Why version 3.1

Version 3.1 differs from version 3.01 in the definition of the scale parameter kappa used to start "secondary showering." In principle the previous definition was not correct for the case that a primary splitting produces an infinitesimally soft gluon and a hard parton. Then the scale for the splitting of the hard parton was not infinitesimal as it should have been. The old definition was

< daughter1%kappasq = min(x*qbarsq/(1.0d0 - x),calQ1**2,mother%kappasq)
< daughter2%kappasq = min((1.0d0-x)*qbarsq/x,calQ2**2,mother%kappasq)
where calQ1 or calQ2 is the absolute value of the three momentum of the corresponding daughther produced by a primary splitting and qbarsq is the virtuality of the splitting and mother%kappasq had been previously assigned based on the topology of the three initial parton momenta. This has a problem for x --> 1 for the first line and x --> 0 for the second line. The new version is
> daughter1%kappasq = min(x*qbarsq/(1.0d0 - x),calQ1**2,ckappa*qbarsq)
> daughter2%kappasq = min((1.0d0 - x)*qbarsq/x,calQ2**2,ckappa*qbarsq)
where ckappa is a constant, 4 by default. When qbarsq --> 0, the daughter kappasq values go to zero. There is also a change in the starting value for kappa for splitting the soft gluon that the program creates to model radiation from the the three jets of the born graph.
< theshower%ptn(4)%kappasq = lsq * theshower%onemthrust
becomes
> theshower%ptn(4)%kappasq = ckappasoft * lsq
where lsq is the square of the three momentum of the soft gluon and ckappasoft = 1/10. There was no reason to involve the thrust of the born event here.

The numerical effect appears to be negligible.


Davison E. Soper
Institute of Theoretical Science
University of Oregon
Eugene OR 97403 USA
soper@physics.uoregon.edu