Mass Scales in the Rs Models: the Μ and Cosmological Constant

The standard model has been extremely successful phenomenologically. However, it has 20 theoretically unexplained parameters, among which the Higgs scalar mass is called the gauge hierarchy problem: Why is the electroweak scale 10 times the Planck mass? To solve this hierarchy problem, technicolor and supersymmetry have been extensively studied in the last twenty years. Recently, there appeared another try toward understanding this gauge hierarchy problem, through large extra dimensions or through warp factor geometry in the so-called RSI model . There are two branes located at y = 0(B1 brane) and π(B2 brane) where y is the fifth coordinate. The B1 brane tension Λ1 = 6k1M 3 > 0, B2 brane tension Λ2 = 6k2M 3 < 0 and the bulk cosmological constant Λb = −6k2M3 < 0 are fine-tuned k1 = k = −k2 to have a flat geometry, where M is the fundamental mass parameter in 5D. With this kind of two fine-tunings the flat-space solution is possible even if R terms are added if their form is of the Gauss-Bonnet type . The RSI model imposes the symmetry S1/Z2 for compactification, with the flat space metric ansatz, ds = edxμdx μ + r cdy , which allows the solution σ = krc|y|. Integrating over y, we obtain an effective 4D Planck mass, MP = (M 3/k)(1− ec) which is again of orderM . This fundamental mass parameter governs the mass scale at y = 0. On the other hand, at B2(y 6= 0) the rescaling of the fields so that the standard kinetic energy terms result gives the mass parameter of order m = Minpute −krc/2 which can be interpreted as a TeV scale if rc is a few tens of M . Thus, interpreting B2 as the brane for housing the visible sector fields, we obtain a long anticipated exponetially suppressed electroweak mass scale compared to the Planck mass. This led to a stimulus since it can be another solution for the gauge hierarchy problem. Note that here the key point is that a warp factor is introduced, i.e. a cuved space in y direction even if 4D is flat.