Initial-State Antenna Showers

  1. On/Off Switches
  2. The Strong Coupling for II and IF antennae
  3. Colour and Charge Factors
  4. Scales
  5. Evolution Variable(s)
  6. Mass Corrections
  7. Recoils and Kinematics for Initial-Initial antennae
  8. Recoils and Kinematics for Initial-Final antennae

Within the dipole-antenna formalism, antenna functions are the analogs of the splitting functions used in traditional parton showers. The antenna functions are constructed so as to reproduce the Altarelli-Parisi splitting functions P(z) in collinear limits and the eikonal dipole factor in the soft limit.

On/Off Switches

flag  Vincia:ISR   (default = on)
Main switch for initial-state radiation on/off.

The default is to leave all antenna functions switched on. For special theory studies, it may be convenient to check what happens when one or more antenna functions are switched off. The switches below give this functionality:

flag  Vincia:QQemitII   (default = on)
Gluon emission of an initial state qqbar pair

flag  Vincia:GQemitII   (default = on)
Gluon emission of an initial state gq pair

flag  Vincia:GGemitII   (default = on)
Gluon emission of an initial state gg pair

flag  Vincia:QXSplitII   (default = on)
Quark in the initial state backwards evolvint into a gluon and emitting an antiquark in the final state

flag  Vincia:GXConvII   (default = on)
Gluon in the initial state backwards evolving into a quark and emitting a quark in the final state (gluon conversion)

flag  Vincia:QQemitIF   (default = on)
Gluon emission of an initial-final qq pair

flag  Vincia:GQemitIF   (default = on)
Gluon emission of an initial-final gq pair

flag  Vincia:QGemitIF   (default = on)
Gluon emission of an initial-final qg pair

flag  Vincia:GGemitIF   (default = on)
Gluon emission of an initial-final gg pair

flag  Vincia:QXSplitIF   (default = on)
Quark in the initial state backwards evolving into a gluon and emitting an antiquark in the final state

flag  Vincia:GXConvIF   (default = on)
Gluon in the initial state backwards evolving into a quark and emitting a quark in the final state (gluon conversion)

flag  Vincia:XGSplitIF   (default = on)
Gluon splitting in the final state

The number of quark flavours allowed in initial-state gluon conversions, phase space permitting, is given by

mode  Vincia:nGluonToQuarkI   (default = 5; minimum = 0; maximum = 5)

The Strong Coupling

The initial state shower uses the same AlphaStrong as the Final State Shower. Any need for different effective values can be absorbed in a scale factor choice below.

Effective Renormalization Scheme

By default, the CMW correction is applied in VINCIA. The choice for the eikonal term are similar to the final state ones:

mode  Vincia:CMWtypeII   (default = 2)
Choice of the eikonal term for initial-intial gluon emission on which the CMW rescaling is applied.
option 0 : No CMW rescaling.
option 1 : CMW rescaling with the eikonal term defined as 2 sAB / ( saj sjb ).
option 2 : CMW rescaling with the eikonal term defined as 2 sab / ( saj sjb ), which is larger compared to the term in option 1.

mode  Vincia:CMWtypeIF   (default = 2)
Choice of the eikonal term for initial-final gluon emission on which the CMW rescaling is applied.
option 0 : No CMW rescaling.
option 1 : CMW rescaling with the eikonal term defined as 2 sAK / ( saj sjk ).
option 2 : CMW rescaling with the eikonal term defined as 2 sak / ( saj sjk ), which can be both, larger or smaller, compared to the term in option 1.

Argument of the Running Coupling

When Vincia:alphaSorder is non-zero, the actual value is regulated by running to the scale kμR, at which the shower evaluates αs. The functional form of μR is given by the evolution variable and the scale factor kμ is given by

parm  Vincia:alphaSkMuI   (default = 0.75; minimum = 0.1; maximum = 10.0)
for gluon emission,

parm  Vincia:alphaSkMuSplitI   (default = 0.75; minimum = 0.1; maximum = 10.0)
for gluon splitting (quark in the initial state backwards evolving into a gluon),

parm  Vincia:alphaSkMuConv   (default = 0.75; minimum = 0.1; maximum = 10.0)
for gluon conversion (gluon in the initial state backwards evolving into a (anti)quark)

and Vincia:alphaSkMuSplitF for gluon splitting in the final state.

Colour Charge Factors

The normalization of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalization choice, 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 normalization of the qqbar → qgqbar antenna function is 2CF.)

parm  Vincia:QQemitII:chargeFactor   (default = 2.66666667)

parm  Vincia:GQemitII:chargeFactor   (default = 2.83333333)

parm  Vincia:GGemitII:chargeFactor   (default = 3.0)

parm  Vincia:QXSplitII:chargeFactor   (default = 1.0)

parm  Vincia:GXConvII:chargeFactor   (default = 2.66666667)

parm  Vincia:QQemitIF:chargeFactor   (default = 2.66666667)

parm  Vincia:GQemitIF:chargeFactor   (default = 2.83333333)

parm  Vincia:QGemitIF:chargeFactor   (default = 2.83333333)

parm  Vincia:GGemitIF:chargeFactor   (default = 3.0)

parm  Vincia:QXSplitIF:chargeFactor   (default = 1.0)

parm  Vincia:GXConvIF:chargeFactor   (default = 2.66666667)

parm  Vincia:XGSplitIF:chargeFactor   (default = 1.0)

Scales

For Vincia:hardJetsQCD and/or Vincia:hardJets being switched off, the first branching is by default limited to the factorization scale used for the hard process. This scale (in GeV) can be enhanced by the factor

parm  Vincia:QmaxEnhanceI   (default = 1.0; minimum = 1.0; maximum = 10.0)

Note however, that for non-unity values the generated Sudakov factor does not have the factorization scale as a starting scale, leading to leftover PDF ratios in the exclusive cross sections produced by the shower.

Evolution Variable for Initial State Radiation

Choice of functional form of the shower evolution variable (a.k.a. ordering variable) for initial state radiation (see illustrations below).

Gluon emissions in initial-initial antennae are ordered in transverse momentum. This evolution variable is the physical (lightcone) transverse momentum for massless partons:

Gluon emissions in initial-final antennae are ordered in transverse momentum. This evolution variable is defined as:

Splittings and conversion in initial-initial and initial-final antennae are by default ordered in the invariant mass of the gq, qq, or qqbar pair respectively. However there is the option to switch to the above transverse momentum ordering by switching Vincia:evolveAllInPT to on. Note that with transverse momentum ordering the ordering variable is no longer the inverse of the singularity associated with the branching process. Also the mass corrections are not applied correctly since they rely on ordering in invariant mass.

flag  Vincia:evolveAllInPT   (default = off)

Evolution Variable: Phase-Space Contours

The contours below illustrate the progression of the evolution variable over the dipole-antenna phase space for four fixed values, with sAB=mH^2 for the initial-initial case and xA=0.6 and sAK=25.2 GeV^2 for the initial-final case.

Type1 Type2

Mass Corrections

Important Note: All flavours will be treated with massless kinematics. However we apply certain corrections.

mode  Vincia:nFlavZeroMassI   (default = 3; minimum = 3; maximum = 5)
Controls the number of flavours that will be treated as strictly massless by VINCIA, ie with no mass corrections whatsoever. The remaining flavours, up to the b quark, will still be treated as having massless kinematics, but certain mass effects can be included, according to the switch described below. Top quarks will always be treated as with fully massive kinematics (and hence are so far precluded from appearing in PDFs).

mode  Vincia:massCorrectionLevelI   (default = 1)
Controls the level of mass corrections that will be applied to all but the lightest Vincia:nFlavZeroMassI flavours.
option 0 : No mass effects. Equivalent to using Vincia:nFlavZeroMassI=5.
option 1 : All heavy flavours in the initial state will undergo a conversion into a gluon when the evolution variable goes towards their mass threshold, using the vanishing PDFs. A quark mass is determined by using the maximum of the input value given below and the mass extracted from the PDFs (if possible).

The following mass thresholds are imposed on the evolution for quarks in the initial state:

parm  Vincia:ThresholdMB   (default = 4.8)
for bottom quark production.

parm  Vincia:ThresholdMC   (default = 1.5)
for charm quark production.

Kinematics and Recoils in the Initial-Initial case

The post-branching momenta are fixed by the following requirements:
1) The direction of the initial state partons is aligned with the beam axis (z-axis).
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.

Kinematics and Recoils in the Initial-Final case

The post-branching momenta are fixed by the following requirements:
1) The direction of the initial state parton is aligned with the beam axis (z-axis).
2) There are no recoils outside of the antenna. This allows a construction of the post-branching momenta in the centre-of-mass frame of the initial-final antenna.