Influence of threshold effects induced by heavy
flavor meson rescattering

Xiao-Hai LiuTokyo Institute of Technology

For Hadrons & Hadron Interactions in QCD 2015 (HHIQCD2015)
YITP, Kyoto, 2015.03.03

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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 heavy
quarkonia;
ccbbqqccbb
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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;
 ……

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Unconventional states in heavy quarkonium region

arXiv:1411.7738

5Status of searches for new statesarXiv:1411.5957

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Y(4260)
BABAR 2005

CLEO 2006

observed in J/ψππBelle, 2007

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Belle 2008 e+e-  DDBelle, PRD79,092001; sum of e+e-open charm

R-value Scan, BES, 20078

Y(4260)
Theoretical explanation
Hybrid S.L. Zhu;Close&Page;Kou &Pene
Tetraquark Ebert et al; Maiani et alBaryonium of Λc anti-Λc C.F. Qiaoχc0ρ , χc1ω molecule, sizeable coupling with χc0ω Liu et al;
Yuan et al; Dai et alInterference of other charmonium

Chen et al

D1D, D0D* molecular state Close et al; Kalashnikova et al;
G.J. Ding
……
9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?
10Model based on HHChPTHQSS allowed coupling(LDOF will also be conserved)

HHSHTHψ(nS)P-waveS-waveD-waveψ(nD)P-waveD-waveS-wave11

Leading Order Effective Lagrangian
According to HHChPT power counting

12Dipion Transitions

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

In the heavy quark limit
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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
…………

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

BESIII, 2013

CLEOc, 2013

Belle, 200716

e + e − → ψ ′ππ via ψ(4160) and THH loops


BarBar, PRL98,212001(2007)

Results are sensitive tokinematics
Same dynamics, different
kinematics
Direct prediction to check themechanism17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)18

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)
 ......

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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 cusps20

Zb Production
Υ(5S)Υ(1S,2S,3S)

Cusps at BB* and B*B* thresholds

Production of Zb(10610) and Zb(10650)
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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 )22Anomalous Threshold Singularity
 Singularity in the complex space
Landau Equation

Necessary conditions
Leading singularity

The position of the singularity is obtained bysolving
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Anomalous Threshold Singularity

Normal thresholdAnomalous threshold24

Anomalous Threshold Singularity
Single dispersion relationBrach points of the log function is at
Work in the kinematical region25

Anomalous Threshold Singularity
Double dispersion relation

Landau typecontribution

Non-Landau typecontribution

Double spectral function can be obtained according
to Cutkosky rule26

Anomalous Threshold Singularity
When

How to amplify the discrepancy between normal andanomalous threshold?
If the discrepancy is larger, it could be used to
distinguish the cusp effects and molecular states.
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Anomalous Threshold Singularity

Γ(K*)=028

Anomalous Threshold Singularity

For investigating J/ψπinteraction

29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.

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Thanks!

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