The Theory of Quark and Gluon Interactions

Ynduráin, Félix

doi:10.1007/978-3-662-02940-4

Cited by 130 publications

(274 citation statements)

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“…µ √ s). After renormalization all the dependence of observables on the energy scale appears through the running coupling in a well prescribed form (for more details see, for instance, [6][7][8][9][10]). …”

Section: Elements Of Qcd 11 Renormalization and The Running Couplingmentioning

confidence: 99%

“…The application of pQCD relies in what are known as factorization theorems [6][7][8][9][10], which prove that factorization is possible for particular processes and observables, i.e., that the singularities which appear in the calculations either cancel or can be absorbed in the definitions of physical quantities. As we have seen, the ultraviolet divergences stemming from virtual radiative corrections are contained in the running coupling constant and are automatically included in the renormalized theory by changing the bare coupling for the running coupling α s (µ 2 ).…”

Section: Factorization and The Rg Evolution Equationsmentioning

confidence: 99%

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Dynamical parton distributions of the nucleon

Jimenez-Delgado¹

2009

Nuclear Physics B - Proceedings Supplements

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Section: Elements Of Qcd 11 Renormalization and The Running Couplingmentioning

confidence: 99%

Section: Factorization and The Rg Evolution Equationsmentioning

confidence: 99%

Dynamical parton distributions of the nucleon

Jimenez-Delgado¹

2009

Nuclear Physics B - Proceedings Supplements

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“…The Strong Coupling Constant The strong coupling constant s = g 2 s =4 [9] e v olves with the energy at which the interaction takes place.…”

Section: The Standard Modelmentioning

confidence: 99%

“…This is possible due to the simplication that the sum over all individual hadronic states jhi must equal one, P jhihhj = 1. See [9] for further details. Figure 1.7 shows the all hadronic cross section in e + e annihilation through the Z exchange.…”

Section: E + E Collisionsmentioning

confidence: 99%

Hadronic Charmless B Decays at the SLD

Reinertsen¹

1999

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“…[6,7]). Notations below closely follow the book by Ynduráin [3].Let us consider an EFT model described by the following bare Lagrangian:whereis the standard QCD Lagrangian [3] and L 1 contains an infinite number of terms of non-renormalizable interactions which are necessary for the cancelation of divergences of loop diagrams. Let us investigate the renormalization group behavior of renormalized coupling constant g R by analyzing the Bψψ Green's function using dimensional regularization (with parameter n) in combination with the MS scheme.…”

mentioning

confidence: 99%

Asymptotic freedom in massive Yang-Mills theory

Gegelia¹

2007

Phys. Rev. D

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An effective field theory model of the massive Yang-Mills theory is considered. Assuming that the renormalized coupling constants of 'non-renormalizable' interactions are suppressed by a large scale parameter it is shown that in analogy to the non-abelian gauge invariant theory the dimensionless coupling constant vanishes logarithmically for large values of the renormalization scale parameter.PACS numbers: 11.10. Gh, 03.70.+k, 11.10.Hi The standard model (SM) is an established consistent theory of strong, electromagnetic and weak interactions. It describes most of the known phenomena in elementary particle physics. The modern point of view is to think of the SM as an effective field theory, "low-energy approximation to a deeper theory that may not even be a field theory, but something different like a string theory" [1]. While the effective Lagrangian consists of an infinite number of terms, the non-renormalizable interactions are suppressed by powers of a large scale. This makes the contributions of these interactions negligible for energies much lower than the large scale. Renormalizability in the traditional sense is not considered as a fundamental principle but rather a property of the leading order approximation to the full effective theory.The SM takes gauge invariance as a starting point. In modern string theories [2] one first notices a state of mass zero and unit spin among the normal modes of a string, and then from that deduces the gauge invariance of the effective field theory that describes such particles [1]. In modern approach one usually takes gauge invariance as the starting point. Referring again to Weinberg's book, "It is too soon to tell which of these two alternatives corresponds to the logical order of nature" [1]. Taking into account the above considerations it is not evident that the gauge invariance principle should be applied to weak interaction as it is not mediated by massless vectors. As the fundamental nature of both the gauge invariance and the renormalizability seems to be questionable, the role of the scalar sector of the electro-weak theory could be also questioned, especially as the experimental status of the scalar Higgs particle remains still unclear. Therefore it seems interesting to have a closer look to effective field theory models of massive vector mesons which are not based on the concept of gauge invariance.In the present work an effective field theory model of the massive vector mesons interacting with fermions is considered. I do not deal here with the most general effective Lagrangian, but instead add the mass term of the vector mesons to the standard QCD Lagrangian [3]. Next I add an infinite number of non-renormalizable interactions which are required to absorb the divergences generated by loop diagrams of the perturbation theory. I assume that all coupling constants of non-renormalizable interactions are suppressed by powers of a Large scale parameter Λ. Under this assumption I study the renormalization group behavior of the dimensionless coupling constant to ...

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The Theory of Quark and Gluon Interactions

Cited by 130 publications

References 0 publications

Dynamical parton distributions of the nucleon

Dynamical parton distributions of the nucleon

Hadronic Charmless B Decays at the SLD

Asymptotic freedom in massive Yang-Mills theory

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