1. Light mesons and structure of QCD vacuum
M.V. Polyakov
Petersburg NPI and Bochum University
What we have learned about QCD vacuum from the lightest mesons?
QCD strings and structure of the meson spectrum
Chiral symmetry restoration for excited mesons ?
Pion strings ?
Conclusions

2. [S. Weinberg `74]

3. Non-trivial statement about QCD vacuum,
topological density
Non-trivial statement about QCD vacuum,
topological density must fluctuate in very specific way !
[G. Veneziano `79]

4. Topological charge density fluctuations in QCD vacuum (cooled lattice)
[Simulation by D. Leinweber]

5. Instanton

6. Instanton transitions on lattice
[Simulation by D. Leinweber]

7. [Simulation by D. Leinweber]

8. Frequently one takes for granted that the flux tube model explains
string picture of QCD.
The flux-tube picture is obtained on lattice for infinitely heavy quarks
The QCD dynamics with light quarks is qualitatively different from
because of
The phenomenon of spontaneous breakdown of the chiral
symmetry!
This phenomenon is ignored in flux-tube picture of mesons

9. [Dolen,Horn,Schmidt `67]
[Lovelace, Shapiro `68]

10. Mass spectrum in a dual (string) model
Leading Regge trajectory _
Trajectory in “daughter direction” _

11. Chiral Sym.Restoration ?
Experimental spectrum of light
nonstrange mesons
(a plot from S.S. Afonin, Eur. Phys. J. A 29 (2006) 327)
Major features:
Clustering
Parity doubling?
Chiral Sym.Restoration ?
(recent review: S.S. Afonin, Int. J. Mod. Phys.
A 22 (2007) 4537)
Need confirmation!! Without them
The „string“ spectrum is not evident.
Particle Data
Crystal Barrel

12. CRYSTAL BARREL D S G D A.V. Anisovich, V.V. Anisovich and
A.V. Sarantsev,
Phys. Rev. D 62 (2000)
V.V. Anisovich, Phys. Usp. 47 (2004) 45
D.V. Bugg, Phys. Rept. 397 (2004) 257 G D

13. [see review by Glozman, Phys.Rept.444 ]
[Glozman, Nevediev ‚07 ]

14. In any case no parity doublets for leading
The spectrum of Ademollo-Veneziano-Weinberg dual amplitude and experimental data
(a plot from S.S. Afonin, Phys. Lett. B 639 (2006) 258)
In any case no parity doublets for leading
Regge trajectory ! Chiral symmetry is
not restored! It remains spontaneously
broken !

15. [Diakonov, Petrov `89]
[Vereshagin, M.V.P. `95]

16. Pion strings ? The cheapest way to construct high J meson
Simple excercise from theoretical mechanics
Find configuration of system of particles various masses with
fixed angular momentum J and minimal energy E.
Minimum of energy corresponds to the situation when the lightest
degrees of freedom rotate at large distances around heavy remnant
What are the lightest dofs in strong interactions ?
Nambu- Goldstone bosons !
The cheapest way to construct high J meson
is to excite pion field !

17. Rotating chiral soliton and its deformation
Slow rotation – low lying baryons:
Octet, decuplet, antideciplet,
Fast rotation – soliton is deformed
Into sigare like form. Linear meson traj.
For higher representations rotation becomes faster

19. S. Weinberg `68
J. Gasser, Leuthwyler `83

21. Conclusions
Studies of the lightest pseudoscalar mesons brought us
invaluable insights into non-perturbative structure of QCD vacuum
Mass spectrum of light mesons show pattern charakteristic for string
models.
BUT
Most of meson states are from single experiment/analysis (CB).
Very important - independent studies !
String models should not be identified with flux-tube models, the
latter are in conflict with SChSB.
Chiral symmetry remains broken for higly excited mesons .
Proof : No chiral partners for mesons on main Regge trajec.
To make QCD strings talking with chiral degrees of freedom is very
important. String made of pions ?
Detailed studies of decay patterns (cascade-like or split-apart)
of highly excited mesons will allow to understand which d.o.f. are
prefereably excited in such mesons.
Quasi-classical picture (symmetries) for highly excited mesons ?

22. Nucleon‘s slice