Triangular and Y-shaped hadrons in QCD Page: 1 of 8
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Triangular and Y-shaped hadrons in QCD
D.S.Kuzmenkoa) and Yu.A.Simonova),a)
a) State Research Center
Institute of Theoretical and Experimental Physics,
Cl 117218 Moscow, Russia
b) Jefferson Laboratory, Newport News, VA 23606, USA
Gauge invariant extended configurations are considered for 3 fundamental (quarks)
or adjoint (gluons) particles. For 3 quarks it is proved that the only possible gauge-
invariant configuration is the Y-shaped one, proposed long ago, while the triangular
one proposed recently is ruled out. For adjoint sources both configurations are possible.
Static potential is computed in all cases. For baryons the Y-shaped configuration leads
to a significant depletion of field-strength density at the string-junction position, which
Cl decreases the effective potential slope at R - 0.5 fm by 10-15%, as observed on the
lattice. For adjoint sources the Y-shaped and A-shaped potentials are very close, leading
to almost degenerate masses of 3-- 3g glueballs and odderon trajectories.
1. The Y-shaped configuration was suggested long ago [1, 2] and since then was accepted
and used in many dynamical calculations [3, 4].
Meanwhile the uniqeness of the Y-shape was questioned in , where some arguments
have been given that the triangular (A-shaped) configuration can be preferred energetically.
Moreover, lattice calculations of 3Q static potential [6, 7] displayed a potential slope smaller
than 3a, which was attributed by the authors to the A-shaped configuration with reference
to . (Note however, that in another lattice study  this result was not confirmed).
It is one of purposes of this communication to show that the gauge-invariant A-shaped
configuration is impossible for baryons (or any 3 fundamental sources in SU(3) QCD). At
the same time we extend our previous results  to show that the static potential of the
Y-shaped configuration has a strong depletion at small distances due to a hole in string
density at the string-junction position.This fact may explain smaller slope of lattice results
in [6, 7].As a second point of this paper we study configuration of 3 adjoint sources (e.g.
of 3 valence gluons) and show that it may have two possible shapes: the Y-type and the
A-type. We compute static potential for both cases. Using that we estimate masses of lowest
3g glueballs, lying on the corresponding odderon trajectories, and show that they are close
to each other, implying that there are two possible odderon trajectories with two not much
different Regge slopes. A short discussion of physical implications of these results concludes
2. Hadron building in SU(3) starts with listing elementary building blocks: quarks
q', a = 1, 2, 3, gluons (or adjoint static sources) g0, a = 1, ...8, parallel transporters (PT) in
fundamental representation b$(x, y) = (P exp ig f A,(z)dz,), adjoint parallel transporters
(Db(x, y), generators tij)'3 symmetric symbols o1, 6,b, dab, and antisymmetric ones, ea, and
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Kuzmenko, D. S. & Simonov, Yu. A. Triangular and Y-shaped hadrons in QCD, article, March 1, 2002; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc735533/m1/1/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.