Search results for "Mathematica"
showing 10 items of 7971 documents
Quantum deformations of singletons and of free zero-mass fields
1993
We consider quantum deformations of the real symplectic (or anti-De Sitter) algebra sp(4), ℝ ≅ spin(3, 2) and of its singleton and (4-dimensional) zero-mass representations. For q a root of −1, these representations admit finite-dimensional unitary subrepresentations. It is pointed out that Uq(sp(4, ℝ)), unlike Uq(su(2, 2)), contains Uq(sl2) as a quantum subalgebra.
When Casimir meets Kibble–Zurek
2012
Verification of the dynamical Casimir effect (DCE) in optical systems is still elusive due to the very demanding requirements for its experimental implementation. This typically requires very fast changes in the boundary conditions of the problem. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way for an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system an…
Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
2011
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the…
Probing Quantum Frustrated Systems via Factorization of the Ground State
2009
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physica…
Flavour Conservation in Two Higgs Doublet Models
2018
In extensions of the Standard Model with two Higgs doublets, flavour changing Yukawa couplings of the neutral scalars may be present at tree level. In this work we consider the most general scenario in which those flavour changing couplings are absent. We re-analyse the conditions that the Yukawa coupling matrices must obey for such \emph{general flavour conservation} (gFC), and study the one loop renormalisation group evolution of such conditions in both the quark and lepton sectors. We show that gFC in the leptonic sector is one loop stable under the Renormalization Group Evolution (RGE) and in the quark sector we present some new Cabibbo like solution also one loop RGE stable. At a pheno…
Renormalization and Scale Evolution of the Soft-Quark Soft Function
2020
Soft functions defined in terms of matrix elements of soft fields dressed by Wilson lines are central components of factorization theorems for cross sections and decay rates in collider and heavy-quark physics. While in many cases the relevant soft functions are defined in terms of gluon operators, at subleading order in power counting soft functions containing quark fields appear. We present a detailed discussion of the properties of the soft-quark soft function consisting of a quark propagator dressed by two finite-length Wilson lines connecting at one point. This function enters in the factorization theorem for the Higgs-boson decay amplitude of the $h\to\gamma\gamma$ process mediated by…
Two-current correlations in the pion in the Nambu and Jona-Lasinio model
2020
We present an analysis of two-current correlations for the pion in the Nambu--Jona-Lasinio model, with Pauli--Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed.
Renormalization group invariant matrix elements of Delta S = 2 and Delta I = 3/2 four fermion operators without quark masses
1999
We introduce a new parameterization of four-fermion operator matrix elements which does not involve quark masses and thus allows a reduction of systematic uncertainties. In order to simplify the matching between lattice and continuum renormalization schemes, we express our results in terms of renormalization group invariant B-parameters which are renormalization-scheme and scale independent. As an application of our proposal, matrix elements of DI=3/2 and SUSY DS =2 operators have been computed. The calculations have been performed using the tree-level improved Clover lattice action at two different values of the strong coupling constant (beta=6/g^2=6.0 and 6.2), in the quenched approximati…
Pentaquarks with anticharm or beauty revisited
2019
We use a constituent model to analyze the stability of pentaquark $\bar Q qqqq$ configurations with a heavy antiquark $\bar c$ or $\bar b$, and four light quarks $uuds$, $ddsu$ or $ssud$. The interplay between chromoelectric and chromomagnetic effects is not favorable, and, as a consequence, no bound state is found below the lowest dissociation threshold.
Classification of the hadronic decays of the Z$^0$ into b and c quark pairs using a neural network
1992
A classifier based on a feed-forward neural network has been used for separating a sample of about 123 500 selected hadronic decays of the Z 0 , collected by DELPHI during 1991, into three classes according to the flavour of the original quark pair: u u +d d +s s (unresolved), c c and b b . The classification has been used to compute the partial widths of the Z 0 into b and c quark pairs. This gave Γ c c /Γ h = 0.151 ± 0.008 ( stat. ) ± 0.041 ( syst. ) , Γ b b /Γ h = 0.232±0.005 ( stat. )±0.017 ( syst. ) .