VINCIA Antenna Functions

Antenna Sets

The default antenna functions used in VINCIA largely resemble those used by Gehrmann, de-Ridder, and Glover (GGG, see below), but also, e.g., the ones used by ARIADNE and a few more are provided as alternatives. Yet others can be defined by the user.

To use an alternative set of antennae (i.e., non-default), for instance to estimate uncertainties, a convenient way of specifying a collection of non-default parameters is to use

word  VinciaShower:antennaFile   (default = none)
Optional name of a file containing predefined settings for one or more non-default antenna functions. Note that this command file will be read in during construction of the VINCIA plug-in. Any desired further modifications of the antenna functions should therefore only be performed after construction of the plug-in. Some pre-defined antennae shipping with VINCIA are stored in a separate subdirectory called antennae/ (see below). More user-defined antennae can be added and stored in the same directory, if desired. To use them with a program that runs in your main VINCIA directory (default), include the following command in your main program or command file:

VinciaShower:antennaFile = antennae/antennae-GGG.cmnd

(Here we used the "GGG" antennae for illustration.) To use a user-defined antenna set with a program that does not run in your VINCIA main directory, or if the antennae you want to use are not stored in the antennae/ directory, give the full path- and filename instead, as in

Vincia:antennaFile = /Users/skands/vincia/antennae/antennae-GGG.cmnd

Note that the format of the antenna files is the same as that of ordinary PYTHIA 8 command files, hence any combination of VINCIA and PYTHIA 8 commands could in principle be included to define an antenna set, but in general we advise to keep only specific antenna-related parameters in the antenna definition files, to avoid confusions/conflicts between your main command file(s) and the antenna file.

The default antennae have been chosen to be close to the GGG ones and have been verified to give a good average agreement with Z→n matrix elements. The following two examples, included with the VINCIA package in the antennae/ subdirectory, have been defined so as to try to span a reasonable min-max uncertainty range:

Other predefined antenna functions included in the same directory are:

Quark and Lepton Masses

Mass corrections are implemented systematically in VINCIA. The following switches control which quarks and leptons are treated as massive during the event evolution.

flag  VinciaShower:isMassiveS   (default = false)

flag  VinciaShower:isMassiveC   (default = true)

flag  VinciaShower:isMassiveB   (default = true)

flag  VinciaShower:isMassiveTau   (default = true)
tau is treated as massless, its decay width will be put to zero in the MadGraph interface.

Note: new-physics particles will generally be treated as massive if their masses are larger than the lightest quark for which mass corrections are switched on.

Gluon Splitting

The number of quark flavours allowed in gluon splittings, phase space permitting, is given by

mode  VinciaShower:nGluonToQuark   (default = 5; minimum = 0; maximum = 5)
Number of allowed quark flavours in gluon splittings, g → q qbar, during the shower evolution. E.g., a change to 4 would exclude g → b bbar but would include the lighter quarks, etc. Note that quark mass effects are currently not taken into account. Note also that this parameter does not directly affect the running coupling (see the section on Couplings).

Laurent Series Representation

AB->arb

The 2→3 (LL) VINCIA antennae have names such as

The generic name format is thus Vincia:AB:x, where A and B 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 A and the anti-colour tag of B, see illustration to the right.

The functional form of the antennae 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 starts at power (-1,-1) corresponding to the double singularity. For so-called "global" antennae (the default in VINCIA), each antenna is fully specified by giving the coefficients LaurentC(i,j) of the following expansion:

A(y_ar,y_rb;s_AB) = 1/s_AB 4 pi alpha_s chargeFactor LaurentC(i,j) pow(y_ar,i) pow(y_rb,j);

where i and j are implicitly summed over, s_AB 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), and y_ar,y_rb are the branching invariants scaled by the mass of the mother antenna, y_ij = s_ij/s_AB.

The coefficients with negative i or j indices are universal and should not be changed by the user. 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), using the following switch

flag  VinciaShower:useCollinearTerms   (default = on)
Global switch for all antenna function collinear-singular non-Eikonal terms. Should be on for normal runs. Setting it to off will set all collinear-singular non-Eikonal term coefficients to zero.

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. They are therefore not to be regarded as "tunable" parameters, but rather as an independent way of estimating the uncertainty due do 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:

flag  VinciaShower:useFiniteTerms   (default = on)
Global switch for all antenna function finite terms. Should be on for normal runs. Setting it to off will set all finite term coefficients to zero.

Splitting of the Collinear Gluon Singularity

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:CollinearGluonSplitting   (default = 0.0; minimum = 0.0; maximum = 1)

Massless Laurent Coefficients

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 section below.

qqbar gluon emission antenna

The default coefficients are derived from Z decay and absorb the tree-level matrix element for Z->qgqbar into the shower off Z->qqbar.

flag  Vincia:qQ:emit   (default = on)

parm  Vincia:qQ:emit:chargeFactor   (default = 2.66666667)

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: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)

parm  Vincia:qQ:emit:LaurentC(2,0)   (default = 0.0)

parm  Vincia:qQ:emit:LaurentC(0,2)   (default = 0.0)

qg gluon emission antenna

The GGG coefficients were derived from neutralino decays and do not absorb any particular physically relevant matrix element into the shower. We have therefore here modified the color factor and the finite terms by comparing to Z->qggqbar. By charge conjugation symmetry, the code also uses this function for qbar-g antennae, with appropriate swapping of invariants.

flag  Vincia:qg:emit   (default = on)

parm  Vincia:qg:emit:chargeFactor   (default = 3.0)

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:qg:emit:LaurentC(0,0)   (default = 2.0)

parm  Vincia:qg:emit:LaurentC(1,0)   (default = 0.0)

parm  Vincia:qg:emit:LaurentC(0,1)   (default = 0.0)

gg gluon emission antenna

The default coefficients are derived from H->gg(g) decay and absorb the tree-level matrix element for H->ggg into the shower off H->gg.

flag  Vincia:gg:emit   (default = on)

parm  Vincia:gg:emit:chargeFactor   (default = 3.0)

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: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)

qg gluon splitting antenna

The default values are derived from neutralino decays and do not absorb any particular physically relevant matrix element into the shower. However, the finite terms have been reduced from GGG, in order to avoid the finite terms being solely responsible for large dead zones. Note: only half a gluon is splitting here.

flag  Vincia:qg:split   (default = on)

parm  Vincia:qg:split:chargeFactor   (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: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)

gg gluon splitting antenna

The default coefficients are derived from H->gg->gqbarq decays and absorb the tree-level matrix element for H->gqbarq into the shower off H->gg. However, the finite terms have been scaled down a bit here, in order to avoid the finite terms being solely responsible for large dead zones. Note: only half of each gluon is splitting here.

flag  Vincia:gg:split   (default = on)

parm  Vincia:gg:split:chargeFactor   (default = 1.0)
Note: the two permutations g-g -> g-q+qbar and g-g -> qbar+q-g are explicitly summed over in the code (with appropriate swapping of invariants in the latter case).

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)

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)

Massive Laurent Coefficients

For every antenna, there is a switch to turn mass terms on or off. This is only implemented for testing purposes, since the mass terms are turned off completely, the massive soft eikonal factor and the quasi-collinear splitting function will not be reproduced anymore.

qqbar gluon emission antenna

flag  Vincia:qq:emit:useMassTerms   (default = on)

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)

qg gluon emission antenna

flag  Vincia:qg:emit:useMassTerms   (default = on)

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)

gg gluon emission antenna

The parameter has no effect for this antenna, but it needs to be present to have no parameters undefined.

flag  Vincia:gg:emit:useMassTerms   (default = on)

qg gluon splitting antenna

The finite massive terms have been reduced by 20% in magnitude compared to the original GGG functions, the same as the finite massless terms, to avoid the appearance of dead zones for secondary quark-antiquark production close to threshold.

flag  Vincia:qg:split:useMassTerms   (default = on)

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)

gg gluon splitting antenna

The finite massive terms have been reduced by 20% in magnitude compared to the original GGG functions, the same as the finite massless terms, to avoid the appearance of dead zones for secondary quark-antiquark production close to threshold.

flag  Vincia:gg:split:useMassTerms   (default = on)

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)