Spacelike Showers
 
  - Main variables
- Dipole showers
- Weak showers
- Further variables
- Technical notes
The PYTHIA algorithm for spacelike initial-state showers is 
based on the article [Sjo05], where a 
transverse-momentum-ordered backwards evolution scheme is introduced, 
with the extension to fully interleaved evolution covered in 
[Cor10a]. 
This algorithm is a further development of the virtuality-ordered one 
presented in [Sjo85], with matching to first-order matrix 
element for Z^0, W^+- and Higgs (in the 
m_t → infinity limit) production as introduced in 
[Miu99]. 
 
 
The normal user is not expected to callSpaceShower 
directly, but only have it called from Pythia, 
via PartonLevel. Nonetheless, some of the parameters below, 
in particular SpaceShower:alphaSvalue, 
would be of interest for uncertainty estimates and tuning exercises. 
Note that 
PYTHIA also incorporates an 
automated framework for shower 
uncertainty variations. 
 
 
Main variables
 
 
The maximum pT to be allowed in the shower evolution is 
related to the nature of the hard process itself. It involves a 
delicate balance between not double-counting and not leaving any 
gaps in the coverage. The best procedure may depend on information 
only the user has: how the events were generated and mixed (e.g. with 
Les Houches Accord external input), and how they are intended to be 
used. Therefore a few options are available, with a sensible default 
behaviour. 
 
mode   SpaceShower:pTmaxMatch   
 (default = 0; minimum = 0; maximum = 2)
Way in which the maximum shower evolution scale is set to match the 
scale of the hard process itself. 
option  0 : (i) if the final state of the hard process 
(not counting subsequent resonance decays) contains at least one quark 
(u, d, s, c ,b), gluon or photon then pT_max 
is chosen to be the factorization scale for internal processes 
and the scale value for Les Houches input; 
(ii) if not, emissions are allowed to go all the way up to 
the kinematical limit. 
The reasoning is that in the former set of processes the ISR 
emission of yet another quark, gluon or photon could lead to 
double-counting, while no such danger exists in the latter case. 
   
option  1 : always use the factorization scale for an internal 
process and the scale value for Les Houches input, 
i.e. the lower value. This should avoid double-counting, but 
may leave out some emissions that ought to have been simulated. 
(Also known as wimpy showers.) 
   
option  2 : always allow emissions up to the kinematical limit. 
This will simulate all possible event topologies, but may lead to 
double-counting. 
(Also known as power showers.) 
   
Note 1: Some processes contain matrix-element matching 
to the first emission; this is the case notably for single 
gamma^*/Z^0, W^+- and H^0 production. Then default 
and option 2 give the correct result, while option 1 should never 
be used. 
Note 2: as enumerated in the text, these options take effect 
both for internal and external processes. Whether a particular option 
makes sense depends on the context. For instance, if events for the same 
basic process to different orders are to be matched, then option 1 would 
be a reasonable first guess. Note, however, that a program like the 
POWHEG BOX uses a pT definition for ISR and FSR that does not 
quite agree with the PYTHIA evolution scale, and thus there will be some 
amount of mismatch. In more sophisticated descriptions, therefore, 
option 2 could be combined with UserHooks vetoes on emissions 
that would lead to double-counting, using more flexible phase space 
boundaries. Further details are found in the 
Matching and Merging description, 
with an example in examples/main152. 
Option 0, finally, may be most realistic when only Born-level 
processes are involved, possibly in combination with a nonzero 
SpaceShower:pTdampMatch. The rules used for avoiding 
double-counting are not foolproof, however. As an example, for the 
t-channel process gamma gamma → e^+ e^- its pT 
scale is the plausible upper shower limit, with only dampened emissions 
above it. But the initial state is not checked and, had only incoming 
quarks and gluons been taken into account, only the s-channel 
process q qbar → gamma^*/Z^0 → e^+ e^- would have 
been possible, where indeed the whole phase space should be populated. 
So this is erroneously used, giving too much emissions. 
Note 3: These options only apply to the hard interaction. 
If a "second hard" process is present, the two are analyzed and 
set separately for the default 0 option, while both are affected 
the same way for non-default options 1 and 2. 
Emissions off subsequent multiparton interactions are always constrained 
to be below the factorization scale of each process itself. 
   
 
parm   SpaceShower:pTmaxFudge   
 (default = 1.0; minimum = 0.25; maximum = 2.0)
In cases where the above pTmaxMatch rules would imply 
that pT_max = pT_factorization, pTmaxFudge 
introduces a multiplicative factor f such that instead 
pT_max = f * pT_factorization. Only applies to the hardest 
interaction in an event, and a "second hard" if there is such a one, 
cf. below. It is strongly suggested that f = 1, but variations 
around this default can be useful to test this assumption. 
   
 
parm   SpaceShower:pTmaxFudgeMPI   
 (default = 1.0; minimum = 0.25; maximum = 2.0)
A multiplicative factor f such that 
pT_max = f * pT_factorization, as above, but here for the 
non-hardest interactions (when multiparton interactions are allowed). 
   
 
mode   SpaceShower:pTdampMatch   
 (default = 3; minimum = 0; maximum = 4)
These options only take effect when a process is allowed to radiate up 
to the kinematical limit by the above pTmaxMatch choice, 
and no matrix-element corrections are available. Then, in many processes, 
the fall-off in pT will be too slow by one factor of pT^2. 
That is, while showers have an approximate dpT^2/pT^2 shape, often 
it should become more like dpT^2/pT^4 at pT values above 
the scale of the hard process. Whether this actually is the case 
depends on the particular process studied, e.g. if t-channel 
gluon exchange is likely to dominate. If so, the options below could 
provide a reasonable high-pT behaviour without requiring 
higher-order calculations. 
option  0 : emissions go up to the kinematical limit, 
with no special dampening. 
   
option  1 : emissions go up to the kinematical limit, 
but dampened by a factor k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac), 
where Q_fac is the factorization scale and k is a 
multiplicative fudge factor stored in pTdampFudge below. 
   
option  2 : emissions go up to the kinematical limit, 
but dampened by a factor k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren), 
where Q_ren is the renormalization scale and k is a 
multiplicative fudge factor stored in pTdampFudge below. 
   
option  3 : as option 1, but in addition to the standard requirements 
for dampening it is further necessary to have at least two top or 
beyond-the-Standard-Model coloured particles in the final state. 
Examples include t tbar and squark gluino production. 
   
option  4 : as option 2, but in addition to the standard requirements 
for dampening it is further necessary to have at least two top or 
beyond-the-Standard-Model coloured particles in the final state. 
Examples include t tbar and squark gluino production. 
   
Note: These options only apply to the hard interaction. 
Specifically, a "second hard" interaction would not be affected. 
Emissions off subsequent multiparton interactions are always constrained 
to be below the factorization scale of the process itself. 
   
 
parm   SpaceShower:pTdampFudge   
 (default = 1.0; minimum = 0.25; maximum = 4.0)
In cases 1 and 2 above, where a dampening is imposed at around the 
factorization or renormalization scale, respectively, this allows the 
pT scale of dampening of radiation by a half to be shifted 
by this factor relative to the default Q_fac or Q_ren. 
This number ought to be in the neighbourhood of unity, but variations 
away from this value could do better in some processes. 
   
 
 
The amount of QCD radiation in the shower is determined by 
parm   SpaceShower:alphaSvalue   
 (default = 0.1365; minimum = 0.06; maximum = 0.25)
The alpha_strong value at scale M_Z^2. 
   
 
 
The actual value is then regulated by the running to the scale 
pT^2, at which it is evaluated 
mode   SpaceShower:alphaSorder   
 (default = 1; minimum = 0; maximum = 3)
Order at which alpha_strong runs, 
option  0 : zeroth order, i.e. alpha_strong is kept 
fixed.   
option  1 : first order, which is the normal value.   
option  2 : second order. Since other parts of the code do 
not go to second order there is no strong reason to use this option, 
but there is also nothing wrong with it.   
option  3 : third order, with the same comment as for second 
order. The expression in the 2006 RPP is used here.   
   
 
 
The CMW rescaling of Lambda_QCD (see the section on 
StandardModelParameters) 
can be applied to the alpha_strong values used for spacelike showers. 
Note that tunes using this option need lower values of 
alpha_strong(m_Z^2) than tunes that do not. 
flag   SpaceShower:alphaSuseCMW   
 (default = off)
option  off : Do not apply the CMW rescaling.    
option  on : Apply the CMW rescaling, increasing 
Lambda_QCD for spacelike showers by a factor roughly 1.6. 
   
   
 
 
QED radiation is regulated by the alpha_electromagnetic 
value at the pT^2 scale of a branching. 
 
mode   SpaceShower:alphaEMorder   
 (default = 1; minimum = -1; maximum = 1)
The running of alpha_em. 
option  1 : first-order running, constrained to agree with 
StandardModel:alphaEMmZ at the Z^0 mass. 
   
option  0 : zeroth order, i.e. alpha_em is kept 
fixed at its value at vanishing momentum transfer.   
option  -1 : zeroth order, i.e. alpha_em is kept 
fixed, but at StandardModel:alphaEMmZ, i.e. its value 
at the Z^0 mass. 
   
   
 
 
The natural scale for couplings and PDFs is pT^2. To explore 
uncertainties it is possibly to vary around this value, however, in 
analogy with what can be done for 
hard processes. (Note that 
there is also an automated framework for shower 
uncertainties.) 
 
parm   SpaceShower:renormMultFac   
 (default = 1.; minimum = 0.1; maximum = 10.)
The default pT^2 renormalization scale is multiplied by 
this prefactor. For QCD this is equivalent to a change of 
Lambda^2 in the opposite direction, i.e. to a change of 
alpha_strong(M_Z^2) (except that flavour thresholds 
remain at fixed scales). Below, when pT^2 + pT_0^2 is used 
as scale, it is this whole expression that is multiplied by the prefactor. 
   
 
parm   SpaceShower:factorMultFac   
 (default = 1.; minimum = 0.1; maximum = 10.)
The default pT^2 factorization scale is multiplied by 
this prefactor. 
   
 
 
There are two complementary ways of regularizing the small-pT 
divergence, a sharp cutoff and a smooth dampening. These can be 
combined as desired but it makes sense to coordinate with how the 
same issue is handled in multiparton interactions. 
 
flag   SpaceShower:samePTasMPI   
 (default = off)
Regularize the pT → 0 divergence using the same sharp cutoff 
and smooth dampening parameters as used to describe multiparton interactions. 
That is, the MultipartonInteractions:pT0Ref, 
MultipartonInteractions:ecmRef, 
MultipartonInteractions:ecmPow and 
MultipartonInteractions:pTmin parameters are used to regularize 
all ISR QCD radiation, rather than the corresponding parameters below. 
This is a sensible physics ansatz, based on the assumption that colour 
screening effects influence both MPI and ISR in the same way. Photon 
radiation is regularized separately in either case. 
Note: For photon-photon collisions these parameters are set 
as in Photoproduction. 
Warning: if a large pT0 is picked for multiparton 
interactions, such that the integrated interaction cross section is 
below the nondiffractive inelastic one, this pT0 will 
automatically be scaled down to cope. Information on such a rescaling 
does NOT propagate to SpaceShower, however. 
   
 
 
The actual pT0 parameter used at a given CM energy scale, 
ecmNow, is obtained from a power law or a logarithmic 
parametrization. The former is default with hadron beams and 
the latter for photon-photon collisions. 
 
mode   SpaceShower:pT0parametrization   
 (default = 0; minimum = 0; maximum = 1)
Choice of pT0 parametrization. 
option  0 :  Power law dependence on ecmNow:
 
 
    pT0 = pT0(ecmNow) = pT0Ref * (ecmNow / ecmRef)^ecmPow 
 
   
option  1 :  Logarithmic dependence on ecmNow: 
 
    pT0 = pT0(ecmNow) = pT0Ref + ecmPow * log (ecmNow / ecmRef) 
 
   
where pT0Ref, ecmRef and ecmPow are the 
three parameters below. 
   
 
parm   SpaceShower:pT0Ref   
 (default = 2.0; minimum = 0.5; maximum = 10.0)
Regularization of the divergence of the QCD emission probability for 
pT → 0 is obtained by a factor pT^2 / (pT0^2 + pT^2), 
and by using an alpha_s(pT0^2 + pT^2). An energy dependence 
of the pT0 choice is introduced by the next two parameters, 
so that pT0Ref is the pT0 value for the reference 
cm energy, pT0Ref = pT0(ecmRef). 
   
 
parm   SpaceShower:ecmRef   
 (default = 7000.0; minimum = 1.)
The ecmRef reference energy scale introduced above. 
   
 
parm   SpaceShower:ecmPow   
 (default = 0.0; minimum = 0.; maximum = 0.5)
The ecmPow energy rescaling pace introduced above. 
   
 
parm   SpaceShower:pTmin   
 (default = 0.2; minimum = 0.1; maximum = 10.0)
Lower cutoff in pT, below which no further ISR branchings 
are allowed. Normally the pT0 above would be used to 
provide the main regularization of the branching rate for 
pT → 0, in which case pTmin is used  mainly for 
technical reasons. It is possible, however, to set pT0Ref = 0 
and use pTmin to provide a step-function regularization, 
or to combine them in intermediate approaches. Currently pTmin 
is taken to be energy-independent. 
   
 
parm   SpaceShower:pTminChgQ   
 (default = 0.5; minimum = 0.01)
Parton shower cut-off pT for photon coupling to a coloured 
particle. 
   
 
parm   SpaceShower:pTminChgL   
 (default = 0.0005; minimum = 0.0001)
Parton shower cut-off mass for pure QED branchings. 
Assumed smaller than (or equal to) pTminChgQ. 
   
 
flag   SpaceShower:rapidityOrder   
 (default = on)
Force emissions, after the first,  to be ordered in rapidity, 
i.e. in terms of decreasing angles in a backwards-evolution sense. 
Could be used to probe sensitivity to unordered emissions. 
Only affects QCD emissions, and only the hard subcollision of an event. 
(For the case "soft QCD" processes the first MPI counts as the hard 
subcollision.) 
 
   
 
flag   SpaceShower:rapidityOrderMPI   
 (default = on)
Same as the last switch, but this time only emissions in secondary 
scattering systems from MPIs are forced to be ordered in rapidity. 
Each MPI is ordered separately from the others. 
   
 
 
Dipole showers
 
 
By default the recoil of an ISR emission is taken by the whole final 
state. The option below gives an alternative approach with local recoils, 
where only one final-state parton takes the recoil of an emission. 
See [Cab17] for further details on the philosophy and 
implementation. 
 
 
The existing initial-initial global recoil scheme is maintained for 
an emission off a colour line that stretches through the hard process, 
so it is the handling of initial-final dipole ends that is changed. 
Here the single recoiler is picked based on the colour flow of the 
hard process. Additionally the description unifies the emission of 
a gluon from the initial-final and final-initial dipole ends, and 
handles both as part of the ISR framework. Therefore the separation 
into ISR and FSR is not a meaningful classification, and either both 
should be simulated or none. 
 
 
Note that this option should not be combined with the global option 
for FSR, TimeShower:globalRecoil. Furthermore some settings 
are neglected internally to ensure the same behaviour as obtained for 
TimeShower:allowBeamRecoil = on, 
TimeShower:dampenBeamRecoil = off, and 
SpaceShower:phiIntAsym = off. 
 
 
The dipole recoil option for the first time allows the simulation 
of Deeply Inelastic Scattering processes in PYTHIA 8, see the 
main341.cc example. Note that the simultaneous emission of 
photons off the lepton leg has not yet been implemented, so you need to 
set PDF:lepton = off and 
TimeShower:QEDshowerByL = off. You are further recommended 
to set SpaceShower:pTmaxMatch = 2 to fill the whole phase 
space with parton showers. This is allowed since the shower and 
matrix-element behaviours match well over the whole phase space 
(at least for the first emission). 
 
flag   SpaceShower:dipoleRecoil   
 (default = off)
Option to switch on the dipole-recoil scheme as described above. 
   
 
 
Weak showers
 
 
The emission of weak gauge bosons is an integrated part of the initial- 
and final-state radiation, see Weak Showers. 
The following settings are those specifically related to the initial-state 
weak radiation, while common settings are found in the 
Weak Showers description. 
 
flag   SpaceShower:weakShower   
 (default = off)
Allow a weak shower, yes or no. 
   
 
mode   SpaceShower:weakShowerMode   
 (default = 0; minimum = 0; maximum = 2)
Determine which branchings are allowed. 
option  0 :  both W^+- and Z^0 branchings. 
   
option  1 :  only W^+- branchings.    
option  2 :  only Z^0 branchings.    
   
 
parm   SpaceShower:pTminWeak   
 (default = 1.0; minimum = 0.1; maximum = 2.0)
Parton shower cut-off pT for weak branchings. 
   
 
 
Further variables
 
 
These should normally not be touched. Their only function is for 
cross-checks. 
 
 
There are three flags you can use to switch on or off selected 
branchings in the shower: 
 
flag   SpaceShower:QCDshower   
 (default = on)
Allow a QCD shower; on/off = true/false. 
   
 
flag   SpaceShower:QEDshowerByQ   
 (default = on)
Allow quarks to radiate photons; on/off = true/false. 
   
 
flag   SpaceShower:QEDshowerByL   
 (default = on)
Allow leptons to radiate photons; on/off = true/false. 
   
 
 
There are some further possibilities to modify the shower: 
 
flag   SpaceShower:MEcorrections   
 (default = on)
Use of matrix element corrections; on/off = true/false. 
   
 
flag   SpaceShower:MEafterFirst   
 (default = on)
Use of matrix element corrections also after the first emission, 
for dipole ends of the same system that did not yet radiate. 
Only has a meaning if MEcorrections above is 
switched on. 
   
 
flag   SpaceShower:phiPolAsym   
 (default = on)
Azimuthal asymmetry induced by gluon polarization; on/off = true/false. 
   
 
flag   SpaceShower:phiPolAsymHard   
 (default = on)
Extend the above azimuthal asymmetry (if on) also back to gluons produced 
in the hard process itself, where feasible; on/off = true/false. 
   
 
flag   SpaceShower:phiIntAsym   
 (default = on)
Azimuthal asymmetry induced by interference; on/off = true/false. 
   
 
parm   SpaceShower:strengthIntAsym   
 (default = 0.7; minimum = 0.; maximum = 0.9)
Size of asymmetry induced by interference. Natural value of order 0.5; 
expression would blow up for a value of 1. 
   
 
mode   SpaceShower:nQuarkIn   
 (default = 5; minimum = 0; maximum = 5)
Number of allowed quark flavours in g → q qbar branchings, 
when kinematically allowed, and thereby also in incoming beams. 
Changing it to 4 would forbid g → b bbar, etc. 
   
 
flag   SpaceShower:useFixedFacScale   
 (default = off)
Allow the possibility to use a fixed factorization scale, set by 
the parm below. This option is unphysical and only 
intended for toy-model and debug studies. 
   
 
parm   SpaceShower:fixedFacScale   
 (default = 100.; minimum = 1.)
The fixed factorization scale, in GeV, that would be used in the 
evaluation of parton densities if the flag above is on. 
   
 
mode   SpaceShower:pdfMode   
 (default = 0; minimum = 0; maximum = 2)
This setting should not be touched by non-experts. Deviating 
from the default setting will only lead to consistent results 
after explicit external intervention. This setting can be useful 
in the context of interfaces to external code as done when using 
the flag Merging:runtimeAMCATNLOInterface described under 
Merging. 
option  0 : this default setting corresponds to the typical 
shower treatment of including PDF ratios in the backwards-evolution 
branching rates, leading to the generation of normal no-emission 
probabilities. 
   
option  1 : disable the PDF dependence, which leads to the 
generation of Sudakov factors according to the momentum sum rule. 
   
option  2 : disable the PDF dependence, which leads to the 
generation of Sudakov factors like option 1, but with a lower cut-off 
zMin = 0.5 on the energy-fraction integral. 
   
   
 
 
Technical notes
 
 
Almost everything is equivalent to the algorithm in 
[Sjo05,Cor10a]. Minor changes are as follows. 
 
-  
It is now possible to have a second-order running alpha_s, 
in addition to fixed or first-order running. 
-  
The description of heavy flavour production in the threshold region 
has been modified, so as to be more forgiving about mismatches 
between the c/b  masses used in Pythia relative to those 
used in a respective PDF parametrization. The basic idea is that, 
in the threshold region of a heavy quark Q, Q = c/b, 
the effect of subsequent Q → Q g branchings is negligible. 
If so, then 
 f_Q(x, pT2) = integral_mQ2^pT2  dpT'2/pT'2 * alpha_s(pT'2)/2pi 
      * integral P(z) g(x', pT'2) delta(x - z x')
 so use this to select the pT2 of the g → Q Qbar 
branching. In the old formalism the same kind of behaviour should 
be obtained, but by a cancellation of a 1/f_Q that diverges 
at the threshold and a Sudakov that vanishes.
 The strategy therefore is that, once pT2 < f * mQ2, with 
f a parameter of the order of 2, a pT2 is chosen 
like dpT2/pT2 between mQ2 and f * mQ2, a 
nd a z flat in the allowed range. Thereafter acceptance 
is based on the product of three factors, representing the running 
of alpha_strong, the splitting kernel (including the mass term) 
and the gluon density weight. At failure, a new pT2 is chosen 
in the same  range, i.e. is not required to be lower since no Sudakov 
is involved.
-  
The QED algorithm now allows for hadron beams with non-zero photon 
content. The backwards-evolution of a photon in a hadron is identical 
to that of a gluon, with CF → eq^2 and CA → 0. 
Note that this will only work in conjunction with parton distributions 
that explicitly include photons as part of the hadron structure, such 
as the NNPDF2.3 QCD+QED sets. The possibility of a fermion 
backwards-evolving to a photon has not yet been included, nor has 
photon backwards-evolution in lepton beams.