# Tetraquark operators in lattice QCD and exotic flavour states in the charm sector

## Abstract

We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to m _{π} = 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Furthermore, there is no strong indication for any bound state or narrow resonance in the channels we study.

- Authors:

- Univ. of Cambridge, Cambridge (United Kingdom)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Laboratory, Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- Contributing Org.:
- for the Hadron Spectrum collaboration

- OSTI Identifier:
- 1416530

- Report Number(s):
- JLAB-THY-17-2541; DOE/OR/23177-4205; arXiv:1709.01417

Journal ID: ISSN 1029-8479; PII: 7009; TRN: US1800952

- Grant/Contract Number:
- AC05-06OR23177; SC0006765

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice field theory simulation; QCD Phenomenology

### Citation Formats

```
Cheung, Gavin K. C., Thomas, Christopher E., Dudek, Jozef J., and Edwards, Robert G. Tetraquark operators in lattice QCD and exotic flavour states in the charm sector. United States: N. p., 2017.
Web. doi:10.1007/JHEP11(2017)033.
```

```
Cheung, Gavin K. C., Thomas, Christopher E., Dudek, Jozef J., & Edwards, Robert G. Tetraquark operators in lattice QCD and exotic flavour states in the charm sector. United States. doi:10.1007/JHEP11(2017)033.
```

```
Cheung, Gavin K. C., Thomas, Christopher E., Dudek, Jozef J., and Edwards, Robert G. Wed .
"Tetraquark operators in lattice QCD and exotic flavour states in the charm sector". United States. doi:10.1007/JHEP11(2017)033. https://www.osti.gov/servlets/purl/1416530.
```

```
@article{osti_1416530,
```

title = {Tetraquark operators in lattice QCD and exotic flavour states in the charm sector},

author = {Cheung, Gavin K. C. and Thomas, Christopher E. and Dudek, Jozef J. and Edwards, Robert G.},

abstractNote = {We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to mπ = 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Furthermore, there is no strong indication for any bound state or narrow resonance in the channels we study.},

doi = {10.1007/JHEP11(2017)033},

journal = {Journal of High Energy Physics (Online)},

number = 11,

volume = 2017,

place = {United States},

year = {2017},

month = {11}

}

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Works referenced in this record:

##
Exotic states in QCD

journal, June 1993

- Manohar, Aneesh V.; Wise, Mark B.
- Nuclear Physics B, Vol. 399, Issue 1

##
Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

journal, October 2016

- Moir, Graham; Peardon, Michael; Ryan, Sinéad M.
- Journal of High Energy Physics, Vol. 2016, Issue 10

##
Lattice QCD signal for a bottom-bottom tetraquark

journal, June 2013

- Bicudo, Pedro; Wagner, Marc
- Physical Review D, Vol. 87, Issue 11

##
Production and detection of doubly charmed tetraquarks

journal, January 2005

- Fabbro, A. Del; Janc, D.; Rosina, M.
- Physical Review D, Vol. 71, Issue 1

##
Solving lattice QCD systems of equations using mixed precision solvers on GPUs

journal, September 2010

- Clark, M. A.; Babich, R.; Barros, K.
- Computer Physics Communications, Vol. 181, Issue 9

##
Diquark-antidiquark states with hidden or open charm and the nature of $X(3872)$

journal, January 2005

- Maiani, L.; Piccinini, F.; Polosa, A. D.
- Physical Review D, Vol. 71, Issue 1

##
Angular momentum on a lattice

journal, July 1982

- Johnson, R. C.
- Physics Letters B, Vol. 114, Issue 2-3

##
Isoscalar $\pi \pi $ Scattering and the $\sigma $ Meson Resonance from QCD

journal, January 2017

- Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.
- Physical Review Letters, Vol. 118, Issue 2

##
Resonances in Coupled $\pi K\text{\u2212}\eta K$ Scattering from Quantum Chromodynamics

journal, October 2014

- Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
- Physical Review Letters, Vol. 113, Issue 18

##
Lattice Prediction for Deeply Bound Doubly Heavy Tetraquarks

journal, April 2017

- Francis, A.; Hudspith, R. J.; Lewis, R.
- Physical Review Letters, Vol. 118, Issue 14

##
Excited spectroscopy of charmed mesons from lattice QCD

journal, May 2013

- Moir, Graham; Peardon, Michael; Ryan, Sinéad M.
- Journal of High Energy Physics, Vol. 2013, Issue 5

##
QCD and strongly coupled gauge theories: challenges and perspectives

journal, October 2014

- Brambilla, N.; Eidelman, S.; Foka, P.
- The European Physical Journal C, Vol. 74, Issue 10

##
Signatures of unstable particles in finite volume

journal, October 1991

- Lüscher, Martin
- Nuclear Physics B, Vol. 364, Issue 1

##
$ud\overline{b}\overline{b}$ tetraquark resonances with lattice QCD potentials and the Born-Oppenheimer approximation

journal, September 2017

- Bicudo, Pedro; Cardoso, Marco; Peters, Antje
- Physical Review D, Vol. 96, Issue 5

##
Energy dependence of the $\rho $ resonance in $\pi \pi $ elastic scattering from lattice QCD

journal, February 2013

- Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
- Physical Review D, Vol. 87, Issue 3

##
Two-particle states on a torus and their relation to the scattering matrix

journal, May 1991

- Lüscher, Martin
- Nuclear Physics B, Vol. 354, Issue 2-3

##
Fate of the Tetraquark Candidate ${Z}_{c}(3900)$ from Lattice QCD

journal, December 2016

- Ikeda, Yoichi; Aoki, Sinya; Doi, Takumi
- Physical Review Letters, Vol. 117, Issue 24

##
Production of doubly charmed tetraquarks with exotic color configurations in electron–positron collisions

journal, April 2013

- Hyodo, Tetsuo; Liu, Yan-Rui; Oka, Makoto
- Physics Letters B, Vol. 721, Issue 1-3

##
Adjoint sources in lattice gauge theory

journal, September 1985

- Michael, C.
- Nuclear Physics B, Vol. 259, Issue 1

##
Multiparticle states and the hadron spectrum on the lattice

journal, September 2006

- Moore, David C.; Fleming, George T.
- Physical Review D, Vol. 74, Issue 5

##
Multiquark resonances

journal, January 2017

- Esposito, A.; Pilloni, A.; Polosa, A. D.
- Physics Reports, Vol. 668

##
Heavy-quark QCD exotica

journal, March 2017

- Lebed, Richard F.; Mitchell, Ryan E.; Swanson, Eric S.
- Progress in Particle and Nuclear Physics, Vol. 93

##
How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation

journal, July 1990

- Lüscher, Martin; Wolff, Ulli
- Nuclear Physics B, Vol. 339, Issue 1

##
The hidden-charm pentaquark and tetraquark states

journal, June 2016

- Chen, Hua-Xing; Chen, Wei; Liu, Xiang
- Physics Reports, Vol. 639

##
Tables of SU(3) Isoscalar Factors

journal, November 1995

- Kaeding, T. A.
- Atomic Data and Nuclear Data Tables, Vol. 61, Issue 2

##
The Octet Model and its Clebsch-Gordan Coefficients

journal, October 1963

- de Swart, J. J.
- Reviews of Modern Physics, Vol. 35, Issue 4

##
The Chroma Software System for Lattice QCD

journal, March 2005

- Edwards, Robert G.; Joó, Bálint
- Nuclear Physics B - Proceedings Supplements, Vol. 140

##
Angular momentum on the lattice: The case of nonzero linear momentum

journal, January 2006

- Moore, David C.; Fleming, George T.
- Physical Review D, Vol. 73, Issue 1