Chapter 5

5.1 Compile-time settings

MCFM allows the user to choose between a number of schemes for defining the electroweak couplings. These choices are summarized in Table 5.1. The scheme is selected by modifying the value of ewscheme in src/User/mdata.f prior to compilation, which also contains the values of all input parameters (see also Table 5.2).

Table 5.1: Different options for the scheme used to fix the electroweak parameters of the Standard Model and the corresponding default input values. MW and MZ are taken from ref. [50].
Parameter Name Input Value
Output Value determined by ewscheme

(_inp) -1 0 1 2
GF Gf 1.16639×105 input calculated input input
α(MZ) aemmz 1/128.89 input input calculated input
sin 2𝜃w xw 0.2223 calculated input calculated input
MW wmass 80.385 GeV input calculated input calculated
MZ zmass 91.1876 GeV input input input calculated
mt mt input.ini calculated input input input

The default scheme corresponds to ewscheme=+1. As described below, this corresponds to a scheme in which the top quark mass is an input parameter so that it is more suitable for many processes now included in the program.

The choice of (ewscheme=-1) enforces the use of an effective field theory approach, which is valid for scales below the top mass. In this approach there are 4 independent parameters (which we choose to be GF, α(MZ), MW and MZ). For further details, see Georgi [51].

For all the other schemes (ewscheme=0,1,2) the top mass is simply an additional input parameter and there are 3 other independent parameters from the remaining 5. The variable ewscheme then performs exactly the same role as idef in MadEvent [52]. ewscheme=0 is the old MadEvent default and ewscheme=1 is the new MadEvent default, which is also the same as that used in Alpgen [53] and LUSIFER [54]. For processes in which the top quark is directly produced it is preferable to use the schemes (ewscheme=0,1,2), since in these schemes one can adjust the top mass to its physical value (in the input file input.ini). Schemes where the W and Z masses are fixed to their measured values are the most appropriate for W and Z production processes.

Table 5.2: Default values for the remaining parameters in MCFM. ΓW and ΓZ from ref. [50].
Parameter Fortran name Default value
m τ mtau 1.777 GeV
mτ2 mtausq 3.1577 GeV2
Γτ tauwidth 2.269×1012 GeV
ΓW wwidth 2.093 GeV
ΓZ zwidth 2.4952 GeV
V ud Vud 0.975
V us Vus 0.222
V ub Vub 0.
V cd Vcd 0.222
V cs Vcs 0.975
V cb Vcb 0.

5.2 Parton distributions

The value of αs(MZ) is not adjustable; it is hardwired with the parton distribution. In addition, the parton distribution also specifies the number of loops that should be used in the running of αs. As default the code uses the LHAPDF library for PDF evaluation; a native implementation of some (mostly older) PDF sets is also retained.

5.3 Electroweak corrections

As of version 8.1, MCFM allows the calculation of weak corrections to a selection of processes: 31 (neutral-current DY), 157 (top-pair production) and 190 (di-jet production). This is controlled by the flag ewcorr in the input file. A complete description of the calculations is provided in Ref. [35].

By setting ewcorr to sudakov, the program performs a calculation of the leading weak corrections to these processes using a Sudakov approximation that is appropriate at high energies. The calculation of the weak corrections using the exact form of the one-loop amplitudes is obtained by using the flag exact. A comparison between the two approaches, together with discussions of the validity of the Sudakov approximation, may be found in Ref. [35].

For the case of top-pair and di-jet production, the weak one-loop corrections contain infrared divergences that must be cancelled against corresponding real radiation contributions (in much the same manner as a regular NLO QCD calculation). For this reason the screen output will contain two sets of iterations corresponding to the virtual and real contributions.

For all processes, performing the calculation of weak corrections enables a special mode of phase-space integration that is designed to better-sample events produced at high-energies. For this reason the VEGAS output that appears on the screen does not correspond to a physical cross-section – and a corresponding warning message to this effect will be displayed. In many cases the quantity of most interest is the relative correction to the leading order result (δwk) given by,

δwk = dσwkNLO dσLO dσLO . (5.1)

It is straightforward to compute this quantity for a distribution by editing the appropriate nplotter routine. This is achieved by filling a histogram with the weight corresponding to the LO result, another with the weight for the NLO weak result and then an additional placeholder histogram that contains the special string ’+RELEW+’. Examples of the syntax and correct calling sequence can be seen in the code. (The appropriate nplotter routine is displayed on the process web-page, reachable from the tables in Section 4.)