Related papers: Some Properties of Amplitudes at Multi Boson Thres…
The amplitude of production of $n$ on-mass-shell scalar bosons by a highly virtual field $\phi$ is considered in a $\lambda \phi^4$ theory with weak coupling $\lambda$ and spontaneously broken symmetry. The amplitude of this process is…
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 $n\sim1/\lambda$. We extend this result to the processes of…
We present exact tree-order amplitudes for $H^* \to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that…
Threshold amplitudes are considered for multi-particle production in $\phi^k$ and $O(N) ~\phi^4$ theories. It is found that the disappearance of tree-level threshold amplitudes of $2$ on-shell particles producing a large number of particles…
It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $\lambda\phi^4$ has the exponential form, $A_n\propto\sqrt{n!}\exp[{1\over\lambda}F(\lambda n,\epsilon)]$, in…
We consider the problem of multiparticle production at threshold in a $\phi^4$-theory with an $O(N_1$$+$$N_2)$ symmetry softly broken down to $O(N_1)\times O(N_2)$ by nonequal masses. We derive the set of recurrence relations between the…
I review some recent work on the problem of multiparticle production in a phi^4-theory with an O(N) symmetry. Threshold amplitudes with fixed number of produced particles are exactly calculated at large-N to all loops and vanish on mass…
Threshold amplitudes are considered for $n$-particle production in arbitrary scalar theory. It is found that, like in $\phi ^4$, leading-$n$ corrections to the tree level amplitudes, being summed over all loops, exponentiate. This result…
Calculations of $1\to N$ amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number $N$ of final state particles. This either indicates an end of perturbative behaviour, or possibly…
It is shown that the technique recently suggested by Lowell Brown for summing the tree graphs at threshold can be extended to calculate the loop effects. Explicit result is derived for the sum of one-loop graphs for the amplitude of…
We use the semiclassical formalism based on singular solutions in complex time to compute scattering rates for multiparticle production at high energies. In a weakly coupled $\lambda \phi^4$ scalar field theory in four dimensions, we…
The method suggested by Lowell Brown for calculating multi-particle threshold amplitudes is extended to the one-loop level in scalar theories with broken reflection symmetry. A result for the threshold amplitude for multiparticle production…
The threshold behavior of a theory with two coupled scalar fields $\chi$ and $\phi$ is investigated. We compute the amplitude for two on-mass-shell $\chi$-particles to produce an arbitrary number of $\phi$-particles at rest in the tree…
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…
Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken \lambda \phi^4 theory,…
A method for calculating loop amplitudes at the multiboson threshold is presented, based on Feynman-diagram techniques. We explicitly calculate the one-loop amplitudes in both $\phi^4$-symmetric and broken symmetry cases, using dimensional…
Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical…
At sufficiently high energies the production of a very large number of particles is kinematically allowed. However, it is well-known that already in the simplest case of a weakly-coupled massive $\lambda \varphi^4$ theory, $n$-particle…
We compute the probability of producing $n$ particles from few colliding particles in the unbroken $(3+1)$-dimensional $\lambda\phi^4$ theory. To this end we numerically implement semiclassical method of singular solutions which works at…
I derive the set of recurrence relations between the amplitudes of multiparticle production at threshold in the standard large-N limit of the O(N)-symmetric phi^4$ theory which sums all relevant diagrams with arbitrary number of loops. I…