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Theory Center Seminar<br>
Mon., June 2, 2014<br>
1:00 p.m. (coffee at 12:45 p.m.)<br>
CEBAF Center, Room L102<br>
<br>
Paul Hoyer<br>
University of Helsinki<br>
<br>
<b>Bound States -- From QED to QCD </b><br>
<br>
The hadron spectrum is characterized by the valence quark degrees of
freedom, even though scattering (DIS)<br>
data shows that hadrons also have sea quarks and gluon constituents.
The Dirac equation demonstrates that<br>
these two features can coexist for relativistic dynamics. Dirac
bound states of an electron have an unlimited <br>
number of electron-positron pair constituents, while the spectrum is
determined by a single electron equation. <br>
Confined fermion-antifermion states can be realized in gauge theory
by imposing a non-vanishing boundary <br>
condition on Gauss' law. Only the simplest homogeneous solution, $A<sup
class="moz-txt-sup"><span>^</span>0</sup>(\boldsymbol{x}) \propto
\boldsymbol{x}$, <br>
is compatible with translation invariance, and then only for neutral
states. This results in a linear instantaneous<br>
potential, similar to the ${\mathcal O}(\alpha_s<sup
class="moz-txt-sup"><span>^</span>0</sup>)$ potential of the quark
model. The bound states are described<br>
by equal-time wave functions in all frames, are rotationally
invariant in the rest frame and have a dynamically <br>
realized boost covariance. Their electromagnetic form factors are
gauge invariant and their parton distributions <br>
have contributions from sea quarks at low $x_{Bj}$. The boost from
the rest frame to the infinite momentum <br>
frame reveals an interesting difference wrt. wave functions defined
at equal light-cone time. The states thus <br>
constructed are candidates for ${\mathcal O}(\alpha_s<sup
class="moz-txt-sup"><span>^</span>0</sup>)$ asymptotic ($in$ and
$out$) states of the QCD $S$-matrix. <br>
This approach is described in the lecture notes of arXiv:1402.5005.
<br>
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