Spacelike Showers

The PYTHIA algorithm for spacelike initial-state showers is based on the recent article [Sjo05], where a transverse-momentum-ordered backwards evolution scheme is introduced. This algorithm is a further development of the virtuality-ordered one presented in [Sj085], with matching to first-order matrix element for Z^0, W^+- and Higgs (in the m_t -> infinity limit) production as introduced in [Miu99].

The normal user is not expected to call SpaceShower directly, but only have it called from Pythia, via PartonLevel. Some of the parameters below, in particular SpaceShower:alphaSvalue, would be of interest for a tuning exercise, however.

Main variables

The amount of QCD radiation in the shower is determined by

parameter name="SpaceShower:alphaSvalue" default="0.127" min="0.06" max="0.25"
The alpha_strong value at scale M_Z^2. Default value is picked equal to the one used in CTEQ 5L.

The actual value is then regulated by the running to the scale pT^2, at which it is evaluated

mode name="SpaceShower:alphaSorder" default="1" min="0" max="2"
Order at which alpha_strong runs,
option value="0": zeroth order, i.e. alpha_strong is kept fixed.
option value="1": first order, which is the normal value.
option value="2": second order. Since other parts of the code do not go to second order there is no strong reason to use this option, but there is also nothing wrong with it.

QED radiation is currently regulated by StandardModel:alphaEMfix, since no QED running is implemented in the shower.

There are two complementary ways of regularizing the small-pT divergence, a sharp cutoff and a smooth dampening. These can be combined as desired but it makes sense to coordinate with how the same issue is handled in multiple interactions.

flag name="SpaceShower:samePTasMI" default="on"
Regularize the pT -> 0 divergence using the same sharp cutoff and smooth dampening parameters as used to describe multiple interactions. That is, the MultipleInteractions:pT0Ref, MultipleInteractions:ecmRef, MultipleInteractions:ecmPow and MultipleInteractions:pTmin parameters are used to regularize all ISR QCD radiation, rather than the corresponding parameters below. This is a sensible physics ansatz, based on the assumption that colour screening effects influence both MI and ISR in the same way. Photon radiation is regularized separately in either case.
Warning:if a large pT0 is picked for multiple interactions, such that the integrated interaction cross section is below the nondiffractive inelastic one, this pT0 will automatically be scaled down to cope. Information on such a rescaling does NOT propagate to SpaceShower, however.

The actual pT0 parameter used at a given cm energy scale, ecmNow, is obtained as
pT0 = pT0(ecmNow) = pT0Ref * (ecmNow / ecmRef)^ecmPow
where pT0Ref, ecmRef and ecmPow are the three parameters below.

parameter name="SpaceShower:pT0Ref" default="2.2" min="0.5" max="10.0"
Regularization of the divergence of the QCD emission probability for pT -> 0 is obtained by a factor pT^2 / (pT0^2 + pT^2), and by using an alpha_s(pT0^2 + pT^2). An energy dependence of the pT0 choice is introduced by the next two parameters, so that pT0Ref is the pT0 value for the reference cm energy, pT0Ref = pT0(ecmRef).

parameter name="SpaceShower:ecmRef" default="1800.0" min="1."
The ecmRef reference energy scale introduced above.

parameter name="SpaceShower:ecmPow" default="0.16" min="0." max="0.5"
The ecmPow energy rescaling pace introduced above.

parameter name="SpaceShower:pTmin" default="0.2" min="0.1" max="10.0"
Lower cutoff in pT, below which no further ISR branchings are allowed. Normally the pT0 above would be used to provide the main regularization of the branching rate for pT -> 0, in which case pTmin is used mainly for technical reasons. It is possible, however, to set pT0Ref = 0 and use pTmin to provide a step-function regularization, or to combine them in intermediate approaches. Currently pTmin is taken to be energy-independent.

parameter name="SpaceShower:pTminChgQ" default="0.5" min="0.01"
Parton shower cut-off pT for photon coupling to a coloured particle.

parameter name="SpaceShower:pTminChgL" default="0.0005" min="0.0001"
Parton shower cut-off mass for pure QED branchings. Assumed smaller than (or equal to) pTminChgQ. Actually, ISR cascades of incoming leptons have not been implemented so far, so should not be used!??

Further variables

These should normally not be touched. Their only function is for cross-checks.

There are three flags you can use to switch on or off selected branchings in the shower:

flag name="SpaceShower:QCDshower" default="on"
Allow a QCD shower; on/off = true/false.

flag name="SpaceShower:QEDshowerByQ" default="on"
Allow quarks to radiate photons; on/off = true/false.

flag name="SpaceShower:QEDshowerByL" default="on"
Allow leptons to radiate photons; on/off = true/false.

There are three further possibilities to simplify the shower:

flag name="SpaceShower:MEcorrections" default="on"
Use of matrix element corrections; on/off = true/false.

flag name="SpaceShower:phiPolAsym" default="on"
Azimuthal asymmetry induced by gluon polarization; on/off = true/false. Not yet implemented.

mode name="SpaceShower:nQuark" default="5" min="0" max="5"
Number of allowed quark flavours in g -> q qbar branchings, when kinematically allowed. Changing it to 4 would forbid g -> b bbar, etc.

Technical notes

Almost everything is equivalent to the algorithm in [1]. Minor changes are as follows.