Letter
Open Access

Anomalous interactions between mesons with nonzero spin and glueballs

Francesco Giacosa ^*

Shahriyar Jafarzade ^†

Robert D. Pisarski ^‡

Institute of Physics, Jan Kochanowski University, ulica Uniwersytecka 7 Street, P-25-406 Kielce, Poland and Institute for Theoretical Physics, Goethe University Frankfurt, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany

Institute of Physics, Jan Kochanowski University, ulica Uniwersytecka 7 Street, P-25-406 Kielce, Poland; Institute of Radiation Problems, Ministry of Science and Education, B. Vahabzade 9 Street, AZ1143 Baku, Azerbaijan; and Center for Theoretical Physics, Khazar University, Mehseti 41 Street, Baku AZ1096, Azerbaijan

Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA

^*francesco.giacosa@gmail.com
^†shahriyar.jzade@gmail.com
^‡pisarski@bnl.gov

PDF

Phys. Rev. D 109, L071502 – Published 8 April, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L071502

Abstract

Topologically nontrivial fluctuations control the anomalous interactions for the $η$ and $η^{'}$ pseudoscalar mesons. We consider the anomalous interactions for mesons with higher spin, the heterochiral nonets with $J^{P C} = 1^{+ -}$ and $2^{- +}$ . Under the approximation of a dilute gas of instantons, the mixing angle between nonstrange and strange mesons decreases strongly as $J$ increases, and oscillates in sign. Anomalous interactions also open up new, rare decay channels. For glueballs, anomalous interactions indicate that the $X (2600)$ state is primarily gluonic.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (71)

S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177, 2426 (1969).
J. S. Bell and R. W. Jackiw, A PCAC puzzle: $π^{0} \to γ γ$ in the $σ$ -model, Nuovo Cimento A 60, 47 (1969).
A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. B 59, 85 (1975).
G. ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37, 8 (1976).
G. ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14, 3432 (1976).
D. J. Gross, S. B. Treiman, and F. Wilczek, Light quark masses and isospin violation, Phys. Rev. D 19, 2188 (1979).
V. P. Nair and R. D. Pisarski, Fractional topological charge in SU(N) gauge theories without dynamical quarks, Phys. Rev. D 108, 074007 (2023).
F. Giacosa, A. Koenigstein, and R. D. Pisarski, How the axial anomaly controls flavor mixing among mesons, Phys. Rev. D 97, 091901 (2018).
H. Gomm, O. Kaymakcalan, and J. Schechter, Anomalous spin 1 meson decays from the gauged Wess-Zumino term, Phys. Rev. D 30, 2345 (1984).
R. D. Pisarski and F. Rennecke, The chiral phase transition and the axial anomaly, arXiv:2401.06130.
G. Amelino-Camelia et al., Physics with the KLOE-2 experiment at the upgraded $DA ϕ NE$ , Eur. Phys. J. C 68, 619 (2010).
T. Feldmann, P. Kroll, and B. Stech, Mixing and decay constants of pseudoscalar mesons, Phys. Rev. D 58, 114006 (1998).
G. ’t Hooft, How instantons solve the $U (1)$ problem, Phys. Rep. 142, 357 (1986).
J. R. Pelaez, From controversy to precision on the sigma meson: A review on the status of the non-ordinary $f_{0} (500)$ resonance, Phys. Rep. 658, 1 (2016).
A. V. Sarantsev, I. Denisenko, U. Thoma, and E. Klempt, Scalar isoscalar mesons and the scalar glueball from radiative $J / ψ$ decays, Phys. Lett. B 816, 136227 (2021).
A. Rodas, A. Pilloni, M. Albaladejo, C. Fernandez-Ramirez, V. Mathieu, and A. P. Szczepaniak (Joint Physics Analysis Center), Scalar and tensor resonances in $J / ψ$ radiative decays, Eur. Phys. J. C 82, 80 (2022).
D. Binosi, A. Pilloni, and R.-A. Tripolt, Study for a model-independent pole determination of overlapping resonances, Phys. Lett. B 839, 137809 (2023).
E. Klempt, A. V. Sarantsev, I. Denisenko, and K. V. Nikonov, Search for the tensor glueball, Phys. Lett. B 830, 137171 (2022).
E. Klempt, Scalar mesons and the fragmented glueball, Phys. Lett. B 820, 136512 (2021).
E. Klempt and A. V. Sarantsev, Singlet-octet-glueball mixing of scalar mesons, Phys. Lett. B 826, 136906 (2022).
D. Guo, W. Chen, H.-X. Chen, X. Liu, and S.-L. Zhu, Newly observed $a_{0} (1817)$ as the scaling point of constructing the scalar meson spectroscopy, Phys. Rev. D 105, 114014 (2022).
Evidence is mounting toward the identification with the Particle Data Group (PDG) resonances $S = {a_{0} (1450)$ , $K_{0}^{*} (1430)$ , $f_{0} (1370)$ , $f_{0} (1500) / f_{0} (1710)}$ , with elements $S_{i j} = \frac{1}{2} \bar{q_{j}} q_{i}$ .
The kaonic pseudovector ${\bar{K}}_{1 B}$ is included in both physical states $K_{1} (1270)$ and $K_{1} (1400)$ [24, 25] which leads $m_{K_{1 B}} = 1.31 GeV$ according to [24]. In the PDG [26], the isoscalar strange-member of the orbitally excited vector meson has been recently identified with resonance $ϕ (2170)$ , see however also the discussion of Ref. [27].
F. Divotgey, L. Olbrich, and F. Giacosa, Phenomenology of axial-vector and pseudovector mesons: Decays and mixing in the kaonic sector, Eur. Phys. J. A 49, 135 (2013).
H. Hatanaka and K.-C. Yang, $K_{1} (1270) - K_{1} (1400)$ mixing angle and new-physics effects in $B \to K_{1} l^{+} l^{-}$ decays, Phys. Rev. D 78, 074007 (2008).
R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
M. Piotrowska, C. Reisinger, and F. Giacosa, Strong and radiative decays of excited vector mesons and predictions for a new $ϕ (1930)$ resonance, Phys. Rev. D 96, 054033 (2017).
We identify $K_{2 P}$ with $K_{2} (1770)$ based on the phenomenological analyses performed in Ref. [29].
A. Koenigstein, F. Giacosa, and D. H. Rischke, Classical and quantum theory of the massive spin-two field, Ann. Phys. (Amsterdam) 368, 16 (2016).
A. Koenigstein and F. Giacosa, Phenomenology of pseudotensor mesons and the pseudotensor glueball, Eur. Phys. J. A 52, 356 (2016).
V. Shastry, E. Trotti, and F. Giacosa, Constraints imposed by the partial wave amplitudes on the decays of $J = 1$ , 2 mesons, Phys. Rev. D 105, 054022 (2022).
These states are still unsettled. According to the relativistic quark model [33], orbitally excited tensor mesons have to be larger than 2 GeV. Indeed, there are few isoscalar tensor mesons above 2 GeV, such as the e.g. $f_{2} (2010)$ , $f_{2} (2150)$ , $f_{2} (2300)$ , and $f_{2} (2340)$ [26] that could be part of this nonet.
S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32, 189 (1985).
R. D. Pisarski and L. G. Yaffe, The density of instantons at finite temperature, Phys. Lett. 97B, 110 (1980).
D. J. Gross, R. D. Pisarski, and L. G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53, 43 (1981).
A. Boccaletti and D. Nogradi, The semi-classical approximation at high temperature revisited, J. High Energy Phys. 03 (2020) 045.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.109.L071502 for details of the instanton solution, computing from instantons to effective Lagrangians, complete forms of the anomalous interactions in terms of mesonic fields, and computations of the associated decay widths.
As $Λ_{\bar{MS}}$ is the only mass scale in our computation, for different values of $Λ_{\bar{MS}}$ the $k_{J}$ change according to their mass dimension.
G. ’t Hooft, The physics of instantons in the pseudoscalar and vector meson mixing, arXiv:hep-th/9903189.
C. Rosenzweig, A. Salomone, and J. Schechter, A pseudoscalar glueball, the axial anomaly and the mixing problem for pseudoscalar mesons, Phys. Rev. D 24, 2545 (1981).
The numerator of the mixing angle $β_{0}$ is proportional to the renormalization constants $Z_{η_{N}} Z_{η_{S}} \approx 2.6$ , which is found from the fit of experimental data to the extended Linear Sigma Model in Ref. [42].
D. Parganlija, P. Kovacs, G. Wolf, F. Giacosa, and D. H. Rischke, Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons, Phys. Rev. D 87, 014011 (2013).
P. Kovács, Z. Szép, and G. Wolf, Existence of the critical endpoint in the vector meson extended linear sigma model, Phys. Rev. D 93, 114014 (2016).
In Ref. [8] instead of $ε [A B C]$ we used the notation $tr (A \times B \cdot C)$ . We prefer the former because as a product of two $ε$ symbols, it is manifestly symmetric: $ε [A B C] = ε [B A C]$ , etc.
We note that the operators considered here are just those of the lowest mass dimension [10, 42, 46, 47, 48, 49, 50]. For spin zero, anomalous operators with higher mass dimensions include those from $Q = \pm 1$ , such as $\sim tr (Φ^{†} Φ) \det Φ$ , and those from $Q = \pm 2$ , such as $\sim (\det Φ)^{2}$ . Obviously, there are also anomalous operators with higher mass dimensions for spin one and above.
P. Kovács and G. Wolf, Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons: Investigation of the $U (1)_{A}$ anomaly term, Acta Phys. Pol. B Proc. Suppl. 6, 853 (2013).
M. Grahl and D. H. Rischke, Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly, Phys. Rev. D 88, 056014 (2013).
M. Grahl, $U (2)_{A} \times U (2)_{V}$ -symmetric fixed point from the functional renormalization group, Phys. Rev. D 90, 117904 (2014).
J. Eser, M. Grahl, and D. H. Rischke, Functional renormalization group study of the chiral phase transition including vector and axial-vector mesons, Phys. Rev. D 92, 096008 (2015).
R. D. Pisarski and F. Rennecke, Multi-instanton contributions to anomalous quark interactions, Phys. Rev. D 101, 114019 (2020).
The x-axis in Fig. 3 is the mass of $h_{1} (1415)$ meson, which represents experimental uncertainty in the mixing of $P_{μ}$ states using the Gell-Mann Okubo relation [52, 53].
M. Gell-Mann, Symmetries of baryons and mesons, Phys. Rev. 125, 1067 (1962).
S. Okubo, Note on unitary symmetry in strong interactions, Prog. Theor. Phys. 27, 949 (1962).
D. Aston et al., Evidence for two strangeonium resonances with $J^{P C} = 1^{+ +}$ and $1^{+ -}$ in $K^{-} p$ interactions at $11 − GeV / c$ , Phys. Lett. B 201, 573 (1988).
A. Abele et al. (Crystal Barrel Collaboration), Anti-proton proton annihilation at rest into $K_{L} K_{S} π^{0} π^{0}$ , Phys. Lett. B 415, 280 (1997).
M. Ablikim et al. (BESIII Collaboration), Study of $χ_{c J}$ decaying into $ϕ$ $K^{*} (892)$ $\bar{K}$ , Phys. Rev. D 91, 112008 (2015).
M. Ablikim et al. (BESIII Collaboration), Observation of $h_{1} (1380)$ in the $J / ψ \to η^{'} K \bar{K} π$ decay, Phys. Rev. D 98, 072005 (2018).
J. J. Dudek, R. G. Edwards, B. Joo, M. J. Peardon, D. G. Richards, and C. E. Thomas, Isoscalar meson spectroscopy from lattice QCD, Phys. Rev. D 83, 111502 (2011).
The result for $β_{2}$ is derived by considering similar mass relations for spin-2 mesons, Eqs. (3.1)–(3.4) of Ref. [60], adding the anomalous coupling in Eq. (13).
S. Jafarzade, A. Vereijken, M. Piotrowska, and F. Giacosa, From well-known tensor mesons to yet unknown axial-tensor mesons, Phys. Rev. D 106, 036008 (2022).
J. J. Dudek, R. G. Edwards, P. Guo, and C. E. Thomas (Hadron Spectrum Collaboration), Toward the excited isoscalar meson spectrum from lattice QCD, Phys. Rev. D 88, 094505 (2013).
W. I. Eshraim, S. Janowski, F. Giacosa, and D. H. Rischke, Decay of the pseudoscalar glueball into scalar and pseudoscalar mesons, Phys. Rev. D 87, 054036 (2013).
M. Ablikim et al. (BESIII Collaboration), Observation of a state $X (2600)$ in the $π^{+} π^{-} η^{'}$ system in the process $J / ψ \to γ π^{+} π^{-} η^{'}$ , Phys. Rev. Lett. 129, 042001 (2022).
We note that the mass found in lattice QCD [65] agrees with the identification of this state as a glueball.
A. Athenodorou and M. Teper, The glueball spectrum of SU(3) gauge theory in $3 + 1$ dimensions, J. High Energy Phys. 11 (2020) 172.
L. Olbrich, M. Zétényi, F. Giacosa, and D. H. Rischke, Influence of the axial anomaly on the decay $N (1535) \to N η$ , Phys. Rev. D 97, 014007 (2018).
A. H. Fariborz, R. Jora, and J. Schechter, Two chiral nonet model with massless quarks, Phys. Rev. D 77, 034006 (2008).
W. I. Eshraim, C. S. Fischer, F. Giacosa, and D. Parganlija, Hybrid phenomenology in a chiral approach, Eur. Phys. J. Plus 135, 945 (2020).
V. Shastry, C. S. Fischer, and F. Giacosa, The phenomenology of the exotic hybrid nonet with $π 1 (1600)$ and $η 1 (1855)$ , Phys. Lett. B 834, 137478 (2022).
S. Gongyo et al., Most strange dibaryon from lattice QCD, Phys. Rev. Lett. 120, 212001 (2018).
J. R. Green, A. D. Hanlon, P. M. Junnarkar, and H. Wittig, Weakly bound $H$ dibaryon from SU(3)-flavor-symmetric QCD, Phys. Rev. Lett. 127, 242003 (2021).

Phys. Rev. D 109, L071502– Published 8 April, 2024

Vol. 109, Iss. 7 — 1 April 2024

Received 5 September 2023
Accepted 1 March 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L071502

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Anomalous interactions between mesons with nonzero spin and glueballs

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (71)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation