Structure of quantum chromodynamics, glueballs and nucleon resonances

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Structure of quantum chromodynamics, glueballs
and nucleon resonances

• H.P. Morsch
• (in collaboration with P. Zupranski)
• Warsaw, 27.4.2007

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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 as(Q)
• 7. Conclusion

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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.
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Strong coupling (constant) as
as shows a dependence on the momentum transfer
µ At large momentum transfers as is rather small
? description of QCD by perturbation
theory possible. Experiments at SLAC, LEP,HERA
How big is as 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?
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Non-perturbative descriptions of QCD
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!
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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 L1 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,
• ?(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)
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Assumption 2 (folding principle) Interaction
between two quarks is described by folding the
1-gluon exchange force with a stable 2-gluon
density
Assumption 2 is equivalent to the conjecture,
that the quarks emerge from the decay of the
2-gluon field 2g?qq2(qq). In this case the
elementary q-q interaction v1g(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 as). Also this form is
consistent with as?0 for Q?8 (asymptotic freedom)
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Deduction of a self-consistent 2-gluon densityby
the Monte Carlo method
Two-gluon density in the interaction between
quarks must be the same as the colour neutral
density formed !
MC-simulation of the decay gg?2g?qq2(qq) with
folding interaction Vqq(R) between the emitted
quarks
1. Use of an initial form of ?F(r) in
2. Relativistic Fourier transform to p-space 3.
Monte Carlo simulation of the decay gg ?
qqand 2q2q using V(p1-p2) between quarks
with momenta p1, p2 ? resulting 2-gluon
momentum distributions Dqq(Q) and
D2q2q(Q) 4. Sum of Dqq(Q) and D2q2q(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).
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Details of the folding potential of the effective
q-q interaction
using an effective 1-gluon exchange force
v1g(R)-as/R. For interaction of the quarks in
the limited volume ?F(r) the 1-gluon exchange
force has to be modified by the size of the
2-gluon density, taken in the simple
form v1g(R)v1g(R)exp(-aR2). This leads to a
finite folding potential Vqq(Q) at Q0, 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
as is now consistent with other results.)
For decay into qq a p-wave density ?pF(r) is
needed, which is constrained by ltrgt0.
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Folding potential and resulting 2-gluon density
Results of simulation of Q2?(Q) in comparison
with the initial values
Mass deduced from relativistic Fourier
transformations mF0.68GeV

• Deduced 2-gluon density is finite!
• forms a (quasi) bound state

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3. Tests of the deduced two-gluon densities QCD
gluon propagator and two-gluon field correlators
(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.
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 mF0.64 GeV much lower than lowest
glueball mass from lattice QCD!

Vector field (Jp1-, L1) has 14 of the
strength of the scalar field
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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
Binding potential
Bali et al. Phys. Rev. D 62, 054503 (2000)
Resulting binding potential is consistent with
confinement potential from lattice QCD (Bali et
al.) !
What are the eigenstates in this potential?
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Eigenstates (glueballs) in the 2g binding
(confinement) potential
Absolute binding energies are obtained by fitting
the potential by a form Vfit(r)as/rbr with the
condition as/r?0 for r?8.
Results Eigenstates (glueballs) exist! Lowest
eigenmode at E00.680.10 GeV Radial
excitations at E11.690.15 GeV
E22.540.17 GeV E0m, where m is the mass
inserted in the Schrödinger equation,
consistent with the mass required in the
relativistic Fourier transformation! ?
The mass of the 2-gluon system can be
interpreted as binding energy of the two gluons!
Deduced mass of glueball ground state consistent
with s(550)! Radially excited states consistent
with glueball states from lattice QCD.
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0 glueball spectrum in comparison with results
from lattice QCD studies
our results
Morningstar and Peardon, PRD 60, 034509 (1999)
0
3
mass (GeV)
2
1
?
s(600)
Is the scalar s(600) the lowest glueball state?
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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
E00.940.04 GeV Radial excitations at
exp. N E11.420.07 GeV
P11(1440) E21.820.12 GeV
P11(1710) Lowest eigenmode has a binding energy
consistent with the nucleon mass!
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Consequence direct relation of the glueball
spectrum to that of radial nucleon
resonances (this allows experimental
investigations)
0 glueballs
Nucleon (N) resonances
0
1/2
3/2,5/2. . .
3
3
mass (GeV)
2
2
1
1
?
s(600)
Is the scalar s(600) the lowest glueball state?
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?
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Study of the radial (breathing) mode of the
nucleon
First evidence from a-p scattering at SATURNE
(Phys. Rev. Lett. 69, 1336 (1992)

• Comparison with operator sum rules
• Cross section covers maximum monopole strength S1
• Extraction of the nucleon compressibility
• KN S1/S-1 1.3 GeV

Strong L0 excitation in the region of the
lowest P11 at about 1400 MeV
Projectile ? excitation
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Study of the breathing mode in p-p scattering at
beam momenta 5-30 GeV/c
Contibuting resonances ?33 (1232) D13 (1520), F15
(1680), strong res. at 1400 MeV
No other resonance seen (high selectivity)
Strongest resonance at 1400 MeV, width 200
MeV (breathing mode)
Detailed analysis in terms of a vibration of the
valence and multi-gluon densities of the nucleon
in Phys. Rev. C 71, 065203 (2005)
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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
?tr(r) (consistent with the results from a-p)
Transition density is not consistent with pure
valence quark excitation (deduced from e-p
scattering)
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Information on the valence quark contribution
from the longitudinal e-p amplitude S1/2
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
S1/2 amplitude supports breathing mode
interpretation !
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How do we understanding the observed (p,p)
transition density ?

• 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
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Study of the strong coupling as at small
momentum transfer
many different theoretical predictions of as(Q)
for Q?0
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Strong coupling constant as(Q) for Q?0
Shirkov and Solovtsov, PRL 79, 1209 (1997)
contribution from 2g vector field
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)
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Strong coupling constant as(Q) for large Q
By adding 2g contributions from smaller and
smaller 2-gluon densities corresponding to ss,
cc, bb as is better and better described
Above tt further qq system(s) expected (may be
in the upper energy range of LHC).
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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 s(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 as(q) consistent with other
results and with asymptotic freedom! Flavour
neutral systems heavier than tt should exist.
Big challenge for LHC, GSI, BESIII, CEBAF
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Are there eigenstates in the q-q potential?
Only one eigenstate with E0-0.01 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 (G 1/E0 500 MeV
from the systematics of heavy 2-gluon states).
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Other flavour neutral and flavoured systems
Generation of other self-consistent 2-gluon
densities with radii corresponding to ss(b),
cc(c), and bbsystems (d).
Self-consistent densities obtained by assuming
massless quarks! Mass explained by strong
binding of quarks!
How can flavoured systems be described?
Decay 2g?qf1qf1 qf2qf2. If the radial size of
the 2g-density is the same for decay in qf1 and
qf2 ? 2g?qf1qf2 qf2qf1. (this may yield a
description of pions)
How can we describe baryons?
Decay 4g?5(q q) ?(3q qq) (3qqq)
? baryon antibaryon
Dashed lines obtained by assuming quark masses
of 1.3 GeV for (c) and 4.5 GeV for (d) (not
self-consistent!).
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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 Vpp 770 MeVfm3 Volume integral of Vpp130
MeVfm3 From these potentials deduction of
potential densities and compressibilities
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Multi-gluon potential densities and
compressibility
From the multi-gluon potentials we can derive a
potential density V?(r) for the proton and the
pion.
Deduced compressibility is consistent with that
deduced from operator sums
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Study of scalar excitation of N resonances in
the p-a ? arec x1x2 reaction at TOF
Experiment was already proposed a long time ago,
but the detector for a-particle recoils had to
be built.
?E-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.