117. Recent lattice QCD simulations – how good is QCD in the infrared?
Save This Post as PDFA very interesting paper on lattice QCD spectroscopy by the European collaboration (DESY, Marceille, Wuppertal, Julich) is published in the recent issue of Science.The authors were able to reproduce the mass scales of light hadrons which coincide with measured ones up to 1% precision (take a look at the Table 1 in the paper). It means that a) QCD does describe the low energy physics perfectly, i.e., we don’t need corrections to the QCD Lagrangian at energies lower than the scale of 
and b) lattice QCD has reached the stage of development when all systematic error effects are under control. No more, no less.
Here are some technical notes:
- Heroes of the day (or better say month?) were able to calculate the fermion determinant for u-, d- and s-quarks. Effects of charm, bottom and top quarks were included in the light quark masses and the coupling.
- They were able to track fields in the volume large enough in order for finite volume effects to be negligible. Namely, they had
. - They performed calculations for larger
using chiral perturbation theory and extrapolated to the physical point by Taylor expansion. - The lattice scale they used was of the order
fm (of course, they also performed simulations or other couplings in order to recover the continuum limit). Note that this lattice spacing is just 10 times larger than the characteristic size of a light hadron. Nevertheless, it is enough to derive masses with 1% deviation from the observed values.
So, my message to you, graduate students, is as follows 
Do not waste your precious time thinking how to modify QCD largrangian in the IR, instead, try to quantitatively understand QCD at low energies, or at least gluodynamics – it’s already a good starting point to get your Nobel Prize, since infrared dynamics of QCD is currently the most important problem in contemporary theoretical physics 
As people say, current mood – extremely enlightened.
Via Marco Frasca.
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Dear Dmitry,
Is your message that we now fully understand the theory behind infrared QCD? Are you saying that lattice QCD is a good-enough computational tool and theorists should not spend any further effort in understanding the physics of infrared QCD?
Best regards,
Ervin
Dear Ervin
No, what I want to say is that QCD is the theory correctly describing not only UV physics of strong interactions (k\gg \Lambda_QCD) but IR physics as well, i.e., it is not necessary to change the QCD Lagrangian at scales k\ll \Lambda_QCD, as lattice QCD simulations show.
However, theoretical understanding of IR behavior of QCD is essentially absent at this point.
Cheers,
Dmitry.