def integral_f(self, k):
r"""
.. math::
32\pi\frac{\nu^2\Gamma_{\gamma\gamma} X_0}{\nu_0(\nu_0^2-\nu^2)m^3} \left| \frac{F_{Q_1Q_2}}{F_{00}} \right|^2
Note that the mass is shifted and :math:`\Gamma_{\gamma\gamma}` is assumed to be proportional to :math:`m^3`,
while :math:`F_{00}` assumed to remain constant.
Parameters
----------
k : float
:math:`\sqrt{2 q_1 \cdot q_2}, \; [GeV]`
Returns
-------
tuple
value of Re(f(k)-f(0)), 0.
"""
m = 0.95766 # physical mass
mon_m = 0.859 # monopole mass parameter
W_gg = 4.3 * 10**-6 # hardcoded physical value of gg-width
nu0 = gg.s2nu(gg.shift_mass(m)**2)
# note that there's no mistake in shifting the mass and width here
X0 = gg.nu2X(nu0)
nu = gg.k2nu(k)
FF = 1. / ((1 + gg.Q1 / mon_m**2) * (1 + gg.Q2 / mon_m**2))
return 32 * pi * nu**2 * W_gg * X0 * FF**2 / (m**3 * nu0 *
(nu0**2 - nu**2)), 0.
def integral_f(self, k):
r"""
.. math::
64\pi\frac{\nu^2\Gamma_{\gamma\gamma} X_0}{\nu_0(\nu_0^2-\nu^2)m^3}
\left( <\sigma_0 \; \mathrm{fraction}> \cdot \frac{20X_0}{m^4} +
<\sigma_2 \; \mathrm{fraction}> \cdot \frac{5\nu_0^2}{X_0} \right)
Parameters
----------
k : float
:math:`\sqrt{2 q_1 \cdot q_2}, \; [GeV]`
Returns
-------
tuple
value of Re(f(k)-f(0)), 0.
"""
m = gg.shift_mass(self.m)
W_gg = self.W_gg * m / self.m
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
nu = gg.k2nu(k)
FF = 1. / ((1 + gg.Q1 / self.mon_m**2) * (1 + gg.Q2 / self.mon_m**2))
h0 = self.h0_fraction
h2 = 1 - h0
return 64 * pi * nu**2 * W_gg * X0 * (
h0 * 20 * X0 / m**4 +
h2 * 5 * nu0**2 / X0) / (m**3 * nu0 * (nu0**2 - nu**2)) * FF**2, 0.
def k_factor(self, *p):
r"""
kinematical factor.
.. math:: <\sigma_2 \; \mathrm{fraction}> \cdot \frac{2 \nu_0^2}{m^2 \sqrt{X_0}} \; + \;
<\sigma_0 \; \mathrm{fraction}> \cdot \frac{8X_0\sqrt{X_0}}{m^6}
Note that 2 factors coming from :math:`\sigma_0` and :math:`\sigma_2` are added here.
Parameters
----------
p : args, optional
`m` (physical :math:`m`)
Returns
-------
float
kinematical factor
"""
m = gg.shift_mass(self.full_p(p)[0])
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
h0 = self.h0_fraction
h2 = 1. - h0
return h2 * 2*nu0**2/(m**2*X0**0.5) + h0 * 8*X0**1.5/m**6
def k_factor(self, *p):
r"""
kinematical factor.
.. math:: <\sigma_2 \; \mathrm{fraction}> \cdot \frac{2 \nu_0^2}{m^2 \sqrt{X_0}} \; + \;
<\sigma_0 \; \mathrm{fraction}> \cdot \frac{8X_0\sqrt{X_0}}{m^6}
Note that 2 factors coming from :math:`\sigma_0` and :math:`\sigma_2` are added here.
Parameters
----------
p : args, optional
`m` (physical :math:`m`)
Returns
-------
float
kinematical factor
"""
m = gg.shift_mass(self.full_p(p)[0])
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
h0 = self.h0_fraction
h2 = 1. - h0
return h2 * 2 * nu0**2 / (m**2 * X0**0.5) + h0 * 8 * X0**1.5 / m**6
def k_factor(self, *p):
r"""
kinematical factor.
.. math:: \frac{(Q_1^2 - Q_2^2)^2}{m^4} \; \frac{2 \nu_0^2}{m^2 \sqrt{X_0}}
Parameters
----------
p : args, optional
`m` (physical :math:`m`)
Returns
-------
float
kinematical factor
"""
m = gg.shift_mass(self.full_p(p)[0])
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
return (gg.Q1 - gg.Q2)**2 * 2 * nu0**2 / (m**6 * X0**0.5)
def k_factor(self, *p):
r"""
default kinematical factor:
.. math:: \frac{2 \nu_0^2}{m^2 \sqrt{X_0}}
Parameters
----------
p : args, optional
`m` (physical :math:`m`)
Returns
-------
float
kinematical factor
"""
m = gg.shift_mass(self.full_p(p)[0])
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
return 2 * nu0**2 / (m**2 * X0**0.5)
def k_factor(self, *p):
r"""
kinematical factor.
.. math:: \frac{(Q_1^2 - Q_2^2)^2}{m^4} \; \frac{2 \nu_0^2}{m^2 \sqrt{X_0}}
Parameters
----------
p : args, optional
`m` (physical :math:`m`)
Returns
-------
float
kinematical factor
"""
m = gg.shift_mass(self.full_p(p)[0])
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
return (gg.Q1 - gg.Q2)**2 * 2 * nu0**2 / (m**6 * X0**0.5)
def k_factor(self, *p):
r"""
default kinematical factor:
.. math:: \frac{2 \nu_0^2}{m^2 \sqrt{X_0}}
Parameters
----------
p : args, optional
`m` (physical :math:`m`)
Returns
-------
float
kinematical factor
"""
m = gg.shift_mass(self.full_p(p)[0])
nu0 = gg.s2nu(m**2)
X0 = gg.nu2X(nu0)
return 2 * nu0**2 / (m**2 * X0**0.5)
def integral_f(self, k):
r"""
.. math:: \frac{\alpha^2}{2\pi^2f_\pi^2}\; \frac{\nu^2 X_0}{\nu_0(\nu_0^2-\nu^2)}\; \left| \frac{F_{Q_1Q_2}}{F_{00}} \right|^2
Parameters
----------
k : float
:math:`\sqrt{2 q_1 \cdot q_2}, \; [GeV]`
Returns
-------
tuple
value of Re(f(k)-f(0)), 0.
"""
mon_m = 0.776 # monopole mass parameter
nu = gg.k2nu(k)
FF = 1. / ((1 + gg.Q1 / mon_m**2) * (1 + gg.Q2 / mon_m**2))
nu0 = gg.s2nu(gg.M_pi**2) # note that we use same mass for pi+ and pi0
X0 = gg.nu2X(nu0)
return 0.5 * (alpha * nu * FF /
(pi * gg.f_pi))**2 * X0 / (nu0 * (nu0**2 - nu**2)), 0.
def test1_mpi_q2(M_pi, f_pi, M_rho, Q2, out_dir='out'):
r"""
for a given :math:`M_\pi`, :math:`f_\pi`, :math:`M_\rho` and :math:`Q_2^2`
plot :math:`\nu`-dependence of the amplitude compared to interpolated lattice results.
Parameters
----------
M_pi : float
pion mass
f_pi : float
pion decay constant
M_rho : float
:math:`\rho`-meson mass
Q2 : float
:math:`Q_2^2`
out_dir : str, optional
root output directory
Examples
--------
.. code-block:: python
from lat import test1_mpi_q2
test1_mpi_q2(0.451, 0.119, 0.952, 0.094)
run and wait for a while; then plot results:
>>> python plot.py out/test1/mpi_451_Q2_094/f
"""
initial_v = gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 # save initial values
e = EtaPrime()
p = Pi0()
w = WholeRegion()
h = WholeRegion(name='h', add_regge=True)
filename = get_lattice_data_filename(M_pi, Q2, s='mpi_%03d_Q2_%03d')
with open(os.path.join('lattice', filename + '__int')) as fi:
data = []
for l in fi:
try:
data.append(map(float, l.split()))
except ValueError:
pass
d = dict()
for nu, Q1, f, err in data:
if Q1 != 0.:
try:
d[Q1] += [[nu, f, err]]
except KeyError:
d[Q1] = [[nu, f, err]]
out_dir = os.path.join(out_dir, 'test1', filename)
make_sure_path_exists(out_dir)
h.plot_cs(var='nu',
xmax=50.,
dx=0.01,
filename=os.path.join(out_dir, 'cs_0'),
raw=True)
gg.M_pi, gg.f_pi, gg.M_rho, gg.Q2 = M_pi, f_pi, M_rho, Q2
plots = []
for gg.Q1 in d.keys():
h.plot_cs(var='nu',
xmax=50.,
dx=0.01,
filename=os.path.join(out_dir, 'cs_%.3f' % gg.Q1),
raw=True)
nu_max = gg.s2nu(gg.M_pi**2) - 0.002
for r in [e + p, p, w, h]:
r.plot_f(var='nu',
xmax=nu_max,
dx=0.01 * nu_max,
filename=os.path.join(out_dir,
'f%s_%.3f' % (r.name[0], gg.Q1)),
raw=True)
with open(os.path.join(out_dir, 'f_%.3f' % gg.Q1), 'w') as fo:
fo.write('\n'.join([' '.join(map(str, l)) for l in d[gg.Q1]]))
colors = [
'r', 'g', 'b', 'c', 'm', 'y', 'k', 'grey', 'purple', 'orange', 'violet'
]
colors = (colors * (1 + len(d.keys()) / len(colors)))[:len(d.keys())]
with open(os.path.join(out_dir, 'cs'), 'w') as fo:
fo.write(r'xylabel: "$\nu \; [GeV ^2]$" "$\sigma \; [\mu b]$"' + '\n')
fo.write('maxx: 3\nmaxy: 0.9\n')
fo.write('plot: 1 2 source=cs_0 color=grey label=physical\n')
for Q1, color in zip(d.keys(), colors):
fo.write('plot: 1 2 source=cs_%.3f color=%s label=' % (Q1, color) +
r'"$Q_1^2 : \, ' + '%.3f' % Q1 + r' \, GeV^2$"' + '\n')
with open(os.path.join(out_dir, 'f'), 'w') as fo:
fo.write(
r"xylabel: '$\nu \, [GeV^2]$' '$\frac{1}{2}(M_{++,++} + M_{+-,+-})$'"
+ '\n')
gg.Q1 = max(d.keys())
fo.write('maxx: %f\nmaxy: 0.00012\nlinewidth: 1.5\n' %
gg.s2nu(gg.M_pi**2))
for Q1, color in zip(d.keys(), colors):
fo.write('plot: 1 2 source=fw_%.3f color=%s ' % (Q1, color) +
r'label="$Q_1^2 : \, ' + '%.3f' % Q1 + r' \, GeV^2$"' +
'\n')
fo.write('plot: 1 2 source=fh_%.3f color=%s linestyle=-.\n' %
(Q1, color))
fo.write('plot: 1 2 source=fp_%.3f color=%s linestyle=--\n' %
(Q1, color))
fo.write('plot: 1 2 source=fe_%.3f color=%s linestyle=:\n' %
(Q1, color))
fo.write(
'plot: 1 2 yerr=3 source=f_%.3f marker=o linestyle=None color=%s\n'
% (Q1, color))
gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 = initial_v # restore initial values
def test3_q1_q2(Q1, Q2, out_dir='out'):
r"""
for given :math:`Q_1^2` and :math:`Q_2^2`, for each of 3 pion masses (277, 324, 451 MeV)
plot :math:`\nu`-dependence of the amplitude compared to interpolated lattice results.
Parameters
----------
Q1 : float
:math:`Q_1^2`
Q2 : float
:math:`Q_2^2`
out_dir : str, optional
root output directory
Examples
--------
.. code-block:: python
from lat import test3_q1_q2
test3_q1_q2(0.377, 0.377)
run and wait for a while; then plot results:
>>> python plot.py out/test3/f
"""
initial_v = gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 # save initial values
d = dict()
for M_pi in [0.277, 0.324, 0.451]:
filename = get_lattice_data_filename(M_pi, Q2, s='mpi_%03d_Q2_%03d')
with open(os.path.join('lattice', filename + '__int')) as fi:
data = []
for l in fi:
try:
data.append(map(float, l.split()))
except ValueError:
pass
for nu, q1, f, err in data:
if q1 == Q1:
try:
d[M_pi] += [[nu, f, err]]
except KeyError:
d[M_pi] = [[nu, f, err]]
print
e = EtaPrime()
p = Pi0()
w = WholeRegion()
h = WholeRegion(name='h', add_regge=True)
out_dir = os.path.join(out_dir, 'test3')
make_sure_path_exists(out_dir)
gg.Q1, gg.Q2 = Q1, Q2
for gg.M_pi, gg.f_pi, gg.M_rho in [(0.277, 0.104, 0.878),
(0.324, 0.109, 0.922),
(0.451, 0.119, 0.952)]:
nu_max = gg.s2nu(gg.M_pi**2) - 0.002
for r in [e + p, p, w, h]:
r.plot_f(var='nu',
xmax=nu_max,
dx=0.01 * nu_max,
filename=os.path.join(
out_dir,
'f%s_%03d' % (r.name[0], int(1000 * gg.M_pi))),
raw=True)
with open(os.path.join(out_dir, 'fl_%03d' % int(1000 * gg.M_pi)),
'w') as fo:
fo.write('\n'.join([' '.join(map(str, l)) for l in d[gg.M_pi]]))
colors = [
'r', 'g', 'b', 'c', 'm', 'y', 'k', 'grey', 'purple', 'orange', 'violet'
]
colors = (colors * (1 + len(d.keys()) / len(colors)))[:len(d.keys())]
with open(os.path.join(out_dir, 'f'), 'w') as fo:
fo.write(
r"xylabel: '$\nu \, [GeV^2]$' '$\frac{1}{2}(M_{++,++} + M_{+-,+-})$'"
+ '\n')
gg.M_pi = max(d.keys())
fo.write('maxx: %f\nmaxy: 0.00012\nlinewidth: 1.5\n' %
0.4) #gg.s2nu(gg.M_pi**2))
for M_pi, color in zip(map(lambda x: int(1000 * x), d.keys()), colors):
fo.write('plot: 1 2 source=fw_%03d color=%s ' % (M_pi, color) +
r'label="$M_\pi : \, ' + '%03d' % M_pi + r' \, MeV$"' +
'\n')
fo.write('plot: 1 2 source=fh_%03d color=%s linestyle=-.\n' %
(M_pi, color))
fo.write('plot: 1 2 source=fp_%03d color=%s linestyle=--\n' %
(M_pi, color))
fo.write('plot: 1 2 source=fe_%03d color=%s linestyle=:\n' %
(M_pi, color))
fo.write(
'plot: 1 2 yerr=3 source=fl_%03d marker=o linestyle=None color=%s\n'
% (M_pi, color))
gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 = initial_v # restore initial values
def test1_mpi_q2(M_pi, f_pi, M_rho, Q2, out_dir='out'):
r"""
for a given :math:`M_\pi`, :math:`f_\pi`, :math:`M_\rho` and :math:`Q_2^2`
plot :math:`\nu`-dependence of the amplitude compared to interpolated lattice results.
Parameters
----------
M_pi : float
pion mass
f_pi : float
pion decay constant
M_rho : float
:math:`\rho`-meson mass
Q2 : float
:math:`Q_2^2`
out_dir : str, optional
root output directory
Examples
--------
.. code-block:: python
from lat import test1_mpi_q2
test1_mpi_q2(0.451, 0.119, 0.952, 0.094)
run and wait for a while; then plot results:
>>> python plot.py out/test1/mpi_451_Q2_094/f
"""
initial_v = gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 # save initial values
e = EtaPrime()
p = Pi0()
w = WholeRegion()
h = WholeRegion(name='h', add_regge=True)
filename = get_lattice_data_filename(M_pi, Q2, s='mpi_%03d_Q2_%03d')
with open(os.path.join('lattice', filename + '__int')) as fi:
data = []
for l in fi:
try:
data .append(map(float, l.split()))
except ValueError:
pass
d = dict()
for nu, Q1, f, err in data:
if Q1 != 0.:
try:
d[Q1] += [[nu, f, err]]
except KeyError:
d[Q1] = [[nu, f, err]]
out_dir = os.path.join(out_dir, 'test1', filename)
make_sure_path_exists(out_dir)
h.plot_cs(var='nu', xmax=50., dx=0.01, filename=os.path.join(out_dir, 'cs_0'), raw=True)
gg.M_pi, gg.f_pi, gg.M_rho, gg.Q2 = M_pi, f_pi, M_rho, Q2
plots = []
for gg.Q1 in d.keys():
h.plot_cs(var='nu', xmax=50., dx=0.01, filename=os.path.join(out_dir,'cs_%.3f'%gg.Q1), raw=True)
nu_max = gg.s2nu(gg.M_pi**2) - 0.002
for r in [e+p, p, w, h]:
r.plot_f(var='nu', xmax=nu_max, dx=0.01*nu_max, filename=os.path.join(out_dir,'f%s_%.3f'%(r.name[0],gg.Q1)), raw=True)
with open(os.path.join(out_dir, 'f_%.3f' % gg.Q1), 'w') as fo:
fo.write('\n'.join([' '.join(map(str, l)) for l in d[gg.Q1]]))
colors = ['r','g','b','c','m','y','k','grey','purple','orange','violet']
colors = (colors * (1 + len(d.keys())/len(colors)))[:len(d.keys())]
with open(os.path.join(out_dir, 'cs'), 'w') as fo:
fo.write(r'xylabel: "$\nu \; [GeV ^2]$" "$\sigma \; [\mu b]$"' + '\n')
fo.write('maxx: 3\nmaxy: 0.9\n')
fo.write('plot: 1 2 source=cs_0 color=grey label=physical\n')
for Q1, color in zip(d.keys(), colors):
fo.write('plot: 1 2 source=cs_%.3f color=%s label=' % (Q1, color) + r'"$Q_1^2 : \, ' + '%.3f'%Q1 + r' \, GeV^2$"' + '\n')
with open(os.path.join(out_dir, 'f'), 'w') as fo:
fo.write(r"xylabel: '$\nu \, [GeV^2]$' '$\frac{1}{2}(M_{++,++} + M_{+-,+-})$'" + '\n')
gg.Q1 = max(d.keys())
fo.write('maxx: %f\nmaxy: 0.00012\nlinewidth: 1.5\n' % gg.s2nu(gg.M_pi**2))
for Q1, color in zip(d.keys(), colors):
fo.write('plot: 1 2 source=fw_%.3f color=%s '%(Q1, color) + r'label="$Q_1^2 : \, ' + '%.3f'%Q1 + r' \, GeV^2$"' + '\n')
fo.write('plot: 1 2 source=fh_%.3f color=%s linestyle=-.\n' % (Q1, color))
fo.write('plot: 1 2 source=fp_%.3f color=%s linestyle=--\n' % (Q1, color))
fo.write('plot: 1 2 source=fe_%.3f color=%s linestyle=:\n' % (Q1, color))
fo.write('plot: 1 2 yerr=3 source=f_%.3f marker=o linestyle=None color=%s\n' % (Q1, color))
gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 = initial_v # restore initial values
def test3_q1_q2(Q1, Q2, out_dir='out'):
r"""
for given :math:`Q_1^2` and :math:`Q_2^2`, for each of 3 pion masses (277, 324, 451 MeV)
plot :math:`\nu`-dependence of the amplitude compared to interpolated lattice results.
Parameters
----------
Q1 : float
:math:`Q_1^2`
Q2 : float
:math:`Q_2^2`
out_dir : str, optional
root output directory
Examples
--------
.. code-block:: python
from lat import test3_q1_q2
test3_q1_q2(0.377, 0.377)
run and wait for a while; then plot results:
>>> python plot.py out/test3/f
"""
initial_v = gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 # save initial values
d = dict()
for M_pi in [0.277, 0.324, 0.451]:
filename = get_lattice_data_filename(M_pi, Q2, s='mpi_%03d_Q2_%03d')
with open(os.path.join('lattice', filename + '__int')) as fi:
data = []
for l in fi:
try:
data .append(map(float, l.split()))
except ValueError:
pass
for nu, q1, f, err in data:
if q1 == Q1:
try:
d[M_pi] += [[nu, f, err]]
except KeyError:
d[M_pi] = [[nu, f, err]]
print
e = EtaPrime()
p = Pi0()
w = WholeRegion()
h = WholeRegion(name='h', add_regge=True)
out_dir = os.path.join(out_dir, 'test3')
make_sure_path_exists(out_dir)
gg.Q1, gg.Q2 = Q1, Q2
for gg.M_pi, gg.f_pi, gg.M_rho in [(0.277, 0.104, 0.878), (0.324, 0.109, 0.922), (0.451, 0.119, 0.952)]:
nu_max = gg.s2nu(gg.M_pi**2) - 0.002
for r in [e+p, p, w, h]:
r.plot_f(var='nu', xmax=nu_max, dx=0.01*nu_max, filename=os.path.join(out_dir,'f%s_%03d'%(r.name[0], int(1000*gg.M_pi))), raw=True)
with open(os.path.join(out_dir, 'fl_%03d' % int(1000*gg.M_pi)), 'w') as fo:
fo.write('\n'.join([' '.join(map(str, l)) for l in d[gg.M_pi]]))
colors = ['r','g','b','c','m','y','k','grey','purple','orange','violet']
colors = (colors * (1 + len(d.keys())/len(colors)))[:len(d.keys())]
with open(os.path.join(out_dir, 'f'), 'w') as fo:
fo.write(r"xylabel: '$\nu \, [GeV^2]$' '$\frac{1}{2}(M_{++,++} + M_{+-,+-})$'" + '\n')
gg.M_pi = max(d.keys())
fo.write('maxx: %f\nmaxy: 0.00012\nlinewidth: 1.5\n' % 0.4)#gg.s2nu(gg.M_pi**2))
for M_pi, color in zip(map(lambda x: int(1000*x), d.keys()), colors):
fo.write('plot: 1 2 source=fw_%03d color=%s '%(M_pi, color) + r'label="$M_\pi : \, ' + '%03d'%M_pi + r' \, MeV$"' + '\n')
fo.write('plot: 1 2 source=fh_%03d color=%s linestyle=-.\n' % (M_pi, color))
fo.write('plot: 1 2 source=fp_%03d color=%s linestyle=--\n' % (M_pi, color))
fo.write('plot: 1 2 source=fe_%03d color=%s linestyle=:\n' % (M_pi, color))
fo.write('plot: 1 2 yerr=3 source=fl_%03d marker=o linestyle=None color=%s\n' % (M_pi, color))
gg.M_pi, gg.f_pi, gg.M_rho, gg.Q1, gg.Q2 = initial_v # restore initial values