A dynamical picture of hadron-hadron collisions with the string-parton model Page: 4 of 14
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which is used to define the string action as
S = -nJdA (2)
where « is the string ’ension and is equal to approximately 0.9 GeV/fm. The
time over which the action is to be considered is defined by an initial time r, and a
final time tj. The string ends are defined to be a — 0 and a = S, and ks represents
the accumulative energy of the string from its zero endpoint to any other point
along the string. Thus, the total energy of the string is kS. The initial and final
configuration of the string will be those seen by a definite observer at a given
instant of time in his Lorentz frame. This action is invariant under general string
coordinate transformations and satisfies energy-momentum conservation.
General equations of motion and the boundary conditions are obtained by
small variations of the surface that joins the initial and final configurations of
the string. Due to the arbitrariness of the parameterization of the surface swept
by the string we can choose additional coordinate conditions (Virasoro gauge
conditions) which simplify the equations of motion. We work with the orthonormal
parameterization
dx,l dx,t
da dr
—■ 0 ,
(3)
which implies that the velocity of a point along the string is always perpendicular
to the string. We also note that the motion perpendicular to the string is time-like
whereas motion along the string is space-like. With this choice, the equations of
motion reduce to the wave equation
d2x,l d2i j'1
Ht* ~ ~daT = ° ’
with the additional coordinate conditions
(4)
(5)
and Eq.(3). In the following we choose the coordinates such that [14] *°(r, a) =
t — ct and x = x(t, j). Therefore, at the endpoints of the string, Eq.(5) gives
dx(T,a) _
dt
(6)
which means that the endpoints move at the speed of light. We also obtain the
spatial endpoint boundary conditions
djc^T-jO) _ dx^fa S)
da da
(7)
which tell us that there is no energy-momentum transfer out from the string
endpoints.
The solution of Eq.(4) subject to the above coordinate conditions and the first
of the conditions in Eq.(7) give
3
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Dean, D. J.; Umar, A. S.; Wu, J. S. & Strayer, M. R. A dynamical picture of hadron-hadron collisions with the string-parton model, article, January 1, 1991; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1092600/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.