1. Structure of quantum chromodynamics, glueballs and nucleon resonances H.P. Morsch (in collaboration with P. Zupranski) Warsaw, 27.4.2007

2. Related to the questions: What is the structure of quantum chromodynamics (QCD)? Do glueballs (structures of pure gluons) exist? What is the structure of hadron resonances (radial nucleon N* resonances) 1. What do we know on the structure of QCD? 2. New method to study gluon-gluon systems (not based on postulated QCD Lagrangian!) Basic assumptions Monte-Carlo method to deduce 2-gluon densities 3. Tests of the deduced 2-gluon densities: The QCD gluon propagator (from lattice data) Two-gluon field correlators (from lattice simulations) 4. Two-gluon binding potential and mass of glueballs 5. Structure of the nucleon and N* resonances 6. The Q-dependence of the strong coupling α s (Q) 7. Conclusion

3. 1. What is the structure of QCD? Three ingredients: 1. coupling of gluon fields (due to non-Abelian form) 2. qq-coupling by 1gluon exchange 3. quark mass term What is the origin of the quark masses? Dynamical structure, relativistic generation of mass? Binding energies between quarks? Coupling to external Higgs field? Experimental search at LHC.

4. Strong coupling (constant) α s α s shows a dependence on the momentum transfer μ At large momentum transfers α s is rather small  description of QCD by perturbation theory possible. Experiments at SLAC, LEP,HERA… How big is α s at small μ? What is the structure of QCD at small momentum transfers? How can we understand the confinement of quarks and gluons? How can we calculate the properties of QCD at small μ?

5. Non- perturbative descriptions of QCD 1. Dyson-Schwinger (gap) equation complicated system of integral equations with not well known quantitites. 2. Lattice QCD approach by solving the QCD Lagrangian on a space-time lattice. Evaluation of results by statistical methods. Problems with lattice spacing, limitation to small momentum transfers, small quark masses, statistical noise, gauge invariance … 3. Method of gluon field correlators (Simonov et al.) many properties derived from gluon field correlators, evaluated by lattice methods.  detailed structure, in particular confinement is not understood!

6. 2. Our method to study gluon-gluon systems (based on two assumptions about coupling of gluons and of quarks) Assumption 1: Colour neutral coupling of two gluons gives rise to finite and stable systems of scalar (0 + ) and tensor (2 + ) structure, by L=1 also of vector (1 - ) form. From the theory of gluon field correlators, DiGiacomo, Dosch, Shovchenko, Simonov, Phys. Rep. 372, 319 (2002)  Two-gluon field correlator is gauge invariant and non-local, θ(x.x‘) are phase factors. From ass.1  only in the colour neutral coupling the colour transformations of the two gluon fields cancel each other giving rise to stable systems. Evidence for finite gluon field correlators from lattice QCD simulations (Di Giacomo et al. Nucl. Phys. B 285, 371 (1997). 2-gluon system is massive! What is the origin of mass? (Cornwall: dynamical mass generation by relativistic effects)

7. Assumption 2 is equivalent to the conjecture, that the quarks emerge from the decay of the 2-gluon field 2g  qq¯+2(qq¯). In this case the elementary q-q interaction v 1g (R) is modified by the formed stable 2-gluon density. Important: Fourier transform of this potential yields a momentum dependent interaction strength (running of the strong coupling α s ). Also this form is consistent with α s  0 for Q  ∞ (asymptotic freedom) Assumption 2 (folding principle): Interaction between two quarks is described by folding the 1-gluon exchange force with a stable 2-gluon density:

8. Deduction of a self-consistent 2-gluon density by the Monte Carlo method 1. Use of an initial form of ρ Φ (r‘) in 2. Relativistic Fourier transform to p-space 3. Monte Carlo simulation of the decay gg  qq¯and 2q2q¯ using V(p 1 -p 2 ) between quarks with momenta p 1, p 2  resulting 2-gluon momentum distributions D qq¯ (Q) and D 2q2q¯ (Q) 4. Sum of D qq¯ (Q) and D 2q2q¯ (Q) retrans- formed to r-space  final 2-gluon density. Self-consistency condition: Initial and final 2-gluon densities should be the same (also their Fourier transforms). Two-gluon density in the interaction between quarks must be the same as the colour neutral density formed ! MC-simulation of the decay g+g  2g  qq¯+2(qq¯) with folding interaction V qq (R) between the emitted quarks

9. Details of the folding potential of the effective q-q interaction For decay into qq¯ a p-wave density ρ p Φ (r) is needed, which is constrained by =0. using an effective 1-gluon exchange force v 1g (R)=-α s /R. For interaction of the quarks in the limited volume ρ Φ (r) the 1-gluon exchange force has to be modified by the size of the 2-gluon density, taken in the simple form v‘ 1g (R)=v 1g (R)·exp(-aR 2 ). This leads to a finite folding potential V qq (Q) at Q=0, needed for a self-consistent solution! (in the earlier calculations this effect has not been taken into account. The results on the gluon densities and confinement are the same, but the strong coupling α s is now consistent with other results.)

10. Deduced 2-gluon density is finite!  forms a (quasi) bound state Folding potential and resulting 2-gluon density Mass deduced from relativistic Fourier transformations: m Φ ~0.68GeV Results of simulation of Q 2 ·ρ(Q) in comparison with the initial values

11. 3. Tests of the deduced two-gluon densities: QCD gluon propagator and two-gluon field correlators 2-gluon field correlators DiGiacomo et al. Nucl. Phys. B 483, 371(1997) Gluon propagators Bowman et al. Phys. Rev. D 66, 074505 (2002) and D 70, 034509 (2004) From pole-fits: m Φ ~0.64 GeV much lower than lowest glueball mass from lattice QCD! Vector field (J π =1 -, L=1) has 14 % of the strength of the scalar field (Gluon propagator is most basic 2-point function in Yang-Mills theory.) Gluon propagator and 2g field correlators must be related to the 2-gluon densities.

12. 4. Two-gluon binding potential and eigenstates Two-gluon system forms a (quasi) bound state  Binding potential of two gluons can be obtained from a 3-dim. reduction of the Bethe-Salpeter eq. in form of a relativistic Schrödinger equation What are the eigenstates in this potential? Bali et al. Phys. Rev. D 62, 054503 (2000) Resulting binding potential is consistent with confinement potential from lattice QCD (Bali et al.) ! Binding potential

13. The mass of the 2-gluon system can be interpreted as binding energy of the two gluons! Eigenstates (glueballs) in the 2g binding (confinement) potential Absolute binding energies are obtained by fitting the potential by a form V fit (r)=α s /r+br with the condition α s /r  0 for r  ∞. Results: Eigenstates (glueballs) exist! Lowest eigenmode at E 0 =0.68±0.10 GeV Radial excitations at E 1 =1.69±0.15 GeV E 2 =2.54±0.17 GeV E 0 =m, where m is the mass inserted in the Schrödinger equation, consistent with the mass required in the relativistic Fourier transformation! ☟ Deduced mass of glueball ground state consistent with σ(550)! Radially excited states consistent with glueball states from lattice QCD.

14. 0 ++ glueball spectrum in comparison with results from lattice QCD studies our results ? mass (GeV) 1 2 3 0 ++ Morningstar and Peardon, PRD 60, 034509 (1999) σ(600) Is the scalar σ(600) the lowest glueball state?

15. 5. Structure of the nucleon Nucleon density obtained by folding two-gluon density with density of three quarks Resulting binding potential becomes more shallow. But attraction between emerging quarks increases by a factor 9! Lowest eigenmode of the nucleon at E 0 =0.94±0.04 GeV Radial excitations at exp. N* E 1 =1.42±0.07 GeV P 11 (1440) E 2 =1.82±0.12 GeV P 11 (1710) Lowest eigenmode has a binding energy consistent with the nucleon mass!

16. 0 ++ glueballs ? mass (GeV) 1 2 3 0 ++ Nucleon (N*) resonances σ(600) Is the scalar σ(600) the lowest glueball state? Consequence: direct relation of the glueball spectrum to that of radial nucleon resonances (this allows experimental investigations) 1 2 3 1/2 + 3/2 +,5/2 +... What is the contribution from gluonic and quark excitations? What can we determine experimentally? 0 ++ glueball excitations correspond to radial N* resonances What is experimentally known on these excitations?

17. Comparison with operator sum rules Cross section covers maximum monopole strength S 1 Extraction of the nucleon compressibility K N ~ S 1 /S -1 ~ 1.3 GeV First evidence from α-p scattering at SATURNE (Phys. Rev. Lett. 69, 1336 (1992) Strong L=0 excitation in the region of the lowest P 11 at about 1400 MeV Projectile Δ excitation Study of the radial (breathing) mode of the nucleon

18. Study of the breathing mode in p-p scattering at beam momenta 5-30 GeV/c Contibuting resonances Δ 33 (1232) D 13 (1520), F 15 (1680), strong res. at 1400 MeV Strongest resonance at 1400 MeV, width 200 MeV (breathing mode) No other resonance seen (high selectivity) Detailed analysis in terms of a vibration of the valence and multi-gluon densities of the nucleon in Phys. Rev. C 71, 065203 (2005)

19. Calculated (p,p‘) differential cross section is sensitive to the nucleon transition density Quantitative description of the p-p data requires a surface peaked transition density ρ tr (r) (consistent with the results from α-p) Transition density is not consistent with pure valence quark excitation (deduced from e-p scattering)

20. Information on the valence quark contribution from the longitudinal e-p amplitude S 1/2 C.Smith, NSTAR2004, I.G.Aznauryan, V.D.Burkert, et al., nucl-th/0407021, L.Tiator, Eur.J.Phys.16 (2004) For the charge transition density is required S 1/2 amplitude supports breathing mode interpretation !

21. How do we understanding the observed (p,p‘) transition density ? 1.Excitation of valence quarks deduced from (e,e‘) 2. Strong sea quark contribution due to multi-gluon structure Conclusion: Multi-gluon contribution of the nucleon breathing mode excitation is ~4 times stronger than the valence quark contribution, consistent with our model

22. Study of the strong coupling α s at small momentum transfer many different theoretical predictions of α s (Q) for Q  0

23. Strong coupling „constant“ α s (Q) for Q  0 Nesterenko and Papavassiliou, PR D 71, 016009 (2005) Lattice data: Weiß, NP B 47, 71 (1996) Furui and Nakajima, PR D 69, 074505 (2004) and PR D 70, 094504 (2004) contribution from 2g vector field Shirkov and Solovtsov, PRL 79, 1209 (1997)

24. Strong coupling „constant“ α s (Q) for large Q By adding 2g contributions from smaller and smaller 2-gluon densities corresponding to ss¯, cc¯, bb¯ … α s is better and better described Above tt¯ further qq¯ system(s) expected (may be in the upper energy range of LHC).

25. 8. Conclusions 1. Our two-gluon field approach gives a consistent and transparent description of the properties of QCD (interactions, confinement, mass, propagators, glueballs, heavy flavour neutral systems…). All quark masses are compatible with zero  no need for coupling to a scalar Higgs field! 2. Lowest glueball state consistent with scalar meson σ(600). 3. Radial nucleon resonances understood as glueballs coupled to 3 quarks. What is the structure of other nucleon resonances? 4. Q-dependence of the strong interaction described by 1-gluon exchange folded with 2-gluon density. This gives rise to a running of α s (q) consistent with other results and with asymptotic freedom! Flavour neutral systems heavier than tt¯ should exist. Big challenge for LHC, GSI, BESIII, CEBAF…

26. Are there eigenstates in the q-q potential? Only one eigenstate with E 0 ~-0.01 GeV (binding energy appears to correspond to about 2x the average „current“ quark mass) Because of a very low binding energy the glueball states should have a large width! Rough estimate of the width: (Γ≈ 1/E 0 ≈ 500 MeV from the systematics of heavy 2-gluon states).

27. Other flavour neutral and flavoured systems Generation of other self-consistent 2-gluon densities with radii corresponding to ss¯(b), cc¯(c), and bb¯systems (d). Self-consistent densities obtained by assuming massless quarks! Mass explained by strong binding of quarks! Dashed lines obtained by assuming quark masses of 1.3 GeV for (c) and 4.5 GeV for (d) (not self-consistent!). How can flavoured systems be described? Decay 2g  q f1 q f1 ¯+ q f2 q f2 ¯. If the radial size of the 2g-density is the same for decay in q f1 and q f2  2g  q f1 q f2 ¯+ q f2 q f1 ¯. (this may yield a description of pions) How can we describe baryons? Decay 4g  5(q q¯)  (3q qq¯) + (3q¯qq¯)  baryon + antibaryon

28. 3. Description of p-p and pion-pion scattering, multi-gluon potential density and compressibility Good description of the data obtained in double folding approach, which determines the multi-gluon potential strength. Volume integral of V pp ~770 MeVfm 3 Volume integral of V ππ ~130 MeVfm 3 From these potentials deduction of potential densities and compressibilities

29. Multi-gluon potential densities and compressibility From the multi-gluon potentials we can derive a potential density Vρ(r) for the proton and the pion. Deduced compressibility is consistent with that deduced from operator sums

30. Study of scalar excitation of N* resonances in the p-α  α rec x 1 x 2 … reaction at TOF Experiment was already proposed a long time ago, but the detector for α-particle recoils had to be built. ΔE-E Si-microstrip detector telescope with 256x256 pixels. Detector is completed and has been sent to Juelich. Needs installation and cabling for commissioning during next Experiment at TOF.