Here we compare the PDFs:
\(m_c=1.51 GeV\) (LHAPDF ID: NNPDF31_nnlo_as_0118
)
\(m_c=1.38 GeV\) (LHAPDF ID: NNPDF31_nnlo_as_0118_mc_138
)
\(m_c=1.64 GeV\) (LHAPDF ID: NNPDF31_nnlo_as_0118_mc_164
)
PDF comparison at 2 GeV
All flavours
\(m_c=1.51 GeV\)
\(m_c=1.38 GeV\)
\(m_c=1.64 GeV\)
Flavour Basis
Absolute
Normalized
Evolution Basis
Absolute
Normalized
PDF comparison at 100 GeV
All flavours
\(m_c=1.51 GeV\)
\(m_c=1.38 GeV\)
\(m_c=1.64 GeV\)
Flavour Basis
Absolute
Normalized
Evolution Basis
Absolute
Normalized
Luminosities at \(\sqrt{s}=13000 GeV\)
Luminosity ratios
We plot:
\[
L(M_{X},s)=\sum_{ij}^{\textrm{channel}}\frac{1}{s}
\int_{\tau}^{1}\frac{dx}{x}
f_{i}(x,M_{X})
f_{j}(\frac{\tau}{x},M_{X})
\]
Where \(i\) and \(j\) are summed as follows:
For \(gg\), \(i = j = g\).
For \(qq\) i and j run over all possible quark and antquark combinations.
For \(qg\), i and j are all possible combinations of a quark ant antiquark and a gluon.
For \(q\bar{q}\), \(i\) and \(j\) correspond to a quark and antiquark of the same flavour.
gg
gq
qq
qqbar
Luminosity uncertainties
We plot the percentage uncertainty of
\[
\tilde{L}(M_{X},y,s)=
\sum_{ij}^{\textrm{channel}}\frac{1}{s}
f_{i}\left(\frac{M_{x}e^{y}}{\sqrt{x}},M_{x}\right)
f_{j}\left(\frac{M_{x}e^{-y}}{\sqrt{x}},M_{x}\right)
\]
in the allowed kinematic range.
gg
\(m_c=1.51 GeV\)
\(m_c=1.38 GeV\)
\(m_c=1.64 GeV\)
gq
\(m_c=1.51 GeV\)
\(m_c=1.38 GeV\)
\(m_c=1.64 GeV\)
qq
\(m_c=1.51 GeV\)
\(m_c=1.38 GeV\)
\(m_c=1.64 GeV\)
qqbar
\(m_c=1.51 GeV\)
\(m_c=1.38 GeV\)
\(m_c=1.64 GeV\)