POWHEG Merging
POWHEG [Nas04] in its character is very much like a parton shower,
with a Sudakov factor arising from the ordering of emissions. Both
POWHEG-BOX [Ali10] and PYTHIA are based on a combined evolution
of ISR and FSR in pT-related "hardness" variables, and thus are
kindred spirits. The hardness definitions differ, however. Frequently we
will therefore need to distinguish between POWHEG-hardness and
PYTHIA-hardness in the following.
The simplest merging solution, of continuing the PYTHIA shower at the LHA
scale
hardness where POWHEG leaves off, is obtained if you
set SpaceShower:pTmaxMatch = 1
and
TimeShower:pTmaxMatch = 1
. But then mismatches are bound to
happen: some regions may be doublecounted, while others may not be counted
at all. Depending on the choice of hardness, such mismatches might be small.
There are no guarantees, however, so a (hopefully) more accurate merging
scheme is coded up in the include/Pythia8Plugins/PowHegHooks.h
file, with a realistic user example in the examples/main31
files. Here we would like to discuss the (POWHEG-specific) input settings
for main31.cc
, see main31.cmnd
, and attempt to
give some recommendations on how to use the main program to perform a
matching of POWHEG-BOX with PYTHIA 8.
POWHEG-BOX inputs contain Born-like events (with no resolved emission) and
Real-type events (containing an additional parton). The mismatch between
POWHEG-hardness and PYTHIA-hardness can be minimised if the PYTHIA shower
knows
a) The POWHEG-hardness criterion (through which the separation of Born-
and Real-like events is defined), and
b) The POWHEG-hardness value (which separates Born- and Real-like
events).
If these definitions are known, then
PYTHIA can fill missing phase space regions through vetoed showering: let
the shower sweep over the full phase space, using its PYTHIA-hardness
ordering, and use the POWHEG-hardness to veto those emissions that POWHEG
should already have covered. This is only possible since the
POWHEG-hardness criterion and the shower ordering criterion are very
similar. In the more general case a truncated showering would be needed
[Nas04].
For vetoed showering, it is necessary to define the POWHEG-hardness
criterion. In the presence of multiple partons, the definition
quickly becomes complicated, and allows for different choices. Similar
decisions have already been made in the implementation of POWHEG, one example
being the choice in defining which "hardness value" is transferred as
POWHEG-hardness, e.g. by deciding if the "singular regions" of the FKS or the
CS approach are used. If the POWHEG-hardness definition were to be changed,
or extended to more objects, the PowhegHooks.h
code would need
to be modified accordingly.
The merging code is designed to be very flexible, and allows access
to many possible choices. However, this flexibility means that many parameters
can be changed, potentially leading to confusion. Thus, recommendations might
prove helpful. All mistakes and inaccuracies rest with the author.
We recommend the usage of vetoed showers. This means using
POWHEG:veto = 1
This means that PYTHIA will sweep over the full phase space, and apply a veto
on parton shower emissions for which the POWHEG-hardness separation between
radiator and emission is above the POWHEG-hardness value of the current input
event. The variation POWHEG:veto = 0
can be used to assess
how much phase space is under- or double-counted.
To define the POWHEG-hardness criterion, use
POWHEG:pTdef = 1
Other values can be used by experts to assess variations.
Both POWHEG-BOX and PYTHIA 8 generate emissions through a parton shower
step, meaning that both programs have a clear definition of a radiator
that emits particles, which is very similar (if not identical).
To fix the ambiguity if the radiator or the emitted particle should be
called "the emission", use
POWHEG:emitted = 0
More complicated choices can be used by experts. For instance, use
POWHEG:emitted = 2
to check the POWHEG-hardness of both
radiator and emitted.
To exhaustively fix the criterion by which to veto parton shower
emissions, it is important to decide which partons/parton pairs
are used to calculate the POWHEG hardness of a PYTHIA 8 emission.
The minimal and recommended choice is
POWHEG:pTemt = 0
This means that only the POWHEG hardness with respect to the radiating leg
is checked, and recoil effects are neglected. This prescription should be
very similar to how a hardness value is assigned to a Real-type event
in the POWHEG-BOX, since in the (implementation of FKS in the) POWHEG-BOX,
initial state splittings only have singular regions with the radiating
initial state parton, and final state splittings only have singular
regions with respect to the radiating final state line. Other choices of
POWHEG:pTemt
are available. A warning is that the impact of
changes can be huge, particularly for inputs with many jets. Other choices
therefore should only be made by experts, and a high degree of caution
is advised.
It is furthermore necessary to decide on a value of the hardness criterion.
POWHEG-BOX transfers this value in the SCALUP
member of
Les Houches Events, and we recommend using this value by setting
POWHEG:pThard = 0
As a variation, in order to estimate the uncertainty due this choice of
POWHEG-hardness definition, it can be useful to also check
POWHEG:pThard = 2
. This will recalculate the POWHEG-hardness
value as promoted in [Ole12].
You need to decide how many emissions the vetoed shower should
check after an allowed emission has been constructed. If the hardness
definitions in POWHEG-BOX and PYTHIA 8 where identical, all checking could
be stopped after the first allowed PS emission. To be prudent, we
recommend setting
POWHEG:vetoCount = 3
which will then check up to three allowed emissions. Higher values of
POWHEG:vetoCount
have not lead to visible differences
for the processes which have been tested.
Finally, for many POWHEG processes, the Sudakov effects from electroweak
emissions (here we are concerned mainly with photon emissions, but this could
apply also to W/Z emissions) are not included. This effect can be
investigated using POWHEG:QEDveto = 0,1,
or 2
.
For the default value of POWHEG:pTemt = 0
, only
POWHEG:QEDveto = 2
has any effect. For this choice, a hard
photon and subsequent QCD radiation is retained. In many cases, particularly
when the Born contributions are small, the choice has little effect.
The modes
Note that the modes have generally been defined with several default values
below corresponding to the "off" state, and thus do not agree with the
recommended values described above.
mode
POWHEG:nFinal
(default = 2
; minimum = 1
)
Number of outgoing particles of POWHEG Born level process,
i.e. not counting additional POWHEG radiation.
mode
POWHEG:veto
(default = 0
; minimum = 0
; maximum = 1
)
Master switch to perform vetoing or not.
option
0 : No vetoing is performed (the user hooks is not loaded).
option
1 : Showers are started at the kinematical limit.
Emissions are vetoed if pTemt > pThard.
See also POWHEG:vetoCount
below.
mode
POWHEG:vetoCount
(default = 3
; minimum = 0
)
After this many accepted emissions in a row, no more emissions
are checked. Value 0 means that no emissions are checked. Using a very
large value (e.g. 100000) will mean that all emissions are checked.
mode
POWHEG:pThard
(default = 0
; minimum = 0
; maximum = 2
)
Selection of the pThard scale. For events where there is no
radiation, pThard is always set to be the SCALUP
value of the LHA/LHEF standard.
option
0 : Set pThard equal to SCALUP
.
option
1 : The pT of the POWHEG emission is tested against
all other incoming and outgoing partons, with the minimal value chosen.
option
2 : The pT of all final-state partons is tested
against all other incoming and outgoing partons, with the minimal value
chosen.
mode
POWHEG:pTemt
(default = 0
; minimum = 0
; maximum = 2
)
Selection of the pTemt scale.
option
0 : It is the pT of the emitted parton with respect
to the radiating parton.
option
1 : The pT of the emission is checked against all
incoming and outgoing partons, and then pTemt is set to the
minimum of these values.
option
2 : The pT of all final-state partons is tested
against all other incoming and outgoing partons, with the minimal value
chosen.
Warning: the choice here can give significant variations
in the final distributions, notably in the tail to large pT values.
mode
POWHEG:emitted
(default = 0
; minimum = 0
; maximum = 3
)
Selection of emitted parton for FSR.
option
0 : The PYTHIA definition of emitted.
option
1 : The PYTHIA definition of radiator.
option
2 : A random selection of emitted or radiator.
option
3 : Both emitted and radiator are tried.
mode
POWHEG:pTdef
(default = 0
; minimum = 0
; maximum = 2
)
Use of pT definitions.
option
0 : The POWHEG ISR pT definition for
both ISR and FSR.
option
1 : The POWHEG ISR pT and FSR d_ij
definitions.
option
2 : The PYTHIA definitions.
mode
POWHEG:MPIveto
(default = 0
; minimum = 0
; maximum = 1
)
MPI vetoing.
option
0 : No MPI vetoing is done.
option
1 : When there is no radiation, MPIs with a scale above
pT_1 are vetoed, else MPIs with a scale above
sum_i pT_i / 2 = (pT_1 + pT_2 + pT_3) / 2 are vetoed.
This option is intended specifically for POWHEG simulations of
2 → 2 + 2 → 3 QCD processes.
mode
POWHEG:QEDveto
(default = 0
; minimum = 0
; maximum = 2
)
Treatment of non-QCD radiation.
option
0 : Colorless partons are not included in pT
calculated from the shower for pTemt>0 .
option
1 : Colorless partons ARE included for pTemt>0 .
option
2 : Colorless partons ARE included for pTemt>0 .
Additionally, if a colorless parton is emitted with pT > pThard
in Born-level events, then the entire event is accepted.
This is relevant for all values of pTemt .