def plotDeltaCPSecond(e_range):
"""Plot P(nu_mu -> nu_e) as a function of E for different values of delta_cp.
The energy range (x-axis) is extended low enough to see the second oscillation peak.
"""
n = 300
deltas = [0, 90, 180, 270]
e_min = e_range[0]
e_max = e_range[1]
e_step = (e_max - e_min) / float(n)
graphs = {}
nu_i = oscillations.nu_mu
nu_f = oscillations.nu_e
osc = oscillations.Oscillations()
for dcp in deltas:
graphs[dcp] = ROOT.TGraph(n + 1)
osc.setDeltaCP(dcp * oscillations.units.degrees)
for i in range(n + 1):
e = e_min + (i * e_step)
osc.setE(e * oscillations.units.GeV)
p = 100.0 * osc.p(nu_i, nu_f)
graphs[dcp].SetPoint(i, e, p)
c = ROOT.TCanvas("c", "c", 1200, 800)
f = c.DrawFrame(e_min, 0.0, e_max, 11)
l = ROOT.TLegend(0.69, 0.69, 0.89, 0.89)
l.SetFillColor(ROOT.kWhite)
l.SetBorderSize(0)
f.SetTitle("Effect of #delta_{CP} on P(#nu_{#mu} #rightarrow #nu_{e})")
f.GetXaxis().SetTitle("E_{#nu} [ GeV ]")
f.GetYaxis().SetTitle("P( #nu_{#mu} #rightarrow #nu_{e} ) [ % ] ")
for dcp in deltas:
graph = graphs[dcp]
graph.SetLineColor(colourDelta(dcp))
graph.SetLineStyle(styleDelta(dcp))
graph.SetLineWidth(3)
graph.Draw()
l.AddEntry(graph, "#delta_{CP} = " + str(dcp) + "#circ", "L")
c.Update()
l.Draw()
c.Update()
c.SaveAs("figure-osc-dcp-e2.png")
input("continue?")
def plotTheta13(e_range):
"""Plot P(nu_mu -> nu_e) as a function of E for different values of theta_13."""
n = 300
thetas = [11, 9, 7]
e_min = e_range[0]
e_max = e_range[1]
e_step = (e_max - e_min) / float(n)
graphs = {}
nu_i = oscillations.nu_mu
nu_f = oscillations.nu_e
osc = oscillations.Oscillations()
for t in thetas:
graphs[t] = ROOT.TGraph(n + 1)
osc.setTheta13(t * oscillations.units.degrees)
for i in range(n + 1):
e = e_min + (i * e_step)
osc.setE(e * oscillations.units.GeV)
p = 100.0 * osc.p(nu_i, nu_f)
graphs[t].SetPoint(i, e, p)
c = ROOT.TCanvas("c", "c", 800, 800)
f = c.DrawFrame(e_min, 0.0, e_max, 10)
l = ROOT.TLegend(0.69, 0.76, 0.89, 0.89)
l.SetFillColor(ROOT.kWhite)
l.SetBorderSize(0)
f.SetTitle("Effect of #theta_{13} on P(#nu_{#mu} #rightarrow #nu_{e})")
f.GetXaxis().SetTitle("E_{#nu} [ GeV ]")
f.GetYaxis().SetTitle("P( #nu_{#mu} #rightarrow #nu_{e} ) [ % ] ")
for t in thetas:
graph = graphs[t]
graph.SetLineColor(colour(nu_f))
graph.SetLineStyle(styleTheta13(t))
graph.SetLineWidth(3)
graph.Draw()
l.AddEntry(graph, "#theta_{13} = " + str(t) + "#circ", "L")
c.Update()
l.Draw()
c.Update()
c.SaveAs("figure-osc-t13.png")
input("continue?")
def plotDM32(e_range):
n = 300
dms = [(2.0e-3), (2.3e-3), (2.6e-3)]
e_min = e_range[0]
e_max = e_range[1]
e_step = (e_max - e_min) / float(n)
graphs = {}
nu_i = oscillations.nu_mu
nu_f = oscillations.nu_mu
osc = oscillations.Oscillations()
for dm in dms:
graphs[dm] = ROOT.TGraph(n + 1)
osc.setDeltaM32(dm * oscillations.units.eV2)
for i in range(n + 1):
e = e_min + (i * e_step)
osc.setE(e * oscillations.units.GeV)
p = 100.0 * osc.p(nu_i, nu_f)
graphs[dm].SetPoint(i, e, p)
c = ROOT.TCanvas("c", "c", 800, 800)
f = c.DrawFrame(e_min, 0.0, e_max, 100)
l = ROOT.TLegend(0.59, 0.19, 0.89, 0.39)
l.SetFillColor(ROOT.kWhite)
l.SetBorderSize(0)
f.SetTitle(
"Effect of #Deltam^{2}_{32} on P(#nu_{#mu} #rightarrow #nu_{#mu})")
f.GetXaxis().SetTitle("E_{#nu} [ GeV ]")
f.GetYaxis().SetTitle("P( #nu_{#mu} #rightarrow #nu_{#mu} ) [ % ] ")
for dm in dms:
graph = graphs[dm]
graph.SetLineColor(colour(nu_f))
graph.SetLineStyle(styleDM32(dm))
graph.SetLineWidth(3)
graph.Draw()
l.AddEntry(graph, "#Deltam^{2}_{32} = " + str(dm) + " eV^{2}", "L")
c.Update()
l.Draw()
c.Update()
c.SaveAs("figure-osc-dm32.png")
input("continue?")
def setUp(self):
# Example experiment oscillations
self.osc = oscillations.Oscillations()
self.osc.setL(295.0 * oscillations.units.km)
self.osc.setE(0.6 * oscillations.units.GeV)
self.osc.setDeltaM21(7.50e-5 * oscillations.units.eV2)
self.osc.setDeltaM32(2.32e-3 * oscillations.units.eV2)
self.osc.setTheta12(33.9 * oscillations.units.degrees)
self.osc.setTheta13(9.1 * oscillations.units.degrees)
self.osc.setTheta23(45.0 * oscillations.units.degrees)
self.osc.setDeltaCP(0.0 * oscillations.units.degrees)
# get an index which does not represent a neutrino or anti-neutrino
non_nu = 1
while (oscillations.isNeutrino(non_nu)
or oscillations.isAntiNeutrino(non_nu)):
non_nu += 1
self.non_neutrino = non_nu
def plotLOverE(mode="short"):
"""Plot P(nu_mu -> nu) for all flavours as a function of L/E.
mode : Specifies either 'short' or 'long' range plot.
"""
n = 4000
if (mode == "short"):
le_max = 4000.0
elif (mode == "long"):
le_max = 40000.0
else:
raise ValueError("Mode must be either 'short' or 'long'.")
le_min = 0.0
le_step = (le_max - le_min) / float(n)
graphs = {}
graphs[oscillations.nu_e] = ROOT.TGraph(n + 1)
graphs[oscillations.nu_mu] = ROOT.TGraph(n + 1)
graphs[oscillations.nu_tau] = ROOT.TGraph(n + 1)
osc = oscillations.Oscillations()
for i in range(n + 1):
le = le_min + (i * le_step)
osc.setLOverE(le * oscillations.units.km_GeV)
p_e = 100 * osc.p(oscillations.nu_mu, oscillations.nu_e)
p_mu = 100 * osc.p(oscillations.nu_mu, oscillations.nu_mu)
p_tau = 100 * osc.p(oscillations.nu_mu, oscillations.nu_tau)
graphs[oscillations.nu_e].SetPoint(i, le, p_e)
graphs[oscillations.nu_mu].SetPoint(i, le, p_mu)
graphs[oscillations.nu_tau].SetPoint(i, le, p_tau)
c = ROOT.TCanvas("c", "c", 800, 800)
f = c.DrawFrame(0.0, 0.0, le_max, 100)
l = ROOT.TLegend(0.91, 0.65, 1.0, 0.9)
l.SetFillColor(ROOT.kWhite)
l.SetBorderSize(0)
f.SetTitle("Neutrino Oscillations")
f.GetXaxis().SetTitle("L / E_{#nu} [ km GeV ^{-1} ]")
f.GetYaxis().SetTitle("P( #nu_{#mu} #rightarrow #nu_{#alpha} ) [ % ] ")
for nu in [oscillations.nu_tau, oscillations.nu_mu, oscillations.nu_e]:
graph = graphs[nu]
graph.SetLineColor(colour(nu))
graph.SetLineStyle(style(nu))
if (mode == "short"):
graph.SetLineWidth(5)
elif (mode == "long"):
graph.SetLineWidth(3)
graph.Draw()
l.AddEntry(graph, name(nu), "L")
c.Update()
l.Draw()
c.Update()
c.SaveAs("figure-osc-le-" + mode + ".png")
input("continue?")
def plotHierarchy(e_range):
"""Plot P(nu_mu -> nu_e) as a function of E for the two choices of mass hierarchy."""
n = 300
dms = [(2.3e-3),
(-2.3e-3)] # (Delta m^2)_31 for normal and inverted hierarchy
e_min = e_range[0]
e_max = e_range[1]
e_step = (e_max - e_min) / float(n)
graphs = {}
nu_i = oscillations.nu_mu
nu_f = oscillations.nu_e
osc = oscillations.Oscillations()
for dm in dms:
graphs[dm] = ROOT.TGraph(n + 1)
osc.setDeltaM32(dm * oscillations.units.eV2)
for i in range(n + 1):
e = e_min + (i * e_step)
osc.setE(e * oscillations.units.GeV)
p = 100.0 * osc.p(nu_i, nu_f)
graphs[dm].SetPoint(i, e, p)
c = ROOT.TCanvas("c", "c", 800, 800)
f = c.DrawFrame(e_min, 0.0, e_max, 10)
l = ROOT.TLegend(0.49, 0.79, 0.89, 0.89)
l.SetFillColor(ROOT.kWhite)
l.SetBorderSize(0)
f.SetTitle("Effect of Mass Hierarchy on P(#nu_{#mu} #rightarrow #nu_{e})")
f.GetXaxis().SetTitle("E_{#nu} [ GeV ]")
f.GetYaxis().SetTitle("P( #nu_{#mu} #rightarrow #nu_{e} ) [ % ] ")
for dm in dms:
graph = graphs[dm]
graph.SetLineColor(colour(nu_f))
graph.SetLineStyle(styleHierarchy(dm))
graph.SetLineWidth(3)
graph.Draw()
if (dm > 0):
l.AddEntry(graph, "Mass Hierarchy = Normal", "L")
else:
l.AddEntry(graph, "Mass Hierarchy = Inverted", "L")
c.Update()
l.Draw()
c.Update()
c.SaveAs("figure-osc-hierarchy.png")
input("continue?")
def plotDeltaCPAnti(e_range):
"""Plot P(nu_mu -> nu_e) and the anti-neutrino equivalent with delta_cp = 0 and 90degrees"""
n = 300
deltas = [0, 90]
e_min = e_range[0]
e_max = e_range[1]
e_step = (e_max - e_min) / float(n)
graphs = {}
nu_is = [oscillations.nu_mu, oscillations.nu_mu_bar]
nu_fs = [oscillations.nu_e, oscillations.nu_e_bar]
osc = oscillations.Oscillations()
for dcp in deltas:
osc.setDeltaCP(dcp * oscillations.units.degrees)
for nu_i, nu_f in zip(nu_is, nu_fs):
graphs[(dcp, nu_f)] = ROOT.TGraph(n + 1)
for i in range(n + 1):
e = e_min + (i * e_step)
osc.setE(e * oscillations.units.GeV)
p = 100.0 * osc.p(nu_i, nu_f)
graphs[(dcp, nu_f)].SetPoint(i, e, p)
c = ROOT.TCanvas("c", "c", 800, 800)
f = c.DrawFrame(e_min, 0.0, e_max, 10)
l = ROOT.TLegend(0.69, 0.69, 0.89, 0.89)
l.SetFillColor(ROOT.kWhite)
l.SetBorderSize(0)
f.SetTitle(
"Effect of #delta_{CP} on P(#nu_{#mu} #rightarrow #nu_{e}) and P(#bar{#nu}_{#mu} #rightarrow #bar{#nu}_{e})"
)
f.GetXaxis().SetTitle("E_{#nu} [ GeV ]")
f.GetYaxis().SetTitle(
"P( #nu_{#mu} #rightarrow #nu_{e} ) or P( #bar{#nu}_{#mu} #rightarrow #bar{nu}_{e} ) [ % ] "
)
for nu_f in [oscillations.nu_e_bar, oscillations.nu_e]:
for dcp in deltas:
if (dcp == 0 and nu_f == oscillations.nu_e_bar):
continue # When delta_cp = 0, the two graphs are identical
graph = graphs[(dcp, nu_f)]
graph.SetLineColor(colourDelta(dcp))
graph.SetLineStyle(style(nu_f))
graph.SetLineWidth(3)
graph.Draw()
if (dcp == 0):
l.AddEntry(graph, "#delta_{CP} = " + str(dcp) + "#circ", "L")
else:
l.AddEntry(graph,
"#delta_{CP} = " + str(dcp) + "#circ " + name(nu_f),
"L")
c.Update()
l.Draw()
c.Update()
c.SaveAs("figure-osc-dcp-anti.png")
input("continue?")