Preheating in bubble collisions

Abstract

In a landscape with metastable minima, the bubbles will inevitably nucleate. We show that during the bubbles collide, due to the dramatically oscillating of the field at the collision region, the energy deposited in the bubble walls can be efficiently released by the explosive production of the particles. In this sense, the collision of bubbles is actually highly inelastic. The cosmological implications of this result are discussed.When the universe is initially set in a metastable minimum of certain landscape of scalar fields, it will undergo a dS expansion, bubbles with lower energy minima will inevitably nucleate in this background [1]. When the radius of bubble is larger than its critical radius, the bubble will expand outwards, and eventually collide with other expanding bubbles. In general, it is expected that during the bubbles collide, the energy deposited in the bubble walls will be released, e.g. The bubble collision has been studied earlier in [9], [10]. In general, when the bubbles collide, the walls of bubbles will pass through each other or be reflected. The region between outgoing walls remains in high energy metastable minimum, while other region is not affected. However, there is a net force, which will compel the walls to rest, and then back and move towards each other. Thus the collision of walls will inevitably occur again and again. This oscillation of walls has be displayed in the numerical simulations for bubble collision [9], [11], [12], [13]. In general, it is thought that during the bubble collision the energy deposited in the walls will be released by the direct decaying of scalar wave into other particles, e.g. [11], [14], or the gravitational radiation, e.g. [12], [15], [16], [17]. However, this release of the energy might be more dramatic than expected. In this paper, we show that due to the oscillation of the background field at the collision region, the energy can be efficiently released by the explosive production of the particles.We begin with a brief review of the numerically simulation of the collision of bubbles nucleating in a given potential in Fig.1, in which the high energy metastable minimum is φ F and the low energy minimum is φ T . We only care the numerical results of the evolution of field at the collision region during the bubble collision. Thus the details of the equations of the nucleation and evolution of bubble are neglected, see e.g. [18], [19].The field φ is initially in φ F . Thus the universe is inflating. Then the bubbles with φ T will be expected to nucleate. The radius of bubble is determined by the *

Charmless weakBsdecays in the relativistic quark model

“…Predictions are mostly available for the weak B s decays to scalar K * 0 mesons. Such transitions were studied in the light-cone sum rules [22,24], QCD sum rules [23,26] and perturbative QCD approach [25,27]. We find that our result for the form factor r + (0) is consistent with Ref.…”

“…We find that our result for the form factor r + (0) is consistent with Ref. [23], but lower than in other calculations [22,[24][25][26][27]. Contrary we predict larger absolute value for the form factor r − (0) than in Refs.…”

“…In Tables V-VII we compare our results for form factors of the weak B s decays to scalar K * 0 , axial vector K 1 and tensor K * 2 mesons at maximum recoil point q 2 = 0 with previous theoretical calculations [17,[22][23][24][25][26][27][28][29]. Predictions are mostly available for the weak B s decays to scalar K * 0 mesons.…”

“…The found value of the mixing angle, ϕ = 43.8 • [5], implies that physical K 1 mesons are nearly equal mixtures of the spin-singlet K( 1 P 1 ) and spin-triplet K( 3 P 1 ) states in accord with the experimental data [2]. We calculate the matrix elements of the weak current between the initial B s meson and final orbitally excited P -wave K ( * ) J meson using the procedure described above and compare the result with the invariant decomposition (22)- (27). In this way we obtain expressions for the decay form factors in terms of the overlap integrals of the initial and final meson wave functions which are valid in the whole accessible kinematical range.…”

“…Using form factors obtained in Sec. IV we get predictions for the nonleptonic branching fractions and present them in Table XI in comparison with previous estimates [27,41]. A few predictions are available for selected modes.…”