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

[S. Weinberg `74]

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

topological density

[Simulation by D. Leinweber]

Topological charge density fluctuations in QCD vacuum (cooled lattice)

Instanton

Instanton transitions on lattice

[Simulation by D. Leinweber]

[Simulation by D. Leinweber]

Frequently one takes for granted that the flux tube model explainsstring 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

[Dolen,Horn,Schmidt `67]

[Lovelace, Shapiro `68]

2m

PJ0 1 2 3

Mass spectrum in a dual (string) model

2 20( ) 'm J m J Leading Regge trajectory

_

Trajectory in “daughter direction”_2 20( )m n n

4

Particle Data Crystal Barrel

Experimental spectrum of lightnonstrange mesons

(a plot from S.S. Afonin, Eur. Phys. J. A 29 (2006) 327)

Major features: 1. Clustering2. Parity doubling? Chiral Sym.Restoration ?

(recent review: S.S. Afonin, Int. J. Mod. Phys. A 22 (2007) 4537)

Need confirmation!! Without themThe „string“ spectrum is not evident.

CRYSTAL BARREL

A.V. Anisovich, V.V. Anisovich andA.V. Sarantsev,Phys. Rev. D 62 (2000) 051502

V.V. Anisovich, Phys. Usp. 47 (2004) 45

D.V. Bugg, Phys. Rept. 397 (2004) 257

SD

DG

ss

[see review by Glozman, Phys.Rept.444 ]

[Glozman, Nevediev ‚07 ]

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 isnot restored! It remains spontaneouslybroken !

[Diakonov, Petrov `89]

[Vereshagin, M.V.P. `95]

Pion strings ?• 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 lightestdegrees 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 !

Rotating chiral soliton and its deformation

Slow rotation – low lying baryons:Octet, decuplet, antideciplet, ......

Fast rotation – soliton is deformedInto sigare like form. Linear meson traj.

For higher representations rotation becomes faster

S. Weinberg `68

J. Gasser, Leuthwyler `83

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 ?

Nucleon‘s slice