Problem solving the EW tadpole equations using Mu and TanBeta

[AForster]

Hi,

I am trying to create a SPheno version which takes the highscale Bilinear coupling B_0 instead of TanBeta as an input. i.e.
MINPAR= {{1,m0},
{2,m12},
{4,SignumMu},
{5,Azero},
{6,Bzero}};

where mHu2 and mHd2 are set to m0^2 by boundary conditions.

The problem is solving the electroweak tadpole equations. I want to solve them using Mu and TanBeta; the 2 remaining parameters in the equations. However the equations are given in terms of vu and vd; not TanBeta. I tried solving for vu/vd: {\[Mu],vu/vd}, and for {\[Mu],vu,vd} none of which worked.

Is there any way of getting around this problem?

Any advise would be much appreciated.

Thanks,

Adam

[Avelino]

Solving the tadpole equations for parameters other than squared mass terms is usually problematic. The reason is that Mathematica may not be able to find an analytical solution to the equations. I am not sure there is a way around this...

[AForster]

Hi Avelino

Thanks very much for your reply!!!

I am used to the form of these equations in Steve Martins SUSY primer (equations 8.1.8 and 8.1.9). These seem like they could be solved analytically. Could I some how try to solve these by hand for TanBeta and Mu and pass these to SARAH and thus to SPheno?

Adam

[Avelino]

That would indeed be a very nice possibility, but I am not sure you can always find an analytical solution. Martin's solution only works for the MSSM. As soon as you complicate the model a little you start finding difficulties to solve the tadpole equations (unless you do it for squared mass terms).

In any case, I ignore whether it's doable with the current version of SARAH. The developers can surely give you a better answer.

[FStaub]

Hi,

there are some issues with solving the tadpoles with respect to TanBeta:
- Steve Martin only considers tree-level in his primer. Of course, you need to include loops at some point
- The SUSY Yukawas are a function of measured quark masses and TanBeta. Thus, solving the tadpoles with respect to TanBeta could cause non-sense (i.e non perturbarive) values for the Yukawas. Even if you might be lucky and your derived tb is somewhere between 2 and 50, it might still jump a lot during the iterative procedure to find a consistent solution for everything. That's a very though (numerically) problem and won't work out of the box.

Cheers,
Florian