Analytic Structure of the Landau-Gauge Gluon Propagator

Abstract

The analytic structure of the non-perturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.

Exciting flavored bound states

“…Incidentally, this approximation bears similarity with common phenomenological Ansätze to the BSA for D mesons [76][77][78][79][80] and this is exactly what the values in Table III represent: masses and decay constants obtained with a model based on the lowest-order approximation for which the eigenvalues and BSA are real. The mass difference, ∆m [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] MeV, between the D and D s mesons is smaller than experimentally observed, i.e. ∆m ∼ 100 MeV.…”

“…Our motivation is to verify whether a fully consistent, simultaneous numerical solution of the heavy-quark DSE and heavy-light pseudoscalar meson BSE can be obtained with a modern approach to the rainbow-ladder (RL) truncation based on the interaction proposed by Qin et al [41]. This Ansatz produces an infrared behavior of the interaction, commonly described by a "dressing function" G(k 2 ) [32], congruent with the decoupling solution found in DSE and lattice studies of the gluon propagator [7][8][9][10][11][12][13][14][15][16][17]21]. Indeed, the gluon propagator is found to be a bounded and regular function of spacelike momenta with a maximum value at k 2 = 0.…”

Phase diagram and thermal properties of strong-interaction matter

“…This associates it with dynamically-driven changes in the analytic structure of QCD's propagators and vertices [50][51][52][53][54][55] that occur because both gluons and quarks acquire running mass distributions, which are large at infrared momenta. This leads to the emergence of a length-scale ς ≈ 0.5 fm, whose existence and size is evident in all continuum and lQCD studies of dressed-gluons and -quarks: ς characterises the material change in their analytic structure [6,35,56,57]. From this perspective, deconfinement occurs when ς → 0 and reflection positivity is thus recovered.…”

Baryons as relativistic three-quark bound states

“…The gluon propagator has been studied intensely in the past both on the lattice, with DSEs and the FRG due to its supposed connection with confinement of the non-Abelian gauge theory, see e.g. [200,216,227,[229][230][231][232][233][234][235][236] and references therein. Due to its much more complicated structure, the nonperturbative three-gluon vertex has only been begun to be explored in numerical simulations in recent years, see e.g.…”