Life-time with thermal tunneling

[FStaub]

Hi Ben and Eliel,

when including the thermal corrections to the tunneling, Vevacious still prints the life-time for zero temperature. As there a way to get the life-time for the thermal tunneling?

Best,
Florian

[benoleary]

Yes.

It depends on what it is exactly that you want.

If you want the decay width at a specific constant temperature without taking into account the effect non-zero temperature has on the expansion of space-time, you can edit Vevacious.py to use vcs.SetTemperature(FloriansTemperatureInUnitsOfGev) early on (as Eliel discussed with Alexander in the other topic), though Vevacious will still print the result as "tunneling time at zero temperature" because I didn't set up the output code to try to notice what temperature the tunneling was performed at.

There are subtle issues to beware of though, and I will only enumerate them when I have some time, which will be after ironing my shirts after work this evening, if you are lucky.

Regards,
Ben

[FStaub]

Hi Ben,

thanks for your quick reply. I'll check the other thread. I just wonder if it might be useful to print in general the decay width for the thermal tunneling in the SLHA file, because this looks a bit confusing (at least to me):

Code: Select all

BLOCK VEVACIOUSRESULTS # results from Vevacious version 1.2.00, documented in arXiv:1307.1477, arXiv:1405.7376 (hep-ph)
    0    0    -2.00000000E+000    long-lived_but_thermally_excluded    # stability of input
    0    1    1.38281597E+002    deformed_path    # tunneling time in Universe ages / calculation type
    0    2    6.19849689E+002    0.0    # estimated best tunneling temperature / survival probability at this temperature
...

It would be nice to have something like

Code: Select all

BLOCK VEVACIOUSRESULTS # results from Vevacious version 1.2.00, documented in arXiv:1307.1477, arXiv:1405.7376 (hep-ph)
    0    0    -2.00000000E+000    long-lived_but_thermally_excluded    # stability of input
    0    1    1.38281597E+002    deformed_path    # tunneling time in Universe ages / calculation type at T=0
    0    2    6.19849689E+002    0.0    # estimated best tunneling temperature / survival probability at this temperature
    0    3    XXX       #  tunneling time in Universe ages / calculation type at T=T_crit
...

However, this is not urgent now, because I decided to show a different plot.

Cheers,
Florian

[benoleary]

Hi, Florian,

eh, the trouble is that the allowed tunneling time depends on the 4-volume of the past light cone - if there is a bubble of true vacuum bigger than the critical volume in your past, it will get you as it begins to expand close to the speed of light basically straight away. The problem with T != 0 is that the volume of space in your past is very variable depending on T - it's not enough to just say (tunneling time * speed of light)^3 as the volume. if you want to say to an audience "at T = 1 TeV, the tunneling time is 3 hours!" then well, a) how long was the Universe at that temperature? and b) how *big* was the Universe at that temperature (meaning the volume of the Universe which could be in causal contact with you)?

But it wouldn't be a huge effort to pull out the decay width for both calculations. I'll talk about it more later.

Cordialmente,
Ben

[benoleary]

So, just have a look at Vevacious.py, and edit it a lot.
You'll need to make sure that vcs.SetTemperature is called with the right temperature
1) before you call RollExtrema (so that MINUIT runs assuming that T = FloriansTemperature);
and 2) just before you calculate an action, and do what you want with the value of the action afterwards.

Just bear in mind that there are 2 ways of calculating the action:
i) the way assuming that quantum fluctuations dominate, which returns a dimensionless action (around 400 being the critical value for Q = 100 GeV and T = 0)
and ii) the way assuming that thermal fluctuations dominate, which returns a dimensionful action in units of GeV (around 240 GeV being the critical value for the SM).
If you call vcs.CalculateAction with thermalNotQuantum = False you get case i), if you call with with thermalNotQuantum = True, you get case ii).

You'd have to read the paper which we wrote together if you want details on how the actions get turned into survival probabilities.

Viele Grüße,
Ben

[FStaub]

Hi Ben,

thanks a lot for the details. I'll try that when I'm back at CERN.

Cheers,
Florian