Narrow Results

The event generator BHAGEN provides a realistic description of Bhabha scattering at Z⁰ energy, for both small and large scattering angles. The algorithms used to build it and the structure of the program are illustrated in detail. A user guide for handling the program is given and some results and computational characteristics are presented to show its behaviour in some cases of interest.

The little Higgs idea is an alternative to supersymmetry as a solution to the gauge hierarchy problem. Here we review various little Higgs models and their phenomenology with emphases on the precision electroweak constraints in these models.

It is shown that a 4D N = 1 softly broken supersymmetric theory with higher derivative operators in the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, can be re-formulated as a theory without higher derivatives but with additional (ghost) superfields and modified interactions. The importance of the analytical continuation Minkowski–Euclidean space–time for the UV behaviour of such theories is discussed in detail. In particular it is shown that power counting for divergences in Minkowski space–time does not always work in models with higher dimensional (derivative) operators.

We discuss the gauge dependence of fermion mass definition under the on-shell and pole mass renormalization prescriptions. By the two-loop-level calculation of the cross section of the physical process , we prove for the first time that the on-shell fermion mass renormalization prescription makes physical result gauge-dependent. On the other hand, such gauge dependence does not appear in the result of the pole mass renormalization prescription. Our calculation also implies that the difference of physical results between the two mass renormalization prescriptions cannot be neglected at two-loop level.

Loop corrections induce a dependence on the momentum squared of the coefficients of the Standard Model Lagrangian, making highly nontrivial (or even impossible) the diagonalization of its quadratic part. Fortunately, the introduction of appropriate counterterms solves this puzzle.

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by log(s), appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and $\gamma Qq$-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop $\gamma \gamma \to q\bar{q}$ amplitude. The cancellation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory (CQFT) in higher orders. It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. Some features of U(1) axial vector gauge theory in Parisi Wu stochastic quantization are reported. These features are not absent if the theory is formulated in the conventional way. In particular we present arguments for renormalizability of the massive axial vector gauge theory coupled to a massless fermion.

Forward–backward (charge) asymmetry in the processes of $e^{+}{e}^{-}$ annihilation into a pair of charged pseudoscalar mesons is recalculated in the one-loop approximation. The exact dependence on the meson masses is taken into account. Results known in the literature are partially corrected. The bulk of the charge asymmetry appears due to double-photon exchange in $s$ channel. Experimental studies of the asymmetry can be used to verify the point-like approximation used in calculation of radiative corrections due to emission of photons by pions or kaons.

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

In this work we rederive the Lamb–Retherford energy shift for an atomic electron in the presence of a thermal radiation. Using the Dalibard, Dupont–Roc and Cohen–Tannoudji (DDC) formalism, where physical observables are expressed as convolutions of suitable statistical functions, we construct the electromagnetic field propagator of thermo field dynamics in the Coulomb gauge in order to investigate finite temperature effects on the atomic energy levels. In the same context, we also analyze the problem of the ground state stability.

We consider the high energy behavior of the amplitudes for pair production of charged leptons, quarks, Higgs bosons, sleptons, squarks and charginos at lepton colliders. We give the general expressions of the leading quadratic and subleading linear logarithms that appear at the one-loop level, and derive the corresponding resummed expansions to subleading logarithmic order accuracy. Under the assumption of a relatively light SUSY scenario and choosing the MSSM as a specific model, we compare the predictions of the one-loop and of the resummed expansions at variable energy. We show that the two predictions are very close in the one TeV regime, but drastically differ in the few (2,3) TeV range.

We review recent progress in the description of heavy-quarkonium production in 2 → 2 processes at next-to-leading order in the factorization framework of nonrelativistic quantum chromodynamics. Specifically, we consider the production of prompt charmonium in association with a hadron jet or a prompt photon in two-photon collisions and exclusive double-charmonium production in e⁺e^- annihilation.

We observe that the electroweak one-loop correction to the quark+gluon to quark+Higgs amplitude at high energy involves both single and quadratic logarithms of the energy in the SM case but only quadratic logarithms in the MSSM case. We explore the origin of this special SUSY cancellation, both in a diagrammatic way and through the splitting+parameter-renormalization procedure. We show that it is not an accident but a remarkable and general SUSY property of the renormalized Higgs–fermion–fermion and Higgsino–sfermion–fermion vertices which directly reflects in such processes, for example in bg→tH^-, bg→bH⁰, bg→bh⁰, bg→bA⁰, and through equivalence in , bg→bZ_long, as well as in . This simplification of the high energy behavior (which only leaves quadratic logarithms involving pure gauge couplings without any free parameter) allows to write simple relations among these various processes which could constitute genuine tests of the assumed SUSY model.

We consider a two-form antisymmetric tensor field ϕ minimally coupled to a non-Abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term for the tensor field eliminates degrees of freedom associated with this field. Explicit one-loop calculations show that an additional coupling m Tr(ϕ ∧ F) (which can be eliminated classically by a tensor field shift) reintroduces tensor field degrees of freedom. We attribute this to the lack of the renormalizability in our vector-tensor model. We also explore a vector-tensor model with a tensor field scalar mass term and coupling m Tr(ϕ ∧ ⋆F). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.

When one uses the Coleman–Weinberg renormalization condition, the effective potential V in the massless theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the (p + 1) order renormalization group function determine the sum of all the N^pLL order contribution to V to all orders in the loop expansion. We discuss here how, in addition to fixing the N^pLL contribution to V, the (p + 1) order renormalization group functions can also be used to determine portions of the N^p+nLL contributions to V. When these contributions are summed to all orders, the singularity structure of V is altered. An alternate rearrangement of the contributions to V in powers of ln ϕ, when the extremum condition V′(ϕ = v) = 0 is combined with the renormalization group equation, show that either v = 0 or V is independent of ϕ. This conclusion is supported by showing the LL, …, N⁴LL contributions to V become progressively less dependent on ϕ.

We introduce a Lorentz-symmetry violating extended quantum electrodynamics (QED) which preserves gauge symmetry. The extended fermionic sector can radiatively induce an extended effective action which simultaneously displays the same electromagnetic terms present in the Carroll–Field–Jackiw, Myers–Pospelov and Aether actions.

Possible realistic scenarios are investigated in the minimal supersymmetric standard model (MSSM) Higgs sector extended by dimension-six effective operators. The CP-odd Higgs boson with low mass around 30–90 GeV could be consistently introduced in the regime of large threshold corrections to the effective MSSM two-doublet Higgs potential.

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

Within the framework of the recently proposed Taylor–Lagrange regularization procedure, we reanalyze the calculation of radiative corrections in quantum electrodynamics (QED) at next to leading order. Starting from a well-defined local bare Lagrangian, the use of this regularization procedure enables us to manipulate fully finite elementary amplitudes in the ultra-violet (UV) as well as infrared (IR) regimes, in physical $D=4$ space–time dimensions and for physical massless photons, as required by gauge invariance. We can thus separately calculate the electromagnetic form factors of the electron and the cross-section for real photon emission, each quantity being finite in these physical conditions. We then discuss the renormalization group (RG) equations within this regularization procedure. Thanks to the taming of IR divergencies, the RG equation associated to the (physical) effective charge exhibits an UV stable fixed point at ${\alpha }^{\ast }=0$, showing an asymptotic freedom-type behavior. We finally consider the case of two mass scales, one low and one heavy, paying particular attention to the natural decoupling properties between heavy and light degrees of freedom. As a direct consequence, the fine structure constant should be zero in the limit of massless electrons.

The 1-loop self-energy of a Dirac electron of mass $m$ propagating in a thin medium simulating graphene in an external magnetic field $B$ is investigated in quantum field theory. Equivalence is shown with the so-called reduced QED${}_{3+1}$ on a 2-brane. Schwinger-like methods are used to calculate the self-mass $\delta m_{\mathrm{\text{LLL}}}$ of the electron when it lies in the lowest Landau level. Unlike in standard QED${}_{3+1}$, it does not vanish at the limit $m\to 0$: $\delta m_{\mathrm{\text{LLL}}}\underset{}{\overset{m\to 0}{\to }}\frac{\alpha }{2}\sqrt{\frac{\pi }{2}}\sqrt{\frac{\hslash \left|e\right|B}{c^2}}$ on-mass-shell renormalization conditions (with $\alpha =\frac{e^2}{4\pi \hslash c}$); all Landau levels of the virtual electron are taken into account and are implemented. Restricting to the sole lowest Landau level of the virtual electron is explicitly shown to be inadequate. Resummations at higher orders lie beyond the scope of this work.