While the CM momenta of a 2→3 branching are fixed by the generated invariants (and hence by the antenna function), the global orientation of the produced 3-parton system with respect to the rest of the event (or, equivalently, with respect to the original dipole-antenna axis) suffers from an ambiguity outside the LL limits, which can affect the tower of subleading logs generated and can be significant in regions where the leading logs are suppressed or absent.
To illustrate this ambiguity, consider the emissision of a gluon from a qqbar antenna with some finite amount of transverse momentum (meaning transverse to the original dipole-antenna axis, in the CM of the dipole-antenna). The transverse momenta of the qqbar pair after the branching must now add up to an equal, opposite amount, so that total momentum is conserved, i.e., the emission generates a recoil. By an overall rotation of the post-branching 3-parton system, it is possible to align either the q or the qbar with the original axis, such that it becomes the other one that absorbs the entire recoil (the default in showers based on 1→2 branchings such as old-fashioned parton showers and Catani-Seymour showers), or to align both of them slightly off-axis, so that they share the recoil (the default in VINCIA, see illustration below).
Vincia:kineMapType
.
mode
Vincia:kineMapType
(default = 3
; minimum = 1
; maximum = 3
)option
1 : The ARIADNE angle (see illustration).
The recoiling mothers share the recoil in
proportion to their energy fractions in the CM of the
dipole-antenna. Tree-level expansions of the VINCIA shower compared
to tree-level matrix elements through third order in alphaS have
shown this strategy to give the best overall approximation,
followed closely by the KOSOWER map below.
option
2 : LONGITUDINAL. The parton which has the
smallest invariant
mass together with the radiated parton is taken to be the "radiator". The
remaining parton is taken to be the "recoiler". The recoiler remains oriented
along the dipole axis in the branching rest frame and recoils
longitudinally against the radiator + radiated partons which have
equal and opposite transverse momenta (transverse to the original
dipole-antenna axis in the dipole-antenna CM). Comparisons to
higher-order QCD matrix elements show this to be by far the worst
option of the ones so far implemented, hence it could be
useful as an extreme case for uncertainty estimates, but should
probably not be considered for central tunes. (Note: exploratory attempts at
improving the behaviour of this map, e.g., by selecting
probabilistically between the radiator and the recoiler according to
approximate collinear splitting kernels, only resulted in
marginal improvements. Since such variations would introduce
additional complications in the VINCIA matching formalism, they
have not been retained in the distributed version.)
option
3 : The KOSOWER map. Comparisons to higher-order QCD
matrix elements show only very small differences between this and
the ARIADNE map above, but since the KOSOWER map is sometimes used in
fixed-order contexts, we deem it interesting to include it as a
complementary possibility. (Note: the KOSOWER maps in fact represent a
whole family of kinematics maps. For experts, the specific choice
made here corresponds to using r=sij/(sij+sjk) in the
definition of the map.)
The values of the masses are in all cases taken from PYTHIA's particle database, minimizing the risk of conflict. The parameters here only control whether the corresponding particles are treated as massive or massless by VINCIA.
For relativistic particles, helicity is a good quantum number and massless matrix-element corrections can be used. The following parameter determines from which speed VINCIA treats a particle as being relativistic.
parm
Vincia:relativisticSpeed
(default = 0.95
; minimum = 0.0
; maximum = 1.0
)Note that the velocity is a frame-dependent quantity. VINCIA checks the above threshold in several relevant frames, and only treats a particle as ultra-relativistic if it passes the threshold in all the frames.
The first frame is the CM of the parton system, relevant for example for matrix-element corrections.
VINCIA then also checks the velocity of the particle in the CM of all two-particle subsystems in the event. This ensures, for example, that a quasi-collinear emission from a massive quark will be treated with mass corrections, since the velocity of the quark in the CM frame of the quark and the emitted quasi-collinear gluon will be low.
Colour non-connected two-particle systems are also included. This ensures that, e.g., two fast-moving massive particles traveling in approximately the same direction will be treated as massive, since they will have low velocities in their common CM frame.
If all checks are passed, the particle can be assigned a helicity and the configuration is allowed to make use of (helicity-dependent) massless matrix-element corrections. Otherwise the particle is treated as unpolarized, and massive matrix-element corrections are used, to the extent available in the program.
Note: NLO corrections have so far only been implemented for massless particles, so for the time being a choice must be made between treating a particle as massless, with NLO corrections, or treating it as massive, without NLO corrections, see the section on Matching for a list of processes for which NLO corrections have been implemented.
Note 2: High-mass new-physics particles will normally be treated as massive, as they will generally not satisfy the relativistic-velocity criterion.
Note 3: For particles that are treated as massive, the mass corrections to the antenna functions are discussed separately, in the section on Antenna Functions.
For systems whose particles are all deemed to be in the ultra-relativistic domain (according to the velocity criterion above), a temporary set of massless momenta are created by rescaling all massive 3-momenta up along their respective directions of motion, thus creating a massless intermediate configuration with a reduced CM energy. All momenta and energies are then rescaled up in order to restore the original CM energy, and finally the system is boosted back to the original system frame, producing a set of massless momenta that are as near equivalent to the original massive ones as possible. This set of rescaled and boosted massless momenta will then be used for purposes of assigning helicities and computing matrix-element corrections.
After a branching has been accepted, when constructing the post-branching event kinematics, all particles (both ones treated as massless and ones treated as massive) are put on their proper mass shell, with their true masses. The massless momenta constructed above are only used to assign helicities and compute corrections, after which they are discarded. This ensures that no unphysical configurations are generated, and that phase-space suppression is acting smoothly over all of phase space.