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11 pages, 646 KB

Open AccessReview

Status and Prospects of the χ_c1(3872) Study at BESIII

by Hongjian Zhou, Xin Liu, Yueming Zhang and Chunhua Li

Symmetry 2025, 17(10), 1595; https://doi.org/10.3390/sym17101595 - 24 Sep 2025

Viewed by 58

The

χ_{c 1} (3872)

plays a pivotal role in understanding hadronic structures, remaining one of the most extensively studied exotic particles among numerous observed unconventional hadronic states. Sustained experimental and theoretical investigations into the particle over the past two decades [...] Read more.

The

χ_{c 1} (3872)

plays a pivotal role in understanding hadronic structures, remaining one of the most extensively studied exotic particles among numerous observed unconventional hadronic states. Sustained experimental and theoretical investigations into the particle over the past two decades have propelled its study into a high-precision regime, marked by refined measurements of its decay dynamics and line shape, thereby offering critical insights for resolving longstanding debates between molecular, tetraquark, hybrid, and charmonium interpretations of this particle. Furthermore, the heavy-quark symmetry in the molecular picture predicts a series of

χ_{c 1} (3872)

partners. The BESIII experiment has made seminal contributions to the study of the

χ_{c 1} (3872)

, leveraging its unique capabilities in high-statistics data acquisition and low-background condition, such as observations of the productions

e^{+} e^{-} \to γ χ_{c 1} (3872)

and

ω χ_{c 1} (3872)

and investigations of its decays. This article gives a concise review and prospects of the study of the

χ_{c 1} (3872)

from the BESIII experiment. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

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14 pages, 356 KB

Open AccessArticle

The Charmed Meson Spectrum Using One-Loop Corrections to the One-Gluon Exchange Potential

by André Capelo-Astudillo, Telmo Aguilar, Marlon Conde-Correa, Álvaro Duenas-Vidal, Pablo G. Ortega and Jorge Segovia

Symmetry 2025, 17(9), 1575; https://doi.org/10.3390/sym17091575 - 20 Sep 2025

Viewed by 158

Abstract

We investigate the charmed meson spectrum using a constituent quark model (CQM) with one-loop corrections applied to the one-gluon exchange (OGE) potential. The study aims to understand if the modified version of our CQM sufficiently account for the charmed meson spectrum observed experimentally, [...] Read more.

We investigate the charmed meson spectrum using a constituent quark model (CQM) with one-loop corrections applied to the one-gluon exchange (OGE) potential. The study aims to understand if the modified version of our CQM sufficiently account for the charmed meson spectrum observed experimentally, without invoking exotic quark and gluon configurations such as hybrid mesons or tetraquarks. Within this model, charmed mesons’ masses are computed, comparing theoretical predictions to experimental data. The results, within uncertainties, suggest that our theoretical framework generally reproduces mass splittings and level ordering observed for charmed mesons. Particularly, large discrepancies between theory and experiment found in P-wave states are, at least, significantly ameliorated by incorporating higher-order interaction terms. Therefore, the findings emphasize that while the traditional quark model is limited in fully describing charmed mesons, enhanced potential terms may bridge the gap with experimental observations. The study contributes a framework for predicting excited charmed meson states for future experimental validation. Full article

(This article belongs to the Section Physics)

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17 pages, 1739 KB

Open AccessArticle

Masses of Hadrons, Tetraquarks, and Pentaquarks Through a Tsallis-Entropy Approach in the MIT Bag Model

by Vanesa Fernández, Gerardo Herrera Corral, Manuel A. Matías Astorga and Jesús M. Sáenz

Entropy 2025, 27(7), 681; https://doi.org/10.3390/e27070681 - 26 Jun 2025

Viewed by 794

Abstract

We propose a new approach to describe hadrons and new forms of quark matter in the MIT bag model. The proposal is an extension that integrates a Tsallis nonextensive statistics description of quarks and gluons and is shown to capture the main features [...] Read more.

We propose a new approach to describe hadrons and new forms of quark matter in the MIT bag model. The proposal is an extension that integrates a Tsallis nonextensive statistics description of quarks and gluons and is shown to capture the main features underlying mass spectroscopy. While the traditional bag model successfully accounts for the masses of light hadrons, it has not been widely used to describe exotic quark configurations. We compute the system’s internal energy and derive expressions for hadronic masses, showing how they depend on the Tsallis parameter. The model reasonably reproduces known mass spectra of conventional hadrons and naturally extends to exotic states such as tetraquarks and pentaquarks. Additionally, we provide estimates of hadron radii within this framework. Our results suggest that nonextensive statistics provide a meaningful generalization of the bag model, capturing both conventional and exotic features of hadronic matter within a unified formalism. Full article

(This article belongs to the Section Statistical Physics)

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21 pages, 439 KB

Open AccessArticle

Exploring the Interpretations of Charmonia and cc

\bar{c} \bar{c}

Tetraquarks in the Relativistic Flux Tube Model

by Wen-Chao Dong, Zhi-Gang Wang and Jian-Wen Zhou

Symmetry 2025, 17(6), 931; https://doi.org/10.3390/sym17060931 - 11 Jun 2025

Viewed by 903

Abstract

Incited by the scant understanding of unsettled charmonia and newly observed

c c \bar{c} \bar{c}

tetraquarks, this work aims to explore the canonical interpretations and spectroscopic properties of these fully hidden-charm states. In the framework of a relativistic flux tube model, [...] Read more.

Incited by the scant understanding of unsettled charmonia and newly observed

c c \bar{c} \bar{c}

tetraquarks, this work aims to explore the canonical interpretations and spectroscopic properties of these fully hidden-charm states. In the framework of a relativistic flux tube model, the centroid masses of the low-lying

n L

-wave states with

1 \leq n + L \leq 4

are unraveled. In order to pin down the complete mass spectra, the hyperfine splittings induced by the spin-dependent interactions are incorporated into the final predictions. Accordingly, fourteen charmonia are well identified, including the

η_{c} (1 S)

,

J / ψ (1 S)

,

χ_{c 0} (1 P)

,

h_{c} (1 P)

,

χ_{c 1} (1 P)

,

χ_{c 2} (1 P)

,

η_{c} (2 S)

,

ψ (2 S)

,

ψ (3770)

,

ψ_{2} (3823)

,

ψ_{3} (3842)

,

χ_{c 0} (3915)

,

χ_{c 2} (3930)

, and

ψ (4040)

states. Additionally, the exotic

T_{ψ ψ} (6400)

,

T_{ψ ψ} (6600)

,

T_{ψ ψ} (6900)

, and

T_{ψ ψ} (7300)

states are interpreted as the

1 S

-wave,

1 P / 2 S

-wave,

1 D / 2 P

-wave, and

2 D / 3 P / 4 S

-wave

c c \bar{c} \bar{c}

tetraquarks, respectively. Based on the achieved outcomes, the spin-parity quantum number is imperative to discriminate the nature of the

c c \bar{c} \bar{c}

structures, pending further experimental measurement in the future. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

24 pages, 651 KB

Open AccessArticle

Triply Heavy Tetraquark States in a Mass-Splitting Model

by Shi-Yuan Li, Yan-Rui Liu, Zi-Long Man, Cheng-Rui Shu, Zong-Guo Si and Jing Wu

Symmetry 2025, 17(2), 170; https://doi.org/10.3390/sym17020170 - 23 Jan 2025

Cited by 1 | Viewed by 775

Abstract

In a modified chromomagnetic interaction model, assuming

X (4140)

to be the lowest

1^{+ +}

c s \bar{c} \bar{s}

tetraquark and treating it as the reference state, we systematically investigated the masses of the triply heavy tetraquark states [...] Read more.

In a modified chromomagnetic interaction model, assuming

X (4140)

to be the lowest

1^{+ +}

c s \bar{c} \bar{s}

tetraquark and treating it as the reference state, we systematically investigated the masses of the triply heavy tetraquark states

Q Q \bar{Q} \bar{q}

(

Q = c, b; q = u, d, s

). Because of their higher masses, no stable tetraquarks were found. Using a simple scheme, we also estimated the partial widths of the rearrangement decay channels and relevant ratios. A compact triply heavy tetraquark candidate would be favored if its observed mass and partial width ratios were comparable with our predictions. We hope that the present work will be helpful for further studies. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

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15 pages, 452 KB

Open AccessEditor’s ChoiceArticle

Strong Decays of the ϕ(2170) as a Fully Strange Tetraquark State

by Yi-Wei Jiang, Wei-Han Tan, Hua-Xing Chen and Er-Liang Cui

Symmetry 2024, 16(8), 1021; https://doi.org/10.3390/sym16081021 - 9 Aug 2024

Cited by 2 | Viewed by 959

Abstract

We study the strong decays of the

ϕ (2170)

, along with its possible partner

X (2436)

, as two fully strange tetraquark states of

J^{P C} = 1^{- -}

. These two states are assumed to [...] Read more.

We study the strong decays of the

ϕ (2170)

, along with its possible partner

X (2436)

, as two fully strange tetraquark states of

J^{P C} = 1^{- -}

. These two states are assumed to contain two strange quarks and two anti-strange quarks, with the flavor symmetry

6_{s s} \otimes {\bar{6}}_{\bar{s} \bar{s}}

. We consider seven decay channels:

ϕ η

,

ϕ η^{'}

,

ϕ f_{0} (980)

,

ϕ f_{1} (1420)

,

h_{1} (1415) η

,

h_{1} (1415) η^{'}

, and

h_{1} (1415) f_{1} (1420)

. Some of these channels are kinematically possible, and we calculate their relative branching ratios through the Fierz rearrangement. Future experimental measurements on these ratios could be useful in determining the nature of the

ϕ (2170)

and

X (2436)

. The

ϕ (2170)

has been observed in the

ϕ f_{0} (980)

,

ϕ η

, and

ϕ η^{'}

channels, and we propose to further examine it in the

h_{1} (1415) η

channel. Evidences of the

X (2436)

have been observed in the

ϕ f_{0} (980)

channel, and we propose to verify whether this structure exists or not in the

ϕ η

,

ϕ η^{'}

,

h_{1} (1415) η

, and

h_{1} (1415) η^{'}

channels. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

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39 pages, 1973 KB

Open AccessReview

Exotic Tetraquarks at the HL-LHC with JETHAD: A High-Energy Viewpoint

by Francesco Giovanni Celiberto

Symmetry 2024, 16(5), 550; https://doi.org/10.3390/sym16050550 - 2 May 2024

Cited by 11 | Viewed by 1649

Abstract

We review the semi-inclusive hadroproduction of a neutral hidden-flavor tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0 determinations of leading-twist fragmentation functions to describe the [...] Read more.

We review the semi-inclusive hadroproduction of a neutral hidden-flavor tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0 determinations of leading-twist fragmentation functions to describe the formation mechanism of a tetraquark state within the next-to-leading order perturbative QCD. This framework builds on the basis of a spin physics-inspired model, taken as a proxy for the lowest-scale input of the constituent heavy-quark fragmentation channel. Then, all parton-to-tetraquark fragmentation functions are consistently obtained via the above-threshold DGLAP evolution in a variable-flavor number scheme. We provide predictions for a series of differential distributions calculated by the hands of the JETHAD method, well-adapted to

NLL / {NLO}^{+}

hybrid-factorization studies, where the resummation of next-to-leading energy logarithms and beyond is included in the collinear picture. We provide corroborating evidence that high-energy observables sensitive to semi-inclusive tetraquark emissions at the HL-LHC exhibit a fair stability under radiative corrections, as well as MHOU studies. Our analysis constitutes a prime contact point between QCD resummations and the exotic matter. Full article

(This article belongs to the Special Issue Symmetry and Quantum Chromodynamics in Heavy-Hadron and Quarkonium Production)

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14 pages, 1379 KB

Open AccessArticle

Investigating Fully Strange Tetraquark System with Positive Parity in a Chiral Quark Model

by Yue Tan, Yuheng Wu, Hongxia Huang and Jialun Ping

Universe 2024, 10(1), 17; https://doi.org/10.3390/universe10010017 - 29 Dec 2023

Cited by 3 | Viewed by 1465

Abstract

Motivated by the intriguing discovery of

X (6900)

by the LHCb collaboration, we undertake a comprehensive study of the

s \bar{s} s \bar{s}

tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We [...] Read more.

Motivated by the intriguing discovery of

X (6900)

by the LHCb collaboration, we undertake a comprehensive study of the

s \bar{s} s \bar{s}

tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark (

s s

-

\bar{s} \bar{s}

) structure and meson–meson (

s \bar{s}

-

s \bar{s}

) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with

J^{P} = 0^{+}

, namely,

R (0, 2150)

and

R (0, 2915)

, as well as a resonant state with

J^{P} = 1^{+}

, denoted as

R (1, 2950)

, and a resonant state with

J^{P} = 2^{+}

, denoted as

R (2, 2850)

, utilizing the real-scaling method. By comparing their energies and widths, we suggest that

R (0, 2915)

and

R (1, 2950)

may share characteristics with

X (6900)

, while

R (0, 2150)

could be a promising candidate for the experimental state

f_{0} (2100)

. We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states. Full article

(This article belongs to the Special Issue Universe: Feature Papers 2024—High Energy Nuclear and Particle Physics)

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12 pages, 373 KB

Open AccessArticle

Mission Target: Tetraquark Mesons of Flavour-Cryptoexotic Type

by Wolfgang Lucha

Universe 2023, 9(8), 358; https://doi.org/10.3390/universe9080358 - 31 Jul 2023

Cited by 2 | Viewed by 2143

Abstract

Currently, flavour-cryptoexotic tetraquarks form the most common sort of all experimentally established exotic multiquark hadrons. This note points out a few promising concepts that should help improve theoretical (but, for several reasons, not quite straightforward) analyses of this kind of states; among others, [...] Read more.

Currently, flavour-cryptoexotic tetraquarks form the most common sort of all experimentally established exotic multiquark hadrons. This note points out a few promising concepts that should help improve theoretical (but, for several reasons, not quite straightforward) analyses of this kind of states; among others, their scope of application encompasses the strong interactions in the limit of (arbitrarily) large numbers of colours, and equally analytical and nonperturbative approaches to multiquark states. Full article

(This article belongs to the Special Issue Recent Progress in Hadron Spectroscopy)

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76 pages, 2612 KB

Open AccessFeature PaperEditor’s ChoiceReview

Tetraquarks and Pentaquarks from Quark Model Perspective

by Hongxia Huang, Chengrong Deng, Xuejie Liu, Yue Tan and Jialun Ping

Symmetry 2023, 15(7), 1298; https://doi.org/10.3390/sym15071298 - 22 Jun 2023

Cited by 37 | Viewed by 4330

Abstract

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review [...] Read more.

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review articles on exotic hadrons available so far; the present article tries to focus on the recent experimental and theoretical progress on the exotic states from the perspective of the quark model. Although lattice quantum chromodynamics may give the final answer of the problem, the phenomenological models are still powerful tools to explore the exotic states and to provide insight on the phenomenology of hadrons. The spatial and color structures of multiquark states and the channel coupling calculation are emphasized through reviewing some bound states, molecular and color structure resonances. Finally, the unquench effects of some exotic states are reviewed. With the accumulation of experimental data on multiquark states and inspiration of underlying theory developments, more reasonable phenomenological models incorporating multi-body interactions and high Fock components to unify the description of normal hadrons and exotic hadrons are expectable. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2022)

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8 pages, 286 KB

Open AccessArticle

T_cs and

T_{c \bar{s}}

Family Production in Multi-Production Processes

by Chuanhui Jiang, Yi Jin, Shi-Yuan Li, Yan-Rui Liu and Zong-Guo Si

Symmetry 2023, 15(3), 695; https://doi.org/10.3390/sym15030695 - 10 Mar 2023

Cited by 5 | Viewed by 1838

Abstract

The production mechanism of multiquark exotic hadrons in high energy multiproduction processes lies in the structure of the relevant exotic hadrons as well as in some important aspects of high energy scattering, such as multi-parton interactions, underlying events, etc. At mass pole around [...] Read more.

The production mechanism of multiquark exotic hadrons in high energy multiproduction processes lies in the structure of the relevant exotic hadrons as well as in some important aspects of high energy scattering, such as multi-parton interactions, underlying events, etc. At mass pole around 2900 MeV, a family of open charm tetraquarks,

T_{c s}

s and

T_{c \bar{s}}

s, are observed in B decay. They are also suitable for study in multiproduction processes to obtain more information on their structure. If these resonances are produced as compact four-quark states, one can predict the production properties based on the similarities in their production mechanism to those of

Ξ_{c}

,

Σ_{c}

, and

Λ_{c}

. Physics implies that the colour and baryon number fluctuations of the preconfinement system in high energy scattering can enhance both the baryon and four-quark state production rates via ‘diquark fragmentation’. We calculate the production properties of the tetraquark family

T_{c s}

s and

T_{c \bar{s}}

s at LHC energy for the forthcoming LHC measurements. Full article

(This article belongs to the Special Issue Heavy-Ion Collisions and Multiparticle Production)

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35 pages, 558 KB

Open AccessFeature PaperArticle

Fully Heavy Tetraquark Spectroscopy in the Relativistic Quark Model

by Rudolf N. Faustov, Vladimir O. Galkin and Elena M. Savchenko

Symmetry 2022, 14(12), 2504; https://doi.org/10.3390/sym14122504 - 26 Nov 2022

Cited by 47 | Viewed by 2853

Abstract

Masses of the ground and excited (1P, 2S, 1D, 2P, 3S) states of the fully heavy tetraquarks, composed of charm (c) and bottom (b) quarks and antiquarks, are calculated in the diquark–antidiquark picture within the relativistic quark model based [...] Read more.

Masses of the ground and excited (1P, 2S, 1D, 2P, 3S) states of the fully heavy tetraquarks, composed of charm (c) and bottom (b) quarks and antiquarks, are calculated in the diquark–antidiquark picture within the relativistic quark model based on the quasipotential approach and quantum chromodynamics. The quasipotentials of the quark–quark and diquark–antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. Relativistic effects are consistently taken into account. A tetraquark is considered a bound state of a diquark and an antidiquark. The finite size of the diquark is taken into account, using the form factors of the diquark–gluon interaction. It is shown that most of the investigated states of tetraquarks lie above the decay thresholds into a meson pair; as a result, they can be observed only as broad resonances. The narrow state X(6900) recently discovered in the di-

J / ψ

production spectrum by the LHCb, CMS and ATLAS Collaborations corresponds to an excited state of the fully charmed tetraquark. Other recently discovered exotic heavy resonances, X(6200), X(6400), X(6600), X(7200), and X(7300), can also be interpreted as the different excitations of the fully charmed tetraquark. Full article

(This article belongs to the Section Physics)

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34 pages, 702 KB

Open AccessFeature PaperArticle

The Interplay between Compact and Molecular Structures in Tetraquarks

by Hagop Sazdjian

Symmetry 2022, 14(3), 515; https://doi.org/10.3390/sym14030515 - 2 Mar 2022

Cited by 17 | Viewed by 2517

Abstract

Due to the cluster reducibility of multiquark operators, a strong interplay exists in tetraquarks between the compact structures, resulting from the direct confining forces acting on quarks and gluons, and the molecular structure, dominated by the mesonic clusters. This issue is studied within [...] Read more.

Due to the cluster reducibility of multiquark operators, a strong interplay exists in tetraquarks between the compact structures, resulting from the direct confining forces acting on quarks and gluons, and the molecular structure, dominated by the mesonic clusters. This issue is studied within an effective field theory approach, where the compact tetraquark is treated as an elementary particle. The key ingredient of the analysis is provided by the primary coupling constant of the compact tetraquark to the two mesonic clusters, considered here in the framework of a scalar interaction. Under the influence of this coupling, an initially formed compact tetraquark bound state evolves towards a new structure, where a molecular configuration is also present. In the strong-coupling limit, the evolution may end with a shallow bound state of the molecular type. The strong-coupling regime is also favored by the large

N_{c}^{}

properties of QCD. The interplay between compact and molecular structures may provide a natural explanation of the existence of many shallow bound states. Full article

(This article belongs to the Special Issue Search for New Phenomena in Heavy-Quark Physics)

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20 pages, 4111 KB

Open AccessArticle

The Genuine Resonance of Full-Charm Tetraquarks

by Xiaoyun Chen

Universe 2021, 7(5), 155; https://doi.org/10.3390/universe7050155 - 18 May 2021

Cited by 5 | Viewed by 1991

Abstract

In this work, the genuine resonance states of full-charm tetraquark systems with quantum numbers

J^{P C} = 0^{+ +}, 1^{+ -}, 2^{+ +}

are searched in a nonrelativistic chiral quark model with the help of the Gaussian [...] Read more.

In this work, the genuine resonance states of full-charm tetraquark systems with quantum numbers

J^{P C} = 0^{+ +}, 1^{+ -}, 2^{+ +}

are searched in a nonrelativistic chiral quark model with the help of the Gaussian Expansion Method. In this calculation, two structures, meson-meson and diquark–antidiquark, as well as their mixing with all possible color-spin configurations, are considered. The results show that no bound states can be formed. However, resonances are possible because of the color structure. The genuine resonances are identified by the stabilization method (real scaling method). Several resonances for the full-charm system are proposed, and some of them are reasonable candidates for the full-charm states recently reported by LHCb. Full article

(This article belongs to the Section High Energy Nuclear and Particle Physics)

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11 pages, 317 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Radiative and Meson Decays of Y(4230) in Flavor SU(3)

by Luciano Maiani, Antonio Davide Polosa and Verónica Riquer

Symmetry 2021, 13(5), 751; https://doi.org/10.3390/sym13050751 - 26 Apr 2021

Cited by 4 | Viewed by 2611

Abstract

The charmonium-like exotic states

Y (4230)

and the less known

Y (4320)

, produced in

e^{+} e^{-}

collisions, are sources of positive parity exotic hadrons in association with photons or pseudoscalar mesons. We analyze the radiative and [...] Read more.

The charmonium-like exotic states

Y (4230)

and the less known

Y (4320)

, produced in

e^{+} e^{-}

collisions, are sources of positive parity exotic hadrons in association with photons or pseudoscalar mesons. We analyze the radiative and pion decay channels in the compact tetraquark scheme, with a method that proves to work equally well in the most studied

D^{*} \to γ / π + D

decays. The decay of the vector Y into a pion and a

Z_{c}

state requires a flip of charge conjugation and isospin that is described appropriately in the formalism used. Rates are found to depend on the fifth power of pion momentum, which would make the final states

π Z_{c} (4020)

strongly suppressed with respect to

π Z_{c} (3900)

. The agreement with BES III data would be improved considering the

π Z_{c} (4020)

events to be fed by the tail of the

Y (4320)

resonance under the

Y (4230)

. These results should renovate the interest in further clarifying the emerging experimental picture in this mass region. Full article

(This article belongs to the Special Issue Search for New Phenomena in Heavy-Quark Physics)

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