Friday, September 04, 2015

Fundamental Parameters from Lattice QCD, Day Five

The first speaker today was Martin Lüscher, who spoke about revisiting numerical stochastic perturbation theory. The idea behind numerical stochastic perturbation theory is to perform a simulation of a quantum field theory using the Langevin algorithm and to perturbatively expand the fields, which leads to a tower of coupled evolution equations, where only the lowest-order one depends explicitly on the noise, whereas the higher-order ones describe the evolution of the higher-order coefficients as a function of the lower-order ones. In Numerical Stochastic Perturbation Theory (NSPT), the resulting equations are integrated numerically (up to some, possibly rather high, finite order in the coupling), and the average over noises is replaced by a time average. The problems with this approach are that the autocorrelation time diverges as the inverse square of the lattice spacing, and that the extrapolation in the Langevin time step size is difficult to control well. An alternative approach is given by Instantaneous Stochastic Perturbation Theory (ISPT), in which the Langevin time evolution is replaced by the introduction of Gaussian noise sources at the vertices of tree diagrams describing the construction of the perturbative coefficients of the lattice fields. Since there is no free lunch, this approach suffers from power-law divergent statistical errors in the continuum limit, which arise from the way in which power-law divergences that cancel in the mean are shifted around between different orders when computing variances. This does not happen in the Langevin-based approach, because the Langevin theory is renormalizable.

The second speaker of the morning was Siegfried Bethke of the Particle Data Group, who allowed us a glimpse at the (still preliminary) world average of αs for 2015. In 2013, there were five classes of αs determinations: from lattice QCD, τ decays, deep inelastic scattering, e+e- colliders, and global Z pole fits. Except for the lattice determinations (and the Z pole fits, where there was only one number), these were each preaveraged using the range method -- i.e. taking the mean of the highest and lowest central value as average, and assigning it an ncertainty of half the difference between them. The lattice results were averaged using a χ2 weighted average. The total average (again a weighted average) was dominated by the lattice results, which in turn were dominated by the latest HPQCD result. For 2015, there have been a number of updates to most of the classes, and there is now a new class of αs determinations from the LHC (of which there is currently only one published, which lies rather low compared to other determinations, and is likely a downward fluctuation). In most cases, the new determinations have not or hardly changed the values and errors of their class. The most significant change is in the field of lattice determinations, where the PDG will change its policy and will no longer perform its own preaverages, taking instead the FLAG average as the lattice result. As a result, the error on the PDG value will increase; its value will also shift down a little, mostly due to the new LHC value.

The afternoon discussion centered on αs. Roger Horsley gave an overview of the methods used to determine it on the lattice (ghost vertices, the Schrödinger functional, the static energy at short distances, current-current correlators, and small Wilson loops) and reviewed the criteria used by FLAG to assess the quality of a given determination, as well as the averaging procedure used (which uses a more conservative error than what a weighted average would give). In the discussion, the points were raised that in order to reliably increase the precision to the sub-percent level and beyond will likely require not only addressing the scale setting uncertainties (which is reflected in the different values for r0 obtained by different collaboration and will affect the running of αs), but also the inclusion of QED effects.

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