arXiv subjects
Publications and source records attributed to M. V. Libanov.
We consider the features of multiparticle tree cross sections in scalar theories in the framework of a semiclassical approach. These cross sections at large multiplicities have exponential form, and the properties of the exponent in different regimes are discussed.
We solve the classical euclidean boundary value problem for tree-level multiparticle production in $ϕ^4$ theory at arbitrary energies in the case of $O(4)$ symmetric field configurations. We reproduce known low-energy results and obtain a lower bound on the tree cross sections at arbitrary energies.
It has been shown recently that the amplitude of the creation of $n$ real scalar particles by one virtual boson near $n$--particle threshold exhibits exponential behavior at $n\sim1/λ$. We extend this result to the processes of multiparticle production at threshold by two virtual bosons. We find that both the tree--level amplitude and leading--$n$ loop corrections have the same exponential behavior, with the common exponent for $1\to n$ and $2\to n$ processes, for various kinematics. This result strongly indicates that the exponent for multiparticle amplitudes is independent of the initial state and that there may exist a semiclassical approach to the study of multiparticle production.
It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $λϕ^4$ has the exponential form, $A_n\propto\sqrt{n!}\exp[{1\overλ}F(λn,ε)]$, in the regime $λ\to 0$, $λn={fixed}$, $ε={fixed}$, where $ε$ is the typical kinetic energy of outgoing particles. Existing results support this conjecture. Several new analytical and numerical results in favor of the exponential behavior of multiparticle amplitudes are presented.
We consider the tree amplitudes of production of $n_2$ scalar particles by $n_1$ particles of another kind, where both initial and final particles are at rest and on mass shell, in a model of two scalar fields with $O(2)$ symmetric interaction and unequal masses. We find that these amplitudes are zero except for the lowest possible $n_1$ and $n_2$, and that the cancellation of the corresponding Feynman graphs occurs due to a special symmetry of the classical mechanical counterpart of this theory. This feature is rather general and is inherent in various other scalar field theories.
Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit interesting factorial and exponential behaviour at large multiplicities. As a by-product we observe that the kinematically allowed decay of one real particle into $n$ real particles of another kind, all at rest, has zero tree amplitude in this model for $n>2$.