Soliton-Antisoliton Pair Production in Particle Collisions

Abstract

We propose general semiclassical method for computing the probability of soliton-antisoliton pair production in particle collisions. The method is illustrated by explicit numerical calculations in (1 + 1)-dimensional scalar field model. We find that the probability of the process is suppressed by an exponentially small factor which is almost constant at high energies.Ever since the discovery of topological solitons, a question remains [1, 2] of whether soliton-antisoliton (SA) pair can be produced at sizable probability in collision of two quantum particles. This process, which involves a transition from perturbative two-particle state to a nonperturbative state containing SA pair, eludes treatment by any of the standard methods. A general expectation [1,3] is that the probability of the process is exponentially suppressed in weak coupling regime,where E is the total energy, g ≪ 1 is the coupling constant. Indeed, crudely speaking, one can think of solitons as bound states of N S ∼ 1/g 2 particles [1]. Then the suppression (1) is due to multiparticle production [3]. In this Letter we propose general semiclassical method for computing the leading suppression exponent F (E) of the inclusive process "two particles → SA pair + particles." As a by-product, we calculate the exponent F N (E) of the same process with N initial particles. In our method the problem is deformed by introducing a small parameter δρ which turns the process of SA pair production into a well-known tunneling process. To the best of our knowledge, no method of this kind has ever been proposed before.For definiteness we consider (1 + 1)-dimensional scalar field theory with action [4]This model possesses topological solitons if the scalar potential V (φ) has a pair of degenerate minima φ − and φ + , see the inset in Fig. 1, solid line. Soliton and antisoliton solutions interpolate between the minima; their profiles are shown in Fig. 2a. An obstacle to the semiclassical description of SA pair production is related to the fact that soliton and antisoliton attract each other and annihilate classically into N SA ∼ 1/g 2 particles. Thus, there is no potential barrier separating SA pair from the particle sector and the process under study cannot be treated as potential tunneling.We get around this obstacle by introducing the potential barrier between SA pair and perturbative states. Namely, we add negative energy density (−δρ) to the vacuum φ + , see dashed line in the inset in Fig. 1. This turns φ − and φ + into false and true vacua, respectively; the process of SA pair production is now interpreted as false vacuum decay [5] induced by particle collisions. The latter is a well-studied tunneling process [6,7]. In the end of calculation we will take the limit δρ → 0.The height of the potential barrier between the false and true vacua is given by the energy E cb of the critical bubble [5] -unstable static solution "sitting" on top of the barrier. The pressure δρ inside this bubble is balanced by the soliton-antisoliton attraction. Let us estimate the criti...

Semiclassical description of soliton-antisoliton pair production in particle collisions

“…Our main idea was previously reported in [49], here we presented the details, confirmations and generalizations of the method.…”

“…In this paper which extends ref. [49] we solve the above difficulty by relating production of the solitons from particles to their Schwinger pair creation in external field. We illustrate our method with explicit numerical calculations and present details of the numerical techniques.…”

Numerical study of multiparticle scattering in λϕ4 theory

“…On the one hand, one can start, as we did in this paper, with processes N i → N f where both initial and final states contain large occupation numbers and apply the same semiclassical techniques. In this case based on the results of the semiclassical studies of baryon number violating processes [48,49] and soliton pair production [50,51] in particle collisions one can expect that corresponding classical solutions will be nonsingular. The classical solutions at the boundary of the classically allowed region obtained in the present study are expected to be close to the solutions describing transitions in the forbidden region.…”

Creation of Magnetic Monopoles in Classical Scattering

“…A more modest objective is to study the creation of magnetic monopoles by scattering classical waves, where the classical waves can themselves be thought of as quantum states containing high occupation numbers of quanta. This is the approach we shall take.Past work on the creation of kinks in 1+1 dimensions [11][12][13][14][15][16][17], on the decay of electroweak sphalerons [18,19], and on the scattering and annihilation of magnetic monopole-antimonopole [20], together with results from magneto-hydrodynamics (MHD) [21], offers some guidance on initial conditions that may be suitable for creating magnetic monopoles. We will further explain these motivations when describing our initial conditions.…”