Impact of NNLO QED on $\ell-p$ scattering at MUSE¶
The results for lepton-proton scattering are tailored to the characteristics of the MUSE experiment. The kinematics of the process is defined by
\begin{equation} \ell^\pm\,(p_1, m) + p\,(p_2, M) \to \ell^\pm\,(p_3, \theta_\ell) + p\,(p_4) \end{equation}
The lepton beam momentum is set to $|\vec{p}_1|=210$ MeV, consistent with one of the MUSE setups. Leptons can be electrons or muons, with both polarities.
Cuts are imposed on the outgoing lepton scattering angle, $20^\circ < \theta_\ell < 100^\circ$, and on the outgoing lepton momentum, $|\vec{p}_3| > 15$ MeV.
A cut on energetic forward photons can be also enforced, \begin{equation} E_\gamma > 0.4\,|\vec{p}_1| \,, \end{equation} where $E_\gamma$ is the sum of the energies carried by photons contained in a 100 mrad cone centred on the beam axis. This simulates the forward-angle calorimeter employed by MUSE to remove radiative events.
Based on the constraints above, we can define two scenarios:
- S0 : $20^\circ < \theta_\ell < 100^\circ$, $|\vec{p}_3| > 15$ MeV
- S1 : $20^\circ < \theta_\ell < 100^\circ$, $|\vec{p}_3| > 15$ MeV, $E_\gamma > 0.4\,|\vec{p}_1|$
NLO and NNLO corrections can be split into gauge-invariant subsets according to their nominal leptonic and protonic charge. If $q$ resp. $Q$ is assigned to each photon emission from a lepton resp. proton line, we will have, on top of the LO charge $q^2\,Q^2$, three subsets at NLO, i.e. $\{q^2,\, qQ,\, Q^2\}$ and five subsets at NNLO, i.e. $\{q^4,\,q^3 Q,\, q^2 Q^2,\,q Q^3,\,Q^4\}$.
The corrections can be generically split into photonic and fermionic, where the latter include all the contributions with VP insertions. Thus we have:
- NLO photonic (@PH) contributions, where @ can be (E, X, M)
- NLO fermionic (@VP) contrbution, where @ is conventionally "E"
- NNLO photonic (@PH) contributions, where @ can be (E, X31, X22, X13, M)
- NNLO fermionic (@VP) contributions, where @ can be (E, X, M)
In addition, the last two characters in the names of the different contributions, i.e. m or p, and 0 or 1, refer to the polarisation of the leptons (minus or plus) and to the scenarios where the elasticity cut is enforced, 1, or not, 0.
Finally, some contributions are presented with a form-factor description of the photon-proton vertex, see (9) in the paper, depending on one parameter, $\Lambda$. This can assume four different values, as shown below. In this case, the label "E" and "X" turn into "F" and "Y", and at the end of the names Lxx denotes the value 0.xx for $\Lambda^2$, in GeV$^2$. "Y" can also denote the sum of the three mixed photonic NNLO corrections.
In [1]:
from pymule import *
from pymule.plot import twopanel
import pymule.mpl_axes_aligner as mpl_axes_aligner
from tabulate import tabulate, SEPARATING_LINE
Before starting, some helper functions for later
In [2]:
def pn(a):
return printnumber(a)
def dn(a,b):
return dividenumbers(a,b)
def tn(a,b):
return timesnumbers(a,b)
Load McMule data¶
In [3]:
setup(cachefolder='/tmp/mcmule/')
$e^\pm p \to e^\pm p$¶
$\bullet$ pure QED
In [4]:
setup(obs='0')
setup(folder='lp2lp_tpe_paper/out-muse-e-qed.tar.bz2')
lo0 = scaleset(mergefks(sigma('em2em0')), alpha**2*conv)
nloEPHm0 = scaleset(mergefks(sigma('em2emFEE'),sigma('em2emREE15'),sigma('em2emREE35')), alpha**3*conv)
nloEVPm0 = scaleset(mergefks(sigma('em2emA')), alpha**3*conv)
nloXPHm0 = scaleset(mergefks(sigma('em2emFEM'),sigma('em2emREM')), alpha**3*conv)
nloMPHm0 = scaleset(mergefks(sigma('em2emFMM'),sigma('em2emRMM')), alpha**3*conv)
nnloEPHm0 = scaleset(mergefks(sigma('em2emFFEEEE',obs='1'),sigma('em2emRFEEEE15'),sigma('em2emRFEEEE35'),sigma('em2emRREEEE1516'),sigma('em2emRREEEE3536')), alpha**4*conv)
nnloX31PHm0 = scaleset(mergefks(sigma('em2emFF31z',obs='1'),sigma('em2emRF3115'),sigma('em2emRF3135'),sigma('em2emRR311516'),sigma('em2emRR313536')), alpha**4*conv)
nnloX22PHm0 = scaleset(mergefks(sigma('em2emFF22z',obs='1'),sigma('em2emRF2215'),sigma('em2emRF2235'),sigma('em2emRR221516'),sigma('em2emRR223536')), alpha**4*conv)
nnloX13PHm0 = scaleset(mergefks(sigma('em2emFF13z',obs='1'),sigma('em2emRF1315'),sigma('em2emRF1335'),sigma('em2emRR131516'),sigma('em2emRR133536')), alpha**4*conv)
nnloMPHm0 = scaleset(mergefks(sigma('em2emFFMMMM',obs='1'),sigma('em2emRFMMMM'),sigma('em2emRRMMMM')), alpha**4*conv)
nnloEVPm0 = scaleset(mergefks(sigma('em2emAFEE'), sigma('em2emAREE15'), sigma('em2emAREE35'),
anyxi1=sigma('em2emAA'), anyxi2=sigma('em2emNFEE')), alpha**4*conv)
nnloXVPm0 = scaleset(mergefks(sigma('em2emAFEM'), sigma('em2emAREM'),anyxi1=sigma('em2emNFEM',obs='0')), alpha**4*conv)
nnloMVPm0 = scaleset(mergefks(sigma('em2emAFMM'), sigma('em2emARMM'),anyxi1=sigma('em2emNFMM',obs='0')), alpha**4*conv)
setup(obs='1')
lo1 = scaleset(mergefks(sigma('em2em0',obs='0')), alpha**2*conv)
nloEPHm1 = scaleset(mergefks(sigma('em2emFEE',obs='0'),sigma('em2emREE15'),sigma('em2emREE35')), alpha**3*conv)
nloEVPm1 = scaleset(mergefks(sigma('em2emA',obs='0')), alpha**3*conv)
nloXPHm1 = scaleset(mergefks(sigma('em2emFEM',obs='0'),sigma('em2emREM')), alpha**3*conv)
nloMPHm1 = scaleset(mergefks(sigma('em2emFMM',obs='0'),sigma('em2emRMM')), alpha**3*conv)
nnloEPHm1 = scaleset(mergefks(sigma('em2emFFEEEE'),sigma('em2emRFEEEE15'),sigma('em2emRFEEEE35'),sigma('em2emRREEEE1516'),sigma('em2emRREEEE3536')), alpha**4*conv)
nnloX31PHm1 = scaleset(mergefks(sigma('em2emFF31z'),sigma('em2emRF3115'),sigma('em2emRF3135'),sigma('em2emRR311516'),sigma('em2emRR313536')), alpha**4*conv)
nnloX22PHm1 = scaleset(mergefks(sigma('em2emFF22z'),sigma('em2emRF2215'),sigma('em2emRF2235'),sigma('em2emRR221516'),sigma('em2emRR223536')), alpha**4*conv)
nnloX13PHm1 = scaleset(mergefks(sigma('em2emFF13z'),sigma('em2emRF1315'),sigma('em2emRF1335'),sigma('em2emRR131516'),sigma('em2emRR133536')), alpha**4*conv)
nnloMPHm1 = scaleset(mergefks(sigma('em2emFFMMMM'),sigma('em2emRFMMMM'),sigma('em2emRRMMMM')), alpha**4*conv)
nnloEVPm1 = scaleset(mergefks(sigma('em2emAFEE',obs='0'), sigma('em2emAREE15'), sigma('em2emAREE35'),
anyxi1=sigma('em2emAA',obs='0'), anyxi2=sigma('em2emNFEE',obs='0')), alpha**4*conv)
nnloXVPm1 = scaleset(mergefks(sigma('em2emAFEM',obs='0'), sigma('em2emAREM'),anyxi1=sigma('em2emNFEM',obs='0')), alpha**4*conv)
nnloMVPm1 = scaleset(mergefks(sigma('em2emAFMM',obs='0'), sigma('em2emARMM'),anyxi1=sigma('em2emNFMM',obs='0')), alpha**4*conv)
$\bullet$ $\Lambda^2=0.86$ GeV^2
In [5]:
setup(folder='lp2lp_tpe_paper/out-muse-e-86.tar.bz2')
setup(obs='0')
lo086 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
nloFPHp0L86 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloFVPp0L86 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
nloYPHp0L86 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
setup(obs='1')
nloFVPp1L86 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
nloFPHp1L86 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloYPHp1L86 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
$\bullet$ $\Lambda^2=0.71$ GeV^2
In [6]:
setup(folder='lp2lp_tpe_paper/out-muse-e-71.tar.bz2')
setup(obs='0')
lo071 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
nloFPHp0L71 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloFVPp0L71 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
nloYPHp0L71 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
nnloFPHp0L71 = scaleset(mergefks(sigma('mp2mpFF'),sigma('mp2mpRF15'),sigma('mp2mpRF35'),sigma('mp2mpRR1516'),sigma('mp2mpRR3536')), alpha**4*conv)
nnloFVPp0L71 = scaleset(mergefks(sigma('mp2mpAF'), sigma('mp2mpAR15'), sigma('mp2mpAR35'),
anyxi1=sigma('mp2mpAA'), anyxi2=sigma('mp2mpNF')), alpha**4*conv)
setup(obs='1')
nloFPHp1L71 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloFVPp1L71 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
nloYPHp1L71 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
nnloFPHp1L71 = scaleset(mergefks(sigma('mp2mpFF',obs='0'),sigma('mp2mpRF15'),sigma('mp2mpRF35'),sigma('mp2mpRR1516'),sigma('mp2mpRR3536')), alpha**4*conv)
nnloFVPp1L71 = scaleset(mergefks(sigma('mp2mpAF',obs='0'), sigma('mp2mpAR15'), sigma('mp2mpAR35'),
anyxi1=sigma('mp2mpAA',obs='0'), anyxi2=sigma('mp2mpNF',obs='0')), alpha**4*conv)
$\bullet$ $\Lambda^2=0.66$ GeV^2
In [7]:
setup(folder='lp2lp_tpe_paper/out-muse-e-66.tar.bz2')
setup(obs='0')
lo066 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
nloFPHp0L66 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloFVPp0L66 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
nloYPHp0L66 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
setup(obs='1')
nloFVPp1L66 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
nloFPHp1L66 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloYPHp1L66 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
$\bullet$ $\Lambda^2=0.60$ GeV^2
In [8]:
setup(folder='lp2lp_tpe_paper/out-muse-e-60.tar.bz2')
setup(obs='0')
lo060 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
nloFPHp0L60 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloFVPp0L60 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
nloYPHp0L60 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
setup(obs='1')
nloFVPp1L60 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
nloFPHp1L60 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
nloYPHp1L60 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
Total cross sections ($\mu$b)¶
$\bullet$ S0
In [9]:
lo00 = lo0['value']
lo86 = lo086['value']
lo71 = lo071['value']
lo66 = lo066['value']
lo60 = lo060['value']
nloXPHp0 = tn(nloXPHm0['value'], [-1., 0])
nloYPHm0L86 = tn(nloYPHp0L86['value'], [-1., 0])
nloYPHm0L71 = tn(nloYPHp0L71['value'], [-1., 0])
nloYPHm0L66 = tn(nloYPHp0L66['value'], [-1., 0])
nloYPHm0L60 = tn(nloYPHp0L60['value'], [-1., 0])
nlom0 = plusnumbers(nloEPHm0['value'], nloEVPm0['value'], nloXPHm0['value'], nloMPHm0['value'], lo00)
nlop0 = plusnumbers(nloEPHm0['value'], nloEVPm0['value'], -nloXPHm0['value'], nloMPHm0['value'], lo00)
nlom071 = plusnumbers(nloFPHp0L71['value'], nloFVPp0L71['value'], -nloYPHp0L71['value'], nloMPHm0['value'], lo71)
nlop071 = plusnumbers(nloFPHp0L71['value'], nloFVPp0L71['value'], nloYPHp0L71['value'], nloMPHm0['value'], lo71)
nnloYPHm0 = plusnumbers( nnloX31PHm0['value'], nnloX22PHm0['value'], nnloX13PHm0['value'])
nnloYPHp0 = plusnumbers(-nnloX31PHm0['value'], nnloX22PHm0['value'], -nnloX13PHm0['value'])
nnloXVPp0 = tn(nnloXVPm0['value'], [-1., 0])
nnlom0 = plusnumbers(nnloEPHm0['value'], nnloYPHm0, nnloMPHm0['value'], nlom0)
nnlop0 = plusnumbers(nnloEPHm0['value'], nnloYPHp0, nnloMPHm0['value'], nlop0)
print("")
tabE0 = [
["\sigma_0", pn(lo0['value']), pn(lo0['value'])],
["\sigma_0_86", pn(lo086['value']), pn(lo086['value'])],
["\sigma_0_71", pn(lo071['value']), pn(lo071['value'])],
["\sigma_0_66", pn(lo066['value']), pn(lo066['value'])],
["\sigma_0_60", pn(lo060['value']), pn(lo060['value'])],
SEPARATING_LINE,
["\sigma^{(1)}_e", pn(nloEPHm0['value']), pn(nloEPHm0['value']), pn(dn(nloEPHm0['value'],lo00)*100.), pn(dn(nloEPHm0['value'],lo00)*100.)],
["\sigma^{(1)}_eF", pn(nloEVPm0['value']), pn(nloEVPm0['value']), pn(dn(nloEVPm0['value'],lo00)*100.), pn(dn(nloEVPm0['value'],lo00)*100.)],
["\sigma^{(1)}_e86", pn(nloFPHp0L86['value']), pn(nloFPHp0L86['value']), pn(dn(nloFPHp0L86['value'],lo86)*100.), pn(dn(nloFPHp0L86['value'],lo86)*100.)],
["\sigma^{(1)}_eF86", pn(nloFVPp0L86['value']), pn(nloFVPp0L86['value']), pn(dn(nloFVPp0L86['value'],lo86)*100.), pn(dn(nloFVPp0L86['value'],lo86)*100.)],
["\sigma^{(1)}_e71", pn(nloFPHp0L71['value']), pn(nloFPHp0L71['value']), pn(dn(nloFPHp0L71['value'],lo71)*100.), pn(dn(nloFPHp0L71['value'],lo71)*100.)],
["\sigma^{(1)}_eF71", pn(nloFVPp0L71['value']), pn(nloFVPp0L71['value']), pn(dn(nloFVPp0L71['value'],lo71)*100.), pn(dn(nloFVPp0L71['value'],lo71)*100.)],
["\sigma^{(1)}_e66", pn(nloFPHp0L66['value']), pn(nloFPHp0L66['value']), pn(dn(nloFPHp0L66['value'],lo66)*100.), pn(dn(nloFPHp0L66['value'],lo66)*100.)],
["\sigma^{(1)}_eF66", pn(nloFVPp0L66['value']), pn(nloFVPp0L66['value']), pn(dn(nloFVPp0L66['value'],lo66)*100.), pn(dn(nloFVPp0L66['value'],lo66)*100.)],
["\sigma^{(1)}_e60", pn(nloFPHp0L60['value']), pn(nloFPHp0L60['value']), pn(dn(nloFPHp0L60['value'],lo60)*100.), pn(dn(nloFPHp0L60['value'],lo60)*100.)],
["\sigma^{(1)}_eF60", pn(nloFVPp0L60['value']), pn(nloFVPp0L60['value']), pn(dn(nloFVPp0L60['value'],lo60)*100.), pn(dn(nloFVPp0L60['value'],lo60)*100.)],
["\sigma^{(1)}_x", pn(nloXPHm0['value']), pn(nloXPHp0), pn(dn(nloXPHm0['value'],lo00)*100.), pn(dn(nloXPHp0,lo00)*100.)],
["\sigma^{(1)}_x86", pn(nloYPHm0L86), pn(nloYPHp0L86['value']), pn(dn(nloYPHm0L86,lo86)*100.), pn(dn(nloYPHp0L86['value'],lo86)*100.)],
["\sigma^{(1)}_x71", pn(nloYPHm0L71), pn(nloYPHp0L71['value']), pn(dn(nloYPHm0L71,lo71)*100.), pn(dn(nloYPHp0L71['value'],lo71)*100.)],
["\sigma^{(1)}_x66", pn(nloYPHm0L66), pn(nloYPHp0L66['value']), pn(dn(nloYPHm0L66,lo66)*100.), pn(dn(nloYPHp0L66['value'],lo66)*100.)],
["\sigma^{(1)}_x60", pn(nloYPHm0L60), pn(nloYPHp0L60['value']), pn(dn(nloYPHm0L60,lo60)*100.), pn(dn(nloYPHp0L60['value'],lo60)*100.)],
["\sigma^{(1)}_p", pn(nloMPHm0['value']), pn(nloMPHm0['value']), pn(dn(nloMPHm0['value'],lo00)*100.), pn(dn(nloMPHm0['value'],lo00)*100.)],
SEPARATING_LINE,
["\sigma^{(2)}_e", pn(nnloEPHm0['value']), pn(nnloEPHm0['value']), pn(dn(nnloEPHm0['value'],nlom0)*100.), pn(dn(nnloEPHm0['value'],nlop0)*100.)],
["\sigma^{(2)}_eF", pn(nnloEVPm0['value']), pn(nnloEVPm0['value']), pn(dn(nnloEVPm0['value'],nlom0)*100.), pn(dn(nnloEVPm0['value'],nlop0)*100.)],
["\sigma^{(2)}_e71", pn(nnloFPHp0L71['value']), pn(nnloFPHp0L71['value']), pn(dn(nnloFPHp0L71['value'],nlom071)*100.), pn(dn(nnloFPHp0L71['value'],nlop071)*100.)],
["\sigma^{(2)}_eF71", pn(nnloFVPp0L71['value']), pn(nnloFVPp0L71['value']), pn(dn(nnloFVPp0L71['value'],nlom071)*100.), pn(dn(nnloFVPp0L71['value'],nlop071)*100.)],
["\sigma^{(2)}_x", pn(nnloYPHm0), pn(nnloYPHp0), pn(dn(nnloYPHm0,nlom0)*100.), pn(dn(nnloYPHp0,nlop0)*100.)],
["\sigma^{(2)}_xF", pn(nnloXVPm0['value']), pn(nnloXVPp0), pn(dn(nnloXVPm0['value'],nlom0)*100.), pn(dn(nnloXVPp0,nlop0)*100.)],
["\sigma^{(2)}_p", pn(nnloMPHm0['value']), pn(nnloMPHm0['value']), pn(dn(nnloMPHm0['value'],nlom0)*100.), pn(dn(nnloMPHm0['value'],nlop0)*100.)],
["\sigma^{(2)}_pF", pn(nnloMVPm0['value']), pn(nnloMVPm0['value']), pn(dn(nnloMVPm0['value'],nlom0)*100.), pn(dn(nnloMVPm0['value'],nlop0)*100.)],
SEPARATING_LINE
]
print(tabulate(tabE0, headers=["MUSE_e 210 [S0]","e+p", "e-p", "dK+%", "dK-%"]))
$\bullet$ S1
In [10]:
nloXPHp1 = tn(nloXPHm1['value'], [-1., 0])
nloYPHm1L86 = tn(nloYPHp1L86['value'], [-1., 0])
nloYPHm1L71 = tn(nloYPHp1L71['value'], [-1., 0])
nloYPHm1L60 = tn(nloYPHp1L60['value'], [-1., 0])
nloYPHm1L66 = tn(nloYPHp1L66['value'], [-1., 0])
nlom1 = plusnumbers(nloEPHm1['value'], nloEVPm1['value'], nloXPHm1['value'], nloMPHm1['value'], lo00)
nlop1 = plusnumbers(nloEPHm1['value'], nloEVPm1['value'], -nloXPHm1['value'], nloMPHm1['value'], lo00)
nlom171 = plusnumbers(nloFPHp1L71['value'], nloFVPp1L71['value'], -nloYPHp1L71['value'], nloMPHm1['value'], lo71)
nlop171 = plusnumbers(nloFPHp1L71['value'], nloFVPp1L71['value'], nloYPHp1L71['value'], nloMPHm1['value'], lo71)
nnloYPHm1 = plusnumbers( nnloX31PHm1['value'], nnloX22PHm1['value'], nnloX13PHm1['value'])
nnloYPHp1 = plusnumbers(-nnloX31PHm1['value'], nnloX22PHm1['value'], -nnloX13PHm1['value'])
nnloXVPp1 = tn(nnloXVPm1['value'], [-1., 0])
nnlom1 = plusnumbers(nnloEPHm1['value'], nnloYPHm1, nnloMPHm1['value'], nlom1)
nnlop1 = plusnumbers(nnloEPHm1['value'], nnloYPHp1, nnloMPHm1['value'], nlop1)
print("")
tabE1 = [
["\sigma_0", pn(lo0['value']), pn(lo0['value'])],
["\sigma_0_86", pn(lo086['value']), pn(lo086['value'])],
["\sigma_0_71", pn(lo071['value']), pn(lo071['value'])],
["\sigma_0_66", pn(lo066['value']), pn(lo066['value'])],
["\sigma_0_60", pn(lo060['value']), pn(lo060['value'])],
SEPARATING_LINE,
["\sigma^{(1)}_e", pn(nloEPHm1['value']), pn(nloEPHm1['value']), pn(dn(nloEPHm1['value'],lo00)*100.), pn(dn(nloEPHm1['value'],lo00)*100.)],
["\sigma^{(1)}_eF", pn(nloEVPm1['value']), pn(nloEVPm1['value']), pn(dn(nloEVPm1['value'],lo00)*100.), pn(dn(nloEVPm1['value'],lo00)*100.)],
["\sigma^{(1)}_e86", pn(nloFPHp1L86['value']), pn(nloFPHp1L86['value']), pn(dn(nloFPHp1L86['value'],lo86)*100.), pn(dn(nloFPHp1L86['value'],lo86)*100.)],
["\sigma^{(1)}_eF86", pn(nloFVPp1L86['value']), pn(nloFVPp1L86['value']), pn(dn(nloFVPp1L86['value'],lo86)*100.), pn(dn(nloFVPp1L86['value'],lo86)*100.)],
["\sigma^{(1)}_e71", pn(nloFPHp1L71['value']), pn(nloFPHp1L71['value']), pn(dn(nloFPHp1L71['value'],lo71)*100.), pn(dn(nloFPHp1L71['value'],lo71)*100.)],
["\sigma^{(1)}_eF71", pn(nloFVPp1L71['value']), pn(nloFVPp1L71['value']), pn(dn(nloFVPp1L71['value'],lo71)*100.), pn(dn(nloFVPp1L71['value'],lo71)*100.)],
["\sigma^{(1)}_e66", pn(nloFPHp1L66['value']), pn(nloFPHp1L66['value']), pn(dn(nloFPHp1L66['value'],lo66)*100.), pn(dn(nloFPHp1L66['value'],lo66)*100.)],
["\sigma^{(1)}_eF66", pn(nloFVPp1L66['value']), pn(nloFVPp1L66['value']), pn(dn(nloFVPp1L66['value'],lo66)*100.), pn(dn(nloFVPp1L66['value'],lo66)*100.)],
["\sigma^{(1)}_e60", pn(nloFPHp1L60['value']), pn(nloFPHp1L60['value']), pn(dn(nloFPHp1L60['value'],lo60)*100.), pn(dn(nloFPHp1L60['value'],lo60)*100.)],
["\sigma^{(1)}_eF60", pn(nloFVPp1L60['value']), pn(nloFVPp1L60['value']), pn(dn(nloFVPp1L60['value'],lo60)*100.), pn(dn(nloFVPp1L60['value'],lo60)*100.)],
["\sigma^{(1)}_x", pn(nloXPHm1['value']), pn(nloXPHp1), pn(dn(nloXPHm1['value'],lo00)*100.), pn(dn(nloXPHp1,lo00)*100.)],
["\sigma^{(1)}_x86", pn(nloYPHm1L86), pn(nloYPHp1L86['value']), pn(dn(nloYPHm1L86,lo86)*100.), pn(dn(nloYPHp1L86['value'],lo86)*100.)],
["\sigma^{(1)}_x71", pn(nloYPHm1L71), pn(nloYPHp1L71['value']), pn(dn(nloYPHm1L71,lo71)*100.), pn(dn(nloYPHp1L71['value'],lo71)*100.)],
["\sigma^{(1)}_x66", pn(nloYPHm1L66), pn(nloYPHp1L66['value']), pn(dn(nloYPHm1L66,lo66)*100.), pn(dn(nloYPHp1L66['value'],lo66)*100.)],
["\sigma^{(1)}_x60", pn(nloYPHm1L60), pn(nloYPHp1L60['value']), pn(dn(nloYPHm1L60,lo60)*100.), pn(dn(nloYPHp1L60['value'],lo60)*100.)],
["\sigma^{(1)}_p", pn(nloMPHm1['value']), pn(nloMPHm1['value']), pn(dn(nloMPHm1['value'],lo00)*100.), pn(dn(nloMPHm1['value'],lo00)*100.)],
SEPARATING_LINE,
["\sigma^{(2)}_e", pn(nnloEPHm1['value']), pn(nnloEPHm1['value']), pn(dn(nnloEPHm1['value'],nlom1)*100.), pn(dn(nnloEPHm1['value'],nlop1)*100.)],
["\sigma^{(2)}_eF", pn(nnloEVPm1['value']), pn(nnloEVPm1['value']), pn(dn(nnloEVPm1['value'],nlom1)*100.), pn(dn(nnloEVPm1['value'],nlop1)*100.)],
["\sigma^{(2)}_e71", pn(nnloFPHp1L71['value']), pn(nnloFPHp1L71['value']), pn(dn(nnloFPHp1L71['value'],nlom171)*100.), pn(dn(nnloFPHp1L71['value'],nlop171)*100.)],
["\sigma^{(2)}_eF71", pn(nnloFVPp1L71['value']), pn(nnloFVPp1L71['value']), pn(dn(nnloFVPp1L71['value'],nlom171)*100.), pn(dn(nnloFVPp1L71['value'],nlop171)*100.)],
["\sigma^{(2)}_x", pn(nnloYPHm1), pn(nnloYPHp1), pn(dn(nnloYPHm1,nlom1)*100.), pn(dn(nnloYPHp1,nlop1)*100.)],
["\sigma^{(2)}_xF", pn(nnloXVPm1['value']), pn(nnloXVPp1), pn(dn(nnloXVPm1['value'],nlom1)*100.), pn(dn(nnloXVPp1,nlop1)*100.)],
["\sigma^{(2)}_p", pn(nnloMPHm1['value']), pn(nnloMPHm1['value']), pn(dn(nnloMPHm1['value'],nlom1)*100.), pn(dn(nnloMPHm1['value'],nlop1)*100.)],
["\sigma^{(2)}_pF", pn(nnloMVPm1['value']), pn(nnloMVPm1['value']), pn(dn(nnloMVPm1['value'],nlom1)*100.), pn(dn(nnloMVPm1['value'],nlop1)*100.)],
SEPARATING_LINE
]
print(tabulate(tabE1, headers=["MUSE_e 210 [S1]","e+p", "e-p", "dK+%", "dK-%"]))
Total cross section -- Bar plots¶
In [11]:
def get_cumulated_array(data, **kwargs):
cum = data.clip(**kwargs)
cum = np.cumsum(cum, axis=0)
d = np.zeros(np.shape(data))
d[1:] = cum[:-1]
return d
def cumulate(countsPH, countsVP, errorFF):
data = np.array([countsPH, countsVP])
data_shape = np.shape(data)
cumulated_data = get_cumulated_array(data, min=0)
cumulated_data_neg = get_cumulated_array(data, max=0)
row_mask = (data<0)
cumulated_data[row_mask] = cumulated_data_neg[row_mask]
data_stack = cumulated_data
return data_stack
def barplot(xorder, countsPH, countsVP, data_stack, errorFF):
a11=ax1.bar(xorder, countsPH, bottom=data_stack[0])
a12=ax2.bar(xorder, countsPH, bottom=data_stack[0])
a13=ax3.bar(xorder, countsPH, bottom=data_stack[0])
a21=ax1.bar(xorder, countsVP, bottom=data_stack[1], yerr=errorFF)
a22=ax2.bar(xorder, countsVP, bottom=data_stack[1], yerr=errorFF)
a23=ax3.bar(xorder, countsVP, bottom=data_stack[1], yerr=errorFF)
ax1.xaxis.set_ticks_position('none')
ax2.xaxis.set_ticks_position('none')
ax1.spines['bottom'].set_visible(False)
ax2.spines['top'].set_visible(False)
ax2.spines['bottom'].set_visible(False)
ax3.spines['top'].set_visible(False)
dslant = .3
kwargs = dict(marker=[(-1, -dslant), (1, dslant)], markersize=12,
linestyle="none", color='k', mec='k', mew=1, clip_on=False)
ax1.plot([0, 1], [0, 0], transform=ax1.transAxes, **kwargs)
ax2.plot([0, 1], [1, 1], transform=ax2.transAxes, **kwargs)
ax2.plot([0, 1], [0, 0], transform=ax2.transAxes, **kwargs)
ax3.plot([0, 1], [1, 1], transform=ax3.transAxes, **kwargs)
ax3.axhline(0, color='black', linewidth=0.2, zorder=1)
ax1.legend((a11[0], a21[0]), ('{\\rm photonic}', '{\\rm fermionic}'),loc='upper right')
xorder = [
'$\sigma_0^{\\infty}$', '$\sigma_0^{71}$',
'$\sigma^{(1)\\infty}_e$', '$\sigma^{(1)71}_e$', '$\sigma^{(1)\\infty}_x$', '$\sigma^{(1)71}_x$', '$\sigma^{(1)\\infty}_p$',
'$\sigma^{(2)\\infty}_e$', '$\sigma^{(2)71}_e$', '$\sigma^{(2)\\infty}_x$', '$\sigma^{(2)\\infty}_p$'
]
$\bullet$ S0
In [12]:
fig, (ax1, ax2, ax3) = subplots(
3, 1,
sharex=True,
gridspec_kw={'hspace': 0.03, 'height_ratios':[.5,.7,1]}
)
countsPH = [
lo0['value'][0], lo071['value'][0],
nloEPHm0['value'][0], nloFPHp0L71['value'][0], nloXPHp0[0], nloYPHp0L71['value'][0], nloMPHm0['value'][0],
nnloEPHm0['value'][0], nnloFPHp0L71['value'][0], nnloYPHp0[0], nnloMPHm0['value'][0]
]
countsVP = [
0., 0.,
nloEVPm0['value'][0], nloFVPp0L71['value'][0], 0., 0., 0.,
nnloEVPm0['value'][0], nnloFVPp0L71['value'][0], nnloXVPp0[0], nnloMVPm0['value'][0]
]
errorFF = [
0., abs(lo086['value'][0]-lo060['value'][0]),
0., np.sqrt((nloFPHp0L86['value'][0]-nloFPHp0L60['value'][0])**2+(nloFVPp0L86['value'][0]-nloFVPp0L60['value'][0])**2),
0., abs(nloYPHp0L86['value'][0]-nloYPHp0L60['value'][0]), 0., 0., 0., 0., 0.
]
stack = cumulate(countsPH, countsVP, errorFF)
barplot(xorder, countsPH, countsVP, stack, errorFF)
ax1.set_title('$e^-p \quad/ {\\rm\\upmu b}\quad [{\\tt S0}]$')
ax1.set_ylim(29., 42.)
ax2.set_ylim(.76, 6.99)
ax3.set_ylim(-0.02, 0.21)
draw()
mulify(fig, delx=3.8, dely=2.2)
fig.savefig("plots/xsec-ep-0.pdf")
$\bullet$ S1
In [13]:
fig, (ax1, ax2, ax3) = subplots(
3, 1,
sharex=True,
gridspec_kw={'hspace': 0.03, 'height_ratios':[.5,.7,1]}
)
countsPH = [
lo0['value'][0], lo071['value'][0],
nloEPHm1['value'][0],nloFPHp1L71['value'][0], nloXPHp1[0],nloYPHp1L71['value'][0], nloMPHm1['value'][0],
nnloEPHm1['value'][0],nnloFPHp1L71['value'][0], nnloYPHp1[0], nnloMPHm1['value'][0]
]
countsVP = [
0., 0.,
nloEVPm1['value'][0],nloFVPp1L71['value'][0], 0., 0., 0.,
nnloEVPm1['value'][0],nnloFVPp1L71['value'][0], nnloXVPp1[0], nnloMVPm1['value'][0]
]
errorFF = [
0., abs(lo086['value'][0]-lo060['value'][0]),
0., np.sqrt((nloFPHp1L86['value'][0]-nloFPHp1L60['value'][0])**2+(nloFVPp1L86['value'][0]-nloFVPp1L60['value'][0])**2),
0., abs(nloYPHp1L86['value'][0]-nloYPHp1L60['value'][0]), 0., 0., 0., 0., 0.
]
stack = cumulate(countsPH, countsVP, errorFF)
barplot(xorder, countsPH, countsVP, stack, errorFF)
ax1.set_ylim(29., 42.)
ax2.set_ylim(.76, 6.99)
ax3.set_ylim(-0.02, 0.21)
ax1.set_title('$e^-p \quad/ {\\rm\\upmu b}\quad [{\\tt S1}]$')
draw()
mulify(fig, delx=3.8, dely=2.2)
fig.savefig("plots/xsec-ep-1.pdf")
Differential distributions $-$ $Q^2$¶
In [14]:
def ebandr0ls(var1, var2, var3, var4, var5, var6, var7, var8, var9, var10, var11, var12, var0, msc, *args, **kwargs):
nlol = addplots(var9['qsql'],addplots(var10['qsql'],addplots(var11['qsql'],var12['qsql'])))
nnlol = addplots(var1['qsql'],
addplots(scaleplot(var2['qsql'],1.,-1.),addplots(var3['qsql'],addplots(scaleplot(var4['qsql'],1.,-1.),
addplots(var5['qsql'],
addplots(var6['qsql'],addplots(scaleplot(var7['qsql'],1.,-1.),var8['qsql'])))))))
errorband(mergebins(scaleplot(divideplots(
addplots(nnlol,nlol), var0['qsql']),1e6,1.), msc), *args, **kwargs)
def ebandr0ps(var1, var2, var3, var4, var5, var6, var7, var8, var9, var10, var11, var12, var0, msc, *args, **kwargs):
nlop = addplots(var9['qsqp'],addplots(var10['qsqp'],addplots(var11['qsqp'],var12['qsqp'])))
nnlop = addplots(var1['qsqp'],
addplots(scaleplot(var2['qsqp'],1.,-1.),addplots(var3['qsqp'],addplots(scaleplot(var4['qsqp'],1.,-1.),
addplots(var5['qsqp'],
addplots(var6['qsqp'],addplots(scaleplot(var7['qsqp'],1.,-1.),var8['qsqp'])))))))
errorband(mergebins(scaleplot(divideplots(
addplots(nnlop,nlop), var0['qsqp']),1e6,1.), msc), *args, **kwargs)
$\bullet$ S0
In [15]:
fig, axs = plt.subplots(
1, sharex=True, gridspec_kw={'hspace': 0, 'height_ratios':[1]},
)
sca(axs)
mmsc=5
ebandr0ls(nnloEPHm0,nnloX31PHm0,nnloX22PHm0,nnloX13PHm0,nnloMPHm0,nnloEVPm0,nnloXVPm0,nnloMVPm0,
nloFPHp0L71,nloFVPp0L71,nloYPHp0L71,nloMPHm0,
lo071, mmsc, col='blue',linestyle='--')
ebandr0ps(nnloEPHm0,nnloX31PHm0,nnloX22PHm0,nnloX13PHm0,nnloMPHm0,nnloEVPm0,nnloXVPm0,nnloMVPm0,
nloFPHp0L71,nloFVPp0L71,nloYPHp0L71,nloMPHm0,
lo071, mmsc, col='red',linestyle='--')
ebandr0ls(nnloEPHm1,nnloX31PHm1,nnloX22PHm1,nnloX13PHm1,nnloMPHm1,nnloEVPm1,nnloXVPm1,nnloMVPm1,
nloFPHp1L71,nloFVPp1L71,nloYPHp1L71,nloMPHm1,
lo071, mmsc, col='cyan',linestyle=':')
ebandr0ps(nnloEPHm1,nnloX31PHm1,nnloX22PHm1,nnloX13PHm1,nnloMPHm1,nnloEVPm1,nnloXVPm1,nnloMVPm1,
nloFPHp1L71,nloFVPp1L71,nloYPHp1L71,nloMPHm1,
lo071, mmsc, col='orange',linestyle=':')
axs.set_title('$e^-p \quad [{\\tt S0, S1}]$')
axs.legend([
r'$[{\tt S0}]\,\, (Q^2_e)$',
r'$[{\tt S0}]\,\, (Q^2_p)$',
r'$[{\tt S1}]\,\, (Q^2_e)$',
r'$[{\tt S1}]\,\, (Q^2_p)$',
], ncol=2, loc='lower center',framealpha=0)
xlabel(r'$Q^2_e\,{\rm or}\,Q^2_p\,/\,{\rm GeV}^2$')
ylabel(r'$\frac{\sigma^{(1)\,71}+\sigma^{(2)\infty}}{\sigma_0^{71}}$')
xlim(8.e-3, 8.e-2)
draw()
fig.tight_layout()
mulify(fig, delx=4.2, dely=-0.1)
fig.savefig("plots/qsql-e-S0S1-2-diff.pdf", bbox_inches='tight')
Differential distributions $-$ $\theta_e$¶
In [16]:
def diffset(a,b):
return addsets([a, scaleset(b,-1)])
def eband(var, msc, *args, **kwargs):
errorband(mergebins(var['thetal'], msc), *args, **kwargs)
def ebanda(var, msc, *args, **kwargs):
errorband(mergebins(abs(var['thetal']), msc), *args, **kwargs)
def ebandp(var, msc, *args, **kwargs):
errorband(mergebins(abs(scaleplot(var['thetal'],2.)), msc), *args, **kwargs)
$\bullet$ S0
In [17]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
nloXPHp0 = scaleset(nloXPHm0,-1)
eband(lo0,mmsc,col='slategray')
eband(addsets([nloEPHm0, nloEVPm0]),mmsc,col='gold')
eband(nloXPHp0,mmsc,col='green')
eband(diffset(lo0, lo071),mmsc,col='tab:red')
ebanda(nnloEPHm0,mmsc,linestyle='--',col='cyan')
ebanda(nnloEVPm0,mmsc,linestyle=':',col='darkcyan')
eband(diffset(nnloX22PHm0, addsets([nnloX31PHm0, nnloX13PHm0])),mmsc)
eband(diffset(nloXPHp0, nloYPHp0L71),mmsc, col='pink')
axs.set_title('$e^-p \quad [{\\tt S0}]$')
axs.legend([
r'$\sigma_0^\infty$', r'$\sigma^{(1)\infty}_e+\sigma^{(1)\infty}_\Pi$', r'$\sigma^{(1)\infty}_x$', r'$\sigma_0^\infty-\sigma_0^{71}$',
r'$|\sigma^{(2)\infty}_e|$', r'$\sigma^{(2)\infty}_{e\Pi}$', r'$\sigma^{(2)\infty}_x$', r'$\sigma^{(1)\infty}_x-\sigma^{(1)71}_x$'
], ncol=2, loc='upper right',framealpha=0)
xlabel(r'$\theta_e\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 9.e1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/the-S0-diff.pdf")
$\bullet$ S0 ($e^-$ and $e^+$)
In [18]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
nloYPHp0L71 = scaleset(nloXPHm0,-1)
ebandp(nloYPHp0L71,mmsc)
ebandp(addsets([nnloX31PHm0, nnloX13PHm0, nnloXVPm0]),mmsc)
axs.set_title('$e^-p - e^+p \quad [{\\tt S0}]$')
axs.legend([
r'$\sigma^{(1)\,71}_x$', r'$\sigma^{(2)\infty}_x+\sigma^{(2)\infty}_{x\Pi}$'
], ncol=1, loc='upper right',framealpha=0)
xlabel(r'$\theta_e\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 2.e-1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/the-S0-diff-x.pdf")
$\bullet$ S1
In [19]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
nloXPHp1 = scaleset(nloXPHm1,-1)
eband(lo0,mmsc,col='slategray')
eband(addsets([nloEPHm1, nloEVPm1]),mmsc,col='gold')
eband(nloXPHp1,mmsc,col='green')
eband(diffset(lo0, lo071),mmsc,col='tab:red')
ebanda(nnloEPHm1,mmsc,linestyle='--',col='cyan')
ebanda(nnloEVPm1,mmsc,linestyle=':',col='darkcyan')
eband(diffset(nnloX22PHm1, addsets([nnloX31PHm1, nnloX13PHm1])),mmsc)
eband(diffset(nloXPHp1, nloYPHp1L71),mmsc, col='pink')
axs.set_title('$e^-p \quad [{\\tt S1}]$')
axs.legend([
r'$\sigma_0^\infty$', r'$\sigma^{(1)\infty}_e+\sigma^{(1)\infty}_\Pi$', r'$\sigma^{(1)\infty}_x$', r'$\sigma_0^\infty-\sigma_0^{71}$',
r'$|\sigma^{(2)\infty}_e|$', r'$\sigma^{(2)\infty}_{e\Pi}$', r'$\sigma^{(2)\infty}_x$', r'$\sigma^{(1)\infty}_x-\sigma^{(1)71}_x$'
], ncol=2, loc='upper right',framealpha=0)
xlabel(r'$\theta_e\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 9.e1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/the-S1-diff.pdf")
$\bullet$ S1 ($e^-$ and $e^+$)
In [20]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
nloXPHp0 = scaleset(nloXPHm0,-1)
ebandp(nloYPHp1L71,mmsc)
ebandp(addsets([nnloX31PHm1, nnloX13PHm1, nnloXVPm1]),mmsc)
axs.set_title('$e^-p - e^+p \quad [{\\tt S1}]$')
axs.legend([
r'$\sigma^{(1)\,71}_x$', r'$\sigma^{(2)\infty}_x+\sigma^{(2)\infty}_{x\Pi}$'
], ncol=1, loc='upper right',framealpha=0)
xlabel(r'$\theta_e\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_e\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 2.e-1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/the-S1-diff-x.pdf")
$\mu^\pm p \to \mu^\pm p$¶
$\bullet$ pure QED
In [21]:
setup(folder='lp2lp_tpe_paper/out-muse-m-qed.tar.bz2')
setup(obs='0')
Mlo0 = scaleset(mergefks(sigma('em2em0')), alpha**2*conv)
MnloEPHm0 = scaleset(mergefks(sigma('em2emFEE'),sigma('em2emREE15'),sigma('em2emREE35')), alpha**3*conv)
MnloEVPm0 = scaleset(mergefks(sigma('em2emA')), alpha**3*conv)
MnloXPHm0 = scaleset(mergefks(sigma('em2emFEM'),sigma('em2emREM')), alpha**3*conv)
MnloMPHm0 = scaleset(mergefks(sigma('em2emFMM'),sigma('em2emRMM')), alpha**3*conv)
MnnloEPHm0 = scaleset(mergefks(sigma('em2emFFEEEE',obs='1'),sigma('em2emRFEEEE15'),sigma('em2emRFEEEE35'),sigma('em2emRREEEE1516'),sigma('em2emRREEEE3536')), alpha**4*conv)
MnnloX31PHm0 = scaleset(mergefks(sigma('em2emFF31z',obs='1'),sigma('em2emRF3115'),sigma('em2emRF3135'),sigma('em2emRR311516'),sigma('em2emRR313536')), alpha**4*conv)
MnnloX22PHm0 = scaleset(mergefks(sigma('em2emFF22z',obs='1'),sigma('em2emRF2215'),sigma('em2emRF2235'),sigma('em2emRR221516'),sigma('em2emRR223536')), alpha**4*conv)
MnnloX13PHm0 = scaleset(mergefks(sigma('em2emFF13z',obs='1'),sigma('em2emRF1315'),sigma('em2emRF1335'),sigma('em2emRR131516'),sigma('em2emRR133536')), alpha**4*conv)
MnnloMPHm0 = scaleset(mergefks(sigma('em2emFFMMMM',obs='1'),sigma('em2emRFMMMM'),sigma('em2emRRMMMM')), alpha**4*conv)
MnnloEVPm0 = scaleset(mergefks(sigma('em2emAFEE'), sigma('em2emAREE15'), sigma('em2emAREE35'),
anyxi1=sigma('em2emAA'), anyxi2=sigma('em2emNFEE')), alpha**4*conv)
MnnloXVPm0 = scaleset(mergefks(sigma('em2emAFEM'), sigma('em2emAREM'),anyxi1=sigma('em2emNFEM',obs='0')), alpha**4*conv)
MnnloMVPm0 = scaleset(mergefks(sigma('em2emAFMM'), sigma('em2emARMM'),anyxi1=sigma('em2emNFMM',obs='0')), alpha**4*conv)
setup(obs='1')
Mlo1 = scaleset(mergefks(sigma('em2em0',obs='0')), alpha**2*conv)
MnloEPHm1 = scaleset(mergefks(sigma('em2emFEE',obs='0'),sigma('em2emREE15'),sigma('em2emREE35')), alpha**3*conv)
MnloEVPm1 = scaleset(mergefks(sigma('em2emA',obs='0')), alpha**3*conv)
MnloXPHm1 = scaleset(mergefks(sigma('em2emFEM',obs='0'),sigma('em2emREM')), alpha**3*conv)
MnloMPHm1 = scaleset(mergefks(sigma('em2emFMM',obs='0'),sigma('em2emRMM')), alpha**3*conv)
MnnloEPHm1 = scaleset(mergefks(sigma('em2emFFEEEE'),sigma('em2emRFEEEE15'),sigma('em2emRFEEEE35'),sigma('em2emRREEEE1516'),sigma('em2emRREEEE3536')), alpha**4*conv)
MnnloX31PHm1 = scaleset(mergefks(sigma('em2emFF31z'),sigma('em2emRF3115'),sigma('em2emRF3135'),sigma('em2emRR311516'),sigma('em2emRR313536')), alpha**4*conv)
MnnloX22PHm1 = scaleset(mergefks(sigma('em2emFF22z'),sigma('em2emRF2215'),sigma('em2emRF2235'),sigma('em2emRR221516'),sigma('em2emRR223536')), alpha**4*conv)
MnnloX13PHm1 = scaleset(mergefks(sigma('em2emFF13z'),sigma('em2emRF1315'),sigma('em2emRF1335'),sigma('em2emRR131516'),sigma('em2emRR133536')), alpha**4*conv)
MnnloMPHm1 = scaleset(mergefks(sigma('em2emFFMMMM'),sigma('em2emRFMMMM'),sigma('em2emRRMMMM')), alpha**4*conv)
MnnloEVPm1 = scaleset(mergefks(sigma('em2emAFEE',obs='0'), sigma('em2emAREE15'), sigma('em2emAREE35'),
anyxi1=sigma('em2emAA',obs='0'), anyxi2=sigma('em2emNFEE',obs='0')), alpha**4*conv)
MnnloXVPm1 = scaleset(mergefks(sigma('em2emAFEM',obs='0'), sigma('em2emAREM'),anyxi1=sigma('em2emNFEM',obs='0')), alpha**4*conv)
MnnloMVPm1 = scaleset(mergefks(sigma('em2emAFMM',obs='0'), sigma('em2emARMM'),anyxi1=sigma('em2emNFMM',obs='0')), alpha**4*conv)
$\bullet$ $\Lambda^2=0.86$ GeV^2
In [22]:
setup(folder='lp2lp_tpe_paper/out-muse-m-86.tar.bz2')
setup(obs='0')
Mlo086 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
MnloFPHp0L86 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloFVPp0L86 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
MnloYPHp0L86 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
setup(obs='1')
MnloFVPp1L86 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
MnloFPHp1L86 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloYPHp1L86 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
$\bullet$ $\Lambda^2=0.71$ GeV^2
In [23]:
setup(folder='lp2lp_tpe_paper/out-muse-m-71.tar.bz2')
setup(obs='0')
Mlo071 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
MnloFPHp0L71 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloFVPp0L71 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
MnloYPHp0L71 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
MnnloFPHp0L71 = scaleset(mergefks(sigma('mp2mpFF'),sigma('mp2mpRF15'),sigma('mp2mpRF35'),sigma('mp2mpRR1516'),sigma('mp2mpRR3536')), alpha**4*conv)
MnnloFVPp0L71 = scaleset(mergefks(sigma('mp2mpAF'), sigma('mp2mpAR15'), sigma('mp2mpAR35'),
anyxi1=sigma('mp2mpAA'), anyxi2=sigma('mp2mpNF')), alpha**4*conv)
setup(obs='1')
MnloFPHp1L71 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloFVPp1L71 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
MnloYPHp1L71 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
MnnloFPHp1L71 = scaleset(mergefks(sigma('mp2mpFF',obs='0'),sigma('mp2mpRF15'),sigma('mp2mpRF35'),sigma('mp2mpRR1516'),sigma('mp2mpRR3536')), alpha**4*conv)
MnnloFVPp1L71 = scaleset(mergefks(sigma('mp2mpAF',obs='0'), sigma('mp2mpAR15'), sigma('mp2mpAR35'),
anyxi1=sigma('mp2mpAA',obs='0'), anyxi2=sigma('mp2mpNF',obs='0')), alpha**4*conv)
$\bullet$ $\Lambda^2=0.66$ GeV^2
In [24]:
setup(folder='lp2lp_tpe_paper/out-muse-m-66.tar.bz2')
setup(obs='0')
Mlo066 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
MnloFPHp0L66 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloFVPp0L66 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
MnloYPHp0L66 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
setup(obs='1')
MnloFVPp1L66 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
MnloFPHp1L66 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloYPHp1L66 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
$\bullet$ $\Lambda^2=0.60$ GeV^2
In [25]:
setup(folder='lp2lp_tpe_paper/out-muse-m-60.tar.bz2')
setup(obs='0')
Mlo060 = scaleset(mergefks(sigma('mp2mp0')), alpha**2*conv)
MnloFPHp0L60 = scaleset(mergefks(sigma('mp2mpF'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloFVPp0L60 = scaleset(mergefks(sigma('mp2mpA')), alpha**3*conv)
MnloYPHp0L60 = scaleset(mergefks(sigma('mp2mpFMP'),sigma('mp2mpRMP')), alpha**3*conv)
setup(obs='1')
MnloFVPp1L60 = scaleset(mergefks(sigma('mp2mpA',obs='0')), alpha**3*conv)
MnloFPHp1L60 = scaleset(mergefks(sigma('mp2mpF',obs='0'),sigma('mp2mpR15'),sigma('mp2mpR35')), alpha**3*conv)
MnloYPHp1L60 = scaleset(mergefks(sigma('mp2mpFMP',obs='0'),sigma('mp2mpRMP')), alpha**3*conv)
Total cross sections ($\mu$b)¶
$\bullet$ S0
In [26]:
Mlo00 = Mlo0['value']
Mlo86 = Mlo086['value']
Mlo71 = Mlo071['value']
Mlo66 = Mlo066['value']
Mlo60 = Mlo060['value']
MnloXPHp0 = tn(MnloXPHm0['value'], [-1., 0])
MnloYPHm0L86 = tn(MnloYPHp0L86['value'], [-1., 0])
MnloYPHm0L71 = tn(MnloYPHp0L71['value'], [-1., 0])
MnloYPHm0L60 = tn(MnloYPHp0L60['value'], [-1., 0])
MnloYPHm0L66 = tn(MnloYPHp0L66['value'], [-1., 0])
Mnlom0 = plusnumbers(MnloEPHm0['value'], MnloEVPm0['value'], MnloXPHm0['value'], MnloMPHm0['value'], Mlo00)
Mnlop0 = plusnumbers(MnloEPHm0['value'], MnloEVPm0['value'], -MnloXPHm0['value'], MnloMPHm0['value'], Mlo00)
Mnlom071 = plusnumbers(MnloFPHp0L71['value'], MnloFVPp0L71['value'], -MnloYPHp0L71['value'], MnloMPHm0['value'], Mlo71)
Mnlop071 = plusnumbers(MnloFPHp0L71['value'], MnloFVPp0L71['value'], MnloYPHp0L71['value'], MnloMPHm0['value'], Mlo71)
MnnloYPHm0 = plusnumbers( MnnloX31PHm0['value'], MnnloX22PHm0['value'], MnnloX13PHm0['value'])
MnnloYPHp0 = plusnumbers(-MnnloX31PHm0['value'], MnnloX22PHm0['value'], -MnnloX13PHm0['value'])
MnnloXVPp0 = tn(MnnloXVPm0['value'], [-1., 0])
Mnnlom0 = plusnumbers(MnnloEPHm0['value'], MnnloYPHm0, MnnloMPHm0['value'], Mnlom0)
Mnnlop0 = plusnumbers(MnnloEPHm0['value'], MnnloYPHp0, MnnloMPHm0['value'], Mnlop0)
print("")
tabM0 = [
["\sigma_0", pn(Mlo0['value']), pn(Mlo0['value'])],
["\sigma_0_86", pn(Mlo086['value']), pn(Mlo086['value'])],
["\sigma_0_71", pn(Mlo071['value']), pn(Mlo071['value'])],
["\sigma_0_66", pn(Mlo066['value']), pn(Mlo066['value'])],
["\sigma_0_60", pn(Mlo060['value']), pn(Mlo060['value'])],
SEPARATING_LINE,
["\sigma^{(1)}_m", pn(MnloEPHm0['value']), pn(MnloEPHm0['value']), pn(dn(MnloEPHm0['value'],Mlo00)*100.), pn(dn(MnloEPHm0['value'],Mlo00)*100.)],
["\sigma^{(1)}_mF", pn(MnloEVPm0['value']), pn(MnloEVPm0['value']), pn(dn(MnloEVPm0['value'],Mlo00)*100.), pn(dn(MnloEVPm0['value'],Mlo00)*100.)],
["\sigma^{(1)}_m86", pn(MnloFPHp0L86['value']), pn(MnloFPHp0L86['value']), pn(dn(MnloFPHp0L86['value'],Mlo86)*100.), pn(dn(MnloFPHp0L86['value'],Mlo86)*100.)],
["\sigma^{(1)}_mF86", pn(MnloFVPp0L86['value']), pn(MnloFVPp0L86['value']), pn(dn(MnloFVPp0L86['value'],Mlo86)*100.), pn(dn(MnloFVPp0L86['value'],Mlo86)*100.)],
["\sigma^{(1)}_m71", pn(MnloFPHp0L71['value']), pn(MnloFPHp0L71['value']), pn(dn(MnloFPHp0L71['value'],Mlo71)*100.), pn(dn(MnloFPHp0L71['value'],Mlo71)*100.)],
["\sigma^{(1)}_mF71", pn(MnloFVPp0L71['value']), pn(MnloFVPp0L71['value']), pn(dn(MnloFVPp0L71['value'],Mlo71)*100.), pn(dn(MnloFVPp0L71['value'],Mlo71)*100.)],
["\sigma^{(1)}_m66", pn(MnloFPHp0L66['value']), pn(MnloFPHp0L66['value']), pn(dn(MnloFPHp0L66['value'],Mlo66)*100.), pn(dn(MnloFPHp0L66['value'],Mlo66)*100.)],
["\sigma^{(1)}_mF66", pn(MnloFVPp0L66['value']), pn(MnloFVPp0L66['value']), pn(dn(MnloFVPp0L66['value'],Mlo66)*100.), pn(dn(MnloFVPp0L66['value'],Mlo66)*100.)],
["\sigma^{(1)}_m60", pn(MnloFPHp0L60['value']), pn(MnloFPHp0L60['value']), pn(dn(MnloFPHp0L60['value'],Mlo60)*100.), pn(dn(MnloFPHp0L60['value'],Mlo60)*100.)],
["\sigma^{(1)}_mF60", pn(MnloFVPp0L60['value']), pn(MnloFVPp0L60['value']), pn(dn(MnloFVPp0L60['value'],Mlo60)*100.), pn(dn(MnloFVPp0L60['value'],Mlo60)*100.)],
["\sigma^{(1)}_x", pn(MnloXPHm0['value']), pn(MnloXPHp0), pn(dn(MnloXPHm0['value'],Mlo00)*100.), pn(dn(MnloXPHp0,Mlo00)*100.)],
["\sigma^{(1)}_x86", pn(MnloYPHm0L86), pn(MnloYPHp0L86['value']), pn(dn(MnloYPHm0L86,Mlo86)*100.), pn(dn(MnloYPHp0L86['value'],Mlo86)*100.)],
["\sigma^{(1)}_x71", pn(MnloYPHm0L71), pn(MnloYPHp0L71['value']), pn(dn(MnloYPHm0L71,Mlo71)*100.), pn(dn(MnloYPHp0L71['value'],Mlo71)*100.)],
["\sigma^{(1)}_x66", pn(MnloYPHm0L66), pn(MnloYPHp0L66['value']), pn(dn(MnloYPHm0L66,Mlo66)*100.), pn(dn(MnloYPHp0L66['value'],Mlo66)*100.)],
["\sigma^{(1)}_x60", pn(MnloYPHm0L60), pn(MnloYPHp0L60['value']), pn(dn(MnloYPHm0L60,Mlo60)*100.), pn(dn(MnloYPHp0L60['value'],Mlo60)*100.)],
["\sigma^{(1)}_p", pn(MnloMPHm0['value']), pn(MnloMPHm0['value']), pn(dn(MnloMPHm0['value'],Mlo00)*100.), pn(dn(MnloMPHm0['value'],Mlo00)*100.)],
SEPARATING_LINE,
["\sigma^{(2)}_m", pn(MnnloEPHm0['value']), pn(MnnloEPHm0['value']), pn(dn(MnnloEPHm0['value'],Mnlom0)*100.), pn(dn(MnnloEPHm0['value'],Mnlop0)*100.)],
["\sigma^{(2)}_mF", pn(MnnloEVPm0['value']), pn(MnnloEVPm0['value']), pn(dn(MnnloEVPm0['value'],Mnlom0)*100.), pn(dn(MnnloEVPm0['value'],Mnlop0)*100.)],
["\sigma^{(2)}_m71", pn(MnnloFPHp0L71['value']), pn(MnnloFPHp0L71['value']), pn(dn(MnnloFPHp0L71['value'],Mnlom071)*100.), pn(dn(MnnloFPHp0L71['value'],Mnlop071)*100.)],
["\sigma^{(2)}_mF71", pn(MnnloFVPp0L71['value']), pn(MnnloFVPp0L71['value']), pn(dn(MnnloFVPp0L71['value'],Mnlom071)*100.), pn(dn(MnnloFVPp0L71['value'],Mnlop071)*100.)],
["\sigma^{(2)}_x", pn(MnnloYPHm0), pn(MnnloYPHp0), pn(dn(MnnloYPHm0,Mnlom0)*100.), pn(dn(MnnloYPHp0,Mnlop0)*100.)],
["\sigma^{(2)}_xF", pn(MnnloXVPm0['value']), pn(MnnloXVPp0), pn(dn(MnnloXVPm0['value'],Mnlom0)*100.), pn(dn(MnnloXVPp0,Mnlop0)*100.)],
["\sigma^{(2)}_p", pn(MnnloMPHm0['value']), pn(MnnloMPHm0['value']), pn(dn(MnnloMPHm0['value'],Mnlom0)*100.), pn(dn(MnnloMPHm0['value'],Mnlop0)*100.)],
["\sigma^{(2)}_pF", pn(MnnloMVPm0['value']), pn(MnnloMVPm0['value']), pn(dn(MnnloMVPm0['value'],Mnlom0)*100.), pn(dn(MnnloMVPm0['value'],Mnlop0)*100.)],
SEPARATING_LINE
]
print(tabulate(tabM0, headers=["MUSE_m 210 [0]","m+p", "m-p", "dK+%", "dK-%"]))
$\bullet$ S1
In [27]:
MnloXPHp1 = tn(MnloXPHm1['value'], [-1., 0])
MnloYPHm1L86 = tn(MnloYPHp1L86['value'], [-1., 0])
MnloYPHm1L71 = tn(MnloYPHp1L71['value'], [-1., 0])
MnloYPHm1L60 = tn(MnloYPHp1L60['value'], [-1., 0])
MnloYPHm1L66 = tn(MnloYPHp1L66['value'], [-1., 0])
Mnlom1 = plusnumbers(MnloEPHm1['value'], MnloEVPm1['value'], MnloXPHm1['value'], MnloMPHm1['value'], Mlo00)
Mnlop1 = plusnumbers(MnloEPHm1['value'], MnloEVPm1['value'], -MnloXPHm1['value'], MnloMPHm1['value'], Mlo00)
Mnlom171 = plusnumbers(MnloFPHp1L71['value'], MnloFVPp1L71['value'], -MnloYPHp1L71['value'], MnloMPHm1['value'], Mlo71)
Mnlop171 = plusnumbers(MnloFPHp1L71['value'], MnloFVPp1L71['value'], MnloYPHp1L71['value'], MnloMPHm1['value'], Mlo71)
MnnloYPHm1 = plusnumbers( MnnloX31PHm1['value'], MnnloX22PHm1['value'], MnnloX13PHm1['value'])
MnnloYPHp1 = plusnumbers(-MnnloX31PHm1['value'], MnnloX22PHm1['value'], -MnnloX13PHm1['value'])
MnnloXVPp1 = tn(MnnloXVPm1['value'], [-1., 0])
Mnnlom1 = plusnumbers(MnnloEPHm1['value'], MnnloYPHm1, MnnloMPHm1['value'], Mnlom1)
Mnnlop1 = plusnumbers(MnnloEPHm1['value'], MnnloYPHp1, MnnloMPHm1['value'], Mnlop1)
print("")
tabM1 = [
["\sigma_0", pn(Mlo0['value']), pn(Mlo0['value'])],
["\sigma_0_86", pn(Mlo086['value']), pn(Mlo086['value'])],
["\sigma_0_71", pn(Mlo071['value']), pn(Mlo071['value'])],
["\sigma_0_66", pn(Mlo066['value']), pn(Mlo066['value'])],
["\sigma_0_60", pn(Mlo060['value']), pn(Mlo060['value'])],
SEPARATING_LINE,
["\sigma^{(1)}_m", pn(MnloEPHm1['value']), pn(MnloEPHm1['value']), pn(dn(MnloEPHm1['value'],Mlo00)*100.), pn(dn(MnloEPHm1['value'],Mlo00)*100.)],
["\sigma^{(1)}_mF", pn(MnloEVPm1['value']), pn(MnloEVPm1['value']), pn(dn(MnloEVPm1['value'],Mlo00)*100.), pn(dn(MnloEVPm1['value'],Mlo00)*100.)],
["\sigma^{(1)}_m86", pn(MnloFPHp1L86['value']), pn(MnloFPHp1L86['value']), pn(dn(MnloFPHp1L86['value'],Mlo86)*100.), pn(dn(MnloFPHp1L86['value'],Mlo86)*100.)],
["\sigma^{(1)}_mF86", pn(MnloFVPp1L86['value']), pn(MnloFVPp1L86['value']), pn(dn(MnloFVPp1L86['value'],Mlo86)*100.), pn(dn(MnloFVPp1L86['value'],Mlo86)*100.)],
["\sigma^{(1)}_m71", pn(MnloFPHp1L71['value']), pn(MnloFPHp1L71['value']), pn(dn(MnloFPHp1L71['value'],Mlo71)*100.), pn(dn(MnloFPHp1L71['value'],Mlo71)*100.)],
["\sigma^{(1)}_mF71", pn(MnloFVPp1L71['value']), pn(MnloFVPp1L71['value']), pn(dn(MnloFVPp1L71['value'],Mlo71)*100.), pn(dn(MnloFVPp1L71['value'],Mlo71)*100.)],
["\sigma^{(1)}_m66", pn(MnloFPHp1L66['value']), pn(MnloFPHp1L66['value']), pn(dn(MnloFPHp1L66['value'],Mlo66)*100.), pn(dn(MnloFPHp1L66['value'],Mlo66)*100.)],
["\sigma^{(1)}_mF66", pn(MnloFVPp1L66['value']), pn(MnloFVPp1L66['value']), pn(dn(MnloFVPp1L66['value'],Mlo66)*100.), pn(dn(MnloFVPp1L66['value'],Mlo66)*100.)],
["\sigma^{(1)}_m60", pn(MnloFPHp1L60['value']), pn(MnloFPHp1L60['value']), pn(dn(MnloFPHp1L60['value'],Mlo60)*100.), pn(dn(MnloFPHp1L60['value'],Mlo60)*100.)],
["\sigma^{(1)}_mF60", pn(MnloFVPp1L60['value']), pn(MnloFVPp1L60['value']), pn(dn(MnloFVPp1L60['value'],Mlo60)*100.), pn(dn(MnloFVPp1L60['value'],Mlo60)*100.)],
["\sigma^{(1)}_x", pn(MnloXPHm1['value']), pn(MnloXPHp1), pn(dn(MnloXPHm1['value'],Mlo00)*100.), pn(dn(MnloXPHp1,Mlo00)*100.)],
["\sigma^{(1)}_x86", pn(MnloYPHm1L86), pn(MnloYPHp1L86['value']), pn(dn(MnloYPHm1L86,Mlo86)*100.), pn(dn(MnloYPHp1L86['value'],Mlo86)*100.)],
["\sigma^{(1)}_x71", pn(MnloYPHm1L71), pn(MnloYPHp1L71['value']), pn(dn(MnloYPHm1L71,Mlo71)*100.), pn(dn(MnloYPHp1L71['value'],Mlo71)*100.)],
["\sigma^{(1)}_x66", pn(MnloYPHm1L66), pn(MnloYPHp1L66['value']), pn(dn(MnloYPHm1L66,Mlo66)*100.), pn(dn(MnloYPHp1L66['value'],Mlo66)*100.)],
["\sigma^{(1)}_x60", pn(MnloYPHm1L60), pn(MnloYPHp1L60['value']), pn(dn(MnloYPHm1L60,Mlo60)*100.), pn(dn(MnloYPHp1L60['value'],Mlo60)*100.)],
["\sigma^{(1)}_p", pn(MnloMPHm1['value']), pn(MnloMPHm1['value']), pn(dn(MnloMPHm1['value'],Mlo00)*100.), pn(dn(MnloMPHm1['value'],Mlo00)*100.)],
SEPARATING_LINE,
["\sigma^{(2)}_m", pn(MnnloEPHm1['value']), pn(MnnloEPHm1['value']), pn(dn(MnnloEPHm1['value'],Mnlom1)*100.), pn(dn(MnnloEPHm1['value'],Mnlop1)*100.)],
["\sigma^{(2)}_mF", pn(MnnloEVPm1['value']), pn(MnnloEVPm1['value']), pn(dn(MnnloEVPm1['value'],Mnlom1)*100.), pn(dn(MnnloEVPm1['value'],Mnlop1)*100.)],
["\sigma^{(2)}_m71", pn(MnnloFPHp1L71['value']), pn(MnnloFPHp1L71['value']), pn(dn(MnnloFPHp1L71['value'],Mnlom171)*100.), pn(dn(MnnloFPHp1L71['value'],Mnlop171)*100.)],
["\sigma^{(2)}_mF71", pn(MnnloFVPp1L71['value']), pn(MnnloFVPp1L71['value']), pn(dn(MnnloFVPp1L71['value'],Mnlom171)*100.), pn(dn(MnnloFVPp1L71['value'],Mnlop171)*100.)],
["\sigma^{(2)}_x", pn(MnnloYPHm1), pn(MnnloYPHp1), pn(dn(MnnloYPHm1,Mnlom1)*100.), pn(dn(MnnloYPHp1,Mnlop1)*100.)],
["\sigma^{(2)}_xF", pn(MnnloXVPm1['value']), pn(MnnloXVPp1), pn(dn(MnnloXVPm1['value'],Mnlom1)*100.), pn(dn(MnnloXVPp1,Mnlop1)*100.)],
["\sigma^{(2)}_p", pn(MnnloMPHm1['value']), pn(MnnloMPHm1['value']), pn(dn(MnnloMPHm1['value'],Mnlom1)*100.), pn(dn(MnnloMPHm1['value'],Mnlop1)*100.)],
["\sigma^{(2)}_pF", pn(MnnloMVPm1['value']), pn(MnnloMVPm1['value']), pn(dn(MnnloMVPm1['value'],Mnlom1)*100.), pn(dn(MnnloMVPm1['value'],Mnlop1)*100.)],
SEPARATING_LINE
]
print(tabulate(tabM1, headers=["MUSE_m 210 [1]","m+p", "m-p", "dK+%", "dK-%"]))
Total cross section -- Bar plots¶
In [28]:
xorder = [
'$\sigma_0^\infty$', '$\sigma_0^{71}$',
'$\sigma^{(1)\infty}_\mu$','$\sigma^{(1)71}_\mu$','$\sigma^{(1)\infty}_x$','$\sigma^{(1)71}_x$','$\sigma^{(1)\infty}_p$',
'$\sigma^{(2)\infty}_\mu$','$\sigma^{(2)71}_\mu$','$\sigma^{(2)\infty}_x$','$\sigma^{(2)\infty}_p$'
]
$\bullet$ S0
In [29]:
fig, (ax1, ax2, ax3) = subplots(
3, 1,
sharex=True,
gridspec_kw={'hspace': 0.03, 'height_ratios':[.5,.7,1]}
)
countsPH = [
Mlo0['value'][0], Mlo071['value'][0],
MnloEPHm0['value'][0],MnloFPHp0L71['value'][0], MnloXPHp0[0],MnloYPHp0L71['value'][0], MnloMPHm0['value'][0],
MnnloEPHm0['value'][0],MnnloFPHp0L71['value'][0], MnnloYPHp0[0], MnnloMPHm0['value'][0]
]
countsVP = [
0., 0.,
MnloEVPm0['value'][0],MnloFVPp0L71['value'][0], 0., 0., 0.,
MnnloEVPm0['value'][0],MnnloFVPp0L71['value'][0], MnnloXVPp0[0], MnnloMVPm0['value'][0]
]
errorFF = [
0., abs(Mlo086['value'][0]-Mlo060['value'][0]),
0., np.sqrt((MnloFPHp0L86['value'][0]-MnloFPHp0L60['value'][0])**2+(MnloFVPp0L86['value'][0]-MnloFVPp0L60['value'][0])**2),
0., abs(MnloYPHp0L86['value'][0]-MnloYPHp0L60['value'][0]), 0.,
0.,0.,0.,0.
]
stack = cumulate(countsPH, countsVP, errorFF)
barplot(xorder, countsPH, countsVP, stack, errorFF)
ax1.set_title('$\mu^-p \quad/ {\\rm\\upmu b}\quad [{\\tt S0}]$')
ax1.set_ylim(38., 53.)
ax2.set_ylim(.59, .81)
ax3.set_ylim(-0.1, 0.25)
draw()
mulify(fig, delx=3.8, dely=1.8)
fig.savefig("plots/xsec-mp-0.pdf")
$\bullet$ S1
In [30]:
fig, (ax1, ax2, ax3) = subplots(
3, 1,
sharex=True,
gridspec_kw={'hspace': 0.03, 'height_ratios':[.5,.7,1]}
)
countsPH = [
Mlo0['value'][0], Mlo071['value'][0],
MnloEPHm1['value'][0],MnloFPHp1L71['value'][0], MnloXPHp1[0],MnloYPHp1L71['value'][0], MnloMPHm1['value'][0],
MnnloEPHm1['value'][0],MnnloFPHp1L71['value'][0], MnnloYPHp1[0], MnnloMPHm1['value'][0]
]
countsVP = [
0., 0.,
MnloEVPm1['value'][0],MnloFVPp1L71['value'][0], 0., 0., 0.,
MnnloEVPm1['value'][0],MnnloFVPp1L71['value'][0], MnnloXVPp1[0], MnnloMVPm1['value'][0]
]
errorFF = [
0., abs(Mlo086['value'][0]-Mlo060['value'][0]),
0., np.sqrt((MnloFPHp1L86['value'][0]-MnloFPHp1L60['value'][0])**2+(MnloFVPp1L86['value'][0]-MnloFVPp1L60['value'][0])**2),
0., abs(MnloYPHp1L86['value'][0]-MnloYPHp1L60['value'][0]), 0.,
0.,0.,0.,0.
]
stack = cumulate(countsPH, countsVP, errorFF)
barplot(xorder, countsPH, countsVP, stack, errorFF)
ax1.set_title('$\mu^-p \quad/ {\\rm\\upmu b}\quad [{\\tt S1}]$')
ax1.set_ylim(38., 53.)
ax2.set_ylim(.59, .81)
ax3.set_ylim(-0.1, 0.25)
draw()
mulify(fig, delx=3.8, dely=1.8)
fig.savefig("plots/xsec-mp-1.pdf")
Differential distributions $-$ $Q^2$¶
$\bullet$ S0
In [31]:
fig, axs = plt.subplots(
1, sharex=True, gridspec_kw={'hspace': 0, 'height_ratios':[1]},
)
sca(axs)
mmsc=5
ebandr0ls(MnnloEPHm0,MnnloX31PHm0,MnnloX22PHm0,MnnloX13PHm0,MnnloMPHm0,MnnloEVPm0,MnnloXVPm0,MnnloMVPm0,
MnloFPHp0L71,MnloFVPp0L71,MnloYPHp0L71,MnloMPHm0,
Mlo071, mmsc, col='blue',linestyle='--')
ebandr0ps(MnnloEPHm0,MnnloX31PHm0,MnnloX22PHm0,MnnloX13PHm0,MnnloMPHm0,MnnloEVPm0,MnnloXVPm0,MnnloMVPm0,
MnloFPHp0L71,MnloFVPp0L71,MnloYPHp0L71,MnloMPHm0,
Mlo071, mmsc, col='red',linestyle='--')
ebandr0ls(MnnloEPHm1,MnnloX31PHm1,MnnloX22PHm1,MnnloX13PHm1,MnnloMPHm1,MnnloEVPm1,MnnloXVPm1,MnnloMVPm1,
MnloFPHp1L71,MnloFVPp1L71,MnloYPHp1L71,MnloMPHm1,
Mlo071, mmsc, col='cyan',linestyle=':')
ebandr0ps(MnnloEPHm1,MnnloX31PHm1,MnnloX22PHm1,MnnloX13PHm1,MnnloMPHm1,MnnloEVPm1,MnnloXVPm1,MnnloMVPm1,
MnloFPHp1L71,MnloFVPp1L71,MnloYPHp1L71,MnloMPHm1,
Mlo071, mmsc, col='orange',linestyle=':')
axs.set_title('$\mu^-p \quad [{\\tt S0, S1}]$')
axs.legend([
r'$[{\tt S0}]\,\, (Q^2_\mu)$',
r'$[{\tt S0}]\,\, (Q^2_p)$',
r'$[{\tt S1}]\,\, (Q^2_\mu)$',
r'$[{\tt S1}]\,\, (Q^2_p)$',
], ncol=2, loc='lower center',framealpha=0)
xlabel(r'$Q^2_\mu\,{\rm or}\,Q^2_p\,/\,{\rm GeV}^2$')
ylabel(r'$\frac{\sigma^{(1)\,71}+\sigma^{(2)\infty}}{\sigma_0^{71}}$')
xlim(8.e-3, 8.e-2)
draw()
fig.tight_layout()
mulify(fig, delx=4.2, dely=-0.1)
fig.savefig("plots/qsql-m-S0S1-2-diff.pdf", bbox_inches='tight')
Differential distributions $-$ $\theta_\mu$¶
$\bullet$ S0
In [32]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
MnloXPHp0 = scaleset(MnloXPHm0,-1)
eband(Mlo0,mmsc,col='slategray')
eband(addsets([MnloEPHm0, MnloEVPm0]),mmsc,col='gold')
eband(MnloXPHp0,mmsc,col='green')
eband(diffset(Mlo0, Mlo071),mmsc,col='tab:red')
ebanda(MnnloEPHm0,mmsc,linestyle='--',col='cyan')
ebanda(MnnloEVPm0,mmsc,linestyle=':',col='darkcyan')
eband(diffset(MnnloX22PHm0, addsets([MnnloX31PHm0, MnnloX13PHm0])),mmsc)
eband(diffset(MnloXPHp0, MnloYPHp0L71),mmsc, col='pink')
axs.set_title('$\mu^-p \quad [{\\tt S0}]$')
axs.legend([
r'$\sigma_0^\infty$', r'$\sigma^{(1)\infty}_\mu+\sigma^{(1)\infty}_\Pi$', r'$\sigma^{(1)\infty}_x$', r'$\sigma_0^\infty-\sigma_0^{71}$',
r'$|\sigma^{(2)\infty}_\mu|$', r'$\sigma^{(2)\infty}_{\mu\Pi}$', r'$\sigma^{(2)\infty}_x$', r'$\sigma^{(1)\infty}_x-\sigma^{(1)71}_x$'
], ncol=2, loc='upper right',framealpha=0)
xlabel(r'$\theta_\mu\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_\\mu\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 9.e1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/thm-S0-diff.pdf")
$\bullet$ S0 ($\mu^-$ and $\mu^+$)
In [33]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
MnloXPHp0 = scaleset(MnloXPHm0,-1)
ebandp(MnloYPHp0L71,mmsc)
ebandp(addsets([MnnloX31PHm0, MnnloX13PHm0, MnnloXVPm0]),mmsc)
axs.set_title('$\mu^-p - \mu^+p \quad [{\\tt S0}]$')
axs.legend([
r'$\sigma^{(1)\,71}_x$',
r'$\sigma^{(2)\infty}_x+\sigma^{(2)\infty}_{x\Pi}$'
], ncol=1, loc='upper right',framealpha=0)
xlabel(r'$\theta_\mu\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_\mu\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 2.e-1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/thm-S0-diff-x.pdf")
$\bullet$ S1
In [34]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
MnloXPHp1 = scaleset(MnloXPHm1,-1)
eband(Mlo0,mmsc,col='slategray')
eband(addsets([MnloEPHm1, MnloEVPm1]),mmsc,col='gold')
eband(MnloXPHp1,mmsc,col='green')
eband(diffset(Mlo0, Mlo071),mmsc,col='tab:red')
ebanda(MnnloEPHm1,mmsc,linestyle='--',col='cyan')
ebanda(MnnloEVPm1,mmsc,linestyle=':',col='darkcyan')
eband(diffset(MnnloX22PHm1, addsets([MnnloX31PHm1, MnnloX13PHm1])),mmsc)
eband(diffset(MnloXPHp1, MnloYPHp1L71),mmsc, col='pink')
axs.set_title('$\mu^-p \quad [{\\tt S1}]$')
axs.legend([
r'$\sigma_0^\infty$', r'$\sigma^{(1)\infty}_\mu+\sigma^{(1)\infty}_\Pi$', r'$\sigma^{(1)\infty}_x$', r'$\sigma_0^\infty-\sigma_0^{71}$',
r'$|\sigma^{(2)\infty}_\mu|$', r'$\sigma^{(2)\infty}_{\mu\Pi}$', r'$\sigma^{(2)\infty}_x$', r'$\sigma^{(1)\infty}_x-\sigma^{(1)71}_x$'
], ncol=2, loc='upper right',framealpha=0)
xlabel(r'$\theta_\mu\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_\\mu\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 9.e1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/thm-S1-diff.pdf")
$\bullet$ S1 ($\mu^-$ and $\mu^+$)
In [35]:
fig, axs = subplots(
1,
sharex=True,
gridspec_kw={'hspace': 0, 'height_ratios':[1]},
figsize=(5.9, 6.)
)
sca(axs)
mmsc=5
MnloXPHp1 = scaleset(MnloXPHm1,-1)
ebandp(MnloYPHp1L71,mmsc)
ebandp(addsets([MnnloX31PHm1, MnnloX13PHm1, MnnloXVPm1]),mmsc)
axs.set_title('$\mu^-p - \mu^+p \quad [{\\tt S1}]$')
axs.legend([
r'$\sigma^{(1)\,71}_x$',
r'$\sigma^{(2)\infty}_x+\sigma^{(2)\infty}_{x\Pi}$'
], ncol=1, loc='upper right',framealpha=0)
xlabel(r'$\theta_\mu\,/\,{\rm deg}$')
ylabel('$\\D\\sigma/\\D\\theta_\\mu\ /\ {\\rm\\upmu b}$')
yscale('log')
ylim(3.e-6, 2.e-1)
draw()
fig.tight_layout()
mulify(fig, delx=0.3, dely=3.4)
fig.savefig("plots/thm-S1-diff-x.pdf")
