Plots Installation Usage References

mr:Matching and Running is a C++ package for NNLO Standard Model stability analysis. It includes full two-loop electroweak threshold corrections connecting input in terms of pole masses with running couplings and three-loop renormalization group equations with additional higher order QCD corrections for evolution of running couplings up to a needed scale.
For package overview see:

mr: a C++ library for the matching and running of the Standard Model parameters By Bernd A. Kniehl, Andrey F. Pikelner, Oleg L. Veretin. Comput.Phys.Commun. 206 (2016) 84-96.

Sample plots

Gauge couplings unification region
Gauge couplings unification region.
Standard Model couplings running up to a Planck scale.
Standard Model couplings running up to a Planck scale.
Phase diagram in terms of top and Higgs mass.
Phase plot in terms of top and Higgs mass.

For example application see:

Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision. By A.V. Bednyakov, B.A. Kniehl, A.F. Pikelner, O.L. Veretin. Phys.Rev.Lett. 115 (2015) 20, 201802.


Latest release is available from github release page

From github repository using git:

$ git clone
$ cd mr
$ autoreconf -i
$ ./configure
$ make && make install

Or downloading tarball and extracting:

$ curl -OL
$ tar zxf mr-1.2.1.tar.gz
$ cd mr-1.2.1
$ ./configure
$ make && make install


Main use case is the following chain of procedure calls. At first step using input in terms of pole masses and Fermi constant obtain running couplings at specified matching scale.

// Input in terms of pole masses
OSinput oi(pdg2014::Mb, pdg2014::MW, pdg2014::MZ, pdg2014::MH, pdg2014::Mt);
// Running QCD coupling as(Mt) from as(MZ)
AlphaS as(oi);
// Set of all running parameters at scale Mt
P2MS pMSmt(oi,pdg2014::Gf, as(oi.Mt()), oi.Mt(), order::all);
// Running Yukawa top at top mass
std::cout << sqrt(*4*Pi << std::endl

At the next step we perform evolution from matching scale up to scale of interest. We use 3-loop RGE for all SM couplings except Yukawa tau. Two last parameters specify orders for running Higgs mass parameter and vacuum expectation value.

Couplings<3,3,3,3,3,0,3,3,0>  av(pMSmt);
//  vector of  couplings  at scale  mu=10^19
SMCouplings  v  =  avP2MS(pow(10,2*19));
std::cout  << sqrt(v[couplings::yt])*4.*Pi << std::endl;


SM running

Threshold corrections

Additional tools

Two-loop massive self-energy integrals evaluated numerically using TSIL library:

Effective potential up to three loops in SM in gaugless limit:

Four-loop QCD corrections to strong and Yukawa couplings running:


Andrey Pikelner, pikelner[at]


GPLv3 License