[Flexiblesusy-commits] [FlexibleSUSY/FlexibleSUSY] ce1ef8: Bugfix: account for mass eigenstate basis in self-...

[GitHub]

  Branch: refs/heads/bugfix-gluino-pole-mass
  Home:   https://github.com/FlexibleSUSY/FlexibleSUSY
  Commit: ce1ef83d6247ae034cc02fafba7ebeebc2f74077
      https://github.com/FlexibleSUSY/FlexibleSUSY/commit/ce1ef83d6247ae034cc02fafba7ebeebc2f74077
  Author: Alexander Voigt <Alexander.Voigt at desy.de>
  Date:   2015-10-25 (Sun, 25 Oct 2015)

  Changed paths:
    M meta/LoopMasses.m

  Log Message:
  -----------
  Bugfix: account for mass eigenstate basis in self-energies of fermion singlets

For a 1-dimensional fermion multiplet SARAH provides the self-energies
in mass eigenstates, i.e. the fermions at the external legs are
multiplied by their phase (= mixing matrix).  This behaviour is
different from fermion multiplets, as the neutralinos for instance.
Therfore, M_tree which is multiplies with the self-energies must be
set to the (positive) tree-level mass.  M_tree must not be set to the
gauge eigenstate mass parameter!

Date: Sun, 25 Oct 2015 12:16:28 +0100
From: Alexander Voigt <alexander.voigt at desy.de>
To: Peter Athron <peter.athron at coepp.org.au>,
 Dylan <dylan.harries at adelaide.edu.au>
Subject: Re: Fwd: Re: Fwd: SLHA files for gluino mass

Hi Dylan and Peter,

many thanks for investigating!

I looked into the details and found the origin of the problem: It is
definitely a bug in FlexibleSUSY.  The origin of the bug was a
misunderstanding on my side: I thought SARAH would treat all Majorana
fermions in the same way, independently of whether they form
multiplets (like the neutralinos) or singlets (like the gluino).

The issue is the following:

In the neutralino sector, the neutralino propagator has the form

   i (p-slash - Y)^-1

where Y is the (non-diagonalized) neutralino mass matrix.  To
calculate the pole masses, SARAH provides the self-energies of the
neutralino.  These self-energies are defined in *gauge eigenstates*.
With them, the loop corrected mass matrix can be calculated like this:

   M_loop = Y + (delta_M + delta_M^*)/2 ,

   delta_M = - Sigma_R * Y - Y * Sigma_L - Sigma_S

Here Y, Sigma_L, Sigma_R and Sigma_S are in the gauge eigenstate
basis.  That this is the case can be seen by looking at the vertices
inside the self-energies: In each vertex the external neutralino is
"unrotated" (UCha), which means it is a gauge-eigenstate field
(i.e. not multiplied by a mixing matrix).

Now, to the gluino case: I was assuming that the propagator is written
as

   i (p-slash - M3)^-1

where M3 is the soft-breaking gluino mass, which is equivalent to Y in
the case of the neutralinos.  To calculate the gluino pole mass, I
then use (equivalently to the neutralino case)

   M_loop = M3 - M3 (Sigma_R + Sigma_L) - Sigma_S

where I am assuming that Sigma_R, Sigma_L and Sigma_S are formulated
in the "gluino gauge eigenstate" basis.  With "gluino gauge
eigenstate" I mean the gluino field which is not multiplied by the
phase (phase = mixing matrix in the case of neutralinos). I.e. I was
assuming, that each vertex in Sigma_R, Sigma_L and Sigma_S contains an
external "unrotated" gluino (UGlu), i.e. a gluino which is not
multiplied by a phase.  However, it turns out that this is not the
case!  Instead, SARAH generates vertices where the external gluino is
a mass eigenstate field (Glu).

The fix would be to formulate the loop-corrected mass matrix as

   M_loop = MGlu - MGlu (Sigma_R + Sigma_L) - Sigma_S

where MGlu is the (positive) gluino mass.