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, non-singular terms of the antenna functions, their colour factors, and the number of flavours 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.
flag
Vincia:FSR
(default = on
)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 final-state gluon splittings (in both final-final and initial-final antennae) is given by
mode
Vincia:nGluonToQuarkF
(default = 5
; minimum = 0
; maximum = 5
)Resummation arguments [Cat91] indicate that a set of universal QCD corrections can be absorbed in coherent parton showers by applying the so-called CMW rescaling of the MSbar value of Lambda_QCD, defined by
mode
Vincia:CMWtypeFF
(default = 1
)option
0 :
No CMW rescaling.
option
1 :
CMW rescaling with the eikonal term defined as
2 sIK / ( sij sjk ).
option
2 :
CMW rescaling with the eikonal term defined as
2 sik / ( sij sjk ),
which is smaller compared to the term in option 1.
Note 1: If using VINCIA with an externally defined matching scheme, be
aware
that the CMW rescaling may need be taken into account in the context of
matrix-element matching. Note also that this option has only been made
available for timelike and spacelike showers, not for hard processes.
Note 2: Tunes using this option need lower values of
alphas(ms2) than tunes that do not.
When Vincia:alphaSorder
is non-zero,
the actual value is regulated by running to the scale
kμ*μR, at which the shower evaluates
αs. μR is
the transverse momentum pT A (without the normalisation
factor) for gluon emission and mQQ for
gluon splitting. The scale factor kμ is given by
parm
Vincia:alphaSkMuF
(default = 0.75
; minimum = 0.1
; maximum = 10.0
)and
parm
Vincia:alphaSkMuSplitF
(default = 0.5
; minimum = 0.1
; maximum = 10.0
)The normalisation of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalisation 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 normalisation of the qqbar → qgqbar antenna function is 2CF.)
parm
Vincia:QQemit:chargeFactor
(default = 2.66666667
)parm
Vincia:QGemit:chargeFactor
(default = 2.85
)parm
Vincia:GGemit:chargeFactor
(default = 3.0
)parm
Vincia:QGsplit:chargeFactor
(default = 1.0
)parm
Vincia:GGsplit:chargeFactor
(default = 1.0
)
For Vincia:hardJetsQCD
being switched off, the first branching in QCD
processes is by default limited to the factorisation
scale used for the hard process. This scale (in GeV) can be enhanced by the factor
parm
Vincia:QmaxEnhanceF
(default = 1.0
; minimum = 1.0
; maximum = 10.0
)The choices below govern how the shower fills phase space, and hence how the logarithms generated by it are ordered. This does not affect the LL behaviour, but does affect the tower of higher (subleading) logs generated by the shower and can therefore be signficiant in regions where the leading logs are suppressed or absent. Note that, by construction, the dipole formalism automatically ensures an exact treatment of coherence effects to leading logarithmic order, and hence additional constraints, such as angular ordering, are not required.
Note 1: Gluon splittings, g→qq, always use mqqbar as their evolution variable, which are interleaved with the choice made here.
Note 2: The absolute normalisation factors cancel in sequential gluon emissions, but enter in the relative interleaving between gluon emissions and gluon splitting.
mode
Vincia:evolutionType
(default = 1
)option
1 :
Transverse Momentum. This evolution variable is roughly equal to the
inverse of the antenna function for gluon emission, and hence is in
some sense the most natural evolution variable. We define it as in
ARIADNE, modulo a normalisation factor:
NT=4
.
option
2 :
Dipole Virtuality. This mass-like variable
represents a fairly moderate variation on the transverse
momentum. It will give slightly more priority to soft branchings
over collinear branchings, as compared to transverse
momentum. We define it as
ND=2
.
The contours below illustrate the progression of each evolution variable (normalized to maximum value unity) over the dipole-antenna phase space for four fixed values of yE = QE2/sIK:
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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 in Z decay.
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:nFlavZeroMassF
(default = 2
; minimum = 0
; maximum = 5
)
mode
Vincia:massCorrectionEmitF
(default = 0
; minimum = 0
; maximum = 0
)Vincia:nFlavZeroMassF
flavours.
option
0 : No mass effects. Equivalent to
using Vincia:nFlavZeroMassF=5
.
mode
Vincia:massCorrectionSplitF
(default = 1
; minimum = 0
; maximum = 2
)Vincia:nFlavZeroMassF
flavours.
option
0 : No mass effects. Equivalent to
using Vincia:nFlavZeroMassF=5
.
option
1 : Gluon splittings, G→QQ, are cut off at
s(QQ) = 4mQ2. This option represents the minimal
physical level
of mass corrections. The cutoff prevents these splittings from being
artificially enhanced by unphysical near-singular behaviour below the
quark production thresholds.
option
2 : In addition to the phase-space threshold, a
universal (positive) mass correction is
applied to the antenna functions for G→QQbar
splittings. Simultaneously, the phase-space constraints are made
more severe, checking if would-be physical massive momenta
could actually be constructed.
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 generalisation 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
)