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Direct detection#

Calculate various direct detection observables.

import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import interp1d
from singletscalar_dm import *

The direct detection part is calculated using the function SI_noomega. This function performs the calculation of the spin independent cross section analytically assuming that \(f_N=0.297\). In the following, we sho the calculation of the spin independent cross section for a specific value of DM mass and coupling.

mS = 70 # GeV
lambda_hs = 0.01
SI_noomega(mS,lambda_hs)

1.7814254243590454e-46

Instead, in order to find the upper limits for \(\lambda_{HS}\), you can use the function GetUL_DD_Mine_nomega. The example below calculates the upper limits for \(\lambda_{HS}\) for the LZ and future DARWIN experiments.

DMmassDD_vec = np.logspace(np.log10(2.),4.,100)
LambdaDD_LZ_HS_vec = np.zeros(len(DMmassDD_vec))
LambdaDD_Darwin_HS_vec = np.zeros(len(DMmassDD_vec))
for t in range(len(DMmassDD_vec)):
    LambdaDD_LZ_HS_vec[t] = GetUL_DD_nomega(DMmassDD_vec[t],'LZ')
    LambdaDD_Darwin_HS_vec[t] = GetUL_DD_nomega(DMmassDD_vec[t],'DARWIN')

fig = plt.figure(figsize=(8,6))
plt.plot(DMmassDD_vec[18:],LambdaDD_LZ_HS_vec[18:],lw=3.0,ls='--',color='black',label=r'DD, LZ+2022')
plt.fill_between(DMmassDD_vec[18:],(0.3/0.2)*LambdaDD_LZ_HS_vec[18:],(0.3/0.6)*LambdaDD_LZ_HS_vec[18:],alpha=0.5,color='grey')
plt.plot(DMmassDD_vec[18:],1e-10*(0.3/0.2)*LambdaDD_LZ_HS_vec[18:],lw=5.0,alpha=0.5,color='grey',label=r'LZ, $\rho_{\odot}=[0.2,0.6]$ GeV/cm$^3$')
plt.plot(DMmassDD_vec[11:],LambdaDD_Darwin_HS_vec[11:],lw=3.0,ls='--',color='red',label=r'DD, DARWIN proj.')
plt.xlabel(r'$m_S$ [GeV]', fontsize=20)
plt.ylabel(r'$\lambda_{\rm{HS}}$', fontsize=20)
plt.axis([5,1e4,1e-4,1e1])
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.tick_params('both', length=8, width=3, which='major')
plt.tick_params('both', length=6, width=3, which='minor')
plt.grid(True)
plt.yscale('log')
plt.xscale('log')
plt.legend(loc=2,prop={'size':16},numpoints=1, scatterpoints=1, ncol=1)
fig.tight_layout(pad=0.5)
plt.show()
plot direct detection

It is also possible to calculate the direct detection constraints including the rescaling due to the density of dark matter of the \(S\) particles. First, we calculate the \(\xi\) term which is the relative ratio of \(S\) particle density over the total dark matter one.

Omegah2_best = 0.120

table = np.loadtxt(import_data_file('Omega_MICROMEGAs_zoom_paper.dat'))

Lambda_vec = np.logspace(-5,1,500)
csi_vec = np.zeros(len(MassDD_vec)*len(Lambda_vec))

cont = 0
for t in range(len(MassDD_vec)):
    for u in range(len(Lambda_vec)):
        if table[cont,2]<0.:
            table[cont,2] = 1e6
        csi_vec[cont] = table[cont,2]/Omegah2_best
        cont = cont + 1

print(csi_vec)

val = GetUL_DD_withomega(60,Lambda_vec,MassDD_vec,csi_vec,'LZ')
print(val)

[1.24166667e+06 1.21250000e+06 1.18416667e+06 ... 2.54083333e-05
 2.40916667e-05 2.28333333e-05]
Optimization terminated successfully.
         Current function value: 0.000000
         Iterations: 31
         Function evaluations: 62
0.13446874237060566

The we use the function GetUL_DD to get the upper limits including also the relic density of \(S\).

LambdaDD_LZ_HS_vec = np.zeros(len(MassDD_vec))
LambdaDD_Darwin_HS_vec = np.zeros(len(MassDD_vec))
for t in range(len(MassDD_vec)):
    LambdaDD_LZ_HS_vec[t] = GetUL_DD_withomega(MassDD_vec[t],Lambda_vec,MassDD_vec,csi_vec,'LZ')
    LambdaDD_Darwin_HS_vec[t] = GetUL_DD_withomega(MassDD_vec[t],Lambda_vec,MassDD_vec,csi_vec,'Darwin')

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table_RD_FB = np.loadtxt(import_data_file('DRAKE_omega_fBE_QCDB_paper.dat'))
mass_RD_FBQCDB = table_RD_FB[:,0]
lambda_RD_FBQCDB = table_RD_FB[:,1]

funcint_RD = interp1d(mass_RD_FBQCDB,lambda_RD_FBQCDB)
for t in range(len(MassDD_vec)):
    if funcint_RD(MassDD_vec[t])>LambdaDD_LZ_HS_vec[t]:
        LambdaDD_LZ_HS_vec[t]=funcint_RD(MassDD_vec[t])
    if funcint_RD(MassDD_vec[t])>LambdaDD_Darwin_HS_vec[t]:
        LambdaDD_Darwin_HS_vec[t]=funcint_RD(MassDD_vec[t])

fig = plt.figure(figsize=(8,6))
plt.fill_between(mass_RD_FBQCDB,lambda_RD_FBQCDB*1e-6,lambda_RD_FBQCDB*1.05,color='grey')
plt.fill_between(MassDD_vec,funcint_RD(MassDD_vec),LambdaDD_LZ_HS_vec,lw=2.0,alpha=0.5,color='green')
plt.fill_between(MassDD_vec,funcint_RD(MassDD_vec),LambdaDD_Darwin_HS_vec,lw=2.0,alpha=0.2,color='orange')
plt.plot(MassDD_vec,LambdaDD_LZ_HS_vec,lw=3.0,ls='-',color='darkgreen',label=r'LZ+2022')
plt.plot(MassDD_vec,LambdaDD_Darwin_HS_vec,lw=2.0,ls='-.',color='red',label=r'DARWIN PROJ.')
plt.plot(mass_RD_FBQCDB,lambda_RD_FBQCDB,lw=2.0,ls=':',color='blue', label=r'$\Omega_{S}h^2=0.12}$')
plt.text(54.2,0.05,r'$\Omega_{S}h^2<0.12}$',color='blue', fontsize=16)
plt.text(54.2,0.003,r'$\Omega_{S}h^2>0.12}$',color='blue', fontsize=16)
plt.xlabel(r'$m_{\rm{S}}$ [GeV]', fontsize=20)
plt.ylabel(r'$\lambda_{\rm{HS}}$', fontsize=20)
plt.axis([54,64,1e-4,1e1])
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.tick_params('both', length=8, width=3, which='major')
plt.tick_params('both', length=6, width=3, which='minor')
plt.grid(True)
plt.yscale('log')
plt.xscale('linear')
plt.legend(loc=2,prop={'size':16},numpoints=1, scatterpoints=1, ncol=1)
fig.tight_layout(pad=0.5)
plt.show()
plot direct detection

Total running time of the script: ( 0 minutes 12.147 seconds)

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