Standard-Model Parameters

The strong coupling

The AlphaStrong class is used to provide a first- or second-order running alpha_strong (or, trivially, a zeroth-order fixed one). Formulae are the standard ones found in [Eid04]. The starting alpha_strong value is defined at the M_Z mass scale. The Lambda values are matched at the b and c flavour thresholds, such that alpha_strong is continuous, using an approximate iterative method for second-order matching. Since we allow alpha_strong to vary separately for hard processes, timelike showers, spacelike showers and multiple interactions, the relevant values are to be set in each of these classes.

The alpha_strong calculation is initialized by init( value, order), where value is the alpha_strong value at M_Z and order is the order of the running, 0, 1 or 2. Thereafter the value can be calculated by alphaS(scale), where scale is the Q^2 scale in GeV^2.

For applications inside shower programs, a second-order alpha_s value can be obtained as the product of the two functions alphaS1Ord(scale) and alphaS2OrdCorr(scale), where the first gives a simple first-order running (but with the second-order Lambda) and the second the correction factor, below unity, for the second-order terms. This allows a compact handling of evolution equations.

The electromagnetic coupling

Currently alpha_electromagnetic is treated in two rather different ways.

For parton-shower emission of photons, the StandardModel:alphaEMfix fix value is used, as relevant for low scales.

parameter name="StandardModel:alphaEMfix" default="0.00729735" min="0.0072973" max="0.0072974"
Fixed alpha_em value used in QED vertices.

For hard processes (also the ones generated in multiple interactions) the AlphaEM class is used, to generate a running alpha_em. Since the main application here is for hard scales, above m_b$, no attempt is made to provide an accurate description of the running at low scales. Instead, by default, the value StandardModel:alphaEMmZat the M_Z mass scale is input [Eid04]. It is then run from there to different scales, using the first-order expression for three lepton and five quark flavours. It is frozen at the low-energy value StandardModel:alphaEM0, should the running value exceed this. (With the default values, this happens for Q < 0.1 GeV.)

mode name="StandardModel:alphaEMorder" default="1" min="-1" max="1"
The running of alpha_em used in hard processes.
option value="1": first-order running, constrained to agree with StandardModel:alphaEMmZ at the Z^0 mass.
option value="0": zeroth order, i.e. alpha_em is kept fixed at its value at vanishing momentum transfer.
option value="-1": zeroth order, i.e. alpha_em is kept fixed, but at StandardModel:alphaEMmZ, i.e. its value at the Z^0 mass.

parameter name="StandardModel:alphaEM0" default="0.00729735" min="0.0072973" max="0.0072974"
The alpha_em value at vanishing momentum transfer.

parameter name="StandardModel:alphaEMmZ" default="0.00781751" min="0.00780" max="0.00783"
The alpha_em value at the m_Z mass scale.

Other electroweak couplings

parameter name="StandardModel:sin2thetaW" default="0.232" min="0.225" max="0.240"
The weak mixing angle.

The quark weak-mixing matrix

The absolute values of the Cabibbo-Kobayashi-Maskawa matrix elements are set by the following nine real values - currently the CP-violating phase is not taken into account in this parametrization. It is up to the user to pick a consistent unitary set of new values whenever changes are made.

parameter name="StandardModel:Vud" default="0.9745" min="0.973" max="0.976"
The V_ud CKM matrix element.

parameter name="StandardModel:Vus" default="0.224" min="0.218" max="0.230"
The V_us CKM matrix element.

parameter name="StandardModel:Vub" default="0.0037" min="0.002" max="0.006"
The V_ub CKM matrix element.

parameter name="StandardModel:Vcd" default="0.224" min="0.218" max="0.230"
The V_cd CKM matrix element.

parameter name="StandardModel:Vcs" default="0.9737" min="0.972" max="0.975"
The V_cs CKM matrix element.

parameter name="StandardModel:Vcb" default="0.0415" min="0.033" max="0.040"
The V_cb CKM matrix element.

parameter name="StandardModel:Vtd" default="0.0094" min="0.004" max="0.020"
The V_td CKM matrix element.

parameter name="StandardModel:Vts" default="0.040" min="0.030" max="0.050"
The V_ts CKM matrix element.

parameter name="StandardModel:Vtb" default="0.9991" min="0.998" max="0.9995"
The V_tb CKM matrix element.