H. Fanchiotti

Quantum Anomaly in Molecular Physics

The interaction of an electron with a polar molecule is shown to be the simplest realization of a quantum anomaly in a physical system. The existence of a critical dipole moment for electron capture and formation of anions, which has been confirmed experimentally and numerically, is derived. This phenomenon is a manifestation of the anomaly associated with quantum symmetry breaking of the classical scale invariance exhibited by the point-dipole interaction. Finally, analysis of symmetry breaking for this system is implemented within two different models: point dipole subject to an anomaly and finite dipole subject to explicit symmetry breaking.

Renormalization of the inverse square potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.

Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics I. General Theory

Abstract This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their general properties are derived. A strategy for dimensional renormalization of these systems in the strong-coupling regime is presented, and the emergence of an energy scale is shown, both for the bound-state and scattering sectors. Finally, dimensional transmutation is explicitly illustrated for the two-dimensional delta-function potential.

Looking for magnetic monopoles at LHC with diphoton events

Magnetic monopoles have been a subject of interest since Dirac established the relation between the existence of monopoles and charge quantization. The intense experimental search carried thus far has not met with success. The Large Hadron Collider is reaching energies never achieved before allowing the search for exotic particles in the TeV mass range. In a continuing effort to discover these rare particles we propose here other ways to detect them. We study the observability of monopoles and monopolium, a monopole-antimonopole bound state, at the Large Hadron Collider in the γγ channel for monopole masses in the range 500–1000 GeV. We conclude that LHC is an ideal machine to discover monopoles with masses below 1TeV at present running energies and with 5 fb−1 of integrated luminosity.

Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics: II. Rotational Invariance

Abstract A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential and the D -dimensional inverse square potential are studied. In particular, the following features are analyzed: the existence of a critical coupling, the boundary condition at the origin, the relationship between the bound-state and scattering sectors, and the similarities displayed by both potentials. It is found that, for rotationally symmetric scale-invariant potentials, there is a strong-coupling regime, for which quantum-mechanical breaking of symmetry takes place, with the appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy.

Influence of the LPM effect and dielectric suppression on particle air showers

An analysis of the influence of the Landau-Migdal-Pomeranchuk (LPM) effect on the development of air showers initiated by astroparticles is presented. The theory of Migdal is studied and compared with other theoretical methods, particularly the Blankenbecler-Drell approach. By means of realistic computer simulations and using algorithms that emulate Migdals theory, including also the so-called dielectric suppression, we study the behavior of the relevant observables in the case of ultrahigh energy primaries. We find that the LPM effect can significantly modify the development of high energy electromagnetic showers in certain cases.

Spontaneous CP violation in an SU(3)L⊗U(1)Y electroweak model

Abstract We study the possibility of finding spontaneous CP violation within an SU(3) L ⊗U(1) Y > electroweak model. We show that the mechanism is allowed for a certain range of the Higgs potential parameters only when a scalar sextuplet is included to provide the lepton masses.

Monopolium: The Key to monopoles

Dirac showed that the existence of one magnetic pole in the universe could offer an explanation for the discrete nature of the electric charge. Magnetic poles appear naturally in most grand unified theories. Their discovery would be of the greatest importance for particle physics and cosmology. The intense experimental search carried out thus far has not met with success. Moreover, if the monopoles are very massive their production is outside the range of present day facilities. A way out of this impasse would be if the monopoles bind to form monopolium, a monopole–antimonopole bound state, which is so strongly bound that it has a relatively small mass. Under these circumstances it could be produced with present day facilities and the existence of monopoles could be indirectly proven. We study the feasibility of detecting monopolium in present and future accelerators.

Exact solution of electrostatic problem for a system of parallel cylindrical conductors

The problem of the calculation of the electric field distribution of a system of infinite parallel cylindrical conductors in the presence of a grounded plane is reexamined. The exact solution of a class of two‐dimensional harmonic problems in multiply connected domains proposed by Burnside in 1893 is reviewed. This is shown to agree with recent generalizations of the method of images. An improved version of the exact solution which is more convergent than the conventional methods when the conductors are very close to one another is presented. The potential usefulness of the theoretical ideas and the mathematical apparatus used here for technological applications is emphasized.

On the Inequivalence of Renormalization and Self-Adjoint Extensions for Quantum Singular Interactions

A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.