VINCIA SM Parameters

  1. The Strong Coupling

Currently, the only SM parameter that can be configured in VINCIA is the definition of the strong coupling constant, specified by providing its reference value (interpreted as given at the Z pole in the MSbar scheme) and running properties (loop order, behaviour at top threshold, and any low-scale regularisation/dampening). All other parameters are taken from the PYTHIA Couplings database.

Note that VINCIA only uses one global value for the definition of the strong coupling constant. The effective couplings used in shower branchings (renormalisation scheme and scale) are governed by separate parameters which are specified under initial- and final-state showers respectively.

The Strong Coupling

VINCIA implements its own instance of PYTHIA's AlphaStrong class for the strong coupling. You can find more documentation of the class in the section on Standard-Model Parameters in the PYTHIA documentation. Here, we list the specific parameters and switches governing its use in VINCIA.

Reference Value

The free parameter of the strong coupling constant is specified by

parm  Vincia:alphaSvalue   (default = 0.118; minimum = 0.06; maximum = 2.0)
The value of αs at the scale mZ, in the MSbar scheme. The default value is chosen to be in agreement with the current world average. The effective value used for showers may be further affected by translation to the CMW scheme (below) and by renormalisation-scale prefactors given for FSR and ISR showers separately.

Running Order

mode  Vincia:alphaSorder   (default = 2; minimum = 0; maximum = 2)
Order at which αs runs,
option 0 : zeroth order, i.e. αs is kept fixed.
option 1 : first order, i.e., one-loop running.
option 2 : second order, i.e., two-loop running.

Effective Renormalisation Scheme

Resummation arguments [Cat91] indicate that a set of universal QCD corrections can be absorbed in coherent parton showers by applying the so-called CMW rescaling of the MSbar value of Lambda_QCD, defined by

αs(CMW) = αs(MSbar) * (1 + K * αs(MSbar) / 2π)
with K = CA * (67/18 - π2/6) - 5/9nf. The translation amounts to an NF-dependent rescaling of Lambda_QCD, relative to its MSbar value, by a factor 1.661 for NF=3, 1.618 for NF=4, 1.569 for NF=5, and 1.513 for NF=6. Although the original argument strictly concerned only the eikonal for soft-gluon emissions, the current version of VINCIA only offers the option of switching the rescaling of Lambda_QCD on or off, applied to all shower branchings.

flag  Vincia:useCMW   (default = true)
If set to on, the alphaS value used for shower branchings will be translated from the MSbar value to the CMW ("MC") scheme. If set to off, the MSbar value will be used.

Note 1: If using VINCIA with an externally defined matching scheme, be aware that the CMW rescaling may need be taken into account in the context of matrix-element matching. Note also that this option has only been made available for timelike and spacelike showers, not for hard processes.
Note 2: Tunes using this option need roughly 10% lower values of alphas(mZ) than tunes that do not.

Flavour Thresholds

For both one- and two-loop running, the AlphaStrong class automatically switches from 3-, to 4-, and then to 5-flavour running as one passes the s, c, and b thresholds, respectively, with matching equations imposed at each flavour treshold to ensure continuous values. By default, a change to 6-flavour running is also included above the t threshold, though this can be disabled using the following parameter:

mode  Vincia:alphaSnfmax   (default = 6; minimum = 5; maximum = 6)

option 5 : Use 5-flavour running for all scales above the b flavour threshold (old default).
option 6 : Use 6-flavour running above the t threshold (new default).

Infrared Freezeout Scale

parm  Vincia:alphaSmuFreeze   (default = 0.5; minimum = 0.0; maximum = 10.0)
The behaviour of the running coupling in the far infrared is regulated by a shift in the effective renormalisation scale, to μeff 2 = μfreeze2 + μR2.

Max Coupling

parm  Vincia:alphaSmax   (default = 1.5; minimum = 0.1; maximum = 10.0)
Largest allowed numerical value for alphaS. I.e., the running is forced to plateau at this value.