β-function for the Higgs self-interaction in the Standard Model at three-loop level

Three-loop beta function for the Higgs self-coupling

“…Every β -function is a power series in all couplings of the theory which is why the β -functions for all numerically relevant couplings are needed. Recently, the β -functions for the gauge couplings [1,2,5], Yukawa couplings [3,7] and for the Higgs self-interaction [3,4,6] have been computed at three-loop level.…”

“…There are many challenges to the computation of the three-loop β -function for the Higgs self-interaction. One is the huge number of Feynman diagrams, 573692 for the Φ 4 1 -vertex even if we factorize the full gauge group factor from the momentum space factor for each diagram (for details see [4]). Another issue is the proper treatment of γ 5 in dimensional regularization.…”

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In the last two years the renormalization group functions for the couplings and fields of the Standard Model have been computed at three-loop level [1][2][3][4][5][6][7]. The evolution of the self-coupling λ of the Standard Model Higgs boson is of particular importance due to its close connection with the stability of the Standard Model vacuum state.

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Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory

“…After discovering the Higgs boson at the LHC [8,9] and a burst of activity on the vacuum stability problem (see, e.g., [10]), it became clear that three-loop RG functions [11][12][13][14][15][16] can play an essential role in precision studies of the SM and its extensions. Partial four-loop results in the SM [17][18][19] and three-loop beta functions in the Two-Higgs-Doublet Model(THDM) [20] became available during the past few years.…”

All two-loop scalar self-energies and tadpoles in general renormalisable field theories

“…The Higgs boson mass has been measured to an accuracy of about O(100) MeV, making it an electroweak precision parameter. In the Standard Model (SM), this is used to extract the Higgs quartic coupling λ, which, through a significant amount of work, can now be done with high precision, where all of the relevant running parameters of the Lagrangian can now be extracted from calculations at full two-loop order [1,2] and partially at the three-and four-loop order [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A code for calculating λ in Landau gauge, SMH [17], and codes for extracting all relevant SM parameters (the gauge couplings, top and bottom Yukawa couplings, and Higgs quartic coupling), mr [18,19] and SMDR [20], exist.…”