Fast fits for lattice QCD correlators

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 85, Issue 3, 2012, Pages

  Hornbostel, K ^a   Lepage, G P ^b   Davies, C T H ^c   Dowdall, R J ^c   Na, H ^d   Shigemitsu, J ^d  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b Newman Laboratory for Elementary Particle Physics   (United States)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

^d OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857702400     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.85.031504     Document Type: Article

References (6)

1. See G.P. Lepage, B. Clark, C.T.H. Davies, K. Hornbostel, P.B. Mackenzie, C. Morningstar, and H. Trottier, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 106-107, 12 (2002). The formula for χ pr 2 generalizes trivially if there are correlations between the priors for different parameters. Since the priors are new input data, leading to new terms in the χ 2 function, the number of degrees of freedom in the fit is the number of pieces of original Monte Carlo data plus the number of priors minus the number of fit parameters. Consequently the number of degrees of freedom always equals the number of pieces of Monte Carlo data since there is a prior for each fir parameter. This is true however many parameters are included, even when the number parameters exceeds the number of data points in the original Monte Carlo data. In practice ones adds terms until the fit results (means and standard deviations, χ 2...) converge. Adding further terms has no effect, but reassures us that systematic errors due to truncation of the fit function are negligible. 10.1016/S0920-5632(01)01638-3 (Pubitemid 36462251)
2. In practice useful priors are easily found. As examples, see the extended analyses in: C.T.H. Davies (HPQCD Collaboration), Phys. Rev. D PRVDAQ 1550-7998 78, 114507 (2008); 10.1103/PhysRevD.78.114507
3. C. McNeile (HPQCD Collaboration), Phys. Rev. D PRVDAQ 1550-7998 82, 034512 (2010). Incorrect priors are immediately evident since the χ 2 per degree of freedom (Fig., for example) does not converge to a reasonable value (of order 1 or less) as more fit parameters are included. This is apparent much more quickly using the new method presented here since convergence occurs with many fewer parameters. 10.1103/PhysRevD.82.034512
4. For a proof, see the appendix of C. McNeile, C.T.H. Davies, E. Follana, K. Hornbostel, and G.P. Lepage, Phys. Rev. D PRVDAQ 1550-7998 82, 034512 (2010). 10.1103/PhysRevD.82.034512
5. f = 4 sea quarks (HISQ discretization), and NRQCD dynamics for the b quark. The gluon configurations were provided by the MILC collaboration. For further details see: R.J. Dowdall, arXiv:1110.6887.
6. f = 3 light sea quarks (ASQTAD discretization), and HISQ relativistic dynamics for valence quarks. The gluon configurations were provided by the MILC collaboration. For further details see (set C 2): H. Na, C.T.H. Davies, E. Follana, J. Koponen, G.P. Lepage, and J. Shigemitsu, Phys. Rev. D PRVDAQ 1550-7998 84, 114505 (2011). 10.1103/PhysRevD.84.114505