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Commit e0a51179 authored by ulrich_y's avatar ulrich_y
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Improved PEP8 compliance

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......@@ -8,7 +8,7 @@ gamma0 = Mmu**5/192/pi**3
setup(folder='with-cut/out.tar.bz2', flavour='mu-e')
loC = scaleset(mergefks(sigma('m2enn0')), 1/gamma0)
fig, ans = mergefkswithplot([[sigma('m2ennR')],[sigma('m2ennF')]])
fig, ans = mergefkswithplot([[sigma('m2ennR')], [sigma('m2ennF')]])
nloC = scaleset(ans, alpha/gamma0)
nnloC = scaleset(mergefks(
sigma('m2ennRF'),
......@@ -22,7 +22,7 @@ fig, _ = kplot(
{'lo': loC['xe'], 'nlo': nloC['xe'], 'nnlo': nnloC['xe']},
labelx=r'$x_e$',
labelsigma=r'$\D\sigma / \D x_e / \sigma_0$',
legendopts={'what':'u'},
legendopts={'what': 'u'},
legend={
'lo': r'$\sigma_0$',
'nlo': r'$\sigma_1$',
......
......@@ -9,36 +9,37 @@ gamma0 = Mmu**5/192/pi**3
## Load data{{{
setup(folder='out.tar.bz2')
openLeptons = mergefks(sigma('m2ennee0', merge={'xh':2,'xs':2}))
openLeptons = addplots(openLeptons['xh'], openLeptons['xs'], sa=0.5,sb=0.5)
openLeptons = mergefks(sigma('m2ennee0', merge={'xh': 2, 'xs': 2}))
openLeptons = addplots(openLeptons['xh'], openLeptons['xs'], sa=0.5, sb=0.5)
nnlo = mergefks(
sigma('m2ennRF', merge={'xe': 5}),
sigma('m2ennRR', merge={'xe': 2}),
sigma('m2ennFF', merge={'xe': 2}, folder='../ff.tar.bz2', flavour='mu-e')
)
xev = np.array([1,1/gamma0,1/gamma0])*addplots(nnlo['xe'], openLeptons)
xev = np.array([1, 1 / gamma0, 1 / gamma0])*addplots(nnlo['xe'], openLeptons)
##########################################}}}
## Load logarithms from [hep-ph/0205172] (Arbuzov et al.){{{
# see also meg2d/arbuzov.py
def fLL(xe):
gam = (
-32*xe**3/9
-32*xe**3/9
+ 4*xe**2*(3 - 2*xe)*(
-Li2(1 - xe) - zeta2 + np.log(xe)**2/2
-Li2(1 - xe) - zeta2 + np.log(xe)**2/2
- 2*np.log(xe)*np.log(1 - xe) + np.log(1 - xe)**2
)
+ 8*xe**2/3 + 17*xe/6
+ (-32*xe**3/3 + 8*xe**2 - 2*xe - 5./6)*np.log(xe)
+ 8*xe**2/3 + 17*xe/6
+ (-32*xe**3/3 + 8*xe**2 - 2*xe - 5./6)*np.log(xe)
+ (32*xe**3/3 - 16*xe**2 + 8*xe + 10./3)*np.log(1 - xe) + 11./36
)
NS = (
8*xe**3/3 + 2*xe**2*(3 - 2*xe)*np.log((1 - xe)/xe)
8*xe**3/3 + 2*xe**2*(3 - 2*xe)*np.log((1 - xe)/xe)
- 4*xe**2 + 2*xe + 5./6
)
S = (
-8*xe**3/9 - 14*xe**2/3 + 3*xe
-8*xe**3/9 - 14*xe**2/3 + 3*xe
+ (4*xe**2 + 4*xe + 5./3)*np.log(xe) + 17./9 + 2/(3*xe)
)
return gam/2 + NS/3 + S/2
......@@ -46,47 +47,55 @@ def fLL(xe):
def fNLL(xe):
def Sot(z):
return 0.5*np.log(1-z)**2*np.log(z) + np.log(1-z)*Li2(1-z) - Li3(1-z)+zeta3
return (
0.5*np.log(1-z)**2*np.log(z)
+ np.log(1-z)*Li2(1-z) - Li3(1-z) + zeta3
)
gam = (
-559*xe**3/54
-559*xe**3/54
+ 2*xe**2*(3 - 2*xe)*(
-2*Sot(xe) + 2*Li2(xe)*np.log(xe) + 2*Li2(xe)*np.log(1 - xe)
- 2*Li3(xe) - 2*zeta2*np.log(xe) - 2*zeta2*np.log(1 - xe)
+ 7*zeta3 + 2*np.log(xe)**3 - 5*np.log(xe)**2*np.log(1 - xe)
+ 7*zeta3 + 2*np.log(xe)**3 - 5*np.log(xe)**2*np.log(1 - xe)
+ 5*np.log(xe)*np.log(1 - xe)**2
)
+ 83*xe**2/3 - 287*xe/12 + (8*xe**3 - 4*xe**2 - 12*xe)*np.log(1 - xe)**2
+ (-98*xe**3/3 + 35*xe**2 - 2*xe - 10./3)*zeta2
+ (-70*xe**3/3 + 22*xe**2 - 5*xe - 25./12)*np.log(xe)**2
+ (-12*xe**3 + 64*xe**2/3 - 53*xe/3 - 17./3)*np.log(1 - xe)
+ (44*xe**3/9 + 4*xe**2/3 + 37*xe/6 - 3./4)*np.log(xe)
+ (92*xe**3/3 - 54*xe**2 + 32*xe + 25./3)*np.log(xe)*np.log(1 - xe)
+ 83*xe**2/3 - 287*xe/12
+ (8*xe**3 - 4*xe**2 - 12*xe)*np.log(1 - xe)**2
+ (-98*xe**3/3 + 35*xe**2 - 2*xe - 10./3)*zeta2
+ (-70*xe**3/3 + 22*xe**2 - 5*xe - 25./12)*np.log(xe)**2
+ (-12*xe**3 + 64*xe**2/3 - 53*xe/3 - 17./3)*np.log(1 - xe)
+ (44*xe**3/9 + 4*xe**2/3 + 37*xe/6 - 3./4)*np.log(xe)
+ (92*xe**3/3 - 54*xe**2 + 32*xe + 25./3)*np.log(xe)*np.log(1 - xe)
+ (92*xe**3/3 - 40*xe**2 + 14*xe + 10./3)*Li2(xe) + 211./216
)
NS = (
-64*xe**3/9
+ 2*xe**2*(3 - 2*xe)*(
-2*Li2(1 - xe) - 2*zeta2/3 - np.log(xe)**2
-2*Li2(1 - xe) - 2*zeta2/3 - np.log(xe)**2
- 2*np.log(xe)*np.log(1 - xe)/3 + 2*np.log(1 - xe)**2/3
)
+ 100*xe**2/9 - 19*xe/3
+ (-76*xe**3/9 + 8*xe**2 + 4*xe/3 + 5./9)*np.log(xe)
+ (12*xe**3 - 46*xe**2/3 - 4*xe/3 + 10./9)*np.log(1 - xe)
)
+ 100*xe**2/9 - 19*xe/3
+ (-76*xe**3/9 + 8*xe**2 + 4*xe/3 + 5./9)*np.log(xe)
+ (12*xe**3 - 46*xe**2/3 - 4*xe/3 + 10./9)*np.log(1 - xe)
- 11./6
)
S = (
10*xe**3/9 + 77*xe**2/18 + 43*xe/18 +
(Li2(1 - xe) + np.log(xe)*np.log(1 - xe))*(4*xe**2 + 4*xe + 5./3)
+ (4*xe**2 + 6*xe + 5./2)*np.log(xe)**2 + (-19*xe**2/3 - 5*xe/6 + 8./9 + 4/(3*xe))*np.log(xe)
+ (4*xe**2 + 6*xe + 5./2)*np.log(xe)**2
+ (-19*xe**2/3 - 5*xe/6 + 8./9 + 4/(3*xe))*np.log(xe)
+ (-8*xe**3/9 - 14*xe**2/3 + 3*xe + 17./9 + 2/(3*xe))*np.log(1 - xe)
- 67./9 - 1/(3*xe)
)
int = (
104*xe**3/9
+ 2*xe**2*(3 - 2*xe)*(-4*Sot(1 - xe) - 2*Li2(1 - xe)*np.log(xe) + 2*Li3(1 - xe))
- 55*xe**2/3 + 41*xe/3 + (26*xe**3/3 - 9*xe**2)*np.log(xe)**2
+ (-28*xe**2/3 - 5*xe/3 - 5./3)*np.log(xe)
104*xe**3/9
+ 2*xe**2*(3 - 2*xe)*(
-4*Sot(1 - xe) - 2*Li2(1 - xe)*np.log(xe)
+ 2*Li3(1 - xe)
)
- 55*xe**2/3 + 41*xe/3 + (26*xe**3/3 - 9*xe**2)*np.log(xe)**2
+ (-28*xe**2/3 - 5*xe/3 - 5./3)*np.log(xe)
+ (52*xe**3/3 - 26*xe**2 + 4*xe + 5./3)*Li2(1 - xe) - 62./9
)
return gam+NS+S+int
......@@ -97,11 +106,11 @@ def f2loop(xe):
f0 = -np.sqrt(xe**2 - 4*z**2)*(2*xe**2 + 4*z**2 - 3*xe*(1 + z**2))
f00 = -xe**2*(-3 + 2*xe)
L = np.log(Mmu**2/Mel**2)
return f0 / f00 * (L**2 * fLL(xe) + L * fNLL(xe) ) / 2 / pi / pi
return f0 / f00 * (L**2 * fLL(xe) + L * fNLL(xe)) / 2 / pi / pi
###########################################################}}}
## Load data from [hep-ph/0505069] (Anastasiou et al.){{{
const = np.array(pymule.compress.uncompress(
"1:eJx11WtQU0cUAOAQ8AFqLRGFgAqCxAfYagBFCnNT5SEWTGtIHB21QuFCGST0BsSqgHU"
"oBWsrAuWRUARtaUu0gkAtFguCRYQEgwgBEiCIQsBoRBRx1LQn/ursTs6Pndn5ZnfP2d3Z"
......@@ -130,22 +139,23 @@ const = np.array(pymule.compress.uncompress(
"F55FtrM+ZpUO+K3q0KjgaPpP+5ei9H0/Affiqv0w=="
))
const[:,1] = (
const[:,1] * (
-np.sqrt(const[:,0]**2 - 4*(Mel/Mmu)**2)*(
2*const[:,0]**2 + 4*(Mel/Mmu)**2 - 3*const[:,0]*(1 + (Mel/Mmu)**2)
const[:, 1] = (
const[:, 1] * (
-np.sqrt(const[:, 0]**2 - 4*(Mel/Mmu)**2)*(
2*const[:, 0]**2 + 4*(Mel/Mmu)**2
- 3*const[:, 0]*(1 + (Mel/Mmu)**2)
)
) / alpha**2 *2e-4
) / alpha**2 * 2e-4
)
###########################################################}}}
## Make plot{{{
xe = np.linspace(0,1,200)[2:-1]
xe = np.linspace(0, 1, 200)[2:-1]
ax = gca()
errorband(xev, ax=ax, col='C3')
ax.plot(xe,f2loop(xe), 'C2', linestyle='dashed')
ax.plot(const[:,0],const[:,1] + f2loop(const[:,0]), 'C1')
ax.set_ylim(-15,25)
ax.plot(xe, f2loop(xe), 'C2', linestyle='dashed')
ax.plot(const[:, 0], const[:, 1] + f2loop(const[:, 0]), 'C1')
ax.set_ylim(-15, 25)
ax.set_xlabel('$x_e$')
ax.set_ylabel("$\\D\\sigma^{(2)} / \\D x_e / \\sigma_0$")
mulify(ax.figure)
......
......@@ -21,7 +21,7 @@ nloEM = scaleset(mergefks(
nlo = {
k: combineNplots(addplots, [
mergebins(nloEE[k],2), nloMM[k], nloEM[k]
mergebins(nloEE[k], 2), nloMM[k], nloEM[k]
])
for k in ['Ee', 'Em', 'tee', 'tmm', 'thetae', 'thetam']
}
......@@ -69,75 +69,75 @@ fignlo, aconlo = mergefkswithplot([
], scale=conv*alpha**3)
mulify(fignlo)
fignlo.axes[0].set_ylim(-55,90)
fignlo.axes[0].set_xlim(1.5e-3,1.4)
fignlo.axes[0].set_ylim(-55, 90)
fignlo.axes[0].set_xlim(1.5e-3, 1.4)
###########################################################}}}
### Load NNLO{{{
fignnlo, aconnlo = mergefkswithplot([
[sigma('em2emRREE1') , sigma('em2emRREE3' )],
[sigma('em2emRREE1'), sigma('em2emRREE3')],
[sigma('em2emRFEE15'), sigma('em2emRFEE35')],
[sigma('em2emFF', folder='ff.tar.bz2')]
], conv*alpha**4)
mulify(fignnlo)
fignnlo.axes[0].set_xlim(1.5e-3,1.4)
fignnlo.axes[0].set_ylim(-7,14)
fignnlo.axes[0].set_xlim(1.5e-3, 1.4)
fignnlo.axes[0].set_ylim(-7, 14)
###########################################################}}}
#####################################################################}}}
## Results{{{
### cross section{{{
def parsestr(s):
n = s.index("(")
p = s.index('.')
y = float(s[:n])
e = float(s[n+1:-1])
return np.array([y,e*10**(p-n+1)])
return np.array([y, e * 10**(p-n+1)])
loPV = parsestr('245.038910(1)')
loPV = parsestr('245.038910(1)')
entries = [
lo['value'], loPV,
timesnumbers(loPV, parsestr('0.04289(1)' )),
timesnumbers(loPV, parsestr('0.04289(1)')),
timesnumbers(loPV, parsestr('-0.08817(1)')),
nloEE['value'],
aconloEE['value'],
timesnumbers(loPV, parsestr('-0.00028(1)')),
timesnumbers(loPV, parsestr('-0.00256(1)')),
nloMM['value'],
[1,100]*aconloMM['value'],
[1, 100] * aconloMM['value'],
timesnumbers(loPV, parsestr('-0.00147(2)')),
timesnumbers(loPV, parsestr('0.00017(2)' )),
timesnumbers(loPV, parsestr('0.00017(2)')),
nloEM['value'],
[1,10]*aconloEM['value'],
timesnumbers(loPV, parsestr('0.04114(1)' )),
[1, 10] * aconloEM['value'],
timesnumbers(loPV, parsestr('0.04114(1)')),
timesnumbers(loPV, parsestr('-0.09055(1)')),
nlo['value'],
aconlo['value'],
nnlo['value'], aconnlo['value'],
plusnumbers(lo['value'],nlo['value'],nnlo['value']),
plusnumbers(lo['value'],aconlo['value'],aconnlo['value'])
plusnumbers(lo['value'], nlo['value'], nnlo['value']),
plusnumbers(lo['value'], aconlo['value'], aconnlo['value'])
]
entries = [printnumber(i) for i in entries]
kfac = [
nloEE['value'][0]/lo['value'][0],aconloEE['value'][0]/lo['value'][0],
nloMM['value'][0]/lo['value'][0],aconloMM['value'][0]/lo['value'][0],
nloEM['value'][0]/lo['value'][0],aconloEM['value'][0]/lo['value'][0],
nlo ['value'][0]/lo['value'][0],aconlo ['value'][0]/lo['value'][0],
nloEE['value'][0] / lo['value'][0], aconloEE['value'][0] / lo['value'][0],
nloMM['value'][0] / lo['value'][0], aconloMM['value'][0] / lo['value'][0],
nloEM['value'][0] / lo['value'][0], aconloEM['value'][0] / lo['value'][0],
nlo ['value'][0] / lo['value'][0], aconlo ['value'][0] / lo['value'][0],
nnlo['value'][0]/nlo['value'][0],aconnlo['value'][0]/aconlo['value'][0]
nnlo['value'][0] / nlo['value'][0], aconnlo['value'][0] / aconlo['value'][0]
]
entries.insert( 6, kfac[0])
entries.insert( 7, kfac[1])
entries.insert(06, kfac[0])
entries.insert(07, kfac[1])
entries.insert(12, kfac[2])
entries.insert(13, kfac[3])
entries.insert(18, kfac[4])
......@@ -161,13 +161,14 @@ tex = "\n".join([
r"$\sigma_m ^{(1)}$ & \tt %13s &\tt %13s &\tt %13s &\tt %13s &\tt %7.4f &\tt %7.4f \\",
r"$\sigma ^{(1)}$ & \tt %13s &\tt %13s &\tt %13s &\tt %13s &\tt %7.4f &\tt %7.4f \\",
"\\hline",
r"$\sigma_e ^{(2)}$ & \multicolumn{2}{c||}{} &\tt %13s & \tt %13s &\tt %7.4f &\tt %7.4f \\",
r"$\sigma_e ^{(2)}$ & \multicolumn{2}{c||}{} &\tt %13s & \tt %13s &\tt %7.4f &\tt %7.4f \\",
"\\hline",
"\\hline",
r"$\sigma $ & \multicolumn{2}{c||}{} &\tt %13s & \tt %13s & \multicolumn{2}{c}{} \\",
r"$\sigma $ & \multicolumn{2}{c||}{} &\tt %13s & \tt %13s & \multicolumn{2}{c}{}\\",
r"\end{tabular}"
]) % tuple(entries)
###########################################################}}}
### theta e{{{
### NLO split{{{
......@@ -175,61 +176,66 @@ tex = "\n".join([
def dogaugeplot(lo, nloEE, nloEM, nloMM, nlo):
def prep(x):
if len(x) == 100:
return scaleplot(x[:37],1e-3)
return scaleplot(x[:37], 1e-3)
elif len(x) == 200:
return scaleplot(mergebins(x,2)[:37],1e-3)
return scaleplot(mergebins(x, 2)[:37], 1e-3)
elif len(x) == 202:
return scaleplot(mergebins(x[1:-1],2)[:37],1e-3)
return scaleplot(mergebins(x[1:-1], 2)[:37], 1e-3)
distLO = prep(lo['thetae'])
distEE = prep(nloEE['thetae'])
distEM = prep(nloEM['thetae'])
distMM = prep(nloMM['thetae'])
distFU = prep(nlo['thetae'])
distEE[:,0] = distLO[:,0]
distEM[:,0] = distLO[:,0]
distMM[:,0] = distLO[:,0]
distFU[:,0] = distLO[:,0]
distLO[36,1:]=0
distEE[36,1:]=0
distEM[36,1:]=0
distMM[36,1:]=0
distFU[36,1:]=0
fig,(ax1,ax2,ax3)=twopanel(
distEE[:, 0] = distLO[:, 0]
distEM[:, 0] = distLO[:, 0]
distMM[:, 0] = distLO[:, 0]
distFU[:, 0] = distLO[:, 0]
distLO[36, 1:] = 0
distEE[36, 1:] = 0
distEM[36, 1:] = 0
distMM[36, 1:] = 0
distFU[36, 1:] = 0
fig, (ax1, ax2, ax3) = twopanel(
labelx="$\\theta_e\,/\,{\\rm mrad}$",
upleft=[distLO, addplots(distLO, distFU)],
colupleft=['C2', 'C0'],
labupleft="$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$",
downleft=[divideplots(distEE,distLO,1)[4:-1]],
downleft=[divideplots(distEE, distLO, 1)[4:-1]],
labdownleft={
'ylabel': "$K^{(1)}_e$",
'color': 'C0'
},
coldownleft=['C0'],
downright=[divideplots(distMM,distLO,1)[:-1], divideplots(distEM,distLO,1)[1:-1]],
downright=[
divideplots(distMM, distLO, 1)[:-1],
divideplots(distEM, distLO, 1)[1:-1]
],
labdownright={
'ylabel': "$K^{(1)}_{\\mu,m}$",
'color': 'C1'
},
downalign=[1,1],
downalign=[1, 1],
coldownright=['C1', 'C1']
)
ax3.collections=[]
ax3.collections = []
ax3.lines[0].set_linestyle(":")
mulify(fig)
fig.legend(
ax1.lines[:1]+ax2.lines+ax3.lines,
ax1.lines[:1] + ax2.lines + ax3.lines,
[
"$\\sigma^{(0)}$",
"$\\sigma^{(1)}_e$",
"$\\sigma^{(1)}_\\mu$",
"$\\sigma^{(1)}_m$"
], loc='upper center',ncol=4
], loc='upper center', ncol=4
)
return fig
#######################################}}}
### Make plots{{{
fig = dogaugeplot(lo, nloEE, nloEM, nloMM, nlo)
......@@ -238,33 +244,40 @@ acofig = dogaugeplot(lo, aconloEE, aconloEM, aconloMM, aconlo)
#################################################}}}
### NNLO {{{
fig,(ax1,ax2,ax3) = kplot(
fig, (ax1, ax2, ax3) = kplot(
{
'lo': mergebins(scaleplot(lo['thetae'],1e-3),2)[:37],
'nlo': mergebins(scaleplot(nloEE['thetae'],1e-3),2)[:37],
'nnlo':mergebins(scaleplot(nnlo['thetae'],1e-3),2)[:37]
'lo': mergebins(scaleplot(lo['thetae'], 1e-3), 2)[:37],
'nlo': mergebins(scaleplot(nloEE['thetae'], 1e-3), 2)[:37],
'nnlo': mergebins(scaleplot(nnlo['thetae'], 1e-3), 2)[:37]
},
labelx="$\\theta_e\,/\,{\\rm mrad}$",
labelsigma="$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$",
legend={'lo': '$\\sigma^{(0)}$', 'nlo': '$\\sigma_e^{(1)}$', 'nnlo': '$\\sigma_e^{(2)}$'},
legend={
'lo': '$\\sigma^{(0)}$',
'nlo': '$\\sigma_e^{(1)}$',
'nnlo': '$\\sigma_e^{(2)}$'
},
legendopts={'what': 'u', 'loc': 'lower right'}
)
ax2.set_ylim(0.8,2.5)
pymule.mpl_axes_aligner.yaxes(ax2,1,ax3,1)
ax2.set_ylim(0.8, 2.5)
pymule.mpl_axes_aligner.yaxes(ax2, 1, ax3, 1)
fig,(ax1,ax2,ax3) = kplot(
fig, (ax1, ax2, ax3) = kplot(
{
'lo': mergebins(scaleplot(lo['thetae'],1e-3),2)[:37],
'nlo': mergebins(scaleplot(aconloEE['thetae'],1e-3),2)[1:38],
'nnlo': mergebins(scaleplot(aconnlo['thetae'],1e-3),2)[1:38]
'lo': mergebins(scaleplot(lo['thetae'], 1e-3), 2)[:37],
'nlo': mergebins(scaleplot(aconloEE['thetae'], 1e-3), 2)[1:38],
'nnlo': mergebins(scaleplot(aconnlo['thetae'], 1e-3), 2)[1:38]
},
labelx="$\\theta_e\,/\,{\\rm mrad}$",
labelsigma="$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$",
legend={'lo': '$\\sigma^{(0)}$', 'nlo': '$\\sigma_e^{(1)}$', 'nnlo': '$\\sigma_e^{(2)}$'},
legend={
'lo': '$\\sigma^{(0)}$',
'nlo': '$\\sigma_e^{(1)}$',
'nnlo': '$\\sigma_e^{(2)}$'
},
legendopts={'what': 'u', 'loc': 'lower right'}
)
#################################################}}}
###########################################################}}}
#####################################################################}}}
......@@ -15,9 +15,9 @@ LO = scaleset(mergefks(sigma('m2enng0')), GF**2*lifetime*alpha)
# Import NLO corrections from the three pieces
NLO = scaleset(mergefks(
sigma('m2enngR'), # real corrections
sigma('m2enngCT'), # counter term
anyxi=sigma('m2enngV') # virtual corrections
sigma('m2enngR'), # real corrections
sigma('m2enngCT'), # counter term
anyxi=sigma('m2enngV') # virtual corrections
), GF**2*lifetime*alpha**2)
#####################################################################}}}
## Results{{{
......@@ -36,7 +36,7 @@ fig1, (ax1, ax2) = kplot(
labelx=r"$E_e\,/\,{\rm MeV}$",
labelsigma=r"$\D\mathcal{B}/\D E_e$"
)
ax2.set_ylim(0.8,1.01)
ax2.set_ylim(0.8, 1.01)
###########################################################}}}
### Visible mass{{{
fig2, (ax1, ax2) = kplot(
......@@ -46,8 +46,8 @@ fig2, (ax1, ax2) = kplot(
)
ax1.set_yscale('log')
ax1.set_xlim(1000,0)
ax1.set_ylim(5e-9,1e-3)
ax2.set_ylim(0.8,1.)
ax1.set_xlim(1000, 0)
ax1.set_ylim(5e-9, 1e-3)
ax2.set_ylim(0.8, 1.)
###########################################################}}}
#####################################################################}}}
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