<chapter name="VINCIA QCD Antenna Shower Settings"> 
<h2>VINCIA QCD Antenna Shower Settings</h2> 
 
<p>Here, parameters specific to VINCIA's QCD antenna 
shower are collected. See the <aidx href="Vincia">main VINCIA 
antenna shower page</aidx> for more general parameters that are 
common to both the QCD and QED showers. 
</p> 
 
<h3>Main Switches</h3> 
 
<flag name="Vincia:doII" default="on"> 
  Main switch for initial-initial (II) antennae on/off (subject to 
  the <code>PartonLevel</code> settings). 
</flag> 
 
<flag name="Vincia:doIF" default="on"> 
  Main switch for initial-final (IF) antennae on/off 
  (subject to the <code>PartonLevel</code> settings). 
  Note: setting this to off will switch off both the initial- and final-state 
ends of corresponding QCD antennae. 
</flag> 
 
<flag name="Vincia:doFF" default="on"> 
  Main switch for final-final (FF) antennae on/off (subject to choices 
  made at <code>PartonLevel</code>). 
</flag> 
 
<flag name="Vincia:doRF" default="on"> 
  Main switch for resonance-final (RF) antennae on/off 
  (subject to the <code>PartonLevel</code> settings). 
  Note: setting this to off will switch off both the resonance- and 
  final-state ends of corresponding QCD antennae. 
</flag> 
 
<modepick name="Vincia:nGluonToQuark" default="5" min="0" max="6"> 
Number of allowed quark flavours in final-state gluon splittings, 
<ei>g &rarr; q qbar</ei>, during the shower evolution, phase space 
permitting. E.g.,  a change to 4 would exclude <ei>g &rarr; b 
bbar</ei> but would include the lighter quarks, etc. Note that this 
parameter does not directly affect the running coupling. 
</modepick> 
 
<flag name="Vincia:convertGluonToQuark" default="on"> 
  Allow incoming gluons to backwards-evolve into (anti)quarks 
  during the initial-state shower evolution. 
</flag> 
 
<flag name="Vincia:convertQuarkToGluon" default="on"> 
  Allow incoming (anti)quarks to backwards-evolve into (anti)quarks 
  during the initial-state shower evolution. 
</flag> 
 
<a name="alphaS"></a> 
<h3>The QCD coupling in the Vincia Shower</h3> 
 
<p>The strong coupling constant is specified by providing 
its reference value (interpreted as given at the Z pole in 
the MSbar scheme) and running properties (loop order, behaviour at top 
threshold, and any low-scale regularisation/dampening). 
</p> 
 
<p>Note that VINCIA only uses one global value for the definition of 
the strong coupling constant. The effective couplings used in shower 
branchings (renormalisation scheme and scale) are governed by separate 
parameters which are specified under initial- and final-state showers 
respectively. 
</p> 
 
<p> 
VINCIA implements its own instance of PYTHIA's <code>AlphaStrong</code> class 
for the strong coupling. You can find more documentation of the class in 
the section on Standard-Model Parameters in the PYTHIA documentation. 
Here, we list the specific parameters and switches governing its use 
in VINCIA. 
</p> 
 
<a name="ref"></a> 
<p>The free parameter of the strong coupling constant is specified by 
<parm name="Vincia:alphaSvalue" default="0.118" 
min="0.06" max="2.0"> 
The value of <ei>&alpha;<sub>s</sub></ei> at 
the scale <ei>m<sub>Z</sub></ei>, in the MSbar scheme. The default 
value is chosen to be in 
agreement with the current world average. The effective value used for 
showers may be further affected by translation to the CMW scheme 
(below) and by renormalisation-scale prefactors given for FSR and ISR 
showers separately. 
</parm> 
</p> 
 
<a name="order"></a> 
<modepick name="Vincia:alphaSorder" default="2" min="0" max="2"> 
Order at which <ei>&alpha;<sub>s</sub></ei> runs, 
<option value="0">zeroth order, i.e. <ei>&alpha;<sub>s</sub></ei> is kept 
fixed.</option> 
<option value="1">first order, i.e., one-loop running. 
</option> 
<option value="2">second order, i.e., two-loop running. 
</option> 
</modepick> 
 
<a name="schemeFSR"></a> 
<p> 
Resummation arguments <ref>Cat91</ref> 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 <ei>Lambda_QCD</ei>, defined by 
<center> 
  <ei>&alpha;<sub>s</sub>(CMW) = &alpha;<sub>s</sub>(MSbar) 
  * (1 + K * &alpha;<sub>s</sub>(MSbar) / 2&pi;)</ei> 
</center> 
with <ei>K = CA * (67/18 - &pi;<sup>2</sup>/6) - 5/9nf</ei>. The 
translation amounts to an <ei>NF</ei>-dependent 
rescaling of <ei>Lambda_QCD</ei>, relative to its MSbar value, by 
a factor 1.661 for NF=3, 1.618 for NF=4, 1.569 for NF=5, 
and 1.513 for NF=6. Although the original argument strictly concerned 
only the eikonal for soft-gluon emissions, the current version of 
VINCIA only offers the option of switching the rescaling of 
<ei>Lambda_QCD</ei> on or off. When on, the rescaling is applied to 
all branching types, not just gluon emissions. 
</p> 
<p> 
<flag name="Vincia:useCMW" default="on"> 
If set to on, the alphaS value used for shower branchings will be 
translated from the MSbar value to the CMW ("MC") scheme. If set to 
off, the MSbar value will be used. 
</flag> 
<p> 
<b>Note 1:</b> 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. <br/> 
<b>Note 2:</b> Tunes using this option need roughly 10% lower values of 
<ei>alpha<sub>s</sub>(m<sub>Z</sub>)</ei> than tunes that do not. 
</p> 
 
<a name="thresholds"></a> 
<p> 
For both one- and two-loop running, the <code>AlphaStrong</code> class 
automatically switches from 3-, to 4-, and then to 5-flavour running as 
one passes the <ei>s</ei>, <ei>c</ei>, and <ei>b</ei> thresholds, 
respectively, with matching equations imposed at each flavour 
treshold to ensure continuous values. 
By default, a change to 6-flavour running is also included above the 
<ei>t</ei> threshold, though this can be disabled using the following 
parameter: 
<modepick name="Vincia:alphaSnfmax" default="6" min="5" max="6"> 
<option value="5">Use 5-flavour running for all scales above the 
<ei>b</ei> 
flavour threshold (old default).</option> 
<option value="6">Use 6-flavour running above the <ei>t</ei> 
threshold (new default).</option> 
</modepick> 
</p> 
 
<a name="ir"></a> 
<parm name="Vincia:alphaSmuFreeze" default="0.75" min="0.0" max="10.0"> 
  The behaviour of the running coupling in the far infrared is 
  regulated by a shift in the effective renormalisation scale, 
  to <ei>&mu;<sub>eff</sub> 
<sup>2</sup> = &mu;<sub>freeze</sub><sup>2</sup> 
   + &mu;<sub>R</sub><sup>2</sup></ei>. 
</parm> 
 
<a name="maxCoup"></a> 
<parm name="Vincia:alphaSmax" default="2.0" min="0.1" max="10.0"> 
Largest allowed numerical value for <ei>alphaS</ei>. I.e., the running 
is forced to plateau at this value. 
</parm> 
 
<a name="scaleFSR"></a> 
<h4>Choice of Renormalisation Scales for Shower Branchings</h4> 
<p> 
When <code>Vincia:alphaSorder</code> is non-zero, 
the actual value of alphaS used for shower branchings is governed by 
the choice of scheme (MSbar or CMW, see the section on AlphaStrong 
and then by running to the scale 
<ei>kR*Q<sup>2</sup></ei>, at which the shower evaluates 
<ei>&alpha;<sub>s</sub></ei>, with <ei>Q<sup>2</sup></ei> the 
Vincia evolution scale of the branching. 
 
The multiplicative scale factor <ei>kR</ei> is given by 
<parm name="Vincia:renormMultFacEmitF" default="0.66" min="0.1" max="10.0"> 
for gluon emission </parm> 
</p> 
<p> 
and 
<parm name="Vincia:renormMultFacSplitF" default="0.8" min="0.1" max="10.0"> 
for gluon splitting. </parm> 
</p> 
 
<a name="scaleISR"></a> 
<p> 
For initial-state branchings, the functional form of <ei>muR</ei> is given by 
the evolution variable and the scale factor <ei>kR</ei> is given by 
<parm name="Vincia:renormMultFacEmitI" default="0.66" min="0.1" max="10.0"> 
for gluon emission, </parm> 
<parm name="Vincia:renormMultFacSplitI" default="0.5" min="0.1" max="10.0"> 
for gluon splitting (quark in the initial state backwards evolving into a 
gluon), </parm> 
<parm name="Vincia:renormMultFacConvI" default="0.5" min="0.1" max="10.0"> 
for gluon conversion (gluon in the initial state backwards evolving into a 
(anti)quark) </parm> 
</p> 
 
<h3>Colour Charges</h3> 
<p>The normalisation of colour factors in VINCIA is chosen such that 
the coupling factor for all antenna functions is &alpha;S/4&pi;. With 
this normalisation, 
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 &rarr; qgqbar antenna function 
is 2CF.) 
</p> 
<p> 
<parm name="Vincia:QQemitII:chargeFactor" default="2.66666667"> 
Emission of a final-state gluon from an initial-state qqbar pair. 
</parm> 
<parm name="Vincia:GQemitII:chargeFactor" default="2.83333333"> 
  Emission of a final-state gluon from an initial-state qg (or gqbar) pair. 
</parm> 
<parm name="Vincia:GGemitII:chargeFactor" default="3.0"> 
Emission of a final-state gluon from an initial-state gg pair. 
</parm> 
<parm name="Vincia:QXSplitII:chargeFactor" default="1.0"> 
  Quark in the initial state backwards evolving into a gluon and emitting 
  an antiquark in the final state 
</parm> 
<parm name="Vincia:GXConvII:chargeFactor" default="2.66666667"> 
  Gluon in the initial state backwards evolving into a quark and emitting 
  a quark in the final state (gluon conversion) 
</parm> 
<parm name="Vincia:QQemitIF:chargeFactor" default="2.66666667"> 
  Gluon emission of an initial-final qq pair 
</parm> 
<parm name="Vincia:GQemitIF:chargeFactor" default="2.83333333"> 
  Gluon emission off an initial-final gq pair 
</parm> 
<parm name="Vincia:QGemitIF:chargeFactor" default="2.83333333"> 
  Gluon emission of an initial-final qg pair 
</parm> 
<parm name="Vincia:GGemitIF:chargeFactor" default="3.0"> 
  Gluon emission of an initial-final gg pair 
</parm> 
<parm name="Vincia:QXSplitIF:chargeFactor" default="1.0"> 
  Quark in the initial state evolving backwards into a gluon and emitting 
  an antiquark in the final state 
</parm> 
<parm name="Vincia:GXConvIF:chargeFactor" default="2.66666667"> 
  Gluon in the initial state backwards evolving into a quark and emitting 
  a quark into the final state (gluon conversion)</parm> 
<parm name="Vincia:XGSplitIF:chargeFactor" default="1.0"> 
Gluon splitting in the final state</parm> 
<parm name="Vincia:QQEmitFF:chargeFactor" default="2.66666667"/> 
<parm name="Vincia:QGEmitFF:chargeFactor" default="2.85"/> 
<parm name="Vincia:GGEmitFF:chargeFactor" default="3.0"/> 
<parm name="Vincia:QGSplitFF:chargeFactor" default="1.0"/> 
<parm name="Vincia:GGSplitFF:chargeFactor" default="1.0"/> 
<parm name="Vincia:GXSplitFF:chargeFactor" default="1.0"/> 
<parm name="Vincia:QQEmitRF:chargeFactor" default="2.66666667"/> 
<parm name="Vincia:QGEmitRF:chargeFactor" default="2.85"> 
<parm name="Vincia:XGSplitRF:chargeFactor" default="1.0"/> 
Note: the two permutations g-g &rarr; g-q+qbar and g-g &rarr; qbar+q-g are 
explicitly summed over in the code (with  appropriate swapping of 
invariants in the latter case). 
</parm> 
</p> 
 
<h3>Kinematics and Recoils</h3> 
<p>While the CM momenta of a <ei>2&rarr;3</ei> 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 be significant in regions where the leading logs are 
suppressed or absent.</p> 
<p> 
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 <ei>1&rarr;2</ei> 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). 
</p> 
 
<p> 
  <a href="http://home.fnal.gov/~skands/vincia/img/vincia-kin.png"> 
    <img src="vincia-kins.png" align="right" border="0" hspace="20" 
         vspace="20" width="300" height="254" alt="2to3-kinematics"/> </a> 
 
 
<h4>Kinematics and Recoils for II Antennae </h4> 
<p>The post-branching momenta are fixed by the following requirements: <br/> 
1) The direction of the initial state partons is aligned with the beam axis 
(z-axis). <br/> 
2) The invariant mass and the rapidity of the final state recoiler are not 
changed by the branching. This allows a direct construction of the 
post-branching momenta in the lab frame.</p> 
 
<a name="kinematicsIF"></a> 
<h4>Kinematics and Recoils for IF Antennae</h4> 
</p> 
For IF branchings, Vincia contains implementations of two different 
kinematics maps, called "local" and "global" in what follows. 
</p> 
<p> 
In the 
"local map", the initial-state parton recoils 
longitudinally, and there is no recoil imparted to any partons 
that do not participate directly in the branching. (I.e., 
recoil effects are absorbed locally within the branching antenna, and 
no partons outside of it are affected.) This is equivalent to saying 
that any transverse momentum associated with the emitted parton (j) is 
absorbed by the other final-state parton (k). This 
allows a simple construction  of the post-branching momenta in the 
centre-of-mass frame of the initial-final antenna. 
</p> 
<p> 
The "global map" allows for an overall transverse recoil associated with the 
initial-state leg to be imparted to the system of final-state partons 
other than those participating directly in the branchings. This is 
equivalent to saying that any transverse momentum associated with the 
emitted parton (j) is absorbed by the initial-stage leg (a), after 
which a Lorentz transformation brings it (plus the final-state system) 
back to having beam-collinear kinematics. The recoil vanishes For 
final-state collinear kinematicsbut is in general nonzero outside that 
limit. 
</p> 
<p> 
Intuitively, the local map should be appropriate for final-state 
splittings, while the global one would be appropriate for initial-state 
ones. The full story is more complicated, partly since soft wide-angle 
radiation intrinsically represents interference between the two cases, 
and partly because the phase-space limits for the two maps (outside of 
the strict soft and collinear limits) are different. (The x &lt; 1 
constraint translates to slightly different constraints on the 
branching invariants for the two maps, as does positivity of the Gram 
determinant.) A probabilistic selection is therefore made between 
the local and 
global maps, using a form obtained by R. Verheyen based on comparisons 
to DIS matrix elements, <ei>P(global) = (sAK - saj)^2/[ (sAK + sjk)^2 + 
(sAK - saj)^2 ] * Theta( sAK - saj )</ei>, with Theta the unit step 
function (since the momenta in the global map always become unphysical 
for saj > sAK). 
</p> 
<p> 
<modepick name="Vincia:kineMapIF" default="1" min="1" max="3"> 
<option value="1">Local recoil map. </option> 
<option value="2">Gluon emissions use a probabilistic selection 
between the global and local maps. Antennae that only contain 
initial-state singularities always use the global one. Antennae that 
only contain final-state singularities always use the local one. </option> 
<option value="3">Probabilistic selection between the global and 
and local maps, for all IF branchings irrespective of their 
singularity structure. </option> 
</modepick> 
</p> 
 
<p>When using the probabilistic selection, it is possible (in 
phase-space regions well away from the strict soft and collinear 
limits) that the selected kinematics map produces unphysical momenta 
(with x &gt; 1 or negative energies) for the given branching 
invariants, while the other map would give physical momenta. In such 
cases, one has to choose whether the given phase-space point should be 
vetoed, or whether the other map should be allowed to be used instead 
to construct the kinematics. 
</p> 
<flag name="Vincia:kineMapIFretry" default="off"> 
<option value="off">If the map selected according to the probabilistic 
choice above returns unphysical momenta, the trial branching is 
vetoed. </option> 
<option value="on">If the map selected according to the probabilistic 
choice above returns unphysical momenta, the other map is tried. Only 
if both maps fail to produce physical momenta is the trial branching 
vetoed.  </option> 
</flag> 
 
<h4>Kinematics and Recoils for FF Antennae </h4> 
 
<modepick name="Vincia:kineMapFFemit" default="3" min="1" max="3"> 
Selects which method to use for choosing the Euler angle for the 
global orientation of the post-branching kinematics construction for 
gluon emissions. 
<option value="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> 
<option value="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> 
<option value="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 <ei>r=sij/(sij+sjk)</ei> in the 
  definition of the map.) 
</option> 
</modepick> 
<modepick name="Vincia:kineMapFFsplit" default="2" min="0" max="3"> 
Selects which method to use for choosing the Euler angle for the 
global orientation of the post-branching kinematics construction for 
gluon splittings. 
<option value="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> 
<option value="2">LONGITUDINAL. For gluon splittings, this choice 
forces the recoiler to always recoil purely longitudinally (in the antenna 
CM) regardless of the size of the branching invariants. 
</option> 
<option value="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 <ei>r=sij/(sij+sjk)</ei> in the 
  definition of the map.) 
</option> 
</modepick> 
 
<h4>Kinematics and Recoils for RF Antennae </h4> 
 
<modepick name="Vincia:kineMapRFemit" default="1" min="1" max="2"> 
  There is only one choice of kinematics map for resonance emissions. 
  However there is a freedom to choose the recoiler(s). 
<option value="1">Takes all non-colour-connected daughters in the 
resonance decay system as the recoilers. 
</option> 
<option value="2">Takes the original non-colour-connected daughter of 
the resonance to always take the full recoil. E.g. in t->bW the 
recoiler is always the W. This is equivalent to setting 
TimeShower:recoilToColoured = off for Pythia. 
</option> 
</modepick> 
<modepick name="Vincia:kineMapRFsplit" default="1" min="1" max="2"> 
Same as above, but for R-g splittings. 
<option value="1">Takes all non-colour-connected daughters in the 
resonance decay system as the recoilers. 
</option> 
<option value="2">Takes the original non-colour-connected daughter of 
the resonance to always take the full recoil. E.g. in t->bW the 
recoiler is always the W. This is equivalent to setting 
TimeShower:recoilToColoured = off for Pythia. 
</option> 
</modepick> 
 
<h3>Lower Cutoffs for the QCD evolution</h3> 
 
<p><b>The hadronisation cutoff</b>, a.k.a. the infrared regularisation scale, 
defines the resolution scale at which the perturbative shower 
evolution is stopped. Thus, perturbative emissions below this scale 
are treated as fundmanentally unresolvable and are in effect 
inclusively summed over. </p> 
<p><b>Important Note:</b> when hadronisation is switched on, 
  there is a delicate interplay between the hadronisation scale used 
  in the shower and the parameters of the hadronisation 
  model. Ideally, 
  the parameters of the hadronisation model should scale as a function 
  of the shower cutoff. This scaling does not happen automatically in 
  current hadronisation models, such as the string model 
  employed by PYTHIA. Instead, the 
  parameters of the hadronisation model are tuned for one specific 
  shower setting at a time and should be retuned if changes are made 
  to the shower cutoff. 
</p> 
 
<parm name="Vincia:cutoffScaleFF" default="0.75" min="0.1" max="10.0"> 
This parameter sets the value (in GeV) of the final state shower 
cutoff. For <code>evolutionType = 1</code> it is interpreted as a 
cutoff on ARIADNE pT, while for <code>evolutionType = 2</code> it is 
interpreted as a cutoff on invariant mass. 
</parm> 
<parm name="Vincia:cutoffScaleII" default="1.6" min="0.1" max="10.0"> 
This parameter sets the value (in GeV) of the shower cutoff for 
initial-initial antennae. 
</parm> 
<parm name="Vincia:cutoffScaleIF" default="1.6" min="0.1" max="10.0"> 
This parameter sets the value (in GeV) of the shower cutoff for 
initial-final antennae. 
</parm> 
 
<parm name="Vincia:ThresholdMB" default="4.8">Minimum 
threshold (mass, in GeV) for bottom quark production.</parm> 
 
<parm  name="Vincia:ThresholdMC" default="1.5">Minimum 
threshold (mass, in GeV) for charm quark production.</parm> 
 
<h3>Other QCD Settings</h3> 
 
<h4>Subleading Colour</h4> 
<p> 
During the perturbative shower evolution, the first aspect of 
subleading colour is simply what colour factors are used for the 
antenna functions. 
In a strict leading-colour limit, one would use <ei>CA</ei> for all antennae, 
thus overestimating the amount of radiation from quarks 
(note that we use a normalisation convention in which the colour factor 
for quarks is <ei>2CF</ei>, 
hence the difference is explicitly subleading in colour). 
A more realistic starting point is to use <ei>2CF</ei> for quark-antiquark 
antennae, <ei>CA</ei> for gluon-gluon ones, and something inbetween for 
quark-gluon ones.  The following switch 
determines whether and how subleading-colour corrections are treated 
in the evolution: 
</p> 
<modepick name="Vincia:modeSLC" default="2" min="0" max="3"> 
<option value="0">Strict LC evolution. All gluon-emission colour 
factors are forced equal to CA thus overcounting the radiation from 
quarks. Note that matrix-element corrections will still generate 
corrections to the evolution up to the matched number of legs. 
</option> 
<option value="1">Simple Colour Factors. The <code>chargeFactor</code> 
parameters for each of the antenna functions are used to set the 
colour factor for each type of gluon-emission antenna; see the section on 
antenna functions. (Typically, 2CF for qqbar antennae, 
CA for gg antennae, and the average of 2CF and CA for qg antennae.) 
</option> 
<option value="2">Interpolating Colour Factors. The colour factor 
for quark-antiquark antennae is forced equal to 2CF. 
Gluon-gluon antennae are normalised to CA. 
The colour factor for QG antennae is 
<ei>2CF * (1-yij)/(2-yij-yjk) + CA * (1-yjk)/(2-yij-yjk)</ei>, which is 
just a simple interpolation between CA in the gluon-collinear limit 
and 2CF in the quark-collinear limit. More sophisticated choices 
could also be motivated and may be interesting to explore in future 
versions. 
</option> 
<option value="3">Only used for development purposes.</option> 
</modepick> 
 
<p> 
Colour flow is traced using Les-Houches style colour tags, augmented 
by letting the last digit encode the "colour index", running from 1 to 
9, described further in the section below on antenna swing. One 
ambiguity arises in gluon emission as to which of the daughter 
antennae should inherit the "parent" colour tag/index, and which 
should be assigned a new one. This is controlled by the following parameter: 
</p> 
<modepick name="Vincia:CRinheritMode" default="1" min="-2" max="2"> 
 <option value="0">Random</option> 
  <option value="1">The daughter with the largest invariant mass has 
  a probability <em>1/(1 + r)</em> to inherit the parent tag, with 
  <em>r &lt; 1</em> the ratio of the smallest to the largest daughter 
  invariant masses squared. 
  </option> 
  <option value="2">The daughter with the largest invariant mass 
  always inherits the parent tag (winner-takes-all extreme variant of 
  option 1). 
  </option> 
  <option value="-1">(Unphysical, intended for theory-level studies 
  only). Inverted variant of option 1, so that the 
  daughter with the smallest invariant mass preferentially inherits 
  the parent colour tag. 
  </option> 
  <option value="-2">(Unphysical, intended for theory-level studies 
  only). Inverted variant of option 2, so that the daughter with the 
  smallest invariant mas always inherits the parent colour tag. 
  </option> 
</modepick> 
 
</chapter> 
