Strong QCD and Dyson–Schwinger equations

Roberts, Craig D.

doi:10.4171/143-1/7

Cited by 19 publications

(23 citation statements)

References 249 publications

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“…Our goal is calculation of the last of these, D(0), and for this we choose to work within the continuum framework provided by QCD's Dyson-Schwinger equations (DSEs) [23][24][25]. To be specific, we perform the computation using a global-symmetry-preserving treatment of a vector×vector contact-interaction because that has proven to be a reliable explanatory and predictive tool for hadron properties measured with probe momenta less-than the dressed-quark mass, M ∼ 0.4 GeV [17][18][19][20][21][22].…”

Section: B Contact Interactionmentioning

confidence: 99%

Electric dipole moment of theρmeson

et al. 2013

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At an hadronic scale the effect of CP-violating interactions that typically appear in extensions of the Standard Model may be described by an effective Lagrangian, in which the operators are expressed in terms of lepton and partonic gluon and quark fields, and ordered by their mass dimension, k ≥ 4. Using a global-symmetry-preserving truncation of QCD's Dyson-Schwinger equations, we compute the ρ-meson's electric dipole moment (EDM), dρ, as generated by the leading dimensionfour and -five CP-violating operators and an example of a dimension-six four-quark operator. The two dimension-five operators; viz., quark-EDM and -chromo-EDM, produce contributions to dρ whose coefficients are of the same sign and within a factor of two in magnitude. Moreover, should a suppression mechanism be verified for the θ-term in any beyond-Standard-Model theory, the contribution from a four-quark operator can match the quark-EDM and -chromo-EDM in importance. This study serves as a prototype for the more challenging task of computing the neutron's EDM.

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Section: B Contact Interactionmentioning

confidence: 99%

Electric dipole moment of theρmeson

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“…Beyond U(1) and SU (2), we find no mass generation for G 2 (N c = 7) and F 4 (N c = 26), both with a relatively small color factor C F = 1 in spite of their large dimension; and also for SO(N c ) with N c = 1 to 5 and for Sp (2). For all these groups, an explicit fermion mass m just yields an M(p 2 ) that slightly separates from the perturbative value without really yielding symmetry breaking.…”

Section: Mass Generation At the Hadron Scale (With Cutoff Regularizatmentioning

confidence: 94%

“…From the figure, it stands out that for U (1) and SU (2) there is no chiral symmetry breaking, i.e. M(0) = 0, for the same coupling intensity that generates the 300 MeV quark mass in SU (3).…”

Section: Mass Generation At the Hadron Scale (With Cutoff Regularizatmentioning

confidence: 99%

“…11: that the fermion mass becomes very large for larger groups, and that it scales for moderate N c as in Eq. (2). Further discussion spans section 5.…”

Section: M(0)mentioning

confidence: 99%

“…Next in difficulty is the rainbow approximation to the Dyson-Schwinger equation [2] of the fermion propagator in the gauge theory, so we settle to it [3]. While a very basic approximation, the simplicity of the scenario we propose does not require more sophisticated many-body methods.…”

Section: Some Properties Of Spontaneous Mass Generationmentioning

confidence: 99%

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Spontaneous mass generation and the small dimensions of the Standard Model gauge groups U(1),SU(2) and SU(3)

Llanes-Estrada¹,

Fernández²,

Rojas³

2018

Proceedings of the European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2017)

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ScienceDirectNuclear Physics B 915 (2017) We observe that fermions charged under large groups acquire much bigger dynamical masses, all things being equal at a high e.g. GUT scale, than ordinary quarks. Should such multicharged fermions exist, they are too heavy to be observed today and have either decayed early on (if they couple to the rest of the Standard Model) or become reliquial dark matter (if they don't).The result follows from strong antiscreening of the running coupling for those larger groups (with an appropriately small number of flavors) together with scaling properties of the Dyson-Schwinger equation for the fermion mass.

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Elastic and Transition Form Factors of the Δ(1232)

et al. 2013

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Predictions obtained with a confining, symmetry-preserving treatment of a vector ⊗ vector contact interaction at leading-order in a widely used truncation of QCD's Dyson-Schwinger equations are presented for ∆ and Ω baryon elastic form factors and the γN → ∆ transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest. The ∆ elastic form factors are very sensitive to m ∆ . Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce ∆-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the ∆(1232). Considering the ∆-baryon's quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the ∆-baryon's deformation in the infinite momentum frame. Results for analogous properties of the Ω baryon are less contentious. In connection with the N → ∆ transition, the Ash-convention magnetic transition form factor falls faster than the neutron's magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and ∆; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.

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Strong QCD and Dyson–Schwinger equations

Cited by 19 publications

References 249 publications

Electric dipole moment of theρmeson

Electric dipole moment of theρmeson

Spontaneous mass generation and the small dimensions of the Standard Model gauge groups U(1),SU(2) and SU(3)

Elastic and Transition Form Factors of the Δ(1232)

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