ABM (Alekhin-Blumlein-Moch)

ABM (Alekhin-Blumlein-Moch)
Name	ABM (Alekhin-Blumlein-Moch)
Field	Particle physics
Notable people	Serguéi Alekhin, Johannes Blümlein, Sebastian Moch
Introduced	2009
Discipline	Quantum Chromodynamics

ABM (Alekhin-Blumlein-Moch)

ABM (Alekhin-Blumlein-Moch) is a perturbative quantum chromodynamics analysis framework developed by Serguéi Alekhin, Johannes Blümlein, and Sebastian Moch for precision determinations of parton distribution functions and strong coupling constants. The approach synthesizes high-order calculations, deep-inelastic scattering data, and collider measurements to produce global fits relevant to Large Hadron Collider, HERA (particle accelerator), and Tevatron phenomenology. ABM emphasizes fixed-flavour-number schemes, heavy-quark treatments, and explicit uncertainties for use in predictions for processes at CERN, DESY, and other facilities.

Introduction

ABM (Alekhin-Blumlein-Moch) was formulated to provide a coherent extraction of parton distribution functions (PDFs) and the strong coupling constant αs using data from HERA (particle accelerator), SLAC National Accelerator Laboratory, CERN, Fermilab, and other experiments. The collaboration combines theoretical results from perturbative Quantum Chromodynamics calculations by groups including Moscow State University, DESY (Deutsches Elektronen-Synchrotron), and institutes associated with practitioners such as Rossen Vogt and W. James Stirling. ABM outputs have been compared with alternative PDF sets from groups like MSTW, NNPDF, CTEQ, and HERAPDF in global analyses relevant to Higgs boson and top quark production.

Historical Development and Motivation

The ABM program grew from earlier fixed-target and collider analyses that traced back to work by groups at Joint Institute for Nuclear Research, Institute for High Energy Physics (Protvino), and collaborations that analyzed data from BCDMS, NMC (experiment), and SLAC. Motivated by discrepancies among global fits and determinations of αs from deep inelastic scattering and jet measurements at Tevatron, the authors sought a framework that incorporated high-order perturbative results from papers by teams including Vogt–Moch–Vermaseren and Altarelli–Parisi style evolution, cross-checked against calculations by Georgi–Politzer and studies at DESY. Early ABM releases emphasized rigorous treatment of experimental correlations from ZEUS, H1 (experiment), D0 (experiment), and CDF (Collider Detector at Fermilab).

Theoretical Framework and Formalism

ABM employs perturbative methods grounded in Quantum Chromodynamics with Wilson coefficient functions computed at next-to-next-to-leading order (NNLO) using techniques related to the Mellin transform and operator product expansion as advanced by researchers at Max Planck Institute for Physics, Institut für Physik (Germany), and collaborations involving Vladimirov. Heavy-flavour schemes in ABM follow fixed-flavour-number prescriptions inspired by works from Buza et al. and comparisons to variable-flavour-number approaches used by Thorne–Roberts and ACOT. Evolution of PDFs uses Dokshitzer–Gribov–Lipatov–Altarelli–Parisi kernels developed in line with computations by Vogt, Moch, and Vermaseren. Renormalization and factorization scale choices are informed by studies linked to Collins–Soper and Sterman formalisms.

Key Results and Phenomenological Applications

ABM analyses have produced compact PDF sets and αs determinations that differ in systematic ways from results by MSTW/MMHT, CTEQ–TEA, and NNPDF collaborations; these differences affect cross sections for Higgs boson production via gluon fusion, top quark pair production, and electroweak observables measured at LHCb and ATLAS (experiment). ABM predictions have been used to interpret precision measurements from CMS (experiment), ATLAS (experiment), and fixed-target experiments such as NuTeV. The framework yields constraints relevant to beyond-Standard-Model searches conducted at CERN and input for Monte Carlo generators like PYTHIA, HERWIG, and SHERPA when interfaced with NNLO matrix elements from codes related to FEWZ and MCFM.

Impact on Parton Distribution Functions and Global Fits

ABM contributes an independent, high-precision PDF set employed in global fits comparing results from groups including MSTW, NNPDF, CTEQ–TEA, and HERAPDF. The ABM philosophy of fixed-flavour-number schemes and dedicated heavy-quark mass treatments has stimulated discussion at venues such as meetings of the Particle Data Group and conferences hosted by CERN and DESY. The ABM determinations of αs(MZ) and gluon distributions influence global electroweak fits undertaken by collaborations like LEP Electroweak Working Group and studies of partonic luminosities for processes at High-Luminosity LHC.

Computational Methods and Tools

Computationally, ABM relies on NNLO coefficient functions and evolution kernels implemented using codes developed in part by the ABM authors and complementary tools like APFEL, QCDNUM, and HOPPET. Fits use statistical frameworks akin to those in analyses by HERAFitter and minimization techniques related to implementations in MINUIT and software from CERNLIB. Validation leverages datasets from HERA Combined analyses and collider measurements archived by HEPData and compared against predictions produced with tools such as FEWZ, MCFM, and NNLO programs associated with Top++.

Criticisms, Limitations, and Extensions

Critics have noted tensions between ABM results and those from alternative groups, particularly regarding the gluon PDF at small Bjorken-x as highlighted in comparisons with HERA (particle accelerator) combined fits and with jet-based determinations from Tevatron. Debates center on treatment of heavy-quark masses, nuclear corrections for datasets from NuTeV and fixed-target experiments like BCDMS, and the role of high-order resummation approaches developed by teams including Catani and Sterman. Extensions of ABM have explored matching to small-x resummation frameworks connected to BFKL and implementations of higher-twist corrections studied by researchers at Moscow State University and St. Petersburg State University.

Category:Parton distribution functions Category:Quantum chromodynamics