Initial-State Antenna Showers

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

Argument of the Running Coupling

When Vincia:alphaSorder is non-zero, the actual value of alphaS used for shower branchings is governed by the choice of scheme (MSbar or CMW, see the section on SM Couplings and then 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 = 0.72; minimum = 0.1; maximum = 10.0)
for gluon emission,

parm  Vincia:alphaSkMuSplitI   (default = 0.72; minimum = 0.1; maximum = 10.0)
for gluon splitting (quark in the initial state backwards evolving into a gluon),

parm  Vincia:alphaSkMuConv   (default = 0.72; 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 normalisation of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalisation 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 normalisation of the qqbar → qgqbar antenna function is 2CF.)

For theory tests, individual antenna functions can be switched off by setting the corresponding colour-charge factor to zero.

parm  Vincia:QQemitII:chargeFactor   (default = 2.66666667)
Emission of a final-state gluon from an initial-state qqbar pair.

parm  Vincia:GQemitII:chargeFactor   (default = 2.83333333)
Emission of a final-state gluon from an initial-state qg (or gqbar) pair.

parm  Vincia:GGemitII:chargeFactor   (default = 3.0)
Emission of a final-state gluon from an initial-state gg pair.

parm  Vincia:QXSplitII:chargeFactor   (default = 1.0)
Quark in the initial state backwards evolvint into a gluon and emitting an antiquark in the final state

parm  Vincia:GXConvII:chargeFactor   (default = 2.66666667)
Gluon in the initial state backwards evolving into a quark and emitting a quark in the final state (gluon conversion)

parm  Vincia:QQemitIF:chargeFactor   (default = 2.66666667)
Gluon emission of an initial-final qq pair

parm  Vincia:GQemitIF:chargeFactor   (default = 2.83333333)
Gluon emission off an initial-final gq pair

parm  Vincia:QGemitIF:chargeFactor   (default = 2.83333333)
Gluon emission of an initial-final qg pair

parm  Vincia:GGemitIF:chargeFactor   (default = 3.0)
Gluon emission of an initial-final gg pair

parm  Vincia:QXSplitIF:chargeFactor   (default = 1.0)
Quark in the initial state evolving backwards into a gluon and emitting an antiquark in the final state

parm  Vincia:GXConvIF:chargeFactor   (default = 2.66666667)
Gluon in the initial state backwards evolving into a quark and emitting a quark into the final state (gluon conversion)

parm  Vincia:XGSplitIF:chargeFactor   (default = 1.0)
Gluon splitting in the final state

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.