### Lattice Calculations

Effective field theories (EFTs) are based on a factorization of scales. In several circumstances, and most of them in QCD, the lowest energy scale considered is non-perturbative and needs a non-perturbative calculation. Then EFTs need non-perturbative input for many quantities in the form of correlators or matrix elements that can be computed only with non-perturbative tools like lattice calculations. At T30f we have established a lattice group for the dedicated calculation of such quantities inside the EFT.

**Lattice QCD** is a numerical method for non-perturbative computations of correlators and matrix elements for QCD.
The lattice method reduces the uncountably infinite number of degrees of freedom of a field theory to a finite number of field variables on a space-time grid.
The path integral can be evaluated with a finite number of field configurations that are generated with importance sampling methods and statistical errors are fully controllable.
For better control in the removal of systematical errors due to the use of a finite space-time grid, **lattice QCD requires EFTs** that predict the form of finite size corrections.

**Applications of lattice QCD** include not only studies of **hadronic physics** at zero temperature, but also the **QGP phase** of **QCD at finite T**.
In recent years, algorithmic advances and better computational facilities have allowed simulations at or close to the physical point and allow for an impact of lattice QCD beyond QCD itself.

**Recent highlights of lattice QCD** include **ab-initio QCD+QED** calculations of the proton-neutron mass splitting, which would not be feasible without the **control of finite size corrections provided by EFTs**.
Precision calculations of QCD form factors have now reached an accuracy to provide **strong constraints on CKM matrix elements** that are competitive with experimental measurements. Our group member
Matrix elements that are required for extension of physics beyond the Standard Model are calculable using lattice QCD.
Synergy of lattice QCD and pNRQCD offers a new method of accurate measurements of the strong coupling constant **from the static QQbar potential**.
Simulations of QCD at finite temperature led to the determination of the **chiral transition temperature** and allows to study QGP.

We study **QCD at finite T**, where light quarks and gluons exist as a thermal medium called quark-gluon-plasma (QGP).
Our research is focused on **heavy quarkonium**, which presents an ideal laboratory for testing the interplay between perturbative and non-perturbative QCD within a controlled environment.
We currently study the free energy and quarkonium spectral functions in terms of static quark correlators.
Our program for the near future includes studies of the **Equation of State** for high temperatures.

Our **state-of-the-art calculations** employ highly improved staggered quarks (**HISQ**), which have greatly reduced cutoff effects, and have sea quarks masses close to the physical point.
We are running programs built with the well-established, publicly available
**MILC code** and
**SciDAC libraries**.
The simulations are running on local computing facilities at
>**LRZ (Leibniz Rechenzentrum)**, which include
**C2PAP**, the dedicated HPC system of the Universe Cluster of Excellence, and also
**Supermuc**, the flagship machine of LRZ.

#### People

*Nora Brambilla, Antonio Vairo, Andreas Kronfeld (Fermilab, TUM-IAS), Peter Petreczky (Brookhaven), Alexei Bazavov (Iowa), Javad Komijani, Matthias Berwein, Johannes Weber.*

#### Some related publications:

**Determination of α**Phys. Rev. D 90 (2014), 074038, arXiv:1407.8437, Inspire

_{s}from the QCD static energy: An updateA.~Bazavov, A.S. Kronfeld

*et al.*[Fermilab Lattice and MILC Collaborations],

**Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks**Phys. Rev. D 90 (2014), 074509, arXiv:1407.3772, Inspire