How to get Metastable region in SM

[smandal123]

Hi,

I was trying to reproduce the metastability region for SM. I gave the input value of \[Lambda] as 0.25 in EW scale and varied the GUT scale to 1.00E+17 and i got the \[Lambda] value around - 0.007. Now if you see the calculation of the paper arXiv:1512.01222, if \[Lambda] lies between 0 and -0.01 we should get metastable vacuum. But when I am running Vevacious, it gives me a stable vacuum. I am geeting the following results from Vevacious,

BLOCK VEVACIOUSRESULTS # results from Vevacious version 1.2.00, documented in arXiv:1307.1477, arXiv:1405.7376 (hep-ph)
0 0 1.00000000E+000 stable # stability of input
0 1 -1.00000000E+000 unnecessary # tunneling time in Universe ages / calculation type
0 2 0.00000000E+000 1.0 # estimated best tunneling temperature / survival probability at this temperature
1 0 -1.06293319E+008 relative_depth # DSB vacuum potential energy
1 1 2.48746787E+002 vN # DSB vacuum VEV
2 0 -1.06293319E+008 relative_depth # panic vacuum potential
2 1 2.48746787E+002 vN # panic vacuum VEV
BLOCK VEVACIOUSWARNINGS # warnings from Vevacious
1 Starting point differed from DSB vacuum but rolled there. Trying again with scaled field configuration ({ { vN -> ( 2.0 ) }, TreeLevelPotentialValue -> -15516.03502, EffectivePotentialValue -> -14745.9051662 }).
2 Starting point differed from DSB vacuum but rolled there. Trying again with scaled field configuration ({ { vN -> ( -2.0 ) }, TreeLevelPotentialValue -> -15516.03502, EffectivePotentialValue -> -14745.9051662 }).


I dont know what I am doing wrong here. I am also attaching input files which I used. Looking forward for your answer.

[Eliel]

Dear smandal123,

I think you are trying to tackle a different problem than what Vevacious is designed for at the moment. Vevacious works at a fixed scale so essentially the question it answers is: at a given scale, are there any deeper minima than the DSB (desired symmetry breaking) and if so what is the tunneling rate to those.

In the SM and for the measured values of m_h and m_t, lambda runs negative and at higher energies a new minimum develops. At high energies, the potential can be approximated as \lambda_eff (H H^\dagger)^2 and the tunneling is calculated actually from a maximum (at v=0) to the panic vacuum.

As I said, Vevacious at the moment works at fixed scale and also the validity of the results depends on the field values not being that far away from the scale at which your parameters are evaluated. For a proper analysis you would have to use the RG-improved potential instead, which is one of the updates we plan to add to Vevacious in the future.

Hope that helps!

Best,
Eliel

[smandal123]

Thanks for the explanation. I have one more question, not related to Vevacious package. Is it always possible to write the effective potential like \lambda_eff (H*H) for any model (with extra fermion or scalar) where quartic coupling are smaller than \lambda ?

Thanks,
Sanjoy

[Eliel]

Dear Sanjoy,

The reason you can approximate the potential as \lambda_eff (H H^\dagger)^2 at high energies (notice the square) is due to the fact that for very high semi-classical field values (H_0 -> ∞ ), the quartic part of the potential dominates. Provided that your potential does not have any flat directions, i.e. directions in field space where the quartic couplings cancel, I think you can always approximate it as effective quartic couplings between all the scalars at high energies (check for example https://arxiv.org/abs/hep-ph/9603227).

[smandal123]

Thank you so much. I will check the paper you mentioned.


Thanks,
Sanjoy