The Meson That Wasn't There

Spoiler alert: A paper describing a predicted kind of meson resonance that isn't observed doesn't provide any solid hypotheses to explain why this is the case, so don't expect a feel good conclusion at the end of this post.

Quantum chromodynamics, the Standard Model theory of the strong force, in at least some ways of operationalizing the theory to a level where one can do calculations with it, predicts that mesons with a quark and an antiquark of valence quarks generally have related states with higher masses whose properties can be predicted theoretically. 

But efforts to operationalize QCD struggle to understand scalar mesons (spin-0, even parity), axial vector mesons (spin-1, even parity) a.k.a. pseudo-vector mesons, and certain higher spin mesons, which are observed but don't flow naturally and obviously from a simple minded valence quark model.

The charged rho anti-meson which is a vector (i.e. spin-1) meson an anti-up quark and a down quark as valence quarks and a measured mass of 775.11 ± 0.34 MeV has several excited states that are predicted. 

One of these predicted states related to it is a spin-2 (i.e. tensor) meson with negative charge and odd parity but a higher mass than the 775 MeV ground state that is known as the ρ2 meson.  The authors of this paper calculate that it should have a mass of about 1663 MeV. 

But, this predicted rho meson state hasn't been observed, even though its predicted mass is at an energy scale that has been studied by many experiments. 

Indeed, there is a crowd of well established meson resonances in the right mass range that have been observed, not all of which are well understood, but none of the observed resonances is an obvious match to the predicted ρ2 meson that the researchers are trying to reconcile with the experimental evidence. 

Two candidate resonances with the right quantum numbers have been identified, but they are significantly more massive than the predicted values.

As the paper below explains in its introduction:

PDG contains various mesons denoted with the letter ρ . These are the isovector resonances with quantum number of isospin (I = 1), of parity (P = −1), and of charge conjugation (C = −1). For instance, the vector mesons ρ(770) with quantum number JPC = 1 −−, the excited vector mesons ρ(1450), ρ(1700), and the tensor meson ρ3 (1690) with quantum number JPC = 3 −−. 

Despite the prediction of the ρ2 in the Relativistic Quark model, it is still missing experimentally. We only have the following data which were observed from different experimental groups and listed as “further states” in PDG: ρ2 (1940) and ρ2 (2225) with the total decay widths Γ tot ρ2 (1940) ≃ 155±40 MeV and Γ tot ρ2 (2225) ≃ 335+100 −50 MeV accordingly. 

Axial tensor mesons are studied in recent LQCD [Lattice QCD] simulations, where the authors consider the mass of ρ2 is about 1.7 GeV as the ρ3 (1690). We present the results about the missing ρ2 within a chiral effective model which is so-called the extended Linear Sigma Model (eLSM).

Part of the problem is that different ways to operationalizing QCD so that QCD calculations can be done produce significantly different predicted decay products for the ρ2 meson as the paper explains with this chart:

Still, despite these discrepancies, all of the predicted decays of the ρ2 meson are very different from the predicted and observed decays of the well established ρ3(1690) meson, so confusion between the two isn't likely.

The conclusion of the paper states:

We have studied ρ2 axial-tensor meson, chiral partner of the tensor meson ρ2 (1320) in the framework of a chiral model for low-energy QCD. We predict its mass to be around 1.663 GeV. A phenomenological note on the missing ρ2 meson similar to the Relativistic Quark model prediction. Because of the chiral symmetry, the parameter determined in the tensor sector allows to make predictions for unknown ground-state axial-tensor resonance. The effective model fitting to the LQCD results is also presented.

The paper and its abstract are:

The ρ2 meson is the missing isovector member of the meson nonet with the quantum numbers JPC=2−−. It belongs to the class of ρ-mesons such as the vector meson ρ(770), the excited vector ρ(1700) and the tensor ρ3(1690). Yet, despite the rich experimental and theoretical studies for other ρ-meson states, no resonance that could be assigned to the ρ2 meson has been measured. In this note, we present the results for the mass and dominant decay channels of the ρ2 meson within the extended Linear Sigma Model.

Shahriyar Jafarzade, "A phenomenological note on the missing ρ2 meson" arXiv:2210.12421 (October 22, 2022) (Contribution to the 41st International Conference on High Energy Physics - ICHEP2022,6-13 July, 2022, Bologna, Italy).