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, the non-singular terms of the antenna functions, their color 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 2→3 (LL) VINCIA antennae have names such as
Vincia:qQ:emit
(for gluon emission off a qqbar
antenna), Vincia:qg:split
(for gluon splitting to a
quark-antiquark pair inside a qg antenna).Vincia:IK:x
, 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 color tag of
I
and the anti-color 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 antenna is fully specified by giving the
coefficients LaurentC(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 color lines created in
the splitting in
the large-NC limit (i.e., the limiting value should be 3 for gluon
emission and 1 for gluon splitting, modulo 1/NC^2 ambiguities),
and y_ij,y_jk
are the
branching invariants scaled by the mass of the mother antenna,
y_ab = s_ab/m2_IK
, with the invariants
defined by s_ab = 2 pa.pb
.
Finite terms, i.e., with both 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.
flag
Vincia:qQ:emit
(default = on
)parm
Vincia:qQ:emit:chargeFactor
(default = 2.66666667
)parm
Vincia:qQ:emit:LaurentC(0,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentC(1,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentC(0,1)
(default = 0.0
)flag
Vincia:qg:emit
(default = on
)parm
Vincia:qg:emit:chargeFactor
(default = 3.0
)parm
Vincia:qg:emit:LaurentC(0,0)
(default = 2.0
)parm
Vincia:qg:emit:LaurentC(1,0)
(default = -1.0
)parm
Vincia:qg:emit:LaurentC(0,1)
(default = 0.0
)flag
Vincia:gg:emit
(default = on
)parm
Vincia:gg:emit:chargeFactor
(default = 3.0
)parm
Vincia:gg:emit:LaurentC(0,0)
(default = 2.0
)parm
Vincia:gg:emit:LaurentC(1,0)
(default = 0.0
)parm
Vincia:gg:emit:LaurentC(0,1)
(default = 0.0
)The number of quark flavours allowed in gluon splittings, phase space permitting, is given by
mode
Vincia:nGluonToQuark
(default = 5
; minimum = 0
; maximum = 5
)flag
Vincia:qg:split
(default = on
)parm
Vincia:qg:split:chargeFactor
(default = 1.0
)parm
Vincia:qg:split:LaurentC(0,0)
(default = 0.3
)parm
Vincia:qg:split:LaurentC(1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentC(0,1)
(default = 0.0
)flag
Vincia:gg:split
(default = on
)parm
Vincia:gg:split:chargeFactor
(default = 1.0
)parm
Vincia:gg:split:LaurentC(0,0)
(default = 0.3
)parm
Vincia:gg:split:LaurentC(1,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentC(0,1)
(default = 0.0
)flag
Vincia:useMassTerms
(default = on
)on
for physics studies.
Note: the coefficients listed in this section are ignored
if useFiniteTerms
is switched off, see above.
parm
Vincia:qQ:emit:DenominatorMassPrefactor
(default = 0.0
)parm
Vincia:qQ:emit:LaurentM(1,0,0,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentM(1,0,1,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentM(2,0,0,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentM(2,0,1,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentM(1,1,0,0)
(default = 0.0
)parm
Vincia:qQ:emit:LaurentM(1,1,1,0)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(1,0,0)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(1,1,0)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(1,0,1)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(2,0,0)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(2,1,0)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(2,0,1)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(2,-1,0)
(default = 0.0
)parm
Vincia:qg:emit:LaurentM(2,-1,1)
(default = 0.0
)parm
Vincia:qg:emit:LaurentMtilde(2,-1,-1,2)
(default = 0.0
)parm
Vincia:qg:emit:LaurentMtilde(3,-1,-1,1)
(default = 0.0
)parm
Vincia:qg:emit:LaurentMtilde(4,-1,-1,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentM(1,0,0,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentM(1,0,1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentM(1,0,0,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentM(2,0,0,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentM(2,0,0,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentM(2,0,1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(0,2,0,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(0,2,0,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(0,2,1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(1,0,0,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(1,0,0,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(1,0,1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(2,0,0,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(2,0,0,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentMtilde(2,0,1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentCtilde(0,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentCtilde(0,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentCtilde(0,2)
(default = 0.0
)parm
Vincia:qg:split:LaurentCtilde(1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentCtilde(1,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentCtilde(2,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentM(2,0,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentM(2,0,1)
(default = 0.0
)parm
Vincia:gg:split:LaurentM(2,1,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentCtilde(0,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentCtilde(0,1)
(default = 0.0
)parm
Vincia:gg:split:LaurentCtilde(0,2)
(default = 0.0
)parm
Vincia:gg:split:LaurentCtilde(1,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentCtilde(1,1)
(default = 0.0
)parm
Vincia:gg:split:LaurentCtilde(2,0)
(default = 0.0
)Important note: The following coefficients pertain to the singular structure of the antenna functions and should not be changed by the user. Moreover, in the current implementation, several of them only act as placeholders, in the base Antenna class implementation, with the singular terms actually used in the code being hardcoded in functions inheriting from the base class.
Strictly for theoretical testing purposes, we provide a possibility to switch off all but the Eikonal terms (i.e., removing the additional collinear-singular terms from the antenna functions, regardless of the values of the coefficients below), using the following switch
flag
Vincia:useCollinearTerms
(default = on
)on
for normal runs. Setting it to off
will
set all collinear-singular non-Eikonal term coefficients to zero.
The collinear singularity of two gluons j and k in a gluon emission antenna is distributed between two antennae, one contains the singularity for j becoming soft, one the singularity for k becoming soft. The parameter below is the value of "half" the gluon splitting function on its finite end.
parm
Vincia:octetPartitioning
(default = 0.0
; minimum = 0.0
; maximum = 1
)
parm
Vincia:qQ:emit:LaurentC(-1,-1)
(default = 2.0
)parm
Vincia:qQ:emit:LaurentC(-1,0)
(default = -2.0
)parm
Vincia:qQ:emit:LaurentC(0,-1)
(default = -2.0
)parm
Vincia:qQ:emit:LaurentC(-1,1)
(default = 1.0
)parm
Vincia:qQ:emit:LaurentC(1,-1)
(default = 1.0
)
parm
Vincia:qg:emit:LaurentC(-1,-1)
(default = 2.0
)parm
Vincia:qg:emit:LaurentC(-1,0)
(default = -2.0
)parm
Vincia:qg:emit:LaurentC(0,-1)
(default = -2.0
)parm
Vincia:qg:emit:LaurentC(1,-1)
(default = 1.0
)parm
Vincia:qg:emit:LaurentC(-1,1)
(default = 1.0
)parm
Vincia:qg:emit:LaurentC(2,-1)
(default = -1.0
)
parm
Vincia:gg:emit:LaurentC(-1,-1)
(default = 2.0
)parm
Vincia:gg:emit:LaurentC(-1,0)
(default = -2.0
)parm
Vincia:gg:emit:LaurentC(0,-1)
(default = -2.0
)parm
Vincia:gg:emit:LaurentC(-1,1)
(default = 1.0
)parm
Vincia:gg:emit:LaurentC(1,-1)
(default = 1.0
)parm
Vincia:gg:emit:LaurentC(2,-1)
(default = -1.0
)parm
Vincia:gg:emit:LaurentC(-1,2)
(default = -1.0
)
parm
Vincia:qg:split:LaurentC(-1,-1)
(default = 0.0
)parm
Vincia:qg:split:LaurentC(-1,0)
(default = 0.0
)parm
Vincia:qg:split:LaurentC(-1,1)
(default = 0.0
)parm
Vincia:qg:split:LaurentC(0,-1)
(default = 0.5
)parm
Vincia:qg:split:LaurentC(1,-1)
(default = -1.0
)parm
Vincia:qg:split:LaurentC(2,-1)
(default = 1.0
)
parm
Vincia:gg:split:LaurentC(-1,-1)
(default = 0.0
)parm
Vincia:gg:split:LaurentC(-1,0)
(default = 0.0
)parm
Vincia:gg:split:LaurentC(-1,1)
(default = 0.0
)parm
Vincia:gg:split:LaurentC(0,-1)
(default = 0.5
)parm
Vincia:gg:split:LaurentC(1,-1)
(default = -1.0
)parm
Vincia:gg:split:LaurentC(2,-1)
(default = 1.0
)