Abstract
I discuss the matching relations for the running renormalizable parameters when the heavy particles (top quark, Higgs scalar, Z and W vector bosons) are simultaneously decoupled from the Standard Model. The complete two-loop order matching for the electromagnetic coupling and all light fermion masses are obtained, augmenting existing results at 4-loop order in pure QCD and complete two-loop order for the strong coupling. I also review the further sequential decouplings of the lighter fermions (bottom quark, tau lepton, and charm quark) from the low-energy effective theory.
Highlights
The discovery of the Higgs scalar boson at the Large Hadron Collider has put the standard model of particle physics on a firm footing
It seems worthwhile to consider the standard model as quite possibly valid and complete up to well above the TeV energy scale, and to study its precise parameters and predictions, assuming that the layer of fundamental new physics particles is heavy enough to be irrelevant at energy scales within direct reach at colliders
The standard model has within it an interesting hierarchy, with four fundamental particles having masses within a factor of 2.2 of each other, and heavier than all others by well over an order of magnitude. This makes it sensible to consider a low-energy effective theory consisting of the b, c, s, u, d quarks, the τ, μ, e leptons, and their neutrinos, with renormalizable interactions coming from the unbroken SUð3Þc × Uð1ÞEM gauge group, and nonrenormalizable four-fermion couplings to describe the weak interactions. This low-energy effective field theory can be matched onto the full SUð3Þc × SUð2ÞL × Uð1ÞY high-energy theory with no particles decoupled, by considering common physical observables calculated in each theory in terms of parameters defined in the MS renormalization scheme [1,2] based on dimensional regularization [3,4,5,6,7]
Summary
The discovery of the Higgs scalar boson at the Large Hadron Collider has put the standard model of particle physics on a firm footing. [79], the relationship between the bottom quark on-shell mass and its Yukawa coupling and running mass were obtained at two-loop order in the gaugeless limit, for both a tree-level VEV schemepffiaffi nd an “on-shell” definition of the VEV, v2on-shell ≡ 1= 2GF This has been extended to full twoloop order in Ref. I will give the analytic results for the matching relations for the bottom quark as well as all other light quark masses, using the tadpole-free scheme to define the standard model VEV (and the running masses) in the nondecoupled theory. ΦðzÞ 1⁄4 4 z 1−z pffiffi Cl2ð2 arcsinð zÞÞ; ð1:18Þ with the Clausen integral function defined by Z
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