Influence of threshold effects induced bycharmed meson rescattering

Xiao-Hai LiuTokyo Institute of Technology

For Workshop on Progress on J-PARC Hadron Physics
Tokai, 2014.12.02

1

Outline Motivation
 Coupled-channel effects and thresholdenhancement phenomenaDipion transitions e+e-J/ψππ, ψ'ππ ,hcππZb production, hunting for some XYZ particles
Anomalous threshold singularity

Summary2

Motivation
Observations of XYZ particles;
Discrepancy between conventional quenchedquark model predictions and experimentaldata;Coupled-channel effects will largely affect themass and decay properties of heavyquarkonia;

ccbb

qq

ccbb
3

Coupled-channel effects
 E. Eichten et al, PRD17,3090(1978), PRD73,104014(2006);
 M.R. Pennington, D.J. Wilson, PRD76,077502(2008);
 T. Barnes, E.S. Swanson, PRC77,055206(2008);
 B.Q. Li, C.Meng, K.T. Chao, PRD80,014012(2009);
 F.K. Guo et al; PRD83,034013(2011);
 Z.Y. Zhou, Z. Xiao, arXiv:1309.1949;
 ……

4

Unconventional states in heavy quarkonium region

arXiv:1010.5827

5

Coupled-channel effects with P-wave states involved Combinations of S- and P-wave charmed mesons
are very close to some conventional highercharmonia(ψ(4160), ψ(4415)) and Y(4260), Y(4360),Z(4430) ……); The coupling with the parity-odd charmonia could
be S-wave, supposed to be strong;
D0D*

D1’D

D1’D*

D1D

D1D*

D2D

D2D*

Ds0Ds*

Ds1Ds

Threshold 4325
[MeV]

4292

4434

4286

4428

4327

4470

4430

4424

Connections between coupled channel effects and XYZ?
6

Model based on HHChPT
Doublets with light degrees of freedom 𝒋𝑷 =1/2-,1/2+,3/2+

HQSS allowed coupling(LDOF will also be conserved)

HHSHTHψ(nS)P-waveS-waveD-waveψ(nD)P-waveD-waveS-wave7

Leading Order Effective Lagrangian
According to HHChPT power counting

8Dipion Transitions

ψ(4160) as the input ψ(nD): Widely accepted as a conventional 𝟐𝟑 𝑫𝟏 charmonia
 Couple to TH via S-wave, respect HQSS
 Close to Y(4260)
M=4153±3 MeV, Γ =103±𝟖 MeV PDG averaged
M=4191.7±6.5 MeV, Γ =71.8±12.3 MeV BES, PLB660,315(2008)
M=4193±7 MeV, Γ =79±14 MeV X.H. Mo et al, PRD82,077501(2010)𝜞𝒆𝒆 =0.83±0.07 KeV, not small

9THH Loop
Triangle singularity (TS)may occur under special
kinematic configurations

In the heavy quark limit
10Triangle Singularity
Largely isospin violation in η(1405/1475)3π
Br~10%, [BESIII, PRL108,182001 (2012)]

Wu,Liu,Zhao&Zou, PRL108,081803(2012)

References:
Landshoff and Treiman, Phys.Rev. 127,649(1962)
Landshoff and Treiman, Nuovo Cimento 19,1249(1961)
Eden et al., <<The Analytic S-Matrix>>, 1966
…………

11

e e → J / ψππ via ψ(4160) and THH loops+ −BESIII, 2013

CLEOc, 2013

Belle, 2007
√𝑠=4.26 GeV√𝑠=4.17 GeV
12e e → ψ ′ππ via ψ(4160) and THH loops+ −BarBar, PRL98,212001(2007)

Results are sensitive tokinematics
Same dynamics, differentkinematics
Direct prediction to check themechanism13

e e → hcππ via ψ(4160) and THH loops+ −Sum of energy points from 3.9 to 4.42

C.Z. Yuan, arXiv:1312.6399

Belle, PRL111,242001(2013)14

Comparison with Molecule Ansatz
Similar points: kinematics, singularities of rescattering loops
 Different points:•Incorporates the D1D, D1D* , D2D* combinations in a single Lagrangianwith the relative phase and coupling strength fixed in the heavy quarklimit;•No matter whether the molecular state exist or not, it seems to be natural
to suppose the coupled channel effects should exist physicallyY(4260) as molecular state:
 D1D, D0D* molecular state, F. Close et al, PRL102,242003(2009),
PRD81,074033(2010); Kalashnikova and Nefediev, PRD77,054025(2008);
 Potential model, G.J. Ding PRD79,014001(2009) Connection with Zc(3900), Wang, Zhao and Hanhart,PRL111,132003(2013); X.H. Liu and G.Li, PRD88,014013(2013)
 ......

15

HHH Loop and SHH Loop

No obvious cusp around 3.9GeV,
inconsistent with CLEOc result

Broad width of D0 and D1’ will lower
the amplitude and smooth the cusps

16

Zb Production
Υ(5S)Υ(1S,2S,3S)

Cusps at BB* and B*B* thresholds

Production of Zb(10610) and Zb(10650)
17

Hunting For Partners of Y4160 &Y4274
Isospin violation processes

ψ(4S)
J/ψη

Cusps at DsDs* and Ds*Ds*thresholds(C=-1 )

Production of partners ofY(4160) and Y(4274)(observed in J/ψφ, C=+1 )18

Anomalous Threshold Singularity
 Singularity in the complex space
Landau Equation

Necessary conditions
Leading singularity

19

Anomalous Threshold Singularity

Normal threshold=Anomalous thresholdwhen20Anomalous Threshold Singularity

Γ(K*)=021

Anomalous Threshold Singularity

For investigating J/ψπinteraction22Summary The lineshape behavior of the cross sections anddistributions for the dipion transitions are studied. Couplechannel effects may largely affect the threshold behavior,especially that induced by the couplings between D-wave
charmonia and TH charmed mesons, taking into accountthese leading order S-wave couplings will respect HQSS.
 Some interesting cusps are obtained, which may have someunderlying connections with the XYZ states observed
around the TH and HH thresholds.
 Kinematics plays a crucial role in generating the cusps.
 Anomalous threshold singularity would be used todiscriminate coupled-channel effects and genuine resonances.
23