Here is collected some possibilities to modify the scale choices
of couplings and parton densities for all internally implemented
hard processes. This is based on them all being derived from the
SigmaProcess base class. The matrix-element coding is
also used by the multiparton-interactions machinery, but there with a
separate choice of alpha_strong(M_Z^2) value and running,
and separate PDF scale choices. Also, in 2 -> 2 and
2 -> 3 processes where resonances are produced, their
couplings and thereby their Breit-Wigner shapes are always evaluated
with the resonance mass as scale, irrespective of the choices below.
Couplings and K factor
The size of QCD cross sections is mainly determined by
The alpha_strong value at scale M_Z^2.
The actual value is then regulated by the running to the Q^2
renormalization scale, at which alpha_strong is evaluated
Order at which alpha_strong runs,
QED interactions are regulated by the alpha_electromagnetic
value at the Q^2 renormalization scale of an interaction.
The running of alpha_em used in hard processes.
In addition there is the possibility of a global rescaling of
cross sections (which could not easily be accommodated by a
changed alpha_strong, since alpha_strong runs)
Multiply almost all cross sections by this common fix factor. Excluded
are only unresolved processes, where cross sections are better
set directly, and
multiparton interactions, which have a separate K factor
of their own.
This degree of freedom is primarily intended for hadron colliders, and
should not normally be used for e^+e^- annihilation processes.
Renormalization scales
The Q^2 renormalization scale can be chosen among a few different
alternatives, separately for 2 -> 1, 2 -> 2 and two
different kinds of 2 -> 3 processes. In addition a common
multiplicative factor may be imposed.
The Q^2 renormalization scale for 2 -> 1 processes.
The same options also apply for those 2 -> 2 and 2 -> 3
processes that have been specially marked as proceeding only through
an s-channel resonance, by the isSChannel() virtual
method of SigmaProcess.
The Q^2 renormalization scale for 2 -> 2 processes.
The Q^2 renormalization scale for "normal" 2 -> 3
processes, i.e excepting the vector-boson-fusion processes below.
Here it is assumed that particle masses in the final state either match
or are heavier than that of any t-channel propagator particle.
(Currently only g g / q qbar -> H^0 Q Qbar processes are
implemented, where the "match" criterion holds.)
The Q^2 renormalization scale for 2 -> 3
vector-boson-fusion processes, i.e. f_1 f_2 -> H^0 f_3 f_4
with Z^0 or W^+-t-channel propagators.
Here the transverse masses of the outgoing fermions do not reflect the
virtualities of the exchanged bosons. A better estimate is obtained
by replacing the final-state fermion masses by the vector-boson ones
in the definition of transverse masses. We denote these combinations
mT_Vi^2 = m_V^2 + pT_i^2.
The Q^2 renormalization scale for 2 -> 1,
2 -> 2 and 2 -> 3 processes is multiplied by
this factor relative to the scale described above (except for the options
with a fix scale). Should be use sparingly for 2 -> 1 processes.
A fix Q^2 value used as renormalization scale for 2 -> 1,
2 -> 2 and 2 -> 3 processes in some of the options above.
Factorization scales
Corresponding options exist for the Q^2 factorization scale
used as argument in PDF's. Again there is a choice of form for
2 -> 1, 2 -> 2 and 2 -> 3 processes separately.
For simplicity we have let the numbering of options agree, for each event
class separately, between normalization and factorization scales, and the
description has therefore been slightly shortened. The default values are
not necessarily the same, however.
The Q^2 factorization scale for 2 -> 1 processes.
The same options also apply for those 2 -> 2 and 2 -> 3
processes that have been specially marked as proceeding only through
an s-channel resonance.
The Q^2 factorization scale for 2 -> 2 processes.
The Q^2 factorization scale for "normal" 2 -> 3
processes, i.e excepting the vector-boson-fusion processes below.
The Q^2 factorization scale for 2 -> 3
vector-boson-fusion processes, i.e. f_1 f_2 -> H^0 f_3 f_4
with Z^0 or W^+-t-channel propagators.
Here we again introduce the combinations mT_Vi^2 = m_V^2 + pT_i^2
as replacements for the normal squared transverse masses of the two
outgoing quarks.
The Q^2 factorization scale for 2 -> 1,
2 -> 2 and 2 -> 3 processes is multiplied by
this factor relative to the scale described above (except for the options
with a fix scale). Should be use sparingly for 2 -> 1 processes.
A fix Q^2 value used as factorization scale for 2 -> 1,
2 -> 2 and 2 -> 3 processes in some of the options above.