# APFEL: A PDF Evolution Library with QED corrections

Valerio Bertone, Stefano Carrazza, Juan Rojo

### Abstract

Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MSbar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD+QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O($\alpha_s^2$). All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in Fortran 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.
Original language English 1647-1668 Computer Physics Communications 185 6 https://doi.org/10.1016/j.cpc.2014.03.007 Published - Jun 2014

### Fingerprint

Flavors
Inelastic scattering
Electrodynamics
Graphical user interfaces
Luminance
Poles
Interpolation
Protons
Photons
quantum chromodynamics
quarks
graphical user interface
plotting
quantum electrodynamics
ingredients
partons
interpolation
inelastic scattering
poles
modules

### Bibliographical note

34 pages, 5 figures. Final version, to be published in CPC. Several corrections and improvements. Program available from http://apfel.hepforge.org/

• hep-ph
• hep-ex
• nucl-ex
• nucl-th

### Cite this

Bertone, Valerio ; Carrazza, Stefano ; Rojo, Juan. / APFEL : A PDF Evolution Library with QED corrections. In: Computer Physics Communications. 2014 ; Vol. 185, No. 6. pp. 1647-1668.
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abstract = "Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MSbar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD+QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O($\alpha_s^2$). All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in Fortran 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.",
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APFEL : A PDF Evolution Library with QED corrections. / Bertone, Valerio; Carrazza, Stefano; Rojo, Juan.

In: Computer Physics Communications, Vol. 185, No. 6, 06.2014, p. 1647-1668.

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AU - Bertone, Valerio

AU - Carrazza, Stefano

AU - Rojo, Juan

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N2 - Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MSbar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD+QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O($\alpha_s^2$). All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in Fortran 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.

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