov , Andrey V. Sadofyev This is my paper
classification hep-ph hep-thnucl-th
keywords axial anomalycharge-flux detectorsenergy correlatorszilch currentsanomaly polesmixed gravitational anomalyhelicity-flipcollider observables
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that quantum anomalies leave a concrete fingerprint on charge-flow detector observables used in collider physics. An axial-charge detector that measures the net axial flux leaving a process resolves the fermionic cut of the classic anomalous triangle as an angular distribution. In the massless limit that contribution vanishes at every fixed non-collinear angle, yet collapses onto the two beam directions so that the integrated flux remains exactly the value fixed by the axial anomaly. Replacing the axial detector by a tower of higher-spin helicity (zilch) detectors yields a family of energy-weighted sum rules controlled by the same anomaly; the same singular localization and finite integrated fluxes survive in the mixed axial-gravitational channel. A sympathetic reader cares because the result turns an abstract UV/IR constraint into a measurable angular pattern of detector fluxes, including energy moments and gravitational sources, without needing non-perturbative matching.

Core claim

In states that excite the anomalous channel, the massless limit of the axial-flux one-point function collapses onto the two beam-collinear directions while the angle-integrated flux remains finite and equal to the anomaly: lim m o0 ∫ d^{2}n Σλ1,2 5(n) = (λ1+λ2). The identical singular localization and finite normalized sum rules hold for the entire tower of zilch-flux detectors and for the mixed axial-gravitational anomaly.

What carries the argument

The axial-flux detector operator Q5(n) (and its higher-spin zilch generalizations Zl(n)), whose angle-integrated form is fixed by the anomalous Ward identity; on the two-body fermionic cut it produces a mass-suppressed helicity-flip weight that loses uniform integrability as m o0 and concentrates at the beam endpoints.

Load-bearing premise

That free-field higher-spin helicity currents continue to define well-behaved flux operators whose divergences receive anomalous contributions of the same strength as the ordinary axial current, even though the paper does not derive those operator divergences.

What would settle it

Compute the fixed-angle massless limit of the polarized two-photon (or two-graviton) fermion-pair production amplitude with the axial or zilch weight: if the non-collinear distribution fails to vanish while the integrated flux fails to equal the expected anomaly coefficient, the claimed localization mechanism is false.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The operator sum rule for integrated axial flux holds inside multipoint detector correlators, so anomaly constraints appear in higher-point energy-flow observables.
  • Energy-weighted zilch detectors measure the same anomalous helicity-flip contribution as the axial detector, now dressed by energy moments.
  • In a strong magnetic field the lowest-Landau-level dynamics make every zilch moment proportional to the integrated E·B anomaly, giving a direct detector realization of spectral flow.
  • The same collinear collapse and finite normalized fluxes appear for the mixed axial-gravitational anomaly and suggest a two-parameter family of detector sum rules labeled by particle helicity and detector spin.
  • Matching the partonic anomaly pole onto the pion channel implies that pion-resolved detector correlations can serve as a hadronic probe of the anomaly.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Crossed electroweak assignments that move the axial insertion into the initial state would let ordinary electric-charge detectors access the same anomalous amplitude in existing e+e- archival data.
  • Because the localization is an angular counterpart of the spectral collapse that produces the anomaly pole, similar detector collapses should appear for other anomalies whose spectral densities become delta functions in the massless limit.
  • If the free-field zilch tower can be promoted to interacting theories with controlled operator mixing, the energy-weighted sum rules would become collider-ready constraints on higher-spin chiral transport.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper studies how the axial anomaly is realized in detector observables built from axial-charge and higher-spin helicity (zilch) fluxes. Starting from the operator Ward identity (Eq. 3) and the axial-flux operator Q5(n) (Eq. 1), it evaluates the one-point function Σλ1,2 5 for polarized two-photon production of a massive fermion pair. The explicit LO amplitude (Eq. 7) and detector weight (Eq. 6) yield a distribution that, in the massless limit at fixed non-collinear angle, vanishes while its angular integral remains finite and equal to the anomaly (Eqs. 8–9). The same singular collinear localization and finite integrated sum rules are shown for the free-field tower of zilch fluxes Zl (Eqs. 16–21) and, by power counting of the same-helicity channel against the total cross section, for the mixed axial-gravitational anomaly. A strong-field LLL realization further sources every zilch moment by the integrated anomalous divergence (Eq. 22). Brief comments address multipoint correlators and hadronic matching.

Significance. If the results hold, the work supplies a concrete collider-language realization of the IR face of the axial anomaly: an angular detector counterpart of the Dolgov–Zakharov spectral collapse. The LO electromagnetic calculation is fully explicit, parameter-free, and directly checkable; the non-commuting limits and the recovery of the anomaly sum rule follow rigorously from that expression. The extension to energy-weighted zilch fluxes and the mixed gravitational channel, while more schematic, opens a natural two-parameter family of anomaly-controlled detector sum rules and connects cleanly to existing literature on zilch vortical effects. The operator identity (Eq. 4) further implies that the integrated constraints survive inside higher-point flow correlators, making the construction potentially relevant for archival e+e− energy-correlator analyses.

major comments (2)
  1. Higher-spin helicity detectors section, Eqs. (16)–(21) and the paragraph after Eq. (21): the finite integrated zilch-flux sum rules are presented as axial-anomaly-controlled, yet the paper explicitly states that it does not derive the complete operator form of the divergences of Zα1…αl. Consequently the sum rules remain free-field kinematic statements for the two-body states considered, not operator identities of the same status as Eq. (4). Either a derivation (or a clear reference) of the anomalous divergences, or a precise restriction of the claim to free-field eigenvalues and LO matrix elements, is required before the tower can be advertised as anomaly-controlled at the operator level.
  2. Mixed axial-gravitational channel (paragraph containing Eq. (23)): the argument that mass powers in the same-helicity amplitude are compensated by the total cross section is only sketched by power counting. An explicit LO two-graviton amplitude (or a reference that supplies it) and the resulting normalized Σλλ Z,l are needed to place the gravitational result on the same footing as the fully explicit electromagnetic calculation of Eqs. (7)–(9).
minor comments (4)
  1. Introduction and Conclusions: the suggestion that pion-resolved detector correlations could probe the anomaly after confinement matching is interesting but undeveloped; a short quantitative remark or a reference to existing pion-pole analyses would strengthen the phenomenological claim.
  2. Eq. (7): the fully polarized amplitude squared is dense; a brief intermediate step or a reference to a standard textbook result would aid independent verification.
  3. Notation: β p and β are used interchangeably for the fermion velocity; a single consistent definition would improve readability.
  4. References: the recent ALEPH energy-correlator revival [43] is cited; a sentence clarifying which crossed electroweak assignment would make the axial insertion experimentally accessible would help experimental readers.

Circularity Check

0 steps flagged

No significant circularity: axial-flux sum rules follow from the standard ABJ Ward identity plus an explicit LO QED calculation; zilch and gravitational extensions are free-field kinematics, not forced by self-citation.

full rationale

The load-bearing chain is: (i) the operator axial anomaly (Eq. 3) treated as a standard input; (ii) the integrated flux identity (Eq. 4); (iii) the tree-level polarized γγ→ff̄ amplitude (Eq. 7) and free-field detector eigenvalues (Eq. 6), which produce Σ5 and, after the non-commuting m→0 limit, the collinear deltas (Eq. 9) whose integral recovers the anomaly (Eq. 8). No parameters are fitted; the sum rule is not a normalization identity. Higher-spin (zilch) fluxes are proportional to Σ5 for the equal-energy two-body state by free-field eigenvalues (Eqs. 18–19), so the same singular structure is kinematic, not a new anomaly derivation. Self-citations to zilch/vortical-effect papers supply motivation and background and are not used as uniqueness theorems or as the sole support for the EM result. The paper explicitly declines to derive operator divergences of the higher-spin currents, so it does not smuggle those in via citation. The mixed gravitational channel is argued by power counting of the same-helicity amplitude against the total cross section, again without circular reduction. Score 0 is therefore appropriate.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The central claims rest on the standard axial (and mixed gravitational) anomaly Ward identities, free-field definitions of higher-spin currents, and the assumption that the leading-order two-body cut dominates the detector one-point functions for the states considered. No free parameters are introduced; the only ad-hoc element is the truncation to LO 2 o2 kinematics.

axioms (4)
  • domain assumption Axial anomaly operator identity ∂μ J5μ = 2im ψ̄ γ5 ψ + (2α/π) E·B (and its gravitational analogue)
    Used as an exact operator relation to constrain the angle-integrated flux (Eq. 4) independently of the state.
  • domain assumption Parity-odd higher-spin currents Zα1…αl are conserved for free massless fermions and define flux operators via the same light-ray limit as the axial current
    Eq. (16)–(17); conservation is free-field; anomalous divergences are not derived.
  • ad hoc to paper Leading-order polarized two-photon (or two-graviton) to fermion-antifermion amplitude saturates the detector one-point function for the states under study
    Explicit |M|^{2} (Eq. 7) is the sole dynamical input; multi-particle and higher-order cuts are neglected.
  • standard math Massless limit and angular integration may be interchanged only after the full angular integral is performed
    Standard distributional statement underlying the non-commuting limits; justified by the explicit eta-dependent expressions.

pith-pipeline@v1.1.0-grok45 · 17247 in / 2688 out tokens · 49541 ms · 2026-07-10T23:46:21.604633+00:00 · methodology

0 comments
read the original abstract

Quantum anomalies provide a bridge between ultraviolet properties of a theory and its infrared sector. We study how this connection appears in axial-charge-flow observables. In the simplest example, an axial-charge detector probes the fermionic cut of the anomalous triangle and resolves its infrared content as an angular distribution. The massless limit does not commute with the angular integration: a contribution suppressed at fixed angle collapses onto the two beam-collinear directions while retaining the finite integrated sum rule fixed by the axial anomaly. We then replace the axial-charge detector by higher-spin helicity (zilch) detectors and study a family of axial-anomaly-controlled energy-weighted sum rules for the corresponding fluxes. We further show that the same singular localization mechanism and finite zilch-flux sum rules persist in the mixed axial-gravitational channel. We briefly comment on extensions to more general states and multipoint correlators.

Figures

Figures reproduced from arXiv: 2607.06667 by Andrey V. Sadofyev, Jo\~ao Barata, Ratmir Jumanov.

Figure 1
Figure 1. Figure 1: Anomalous triangle embedded in an e +e −–initiated process. The dashed line schematically indicates the cut through the on-shell fermionic state resolved by Q5. The axial anomaly is often introduced through its UV face: the regularization of the corresponding triangle di￾agram. However, it also possesses an IR face, encoded in the spectral representation of the same triangle. In particular, the anomalous s… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages · 44 internal anchors

  1. [1]

    Anomalies in Quantum Field The- ory

    R.A.Bertlmann,“Anomalies in Quantum Field The- ory”, Oxford Univ. Press (1996)

    work page 1996

  2. [2]

    The Trace Anomaly and Massless Scalar Degrees of Freedom in Gravity

    M. Giannotti & E. Mottola,“The Trace Anomaly and Massless Scalar Degrees of Freedom in Gravity”, Phys. Rev. D79, 045014 (2009),arXiv:0812.0351

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  3. [3]

    On Conservation of the axial current in massless electrodynamics

    A. D. Dolgov & V. I. Zakharov,“On Conservation of the axial current in massless electrodynamics”, Nucl. Phys.B27, 525 (1971)

    work page 1971

  4. [4]

    The Axial Anomaly and the Bound State Spectrum in Confining Theories

    Y. Frishman, A. Schwimmer, T. Banks & S. Yankielowicz,“The Axial Anomaly and the Bound State Spectrum in Confining Theories”, Nucl. Phys. B177, 157 (1981)

    work page 1981

  5. [5]

    ’t Hooft’s Consis- tency Condition as a Consequence of Analyticity and Unitarity

    S. R. Coleman & B. Grossman,“’t Hooft’s Consis- tency Condition as a Consequence of Analyticity and Unitarity”, Nucl. Phys. B203, 205 (1982)

    work page 1982

  6. [6]

    Chiral Magnetic and Vortical Effects in High-Energy Nuclear Collisions --- A Status Report

    D. E. Kharzeev, J. Liao, S. A. Voloshin & G. Wang,“Chiral magnetic and vortical effects in high-energy nuclear collisions—A status re- port”, Prog. Part. Nucl. Phys.88, 1 (2016), arXiv:1511.04050

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  7. [7]

    Electromagnetic fields and anomalous transports in heavy-ion collisions --- A pedagogical review

    X.-G. Huang,“Electromagnetic fields and anoma- lous transports in heavy-ion collisions — A pedagog- ical review”, Rept. Prog. Phys.79, 076302 (2016), arXiv:1509.04073

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    Notes on Anomaly Induced Transport

    K. Landsteiner,“Notes on Anomaly Induced Trans- port”, Acta Phys. Polon. B47, 2617 (2016), arXiv:1610.04413

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  9. [9]

    Chiral effects in astrophysics and cosmology

    K. Kamada, N. Yamamoto & D.-L. Yang, “Chiral effects in astrophysics and cosmology”, Prog. Part. Nucl. Phys.129, 104016 (2023), arXiv:2207.09184

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  10. [10]

    Conformal collider physics: Energy and charge correlations

    D. M. Hofman & J. Maldacena,“Conformal collider physics: Energy and charge correlations”, JHEP 0805, 012 (2008),arXiv:0803.1467

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  11. [11]

    Event shapes in N=4 super-Yang-Mills theory

    A. Belitsky, S. Hohenegger, G. Korchemsky, E. Sokatchev & A. Zhiboedov,“Event shapes in N= 4super-Yang-Mills theory”, Nucl. Phys. B884, 206 (2014),arXiv:1309.1424

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  12. [12]

    N=4 superconformal Ward identities for correlation functions

    A. Belitsky, S. Hohenegger, G. Korchemsky & E. Sokatchev,“N=4 superconformal Ward identities for correlation functions”, Nucl. Phys. B904, 176 (2016),arXiv:1409.2502

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  13. [13]

    Averaged Null Energy Condition from Causality

    T. Hartman, S. Kundu & A. Tajdini,“Averaged Null Energy Condition from Causality”, JHEP1707, 066 (2017),arXiv:1610.05308

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  14. [14]

    Averaged Null Energy and the Renormalization Group

    T.Hartman&G.Mathys,“Averaged null energy and the renormalization group”, JHEP2312, 139 (2023), arXiv:2309.14409

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  15. [15]

    Energy Correlators: A Journey From Theory to Experiment

    I. Moult & H. X. Zhu,“Energy Correla- tors: A Journey From Theory to Experiment”, arXiv:2506.09119

    work page internal anchor Pith review Pith/arXiv arXiv

  16. [16]

    En- ergy Correlations in electron-Positron Annihilation in Quantum Chromodynamics: Asymptotically Free Perturbation Theory

    C. Basham, L. Brown, S. Ellis & S. Love,“En- ergy Correlations in electron-Positron Annihilation in Quantum Chromodynamics: Asymptotically Free Perturbation Theory”, Phys. Rev. D19, 2018 (1979)

    work page 2018

  17. [17]

    Energy Correlations in Perturbative Quan- tum Chromodynamics: A Conjecture for All Orders

    C. L. Basham, L. S. Brown, S. D. Ellis & S. T. Love,“Energy Correlations in Perturbative Quan- tum Chromodynamics: A Conjecture for All Orders”, Phys. Lett. B85, 297 (1979)

    work page 1979

  18. [18]

    Electron - Positron Annihilation Energy Pat- tern in Quantum Chromodynamics: Asymptotically Free Perturbation Theory

    C. L. Basham, L. S. Brown, S. D. Ellis & S. T. Love,“Electron - Positron Annihilation Energy Pat- tern in Quantum Chromodynamics: Asymptotically Free Perturbation Theory”, Phys. Rev. D17, 2298 (1978)

    work page 1978

  19. [19]

    Energy Correlations in electron - Positron Annihi- lation: Testing QCD

    C. Basham, L. S. Brown, S. D. Ellis & S. T. Love, “Energy Correlations in electron - Positron Annihi- lation: Testing QCD”, Phys. Rev. Lett.41, 1585 (1978)

    work page 1978

  20. [20]

    AN OP- ERATOR APPROACH TO WEIGHTED CROSS- SECTIONS

    F. R. Ore, Jr. & G. F. Sterman,“AN OP- ERATOR APPROACH TO WEIGHTED CROSS- SECTIONS”, Nucl. Phys. B165, 93 (1980)

    work page 1980

  21. [21]

    Jets and Quantum Field Theory

    N. Sveshnikov & F. Tkachov,“Jets and quan- tum field theory”, Phys. Lett. B382, 403 (1996), hep-ph/9512370

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  22. [22]

    Measuring Multijet Structure of Hadronic Energy Flow Or What IS A Jet?

    F. V. Tkachov,“Measuring multi - jet struc- ture of hadronic energy flow or What is a jet?”, Int. J. Mod. Phys. A12, 5411 (1997), hep-ph/9601308

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  23. [23]

    Power corrections to event shapes and factorization

    G. P. Korchemsky & G. F. Sterman,“Power corrections to event shapes and factorization”, Nucl. Phys. B555, 335 (1999),hep-ph/9902341

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  24. [24]

    From correlation functions to event shapes in QCD

    D. Chicherin, J. M. Henn, E. Sokatchev & K. Yan, “From correlation functions to event shapes in QCD”, JHEP2102, 053 (2021),arXiv:2001.10806

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  25. [25]

    On the Edge of Safety: Charge-Charge Correlation in the Back-to-Back Limit

    P. F. Monni, G. Vita, Z. Xu & H. X. Zhu,“On the Edge of Safety: Charge-Charge Correlation in the Back-to-Back Limit”,arXiv:2508.00977

    work page internal anchor Pith review Pith/arXiv arXiv

  26. [26]

    Axial vector vertex in spinor electrody- namics

    S. L. Adler,“Axial vector vertex in spinor electrody- namics”, Phys. Rev.177, 2426 (1969)

    work page 1969

  27. [27]

    A PCAC puzzle: pi0→ gamma gamma in the sigma model

    J. S. Bell & R. Jackiw,“A PCAC puzzle: pi0→ gamma gamma in the sigma model”, Nuovo Cimento A60, 47 (1969)

    work page 1969

  28. [28]

    Nonperturbative evaluation of the anomalies in low-energy theorems

    R. J. Crewther,“Nonperturbative evaluation of the anomalies in low-energy theorems”, Phys. Rev. Lett. 28, 1421 (1972)

    work page 1972

  29. [29]

    Energy- Momentum-Tensor Trace Anomaly in Spin 1/2 Quantum Electrodynamics

    S. L. Adler, J. C. Collins & A. Duncan,“Energy- Momentum-Tensor Trace Anomaly in Spin 1/2 Quantum Electrodynamics”, Phys. Rev. D15, 1712 (1977)

    work page 1977

  30. [30]

    Trace and Dilatation Anomalies in Gauge Theo- ries

    J. C. Collins, A. Duncan & S. D. Joglekar, “Trace and Dilatation Anomalies in Gauge Theo- ries”, Phys. Rev. D16, 438 (1977)

    work page 1977

  31. [31]

    The Energy Momentum Tensor in a Nonabelian Quark Gluon Theory

    N. K. Nielsen,“The Energy Momentum Tensor in a Nonabelian Quark Gluon Theory”, Nucl. Phys. B 120, 212 (1977)

    work page 1977

  32. [32]

    Observations on Conformal Anomalies

    M.J.Duff,“Observations on Conformal Anomalies”, 7 Nucl. Phys. B125, 334 (1977)

    work page 1977

  33. [33]

    Chiral and trace anomalies in Deeply Virtual Compton Scattering

    S. Bhattacharya, Y. Hatta & W. Vogelsang,“Chi- ral and trace anomalies in deeply virtual Comp- ton scattering”, Phys. Rev. D107, 014026 (2023), arXiv:2210.13419

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  34. [34]

    Anomaly Poles as Common Signatures of Chiral and Conformal Anomalies

    R. Armillis, C. Coriano & L. Delle Rose,“Anomaly Poles as Common Signatures of Chiral and Con- formal Anomalies”, Phys. Lett. B682, 322 (2009), arXiv:0909.4522

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  35. [35]

    Anomaly and long-range forces

    V. P. Kirilin, A. V. Sadofyev & V. I. Zakharov, “Anomaly and long-range forces”, in“100th anniver- sary of the birth of I.Ya. Pomeranchuk”, p. 272–286

    work page

  36. [36]

    Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly

    E. Mottola & A. V. Sadofyev,“Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly”, Nucl. Phys. B966, 115385 (2021), arXiv:1909.01974

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  37. [37]

    The role of the chiral anomaly in polarized deeply inelastic scattering I: Finding the triangle graph inside the box diagram in Bjorken and Regge asymptotics

    A. Tarasov & R. Venugopalan,“Role of the chi- ral anomaly in polarized deeply inelastic scattering: Finding the triangle graph inside the box diagram in Bjorken and Regge asymptotics”, Phys. Rev. D102, 114022 (2020),arXiv:2008.08104

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  38. [38]

    The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

    A. Tarasov & R. Venugopalan,“The role of the chi- ral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emer- gent axion-like dynamics”, Phys. Rev. D105, 014020 (2022),arXiv:2109.10370

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  39. [39]

    Axions and Superfluidity in Weyl Semimetals

    E. Mottola, A. V. Sadofyev & A. Stergiou,“Axions and superfluidity in Weyl semimetals”, Phys. Rev. B 109, 134512 (2024),arXiv:2310.08629

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  40. [40]

    Parity-Odd 3-Point Functions from CFT in Momentum Space and the Chiral Anomaly

    C. Corianò, S. Lionetti & M. M. Maglio,“Parity-odd 3-point functions from CFT in momentum space and the chiral anomaly”, Eur. Phys. J. C83, 502 (2023), arXiv:2303.10710

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  41. [41]

    Axion-like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

    C. Corianò, M. Cretì, S. Lionetti, D. Melle & R. Tommasi,“Axion-Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect”, Adv. Phys. Res.4, 2400043 (2025), arXiv:2403.15641

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  42. [42]

    Dy- namics of the Standard Model

    J. F. Donoghue, E. Golowich & B. R. Holstein,“Dy- namics of the Standard Model”, Cambridge Univ. Press (2014)

    work page 2014

  43. [43]

    Energy Correlators from Partons to Hadrons: Unveiling the Dynamics of the Strong Interactions with Archival ALEPH Data

    Electron-Positron Alliance Collaboration, H. Bossi et al.,“Energy Correlators from Partons to Hadrons: Unveiling the Dynamics of the Strong Interactions with Archival ALEPH Data”,arXiv:2511.00149

    work page arXiv

  44. [44]

    Existence of a New Conservation Law in Electromagnetic Theory

    D. M. Lipkin,“Existence of a New Conservation Law in Electromagnetic Theory”, Journal of Mathemati- cal Physics5, 696 (1964)

    work page 1964

  45. [45]

    Conservation Laws for Free Fields

    T. W. B. Kibble,“Conservation Laws for Free Fields”, Journal of Mathematical Physics6, 1022 (1965)

    work page 1965

  46. [46]

    The Zilch Vortical Effect

    M. N. Chernodub, A. Cortijo & K. Landsteiner, “Zilch vortical effect”, Phys. Rev. D98, 065016 (2018),arXiv:1807.10705

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  47. [47]

    Zilch Vortical Effect, Berry Phase, and Kinetic Theory

    X.-G. Huang, P. Mitkin, A. V. Sadofyev & E. Speranza,“Zilch Vortical Effect, Berry Phase, and Kinetic Theory”, JHEP2010, 117 (2020), arXiv:2006.03591

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  48. [48]

    Zilch Vortical Effect for Fermions

    A. Alexandrov & P. Mitkin,“Zilch Vortical Ef- fect for Fermions”, JHEP2105, 070 (2021), arXiv:2011.09429

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  49. [49]

    Wigner functions and quantum kinetic theory of polarized photons

    K. Hattori, Y. Hidaka, N. Yamamoto & D.-L. Yang,“Wigner functions and quantum kinetic the- ory of polarized photons”, JHEP2102, 001 (2021), arXiv:2010.13368

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  50. [50]

    Chiral Vortical Effect for Bosons

    A. Avkhadiev & A. V. Sadofyev,“Chiral Vortical Effect for Bosons”, Phys. Rev. D96, 045015 (2017), arXiv:1702.07340

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  51. [51]

    Photonic chiral vortical effect

    N. Yamamoto,“Photonic chiral vortical effect”, Phys.Rev.D96, 051902(2017),arXiv:1702.08886

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  52. [52]

    Chiral magnetic effect of light

    T. Hayata,“Chiral magnetic effect of light”, Phys. Rev. B97, 205102 (2018),arXiv:1705.09926

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  53. [53]

    Chiral Vortical Effect For An Arbitrary Spin

    X.-G. Huang & A. V. Sadofyev,“Chiral Vortical Ef- fect For An Arbitrary Spin”, JHEP1903, 084(2019), arXiv:1805.08779

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  54. [54]

    Chiral vortical effect for vector fields

    G. Y. Prokhorov, O. V. Teryaev & V. I. Zakharov, “Chiral vortical effect for vector fields”, Phys. Rev. D 103, 085003 (2021),arXiv:2009.11402

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  55. [55]

    Anomaly/Transport in an Ideal Weyl gas

    R. Loganayagam & P. Surowka, “Anomaly/Transport in an Ideal Weyl gas”, JHEP 1204, 097 (2012),arXiv:1201.2812

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  56. [56]

    Constraints on Anomalous Fluid in Arbitrary Dimensions

    N. Banerjee, S. Dutta, S. Jain, R. Loganayagam & T. Sharma,“Constraints on Anomalous Fluid in Arbitrary Dimensions”, JHEP1303, 048 (2013), arXiv:1206.6499

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  57. [57]

    Chiral kinetic theory and anomalous hydrodynamics in even spacetime dimensions

    V. Dwivedi & M. Stone,“Chiral kinetic the- ory and anomalous hydrodynamics in even space- time dimensions”, J. Phys. A50, 155202 (2017), arXiv:1606.04945

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  58. [58]

    Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion

    M. Stone & J. Kim,“Mixed Anomalies: Chi- ral Vortical Effect and the Sommerfeld Expansion”, Phys.Rev.D98, 025012(2018),arXiv:1804.08668

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  59. [59]

    Divergence of axial-vector current in the gravitational field

    T. Kimura,“Divergence of axial-vector current in the gravitational field”, Prog. Theor. Phys.42, 1191 (1969)

    work page 1969

  60. [60]

    The gravitational cor- rection to pcac

    R. Delbourgo & A. Salam,“The gravitational cor- rection to pcac”, Phys. Lett. B40, 381 (1972)

    work page 1972

  61. [61]

    Quantum Gravity and World Topology

    T.Eguchi &P.G.O.Freund,“Quantum Gravity and World Topology”, Phys. Rev. Lett.37, 1251 (1976)

    work page 1976

  62. [62]

    Gravitational Anomalies

    L. Alvarez-Gaume & E. Witten,“Gravitational Anomalies”, Nucl. Phys. B234, 269 (1984)

    work page 1984

  63. [63]

    Parity-Violating CFT and the Gravitational Chiral Anomaly

    C. Corianò, S. Lionetti & M. M. Maglio, “Parity-violating CFT and the gravitational chi- ral anomaly”, Phys. Rev. D109, 045004 (2024), arXiv:2309.05374

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  64. [64]

    Topological Sum Rules and Spectral Flows of Chiral and Gravitational Axion-like Interactions

    C. Corianò, S. Lionetti & D. Melle,“Topological sum rules and spectral flows of chiral and gravitational axionlike interactions”, Phys. Rev. D112, 015031 (2025),arXiv:2502.03182

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  65. [65]

    Chiral Boson Anomaly in a Gravitational Field

    A. D. Dolgov, I. B. Khriplovich & V. I. Zakharov, “Chiral Boson Anomaly in a Gravitational Field”, JETP Lett.45, 651 (1987). 8

    work page 1987

  66. [66]

    MACROSCOPIC MANIFESTATIONS OF THE CHIRAL ANOMALY IN GRAVITATIONAL FIELD

    A. D. Dolgov, I. B. Khriplovich & V. I. Za- kharov,“MACROSCOPIC MANIFESTATIONS OF THE CHIRAL ANOMALY IN GRAVITATIONAL FIELD”, Sov. Phys. JETP67, 237 (1988)

    work page 1988

  67. [67]

    CHIRAL PHOTON CURRENT AND ITS ANOMALY IN A GRAVITATIONAL FIELD

    A.I.Vainshtein, A.D.Dolgov, V.I.Zakharov&I.B. Khriplovich,“CHIRAL PHOTON CURRENT AND ITS ANOMALY IN A GRAVITATIONAL FIELD”, Sov. Phys. JETP67, 1326 (1988)

    work page 1988

  68. [68]

    Photonic Chiral Current and Its Anomaly in a Gravitational Field

    A. D. Dolgov, I. B. Khriplovich, A. I. Vainshtein & V. I. Zakharov,“Photonic Chiral Current and Its Anomaly in a Gravitational Field”, Nucl. Phys. B 315, 138 (1989)

    work page 1989

  69. [69]

    VANISHING OF THE CHI- RAL ANOMALY FOR ANTISYMMETRIC TEN- SOR FIELD

    A. D. Dolgov, I. B. Khriplovich, A. I. Vainshtein & V. I. Zakharov,“VANISHING OF THE CHI- RAL ANOMALY FOR ANTISYMMETRIC TEN- SOR FIELD”, Nucl. Phys. B313, 73 (1989)

    work page 1989

  70. [70]

    Gravitational Axial Anomaly for Four Dimensional Conformal Field Theories

    J.Erdmenger,“Gravitational axial anomaly for four- dimensional conformal field theories”, Nucl. Phys. B 562, 315 (1999),hep-th/9905176

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  71. [71]

    Noticethatthisanomalyre-appearsindifferentmea- sures of the helicity current, see e.g. [? ? ?]

    work page

  72. [72]

    Rethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation

    H. Chen, I. Moult, X. Zhang & H. X. Zhu,“Rethink- ing jets with energy correlators: Tracks, resumma- tion, and analytic continuation”, Phys. Rev. D102, 054012 (2020),arXiv:2004.11381

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  73. [73]

    One-point correlators of conserved and non-conserved charges in QCD

    M. Riembau & M. Son,“One-point corre- lators of conserved and nonconserved charges in QCD”, Phys. Rev. D111, 014004 (2025), arXiv:2407.12082

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  74. [74]

    Exploitingν- dependence of projected energy correlators in HICs

    A. Budhraja & B. Singh,“Exploitingν- dependence of projected energy correlators in HICs”, Phys. Lett. B872, 140079 (2026), arXiv:2503.20019

    work page arXiv 2026

  75. [75]

    Energy cor- relators beyond angles

    S. Alipour-fard & W. J. Waalewijn,“Energy cor- relators beyond angles”, JHEP2507, 043 (2025), arXiv:2501.17218

    work page arXiv 2025

  76. [76]

    [77, 78]

    Closely related higher-spin generalizations of the ax- ial anomaly were considered in the literature, see e.g. [77, 78]

    work page

  77. [77]

    Gauge symmetry and the EMC spin effect

    S. D. Bass,“Gauge symmetry and the EMC spin ef- fect”, Z. Phys. C60, 343 (1993),hep-ph/9305323

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  78. [78]

    Non-local generalization of the axial anomaly and $x$-dependence of the anomalous gluon contribution

    D. Mueller & O. V. Teryaev,“Nonlocal generaliza- tion of the axial anomaly and x dependence of the anomalous gluon contribution”, Phys. Rev. D56, 2607 (1997),hep-ph/9701413

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  79. [79]

    ADLER-BELL- JACKIW ANOMALY AND WEYL FERMIONS IN CRYSTAL

    H. B. Nielsen & M. Ninomiya,“ADLER-BELL- JACKIW ANOMALY AND WEYL FERMIONS IN CRYSTAL”, Phys. Lett. B130, 389 (1983)

    work page 1983