A transfer matrix method for resonances in Randall-Sundrum models II: the deformed case

Abstract

Here we consider resonances of the Gauge, Gravity and Spinor fields in Randall-Sundrum-like scenarios. We consider membranes that are generated by a class of topological defects that are deformed domain walls obtained from other previously known ones. They are obtained by a deformation procedure generate different potentials to the associated Schrödinger-like equation. The resonance spectra are calculated numerically using the method of Transfer Matrix developed by the authors and presented in JHEP 1108 (2011) 071. The new deformed defects change the resonances spectra of all fields considered and the associated phenomenology as well. 1

Spinors fields in co-dimension one braneworlds

“…Here we will give the details of the program used to compute the transmission coefficients by transfer matrix [23][24][25]. First, we write the equation of motion for massive modes as a Schrödinger like equation, as demonstrated in (3.17).…”

“…This fact is a consequence of decomposition (3.22), that is different of odd case (3.11). The potential for left handed and Dirac fermions for s = 1 is very similar to a double barrier and we should expect the existence of resonant modes [23][24][25]. But for right handed fermions, when s = 1 this will not be true, because the potential in this case is a single barrier.…”

“…Therefore, as mentioned previously, our problem can be addressed as if we were dealing with an one dimensional quantum mechanical problem with potential given by U (z), as in the refs. [23][24][25]. The unstable modes can be found by looking for resonances of the effective potential.…”

“…Asymptotically, when y → ±∞, we have A(y) → −2β p |y|, and therefore the tensor T 00 becomes 24) where δ(y) is the Dirac's delta. Therefore the behavior of T 00 when y → ±∞ is…”

“…The last case of our interest, is the deformed brane, approached in [24]. The deformation method is based in modifications of the potential of models containing solitons in order to produce new and unexpected solutions [32].…”