Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Revisiting extremely high energy QED bremsstrahlung in matter: large modifications to the LPM effect

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Pair production weakens the LPM suppression of very soft bremsstrahlung.

desk verdict A real result in large-Nf QED with a plausible but unproven leap to Nf=1; the enhancement claim for real matter deserves peer review but not uncritical acceptance. read the letter →

arxiv 2508.21120 v1 pith:IJ455A3Z submitted 2025-08-28 hep-ph nucl-th

Peter Arnold , Joshua Bautista , Omar Elgedawy , Shahin Iqbal This is my paper
classification hep-phnucl-th PACS 12.20.-m13.40.-f41.60.-m
keywords Landau-Pomeranchuk-Migdaleffectbremsstrahlungpairproductionquantumoverlapultra-highenergyQEDformationtimeelectromagneticshowerslarge-Nf
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the Landau-Pomeranchuk-Migdal (LPM) suppression of bremsstrahlung, the main energy-loss mechanism for extremely high energy electrons in matter, is substantially weaker for very soft photons than the standard LPM formula predicts. The reason is that, when the photon is soft enough, it converts to an electron-positron pair during the quantum-mechanical formation time of the bremsstrahlung, and the charged pair is deflected by the medium much more easily than the parent electron. That deflection disrupts the long-lived coherence that causes LPM suppression, effectively shortening the formation time and raising the rate. The paper verifies the qualitative argument with an analytic calculation in a simplified many-flavor version of QED, obtaining an explicit formula for the corrected rate, and argues the result applies to the real single-flavor case. If correct, the finding reverses the direction of an effect predicted in the 1960s, from further suppression to significant enhancement.

What carries the argument

The central object is the resummed fermion-loop (pair-production) insertion in the photon propagator of the bremsstrahlung diagram. In the soft-photon limit the medium-averaged four-particle evolution factorizes into independent pair and electron-positron pieces, and the sum over n bubble insertions exponentiates to e^{-G_pair Delta t}, where G_pair is a complex quantity whose real part is half the total LPM pair-production rate. This exponential truncates the formation-time integral at ~1/Gamma_pair, replacing the usual LPM formation time in the very-soft regime. The remaining integrals are evaluated analytically using the harmonic-oscillator form of the medium-averaged Hamiltonian and stan

What would settle it

Compute the full single-flavor rate for soft bremsstrahlung including the interference diagrams that mix the two final-state electrons, and compare the coefficient of the x_gamma^{-3/2} term with eq. (1.19); a mismatch would show the large-flavor extrapolation fails. A dedicated accelerator measurement of very-soft photon emission from electrons with E >> ELPM/alpha in a thick target could also settle the question.

Watch

Extended reading notes

Core claim

The central result is an analytic expression for the differential bremsstrahlung rate including quantum overlap with pair production, eq. (1.19): the rate equals the ordinary LPM rate multiplied by 1 + Nf alpha/(2 x_gamma) f(x_gamma), where x_gamma = k_gamma/E is the photon energy fraction, Nf is the number of lepton flavors, and f involves a digamma function plus logarithms. In the very-soft limit x_gamma << Nf alpha, the correction term dominates and the rate grows like x_gamma^{-3/2} times a logarithmic factor, far above the ordinary LPM rate. The mechanism is shown diagrammatically: summing fermion-loop bubbles in the photon line produces a factor e^{-G Delta t} that cuts off the bremsst

Load-bearing premise

The load-bearing premise is that the result obtained in the simplified many-flavor QED, where pair-produced leptons are distinguishable from the original electron, carries over to the physical one-flavor case; the authors state explicitly that they do not claim a fully systematic and rigorous diagrammatic analysis for that transfer.

Editorial extensions

If this is right

  • Electromagnetic shower simulations at energies above roughly ELPM/alpha will underpredict very-soft photon emission if they use the ordinary LPM rate.
  • The rate formula predicts a parametric x_gamma^{-3/2} growth in the very-soft region, a sharp, testable signature.
  • The 1960s expectation that pair production deepens LPM suppression is replaced by the opposite: pair production weakens it.
  • Because the result is parameter-free (only alpha and the medium's transport coefficient enter), it can be checked by a dedicated accelerator experiment at sufficiently high energy.
  • The same formation-time cutoff mechanism is expected to modify other in-medium processes where an emitted particle is itself unstable in the medium.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A symmetric enhancement should appear in LPM-suppressed pair production when the produced lepton emits a soft photon during pair formation; the authors do not compute this.
  • The large-flavor formula could be tested by performing the full single-flavor calculation in the soft-photon limit, where the flavor-distinguishability complication is least severe.
  • The principle that the formation time is the smaller of the LPM formation time and the pair-conversion time could serve as a simple diagnostic for other media, including strongly coupled plasmas, where this paper's QED setting provides a clean quantitative test.
  • The logarithmic factor in the final rate admits a Weizsäcker-Williams interpretation as a medium-modified photon distribution, suggesting the result can be rephrased in distribution-function language for shower codes.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper revisits the LPM suppression of ultra-high-energy QED bremsstrahlung in amorphous matter, in the deep-LPM regime E >= k_gamma >> E_LPM. It argues that, when the emitted photon is very soft, k_gamma <~ alpha E, the bremsstrahlung formation process overlaps with subsequent pair production of the photon. Contrary to Galitsky and Gurevich, the authors find that this overlap increases the bremsstrahlung rate relative to the standard LPM rate. The central analytic result, eq. (1.19), gives [dGamma/dx_gamma]_{LPM+} = [dGamma/dx_gamma]_{LPM} [1 + N_f alpha/(2 x_gamma) f(x_gamma)], with the explicit f(x_gamma) in eq. (1.19b); in the very-soft limit x_gamma << N_f alpha the rate grows as x_gamma^{-3/2} times a logarithmic factor, eq. (1.21). The calculation is performed in large-N_f QED, using the multiple-scattering (q-hat) approximation and soft-photon factorization. The NLO large-N_f limit is shown to match the numerical result of ref. [25], and section 6 argues heuristically that the result should apply to N_f=1.

Significance. If correct, the result is significant: it predicts that the LPM suppression of very soft bremsstrahlung is substantially weakened once pair-production overlap is included, reversing the qualitative conclusion of Galitsky and Gurevich. The paper is refreshingly explicit about its assumptions and limitations, and it gives a parameter-free analytic formula rather than a fit. The independent cross-check against the numerical result of ref. [25] in the NLO limit, including the constant 0.567, is a genuine strength, as is the physical interpretation of the logarithm in section 7. The main uncertainty is not internal consistency of the large-N_f calculation but the extrapolation to physical N_f=1, which the authors themselves flag as not fully rigorous.

major comments (3)
  1. [Section 6, eqs. (1.19)-(1.21)] The physical prediction for real electrons relies on the transfer of the large-N_f result to N_f=1. The authors state, 'we do not claim a fully systematic and rigorous diagrammatic analysis.' At N_f=1 the pair-produced electron is identical to the initial electron, so the interference diagrams of fig. 28 and additional-photon-line diagrams are no longer suppressed by 1/N_f. Since the predicted enhancement in eq. (1.21) scales as x_gamma^{-3/2} and can be orders of magnitude above the ordinary LPM rate, an O(1) contribution from these omitted diagrams could change the coefficient or the functional form. The argument that soft-photon distinguishability suppresses these contributions is plausible but is not backed by a diagrammatic estimate. A concrete evaluation of fig. 28 in the soft limit, or a numerical extension of the methods of refs. [13,25] to N_f=1, is needed to make the central cl
  2. [Sections 4.4.2 and 5.2, around eqs. (4.22) and (5.12)] The vacuum-loop contribution to the overlap diagram is dropped without explicit calculation. The authors give two qualitative arguments and cite ref. [13] for renormalization consistency, but the n>=2 bubble resummation in section 5.2 relies on replacing the pair-production loop by the vacuum-subtracted quantity G_pair, eq. (5.12). If the omitted vacuum contribution carries a ln(1/x_gamma) or ln(1/alpha) enhancement, it would affect the coefficient of the leading x_gamma^{-3/2} behavior in eq. (1.21). The NLO cross-check in the regime N_f alpha << x_gamma << 1 is reassuring but does not validate the very-soft regime x_gamma << N_f alpha where the claimed effect is largest. An explicit check, even at the level of a regulated one-loop calculation, would strengthen this step.
  3. [Section 2.2 and eq. (1.4b)] The qualitative preview and the final formula are for the 'net rate' of energy loss, but the abstract and introduction state the result as a modification of the bremsstrahlung rate. For N_f=1, the descendant of the original electron is ambiguous when pair production overlaps, as the authors themselves explain in section 6 using fig. 28. The paper should either define the observable more prominently at the outset or present eq. (1.19) explicitly as the net e->e rate. This is not a numerical error, but it affects how the prediction should be compared with future experiments and with existing LPM calculations.
minor comments (4)
  1. [Eq. (7.3)] The equation for the Weizsäcker-Williams distribution writes alpha_s in a QED context; this should presumably be alpha, the QED fine-structure constant. Please check.
  2. [Figs. 2 and 3 and surrounding text] The notation 'LPM /BH' and 'LPM /LPM' is missing the '+' subscript in several places, making it easy to confuse LPM+ with the ordinary LPM rate. Please typeset consistently as LPM_+.
  3. [Section 1.2, eq. (1.4b)] The preview in eq. (1.4b) is for N_f=1, but eq. (1.21) contains explicit N_f and alpha dependence. The relationship between the two is clear from the text, but a short sentence noting that eq. (1.4b) is the parametric N_f=1 version would help the reader.
  4. [General] The paper is long and somewhat repetitive in the introductory sections; a short table of the main approximations (deep LPM, massless electron, soft-photon, large-N_f, large-log q-hat) would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the large-Nf derivation is self-contained; the Nf=1 extrapolation is an acknowledged non-rigorous argument (correctness risk), not a circle.

full rationale

The paper's central formula (1.19) is obtained by an explicit analytic calculation in large-Nf QED (Sections 4-5): the NLO correction is derived from time-ordered diagrams (eq. 4.32), and the x_gamma << Nf-alpha extension follows from resumming photon self-energy bubbles (fig. 26, eqs. 5.14-5.22), with the integral evaluated in appendix E. No parameter is fitted to the target rate: the previous numerical result of ref. [25] is used only as a post-hoc cross-check ('matches fairly well the previous, numerically-extracted result (2.24b)'), and the analytic coefficients (4.29), (4.31) are computed, not imported. The heavy use of the authors' own formalism (refs. [13,25-28]) is not circular: those works provide the Zakharov/Migdal framework and prior cross-checks, and the present paper re-derives the soft-photon factorization and evaluates the relevant integrals. The genuine weakness is Section 6, where the transfer to Nf=1 is admittedly not rigorous: 'we do not claim a fully systematic and rigorous diagrammatic analysis.' This is an explicit limitation of the extrapolation, not a definitional reduction or a fitted-input prediction, and therefore belongs to correctness risk rather than circularity. Accordingly no circular step is identified.

Assumptions & free parameters 0 free parameters · 8 assumptions · 0 invented entities

No fitted parameters appear in the derivation. The central calculation rests on the Zakharov effective-Hamiltonian formalism, the qhat harmonic-oscillator approximation, the large-Nf limit, soft-photon factorization of the 4-body potential, and the heuristic extension to Nf=1; all are listed as axioms above.

assumptions (8)
  • domain assumption Zakharov's effective Hamiltonian formalism correctly describes medium-averaged splitting rates in high-energy QED.
    Invoked throughout Section 3 to compute LPM rates and overlap corrections; standard in the medium-induced radiation literature but used as an unproved background framework.
  • domain assumption Medium elastic scattering can be approximated by multiple soft Gaussian scatterings with parameter qhat, giving V(b) = -i qhat b^2/4.
    Section 3.2; leading-log approximation that ignores power-law tails. The paper states this is the only large-logarithm approximation made.
  • ad hoc to paper In the large-Nf limit, fermion-loop insertions dominate over extra photon lines by 1/Nf, and pair-produced leptons are distinguishable from the initial electron.
    Section 5.1; enables the bubble resummation and defines the energy-loss rate without final-state identification ambiguity. This is a simplifying but non-physical limit for Nf=1.
  • domain assumption Soft-photon factorization: during the brief virtual pair interval, the 4-body potential decouples into independent 2-body terms, eq. (4.14).
    Section 4.3; relies on the separation of scales |b_e-e+| << |b_E-E+| and t_pair << t_brem. This is a controlled approximation in the x_gamma << 1 limit.
  • ad hoc to paper The vacuum-loop contribution to the overlap diagram is negligible in the soft-photon limit without explicit calculation.
    Section 4.4.2; justified qualitatively and delegated to prior ref [13] for verification, but not computed in this paper. This is a derivation gap.
  • ad hoc to paper The n>=2 bubble time integrals may have their upper limits replaced by infinity, with the final result dominated by the expected time scales.
    Section 5.2; the paper claims and verifies a posteriori that the dominant scales are Delta t0 ~ t_LPM and bubble separations ~ 1/Gamma_pair, but no rigorous bound is given.
  • domain assumption Electron mass and dielectric photon mass can be neglected in the region (1.2).
    Section 1.2; restricts validity to k_gamma >> E_LPM and 1-x_gamma >> E_LPM/E. Future work is needed for the massive case.
  • ad hoc to paper The large-Nf result applies to Nf=1 after replacing dGamma/dx_gamma by a net e->e rate.
    Section 6; argued via soft-photon distinguishability and net-rate reinterpretation, but explicitly not a fully systematic diagrammatic proof. This is the main fragility for the headline claim.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Revisiting extremely high energy QED bremsstrahlung in matter: large modifications to the LPM effect." pith.science (2026). https://pith.science/paper/IJ455A3Z

@misc{pith2026250821120,
  author       = {Pith},
  title        = {Pith review of: Revisiting extremely high energy QED bremsstrahlung in matter: large modifications to the LPM effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IJ455A3Z}},
  note         = {Machine review of arXiv:2508.21120}
}
abstract

Very high energy electrons initiate electromagnetic showers in ordinary matter that branch and multiply through bremsstrahlung and pair production. At extremely high energies, the quantum mechanical duration of these processes becomes longer than the mean free time to elastically scatter from the medium, which leads to a very significant suppression of bremsstrahlung (and pair production) known as the Landau-Pomeranchuk-Migdal (LPM) effect. We revisit the LPM effect for bremsstrahlung of energy $k_\gamma$ from an electron of energy $E$. We find that there are very large corrections to the LPM bremsstrahlung rate for certain regions of $(k_\gamma,E)$ due to quantum overlap of bremsstrahlung and subsequent pair production. This possibility was first raised in the 1960s, when it was argued qualitatively that pair production would significantly decrease the bremsstrahlung rate in those regions of $(k_\gamma,E)$ compared to the already-suppressed LPM bremsstrahlung rate. We find the opposite -- quantum overlap of bremsstrahlung with pair production significantly *increases* the bremsstrahlung rate compared to the LPM calculation -- and we verify our qualitative arguments with an analytic calculation of the effect.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Mapping jet substructure in heavy-ion collisions with track functions

    hep-ph 2026-06 unverdicted novelty 6.0 of 10

    Track functions exhibit model-dependent modifications to higher moments in heavy-ion jets, with RG flows qualitatively preserved, enabling discrimination between jet quenching pictures.

Reference graph

Works this paper leans on

51 extracted references · 16 canonical work pages · cited by 1 Pith paper

  1. [25]

    Strong vs. weakly coupled in-medium showers: energy stopping in large-Nf QED,

    P. Arnold, O. Elgedawy and S. Iqbal, “Strong vs. weakly coupled in-medium showers: energy stopping in large-Nf QED,” arXiv:2404.19008 [hep-ph]

    arXiv

  2. [13]

    In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers

    P. Arnold and S. Iqbal, “In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers,” JHEP12, 120 (2018) doi:10.1007/JHEP12(2018)120 [errata: JHEP12, 098 (2023); JHEP09, 169 (2024)] [arXiv:1806.08796 [hep-ph]]

    work page Pith review arXiv 2018

  3. [1]

    Review of particle physics,

    S. Navaset al.[Particle Data Group], “Review of particle physics,” Phys. Rev. D110, no.3, 030001 (2024) doi:10.1103/PhysRevD.110.030001

    doi:10.1103/physrevd.110.030001 2024

  4. [2]

    On the Stopping of fast particles and on the creation of positive electrons,

    H. Bethe and W. Heitler, “On the Stopping of fast particles and on the creation of positive electrons,” Proc. Roy. Soc. Lond. A146, 83-112 (1934) doi:10.1098/rspa.1934.0140

    arXiv 1934

  5. [3]

    Limits of applicability of the theory of bremsstrahlung electrons and pair production at high-energies,

    L. D. Landau and I. Pomeranchuk, “Limits of applicability of the theory of bremsstrahlung electrons and pair production at high-energies,” Dokl. Akad. Nauk Ser. Fiz.92 (1953) 535

    work page 1953

  6. [4]

    Electron cascade process at very high energies,

    L. D. Landau and I. Pomeranchuk, “Electron cascade process at very high energies,” Dokl. Akad. Nauk Ser. Fiz.92 (1953) 735

    work page 1953

  7. [5]

    Landau, The Collected Papers of L.D

    L. Landau, The Collected Papers of L.D. Landau (Pergamon Press, New York, 1965)

    work page 1965

  8. [6]

    Suppression of Bremsstrahlung and Pair Production due to Environmental Factors

    S. Klein, “Suppression of bremsstrahlung and pair production due to environmental factors,” Rev. Mod. Phys. 71, 1501-1538 (1999) doi:10.1103/RevModPhys.71.1501 [arXiv:hep-ph/9802442 [hep-ph]]

    work page Pith review arXiv 1999

Show all 51 references
  1. [7]

    The interaction of relativistic particles with strong crystalline fields,

    U. I. Uggerhøj, “The interaction of relativistic particles with strong crystalline fields,” Rev. Mod. Phys. 77, 1131-1171 (2005) doi:10.1103/RevModPhys.77.1131

    2005 doi

  2. [8]

    Bremsstrahlung and pair production in condensed media at high-energies,

    A. B. Migdal, “Bremsstrahlung and pair production in condensed media at high-energies,” Phys. Rev. 103, 1811 (1956)

    1956

  3. [9]

    An Accurate measurement of the Landau-Pomeranchuk-Migdal effect,

    P. L. Anthony, R. Becker-Szendy, P. E. Bosted, M. Cavalli-Sforza, L. P. Keller, L. A. Kelley, S. R. Klein, G. Niemi, M. L. Perl and L. S. Rochester,et al.“An Accurate measurement of the Landau-Pomeranchuk-Migdal effect,” Phys. Rev. Lett.75, 1949-1952 (1995) doi:10.1103/PhysRev...

    1949 doi

  4. [10]

    Bremsstrahlung suppression due to the LPM and dielectric effects in a variety of materials,

    P. L. Anthonyet al.[SLAC-E-146], “Bremsstrahlung suppression due to the LPM and dielectric effects in a variety of materials,” Phys. Rev. D56, 1373-1390 (1997) doi:10.1103/PhysRevD.56.1373

    1997 doi

  5. [11]

    Coherence effects in ultra-relativistic electron bremsstrahlung,

    V. M. Galitsky and I. I. Gurevich, “Coherence effects in ultra-relativistic electron bremsstrahlung,” Nuovo Cimento32, 396 (1964)

    1964

  6. [12]

    Arnold, J

    P. Arnold, J. Bautista, O. Elgedawy, S. Iqbal,work in preparation

  7. [14]

    Gluon bremsstrahlung in finite media beyond multiple soft scattering approximation,

    Y. Mehtar-Tani, “Gluon bremsstrahlung in finite media beyond multiple soft scattering approximation,” JHEP 07, 057 (2019) doi:10.1007/JHEP07(2019)057 [arXiv:1903.00506 [hep-ph]]

    2019 arXiv

  8. [15]

    Medium-induced radiative kernel with the Improved Opacity Expansion,

    J. Barata, Y. Mehtar-Tani, A. Soto-Ontoso and K. Tywoniuk, “Medium-induced radiative kernel with the Improved Opacity Expansion,” JHEP09, 153 (2021) [arXiv:2106.07402 [hep-ph]]

    2021 arXiv

  9. [16]

    Improved opacity expansion at NNLO for medium induced gluon radiation,

    J. Barata and Y. Mehtar-Tani, “Improved opacity expansion at NNLO for medium induced gluon radiation,” JHEP10, 176 (2020) [arXiv:2004.02323 [hep-ph]]

    2020 arXiv

  10. [17]

    Are in-medium quark-gluon showers strongly coupled? results in the large-Nf limit,

    P. Arnold, O. Elgedawy and S. Iqbal, “Are in-medium quark-gluon showers strongly coupled? results in the large-Nf limit,” JHEP 01, 193 (2025) doi:10.1007/JHEP01(2025)193 [arXiv:2408.07129 [hep-ph]] – 68 –

    2025 arXiv

  11. [18]

    The Landau-Pomeranchuk-Migdal effect in QED,

    R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne and D. Schiff, “The Landau-Pomeranchuk-Migdal effect in QED,” Nucl. Phys. B478, 577 (1996) doi:10.1016/0550-3213(96)00426-9 [arXiv:hep-ph/9604327]

    1996 arXiv

  12. [19]

    Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma,

    R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne and D. Schiff, “Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma,” Nucl. Phys. B483, 291 (1997) doi:10.1016/S0550-3213(96)00553-6 [arXiv:hep-ph/9607355]

    1997 arXiv

  13. [20]

    Radiative energy loss and p⊥-broadening of high energy partons in nuclei,

    R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne and D. Schiff, “Radiative energy loss and p⊥-broadening of high energy partons in nuclei,” Nucl. Phys. B484 (1997) doi:10.1016/S0550-3213(96)00581-0 [arXiv:hep-ph/9608322]

    1997 arXiv

  14. [21]

    Medium induced radiative energy loss: Equivalence between the BDMPS and Zakharov formalisms,

    R. Baier, Y. L. Dokshitzer, A. H. Mueller and D. Schiff, “Medium induced radiative energy loss: Equivalence between the BDMPS and Zakharov formalisms,” Nucl. Phys. B531, 403-425 (1998) doi:10.1016/S0550-3213(98)00546-X [arXiv:hep-ph/9804212 [hep-ph]]

    1998 arXiv

  15. [22]

    Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD,

    B. G. Zakharov, “Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD,” JETP Lett.63, 952 (1996) doi:10.1134/1.567126 [Pis’ma Zh. Éksp. Teor. Fiz.63, 906 (1996)] [arXiv:hep-ph/9607440]

    1996 arXiv

  16. [23]

    Radiative energy loss of high-energy quarks in finite size nuclear matter and quark-gluon plasma,

    B. G. Zakharov, “Radiative energy loss of high-energy quarks in finite size nuclear matter and quark-gluon plasma,” JETP Lett.65, 615 (1997) doi:10.1134/1.567389 [Pis’ma Zh. Éksp. Teor. Fiz. 65, 585 (1997)] [arXiv:hep-ph/9704255]

    1997 arXiv

  17. [24]

    Light cone path integral approach to the Landau-Pomeranchuk-Migdal effect,

    B. G. Zakharov, “Light cone path integral approach to the Landau-Pomeranchuk-Migdal effect,” Phys. Atom. Nucl.61, 838-854 (1998) [Yad. Fiz.61, 924-940 (1998)] [arXiv:hep-ph/9807540 [hep-ph]]

    1998 arXiv

  18. [26]

    The LPM effect in sequential bremsstrahlung,

    P. Arnold and S. Iqbal, “The LPM effect in sequential bremsstrahlung,” JHEP04, 070 (2015) [erratum JHEP 09, 072 (2016)] doi:10.1007/JHEP09(2016)072, 10.1007/JHEP04(2015)070 [arXiv:1501.04964 [hep-ph]]

    2015 arXiv

  19. [27]

    The LPM effect in sequential bremsstrahlung 2: factorization,

    P. Arnold, H. C. Chang and S. Iqbal, “The LPM effect in sequential bremsstrahlung 2: factorization,” JHEP 09, 078 (2016) [arXiv:1605.07624 [hep-ph]]

    2016

  20. [28]

    The LPM effect in sequential bremsstrahlung: dimensional regularization,

    P. Arnold, H. C. Chang and S. Iqbal, “The LPM effect in sequential bremsstrahlung: dimensional regularization,” JHEP 10, 100 (2016) doi:10.1007/JHEP10(2016)100 [arXiv:1606.08853 [hep-ph]]

    2016 arXiv

  21. [29]

    The LPM effect in sequential bremsstrahlung: nearly complete results for QCD,

    P. Arnold, T. Gorda and S. Iqbal, “The LPM effect in sequential bremsstrahlung: nearly complete results for QCD,” JHEP11, 053 (2020) [erratum JHEP 05, 114 (2022)] doi:10.1007/JHEP11(2020)053, 10.1007/JHEP05(2022)114 [arXiv:2007.15018 [hep-ph]]

    2020 arXiv

  22. [30]

    The LPM effect in sequential bremsstrahlung: incorporation of

    P. Arnold, T. Gorda and S. Iqbal, “The LPM effect in sequential bremsstrahlung: incorporation of ”instantaneous” interactions for QCD,” JHEP11, 130 (2022) doi:10.1007/JHEP11(2022)130 [arXiv:2209.03971 [hep-ph]]

    2022 arXiv

  23. [31]

    Transverse spectra of radiation processes in-medium,

    B. G. Zakharov, “Transverse spectra of radiation processes in-medium,” JETP Lett.70, 176-182 (1999) doi:10.1134/1.568149 arXiv:hep-ph/9906536 [hep-ph]]

    1999 arXiv

  24. [32]

    Transverse momentum dependence of the – 69 – Landau-Pomeranchuk-Migdal effect,

    U. A. Wiedemann and M. Gyulassy, “Transverse momentum dependence of the – 69 – Landau-Pomeranchuk-Migdal effect,” Nucl. Phys. B560, 345-382 (1999) doi:10.1016/S0550-3213(99)00458-7 [arXiv:hep-ph/9906257 [hep-ph]]

    1999 arXiv

  25. [33]

    Gluon radiation off hard quarks in a nuclear environment: Opacity expansion,

    U. A. Wiedemann, “Gluon radiation off hard quarks in a nuclear environment: Opacity expansion,” Nucl. Phys. B588, 303-344 (2000) doi:10.1016/S0550-3213(00)00457-0 [arXiv:hep-ph/0005129 [hep-ph]]

    2000 arXiv

  26. [34]

    Medium-induced gluon branching,

    J. P. Blaizot, F. Dominguez, E. Iancu and Y. Mehtar-Tani, “Medium-induced gluon branching,” JHEP 01, 143 (2013) doi:10.1007/JHEP01(2013)143 [arXiv:1209.4585 [hep-ph]]

    2013 arXiv

  27. [35]

    Medium-induced gluon radiation and colour decoherence beyond the soft approximation,

    L. Apolinário, N. Armesto, J. G. Milhano and C. A. Salgado, “Medium-induced gluon radiation and colour decoherence beyond the soft approximation,” JHEP02, 119 (2015) doi:10.1007/JHEP02(2015)119 [arXiv:1407.0599 [hep-ph]]

    2015 arXiv

  28. [36]

    Calculating the jet quenching parameter from AdS/CFT,

    H. Liu, K. Rajagopal and U. A. Wiedemann, “Calculating the jet quenching parameter from AdS/CFT,” Phys. Rev. Lett.97, 182301 (2006) doi:10.1103/PhysRevLett.97.182301 [hep-ph/0605178]

    2006 arXiv

  29. [37]

    Wilson loops in heavy ion collisions and their calculation in AdS/CFT,

    H. Liu, K. Rajagopal and U. A. Wiedemann, “Wilson loops in heavy ion collisions and their calculation in AdS/CFT,” JHEP0703, 066 (2007) doi:10.1088/1126-6708/2007/03/066 [hep-ph/0612168]

    2007 arXiv

  30. [38]

    Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parametersˆq,

    P. Arnold, “Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parametersˆq,” Phys. Rev. D99, no. 5, 054017 (2019) doi:10.1103/PhysRevD.99.054017 [arXiv:1901.05475 [hep-ph]]

    2019 arXiv

  31. [39]

    Diagrammar,

    G. ’t Hooft and M. J. G. Veltman, “Diagrammar,” NATO Sci. Ser. B4, 177-322 (1974) doi:10.1007/978-1-4684-2826-1_5 [CERN report 73-9]

    1974 doi

  32. [40]

    Exclusive Processes in Perturbative Quantum Chromodynamics,

    G. P. Lepage and S. J. Brodsky, “Exclusive Processes in Perturbative Quantum Chromodynamics,” Phys. Rev. D22, 2157 (1980) doi:10.1103/PhysRevD.22.2157

    1980 doi

  33. [41]

    Exclusive Processes in Quantum Chromodynamics,

    S. J. Brodsky and G. P. Lepage, “Exclusive Processes in Quantum Chromodynamics,” Adv. Ser. Direct. High Energy Phys.5, 93 (1989) doi:10.1142/9789814503266_0002

    1989 doi

  34. [42]

    Quantum chromodynamics and other field theories on the light cone,

    S. J. Brodsky, H. C. Pauli and S. S. Pinsky, “Quantum chromodynamics and other field theories on the light cone,” Phys. Rept.301, 299 (1998) doi:10.1016/S0370-1573(97)00089-6 [hep-ph/9705477]

    1998 arXiv

  35. [43]

    Quantum chromodynamics at high energy,

    Y. V. Kovchegov and E. Levin, “Quantum chromodynamics at high energy,” Cambridge Monogr. Part. Phys. Nucl. Phys. Cosmol.33 (2012); errata available, as of this writing, at ⟨https://www.asc.ohio-state.edu/kovchegov.1/typos.pdf⟩ or on the publisher’s web site under the book’s resources

    2012

  36. [44]

    Radiativep⊥-broadening of high-energy quarks and gluons in QCD matter,

    T. Liou, A. H. Mueller and B. Wu, “Radiativep⊥-broadening of high-energy quarks and gluons in QCD matter,” Nucl. Phys. A916, 102 (2013) doi:10.1016/j.nuclphysa.2013.08.005 [arXiv:1304.7677 [hep-ph]]

    2013 arXiv

  37. [45]

    Renormalization of the jet-quenching parameter,

    J. P. Blaizot and Y. Mehtar-Tani, “Renormalization of the jet-quenching parameter,” Nucl. Phys. A 929, 202 (2014) doi:10.1016/j.nuclphysa.2014.05.018 [arXiv:1403.2323 [hep-ph]]

    2014 arXiv

  38. [46]

    The non-linear evolution of jet quenching,

    E. Iancu, “The non-linear evolution of jet quenching,” JHEP10, 95 (2014) doi:10.1007/JHEP10(2014)095 [arXiv:1403.1996 [hep-ph]] – 70 –

    2014 arXiv

  39. [47]

    Radiative energy loss and radiativep⊥-broadening of high-energy partons in QCD matter,

    B. Wu, “Radiative energy loss and radiativep⊥-broadening of high-energy partons in QCD matter,” JHEP 12, 081 (2014) doi:10.1007/JHEP12(2014)081 [arXiv:1408.5459 [hep-ph]]

    2014 arXiv

  40. [48]

    Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: Gluon shower development,

    P. Arnold, O. Elgedawy and S. Iqbal, “Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: Gluon shower development,” Phys. Rev. D108, no.7, 074015 (2023) doi:10.1103/PhysRevD.108.074015 [arXiv:2302.10215 [hep-ph]]

    2023 arXiv

  41. [49]

    Strong- vs. weak-coupling pictures of jet quenching: a dry run using QED,

    P. Arnold, S. Iqbal and T. Rase, “Strong- vs. weak-coupling pictures of jet quenching: a dry run using QED,” JHEP05, 004 (2019) doi:10.1007/JHEP05(2019)004 [arXiv:1810.06578 [hep-ph]]

    2019 arXiv

  42. [50]

    M. E. Peskin and D. V. Schroeder,An Introduction to quantum field theory, Addison-Wesley, 1995, ISBN 978-0-201-50397-5, 978-0-429-50355-9, 978-0-429-49417-8 doi:10.1201/9780429503559

    1995 doi

  43. [51]

    Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium,

    P. B. Arnold, “Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium,” Phys. Rev. D79, 065025 (2009) doi:10.1103/PhysRevD.79.065025 [arXiv:0808.2767 [hep-ph]]. – 71 –

    2009 arXiv

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.