Quarkonium Physics

From a theoretical perspective, heavy quarkonium is the ideal system to study the multiple energy scales of QCD, at high energies it can be studied through perturbative expansions in the strong coupling constant, while at low energies lattice calculations are required. On the experimental side, quarkonium is actively studied in experiments like LHCb , CMS , ATLAS, BESIII, the B-factories (BaBar and BELLE) as well as at the future PANDA experiment where the amount and precision of data has increased considerably in recent years. A comprehensive and coordinated effort to study all aspects of quarkonium physics from spectroscopy and decay to production, medium behaviour and quarkonium as a probe for SM parameter extraction and BSM investigations is carried on by members of the Quarkonium Working Group (QWG), an international group of more than one hundred researches of which Nora Brambilla and Antonio Vairo are founding members. To get an idea of the richness and broadness of this physics see the QWG report : arXiv:1010.5827 and the heavy quark chapter of arXiv:1404.3723

In our research we concentrate on the development and applications of non-relativistic Effective Field Theories (EFTs) to study heavy quarkonium. These theories are obtained from QCD integrating out degrees of freedom with high energies that are not relevant for the description of the bound system. The resulting theories are by construction equivalent to QCD when describing the same energy regime but more suitable to study low-energy physics. In particular we focus in non-relativistic QCD (NRQCD) and potential non-relativistic QCD (pNRQCD), two EFTs that exploit non-relativistic nature of the bound system to factorize the different energy scales. Our efforts are oriented (but not limited) to the study of quarkonium production and decays.


The state of the art tool to study the production of heavy quarkonia (bound states of a bottom or charm quark with its antiparticles) is Non-Relativistic QCD (NRQCD), an EFT of strong interactions that exploits the hierarchy of scales between the mass of the heavy quark, its relative velocity in quarkonium and the binding energy of the bound state.

The predictive power of the theory comes from the so-called NRQCD factorization conjecture that allows us to express production cross sections as products of perturbative short distance coefficients and non-perturbative long distance matrix elements (LDME). The LDME can be determined from experimental measurements and are believed to be universal, in the sense that they depend only on the quantum numbers of the quarkonium but not on the process in which it is produced.

In principle, it should not matter from which experiments the LDME are extracted. In practice, low statistics, large systematic uncertainties and experimental inconsistencies can lead to significant deviations for fits done using different combinations of the available data sets.

At T30f we study not only phenomenological applications of NRQCD but also the field theoretical foundations of the theory. One of our aims is to derive relations between different LDME by using potential Non-Relativistic QCD (pNRQCD), an EFT of QCD that works at the scale of the heavy quarkonium binding energy and thus avoids some complications present in NRQCD. By reducing the number of independent LDME that are required to describe quarkonium production processes we hope to solve some of the existing issues related to the determination of the LDME.


When coupled to electromagnetism pNRQCD is the ideal framework for studying the electromagnetic heavy quarkonium transitions. These transitions consist in the decay of heavy quarkonium into a another lighter quarkonium state through the emission of electromagnetic radiation. In particular we are interested in the M1 and E1 transitions in which the final states consist of a photon and quarkonium state. In the M1 transitions the spin of the final state have been changed by a unity with respect to the initial state while the angular momentum remains the same. For the E1 transition the opposite occurs, the spin is kept unchanged and the angular momentum changes by a unity.

We know from the experiment that for some quarkonium states these decay modes are important, for instance, for certain quarkonium states the E1 transition accounts for around the 50% of the total width. Within a pNRQCD framework we have obtained model-independent expressions for the decay rate of these two transitions. An active research project within the group is the study of the phenomenology of these transitions through the evaluation of these expressions.

Written by H. Martinez and V. Shtabovenko.


Nora Brambilla, Antonio Vairo, Michael Benzke (Hamburg), Hector Martinez, Vladyslav Shtabovenko

Some related publications

N. Brambilla et al.
Heavy quarkonium: progress, puzzles, and opportunities
Eur. Phys. J. C71 (2011) 1534
arXiv:1010.5827 Inspire

Nora Brambilla, Piotr Pietrulewicz, Antonio Vairo
Model-independent Study of Electric Dipole Transitions in Quarkonium
Phys. Rev. D 85, (2012) 094005
arXiv:1203.3020 Inspire