Matteo Giordano

Hadronic total cross sections at high energy and the QCD spectrum

A bstractWe show how to obtain the leading energy dependence of hadronic total cross sections, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlation functions, if certain nontrivial analyticity assumptions are satisfied. The total cross sections turn out to be of “Froissart” type,

Universality and the QCD Anderson transition

\sigma_{\mathrm{tot}}^{{\left( {hh} \right)}}

Comments on high-energy total cross sections in QCD

(s) ~ B log2s for s → ∞. We also discuss under which conditions the coefficient B is universal, i.e., independent of the hadrons involved in the scattering process. In the most natural scenarios for universality, B can be related to the stable spectrum of QCD, and is predicted to be Bth ≃ 0.22 mb, in fair agreement with experimental results. If we consider, instead, the stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite larger value

Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature

B_{\mathrm{th}}^{(Q) }

An Ising-Anderson model of localisation in high-temperature QCD

≥ 0.42 mb, suggesting (quite surprisingly) large unquenching effects due to the sea quarks.

Anderson localization in QCD-like theories

We study the Anderson-type transition previously found in the spectrum of the QCD quark Dirac operator in the high-temperature, quark-gluon plasma phase. Using finite size scaling for the unfolded level spacing distribution, we show that in the thermodynamic limit there is a genuine mobility edge, where the spectral statistics changes from Poisson to Wigner-Dyson statistics in a nonanalytic way. We determine the correlation length critical exponent ν and find that it is compatible with that of the unitary Anderson model.

Investigation of the leading and subleading high-energy behavior of hadron-hadron total cross sections using a best-fit analysis of hadronic scattering data

Abstract We discuss how hadronic total cross sections at high energy depend on the details of QCD, namely on the number of colours N c and the quark masses. We find that while a “Froissart”-type behaviour σ tot ∼ B log 2 ⁡ s is rather general, relying only on the presence of higher-spin stable particles in the spectrum, the value of B depends quite strongly on the quark masses. Moreover, we argue that B is of order O ( N c 0 ) at large N c , and we discuss a bound for B which does not become singular in the N f = 2 chiral limit, unlike the Froissart–Łukaszuk–Martin bound.

Understanding localisation in QCD through an Ising-Anderson model

We investigate the Anderson transition found in the spectrum of the Dirac operator of quantum chromodynamics at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determine the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high temperature, and further support that it belongs to the 3D unitary Anderson model class.

Dirac eigenmodes at the QCD Anderson transition

A bstractWe discuss a possible mechanism leading to localisation of the low-lying Dirac eigenmodes in high-temperature lattice QCD, based on the spatial fluctuations of the local Polyakov lines in the partially ordered configurations above Tc. This mechanism provides a qualitative explanation of the dependence of localisation on the temperature and on the lattice spacing, and also of the phase diagram of QCD with an imaginary chemical potential. To test the viability of this mechanism we propose a three-dimensional effective, Anderson-like model, mimicking the effect of the Polyakov lines on the quarks. The diagonal, on-site disorder is governed by a three-dimensional Ising-like spin model with continuous spins. Our numerical results show that localised modes are indeed present in the ordered phase of the Ising model, thus supporting the proposed mechanism for localisation in QCD.

Quark localization in QCD above Tc

We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and staggered valence fermions as well as in Nf=2+1 QCD with staggered quarks. We draw an analogy between the transition from localized to delocalized modes in the Dirac spectrum and the Anderson transition in electronic systems. The QCD transition turns out to be in the same universality class as the transition in the corresponding Anderson model. We also speculate on the possible physical relevance of this transition to QCD at high temperature and the possible finite temperature phase transition in QCD-like models with different fermion contents.