ePDF: A code for the computation and the evolution of electron parton distribution in QED at the next-to-leading logarithmic accuracy
ePDF is a library that implements the evolution in pure QED of the
unpolarised electron parton distribution functions (PDFs) up to
next-to-leading logarithmic (NLL) approximation. The initial
conditions, computed here, can
be evolved either numerically, by solving the DGLAP equation through
different numerical algorithms, or analytically. The analytical
solutions are obtained by means of an additive formula that matches a
large-z solution, that includes all orders in the QED coupling
constant, with a small- and intermediate-z solution that includes
terms up to third order in the coupling constant.
You can obtain ePDF directly from the github repository:
https://github.com/gstagnit/ePDF/releases
For the last development branch you can clone the master code:
git clone https://github.com/gstagnit/ePDF.gitIn order to install the code, you need to have installed:
The code can be compiled using the following procedure:
cd ePDF
cmake -DCMAKE_INSTALL_PREFIX=/your/installation/path/ .
make && make installBy the default, if no prefix specification is given, the program will
be installed in the /usr/local folder. If you want (or need) to use a
different path, remember to export the ePDF /lib folder into the
LD_LIBRARY_PATH. More configuration options can be accessed through:
ccmake .If the installation was successful, the test code Evolution will be generated in the run/ folder.
This code takes as an input a card containing the evolution settings. An example of such a card is in cards/default.yaml.
To run the code type:
cd run/
./Evolution ../cards/default.yamlYou should get the following output:
Q = 1.0000000000e+01 GeV
AlphaQED(Q) = 5.8974514709e-04
Sum rules at the initial scale...
Momentum sum rule: (1.0000000000e+00,0.0000000000e+00)
Valence sum rule: (1.0000000000e+00,0.0000000000e+00)
Sum rules at the final scale...
Momentum sum rule: (9.9999999995e-01,0.0000000000e+00)
Valence sum rule: (1.0000000000e+00,0.0000000000e+00)
Numerical solution:
x e- + e+ photon e- - e+
1.00e-01 3.2572e-02 4.8721e-01 2.5949e-02
2.00e-01 3.2542e-02 2.0718e-01 3.0245e-02
3.00e-01 3.7671e-02 1.2061e-01 3.6540e-02
4.00e-01 4.6451e-02 8.0161e-02 4.5805e-02
5.00e-01 6.0240e-02 5.7539e-02 5.9841e-02
6.00e-01 8.2542e-02 4.3574e-02 8.2286e-02
7.00e-01 1.2188e-01 3.4411e-02 1.2171e-01
8.00e-01 2.0418e-01 2.8134e-02 2.0408e-01
9.00e-01 4.6076e-01 2.3595e-02 4.6071e-01
9.50e-01 9.8654e-01 2.1589e-02 9.8652e-01
9.90e-01 5.2837e+00 1.9248e-02 5.2837e+00
9.99e-01 5.3974e+01 1.6660e-02 5.3974e+01
Analytic solution:
x e- + e+ photon e- - e+
1.00e-01 3.2568e-02 4.8722e-01 2.5948e-02
2.00e-01 3.2540e-02 2.0719e-01 3.0245e-02
3.00e-01 3.7671e-02 1.2062e-01 3.6540e-02
4.00e-01 4.6452e-02 8.0163e-02 4.5807e-02
5.00e-01 6.0243e-02 5.7540e-02 5.9844e-02
6.00e-01 8.2548e-02 4.3574e-02 8.2292e-02
7.00e-01 1.2189e-01 3.4411e-02 1.2172e-01
8.00e-01 2.0419e-01 2.8133e-02 2.0409e-01
9.00e-01 4.6077e-01 2.3594e-02 4.6073e-01
9.50e-01 9.8655e-01 2.1589e-02 9.8653e-01
9.90e-01 5.2836e+00 1.9254e-02 5.2836e+00
9.99e-01 5.3974e+01 1.6674e-02 5.3974e+01Different options can be accessed by feeding the executable with the appropriate input card.
Code documentation generated with Doxygen can be found here: https://vbertone.github.io/ePDF/html/index.html.
- S. Frixione, Initial conditions for electron and photon structure and fragmentation functions, arXiv:1909.03886.
- V. Bertone, M. Cacciari, S. Frixione, G. Stagnitto, The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED, arXiv:1911.12040
- Valerio Bertone: valerio.bertone@cern.ch
- Matteo Cacciari: matteo.cacciari@cern.ch
- Stefano Frixione: stefano.frixione@cern.ch
- Giovanni Stagnitto: giovanni.stagnitto@gmail.com