Couplings and Masses

  1. The Strong Coupling
  2. Quark and Lepton Masses

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 amount of QCD radiation in the shower is determined by

parm  Vincia:alphaSvalue   (default = 0.122; minimum = 0.06; maximum = 0.25)
The value of αs at the scale mZ, in the MSbar scheme. The default is chosen to obtain a reasonable agreement with LEP event shapes for default shower settings.

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.

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).

Effective Renormalization 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.

By default, the CMW correction is applied in VINCIA. If desired, it can be switched off by using the following switch:

flag  Vincia:alphaScmw   (default = on)

option on : CMW. This option is recommended for the most accurate shower resummation.
option off : MSbar.

Note: The CMW arguments were derived using two-loop running (the default in VINCIA).
Note 2: When this correction is switched on, the rescaling of the coupling away from its MSbar value is properly taken into account by VINCIA's one-loop matching. When switched off, the one-loop corrections generally become larger, to compensate for the missing universal factor.
Note 3: 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 4: tunes using this option need lower values of alpha_strong(m_Z^2) than tunes that do not.

Argument of 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 Vincia:alphaSmode and the scale factor kμ is given by Vincia:alphaSkMu.

The functional form of μR is given by

mode  Vincia:alphaSmode   (default = 1; minimum = 0; maximum = 1)

option 0 : The invariant mass of the mother antenna, m(ijk).
option 1 : For gluon emissions: transverse momentum, defined as in ARIADNE, pT = m(ij)*m(jk)/m(ijk). For gluon splittings, g→qq, the qqbar invariant mass, m(qqbar).

The scale factor kμ is given by

parm  Vincia:alphaSkMu   (default = 1.0; minimum = 0.1; maximum = 10.0)
If different from unity, αs is evaluated at the scale defined by Vincia:alphaSmode times this scale factor, i.e., it gives the value of kμ in the argument to alphaS(kμR).

Infrared Freezeout Scale

parm  Vincia:alphaSmuFreeze   (default = 0.5; minimum = 0.1; maximum = 10.0)
In the far infrared, the behaviour of the running coupling is regulated by a shift in the effective renormalization scale, to μeff 2 = μfreeze2 + (kμR)2.

Max Coupling

parm  Vincia:alphaSmax   (default = 1.0; minimum = 0.1; maximum = 10.0)
Largest allowed numerical value for alphaS.

Quark and Lepton Masses

The values of the masses are in all cases taken from PYTHIA's particle database, minimizing the risk of conflict. The parameters here only control whether the corresponding particles are treated as massive or massless by VINCIA.

For relativistic particles, helicity is a good quantum number and massless matrix-element corrections can be used. The following parameter determines from which speed VINCIA treats a particle as being relativistic.

parm  Vincia:relativisticSpeed   (default = 0.9; minimum = 0.0; maximum = 1.0)

Note that the velocity is a frame-dependent quantity. VINCIA checks the above threshold in several relevant frames, and only treats a particle as ultra-relativistic if it passes the threshold in all the frames.

The first frame is the CM of the parton system, relevant for example for matrix-element corrections.

VINCIA then also checks the velocity of the particle in the CM of all two-particle subsystems in the event. This ensures, for example, that a quasi-collinear emission from a massive quark will be treated with mass corrections, since the velocity of the quark in the CM frame of the quark and the emitted quasi-collinear gluon will be low.

Colour non-connected two-particle systems are also included. This ensures that, e.g., two fast-moving massive particles traveling in approximately the same direction will be treated as massive, since they will have low velocities in their common CM frame.

If all checks are passed, the particle can be assigned a helicity and the configuration is allowed to make use of (helicity-dependent) massless matrix-element corrections. Otherwise the particle is treated as unpolarized, and massive matrix-element corrections are used, to the extent available in the program.

Note: NLO corrections have so far only been implemented for massless particles, so for the time being a choice must be made between treating a particle as massless, with NLO corrections, or treating it as massive, without NLO corrections, see the section on Matching for a list of processes for which NLO corrections have been implemented.

Note 2: High-mass new-physics particles will normally be treated as massive, as they will generally not satisfy the relativistic-velocity criterion.

Note 3: For particles that are treated as massive, the mass corrections to the antenna functions are discussed separately, in the section on Antenna Functions.

For systems whose particles are all deemed to be in the ultra-relativistic domain (according to the velocity criterion above), a temporary set of massless momenta are created by rescaling all massive 3-momenta up along their respective directions of motion, thus creating a massless intermediate configuration with a reduced CM energy. All momenta and energies are then rescaled up in order to restore the original CM energy, and finally the system is boosted back to the original system frame, producing a set of massless momenta that are as near equivalent to the original massive ones as possible. This set of rescaled and boosted massless momenta will then be used for purposes of assigning helicities and computing matrix-element corrections.

After a branching has been accepted, when constructing the post-branching event kinematics, all particles (both ones treated as massless and ones treated as massive) are put on their proper mass shell, with their true masses. The massless momenta constructed above are only used to assign helicities and compute corrections, after which they are discarded. This ensures that no unphysical configurations are generated, and that phase-space suppression is acting smoothly over all of phase space.