1. Mitja Rosina POSSIBILITIES OF DETECTING THE DD* DIMESONS at Belle2
Faculty of Mathematics and Physics, University of Ljubljana
and Institute Jožef Stefan, Ljubljana, Slovenia
Talk presented at the
Mini-Workshop BLED 2017:
ADVANCES IN HADRONIC RESONANCES
2 – 9 July 2017

2. ABSTRACT
I shall present an interesting comparison between the “molecule“ of two heavy (charmed) mesons and the hydogen molecule.
At short distance, the two protons in the hydrogen molecule are repelled by the electrostatic interaction, while the two heavy (charm) quarks in the mesonic molecule are attracted by the chromodynamic interaction because they can recouple their colour charges.
The BB* dimeson (tetraquark) is expected to be strongly bound (>100 MeV) while the DD* dimeson is weakly bound (~2 MeV) or a low resonance.
AIM:
Effective quark-quark interaction
(Is Vuu = Vcu = Vcc = Vcc = Vbu = Vbb ?)
Interesting 4-body problem, for binding and for production mechanism
CHALLENGE:
Old theory, but a new chance for measurement of LHC and DD*=(cu,cd) at upgraded KEK, Tsukuba (Japan).

3. Comparison between charmed dimesons and hydrogen molecule
OUTLINE
Comparison between charmed dimesons and hydrogen molecule
2. Is the D+D* dimeson bound?
3. The production of dimesons in p-p colliders
4. The production of Belle & Belle2
5. The decay of the dimeson DD* detection

4. 1. Comparison between charmed . dimesons and hydrogen moleculeHe u c c d d
He atom
Meson π+
Atom-like tetraquark c u
p e
e p u u d d c
Molecule H+H
Baryon (nucleon)
Dimeson D+D*

5. PHENOMENOLOGICAL ESTIMATE OF BINDINGu u b u bb b b d b d d
Dimeson B+B*
( =10604)MeV
like Λb antibaryon ( )MeV
Tetraquark u u c u c c cc d c d d
like Λ c antibaryon ( )MeV
Dimeson D+D*
( =3875)MeV
Tetraquark

6. COMPARISON BETWEEN DIMESON AND HYDROGEN MOLECULE POTENTIALV
rcc u cc c c c
D + D* d

7. 2. Is the D+D* dimeson bound?
In the restricted 4-body space assuming "cc" in a bound diquark state + general wavefunction of u and d, the energy is above the D+D* threshold. In the restricted "molecular" 4-body space assuming the two c quarks far apart + general wavefunction of ubar and dbar (as assumed by several authors), the energy is also above the D+D* threshold. Only combining both spaces (we took a rich 4-body space) brings the energy below the threshold.
We should verify whether it happens also for other interactions ( we have used the one-gluon exchange+linear confinement).

8. It is an interesting question whether in the first step "cc" diquark is formed and later automatically dressed by u or d or ubar+dbar, or is the first step to form D + D* which merge into DD*.The later choice can profit from resonance formation, but due to ther dense environement it is a danger that the D + D* system would again dissociate before really forming the dimeson.
We intend to see which formalism would be appropriate for this. The title of the Bled Workshop is anyway "Advances in hadronic resonances".

9. We failed to calculate the energy of X(3872) using the same method and interaction as for DD*, [Bled Proceedings 2005]. The reason is that a perfect variational calculation in a rather complete 4-body space finds the absolute minimum of energy which correspnds to J/psi+eta rather than DD* A demanding coupled channel calculation would be needed for a reliable result, and we have posponed it.

10. 3. The production of dimesons in p-p colliders
1.step: double two-gluon fusion
(g + g) + (g + g) (c + c) + (c + c)
2.step: two c fly close enough in phase space
(c + c) cc [colour antisymmetric diquark]
3.step: the diquark cc gets dressed, cc ccud.
4.step: dimeson forms, cc u d cu cd = D D*
The upper bound for a luminosity 1033/cm2s was estimated to be 104 events/hour (or 5 events per hour for bbud)
The alternative process that first two D mesons form and later they find each other and merge, is less probable.

11. In our 2005 paper (PRD 71, 014008) we made a simple
(optimistic!) estimate assuming the known cross-section of double ccbar pairs as seen in J/ψ ccbar production (about 1pb).
We used an impulse approximation, essentialy the overlap between the cc diquark wavefunction and the wavefunction of two separate c quarks smeared in the volume of the size of proton. +
If SELEX has really seen ,
then it could have seen 4 T+cc too few!
There are much better chances at Belle2 ! cc

12. The estimate of the diquark formation (Del Fabro, Janc, Rosina Treleani 2005)
We make an impulse approximation that this two-
quark state is instantaneously transformed in any of the
27 nb (LHCb) ; 58 nb (ALICE)

13. b B- = bu ….. 0.375+0.015 B0 = bd Bs = bs 0.160+0.025 Λb = bud
The dressing (fragmentation) of the b quark b B-
= bu
….. B0
= bd Bs
= bs Λb
= bud
Fermilab CDF 2000
The dressing (fragmentation) of the cc diquark cc
cc++
= ccu
…..
37 %
cc+
= ccd
Ω cc+
= ccs
16 %
T cc+
=ccud
9 %

14. 4. The production of dimesons @ Belle & Belle2
Belle till now: 1 ab
15% below, 50% at, 35% above Y(4s)
Total σ ~ nb
σ(J/ψ X) ~ 1pb
σ(J/ψ cc) ~ 0.5 pb [mostly J/ψ ηc]
σ(DD) < 1pb

15. Inclusive Production of Four Charm Hadrons
in e+e− Annihilation at B Factories
Daekyoung Kang, Jong-Wan Lee, and Jungil Lee
Department of Physics, Korea University, Seoul , Korea PRD71 (2005) (R)
E0=10.6GeV

16. A SIMPLIFIED ESTIMATE In order to understand why σ ~ picobarn Q ε,p q
Q=10 GeV, mc=1.5 GeV
α = 1/137, αs = 0.2
Assume:

17. 5. The decay of the dimeson DD* detection
(65 %)
(67 %)
(31 %)
or:
D0* D0 + γ MeV
D+* D+ + γ MeV
(35 %)
(2 %)
DD* D + D + γ + ~140 MeV

18. WHY DO WE PREFER Tcc to Tbb ?
It is more abundant (perhaps : 5)
It is easier to detect, Tcc D+ + K- + π+
(in analogy to Λ c+ + K- + π+ )
It is more delicate, barely bound or barely unbound, would distinguish between different models.
Might help to understand the mechanism of high production rate of double cc + cc Belle.

19. THANKS FOR YOUR ATTENTION! YOUR CRITICISM AND SUGGESTIONS
I SHALL APPRECIATE
YOUR CRITICISM AND SUGGESTIONS

20. (is Vuu = Vcu = Vcc = Vcc = Vbb ?)
6. Test of the effective quark-quark interaction
(is Vuu = Vcu = Vcc = Vcc = Vbb ?)
A. One-gluon exchange + confinement (color.color) [GRENOBLE]
B.One-Goldstone boson exch.+ confinement (flavor.flavor) [GRAZ ]

21. The „Vqq = Vqq rule“ , cc ud = cud + c + cc - cc12 ,
cc ud = cud + c cc cc
[A]: (color.color)=4/3 for cc
=2/3 for cc
[B]: Flux tube model c c c c c

22. α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω
Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω