Colleagues and I are investigating one-loop effects to scalar VEVs in the THDM (with a Z_2 symmetry so that Lambda6 and Lambda7 are zero). We have a large set of parameter-space points (consisting of M_{11}^{2}, M_{22}^{2}, M_{12}^{2}, \Lambda_{1}, ..., \Lambda_{5} from https://arxiv.org/pdf/1106.0034.pdf Eqn. (98)) for which a charge breaking extrema and normal minimum exist, at tree-level. We wish to determine the one-loop effects. Namely, if one-loop effects allow the normal minimum to remain the deepest minimum. We figure that Vevacious is the best way to investigate. Right now, we are ignoring gauge boson and fermions.

I am having difficulties figuring out what the <input_vevs> does. If I put in the charge breaking extrema, I get different results than if I put in the normal extrema. For example, the SPheno file I am using is:

Code: Select all

`Block MINPAR Q= 1.60000000E+02 # Input parameters`

1 3.8624972E+01 #v1

2 1.5942701E+02 #v2

3 7.0762566E+01 #alpha

Block GAUGE Q= 1.60000000E+02 # (Renormalization Scale)

1 3.5912481E-01 #g1

2 6.4500093E-01 #g1

3 1.1769405E-01 #g1

Block HMIX Q= 1.60000000E+02 # (Renormalization Scale)

35 -3.9958700E-01 #Lambda5

31 6.9360059E+00 #Lambda1

34 -1.8689667E+00 #Lambda4

33 2.0303633E+00 #Lambda3

32 3.8802934E-01 #Lambda2

22 -6.9847223E+03 #M12

20 -4.8342188E+04 #M112

21 -1.1529163E+04 #M222

The tree-level normal minimum is located at :

- alpha 0.00000

v1 107.03483

v2 221.49389

The tree-level charge breaking extrema is located at :

- alpha 70.762566

v1 38.624972

v2 159.427010

If I set the <input_vevs> to the tree-level normal minimum, I get:

- global = {'alpha': 0.0, 'v2': 225.771957156, 'rel_depth': -194091630.339, 'v1': 108.77759553}

input = {'alpha': 0.0, 'v2': 225.771969622, 'rel_depth': -194091630.331, 'v1': 108.777595947}

If I set the <input_vevs> to the tree-level charge breaking extremum, I get:

- global = {'alpha': 0.00111456911801, 'v2': 288.501203148, 'rel_depth': -640892745.669, 'v1': -135.597882641}

input = {'alpha': 0.0184444018859, 'v2': 288.588504063, 'rel_depth': -640892504.23, 'v1': -135.624102169}

I would assume that Vevacious would find the same global minimum regardless of what I specify for <input_vevs>. Is this a numerical issue? If so, how can I increase the precision (currently I've set roll_tolerance=0.00000001).

Thank you.

- Logan A. Morrison

Additional notes: I run Vevacious with --should_tunnel=False since cosmotransitions often fails for me. Here are initialization file an my .vin:

initialization file

Code: Select all

`<Vevacious_defaults>`

<!--

# VevaciousInitialization.xml

#

# Created on: Oct 8, 2012

# Author: Ben O'Leary (benjamin.oleary@gmail.com)

# Copyright 2012 Ben O'Leary

#

# This file is part of Vevacious, released under the

# GNU General Public License. Please see the accompanying

# README.Vevacious.txt file for a full list of files, brief documentation

# on how to use these classes, and further details on the license.

#

-->

<!-- hom4ps2_dir is where the executable hom4ps2 is. absolute paths such as

/home/hom4ps2/ can be used. -->

<hom4ps2_dir>

~/HEP-Tools/HOM4PS2_Mac/

</hom4ps2_dir>

<!-- homotopy_type is 1 for polyhedral homotopy or 2 for linear homotopy.

actually, for generic QFT potentials, linear homotopy is probably the

faster option. -->

<homotopy_type>

2

</homotopy_type>

<!-- imaginary_tolerance is the tolerance for imaginary parts of VEVs found

as solutions to the tree-level tadpole equations, since it is possible

that a numerical precision error could lead to what should be an exact

cancellation leaving behind a small imaginary part. it is in units of

GeV, as the other dimensionful values are assumed so since that is how

they are in the SLHA standard. -->

<imaginary_tolerance>

0.00000001

</imaginary_tolerance>

<!-- python_wrapper is which Python wrapper for MINUIT to use. originally

Vevacious required PyMinuit specifically, but now IMinuit can be used

instead, which is probably preferable, as PyMinuit has been abandoned by

its author. the choice here is either PYMINUIT or IMINUIT, but is not

case-sensitive (e.g. iminuit or PyMinuit will also be accepted). -->

<python_wrapper>

IMINUIT

</python_wrapper>

<!-- model_file is where the loop-corrected potential stuff as written by

SARAH is. absolute paths such as /home/vevacious/MyModel/MyModel.vin can

be used. -->

<model_file>

~/HEP-Tools/Vevacious/THDM/THDM.vin

</model_file>

<!-- slha_file is where the Lagrangian parameters in SLHA format are.

absolute paths such as /home/spheno/MyModel/SPheno.spc.MyModel can be

used. -->

<slha_file>

~/HEP-Tools/Vevacious/THDM/SPheno.spc.THDM

</slha_file>

<!-- output is where the loop-corrected minimum, as found by PyMinuit

starting from the HOM4PS2 extrema, should be written. absolute paths

such as /home/vevacious/MyModel/MyResult.vout can be used. -->

<result_file>

~/HEP-Tools/Vevacious/THDM/THDM_vout.xml

</result_file>

<!-- saddle_nudges is the comma-separated list of nudges in GeV that should

be used to nudge PyMinuit off any saddle points where it has come to

rest. -->

<saddle_nudges>

1.0, 5.0, 20.0

</saddle_nudges>

<!-- roll_tolerance is the tolerance for whether extrema are identified with

each other. If roll_tolerance is for example 0.05, then extrema A and B

are considered to be both at the same extremum within numerical errors

if the length of the vector of VEV differences is less than 0.05 * the

length of the longer of the 2 vectors of VEVs. E.g. if A is

vd = 24.42, vu = 245.0 and B is vd = 24.39, vu = 242.7, the length of A

is 246.2140, the length of B is 243.9225, so the longer length is

246.2140; the length of their difference is 2.300196 which is less than

0.05 * 246.2140, so A & B are considered to be the same extremum. (This

is important to avoid attempting calculating the tunneling time from the

input VEVs to what should be exactly the same point, that was just not

found exactly due to numerical issues.) -->

<roll_tolerance>

0.00000001

</roll_tolerance>

<!-- ct_path is the path to where pathDeformation.py & tunneling1D.py are

found. absolute paths such as /home/cosmotransitions/ can be used. -->

<ct_path>

~/HEP-Tools/Vevacious/CosmoTransitions-2.0.2/CosmoTransitions/

</ct_path>

<direct_time>

100000000.

</direct_time>

<deformed_time>

10000.

</deformed_time>

<!-- lifetime_threshold is the fraction of the age of the known Universe used

as a threshold for whether a parameter point is denoted as short-lived

or long-lived by comparison with its calculated tunneling time at zero

temperature. The default of 0.217 (about 3 gigayears) corresponds to a

survival probability of about 1% assuming a Poisson distribution. -->

<lifetime_threshold>

-1.

</lifetime_threshold>

<!-- thermal_survival_threshold is the fraction used as a threshold for

whether a parameter point is denoted as having a low or high probability

to survive thermal tunneling. -->

<thermal_survival_threshold>

0.99

</thermal_survival_threshold>

</Vevacious_defaults>

.vin

Code: Select all

`<Vevacious_stuff>`

<input_vevs alpha="SLHA::MINPAR[3]" v1="SLHA::MINPAR[1]" v2="SLHA::MINPAR[2]">

</input_vevs>

<polynomial_part>

(0.5*alpha^2*SLHA::HMIX[20.])

+ (0.5*v1^2*SLHA::HMIX[20.])

+ (0.5*v2^2*SLHA::HMIX[21.])

+ (-1.*v1*v2*SLHA::HMIX[22.])

+ (0.125*alpha^4*SLHA::HMIX[31.])

+ (0.25*alpha^2*v1^2*SLHA::HMIX[31.])

+ (0.125*v1^4*SLHA::HMIX[31.])

+ (0.125*v2^4*SLHA::HMIX[32.])

+ (0.25*alpha^2*v2^2*SLHA::HMIX[33.])

+ (0.25*v1^2*v2^2*SLHA::HMIX[33.])

+ (0.25*v1^2*v2^2*SLHA::HMIX[34.])

+ (0.25*v1^2*v2^2*SLHA::HMIX[35.])

</polynomial_part>

<tadpoles>

{

(alpha*SLHA::HMIX[20.])

+(0.5*alpha^3*SLHA::HMIX[31.])

+(0.5*alpha*v1^2*SLHA::HMIX[31.])

+(0.5*alpha*v2^2*SLHA::HMIX[33.])

;

(v1*SLHA::HMIX[20.])

+(-1.*v2*SLHA::HMIX[22.])

+(0.5*alpha^2*v1*SLHA::HMIX[31.])

+(0.5*v1^3*SLHA::HMIX[31.])

+(0.5*v1*v2^2*SLHA::HMIX[33.])

+(0.5*v1*v2^2*SLHA::HMIX[34.])

+(0.5*v1*v2^2*SLHA::HMIX[35.])

;

(v2*SLHA::HMIX[21.])

+(-1.*v1*SLHA::HMIX[22.])

+(0.5*v2^3*SLHA::HMIX[32.])

+(0.5*alpha^2*v2*SLHA::HMIX[33.])

+(0.5*v1^2*v2*SLHA::HMIX[33.])

+(0.5*v1^2*v2*SLHA::HMIX[34.])

+(0.5*v1^2*v2*SLHA::HMIX[35.])

;

}

</tadpoles>

<mass-squared_matrix

particle="hh" rotationmatrix="ZH" spin="scalar" factor="1" >

(SLHA::HMIX[20.]+0.5*alpha^2*SLHA::HMIX[31.]+1.5*v1^2*SLHA::HMIX[31.]+0.5*v2^2*SLHA::HMIX[33.]+0.5*v2^2*SLHA::HMIX[34.]+0.5*v2^2*SLHA::HMIX[35.]),

(-1.*SLHA::HMIX[22.]+v1*v2*SLHA::HMIX[33.]+v1*v2*SLHA::HMIX[34.]+v1*v2*SLHA::HMIX[35.]),

(0.),

(0.),

(0.),

(alpha*v1*SLHA::HMIX[31.]),

(0.),

(0.5*alpha*v2*SLHA::HMIX[34.]+0.5*alpha*v2*SLHA::HMIX[35.]),

(-1.*SLHA::HMIX[22.]+v1*v2*SLHA::HMIX[33.]+v1*v2*SLHA::HMIX[34.]+v1*v2*SLHA::HMIX[35.]),

(SLHA::HMIX[21.]+1.5*v2^2*SLHA::HMIX[32.]+0.5*alpha^2*SLHA::HMIX[33.]+0.5*v1^2*SLHA::HMIX[33.]+0.5*v1^2*SLHA::HMIX[34.]+0.5*v1^2*SLHA::HMIX[35.]),

(0.),

(0.),

(0.),

(alpha*v2*SLHA::HMIX[33.]),

(0.),

(0.5*alpha*v1*SLHA::HMIX[34.]+0.5*alpha*v1*SLHA::HMIX[35.]),

(0.),

(0.),

(SLHA::HMIX[20.]+0.5*alpha^2*SLHA::HMIX[31.]+0.5*v1^2*SLHA::HMIX[31.]+0.5*v2^2*SLHA::HMIX[33.]+0.5*v2^2*SLHA::HMIX[34.]-0.5*v2^2*SLHA::HMIX[35.]),

(-1.*SLHA::HMIX[22.]+v1*v2*SLHA::HMIX[35.]),

(0.),

(0.),

(-0.5*alpha*v2*SLHA::HMIX[34.]+0.5*alpha*v2*SLHA::HMIX[35.]),

(0.),

(0.),

(0.),

(-1.*SLHA::HMIX[22.]+v1*v2*SLHA::HMIX[35.]),

(SLHA::HMIX[21.]+0.5*v2^2*SLHA::HMIX[32.]+0.5*alpha^2*SLHA::HMIX[33.]+0.5*v1^2*SLHA::HMIX[33.]+0.5*v1^2*SLHA::HMIX[34.]-0.5*v1^2*SLHA::HMIX[35.]),

(0.),

(0.),

(0.5*alpha*v1*SLHA::HMIX[34.]-0.5*alpha*v1*SLHA::HMIX[35.]),

(0.),

(0.),

(0.),

(0.),

(0.),

(SLHA::HMIX[20.]+0.5*alpha^2*SLHA::HMIX[31.]+0.5*v1^2*SLHA::HMIX[31.]+0.5*v2^2*SLHA::HMIX[33.]),

(0.),

(-1.*SLHA::HMIX[22.]+0.5*v1*v2*SLHA::HMIX[34.]+0.5*v1*v2*SLHA::HMIX[35.]),

(0.),

(alpha*v1*SLHA::HMIX[31.]),

(alpha*v2*SLHA::HMIX[33.]),

(0.),

(0.),

(0.),

(SLHA::HMIX[20.]+1.5*alpha^2*SLHA::HMIX[31.]+0.5*v1^2*SLHA::HMIX[31.]+0.5*v2^2*SLHA::HMIX[33.]),

(0.),

(-1.*SLHA::HMIX[22.]+0.5*v1*v2*SLHA::HMIX[34.]+0.5*v1*v2*SLHA::HMIX[35.]),

(0.),

(0.),

(-0.5*alpha*v2*SLHA::HMIX[34.]+0.5*alpha*v2*SLHA::HMIX[35.]),

(0.5*alpha*v1*SLHA::HMIX[34.]-0.5*alpha*v1*SLHA::HMIX[35.]),

(-1.*SLHA::HMIX[22.]+0.5*v1*v2*SLHA::HMIX[34.]+0.5*v1*v2*SLHA::HMIX[35.]),

(0.),

(SLHA::HMIX[21.]+0.5*v2^2*SLHA::HMIX[32.]+0.5*alpha^2*SLHA::HMIX[33.]+0.5*v1^2*SLHA::HMIX[33.]+0.5*alpha^2*SLHA::HMIX[34.]-0.5*alpha^2*SLHA::HMIX[35.]),

(0.),

(0.5*alpha*v2*SLHA::HMIX[34.]+0.5*alpha*v2*SLHA::HMIX[35.]),

(0.5*alpha*v1*SLHA::HMIX[34.]+0.5*alpha*v1*SLHA::HMIX[35.]),

(0.),

(0.),

(0.),

(-1.*SLHA::HMIX[22.]+0.5*v1*v2*SLHA::HMIX[34.]+0.5*v1*v2*SLHA::HMIX[35.]),

(0.),

(SLHA::HMIX[21.]+0.5*v2^2*SLHA::HMIX[32.]+0.5*alpha^2*SLHA::HMIX[33.]+0.5*v1^2*SLHA::HMIX[33.]+0.5*alpha^2*SLHA::HMIX[34.]+0.5*alpha^2*SLHA::HMIX[35.])

</mass-squared_matrix>