A Higher Order Perturbative Parton Evolution Toolkit (HOPPET)

By G. Salam, Juan Rojo. Computer Physics Communications, 2008

303 citations recorded by the source corpus.

Abstract This document describes a Fortran 95 package for carrying out DGLAP evolution and other common manipulations of parton distribution functions (PDFs). The PDFs are represented on a grid in x -space so as to avoid limitations on the functional form of input distributions. Good speed and accuracy are obtained through the representation of splitting functions in terms of their convolution with a set of piecewise polynomial basis functions, and Runge–Kutta techniques are used for the evolution in Q . Unpolarised evolution is provided to NNLO, including heavy-quark thresholds in the MS ¯ scheme, and longitudinally polarised evolution to NLO. The code is structured so as to provide simple access to the objects representing splitting functions and PDFs, making it possible for a user to extend the facilities already provided. A streamlined interface is also available, facilitating use of the evolution part of the code from F77 and C/C++. Program summary Program title: HOPPET Catalogue identifier: AEBZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Public License No. of lines in distributed program, including test data, etc.: 61 001 No. of bytes in distributed program, including test data, etc.: 270 312 Distribution format: tar.gz Programming language: Fortran 95 Computer: All Operating system: All RAM: ≲10 MB Classification: 11.5 Nature of problem: Solution of the DGLAP evolution equations up to NNLO (NLO) for unpolarised (longitudinally polarised) PDFs, and provision of tools to facilitate manipulation (convolutions, etc.) of PDFs with user-defined coefficient and splitting functions. Solution method: Representation of PDFs on a grid in x , adaptive integration of splitting functions to reduce them to a discretised form, obtaining fast convolutions that are equivalent to integration with an interpolated form of the PDFs; Runge–Kutta solution of the Q evolution, and its caching so as to speed up repeated evolution with different initial conditions. Restrictions: PDFs should be smooth on the scale of the discretisation in x . Running time: A few seconds for initialisation, then ∼10 ms for creating a tabulation with a relative accuracy of 10 −4 from a new initial condition (on a 3.4 GHz Pentium IV processor). Further details in Section 9.2.

Subfields: Nuclear and High Energy Physics

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Citations in the corpus

A critical appraisal and evaluation of modern PDFs (2016, methodology): “Benchmark numbers for the PDF evolution have long been established, see e.g., the Les Houches report [209], and open-source evolution codes such as QCDNUM [210,211] and Hoppet [212] are available in Bjorken x-space and QCD-Pegasus [123] in Mellin N -space.”
Double parton distributions incorporating perturbative QCD evolution and momentum and quark number sum rules (2009, methodology): “One could choose to adapt either the direct x space or Mellin transform methods which are commonly used to numerically integrate the sDGLAP equation (see, for example, [51,52] for routines using the x space method for solution of the sDGLAP equation, and [53] for a routine using the Mellin transform”
Parton distributions from high-precision collider data (2017, methodology): “As far as perturbative evolution is concerned, APFEL has been extensively tested against other publicly available codes, such as HOPPET [109] and QCDNUM [171] for the PDF evolution and OpenQCDrad [172] for the calculation of heavy-quark structure functions in the massive scheme.”
Illuminating the photon content of the proton within a global PDF analysis (2017, methodology): “This generalisation is made possible thanks to the computation of the splitting functions up to O α2 and O (ααs) [25,26], with the resulting QED-corrected evolution equations implemented in public PDF evolution codes such as APFEL [27], HOPPET [28], and QEDEVOL [29].”
The Structure of the Proton in the LHC Precision Era (2017, methodology): “Several public codes implement the numerical solution of the DGLAP equations, with the HOPPET [59], APFEL [58] and QCDNUM [60] codes using x–space methods, while the PEGASUS [146] code performs the evolution in Mellin (moment) space.”
Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report (2016, methodology): “Then, we reduce the 900-member into the 30-member set at scale Q0 = 8 GeV and evolve all replicas to other Q values using HOPPET.”
Les Houches 2013: Physics at TeV Colliders: Standard Model Working Group Report (2014, unknown): “[219], where the HOPPET [220] and PEGASUS [221] codes were compared, including the effect of scale variations.”
Small-radius jets to all orders in QCD (2014, methodology): “QCDNUM [43], QCD-Pegasus [44], HOPPET [45] or Apfel [46].”
PDF4LHC recommendations for LHC Run II (2015, methodology): “1 Evolution of αs and PDFs should be performed up to three loops, using public codes such as HOPPET [105] or QCDNUM [106], or a code benchmarked to these.”
The photon content of the proton (2017, methodology): “We will use NNLO coefficient functions [38, 55–57], implemented in HOPPET [58–60].”