  We show that it is possible to realize a "mu-split SUSY" scenario [1] in the
context of large volume limit of type IIB compactifications on Swiss-Cheese
Calabi-Yau's in the presence of a mobile space-time filling D3-brane and a
(stack of) D7-brane(s) wrapping the "big" divisor Sigma_B. For this, we
investigate the possibility of getting one Higgs to be light while other to be
heavy in addition to a heavy Higgsino mass parameter. Further, we examine the
existence of long lived gluino that manifests one of the major consequences of
mu-split SUSY scenario, by computing its decay width as well as lifetime
corresponding to the 3-body decays of the gluino into a quark, a squark and a
neutralino or Goldstino, as well as 2-body decays of the gluino into either a
neutralino or a Goldstino and a gluon. Guided by the geometric Kaehler
potential for Sigma_B obtained in [2] based on GLSM techniques, and the
Donaldson's algorithm [3] for obtaining numerically a Ricci-flat metric, we
give details of our calculation in [4] pertaining to our proposed metric for
the full Swiss-Cheese Calabi-Yau, but for simplicity of calculation, close to
Sigma_B, which is Ricci-flat in the large volume limit. Also, as an application
of the one-loop RG flow solution for the Higgsino mass parameter, we show that
the contribution to the neutrino masses at the EW scale from dimension-six
operators arising from the Kaehler potential, is suppressed relative to the
Weinberg-type dimension-five operators.
