Benchmarks
Benchmarks are implemented against external code, where they overlap with yadism. Benchmarks are implemented using an independent package called yadmark described in the relative section.
We compare yadism with three external tools: APFEL, QCDNUM and xspace-bench, which are described in details below.
Different definition of SF
Due to a different definition SF in yadism, APFEL, QCDNUM and xspace-bench it is not possible to compare all the structure functions in all the schemes.
Important
For the actual definition of SF in yadism (which is of course FNS dependent) look at Flavor Number Schemes section.
The following tables summarize the possible combination of benchmarks, including also incoming projectiles, different type of currents, SV and TMC.
FNS \ reference |
APFEL |
QCDNUM |
xspace-bench |
APFEL++ |
|---|---|---|---|---|
FFNS |
✓ |
✓ |
✓ [1] |
✓ |
ZM-VFNS |
✓ |
✓ |
✓ |
✓ |
FFN0 |
✓ |
✓ |
✓ |
feature \ reference |
APFEL |
QCDNUM |
xspace-bench |
APFEL++ |
|---|---|---|---|---|
projectiles |
✓ |
✓ |
✓ |
|
EM |
✓ |
✓ |
✓ |
✓ |
NC |
✓ |
✓ |
✓ |
✓ |
CC |
✓ |
✓ |
✓ |
|
scale-variatons |
✓ |
✓ |
✓ |
|
target-mass-corrections |
✓ |
✓ |
APFEL
APFEL is a tool aimed to the evolution of PDFs and DIS observables’ calculation (and FTDY as well).
It has been used by the NNPDF collaboration up to NNPDF4.0
SF in APFEL
The APFEL definitions are such that the following relation always holds:
In order to keep this relation the following definitions are adopted:
\(F_X^{light}\) is called the hood collecting all the contributions in which \(u, d, s\) quarks are coupling to the EW boson and nothing else
\(F_X^{heavy}\) are defined as the collections of contributions in which only the specified heavy quark it’s coupling to the EW boson, and they account only for the corresponding \(m_{heavy}\) effects (but not for the mixed ones)
These definitions are consistent up to NNLO, but they are not easy to apply to all the FNS at higher orders because:
in the VFNS the light quarks are dynamical, so the number of objects running in quark loops as well: when this causes a non-linear dependence on the number of light flavors \(n_l\) (e.g. a quadratic one) it is difficult (if not impossible) to split up into \(F_X^{light}\) and not
since not all the massive contributions are accounted for in the proper \(F_X^{heavy}\) (some of them are collected in \(F_X^{light}\), or in other heavy ones) these are not well-defined observables on their own (from a pure QFT-theoretical point of view), then they could not be compared with tagged experimental data
mixed mass effects are known to be small, but it’s rather inconsistent to account for certain mass effects that are even smaller in suitable \(Q^2\) regimes and not for them; e.g. charm-bottom interplay may be more relevant then top contributions much below top production threshold
QCDNUM
QCDNUM is a tool aimed to the evolution of PDFs and DIS observables’ calculation in a restricted number of schemes.
It is/has been used by the xFitter framework.
SF in QCDNUM
QCDNUM is using a different definition of the SF that is not matching the other one and from which it is not possible to recover the other results at higher orders (in particular it becomes completely impossible since NNLO). The different definition is:
\(F_X^{light}\) is defined by having only light quarks in the quark lines
\(F_X^{charm}\) is defined by having light and charm quarks in the quark lines (at least one charm), given that charm is not light (otherwise it’s not defined)
and so on for \(F_X^{bottom}\) (that will include at least one bottom) and \(F_X^{top}\) (that will include at least one top)
Only EM and NC currents are available in QCDNUM.
xspace-bench
xspace-bench is a tool aimed to the evolution of PDFs and DIS observables’ calculation for NC and CC, with different type of projectiles and targets. SF can be computed up to NLO, and few FNS configurations are available, since their settings are hardcoded.
SF in xspace-bench
In xspace-bench SF are defined as follows:
\(F_X^{light}\) is defined by having only light quarks in the quark lines (u,d,s)
\(F_X^{charm}\) is defined by having light and charm quarks in the quark lines (at least one charm), given that charm is not light (otherwise it’s not defined)
and so on for \(F_X^{bottom}\) (that will include at least one bottom) and \(F_X^{top}\) (that will include at least one top)
\(F_X^{total}\) is defined as the sum of the previous ones.
Given these definitions, benchmarks with yadism are possible only in the region \(m^2_{charm} < Q^2 < m^2_{bottom}\) selecting either ZM-VFNS with \(F_X^{total}\) or FFNS with NfFF=3. FONLL is implemented in the so called scheme A with and without damping factor.
APFEL++
APFEL++ is a C++ rewriting of the Fortran 77 evolution code APFEL. However, APFEL++ is based on a completely new code design and guarantees a better performance along with a more optimal memory management. APFEL++ is suitable for a wide range of tasks: from the solution of the DGLAP evolution equations to the computation of DIS and single-inclusive-annihilation cross sections.
APFEL++ is also currently interfaced to PARTONS, a software dedicated to the phenomenology of Generalised Parton Distributions (GPDs) and TMDs, and to xFitter.