Nonrelativistic QCD
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| Nonrelativistic QCD | |
|---|---|
| Name | Nonrelativistic QCD |
| Field | Theoretical physics |
| Developed in | CERN; SLAC National Accelerator Laboratory; Fermilab |
| Introduced | 1980s |
| Key people | Geoffrey Bodwin, Eric Braaten, G. Peter Lepage, Stanley Brodsky, Alexander Voloshin |
| Related | Quantum chromodynamics, Effective field theory, Heavy quarkonium |
Nonrelativistic QCD Nonrelativistic QCD is an effective field theory designed to describe bound states of heavy quarks by separating high-energy modes from low-energy dynamics. It was developed to connect perturbative calculations in Quantum chromodynamics with nonperturbative phenomena observed at facilities such as CERN, Fermilab, and KEK. Foundational work by researchers at institutions like MIT, Cornell University, and Caltech established its role alongside approaches from Heavy Quark Effective Theory and inputs used in analyses at Brookhaven National Laboratory and DESY.
Introduction
Nonrelativistic QCD provides a systematic framework to study heavy-flavor systems encountered in experiments at Large Hadron Collider, Belle II, and BESIII. Influential contributors from University of Chicago, University of Oxford, and Princeton University formulated matching procedures referenced in calculations connected to data from Tevatron and LEP. The approach complements techniques developed by groups at Institute for Advanced Study and Perimeter Institute while informing lattice computations performed at Riken and JLab.
Theoretical Framework
The theory builds on the Lagrangian structure of Quantum chromodynamics and incorporates velocity-scaling rules motivated by studies at Stanford Linear Accelerator Center and theoretical analyses by teams at Columbia University and University of California, Berkeley. It invokes operators classified and organized following methodologies related to work by scholars from Harvard University, Yale University, and Imperial College London. Foundational operator bases are analogous in spirit to constructions used in Fermi National Accelerator Laboratory collaborations and are cross-checked against results from Max Planck Institute for Physics.
Matching and Power Counting
Matching coefficients are determined by relating amplitudes computed in Quantum chromodynamics to those in the effective theory, a procedure refined in seminars at Institute for Nuclear Theory and workshops at CERN. Power counting uses the heavy-quark velocity v and is often discussed in contexts associated with G. Peter Lepage and groups at University of Illinois Urbana-Champaign and University of Washington. Techniques for separating scales draw parallels with methods applied at Los Alamos National Laboratory and in analyses by researchers at Yale University and University of Cambridge.
Applications to Heavy Quarkonium
Nonrelativistic QCD is applied to spectroscopy and decay rates of systems studied at CLEO, BaBar, and LHCb, including bottomonium and charmonium families investigated by teams at University of Bologna and University of Pisa. The framework informs extractions of quark masses used in global fits by collaborations at CERN and Jefferson Lab, and complements potential-model approaches historically developed at University of Vienna and Moscow State University. It has been employed in predicting production cross sections measured in experiments by ATLAS, CMS, and HERA.
Calculational Techniques and Renormalization
Renormalization within Nonrelativistic QCD utilizes diagrammatic methods and regularization schemes familiar from treatments at Princeton University and Cambridge University Press-hosted schools. Loop computations and anomaly analyses parallel work done in groups at Stanford University and Yale University, while lattice implementations are carried out by collaborations affiliated with Brookhaven National Laboratory and Riken BNL Research Center. Perturbative matching calculations often reference results disseminated in lectures at Perimeter Institute and review articles authored by researchers at University of Minnesota.
Phenomenological Predictions and Experimental Tests
Predictions for production rates, polarization observables, and decay widths have been tested against data from Large Hadron Collider, Tevatron, Belle, and BESIII. Global analyses by collaborations at CERN and Fermilab compare NRQCD-based extractions with determinations from sum-rule studies affiliated with IHEP and National Taiwan University. Outcomes influence the interpretation of new states observed by groups at LHCb and Belle II and guide searches reported by teams at SLAC National Accelerator Laboratory.
Extensions and Related Effective Field Theories
Related frameworks include Potential Nonrelativistic QCD developed in contexts involving researchers at Universität Heidelberg and École Normale Supérieure, and approaches that intersect with Soft Collinear Effective Theory as formulated by scholars at Caltech and Cornell University. Connections to lattice QCD studies performed at Riken, Fermilab, and RIKEN BNL Research Center enable nonperturbative input, while interfaces with methods from Institute of Theoretical Physics, Chinese Academy of Sciences and Stony Brook University continue to expand applications.