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B. G. Giraud

Publications and source records attributed to B. G. Giraud.

At least 19 recordsLinked to original sources
arXiv2026

Determination of the Odderon amplitude in elastic cross-sections at high energies from scaling and analyticity

Scaling amplitudes describing $pp$ elastic scattering differential cross-sections in the dip-bump region of momentum transfer at the LHC have been recently derived~\cite{scaling}. We check that the same scaling is verified by the $p\bar p$ cross-section at the highest energy of the Tevatron. Applying the general "energy to phase" relation for a given signature, coming from the analiticity properties inherent to the S-Matrix formalism~\cite{chew}, we derive the scaling amplitude with positive signature (i.e. the Pomeron). Fitting the $pp$ differential cross-sections measured by the TOTEM collaboration leads to some tension with data in the experimental dip observed at moderate momentum transfer. Concentrating the study to the dip/bump region, we are able to determine a contribution of a negative signature amplitude (i.e. the Odderon) leading to a parameter free prediction for the $p\bar p$ differential cross-section which is in agreement with the D0 data. The extraction of the Odderon amplitude in both modulus and phase is then performed and discussed.

hep-ph↗
arXiv2026

The scaling Pomeron

We examine the Regge theoretical properties for the scaling observed in pp elastic scattering differential cross-sections at the LHC. A positive signature amplitude (i.e. the Pomeron) with scaling properties has been derived. It is found to describe the dip-bump region of momentum transfer at LHC energies in agreement with data. We derive the analytic continuation in the whole plane of the t-channel partial waves of index $l_t$ specific to the Regge formalism. The analytic form of the amplitude exhibits a specific scaling property without singularities, except for a series of poles in the $l_t$ real axis at fractional values.

hep-ph↗
arXiv2025

Matrix approximations of operators

The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak approximation of the $δ$ function, but this peak may be perturbed by small, residual, oscillations. The peak does not shrink nor grows quickly, and the oscillations only diminish slowly as the size of the matrix increases. For the kinetic energy operator, a triple peak (one positive, two negative) representation of $-δ''$ is obtained, but that is affected also by residual oscillations. Again, convergence is slow as the matrix dimension increases. We find compact formulas to explain such oscillations. Similar observations are found for representations of local interactions, while separable potentials are better represented. As a comparison, in the context of a toy model, the effects of choosing an alternative single particle basis are studied. A formal approach for the approximation of operators is considered for comparison. We conclude with a word of caution for (finite) matrix approximations of operators.

math-ph↗
arXiv2024

A QCD interpretation of the scaling observed in the LHC proton-proton elastic cross-sections at moderate transfer momentum

A phenomenological scaling property of the LHC proton-proton elastic scattering cross sections at moderate transfer momentum has been recently observed. The theoretical QCD saturation framework for hard elastic scattering on the proton, which we recall, predicts a strikingly similar scaling property in the same configuration of energy and momentum transfer. This similarity favors a theoretical interpretation where the hard amplitude is the building block of the $pp$ amplitude via unitarization. The values of the scaling exponents favor two QCD saturation approaches where the saturation scale exponent is of order one half of that which is found for hard elastic scattering and deep inelastic processes on the proton.

hep-ph↗
arXiv2023

On the strong local potential limit

Finite, bound, many-body systems, where the interaction operator, $V=\sum v_{ij}$, is local and happens to strongly dominate the kinetic energy operator, $T=\sum t_i$, display a classical limit from diagonalizing $V$ alone, hence a clear picture of interparticle correlations, such as steric blocking emerges. This limit exhibits intrinsic symmetries and also fluctuations from mass formulae. The present work investigates how such emergent symmetries and fluctuations might be extrapolated to physical situations where $T$ is reinstated.

nucl-th↗
arXiv2018

Profile of a Galactic Spherical Cloud of Self-Gravitating Fermions

The field which binds a thermal fermionic cloud is defined as a Hartree integral upon its density. In turn, the density results from the field via a Thomas-Fermi occupation of the local phase space. This defines a complete theory of all properties and observables for the cloud. As an application to dark matter halos, comparisons with astronomic data on dwarf spheroidal galaxies are provided and discussed. Estimates of the elementary fermion mass are obtained, serving as a phase-space bound on fermionic dark matter.

hep-th↗
arXiv2016

Fluctuations of collective coordinates and convexity theorems for energy surfaces

Constrained energy minimizations of a many-body Hamiltonian return energy landscapes e(b) where b= representes the average value(s) of one (or several) collective operator(s), B, in an "optimized" trial state Phi_b, and e = is the average value of the Hamiltonian in this state Phi_b. It is natural to consider the uncertainty, Delta e, given that Phi_b usually belongs to a restricted set of trial states. However, we demonstrate that the uncertainty, Delta b, must also be considered, acknowledging corrections to theoretical models. We also find a link between fluctuations of collective coordinates and convexity properties of energy surfaces.

nucl-th↗
arXiv2013

Concavity Theorems for Energy Surfaces

Concavity properties prevent the existence of significant landscapes in energy surfaces obtained by strict constrained energy minimizations. The inherent contradiction is due to fluctuations of collective coordinates. A solution to those fluctuations is given.

nucl-th↗
arXiv2011

Algebraic Density Functionals

A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham potentials (KSPs) are then obtained by standard elimination procedures of such degrees of freedom between the polynomials. Numerical examples illustrate the formalism.

nucl-th↗
arXiv2009

Open problems in nuclear density functional theory

This note describes five subjects of some interest for the density functional theory in nuclear physics. These are, respectively, i) the need for concave functionals, ii) the nature of the Kohn-Sham potential for the radial density theory, iii) a proper implementation of a density functional for an "intrinsic" rotational density, iv) the possible existence of a potential driving the square root of the density, and v) the existence of many models where a density functional can be explicitly constructed.

nucl-th↗
arXiv2009

Concavity for nuclear binding energies, thermodynamical functions and density functionals

Sequences of experimental ground-state energies for both odd and even $A$ are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential $Ω(β,μ)$ for a mixture of nuclei at low or moderate temperatures $T=β^{-1}$ and at many chemical potentials $μ.$ The average nucleon number $<{\bf A} >(β,μ)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of $<{\bf A} >.$ Concavity, which always occur for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.

nucl-th↗
arXiv2009

Schrödinger equations for the square root density of an eigenmixture and % the square root of an eigendensity spin matrix

We generalize a "one eigenstate" theorem of Levy, Perdew and Sahni (LPS) to the case of densities coming from eigenmixture density operators. The generalization is of a special interest for the radial density functional theory (RDFT) for nuclei, a consequence of the rotational invariance of the nuclear Hamiltonian; when nuclear ground states (GSs) have a finite spin, the RDFT uses eigenmixture density operators to simplify predictions of GS energies into one-dimensional, radial calculations. We also study Schrödinger equations governing spin eigendensity matrices.

nucl-th↗
arXiv2009

From Di-Nucleus to Mono-Nucleus - Neck Evolution in Fusion of Massive Systems -

Dynamics of the neck degree of freedom during fusioning process between heavy ions is studied. Time scales of the three degrees of freedom (the relative distance, the neck and the mass-asymmetry) are studied, showing an early equilibration of the neck. This means that a di-nucleus formed by the incident combination of ions quickly forms a mono-nucleus with a superdeformation during the fusion process and that the other two degrees of freedom have to be solved in a coupled way. A brief introduction of Langevin approach and dissipation-fluctuation dynamics is also given and of the application to the synthesis of the superheavy elements.

nucl-th↗
arXiv2008

Scalar Nature of the Nuclear Density Functional

Because of the rotational invariance of the nuclear Hamiltonian, there exists a density functional for nuclei that depends only on two scalar densities. Practical calculations boil down to radial, one-dimensional ones.

nucl-th↗
arXiv2007

Bounds to binding energies from the concavity of thermodynamical functions

Sequences of experimental ground-state energies are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, can be used to give numerical estimates of the grand potential $Ω(β,μ)$ for a mixture of nuclei at low or moderate temperatures $T=β^{-1}$ and at many chemical potentials $μ.$ The average nucleon number $<{\bf A} >(β,μ)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of $<{\bf A} >.$ Concavity, when present in such functions, allows trivial interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. An extrapolation scheme for such concave functions is tested. We conclude with numerical estimates of the binding energies of a few nuclei closer to drip lines.

nucl-th↗
arXiv2007

Laboratory Density Functionals

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals.

nucl-th↗