Two-Pole Structures in QCD: Facts, Not Fantasy!

• Main Author: Ulf-G. Meißner
• Format: Article
• Language: English
• Published: MDPI AG 2020-06-01
• Series: Symmetry
• Subjects: Chiral symmetry; coupled channels; hadron spectrum; lattice QCD; chiral perturbation theory; unitarization
• Online Access: https://www.mdpi.com/2073-8994/12/6/981

The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Λ</mi> <mo>(</mo> <mn>1405</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, when in 2001, using unitarized chiral perturbation theory, it was observed that there are two poles in the complex plane, one close to the <inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>K</mi> <mo>¯</mo> </mover> <mi>p</mi> </mrow> </semantics> </math> </inline-formula> and the other close to the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>π</mi> <mi>Σ</mi> </mrow> </semantics> </math> </inline-formula> threshold. This was later understood combining the SU(3) limit and group-theoretical arguments. Different unitarization approaches that all lead to the two-pole structure have been considered in the mean time, showing some spread in the pole positions. This fact is now part of the PDG book, although it is not yet listed in the summary tables. Here, I discuss the open ends and critically review approaches that cannot deal with this issue. In the meson sector, some excited charm mesons are good candidates for such a two-pole structure. Next, I consider in detail the <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>D</mi> <mn>0</mn> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mn>2300</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, which is another candidate for this scenario. Combining lattice QCD with chiral unitary approaches in the finite volume, the precise data of the Hadron Spectrum Collaboration for coupled-channel <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mi>π</mi> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mi>η</mi> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <mover accent="true"> <mi>K</mi> <mo>¯</mo> </mover> </mrow> </semantics> </math> </inline-formula> scattering in the isospin <inline-formula> <math display="inline"> <semantics> <mrow> <mi>I</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> channel indeed reveal its two-pole structure. Further states in the heavy meson sector with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>I</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> exhibiting this phenomenon are predicted, especially in the beauty meson sector. I also discuss the relation of these two-pole structures and the possible molecular nature of the states under consideration.