Three loop gauge β-function for the most general single gauge-coupling theory

Pickering, A.; Gracey, J.A.; Jones, D.R.T.

doi:10.1016/s0370-2693(01)00624-4

Cited by 76 publications

(89 citation statements)

References 38 publications

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“…subsection 2.3), including corrections from the Yukawa couplings. We did the calculation in our framework and found agreement with the known result in the literature [21,44,45].…”

Section: Heavy Gauge Bosonsupporting

confidence: 86%

“…For the MSSM full three-loop RGEs are available [19,20] in the so-called DR scheme. The same is true for the most general single gauge coupling theory in MS and a general supersymmetric GUT in DR [21,22]. Matching corrections at the SUSY scale are known to one-loop order for the U(1) and SU(2) gauge couplings α 1/2 [7] and to two-loop for the strong coupling α s [12,13].…”

Section: Introductionmentioning

confidence: 75%

“…(37) and (32)) as well as the numerical values for the group theory factors into the general formulas of refs. [21,45] (see appendix C for the details).…”

Section: Numerical Study For the Georgi-glashow Modelmentioning

confidence: 99%

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Towards a two-loop matching of gauge couplings in grand unified theories

Martens

2011

J. High Energ. Phys.

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We calculate the two-loop matching corrections for the gauge couplings at the Grand Unification scale in a general framework that aims at making as few assumptions on the underlying Grand Unified Theory (GUT) as possible. In this paper we present an intermediate result that is general enough to be applied to the GeorgiGlashow SU (5) as a "toy model". The numerical effects in this theory are found to be larger than the current experimental uncertainty on α s . Furthermore, we give many technical details regarding renormalization procedure, tadpole terms, gauge fixing and the treatment of group theory factors, which is useful preparative work for the extension of the calculation to supersymmetric GUTs.

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“…subsection 2.3), including corrections from the Yukawa couplings. We did the calculation in our framework and found agreement with the known result in the literature [21,44,45].…”

Section: Heavy Gauge Bosonsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 75%

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Towards a two-loop matching of gauge couplings in grand unified theories

Martens

2011

J. High Energ. Phys.

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“…Thus, we can show curves for N = 1, 2, 3 and 4 which corresponds to the (thick) dotted, dash-dotted, dashed and solid line, respectively. Within QCD the beta function is known to four-loop accuracy [32,33], however, the supersymmetric analogue only to three loops [19,34,35]. 2 As a consequence for the four-loop curve in Fig.…”

Section: Decoupling Of Heavy Supersymmetric Particlesmentioning

confidence: 99%

Decoupling constant for α s and the effective gluon-Higgs coupling to three loops in supersymmetric QCD

Kurz

Steinhauser

Zerf

2012

J. High Energ. Phys.

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We compute the three-loop QCD corrections to the decoupling constant for α s which relates the Minimal Supersymmetric Standard Model to Quantum Chromodynamics with five or six active flavours. The new results can be used to study the stability of α s evaluated at a high scale from the knowledge of its value at M Z . We furthermore derive a low-energy theorem which allows the calculation of the coefficient function of the effective Higgs boson-gluon operator from the decoupling constant. This constitutes the first independent check of the matching coefficient to three loops.

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“…For a general theory based on a simple gauge group the three-loop corrections to the gauge coupling beta function have been calculated in Ref. [22]. In this Letter we provide results for the three-loop gauge coupling beta functions taking into account all sectors of the Standard Model, i.e., the gauge, Yukawa and Higgs boson self-couplings.…”

mentioning

confidence: 98%

Gauge coupling beta functions in the standard model to three loops

2012

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In this Letter we compute the three-loop corrections to the beta functions of the three gauge couplings in the Standard Model of particle physics using the minimal subtraction scheme and taking into account Yukawa and Higgs self-couplings.PACS numbers: 11.10.Hi 11.15.BtRenormalization group functions are fundamental quantities of each quantum field theory and play an important role in various aspects. Besides controlling the energy dependence of parameters and fields they are also crucial for the resummation of large logarithms. Furthermore, renormalization group functions are important for the development of grand unified theories and the extrapolation of low-energy precision data to high energies, not accessible by collider experiments.As far as the strong interaction part of the Standard Model is concerned the corresponding gauge coupling beta function is known up to four-loop order [1][2][3][4][5][6][7][8][9][10] [21].) For a general theory based on a simple gauge group the three-loop corrections to the gauge coupling beta function have been calculated in Ref. [22]. In this Letter we provide results for the three-loop gauge coupling beta functions taking into account all sectors of the Standard Model, i.e., the gauge, Yukawa and Higgs boson self-couplings.Let us in a first step define the beta functions. We denote the three gauge couplings by α 1 , α 2 and α 3 and adopt a SU (5)-like normalization withwhere α is the fine structure constant, θ W the weak mixing angle and α s the strong coupling. In our calculation we consider in addition to the gauge couplings also the third-generation Yukawa couplings [34] α 4 = α t , α 5 = α b and α 6 = α τ , and the Higgs boson self-couplingwhere m x and M W are the fermion and W boson mass, respectively, and −λ(Φ † Φ) 2 is the part of the Lagrange density describing the quartic Higgs self interaction.The functions β i are obtained from the renormalization constants of the corresponding gauge couplings that are defined as g bare i = µ ǫ Z gi g i where α i = g 2 i /(4π). Exploiting the fact that the g bare i are µ-independent and taking into account that Z gi may depend on all seven couplings leads to the following formulawhere ǫ = (4 − d)/2 is the regulator of Dimensional Regularization with d being the space-time dimension used for the evaluation of the momentum integrals and the dependence of α i on the renormalization scale µ is suppressed. From Eq. (2) it is clear that the renormalization constants Z gi (i = 1, 2, 3) have to be computed up to three-loop order.In the modified minimal subtraction (MS) renormalization scheme the perturbative expansion of the gauge coupling beta functions can be written asIn this Letter we evaluate the three-loop terms (coefficients c ijk ) only for the gauge couplings (i.e. i = 1, 2, 3). For our calculation the beta functions for the Yukawa couplings are needed to the one-loop order and the treelevel expression [first term in Eq. (3)] is sufficient for β λ . In the MS scheme the beta functions are mass independent that allows us to use th...

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Three loop gauge β-function for the most general single gauge-coupling theory

Cited by 76 publications

References 38 publications

Towards a two-loop matching of gauge couplings in grand unified theories

Towards a two-loop matching of gauge couplings in grand unified theories

Decoupling constant for α s and the effective gluon-Higgs coupling to three loops in supersymmetric QCD

Gauge coupling beta functions in the standard model to three loops

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