Note: for how to include new (LO) matrix elements, see the section on the MADGRAPH Interface.
Note: matching corrections beyond first order can only be applied for smoothly ordered showers. Matching corrections beyond first order will therefore be automatically switched off when strongly ordered showers are used, see the section on ordering on the main settings page.
mode
Vincia:matchingLO
(default = 2
; minimum = 0
; maximum = 4
)
Selects the order of treelevel matrixelement corrections,
also called LeadingOrder matching. The value should be
interpreted as counting the
total number of powers of alphaS beyond the Born that are matched to
matrix elements.
I.e., for the basic process X, setting this switch
to 2
would invoke treelevel matching
up to and including X+2
partons, to the extent the
relevant matrix elements are available in the code, see
the list below. The
value 0
is equivalent to switching matching off.
flag
Vincia:matchingFullColor
(default = true
)
option
off : Leading Color. Only include matching to leadingcolor matrix
elements.
option
on : Full Color. Include the full color structure of the
matched matrix elements, absorbing the subleadingcolor pieces into
each leadingcolor one in proportion to the relative sizes of the
leadingcolor pieces. This procedure effectively diagonalises the
full color matrix and guarantees positiveweight corrections.
flag
Vincia:Hinterference
(default = on
)
option
off : On an event by event basis, depending on hard process
at hand, either the Higgs to gluon
coupling or all Yukawa couplings are set to zero.
option
on : Full interference, no dependence on what the hard
process is chosen to be.
Matrixelement corrections have been implemented for the following types of processes:
Basic Process  LO (Born * α_{s}^{n})  
Z → jj (massless)  1, 2, 3, 4  
W → jj (massless)  1, 2, 3, 4  
H^{0} → jj (massless), heft to g and yukawa to quarks  1, 2, 3, 4  
pp → Z (massless)  1, 2, 3  
pp → W (massless)  1, 2, 3  
pp → H^{0} (massless), heft to g and yukawa to quarks  1, 2, 3  
pp → jj (massless), pure QCD  1, 2, 3  

Note: In pure QCD processes the 3rd power of α_{s} can only be calculated for the MHV case, and that the 7gluon QCD amplitude can only be calculated at leading color order. The shower will skip the correction process if it doesn't have the required amplitude. Further, for W production, the following flavour combination can not be reached by a QCD shower off pp → W events and is therefore not included in the event generation:
We use the term matching regulator to refer to a generic sharp or smooth dampening of the ME corrections as one crosses into a specified region of phase space. The purpose of this is to restrict the matching to regions of phase space that are free from subleading logarithmic divergences in the matrix elements. This is familiar from the CKKW and MLM approaches, where the matching scale is imposed as a step function in pT, with full ME corrections above that scale and no ME corrections below it. We explore a few alternatives to this approach.
mode
Vincia:matchingRegOrder
(default = 3
; minimum = 0
; maximum = 5
)
Choose starting order from which matrix element corrections are regulated.
option
0 : Off. Matrix element corrections are not regulated at
all. Not advised for production runs, but can be useful for theory
studies.
option
1 : On, starting from 1st order in QCD. This would
normally be overkill since the LL shower exactly reproduces the
1st order matrixelement singularities  the firstorder correction
should therefore normally be free of divergencies and should not
need to be regulated.
option
2 : On, starting from 2nd order in QCD. The
2ndorder matrix element correction generally contains subleading
logarithmic divergences which do not correspond exactly to those
generated by the pure shower. Nonetheless, due to the unitary properties of VINCIA's matching formalism and the close approximation of its shower expansions to 2nd order matrix elements, however, 2nd order corrections can typically be applied over all of phase space, without ill effects.
option
3 : On, starting from 3rd order in QCD. This is the
recommended option for the multiplicative matching
strategy. Since the matrixelement corrections are exponentiated,
the subleading divergencies in the higherorder
corrections are effectively resummed. However,
due to the LL nature of the underlying shower,
it appears from empirical studies that a matching
scale is still needed starting from 3rd order even in the
multiplicative case.
option
4 : On, starting from 4th order in QCD. Not recommended
for production runs, but can be useful for theory studies.
option
5 : On, starting from 5th order in QCD. Not recommended
for production runs, but can be useful for theory studies.
mode
Vincia:matchingRegShape
(default = 1
; minimum = 0
; maximum = 1
)
When Vincia:matchingRegOrder >= 1
,
choose the functional form of the regulator. (See below for how to
modify the choice of Q and Q_{match}.)
option
0 : Step function at Q=Q_{match}, i.e.,
option
1 : Suppress the showersubtracted ME corrections by a
function that is unity above Q2 =
2*Q2match, zero below Q2 = Q2match/2, with a simple
interpolation (logarithmic in Q2) between those scales, i.e.,
flag
Vincia:matchingRegScaleIsAbsolute
(default = false
)
Selects whether the user wants to input the value of Q_{match}
either by giving an an absolute number in GeV or by giving a ratio
with respect to the hard scale.
option
false : Relative. The matching scale is determined automatically
in relation to the hard scale in the process (e.g., the Z mass) by
the factor Vincia:matchingRegScaleRatio
below. This is the
default option and the one recommended for nonexperts. It should
allow a wide range of processes to be considered without having to
manually adjust the matching scale.
option
true : Absolute. The matching scale is set by the
value Vincia:matchingRegScale
(in GeV). Care must then be
taken to select a matching scale appropriate to the specific process
and hard scales under consideration. For nonexperts, the relative
method above is recommended instead.
parm
Vincia:matchingRegScaleRatio
(default = 0.05
; minimum = 0.0
; maximum = 1.0
)
When Vincia:matchingRegScaleIsAbsolute == false
(default),
this sets the ratio of the matching scale to the processdependent
hard scale; inactive otherwise. Since the
unresummed logarithms depend on ratios of scales, it is more natural
to express the matching scale in this way than as an absolute number
in GeV. Note that this parameter
should normally not be varied by more than a factor of 2 in either
direction. The default value has been chosen so as to allow one order
of magnitude between the hard scale and the matching scale. Setting it
too close to unity will effectively switch off the matching, even at
high scales. Settings around 0.01 and below risk reintroducing large
unresummed logarithms in the matching coefficients.
parm
Vincia:matchingRegScale
(default = 20.0
; minimum = 0.0
)
When Vincia:matchingRegScaleIsAbsolute == true
, this sets the
absolute value of the matching scale, in GeV; inactive otherwise.
Care must be taken to select a matching scale appropriate to the
specific process and hard scales under consideration.
Due to the freezing of alphaS in the infrared, it is possible to run VINCIA with very low hadronisation cutoffs. Though this formally continues the perturbative treatment into the infrared, allowing the emission of gluons with very soft momenta, it is doubtful whether matching corrections would be of any value in that region.
Our intuition is that, at best, continuing such corrections into the region below ~ 1 GeV would merely slow down the code. At worst they could generate unphysically large corrections (e.g., the scaledependent terms in the NLO corrections are unphysical at scales near Λ_{QCD}).
The parameter below sets an absolute lower scale for the evolution variable, in GeV, below which matrixelement corrections are not applied. Note that the normalisation of the evolution variable will affect how this translates to invariants.
parm
Vincia:matchingIRcutoff
(default = 2.0
; minimum = 0.0
; maximum = 100.0
)