# Subproject A4: Chirally invariant and twisted mass formulations of QCD on the lattice

Project Leader:

Prof. Dr.sc.nat. Michael Müller-Preußker, Department of Physics,
Humboldt-University Berlin

Dr.rer.nat.habil. Karl Jansen, John-von-Neumann-Institute of Computing, DESY Zeuthen)

**Summary:**

In this project two kind of lattice fermions, maximally twisted mass quarks and chiral invariant overlap fermions will be considered.

When including in the maximally twisted mass formulation of lattice QCD
a mass-degenerate up and down quark-doublet (*N*_{f}=2), the lattice theory
has been proved to lead to a very good O(a^{2}) lattice spacing scaling
such that precise values of many physical observables can be obtained in the
continuum limit.
We want to continue this research direction by including now also the strange
and the charm quark as dynamical degrees of freedom in the twisted mass
setup (*N*_{f}=2+1+1). This is a novel approach that will allow for the first
time to realistically explore the heavy quark sector and in particular
the charm sector.

We plan to essentially repeat the very successful research programme of the
*N*_{f}=2 studies with *N*_{f}=2+1+1 flavours. A special emphasis will be the approach
to the physical point where the pion mass assumes its experimentally measured
value. To this end, a detailed and precise map of the quark mass dependence
of many physical observables will be performed.
We emphasize that in this project the methodological and conceptual questions
will be in the focus of our research. This concerns in particular the study of
cut-off and finite volume effects as well as the description of the quark mass
behaviour of physical quantities towards the physical point.

As another research direction, we aim at investigations of the theory at non-vanishing temperature. We will make use of the improved continuum limit behaviour of maximally twisted mass fermions in order to reach physical results in a controlled way. Employing the knowledge of the phase diagram obtained by us, we are going to determine the critical behaviour and to explore the equation of state.

Finally, for quantities where chiral symmetry is expected to play an important
role,
such as *B*_{K},*K* → π π,ε'/ε, or questions related to topology,
we want to use chirally invariant overlap fermions as valence quarks on a
twisted mass sea.

The larger subproject (for *T*=0) is embedded into the large European Twisted
Mass
Collaboration (ETMC) with partners from 16 institutes from 9 different European
countries, whereas the subproject at*T*>0 is related to a collaboration
of HU Berlin with University of Bonn (C. Urbach), University of
Frankfurt and INFN Frascati (tmfT Collaboration).

Last Change: 15^{th} June 2011