Two-Pole Structures in QCD: Facts, Not Fantasy!
Abstract
:1. Introduction
- Conventional hadrons, that is mesons and baryons as described before;
- Multiquark hadrons, such as tetraquark states (mesons from two quarks and two antiquarks), pentaquark states (baryons made from four quarks and one antiquark) and so on;
- Hadronic molecules and atomic nuclei, that is multiquark states composed of a certain number of conventional hadrons (as discussed in more detail below);
- Hybrid states, which are composed of quarks and (valence) gluons; and
- Glueballs, bound states solely made of gluons, arguably the most exotic form of matter, which has so far been elusive in all searches.
2. Methods
2.1. Limits of QCD
- Light quarks:In this limit, left- and right-handed quarks decouple which, is the chiral symmetry. As stated, it is spontaneously broken leading to the appearance of eight pseudo-Goldstone bosons. The pertinent EFT is chiral perturbation theory (CHPT) (see Section 2.2). Note that the corrections due to the quark masses are powers in .
- Heavy quarks:
- Heavy-light systems: Here, heavy quarks act as matter fields coupled to light pions and one thus can combine CHPT and HQEFT, as pioneered in [7,8,9] (see also Section 2.3).
2.2. A Factsheet on Chiral Perturbation Theory
- is symmetric under some Lie group ; here, = SU(3) SU(3).
- The ground state is asymmetric and is spontaneously broken to , leading to the the appearance of Goldstone bosons (GBs) . In QCD, = SU(3) and the Goldstone bosons are the aforementioned eight pseudoscalar mesons.
- In QCD, the matrix element of the axial-vector current , , where F is related to the pseudoscalar decay constant in the chiral limit. is a sufficient and necessary condition for spontaneous chiral symmetry breaking.
- There are no other massless strongly interacting particles.
2.3. Chiral Perturbation Theory for Heavy-Light Systems
2.4. Unitarization Schemes
2.5. Unitarized Chiral Perturbation Theory in a Finite Volume
3. The Story of the
3.1. Basic Facts
3.2. Enter Chiral Dynamics
3.3. The Two-Pole Structure
3.4. Beyond Leading Order
3.5. Where Do We Stand?
4. Meson Sector: The and Related States
4.1. Two-Pole Structure
4.2. Other Candidates
4.3. Analysis of Data
4.4. The Meson
5. Discussion and Outlook
- The story with the two-pole structure started with the , which can now be considered as established. However, the position of lighter pole close to the threshold needs to be determined better, whereas the higher pole close to the threshold is pretty well pinned down. It is comforting to note that the re-analysis of the Jülich meson-exchange model from the 1990s also confirmed the two-pole structure of the (see [99] and references therein). I again point out that approaches that do not allow for the dynamical generation of resonances, e.g., the BnGa model, are insufficient for describing the whole hadron spectrum.
- Further support of the two-pole scenario comes from charmed baryons. Recently, an analysis of the LHCb data on in the near--threshold region also revealed a two-pole structure of the when isospin-breaking is taken into account [100].
- The spectrum of excited charmed mesons, made from a heavy c quark and a light quark, offers further support of the two-pole structure and the dynamical generation of hadron resonances. Here, a beautiful interplay of experimental results, unitarized chiral perturbation theory and lattice QCD gives very strong indications that this picture is indeed correct. Further lattice calculations and the measurement of the corresponding B-mesons will serve as further tests.
- This leads to a new paradigm in hadron physics: The hadron spectrum must not be viewed as a collection of quark model states, but rather as a manifestation of a more complex dynamics that leads to an intricate pattern of various types of states that can only be understood by an interplay of theory and experiment (cf. the light scalar mesons or the states discussed here).
- The dynamical generation of hadron states through hadron–hadron interactions ties together nuclear and particle physics, as these molecular compounds bear resemblance to the light nuclei, the deuteron, the triton and so on. Therefore, such molecular states were called “deusons” by Törnquist, one of the pioneers in the field of hadronic molecules [101].
Funding
Acknowledgments
Conflicts of Interest
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Meißner, U.-G. Two-Pole Structures in QCD: Facts, Not Fantasy! Symmetry 2020, 12, 981. https://doi.org/10.3390/sym12060981
Meißner U-G. Two-Pole Structures in QCD: Facts, Not Fantasy! Symmetry. 2020; 12(6):981. https://doi.org/10.3390/sym12060981
Chicago/Turabian StyleMeißner, Ulf-G. 2020. "Two-Pole Structures in QCD: Facts, Not Fantasy!" Symmetry 12, no. 6: 981. https://doi.org/10.3390/sym12060981
APA StyleMeißner, U.-G. (2020). Two-Pole Structures in QCD: Facts, Not Fantasy! Symmetry, 12(6), 981. https://doi.org/10.3390/sym12060981