{'fraction_non_alphanumeric': 0.03957528957528957, 'fraction_numerical': 0.013513513513513514, 'mean_word_length': 4.411227154046998, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Effective SU(2)_L x U(1) theory and the Higgs boson mass

We assume the stability of vacuum under radiative corrections in the context of the standard electroweak theory. We find that this theory behaves as a good effective model already at cut off energy scales as low as 0.7 TeV. This stability criterion allows to predict m_H= 318 +- 13 GeV for the Higgs boson mass.

Since the standard electroweak theory is renormalizable, the ultraviolet (quadratic and logarithmic) divergencies appearing in loop calculations can be removed by proper redefinitions of a small number of parameters (e.g., masses). The renormalization program allows to get finite predictions for physical quantities except for those few parameters which require redefinitions. In this way, we renounce to give some physical content to the divergent behaviour of the theory at very high energies [1].
Instead of following the renormalization program, we can consider that SU(2) L ⊗ U(1) is an effective theory with an ultraviolet cut off at the energy scale Λ and try to trigger some information on the model itself from the behaviour of divergent terms. In other words, we assume that a more complete theory than SU(2) L ⊗ U(1) introduces new physical effects at high energy that cut off the ultraviolet divergencies. Below Λ, SU(2) L ⊗ U(1) is supposed to describe all the electroweak processes in a satisfactory way.
In this letter we consider SU(2) L ⊗ U(1) as an effective theory below Λ and assume the vanishing of the common divergent contributions (tadpoles) to the masses of all the particles. We find that the electroweak theory becomes effective even at cut off energies as small as Λ ∼ 0.7 TeV. This criterion for vacuum stability under radiative corrections allows to derive a mass for the Higgs boson that differs from its asymptotic [3] by less than 0.6 % already at Λ ∼ 0.7 TeV.
Let us start by considering the divergent one-loop tadpole contributions. These tadpoles give a universal contribution to self-mass corrections because the bare masses of all the particles are proportional to the vacuum expectation value v of the Higgs field. The tadpoles are gauge-dependent and are given by [4] δv and [4] A 0 (m) = The two expressions in Eq. (2) are obtained by using the n-dimensional and corresponding cut off regularization methods, respectively.
In a similar way, we can compute the corrections to the neutrino mass (we assume a non-vanishing value for the neutrino mass). We get where [4] B 0 (0, 0, m) = respectively, using the n-dimensional and cut off methods. Eq. (3) is in agreement with corresponding results in Ref. [5] where finite terms of the form m 2 and m 4 are neglected.
As it can be easily checked from the previous expressions, δm ν /m ν is explicitly gauge-independent. This means that if we write the tadpoles in the Landau gauge we i.e., this quantity is SU(2) L ⊗ U(1) gauge-invariant. As is well known, the tadpoles can be computed from an effective potential only in the Landau gauge [6].
Eq. (6) corresponds to the condition for the cancellation of quadratic divergencies [2]- [3] in the self-masses of all the particles in the standard electroweak theory.
If we have chosen δm ν /m ν = 0 instead of δv t /v = 0, the plots obtained would have been almost identical for Λ ≥ 0.7 TeV because finite terms in Eq. (5) are negligible above these cut off energies. It is interesting to note that our predicted value for m H is somewhat higher than the one predicted in another version of the effective electroweak theory [8] where the Higgs potential is reduced to its quartic term.
In conclusion, by assuming the vanishing of tadpole radiative corrections we find that the standard electroweak theory behaves as a good effective model with a relatively small cut off energy scale. The mass obtained for the Higgs boson departs by less than 0.6 % from the value obtained by requiring cancellation of quadratic divergencies [2]- [3] already at Λ ∼ 0.7 TeV. Thus, no fine-tunning of physical masses [1] are required to suppress the quadratic divergent corrections to self-masses in the effective version of the standard electroweak theory.