Within the dipole-antenna formalism, antenna functions are the analogs of the splitting functions used in traditional parton showers. The antenna functions are constructed so as to reproduce the Altarelli-Parisi splitting functions P(z) in collinear limits and the eikonal dipole factor in the soft limit.
We here describe the parameters and switches used to control, for instance, helicity dependence, non-singular terms of the antenna functions, their colour factors, and the number of flavors allowed in gluon splittings during the shower evolution. Predefined sets of alternative antenna functions are also provided (or can be defined by the user), as described in the section on Antenna Sets.
The default is to leave all antenna functions switched on. For special theory studies, it may be convenient to check what happens when one or more antenna functions are switched off. The switches below give this functionality:
flag
Vincia:QQemit
(default = on
)flag
Vincia:QGemit
(default = on
)flag
Vincia:GGemit
(default = on
)flag
Vincia:QGsplit
(default = on
)flag
Vincia:GGsplit
(default = on
)The number of quark flavours allowed in gluon splittings, phase space permitting, is given by
mode
Vincia:nGluonToQuark
(default = 5
; minimum = 0
; maximum = 5
)The normalization of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalization choice, all gluon-emission colour factors tend to NC in the large-NC limit while all gluon-splitting colour factors tend to unity. (Thus, e.g., the default normalization of the qqbar → qgqbar antenna function is 2CF.)
parm
Vincia:QQemit:chargeFactor
(default = 2.66666667
)parm
Vincia:QGemit:chargeFactor
(default = 3.0
)parm
Vincia:GGemit:chargeFactor
(default = 3.0
)parm
Vincia:QGsplit:chargeFactor
(default = 1.0
)parm
Vincia:GGsplit:chargeFactor
(default = 1.0
)For massless partons, the default set of antenna functions in VINCIA depend explicitly on parton helicities. This gives a more accurate shower (since contributions from unphysical polarization states are removed) and speeds up the matching to matrix elements (since only a single helicity amplitude at a time needs to be evaluated). Note that, for partons treated as massive, the default is still to use helicity-summed antenna functions (see below).
flag
Vincia:helicityShower
(default = on
)off
.
Further parameters controlling the helicity-dependent antenna functions are found below under Laurent Series Representation.
The 2→3 (LL) VINCIA antennae have names such as
Vincia:QQemit
(for gluon emission off a qqbar
antenna), Vincia:QGsplit
(for gluon splitting to a
quark-antiquark pair inside a qg antenna).Vincia:IKx
, where I
and K
are
the "mothers" and x
is either emit
or
split
, depending on whether the process is gluon emission
or gluon splitting.
The radiating (parent) antenna is interpreted as
spanned between the Les Houches colour tag of
I
and the anti-colour tag of K
, see
illustration to the right.
The functional forms of the antenna functions are specified by giving the coefficients of a double Laurent series in the two branching invariants (the third invariant, specifying a rotation around the dipole axis, is chosen uniformly). The Laurent expansion formally starts at power (-1,-1) corresponding to the double singularity, but in most cases only the non-singular coefficients are modifiable by the user, see below.
Each massless antenna is fully specified by giving the
coefficients C(α,β)
of the following expansion:
where α
and
β
are implicitly summed over,
m_IK
is the mass of the mother antenna,
chargeFactor
should be normalized to tend to NC
raised to the number of new colour lines created in
the splitting in
the large-NC limit (see above),
and y_ij,y_jk
are the
branching invariants scaled by the mass of the mother antenna,
y_ab = s_ab/m2_IK
.
Finite terms, i.e., with both Laurent indices greater than or equal to zero, are arbitrary and in general the best choice to make will depend on the specific process considered. In VINCIA, they are regarded as an independent way of estimating the uncertainty due to uncalculated higher orders, an uncertainty which can be explicitly reduced by matrix-element matching. The default is therefore to allow these terms to be nonzero, but for special applications it may be convenient to have one global switch that switches them on and off, regardless of the values given below:
flag
Vincia:useFiniteTerms
(default = on
)on
for normal runs. Setting it to off
will
set all finite term coefficients to zero.
To avoid clutter, we first give the coefficients for antennae
involving only massless partons. The additional correction terms when
one or more partons are massive are collected in a separate subsection
below.
The default coefficients are derived from H and Z decays (for S- and P-wave antennae, respectively) and absorb the tree-level matrix element for H→qgqbar and Z→qgqbar into the shower off H→qqbar and Z→qqbar, respectively.
S-wave (++ and --) antennae emitting without spin-flip (MHV):
parm
Vincia:QQemit:Cs00
(default = 0.0
)parm
Vincia:QQemit:Cs10
(default = 0.0
)parm
Vincia:QQemit:Cs01
(default = 0.0
)S-wave (++ and --) antennae emitting with spin flip (NMHV):
parm
Vincia:QQemit:Cf00
(default = 2.0
)parm
Vincia:QQemit:Cf10
(default = 0.0
)parm
Vincia:QQemit:Cf01
(default = 0.0
)P-wave (+- and -+) antennae:
parm
Vincia:QQemit:Cp00
(default = 0.0
)parm
Vincia:QQemit:Cp10
(default = 0.0
)parm
Vincia:QQemit:Cp01
(default = 0.0
)Note: by charge conjugation symmetry, the code also uses this function for qbar-g antennae, with appropriate swapping of invariants.
S-wave (++ and --) antennae emitting without spin-flip (MHV):
parm
Vincia:QGemit:Cs00
(default = 0.0
)parm
Vincia:QGemit:Cs10
(default = 0.0
)parm
Vincia:QGemit:Cs01
(default = 0.0
)S-wave (++ and --) antennae emitting with spin flip (NMHV):
parm
Vincia:QGemit:Cf00
(default = 3.0
)parm
Vincia:QGemit:Cf10
(default = 0.0
)parm
Vincia:QGemit:Cf01
(default = 0.0
)P-wave (+- and -+) antennae:
parm
Vincia:QGemit:Cp00
(default = 0.0
)parm
Vincia:QGemit:Cp10
(default = 0.0
)parm
Vincia:QGemit:Cp01
(default = 0.0
)S-wave (++ and --) antennae emitting without spin-flip (MHV):
parm
Vincia:GGemit:Cs00
(default = 0.0
)parm
Vincia:GGemit:Cs10
(default = 0.0
)parm
Vincia:GGemit:Cs01
(default = 0.0
)S-wave (++ and --) antennae emitting with spin flip (NMHV):
parm
Vincia:GGemit:Cf00
(default = 3.0
)parm
Vincia:GGemit:Cf10
(default = 1.0
)parm
Vincia:GGemit:Cf01
(default = 1.0
)P-wave (+- and -+) antennae:
parm
Vincia:GGemit:Cp00
(default = 0.0
)parm
Vincia:GGemit:Cp10
(default = 0.0
)parm
Vincia:GGemit:Cp01
(default = 0.0
)Coefficients for q' inheriting the helicity of the splitting gluon:
parm
Vincia:QGsplit:Cs00
(default = 0.0
)parm
Vincia:QGsplit:Cs10
(default = 0.0
)parm
Vincia:QGsplit:Cs01
(default = 0.0
)Coefficients for qbar' inheriting the helicity of the splitting gluon:
parm
Vincia:QGsplit:Cf00
(default = 0.0
)parm
Vincia:QGsplit:Cf10
(default = 0.0
)parm
Vincia:QGsplit:Cf01
(default = 0.0
)Coefficients for q inheriting the helicity of the splitting gluon:
parm
Vincia:GGsplit:Cs00
(default = 0.0
)parm
Vincia:GGsplit:Cs10
(default = 0.0
)parm
Vincia:GGsplit:Cs01
(default = 0.0
)Coefficients for qbar inheriting the helicity of the splitting gluon:
parm
Vincia:GGsplit:Cf00
(default = 0.0
)parm
Vincia:GGsplit:Cf10
(default = 0.0
)parm
Vincia:GGsplit:Cf01
(default = 0.0
)flag
Vincia:GluonSplittingCorrection
(default = on
)option
on : Use the factor PAri. Default
since it greatly improves the shower's approximation to matrix
emelents.
option
off : Don't use the factor PAri.
Included mostly for testing purposes.
Note 1: in VINCIA this correction is only applied when the neighbouring antenna is a qg one, not if it is gg.
Note 2: this correction does not affect the total collinear gluon-splitting singularity, though it does redistribute it; the total size of the gluon-splitting singularity is obtained as a sum over the two sides of the splitting gluon, with the ARIADNE factor summing to give a simple factor 2 on the singular term.
mode
Vincia:nFlavZeroMass
(default = 2
; minimum = 0
; maximum = 5
)
mode
Vincia:massCorrectionLevel
(default = 2
)Vincia:nFmassless
flavours.
option
0 : No mass effects. Equivalent to
using Vincia:nFmassless=5
.
option
1 : Massive Phase-Space Effects. Take the restricted
size of phase-space into account for processes involving massive
flavours.
option
2 : Phase-Space and Antenna Mass Effects. As for
option 1 but also include the negative corrections to the eikonal
emission probabilities for gluon emissions from massive flavours,
and the positive corrections to the probabilities for gluon
splitting to massive flavours.
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).
Note: this setting only applies to massless partons.
For partons treated as massive (see below), a generalization of the
Kosower map (option 3 below) will be used regardless of the value of
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.)
Important note: The following parameters give limited possibilities to modify the singular structure of individual antenna functions. These should not be changed in ordinary physics runs, but can be used to test, e.g., the effects of soft-eikonal vs collinear terms and of the choice of partitioning of gluon-collinear singularities.
flag
Vincia:useCollinearTerms
(default = on
)on
for normal runs. Setting it to off
will
set all collinear-singular non-Eikonal term coefficients to zero.
Within the antenna formalism, the collinear singularity of two gluons j and k is distributed between two neighboring antennae. One contains the singularity for j becoming soft, one the singularity for k becoming soft. In global showers, the two antennae share the collinear singularity, j||k, point by point in phase space, and only after summing over both is the full collinear AP splitting kernel recovered. (In sector showers, instead, each antenna contains the full AP kernel, but only one of them is allowed to contribute to each phase-space point.) In global showers, the parameter below controls the repartition ambiguity and gives the value of "half" the gluon splitting function on its finite end.
parm
Vincia:octetPartitioning
(default = 0.0
; minimum = 0.0
; maximum = 1
)The following parameters adjust the collinear partitioning of helicity-dependent antennae.
parm
Vincia:polGlbAntPartitioning1
(default = 0.0
)parm
Vincia:polGlbAntPartitioning2
(default = 0.0
)