Note on the Radiation Field of the Electron

Bloch, F.; Nordsieck, A.

doi:10.1103/physrev.52.54

Cited by 1,276 publications

(1,020 citation statements)

References 4 publications

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“…Gauge theory scattering amplitudes are known to be infrared singular [1]. Understanding the detailed structure of these singularities is important for collider physics : it is a prior condition to cross-section calculations in which these singularities cancel in the sum of real and virtual corrections.…”

Section: Jhep04(2014)044mentioning

confidence: 99%

“…Individual webs will be identified by the number of gluon attachments to each of the Wilson lines. We will compute the 1-1 web at one loop (figure 4), which contributes to the leading-order cusp anomalous dimension Γ (1) 2 , the 1-2-1 web at two-loops (upper diagrams in figure 6), which contributes to Γ (2) 3 , and the 1-2-2-1 and 1-1-1-3 webs at three loops (figures 7 and 8, respectively) both contributing to Γ (3) 4 . It should be noted that for this class of webs, the renormalization of the coupling becomes irrelevant, and it will not be discussed further in this paper.…”

Section: Jhep04(2014)044mentioning

confidence: 99%

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From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1/α ij , at the level of the symbol the result also admits a crossing symmetry α ij → −α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and 1 − α 2 ij . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

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Section: Jhep04(2014)044mentioning

confidence: 99%

Section: Jhep04(2014)044mentioning

confidence: 99%

From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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“…[242,243]). The main outcome of these approximations is the replacement of the Dirac equation (6.11) by the following equation, known as the Bloch-Nordsieck (BN) equation [241,242] : 18) where v µ = (1, v) and v is a fixed parameter, to be identified with the velocity of the hard quasiparticle (here v is a unit vector).…”

Section: The Bloch-nordsieck Approximationmentioning

confidence: 99%

The quark–gluon plasma: collective dynamics and hard thermal loops

Blaizot¹,

Iancu²

2002

Physics Reports

511

714

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We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling g is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale gT , which is well separated from the typical energy of single particle excitations which is the temperature T . We show that the short wavelength thermal fluctuations, i.e., the plasma particles, provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in g, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. By solving these equations, we effectively integrate out the hard degrees of freedom, and are left with an effective theory for the soft collective excitations. As a by-product, the "hard thermal loops" emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. This can be used to estimate the effect of the soft thermal fluctuations on the correlation functions. The effect of collisions among the hard particles is also studied. In particular we discuss how the collisions affect the lifetimes of quasiparticle excitations in a regime where the mean free path is comparable with the range of the relevant interactions. Collisions play also a decisive role in the construction a Member of CNRS. E-mail: blaizot@spht.saclay.cea.fr b Member of CNRS. E-mail: iancu@spht.saclay.cea.fr c Laboratoire de la Direction des Sciences de la Matière du Commissariatà l'Energie Atomique of the effective theory for ultrasoft excitations, with momenta ∼ g 2 T , a topic which is briefly addressed at the end of this paper.

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“…The Bloch Nordsiek theorem [37] assures the cancellation of infrared divergences in any inclusive cross section. Collinear divergences, instead, come from massless particles having a vanishing value of the relative emission angle.…”

Section: Cancellation Of Mass Singularitiesmentioning

confidence: 99%

Light mesons and muon radiative decays and photon polarization asymmetry

Gabrielli

Trentadue

2008

Nuclear Physics B

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We systematically compute and discuss meson and muon polarized radiative decays. Doubly differential distributions in terms of momenta and helicities of the final lepton and photon are explicitly computed. The undergoing dynamics giving rise to lepton and photon polarizations is examined and analyzed in the soft and hard region of momenta. The particular configurations made by right-handed leptons with accompanying photons are investigated and interpreted as a manifestation of the axial anomaly. The photon polarization asymmetry is evaluated. Finiteness of polarized amplitudes against infrared and collinear singularities is shown to take place with mechanisms distinguishing between right handed and left handed final leptons. We propose a possible test using photon polarization to clarify a recently observed discrepancy in radiative meson decays.

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Note on the Radiation Field of the Electron

Cited by 1,276 publications

References 4 publications

From webs to polylogarithms

From webs to polylogarithms

The quark–gluon plasma: collective dynamics and hard thermal loops

Light mesons and muon radiative decays and photon polarization asymmetry

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