Related papers: Large Nc and Chiral Dynamics
We investigate the linear chromatic number $\chi_{\text{lin}}(G(n,p))$ of the binomial random graph $G(n,p)$ on $n$ vertices in which each edge appears independently with probability $p=p(n)$. For dense random graphs ($np \to \infty$ as $n…
We critically reconsider the argument based on 't Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional QCD-like theories with $N_c>2$ colors and $N_f$ flavors. The main line of reasoning relies…
We consider lattice gauge theories at strong coupling with gauge group $U(N_C)$, or $SU(N_C)$ restricted to the meson sector, and coupled to $N_F$ flavors of fundamental representation staggered fermions. We study the formation of a chiral…
The spontaneous breakdown of the chiral symmetry of the QCD Lagrangian ensures that $\pi\pi$ interactions are weak at low energies. How weak depends on the nature of explicit symmetry breaking. Measurements of $K_{e4}$ decays at DA$\Phi$NE…
We study the pion-baryon scattering process $\pi+B \to (n-1)\pi+B$ in a QCD theory with a large number (N_c) of colors. It is known that this scattering amplitudes decreases with N_c like N_c^{1-n/2}, and that its individual tree diagrams…
We discuss the Pad\'e approximation to the $\pi\pi$ scattering amplitudes in 1--loop chiral perturbation theory. The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing…
The energy dependence of $90^o$ $cm$ fixed angle scattering of $\pi p \to \pi' p'$ and $\gamma p\to \pi^+ n$ at large momentum transfer are found to be well described in terms of interfering short and long distance amplitudes with dynamical…
We review the unitarization of Chiral Perturbation Theory with dispersion relations and how it describes meson-meson scattering data, generating light resonances whose mass, width and nature can be related to QCD parameters like quark…
We study the dynamics of non-interacting quantum particles with two bands in the presence of random scattering. The two bands are associated with a chiral symmetry. After breaking the latter by a potential, we still find that the quantum…
We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For $N_f$ flavors, the chiral flavor symmetry of these theories is…
We present preliminary results from our calculation of the low energy constants (LECs) of the chiral effective theory for 3, 4 and 5 color QCD with $N_f=2$ dynamical fermion flavors. We simulate with clover fermions over a range of lattice…
Let $G$ be the unit distance graph in the plane. A well-known problem in combinatorial geometry is that of determining the chromatic number of $G$. It is known that $4\le \chi(G)\le 7$. The upper bound of 7 is obtained using tilings of the…
We present a study of the $\pi\pi$ scattering amplitude in the $\sigma$ and $\rho$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which…
The bootstrap approach (demanding consistency conditions to scattering amplitudes) has shown to be quite powerful to tightly constrain gauge theories at large $N_c$. We extend previous analysis to scattering amplitudes involving pions and…
We present the scattering lengths for the $\pi K$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include…
We extract the statistical uncertainties for the pion-nucleon ($\pi N$) low energy constants (LECs) up to fourth order $\mathcal{O}(Q^4)$ in the chiral expansion of the nuclear effective Lagrangian. The LECs are optimized with respect to…
Combining large $N_C$ techniques and partial wave dispersion theory to analyze the $\pi\pi$ scattering, without relying on any explicit resonance lagrangian, some interesting results are derived: (a) a general KSRF relation including the…
The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass…
We extend the 1/N_c expansion meson-baryon scattering formalism to cases in which the final state contains more than two particles. We first show that the leading-order large N_c processes proceed through resonant intermediate states (e.g.,…
Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard Nf=3 chiral expansions at next-to-leading order, yielding low values of the quark…