arXiv subjects

L. Girlanda

Publications and source records attributed to L. Girlanda.

At least 55 records · Page 3Linked to original sources

arXiv2010

Relativity constraints on the two-nucleon contact interaction

We construct the most general, relativistically invariant, contact Lagrangian at order Q^2 in the power counting, Q denoting the low momentum scale. A complete, but non-minimal, set of (contact) interaction terms is identified, which upon non-relativistic reduction generate 2 leading independent operator combinations of order Q^0 and 7 sub-leading ones of order Q^2 - a result derived previously in the heavy-baryon formulation of effective field theories (EFT's). We show that Poincare covariance of the theory requires that additional terms with fixed coefficients be included, in order to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass number A>2, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied.

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arXiv2009

Electromagnetic Structure and Reactions of Few-Nucleon Systems in $χ$EFT

We summarize our recent work dealing with the construction of the nucleon-nucleon potential and associated electromagnetic currents up to one loop in chiral effective field theory ($χ$EFT). The magnetic dipole operators derived from these currents are then used in hybrid calculations of static properties and low-energy radiative capture processes in few-body nuclei. A preliminary set of results are presented for the magnetic moments of the deuteron and trinucleons and thermal neutron captures on $p$, $d$, and $^3$He.

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arXiv2009

Electromagnetic processes in a $χ$EFT framework

Recently, we have derived a two--nucleon potential and consistent nuclear electromagnetic currents in chiral effective field theory with pions and nucleons as explicit degrees of freedom. The calculation of the currents has been carried out to include N$^3$LO corrections, consisting of two--pion exchange and contact contributions. The latter involve unknown low-energy constants (LECs), some of which have been fixed by fitting the $np$ S- and P-wave phase shifts up to 100 MeV lab energies. The remaining LECs entering the current operator are determined so as to reproduce the experimental deuteron and trinucleon magnetic moments, as well as the $np$ cross section. This electromagnetic current operator is utilized to study the $nd$ and $n^3$He radiative captures at thermal neutron energies. Here we discuss our results stressing on the important role played by the LECs in reproducing the experimental data.

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arXiv2009

Electromagnetic Currents and Magnetic Moments in $χ$EFT

A two-nucleon potential and consistent electromagnetic currents are derived in chiral effective field theory ($χ$EFT) at, respectively, $Q^{2}$ (or N$^2$LO) and $e Q$ (or N$^3$LO), where $Q$ generically denotes the low-momentum scale and $e$ is the electric charge. Dimensional regularization is used to renormalize the pion-loop corrections. A simple expression is derived for the magnetic dipole ($M1$) operator associated with pion loops, consisting of two terms, one of which is determined, uniquely, by the isospin-dependent part of the two-pion-exchange potential. This decomposition is also carried out for the $M1$ operator arising from contact currents, in which the unique term is determined by the contact potential. Finally, the low-energy constants (LEC's) entering the N$^2$LO potential are fixed by fits to the $np$ S- and P-wave phase shifts up to 100 MeV lab energies.

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arXiv2009

N-d Elastic Scattering Using the Hyperspherical Harmonics Approach with Realistic Local and Non-Local Interactions

The application of the hyperspherical harmonic approach to the case of the N-d scattering problem below deuteron breakup threshold is described. The nuclear Hamiltonian includes two- and three-nucleon interactions, in particular the Argonne v_{18}, the N3LO-Idaho, and the V_{low k} two-nucleon, and the Urbana IX and N2LO three-nucleon interactions. Some of these models are local, some are non-local. Also electromagnetic effects are included. Accurate calculations for many scattering observables at various center-of-mass energies are performed and the results are compared with the available experimental data. Furthermore, a χ^2 analysis of some of the Hamiltonian models has been performed to compare their capability to describe the scattering process.

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arXiv2008

Neutron-triton elastic scattering

The Kohn variational principle and the hyperspherical harmonics technique are applied to study n-3H elastic scattering at low energies. In this contribution the first results obtained using a non-local realistic interaction derived from the chiral perturbation theory are reported. They are found to be in good agreement with those obtained solving the Faddeev-Yakubovsky equations. The calculated total and differential cross sections are compared with the available experimental data. The effect of including a three-nucleon interaction is also discussed.

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arXiv2008

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh-Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A=3 and 4 nuclear systems. When the wave function of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this paper, the main aspects of the method are discussed together with its application to the A=3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon-nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this paper is two-fold. First, to present a complete description of the HH method for bound and scattering states, including also detailed formulas for the computation of the matrix elements of the NN and 3N interactions. Second, to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.

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arXiv2008

Neutron spin rotation in \vec{n}-d scattering

The neutron spin rotation induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in \vec{n}-d scattering at zero energy. Results are obtained corresponding to the Argonne v_{18} two-nucleon and Urbana-IX three-nucleon strong-interaction potentials in combination with either the DDH or pionless EFT model for the weak-interaction potential. We find that this observable is dominated by the contribution of the long-range part of the PV potential associated with pion exchange. Thus its measurement could provide a further constraint, complementary to that coming from measurements of the photon asymmetry in \vec{n}-p radiative capture, on the strength of this component of the hadronic weak interaction.

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arXiv2007

Structure of A=3 Nuclear Systems Using Realistic Hamiltonians

The structure of A=3 low-energy scattering states is described using the hyperspherical harmonics method with realistic Hamiltonian models, consisting of two- and three-nucleon interactions. Both coordinate and momentum space two-nucleon potential models are considered.

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arXiv2007

Bakamjian-Thomas mass operator for the few-nucleon system from chiral dynamics

We present an exploratory study consisting in the formulation of a relativistic quantum mechanics to describe the few-nucleon system at low energy, starting from the quantum field theoretical chiral Lagrangian involving pions and nucleons. To this aim we construct a Bakamjian-Thomas mass operator and perform a truncation of the Fock space which respects at each stage the relativistic covariance. Such truncation is justified, at sufficiently low energy, in the framework of a systematic chiral expansion. As an illustration we discuss the bound state observables and low-energy phaseshifts of the nucleon-nucleon and pion-nucleon scattering at the leading order of our scheme.

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arXiv2007

Lightest scalar in the SU_L(2)*SU_R(2) linear σmodel

We consider the lightest scalar meson in the frame of the $SU_L(2)\times SU_R(2)$ linear $σ$ model, keeping in mind that this model could be the low energy realization of the two-flavour QCD. We show that the $σ$ field is described by its four-quark component at least in the $σ$ resonance energy (virtuality) region and the $σ\toγγ$ decay is the four quark transition. We emphasize that residues of the $σ$ pole in the $ππ\toππ$ and $γγ\toππ$ amplitudes do not give an idea about the $σ$ meson nature, and the progress in studying the $σ$ meson production mechanisms in different processes could essentially further us in understanding its nature.

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arXiv2005

Variational Calculation on A=3 and 4 Nuclei with Non-Local Potentials

The application of the hyperspherical harmonic approach to the case of non-local two-body potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both coordinate and momentum space. The binding energies and other ground state properties of A=3 and 4 nuclei are calculated using the CD Bonn 2000 and N3LO two-body potentials. The results are shown to be in excellent agreement with corresponding ones obtained by other accurate techniques.

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arXiv2005

The anomalous chiral Lagrangian of order $p^6$

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavours, 23 terms for three and 5 for two flavours. In the two flavour case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.

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arXiv2003

Chiral Perturbation Theory in a Nuclear Background

We propose a novel way to formulate Chiral Perturbation Theory in a nuclear background, characterized by a static, non-uniform distribution of the baryon number that describes the finite nucleus. In the limiting case of a uniform distribution, the theory reduces to the well-known zero-temperature in-medium ChPT. The proposed approach is used to calculate the self-energy of the charged pion in the background of the heavy nucleus at O(p^5) in the chiral expansion, and to derive the leading terms of the pion-nucleus optical potential.

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arXiv2003

Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory

Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline how additional information may be incorporated to further constrain the pattern of ChSB in the N_f=3 chiral limit.

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arXiv2002

Chiral order and fluctuations in multi-flavour QCD

Multi-flavour (N_f>=3) Chiral Perturbation Theory (ChPT) may exhibit instabilities due to vacuum fluctuations of sea q-bar q pairs. Keeping the fluctuations small would require a very precise fine-tuning of the low-energy constants L_4 and L_6 to L_4[crit](M_rho) = - 0.51 * 10^(-3), and L_6[crit](M_rho) = - 0.26 * 10^(-3). A small deviation from these critical values -- like the one suggested by the phenomenology of OZI-rule violation in the scalar channel -- is amplified by huge numerical factors inducing large effects of vacuum fluctuations. This would lead in particular to a strong N_f-dependence of chiral symmetry breaking and a suppression of multi-flavour chiral order parameters. A simple resummation is shown to cure the instability of N_f>=3 ChPT, but it modifies the standard expressions of some O(p^2) and O(p^4) low-energy parameters in terms of observables. On the other hand, for r=m_s/m > 15, the two-flavour condensate is not suppressed, due to the contribution induced by massive vacuum s-bar s pairs. Thanks to the latter, the standard two-flavour ChPT is protected from multi-flavour instabilities and could provide a well-defined expansion scheme in powers of non-strange quark masses.

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arXiv2002

Analysis and interpretation of new low-energy Pi-Pi scattering data

The recently published E865 data on charged K_e4 decays and Pi-Pi phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters alpha and beta, of the low-energy constants l3-bar and l4-bar as well as of the main two-flavour order parameters: and F_pi in the limit m_u = m_d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on Pi-Pi phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2 a_0^0 - 5 a_0^2 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1-sigma level is found and commented upon.

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arXiv2001

Double chiral logarithms of Generalized Chiral Perturbation Theory for low-energy pi-pi scattering

We express the two-massless-flavor Gell-Mann--Oakes--Renner ratio in terms of low-energy pi-pi observables, including the O(p^6) double chiral logarithms of generalized chiral perturbation theory. Their contribution is sizeable and tends to compensate the one from the single chiral logarithms. However it is not large enough to spoil the convergence of the chiral expansion. As a signal of reduced theoretical uncertainty, we find that the scale dependence from the one-loop single logarithms is almost completely canceled by the one from the two-loop double logarithms.

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