XYZ Particles from Lattice QCD Ying Chen Institute of High Energy Physics, Chinese Academy of Sciences, China XYZ 2020, Fudan Univ, Jan. 11, 2020
XYZ Particles from Lattice QCD
Ying Chen
Institute of High Energy Physics,
Chinese Academy of Sciences, China
XYZ 2020, Fudan Univ, Jan. 11, 2020
Outline
I. Introduction
II. ๐ฟ(๐๐๐๐) relevant
III. ๐๐ states from lattice QCD
IV. ๐(๐๐๐๐) relevant studies
V Summary
I. Introduction
meson baryon
hadron molecule
tetraquark pentaquark
hybrid glueball
Exotic hadrons
On the other hand, many XYZ particle have been discovered
in recent years.
Charmoinum(-like) family
(N. Brambilla et al, arXiv:1907.07583[hep-ph])
Present status of lattice QCD study on hadron spectroscopy
II. ๐ฟ(๐๐๐๐) relevant lattice studies
S. Prelovsek & L. Leskovec, PRL111(2013)192001
1. ๐ซเดฅ๐ซโ scattering and ๐ฟ(๐๐๐๐)
Operators (๐ถ๐ = ๐ซเดฅ๐ซโ, ฮค๐ฑ ๐ ๐ , ๐เดค๐ )
๐ช๐๐ ๐ = ๐ถ๐ ๐ ๐ถ๐+ ๐ =
๐
๐๐๐๐๐
๐ โ๐โ๐๐๐
Only ๐เดค๐-type operator : The 2nd state higher than ๐ซเดฅ๐ซโ threshold
๐ซเดฅ๐ซโ + ๐เดค๐-type operator : The 2nd state lower than ๐ซเดฅ๐ซโ threshold
๐ฌ ๐ = ๐๐ซ๐ + ๐๐ + ๐๐ซโ
๐ + ๐๐ โน ๐๐ โก๐๐
๐ณ
๐
๐๐
Phase shift:
Effective range expansion:
๐ ๐๐๐ ๐น ๐ =๐๐๐๐ ๐; ๐๐
๐ ๐ณ
๐๐๐จ๐ญ ๐น ๐ =๐
๐๐๐ซเดฅ๐ซโ
+๐
๐๐๐๐ซเดฅ๐ซโ๐๐
๐๐๐ซเดฅ๐ซโ = โ๐. ๐ ยฑ ๐. ๐ fm
๐๐๐ซเดฅ๐ซโ = โ๐. ๐ ยฑ ๐. ๐ fm
In the ๐ณ โ โ limit, the existence of a bound state implies
๐ป โ๐
๐๐๐ ๐น ๐๐ฉ โ ๐= โโน แ
๐๐๐ ๐น ๐๐ฉ = ๐๐๐ฉ = โ๐|๐๐ฉ|
Effective range expansion:
โ ๐๐ฉ =๐
๐๐๐ซเดฅ๐ซโ
โ๐
๐๐๐๐ซเดฅ๐ซโ ๐๐ฉ
๐
๐ฌ ๐๐ฉ, ๐ณ = โ = ๐๐ซ๐ + ๐๐ฉ
๐ + ๐๐ซโ๐ + ๐๐ฉ
๐ โก ๐๐ฟ
Binding Energy๏ผ ๐ซ๐ฌ๐ฉ = ๐๐ฟ โ ๐๐ซ +๐เดฅ๐ซโ
๐๐(๐๐๐๐) : first observed as a structure in ๐ฑ/๐๐ + invariant mass
spectrum, its โmassโ is close to the ๐ซเดฅ๐ซโ threshold
๐๐(๐๐๐๐) : first observed as a structure in ๐๐๐ + invariant mass
spectrum, its โmassโ is close to the ๐ซโเดฅ๐ซโ threshold.
๐๐(๐๐๐๐) : first observed as a structure in ๐โฒ๐ + invariant mass
spectrum, its โmassโ is close to the ๐ซโเดฅ๐ซ๐ threshold.
Lattice studies from three aspects:
1. ๐ซเดฅ๐ซ scattering
๐๐ ๐๐๐๐ : Y. Chen et al. (CLQCD), PRD89(2014)094506,
๐๐ ๐๐๐๐ : Y. Chen et al. (CLQCD), PRD92(2015)054507.
๐๐ ๐๐๐๐ : T. Chen et al. (CLQCD), PRD93(2016)114501,
G. Meng et al. (CLQCD), PRD 70(2009) 034503
2. Spectroscopy study (S. Prelovsek et al., PRD91(2015)014504)
3. Potential matrix and scattering amplitudes
Y. Ikeda et al (HAL Collab.), PRL117(2016) 2420014. ๐ซเดฅ๐ซโ and ฮค๐ฑ ๐ ๐ coupled-channel effects relevant to ๐๐(๐๐๐๐)
T. Chen et al. (CLQCD), Chin. Phys. C43 (2019) no.10, 103103
III. ๐๐ State relevant lattice studies
1. Scattering:
i) The masses of ๐ซ mesons
ii) The energies of ๐ซเดฅ๐ซโ system
iii) Define the scattering momenta of ๐ซ mesons in the ๐ซเดฅ๐ซโ system
iv) Use the Lรผscher formular to get the scattering phase shift
v) For near threshold scattering, one can use the effective range
expansion to parameterize the phase shift versus q.
Calculation procedure:
๐ฌ๐,๐ ๐ = ๐๐๐ + ๐๐ + ๐๐
๐ + ๐๐ , ๐๐ = ๐๐๐ณ
๐๐
๐
๐ ๐๐จ๐ญ ๐น๐(๐) =๐
๐ ฮค๐ ๐๐ฉ๐๐ ๐; ๐๐
๐๐๐+๐ ๐๐จ๐ญ ๐น๐ ๐ = ๐๐โ๐ +
๐
๐๐๐๐
๐ +โฏ
๐๐ ๐๐๐๐ and ๐๐ ๐๐๐๐ : In the ๐ฝ๐ = 1+ channel, the scattering lengths are
negative, indicating a weak repulsive interaction between D(D*) and D*bar.
These results does not support a bound state in this channel. However, since
the pion mass is still much higher than the physical pion mass, we cannot rule
out the possible appearance of a bound state. A more systematic lattice study is
demanding.
๐๐(๐๐๐๐) : In ๐ฝ๐ = 1+ , 0โ channels, the interaction between the two
charmed mesons is attractive near the threshold in both channels.
2. Spectroscopy study on Zc statesS. Prelovsek et al., Phys. Rev. D 91, 014504 (2015) arXiv:1405.7623(hep-lat)
โข Spectroscopic study
โข Quite a lot of two-particle operators and tetraquark operators
are involved
All the scatering states below 4.2 GeV are obtained.
They concluded that No convincing exotic Zc state is observed.
3. On the structure of Zc(3900) from lattice QCD
a) BS wave functions of two-meson systems are extracted
from lattice QCD.
b) Subsequently, the interaction potentials are obtained.
c) Couple channel effects of eta_c rho, J/psi pi and DD*bar is
considered.
d) They conclude the near DD*bar threshold enhancement
is due to the J/psi pi and DD*bar coupling.
(Y. Ikeda et al (HAL Collab.), PRL117(2016) 242001)
Two-body ๐ป matrix on the basis of the potential matrix ๐ฝ๐ถ๐ท
๐๐ถ๐ท ๐๐ถ, ๐๐ท;๐พ๐๐ = ๐ฝ๐ถ๐ท(๐๐ถ, ๐๐ท)
+
๐ธ
เถฑ๐ ๐๐ธ๐ฝ๐ถ๐ธ ๐๐ถ, ๐๐ธ ๐๐ธ๐ท(๐๐ธ, ๐๐ท;๐พ๐๐)
๐พ๐๐ โ ๐ฌ๐ธ ๐๐ธ + ๐๐
๐๐ถ๐ท ๐พ๐๐๐=๐ ๐๐ถ๐ท
๐ ๐
4. ๐ซเดฅ๐ซโ and ฮค๐ฑ ๐ ๐ coupled-channel effects relevant to ๐๐(๐๐๐๐)T. Chen et al. (CLQCD), Chin. Phys. C43 (2019) no.10, 103103
The two-channel Lรผscher formula now takes the form
The best fit parameters do not correspond to the peak in the
elastic scattering cross-section near the threshold
In the zero-range Ross-Shaw theory,the scenario of a narrow
resonance close to the threshold is disfavored
beyond the 3๐ level
IV. ๐ ๐๐๐๐ relevant lattice studies
Latest charmonium spectrum from lattice QCD
1. 1โ hybrid-like interpolation field operator
แ๐๐๐พ5๐๐๐ต๐
๐๐
Nonrelativistic decomposition
0โ+ แ๐๐พ5๐ ๐+๐
1โโ แ๐๐พ๐๐ ๐+๐๐๐
1โโ๐ป แ๐๐๐พ5๐๐๐ต๐
๐๐ ๐๐+๐๐๐ต๐
๐๐
c-cbar spin triplet
c-cbar spin singlet
Y. Chen, W. Chiu et al., Chin. Phys. C40, 081002 (2016)
ิฆ๐
๐ต๐๐๐(ิฆ๐)
๐
ว๐
๐(ิฆ๐) = ( ว๐๐๐พ5๐๐)(0)๐ต๐
๐๐(ิฆ๐)In the Coulomb gauge,
This is equivalent to giave
a c-cbar center of mass
motion, which describes
the recoil of the c-cbar
against additional degrees
of freedom.
2. Spatially extended interpolation field operator for
the vector charmonium-like state
Intuitively, the coupling of this kind of operators to conventional
vector charmonia can be suppressed from two aspects:
a) spin states of the c-cbar (spin flipping is suppressed by the
heavy quark mass.
b) center-of-mass motion ( to the leading order of NR, there is
no cneter-of-mass motions for conventional charmonia.)
This kind of operator does couple strongly to a state with mass
near 4.3 GeV, as seen in the effective mass plateau
ฮ(๐(4260) โ ๐+๐โ)ฮ(๐(4260) โ ๐ฝ/๐๐+๐โ)/ฮ๐ก๐๐ก = 5.8๐๐
1. The leptonic decay width of this exotic vector chamonium
is an important quantity, which can shed light on the
nature of Y(4260).
2. The leptonic decay constant of the exotic state can be
calculated directly in lattice QCD.
0 ว๐๐พ๐๐ ๐( ิฆ๐, ๐) = ๐๐๐๐๐๐( ิฆ๐, ๐)
The decay constant of a vector meson is defined as
where the matrix element on the left can be derived
by calculate the two point function
ิฆ๐ฅ
0 ว๐๐พ๐๐( ิฆ๐ฅ, ๐ก)๐(๐ค)(0) 0 =
๐,๐
1
2๐๐0 ว๐๐พ๐๐ ๐๐ , ๐ ๐๐ , ๐ ๐
(๐ค) 0 ๐โ๐๐๐ก
3. The leptonic decay width of the exotic vector charnomium
Using the formula
One can predict
ฮ(๐(4260) โ ๐+๐โ)ฮ(๐(4260) โ ๐ฝ/๐๐+๐โ)/ฮ๐ก๐๐ก = 5.8๐๐
> 10%
โHalo charmoniumโ:
A relatively localized kernal of color octet ccbar surrounded by a
gluonic cloud.
The glounic cloud can be easily hadronized into light hadrons
by emitting or absorbing a soft gluon.
Consequently halo charmonium has large branching ratios to
decay into a conventional charmoium by emitting light hadrons.
๐+๐โ โ ๐ฝ/๐๐+๐โ
BESIII, PRL118(2017)092001 [arXiv: 1611.01317(hep-ex)]
BESIII, PRL118(2017)092002
arXiv: 1610.07044(hep-ex)
๐+๐โ โ ๐๐0๐
๐+๐โ โ โ๐๐+๐โ
๐ฝ/๐๐+๐โ mode: relative S-wave between ๐ฑ/๐ and ๐+๐โ
โ๐๐+๐โ mode: relative P-wave between ๐๐ and ๐+๐โ
๐๐0๐ mode: relative S-wave between and ๐๐0 ๐
The ๐เดค๐ in the halo charmonium is spin singlet (S=0),
๐ฑ/๐๐ +๐ โ mode: ๐ฑ/๐ (S=1), spin flipping, ๐๐ suppressed,
no refugal barrier
๐๐๐๐ mode: ๐๐๐ (S=1), spin flipping, ๐๐ suppressed,
no centrifugal barrier
๐๐๐ +๐ โ mode: ๐๐ (S=0), no spin flipping,
but suppressed by the centrifugal barrier .
In this picture, it is understandable that the above three
modes have similar cross section at ๐ โผ ๐. ๐๐ ๐ฎ๐๐ฝ
A state is missing between ฯ(4040) and ฯ(4415) in the ฯ(nS) family.
Y (4230) can be a candidate for this state, but properties are very different.
Therefore, it is intriguing that there be an additional ฯ state here to be
discovered.
3: Bethe-Salpeter Wave functions of Hybrid Charmonia
Y. Ma, W. Sun, Y. Chen M. Gong, Z. Liu, arXiv: 1910.09819 (hep-lat)
ิฆ๐
๐ต๐๐๐(ิฆ๐)
๐
ว๐
Intuitively, the coupling of this kind of
operators to conventional charmonia
can be suppressed from two aspects:
a) spin states of the c-cbar (spin
flipping is suppressed by the
heavy quark mass.
b) center-of-mass motion ( to the
leading order of NR, there is
no cneter-of-mass motions for
conventional charmonia.)
This is equivalent to give a
c-cbar center of mass
motion, which describes
the recoil of the c-cbar
against additional degrees
of freedom.
In the Coulomb gauge,
๐(ิฆ๐) = ( ว๐๐๐พ5๐๐)(0)๐ต๐
๐๐(ิฆ๐)
๐โ +
๐โ +
Decay modes of ๐, ๐, ๐ โ+ charmonia: ฮค๐ฑ ๐๐(๐) (P-wave), ๐๐๐ฑ๐ผ (S-wave)
BelleII and LHCb could take the mission to search them.
โข XYZ particles are hot topics in lattice QCD study,
but no decisive conclusions have not be obtained.
โข There are still many difficulties for lattice QCD to study
exotic hadrons, from both the theoretical tools and
numerical calculations.
IV. Summary
Thanks!