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 Evolution and Ordering.
mode
Vincia:matchingLO
(default = 3
; minimum = 0
; maximum = 4
)2
would invoke tree-level 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.
mode
Vincia:matchingNLO
(default = 2
; minimum = 0
; maximum = 2
)2
would invoke one-loop matching
up to and including X+1
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.
Note: values larger than the leading-order value above will be
ignored. Thus, to switch off all matrix-element corrections,
it is sufficient to switch off the LO ones.
The choice of functional form of the renormalization scale used for the alphaS power associated with the one-loop correction amounts to an NNLO effect and is hence formally beyond the explicit control of the NLO matching. It is controlled by the following parameter:
mode
Vincia:alphaSmodeNLO
(default = 0
; minimum = 0
; maximum = 1
)option
0 : The invariant mass of the parton system, m(ijk).
option
1 : Transverse momentum, defined as in ARIADNE, pT = m(ij)*m(jk)/m(ijk).
Note 1: for a generic multileg topology, the effective renormalization
scale is computed as the geometric mean of such scales, taken
over all ordered three-parton clusterings in the event.
Note 2: the default value, 0
, has been chosen to limit the absolute size of the NLO corrections, especially for soft branchings. For hard corrections, there should not be much difference between the two choices (though one can of course always argue about factors of 2). For soft corrections, differences appear starting from order aS2*Log(s/pT2). Thus, changing to 1
increases the absolute size of the NLO corrections for soft branchings. Ideally, the shower and hadronization parameters should then be retuned.
Note 3: In the current formulation of the VINCIA NLO matching formalism,
option 1
is intended mostly for theoretical reference. The matching expression used in the code is of the form (1 + V), which implicitly assumes that the correction, V, is small. For option 1
, however, V becomes large for soft branchings. In this case, a resummed form of the matching expression would have to be used instead, but such an expression has so far not been derived.
flag
Vincia:matchingFullColor
(default = true
)option
off : Leading Color. Only include matching to leading-color matrix
elements.
option
on : Full Color. Include the full color structure of the
matched matrix elements, absorbing the subleading-color pieces into
each leading-color one in proportion to the relative sizes of the
leading-color pieces. This procedure effectively diagonalizes the
full color matrix and guarantees positive-weight corrections.
Matrix-element corrections have been implemented for the following types of processes:
Basic | LO | Helicity- | NLO | |
Process | Born * αsn | Dependent | Born * αsn | |
|
||||
H0 → gg | 1, 2, 3 | y | - | |
H0/H+/- → qq (massless) | 1, 2, 3, 4 | y | - | |
H0 → qq (massive) | 1, 2, 3, 4 | n | - | |
H+/- → qq (massive) | 1, 2(g) | n | - | |
Z/W → qq (massless) | 1, 2, 3, 4 | y | 1, 2 | |
W → qq (massive) | 1, 2(g) | n | - | |
Z → qq (massive) | 1, 2, 3, 4 | n | - | |
|
Note: for helicity-dependent matrix elements, the symbols Z, W, H0, H+, are used for generic spin-charge states and thus apply also to, e.g., Z', W', etc.
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
)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 matrix-element singularities - the first-order 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
2nd-order 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 matrix-element corrections are exponentiated,
the subleading divergencies in the higher-order
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
)Vincia:matchingRegOrder >= 1
,
choose the functional form of the regulator. (See below for how to
modify the choice of Q and Qmatch.)
option
0 : Step function at Q=Qmatch, i.e.,
option
1 : Suppress the shower-subtracted 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.,
mode
Vincia:MatchingRegType
(default = 1
; minimum = 1
; maximum = 2
)Vincia:matchingRegOrder >= 1
, choose
argument of the regulator function (i.e., Q in the equations
listed under Vincia:matchingRegShape
).
option
1 : Impose matching scale in the type 1 evolution
variable, Qmatch = pT (with unit normalization).
The smallest pT scale of the current
branching and the color neighbor on
either side (if any) is used.
option
2 : Impose matching scale in the type 2 evolution
variable, Qmatch =
min(sij,sjk) (with unit normalization).
flag
Vincia:matchingRegScaleIsAbsolute
(default = false
)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 non-experts. 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 non-experts, the relative
method above is recommended instead.
parm
Vincia:matchingRegScaleRatio
(default = 0.05
; minimum = 0.0
; maximum = 1.0
)Vincia:matchingRegScaleIsAbsolute == false
(default),
this sets the ratio of the matching scale to the process-dependent
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 re-introducing large
unresummed logarithms in the matching coefficients.
parm
Vincia:matchingRegScale
(default = 20.0
; minimum = 0.0
)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 hadronization 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 scale-dependent terms in the NLO corrections are unphysical at scales near ΛQCD).
The parameter below sets an absolute lower scale for the evolution variable, in GeV, below which matrix-element corrections are not applied. Note that the normalization of the evolution variable will affect how this translates to invariants.
parm
Vincia:matchingIRcutoff
(default = 1.0
; minimum = 0.0
; maximum = 10
)