Related papers: A Bound on $m_\eta/m_{\eta'}$ for Large $N_C$

Given $\eta \in [0, 1]$, a colouring $C$ of $V(G)$ is an $\eta$-majority colouring if at most $\eta d^+(v)$ out-neighbours of $v$ have colour $C(v)$, for any $v \in V(G)$. We show that every digraph $G$ equipped with an assignment of lists…

We reconcile the 1/N_c expansion with the observed eta-eta' mass spectrum. The chiral corrections introduced for that purpose are natural and consistent with the octet-singlet mixing angle theta=-(22\pm 1)^{\circ} extracted from…

We investigate the decays eta, eta-prime --> pi^+ pi^- gamma up to next-to-leading order in the framework of the combined 1/N_c and chiral expansions. Counter terms of unnatural parity at next-to-leading order with unknown couplings are…

The decays pi^0, eta, eta-prime -> gamma gamma are investigated up to next-to-next-to-leading order in the framework of the combined 1/N_c and chiral expansions. Without mixing of the pseudoscalar mesons the N_c independence of the pi^0 and…

A range of experimental results point to the existence of a massive neutrino. The recent high precision measurements of the cosmic microwave background and the large scale surveys of galaxies can be used to place an upper bound on this…

In the paper we state and prove theorem describing the upper bound on number of the graphs that have fixed number of vertices |V| and can be colored with the fixed number of n colors. The bound relates both numbers using power of 2, while…

We propose a relation between the $\eta$ invariant on a manifold with boundary, the $\eta$ invariants of edge states, and the $\eta$ invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary…

A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let $\mathcal{A}(G)$ be…

We argue that a so far neglected dimensionless scale, the number of neighbors in a closely packed system, is relevant for the convergence of the large $N_c$ expansion at high chemical potential. It is only when the number of colors is large…

An urn contains balls of d colors. At each time, a ball is drawn and then replaced together with a random number of balls of the same color. Assuming that some colors are dominated by others, we prove central limit theorems. Some…

The problem of nucleon resonances N' with masses below the Delta is considered. We derive bounds for the properties of such states. Some of these are new, while others improve upon existing limits. We discuss the nature of N' states, and…

In the limit of large $N_c$ we first consider the $N_c$ ordering of the various parity violating $\pi, N, \Delta$ couplings. Then we derive the relations among these couplings and consistency relations from the stability of these couplings…

We argue that lattice calculations of the $\eta'$ mass in QCD with $N_c=2$ colors performed at non-zero baryon chemical potential can be used to study the mechanism responsible for the mass of the $\eta'$. QCD with two colors is an ideal…

We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed number of colors greater than two.

Suppose that the vertices of a graph $G$ are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority…

It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here…

The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…

We consider a class of theories involving an extension of the Standard Model gauge group to an {\it a priori} arbitrary number of colors, $N_c$, and derive constraints on $N_c$. One motivation for this is the string theory landscape. For…

We prove that for every $d\in \mathbb{N}$ and a graph class of bounded expansion $\mathscr{C}$, there exists some $c\in \mathbb{N}$ so that every graph from $\mathscr{C}$ admits a proper coloring with at most $c$ colors satisfying the…

The energies and widths of bound states of the $\eta$ meson in different nuclei are obtained using the results for its selfenergy in a nuclear medium, which is evaluated in a selfconsistent manner using techniques of unitarized chiral…