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
- alpha 0.00000
v1 107.03483
v2 221.49389
- alpha 70.762566
v1 38.624972
v2 159.427010
- 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}
- 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}
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>
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>