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Register a new userOn Naturalness of Scalar Fields and Standard Model
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Authors
Grigorii B. Pivovarov
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We discuss how naturalness predicts the scale of new physics. Two conditions on the scale are considered. The first is the more conservative condition due to Veltman (Acta Phys. Polon. B 12, 437 (1981)). It requires that radiative corrections to the electroweak mass scale would be reasonably small. The second is the condition due to Barbieri and Giudice (Nucl. Phys. B 306, 63 (1988)), which is more popular lately. It requires that physical mass scale would not be oversensitive to the values of the input parameters. We show here that the above two conditions behave differently if higher order corrections are taken into account. Veltmans condition is robust (insensitive to higher order corrections), while Barbieri-Giudice condition changes qualitatively. We conclude that higher order perturbative corrections take care of the fine tuning problem, and, in this respect, scalar field is a natural system. We apply the Barbieri-Giudice condition with higher order corrections taken into account to the Standard Model, and obtain new restrictions on the Higgs boson mass.
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A new localization scheme for Klein-Gordon particle states is introduced in the form of general space and time operators. The definition of these operators is achieved by establishing a second quantum field in the momentum space of the standard field we want to localize (here Klein-Gordon field). The motivation for defining a new field in momentum space is as follows. In standard field theories one can define a momentum (and energy) operator for a field excitation but not a general position (and time) operator because the field satisfies a differential equation in position space and, through its Fourier transform, an algebraic equation in momentum space. Thus, in a field theory which does the opposite, namely it satisfies a differential equation in momentum space and an algebraic equation in position space, we will be able to define a position and time operator. Since the new field lives in the momentum space of the Klein-Gordon field, the creation/annihilation operators of the former, which build the new space and time operators, reduce to the field operators of the latter. As a result, particle states of Klein-Gordon field are eigenstates of the new space and time operators and therefore localized on a space-time described by their spectrum. Finally, we show that this space-time is flat because it accommodates the two postulates of special relativity. Interpretation of special relativistic notions as inertial observers and proper acceleration in terms of the new field is also provided.
Light states associated with the hierarchy problem affect the Higgs LHC production and decays. We illustrate this within the MSSM and two simple extensions applying the latest bounds from LHC Higgs searches. Large deviations in the Higgs properties are expected in a natural SUSY spectrum. The discovery of a non-Standard-Model Higgs may signal the presence of light stops accessible at the LHC. Conversely, the more the Higgs is Standard-Model-like, the more tuned the theory becomes. Taking the ratio of different Higgs decay channels at the LHC cancels the leading QCD uncertainties and potentially improves the accuracy in Higgs coupling measurements to the percent level. This may lead to the possibility of doing precision Higgs physics at the LHC. Finally, we entertain the possibility that the ATLAS excess around 125 GeV persists with a Higgs production cross-section that is enhanced compared to the SM. This increase can only be accommodated in extensions of the MSSM and it may suggest that stops lie below 400 GeV, likely within reach of next years LHC run.
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