In [1]:

from pymule import *
import tabulate

Populating the interactive namespace from numpy and matplotlib

Settings¶

In [2]:

SMALL_SIZE = 10
MEDIUM_SIZE = 12
BIGGER_SIZE = 14

rc('font', size=SMALL_SIZE)          # controls default text sizes
rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title
rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels
rc('xtick', labelsize=MEDIUM_SIZE)   # fontsize of the tick labels
rc('ytick', labelsize=MEDIUM_SIZE)   # fontsize of the tick labels
rc('legend', fontsize=MEDIUM_SIZE)   # legend fontsize
rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title

Import results¶

In [3]:

setup(folder='eb2eb_daphne/out.tar.bz2')
loConv=1000*conv*alpha**2
nloConv=1000*conv*alpha**3
nnloConv=1000*conv*alpha**4

In [4]:

lo = scaleset(mergefks(
        sigma('eb2eb0')
), loConv)

In [5]:

nlo = scaleset(mergefks(
        sigma('eb2ebF'),
        sigma('eb2ebR125'),
        sigma('eb2ebR35'),
        sigma('eb2ebR45')
), nloConv)

In [6]:

nnlo = scaleset(mergefks(
        sigma('eb2ebFF'),
        sigma('eb2ebRF125'),
        sigma('eb2ebRF35'),
        sigma('eb2ebRF45'),
        sigma('eb2ebRR15162526'),
        sigma('eb2ebRR3536'),
        sigma('eb2ebRR4546')
), nnloConv)

Total cross section & $K$-factors¶

In [7]:

sigma0 = lo['value']
sigma1 = plusnumbers([sigma0,nlo['value']])
sigma2 = plusnumbers([sigma1,nnlo['value']])

In [8]:

dk1=100*dividenumbers(nlo['value'], sigma0)
dk2=100*dividenumbers(nnlo['value'], sigma1)

In [9]:

print(tabulate.tabulate([
    ['LO'  , '+'+printnumber(  lo['value']/1000.), None],
    ['NLO' ,     printnumber( nlo['value']/1000.), printnumber(dk1)],
    ['NNLO', '+'+printnumber(nnlo['value']/1000.), '+ '+printnumber(dk2)]
], headers=['$\\sigma / ub$', '$\\delta K / \\%$']))

      $\sigma / ub$    $\delta K / \%$
----  ---------------  -----------------
LO    +6.855734(4)
NLO   -0.795679(5)     -11.60603(8)
NNLO  +0.03121(4)      + 0.5151(6)

Angular distribution¶

combine plots

In [10]:

dsdm0 = lo['th_e']
dsdm1 = addplots(dsdm0,nlo['th_e'])
dsdm2 = addplots(dsdm1,nnlo['th_e'])

generate plot

In [11]:

fig, (ax1, ax2, ax3) = kplot(
    {
        'lo':   lo['th_e'],
        'nlo':  nlo['th_e'],
        'nnlo': nnlo['th_e'],
    },
    labelx="$\\theta_{-}\,/\,{\\rm deg}$",
    labelsigma="$\\D\\sigma/\\D\\theta_{-}\ /\ {\\rm\\upmu b}$",
    legend={
        'lo': '$\\sigma_{0}$',
        'nlo': '$\\sigma_{1}$',
        'nnlo': '$\\sigma_{2}$'
    },
    legendopts={'what': 'u', 'loc': 'upper right'}
)
ax1.set_yscale('log')
gcf().subplots_adjust(right=0.89)
fig.savefig('th_e.pdf')

comparison with BabaYaga¶

BabaYaga results (from C.M. Carloni Calame):

In [12]:

loB       = np.array([6855.73536,0.00003])
nloBFull  = np.array([6060.042,0.007])
nnloBFull = np.array([6086.81,0.01])
nloB      = plusnumbers(nloBFull,-loB)
nnloB     = plusnumbers(nnloBFull,-nloBFull)

BabaYaga is exact up to NLO. We therefore see agreement at LO and NLO:

In [13]:

chisq0=chisq([lo['value'],loB])
chisq1=chisq([nlo['value'],nloB])

At NNLO BabaYaga yields a logarihtmic approximation. We therefore only expect approximate agreement.

In [14]:

dev2=100*(nnlo['value'][0]-nnloB[0])/nnloB[0]

for the total cross section we find agreement belov 0.01%

In [15]:

sigma2=plusnumbers([lo['value'],nlo['value'],nnlo['value']])
sigma2B=plusnumbers([loB,nloB,nnloB])

In [16]:

devTot=100*(sigma2[0]-sigma2B[0])/sigma2B[0]

In [17]:

print(tabulate.tabulate([
    [  'LO', '+'+printnumber(  lo['value']/1000.), '+'+printnumber(  loB/1000.), None],
    [ 'NLO',     printnumber( nlo['value']/1000.),     printnumber( nloB/1000.), printnumber(dk1)],
    ['NNLO', '+'+printnumber(nnlo['value']/1000.), '+'+printnumber(nnloB/1000.), '+ '+printnumber(dk2)],
    ['sum' , '+'+printnumber(sigma2       /1000.), '+'+printnumber(nnloBFull/1000.)]
], headers=['', 'McMule', 'BABAYAGA', '$\\delta K / \\%$']))

      McMule        BABAYAGA        $\delta K / \%$
----  ------------  --------------  -----------------
LO    +6.855734(4)  +6.85573536(3)
NLO   -0.795679(5)  -0.795693(7)    -11.60603(8)
NNLO  +0.03121(4)   +0.02677(1)     + 0.5151(6)
sum   +6.09127(4)   +6.08681(1)