Quantum bubble nucleation beyond the WKB approximation: Resummation of vacuum bubble diagrams

Abstract

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-with an attractive interaction. The validity of our proposal is tested in D = 1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D = 2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.

Strong-coupling-expansion analysis of the false-vacuum decay rate of the lattice ϕ4model in 1 + 1 dimensions

“…In the above, we found that at 1/g ≈ 1, there exists a crossover boundary separating two distinctive regimes. Our result supports the previous proposal of [13]. The authors calculated the effective potential, and found that for g > 1.17, the potential barrier is smeared out by quantum fluctuations.…”

“…So far, several ab initio approaches have been proposed in order to calculate the decay rate beyond semiclassical approximation. In particular, the φ 4 model in 0 + 1 dimension has come under through investigation [11,12,13,14], while the extension to manybody case remains unsuccessful. In the present paper, by means of the strong-coupling expansion, we studied the (1 + 1)-dimensional lattice φ 4 model (1).…”

“…As a consequence, these theories clarified how the instanton description fails for low potential barrier; true decay rate is suppressed owing to inter-instanton interaction. At present, extension to many-body case appears to be unsuccessful [13].…”

“…This feature is to be contrasted with that of 0 + 1 dimension, where the inter-instanton correlation results in suppression of decay rate. Enhancement in 1 + 1 dimensions was speculated in the former study [13], where the authors utilized the weak-coupling expansion and the Borel technique. Although their series does not show any indication of convergence, their result actually captures a signal of relaxation enhancement.…”

“…On the contrary, as for continuous-variable model such as the φ 4 model, the above approach does not apply, and so far, no attempt at ab initio calculation has been reported. For quantum-mechanics level (0 + 1 dimension), however, a number of substantial progresses are made [11]: Suzuki and Yasuta obtained a compact expression for the decay (tunnelling) rate based on the weak-coupling expansion and succeeding Borel resummation [12,13]. They succeeded in calculating the tunnelling rate beyond instanton calculus.…”