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Register a new userNaturalness after LHC8
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Gian F. Giudice
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I review the status of naturalness of the weak scale after the results from the LHC operating at an energy of 8 TeV. Talk delivered at the 2013 Europhysics Conference on High Energy Physics (EPS), Stockholm, Sweden, 18-24 July 2013.
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The nature of the electroweak phase transition in two-Higgs-doublet models is revisited in light of the recent LHC results. A scan over an extensive region of their parameter space is performed, showing that a strongly first-order phase transition favours a light neutral scalar with SM-like properties, together with a heavy pseudo-scalar (m_A^0 > 400 GeV) and a mass hierarchy in the scalar sector, m_H^+ < m_H^0 < m_A^0. We also investigate the h^0 -> gamma gamma decay channel and find that an enhancement in the branching ratio is allowed, and in some cases even preferred, when a strongly first-order phase transition is required.
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.
In MSSM models with various boundary conditions for the soft breaking terms (m_{soft}) and for a higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning Deltaapprox 800 to 1000 for the constrained MSSM and Deltaapprox 500 for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector (sqrt f) to few TeV, which we show to restore naturalness to more acceptable levels Deltaapprox 80 for the most conservative case of low tan_beta and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce Delta. In the present case Delta is reduced due to additional (effective) quartic higgs couplings proportional to the ratio m_{soft}/(sqrt f) of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale sqrt f one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.
We consider the extension of the Standard Model (SM) with a strongly interacting QCD-like hidden sector, at least two generations of right-handed neutrinos and one scalar singlet. Once scalar singlet obtains a nonzero vacuum expectation value, active neutrino masses are generated through type-I seesaw mechanism. Simultaneously, the electroweak scale is generated through the radiative corrections involving these massive fermions. This is the essence of the scenario that is known as the neutrino option for which the successful masses of right-handed neutrinos are in the range $10^7-10^8$ GeV. The main goal of this work is to scrutinize the potential to accommodate dark matter in such a realization. The dark matter candidates are Nambu-Goldstone bosons which appear due to the dynamical breaking of the hidden chiral symmetry. The mass spectrum studied in this work is such that masses of Nambu-Goldstone bosons and singlet scalar exceed those of right-handed neutrinos. Having the masses of all relevant particles several orders of magnitude above $mathcal{O}$(TeV), the freeze-out of dark matter is not achievable and hence we turn to alternative scenarios, namely freeze-in. The Nambu-Goldstone bosons can interact with particles that are not in SM but, however, have non-negligible abundance through their not-too-small couplings with SM. Utilizing this, we demonstrate that the dark matter in the model is successfully produced at temperature scale where the right-handed neutrinos are still stable. We note that the lepton number asymmetry sufficient for the generation of observable baryon asymmetry of the Universe can be produced in right-handed neutrino decays. Hence, we infer that the model has the potential to simultaneously address several of the most relevant puzzles in contemporary high-energy physics.
The dynamical cascade of momentum, spin, charge, and other quantum numbers from an ultra-violet process into the infra-red is a fundamental concern for asymptotically free or conformal gauge field theories. It is also a practical concern for any high energy scattering experiment with energies above tens of GeV. We present a formulation of the evolution equation that governs this cascade, the Banfi-Marchesini-Smye equation, from both an effective field theory point of view and a direct diagrammatic argument. The equation uses exact momentum conservation, and is applicable to both scattering with initial and final state hard partons. The direct diagrammatic formulation is organized by constructing a generating functional. This functional is also automatically realized with soft wilson lines and collinear field operators coupled to external currents. The two approaches are directly connected by reverse engineering the Lehman-Symanzik-Zimmermann reduction procedure to insert states within the soft and collinear matrix elements. At leading order, the cascade is completely controlled by the soft anomalous dimension. By decomposing the anomalous dimension into on-shell and off-shell regions as would be realized in the effective field theory approach with a Glauber mediating potential, we are forced to choose a transverse momentum ordering in order to trivialize the overlap between Glauber potential contributions and the pure soft region. The evolution equation then naturally incorporates factorization violating effects driven by off-shell exchanges for active partons. Finally, we examine the consequences of abandoning exact momentum conservation as well as terminating the evolution at the largest inclusive scale, procedures often used to simplify the analysis of the cascade.
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