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Register a new userNonperturbative Contributions to the Hot Electroweak Potential and the Crossover
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We discuss nonperturbative contributions to the 3-dimensional one-loop effective potential of the electroweak theory at high temperatures in the framework of the stochastic vacuum model. It assumes a gauge-field background with Gaussian correlations which leads to confinement. The instability of <F^2>=0 in Yang-Mills theory appears for small Higgs expectation value <phi^2> in an IR regularized form. The gauge boson propagator obtains a positive momentum-dependent ``diamagnetic effective (mass)^2 due to confinement effects and a negative one due to ``paramagnetic spin-spin interactions which are related to the <F^2>=0 instability. Numerical evaluation of an approximate effective potential containing these masses shows qualitatively the fading away of the first-order phase transition with increasing Higgs mass which was observed in lattice calculations. The crossover point can be roughly determined postulating that the effective phi^4 and phi^2 terms vanish there.
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The hot electroweak potential for small Higgs field values is argued to obtain contributions from a fluctuating gauge field background leading to confinement. The destabilization of F^2=0 and the crossover are discussed in our phenomenological approach, also based on lattice data.
In this paper, we construct a simple model for the complex heavy quark potential which is defined through the Fourier transform of the static gluon propagator. Besides the hard thermal loop resummed contribution, the gluon propagator also includes a non-perturbative term induced by the dimension two gluon condensate. Within the framework of thermal field theory, the real and imaginary parts of the heavy quark potential are determined in a consistent way without resorting to any extra assumption as long as the exact form of the retarded/advanced gluon propagator is specified. The resulting potential model has the desired asymptotic behaviors and reproduces the data from lattice simulation reasonably well. By presenting a direct comparison with other complex potential models on the market, we find the one proposed in this work shows a significant improvement on the description of the lattice results, especially for the imaginary part of the potential, in a temperature region relevant to quarkonium studies.
The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.
We reanalyze the two-loop electroweak hadronic contributions to the muon g-2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Greens function.
Nonperturbative QCD corrections are important to many low-energy electroweak observables, for example the muon magnetic moment. However, hadronic corrections also play a significant role at much higher energies due to their impact on the running of standard model parameters, such as the electromagnetic coupling. Currently, these hadronic contributions are accounted for by a combination of experimental measurements, effective field theory techniques and phenomenological modeling but ideally should be calculated from first principles. Recent developments indicate that many of the most important hadronic corrections may be feasibly calculated using lattice QCD methods. To illustrate this, we will examine the lattice computation of the leading-order QCD corrections to the muon magnetic moment, paying particular attention to a recently developed method but also reviewing the results from other calculations. We will then continue with several examples that demonstrate the potential impact of the new approach: the leading-order corrections to the electron and tau magnetic moments, the running of the electromagnetic coupling, and a class of the next-to-leading-order corrections for the muon magnetic moment. Along the way, we will mention applications to the Adler function, which can be used to determine the strong coupling constant, and QCD corrections to muonic-hydrogen.
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