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B. Moussallam

Publications and source records attributed to B. Moussallam.

44 records · Page 3Linked to original sources
arXiv1996

Determination of Two-Loop $ππ$ Scattering Amplitude Parameters

The chiral expansion of the $ππ$ amplitude to the order of two loops was expressed in terms of six independent parameters in a previous paper: four of these are shown here to satisfy sum rules. Their derivation, where crossing symmetry plays a key role, is explained. Their convergence properties are studied and their practical evaluation, in terms of the available data on $ππ$ phase shifts above 0.5 GeV, is discussed. Below 0.5 GeV, the chiral amplitude itself is employed, such that the parameters are determined in a self-consistent way. Some care is devoted to the estimate of the errors.

hep-ph↗
arXiv1995

The Low Energy $π\,π$ Amplitude to One and Two Loops

The low-energy $ππ$ amplitude is computed explicitly to two-loop accuracy in the chiral expansion. It depends only on six independent (combinations of) low-energy constants which are not fixed by chiral symmetry. Four of these constants are determined {\it via} sum rules which are evaluated using $ππ$ scattering data at higher energies. Dependence of the low-energy phase shifts and of the threshold parameters on the remaining two constants (called $α$ and $β$) are discussed and compared to the existing data from $K_{l4}$ experiments. Using generalised $χ$PT, the constants $α$ and $β$ are related to fundamental QCD parameters such as the quark condensate $\langle 0|\bar{q}q|0\rangle$ and the quark mass ratio $m_s/\widehat{m}$. It is shown that forthcoming accurate low-energy $ππ$ data can be used to provide, for the first time, experimental evidence in favour of or against the existence of a large quark-antiquark condensate in the QCD vacuum.

hep-ph↗
arXiv1995

Chiral Sum-Rules for ${\cal L}^{WZ}_{(6)}$ Parameters and Application to $π^0,η,η'$ Decays

The chiral expansion of the low energy processes $π^0\toγγ$ and $η\toγγ$ is reconsidered with particular emphasis on the question of the evaluation of the two low-energy parameters from ${\cal L}^{WZ}_{(6)}$ which are involved at chiral order six. It is shown how extensive use of sum-rules and saturation with resonances as well as constraints from asymptotic QCD effectively determine their values. Predictions for the widths are presented for both standard and non-standard values of the quark mass ratio $m_s/{\hat m}$. A precise relation is established between the usual phenomenological $η-η'$ mixing parameters and those of the chiral expansion. The large size of the chiral correction to the $η$ decay can be understood on the basis of a simple counting rule: $O(1/N_c)\sim\ O(m_q)$. It is shown how this counting rule eventually allows one to include the $η'$ into the effective lagrangian in a consistent and systematic way.

hep-ph↗
arXiv1994

Chiral Symmetry Aspects of the Scalars

Electromagnetic decays of the scalar mesons are shown to be constrained by chiral symmetry as a consequence of the fact that, in the chiral limit, the two and three-point functions $ $ and $ $ satisfy super-convergent dispersion relations. The QCD asymptotic behavior of the latter is canonical and it can be saturated by a finite number of resonances. The corresponding chiral lagrangian for vector and scalar resonances is constructed. Matching to the correct asymptotic structure generates non-minimal terms which have so far been ignored. It is found that the width $a_0(980)\to2γ$ can be naturally reproduced suggesting that the $a_0(980)$ is not an exotic particle.

hep-ph↗
arXiv1994

The Reaction $γγ\toπ^0π^0$ in Generalized Chiral Perturbation Theory

The cross section for $γγ\toπ^0π^0$ and the pion polarizabilities are computed, within generalized chiral perturbation theory, in the full one loop approximation, {\it i.e.} up to and including order $O({p^5})$. The result depends on the parameter $α_{ππ}$ defining the tree level $π- π$ scattering amplitude and on an additional low energy constant. The latter is shown to be related by an exact sum-rule to the $e^+ e^-$ data. The parameter $α_{ππ}$ is related to the quark mass ratio $r = m_s /{\hat m}$ via the expansion of pseudoscalar meson masses. The generalized one loop $γγ\toπ^0π^0$ amplitude agrees with the experimental data in the threshold region provided $r= {m_s}/{\hat m}\lapprox 10$. Higher order corrections are estimated comparing our calculation with the dispersive approach.

hep-ph↗
arXiv1992

Casimir Energy in the Skyrme Model

The so called Casimir energy embodies the O($(N_c)^0$) contribution to the skyrmion mass according to the semi-classical expansion theory of solitons. We claim that this contribution can be accurately estimated despite the fact that some of the counterterms, provided in principle by chiral perturbation theory, are not known in practice. Using $ζ$ function techniques we show that $E_{cas}=E_{cas}(μ)+E_{ct}(μ)$ where $E_{cas}(μ)>>E_{ct}(μ)$ because it incorporates all the zero-mode contributions and it can be exactly calculated. Our results confirm that the fourth order Skyrme lagrangian does not seem to provide a correct description of the lightest baryons as solitons. We show that a simple extension to order six gives, on the contrary, good results without tuning the parameters of the chiral lagrangian.

hep-ph↗
arXiv1992

On the role of vector mesons in topological soliton stability

Isospin one vector mesons (in particular the $ρ$) are usually described as massive Yang-Mills particles in the chiral Lagrangian. We investigate some aspects of an alternative approach in the soliton sector. It is found that the soliton is stable in very much the same way as with the $ω$-meson and that spontaneous parity violating classical solutions do not exist. The formulation in terms of antisymmetric tensors is shown to be canonically related to a vector field description provided the Skyrme term is added to the latter.

hep-ph↗