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SUMMARY:Classical binding of hadrons
DTSTART;VALUE=DATE-TIME:20180514T185000Z
DTEND;VALUE=DATE-TIME:20180514T191500Z
DTSTAMP;VALUE=DATE-TIME:20211127T171014Z
UID:indico-contribution-3157@indico.jlab.org
DESCRIPTION:Speakers: Paul Hoyer (University of Helsinki)\nA perturbative
expansion for bound states starts with a lowest order approximation that h
as a non-perturbative wave function\, with all powers in the coupling $\\a
lpha$.\nThe distinction between lowest and higher orders is blurred since
contributions of finite order in $\\alpha$ may be assigned to either one.
A criterion beyond powers of $\\alpha$ is needed to fully define a perturb
ative expansion for bound states. \n\nI consider the criterion that the ga
uge field should satisfy the classical field equations at lowest order. Th
is corresponds to lowest order in $\\hbar$\, but all orders in $\\alpha$\,
and ensures that the expansion starts from a configuration with stationar
y action. Poincare invariance as well as unitarity is expected to hold at
each order in the fundamental constant $\\hbar$. \n\nHigher order correcti
ons are defined by an expression for the S-matrix similar to the Interacti
on Picture\, but with in- and out-states that are eigenstates of a Hamilto
nian that includes the classical gauge field. The formal derivation and hi
gher order terms of this "Potential Picture" remain to be studied.\n\nWhen
applied to non-relativistic QED atoms the classical criterion leads to lo
west order atoms described by the SchrÃ¶dinger equation. The SchrÃ¶dinger
equation cannot be derived from QED based only on a power expansion in $\\
alpha$\, for reasons stated in the beginning.\n\nThe QCD scale $\\Lambda_{
QCD}$ can arise through a boundary condition on the classical gluon field
equations. The homogeneous solution for the classical gluon field that sat
isfies basic physical requirements appears to be unique\, up to an overall
scale. It is of O($\\alpha_s^0$) and leads to a strictly linear potential
for mesons and a related one for baryons.\n\nMeson wave functions may be
found iteratively\, corresponding to an expansion in $1/N_c$. At lowest or
der in $1/N_c$ there is no string breaking and the states lie on linear Re
gge trajectories for vanishing quark mass $m$. The overlap of these states
determine decays and meson loop corrections\, as required by unitarity at
higher orders in $1/N_c$.\n\nThere are massless solutions which allow to
include the effect of spontaneous chiral symmetry breaking when $m=0$. The
massless $0^{++}$ sigma state can mix with the perturbative vacuum withou
t breaking Poincare invariance. A chiral transformation of such a condensa
te creates massless pions. For a small quark mass $m \\neq 0$ the $0^{-+}$
pion gains a mass $M \\propto \\sqrt{m}$ and is annihilated by the axial
vector current as expected for a Goldstone boson.\n\nhttps://indico.jlab.o
rg/event/252/contributions/3157/
LOCATION:Jefferson Lab - CEBAF Center Auditorium
URL:https://indico.jlab.org/event/252/contributions/3157/
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