C++ tutorial

Use PDFSet for set-level calculations and uncertainty analysis. Use factories or custom template components when you need a single member or specialized numerical behavior.

Before compiling

Make sure that PDFxTMDLib is installed and that the parent directory of each data set is listed in config.yaml. The examples use:

MSHT20nlo_as120 for collinear calculations.
PB-LO-HERAI+II-2020-set2 for TMD calculations.
x as a dimensionless momentum fraction.
mu2 and kt2 as squared scales in GeV².

Collinear calculation with `PDFSet`

PDFSet<CollinearPDFTag> manages every member in a collinear set. Member 0 is used as the central member in this example.

#include <PDFxTMDLib/PDFSet.h>
#include <iostream>

int main() {
    PDFxTMD::PDFSet<PDFxTMD::CollinearPDFTag> set("MSHT20nlo_as120");
    auto central = set[0];

    const double x = 0.1;
    const double mu2 = 10000.0;

    const double gluon = central->pdf(PDFxTMD::PartonFlavor::g, x, mu2);
    std::cout << "Gluon value: " << gluon << '\n';
}

TMD calculation with `PDFSet`

Specialize the same interface with TMDPDFTag and supply k_T² to tmd:

#include <PDFxTMDLib/PDFSet.h>
#include <iostream>

int main() {
    PDFxTMD::PDFSet<PDFxTMD::TMDPDFTag> set(
        "PB-LO-HERAI+II-2020-set2"
    );
    auto central = set[0];

    const double x = 0.001;
    const double kt2 = 10.0;
    const double mu2 = 100.0;

    const double gluon = central->tmd(
        PDFxTMD::PartonFlavor::g, x, kt2, mu2
    );
    std::cout << "Gluon TMD value: " << gluon << '\n';
}

Uncertainty and correlation

The set-level interface uses the set metadata to combine its members:

PDFxTMD::PDFSet<PDFxTMD::CollinearPDFTag> set("MSHT20nlo_as120");

const double x = 0.1;
const double mu2 = 10000.0;

const auto uncertainty = set.Uncertainty(
    PDFxTMD::PartonFlavor::g, x, mu2
);

std::cout << "central = " << uncertainty.central << '\n'
          << "+error  = " << uncertainty.errplus << '\n'
          << "-error  = " << uncertainty.errminus << '\n';

const double correlation = set.Correlation(
    PDFxTMD::PartonFlavor::g, x, mu2,
    PDFxTMD::PartonFlavor::u, x, mu2
);

std::cout << "correlation(g, u) = " << correlation << '\n';

An explicit confidence level can be supplied as the final argument when required by the set and analysis:

const auto uncertainty90 = set.Uncertainty(
    PDFxTMD::PartonFlavor::g, x, mu2, 90.0
);

Metadata

Use the structured metadata objects when you need common fields:

const auto standard_info = set.getStdPDFInfo();
const auto error_info = set.getPDFErrorInfo();

std::cout << "Description: " << standard_info.SetDesc << '\n';
std::cout << "Members: " << standard_info.NumMembers << '\n';
std::cout << "Error type: " << error_info.ErrorType << '\n';

For less common keys, use the set’s general configuration interface exposed by info().

Single-member factory interface

Factories avoid constructing a complete set when an application only needs one member:

#include <PDFxTMDLib/Factory.h>
#include <iostream>

int main() {
    auto cpdf_factory = PDFxTMD::GenericCPDFFactory();
    auto cpdf = cpdf_factory.mkCPDF("MMHT2014lo68cl", 0);

    const double value = cpdf.pdf(
        PDFxTMD::PartonFlavor::g, 0.001, 100.0
    );
    std::cout << value << '\n';
}

The corresponding TMD factory is GenericTMDFactory, and individual TMD members are created with mkTMD.

Strong coupling

Calculate α_s(μ²) from the loaded set or through a coupling factory:

#include <PDFxTMDLib/Factory.h>
#include <PDFxTMDLib/PDFSet.h>

PDFxTMD::PDFSet<PDFxTMD::CollinearPDFTag> set("MSHT20nlo_as120");
const double alpha_from_set = set.alphasQ2(10000.0);

auto coupling_factory = PDFxTMD::CouplingFactory();
auto coupling = coupling_factory.mkCoupling("MMHT2014lo68cl");
const double alpha_from_factory = coupling.AlphaQCDMu2(10000.0);

Custom implementations

Advanced users can combine a reader, interpolator, and extrapolator through GenericPDF:

#include <PDFxTMDLib/GenericPDF.h>
#include <PDFxTMDLib/Implementation/Extrapolator/Collinear/CErrExtrapolator.h>
#include <PDFxTMDLib/Implementation/Interpolator/Collinear/CLHAPDFBilinearInterpolator.h>
#include <PDFxTMDLib/Implementation/Reader/Collinear/CDefaultLHAPDFFileReader.h>

using Reader = PDFxTMD::CDefaultLHAPDFFileReader;
using Interpolator = PDFxTMD::CLHAPDFBilinearInterpolator<Reader>;
using Extrapolator = PDFxTMD::CErrExtrapolator;

using CustomPDF = PDFxTMD::GenericPDF<
    PDFxTMD::CollinearPDFTag,
    Reader,
    Interpolator,
    Extrapolator
>;

CustomPDF pdf("MMHT2014lo68cl", 0);
const double value = pdf.pdf(PDFxTMD::PartonFlavor::g, 0.001, 100.0);

The interpolator is parameterized by the reader type; omitting that template argument produces an invalid type.

Compile an example

When PDFxTMDLib is installed in a standard prefix:

g++ -std=c++17 example.cpp -lPDFxTMDLib -o example
./example

For reproducible projects, prefer the CMake target shown in the installation guide.