g2tools

This module contains a small number of tools useful for analyzing contributions to the muon's magnetic moment from (lattice) QCD vacuum polarization. The functions or classes include:

moments(G)

Compute moments of jj correlator G.

mom2taylor(mom)

Convert moments mom into Taylor coefficients for q²-expansion.

taylor2mom(tayl)

Convert Taylor expansion coefficients tayl into moments.

vacpol(mom)

Create a Pade approximant for the subtracted vacuum polarization (PI-hat) from the jj correlator whose moments (or Taylor coefficients) are in mom.

fourier_vacpol(G)

Create subtracted vacuum polarization (PI-hat) by Fourier transforming jj correlator G(t).

a_mu(pihat, Q)

Compute the contribution to the muon's g-2 anomaly from function pihat (usually built by vacpol).

R2G(E, R)

Compute the Euclidean G(t) corresponding to data for Re+e-.

R2a_mu(E, R)

Compute the leading-order contribution to the muon's g-2 anomaly corresponding to data for Re+e-.

TanhWin(t0, t1, dt)

Create a filter for applying a t-window in monents(...) or fourier_vacpol(...).

pade_gvar(f, m, n)

General-purpose code for determining Pade approximants to a power series whose coefficients are GVars (ie, Gaussian random variables, for error propagation).

pade_svd(f, m, n)

General-purpose code for determining Pade approximants for a power series whose coefficients are floats. Uses svd regularization to stabilize results when the input data are noisy.

Information on how to install the module is in the file INSTALLATION.

To test the module try make tests.

Documentation is in the doc directory: open doc/html/index.html or look online at <https://g2tools.readthedocs.io>.

The examples directory has a complete example, showing how to go from Monte Carlo data for a jj correlator to a contribution to the muon's magnetic moment anomaly a_µ. See also the introduction in the documentation.

The general technique that underlies this module is described in Chakraborty et al, Phys.Rev. D89 (2014) no.11, 114501. Google arXiv:1403.1778 to find a preprint on the web.

Created by G. Peter Lepage (Cornell University) on on 2014-09-13.

Copyright (c) 20014-22 G. Peter Lepage.