#### 09 - 16 - 2013

Paper "Nonperturbative renormalization for improved staggered bilinears" published in Phys. Rev. D. Also available on the arXiv.

#### 07 - 19 - 2012

Talk by A. Lytle at 2012 Lattice Conference, containing updated results for bilinear Z-factors and comparison with 1-loop perturbation theory. Results are now for the entire momentum range and on coarse and fine MILC lattices. Also, first results using S-MOM scheme for scalar bilinears.

#### 03 - 9 - 2012

Proposal submitted for 2.5 M Jpsi-hours on the clusters at FNAL. (Granted 2.34 M Jpsi-hours.) Contains new results for (a) momentum dependence of ratios of Z-factors; (b) a first comparison of these ratios on fine and coarse lattices; and (c) the first results for the scalar and pseudoscalar bilinears on the coarse lattices with non-exceptional momenta.

#### 07 - 16 - 2011

Talk by S. Sharpe at 2011 Lattice Conference, containing updated results for bilinear Z-factors and comparison with 1-loop perturbation theory.

#### 05 - 7 - 2011

Talk at 2011 All Hands meeting. Second half concerns this project.

#### 03 - 11 - 2011

Proposal submitted for 2.5 M Jpsi-hours on the clusters at FNAL. Contains preliminary results on matching factors for all hypercube bilinears for asqtad and HYP valence quarks. Proposal awarded 2.42 M Jpsi-equivalent core-hrs.

#### 09 - 01 - 2010

Andrew Lytle's thesis, which gives detailed background to the present calculations, and many results, including a result for Z_m from coarse and fine lattices.

#### 05 - 01 - 2010

Presentation on proposal at USQCD All Hands meeting, April 16th 2010.

#### 03 - 01 - 2010

Renewal proposal submitted.

#### 12 - 31 - 2009

We have now included vector bilinear vertices, both the hypercube version (which is the conserved current for naive or HYP-smeared staggered fermions), and the asqtad conserved current (which gives a second method of calculating Z_q).

#### 09 - 01 - 2009

Preliminary analysis on coarse lattices completed, and presented at Lattice 2009. For write-up, see here. We find that the strange-quark mass in the MS-bar scheme at 2 GeV is 106(6) MeV, to be compared to the 84(5) MeV obtained using 2-loop matching. These results are not directly comparable, since they contain different $O(a^2\Lambda_{\rm QCD}^)$ corrections. To study this, we need at least one further lattice spacing.

#### 03 - 20 - 2009

Status report is contained in our renewal proposal submitted to USQCD. Running is now focusing on fine lattices, in order to compare $Z_m$ with that obtained on the coarse lattices.

#### 10 - 20 - 2008

Tuning runs on coarse MILC lattices underway, using asqtad valence quarks, and calculating Zq, ZS and ZP for a variety of momenta and quark masses.

## Proposals Summary

• 2012-13 Proposal submitted (March 9, 2012) to the US lattice QCD Scientific Program Committee, asking for time on USQCD clusters at FNAL.
Abstract
This is a class B proposal, asking for continuation of time on the clusters to study the systematic errors of non-perturbative renormalization (NPR) with improved staggered fermions.

The project has two main focuses. First, the calculation of Z-factors for bilinear operators of all tastes and spins so as to allow a detailed study of the chiral and continuum extrapolations and the comparison with perturbation theory. In the 2010-11 allocation year, we calculated such Z-factors with valence asqtad and HYP-smeared fermions on the coarse MILC lattices, and during the present (2011-12) allocation year we have been extending these results to the fine lattices. Our allocation is sufficient for somewhat less than 8 configurations per mass, but we now think that 16 configurations per mass is preferable. Thus part of our request for the upcoming year is to allow this more than doubling of statistics.

The second focus is to implement state-of-the-art NPR techniques, in particular the use of non-exceptional momenta and twisted boundary conditions. Our main aim here is a calculation of $Z_m$. We have preliminary results using non-exceptional momenta, and find that these lead to the expected improvement in the chiral extrapolation and reduction in long-distance non-perturbative contributions. The second part of our request is for the continuation of this study.

We use the Chroma package, augmented by the addition of momentum sources and general bilinear operators. We are asking for time on clusters, and prefer to continue running at Fermilab.

We are requesting 2,500,000 Jpsi core-hours on clusters (165,000 of which are for storage).
• 2011-12 Proposal submitted (March 11, 2011) to the US lattice QCD Scientific Program Committee, asking for time on USQCD clusters at FNAL.
Abstract
This is a class B proposal, asking for continuation of time on the clusters to calculate matching (Z-'') factors using non-perturbative renormalization (NPR) for bilinear and four-fermion operators with staggered quarks.

By the end of the present (2010-11) allocation year, we will have completed the calculation of Z-factors for bilinear operators of all tastes and spins using valence asqtad and HYP-smeared fermions on the coarse MILC lattices, with some preliminary results on the fine lattices. This is the first such detailed study using improved staggered fermions. We have compared these to one-loop perturbative predictions, and find that ratios of Z-factors (which have no anomalous dimensions) for vector, axial-vector and tensor spins agree at the 1% level, while the agreement is 5-10% for the Z-factors themselves.

We propose here to extend this calculation in several ways. First, to complete the calculations on the fine MILC lattices. Second, to implement twisted boundary conditions for the valence quarks so as to allow continuous tuning of momenta. Third, aided by the use of twisted boundary conditions, to consider bilinears with non-exceptional momenta (thus reducing non-perturbative contamination). Our final goal is then to apply these improved methods to the calculation of four-fermion Z-factors with HYP-smeared staggered valence quarks, results which are needed to reduce and control the systematic error in the calculation of B_K and other kaon matrix elements.

We use the Chroma package, augmented by the addition of momentum sources and general bilinear operators. We are asking for time on clusters, and prefer to continue running at Fermilab.

We are requesting 2,500,000 Jpsi-equivalent node-hours on clusters (135,000 of which are for storage).
• 2010-11 Proposal submitted (March 1, 2010) to the US lattice QCD Scientific Program Committee, asking for time on USQCD clusters at FNAL. Proposal was granted 1.3M Jpsi-equivalent coree-hours.
Abstract
This is a class B proposal, asking for continuation of time on the clusters to calculate matching (Z'') factors using non-perturbative renormalization (NPR) for the quark mass, bilinear and four-fermion operators with staggered quarks.

During the present (2009-10) allocation year, we will have completed the calculation of the propagators and vertices necessary for determining the mass renormalization for asqtad quarks (as well as those for related bilinears) on coarse and fine MILC lattices. We propose here to extend this calculation to HYP-smeared staggered valence quarks, for both the bilinears and four-fermion operators. These matching factors are needed to reduce and control the systematic error in the calculation of B_K and other kaon matrix elements using HYP-fermions. Matching is the dominant source of error in this calculation.

We use the Chroma package, augmented by the addition of momentum sources. We are asking for time on clusters, and prefer to continue running at Fermilab.

We are requesting 1,640,000 Jpsi-equivalent node-hours on the clusters (140,000 of which are for storage).
• 2009-10 Proposal submitted to the US lattice QCD Scientific Program Committee, asking for time on USQCD clusters at FNAL. Proposal was granted 500,000 6n-equivalent node-hours.
Abstract
This is a class B proposal, asking for continuation of time on the clusters to calculate matching (Z'') factors using non-perturbative renormalization (NPR) for the quark mass, bilinear and four-fermion operators with staggered quarks.

Due to a variety of factors, we have made less progress during the present (2008-9) allocation year than anticipated, and are likely only to have completed the calculation of the mass renormalization for asqtad quarks (as well as those for related bilinears) on coarse and fine MILC lattices. We propose here to extend this calculation to HYP-smeared staggered valence quarks, for both the bilinears and four-fermion operators. These matching factors are needed to reduce and control the systematic error in the calculation of B_K and other kaon matrix elements using HYP-fermions. Matching is, or is likely soon to be, the dominant source of error in this calculation. We propose to use the standard NPR methodology, adapted to staggered fermions, which our results to date indicate will be successful with relatively small ensembles. We use the Chroma package, augmented by the addition of momentum sources. We are asking for time on clusters, and prefer to continue running at Fermilab.

We are requesting 500,000 6n-equivalent node-hours on the clusters.
• 2008-09 Proposal submitted to the US lattice QCD Scientific Program Committee, asking for time on USQCD clusters at FNAL. Proposal was granted 500,000 node-hours (including small increment in October).
Abstract
This is a class B proposal, asking for time on the clusters to calculate matching (Z'') factors using non-perturbative renormalization (NPR) for the quark mass, bilinear and four-fermion operators, using valence asqtad and HYP-smeared staggered quarks on a subset of the coarse and fine MILC lattices. These matching factors are needed to reduce and control the systematic error in the quark mass obtained by the MILC collaboration using asqtad fermions, and in the calculation of BK and other kaon matrix elements using HYP-fermions. For both calculations, matching is, or is likely soon to be, the dominant source of error. We propose to use the standard NPR methodology, adapted to staggered fermions. We use the Chroma package, augmented by the addition of momentum sources. We are asking for time on clusters, and have a slight preference for running at Fermilab (where we have done our test runs).

We are requesting 500,000 6n-equivalent node-hours on the clusters.