Three-loop gauge beta function in non-simple gauge groups

Mihaila, L.

doi:10.22323/1.197.0060

Cited by 20 publications

(43 citation statements)

References 19 publications

(26 reference statements)

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“…The three-loop (NNLO) β-functions of a gauge theory with simple groups were given partially in [48], then in [49]. The full NNLO β-functions for the SM were presented in [50] and those for generic representations of non-simple gauge groups in [51]. In this last paper, some contributions from the Yukawa and quartic Higgs interactions were not included.…”

Section: Perturbative β-Functions: a Digest Of The Literaturementioning

confidence: 99%

In search of a UV completion of the standard model — 378,000 models that don’t work

Barducci

Fabbrichesi

Nieto

et al. 2018

J. High Energ. Phys.

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Asymptotically safe extensions of the Standard Model have been searched for by adding vector-like fermions charged under the Standard Model gauge group and having Yukawa-like interactions with new scalar fields. Here we study the corresponding renormalization group β-functions to next and next-to-next to leading order in the perturbative expansion, varying the number of extra fermions and the representations they carry. We test the fixed points of the β-functions against various criteria of perturbativity to single out those that are potentially viable. We show that all the candidate ultraviolet fixed points are unphysical for these models: either they are unstable under radiative corrections, or they cannot be matched to the Standard Model at low energies. arXiv:1807.05584v2 [hep-ph] 27 Jul 2018 39 A. Analysis of marginal couplings 39 B. Conformal field theory and central charges 41 C. All the fixed points in the 210 approximation scheme 43 D. Coefficients of the NLO and NNLO β-functions 43 References 46

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Section: Perturbative β-Functions: a Digest Of The Literaturementioning

confidence: 99%

In search of a UV completion of the standard model — 378,000 models that don’t work

Barducci

Fabbrichesi

Nieto

et al. 2018

J. High Energ. Phys.

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“…Following [35], we use the notation d(F i ) to specify the dimension of the representation R with respect to the ith gauge group G i . Furthermore, we also define the multiplicity of a representation with respect to a subset of the original direct product of simple gauge groups as…”

Section: Jhep05(2015)046mentioning

confidence: 99%

“…In [35], one may also find the additional contributions from scalars that we do not use in this paper.…”

Section: Jhep05(2015)046mentioning

confidence: 99%

“…In this appendix, we review the recent results of three-loop beta functions of gauge coupling constants for general multiple gauge theories [35] (see also [36] for a single gauge group). We consider the direct product of simple gauge groups G i with the gauge coupling constants g i (i = 1, · · · , n).…”

Section: A Three-loop Beta Functions Of General Multiple Gauge Theoriesmentioning

confidence: 99%

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Perturbative search for dead-end CFTs

Nakayama

2015

J. High Energ. Phys.

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To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as O(10 −5 ) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.

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“…(I) Below a scale µ EW ∼ M Z , we work in 5 or 4-flavor QCD×QED theory (decoupling of b at µ = m b (m b ) is properly taken into account [6]). We solve QCD 3-loop and QED 1-loop RG equation [7] for QCD coupling α s in the range µ EW > µ > 2 GeV and that for QED coupling α em in the range µ EW > µ > 13 GeV (we ignore QED effects below 13 GeV), with the initial values of α (III) We match 5-flavor QCD×QED theory with the full SM at µ = µ EW . For t quark mass, we adopt the pole mass obtained from the exclusive t pair production cross section at the LHC [12], M t = 173.7 +2.3 −2.1 GeV, and for W, Z and Higgs boson masses and G F , we use Particle Data Group values [13].…”

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confidence: 99%

Prediction on neutrino Dirac and Majorana phases and absolute mass scale from the CKM matrix

Haba

Yamada

2018

Phys. Rev. D

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In Type-I seesaw model, the lepton flavor mixing matrix (PMNS matrix) and the quark flavor mixing matrix (CKM matrix) may be connected implicitly through a relation between the neutrino Dirac Yukawa coupling Y D and the quark Yukawa couplings. In this paper, we study whether Y D can satisfy, in the flavor basis where the charged lepton Yukawa and righthanded neutrino Majorana mass matrices are diagonal, the relationCKM without contradicting the current experimental data on quarks and neutrino oscillations. We search for sets of values of the neutrino Dirac CP phase δ CP , Majorana phases α 2 , α 3 , and the lightest active neutrino mass that satisfy either of the above relations, with the normal or inverted hierarchy of neutrino mass. In performing the search, we consider renormalization group evolutions of the quark masses and CKM matrix and the propagation of their experimental errors along the evolutions. We find that only the former relation Y D ∝ diag(y d , y s , y b )V T CKM with the normal neutrino mass hierarchy holds, based on which we make a prediction for δ CP , α 2 , α 3 and the lightest active neutrino mass.

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Three-loop gauge beta function in non-simple gauge groups

Cited by 20 publications

References 19 publications

In search of a UV completion of the standard model — 378,000 models that don’t work

In search of a UV completion of the standard model — 378,000 models that don’t work

Perturbative search for dead-end CFTs

Prediction on neutrino Dirac and Majorana phases and absolute mass scale from the CKM matrix

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