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Lattice QCD Research at Baylor: Exploring Disconnected Diagrams and Quantum Chromodynamics

Baylor University's Physics Department boasts 15 research-active faculty members, ranking #18 in faculty citation percentage and #16 in research grant dollars. Our active experimental research in Lattice Quantum Chromodynamics (QCD) tackles the complexities of quark and gluon interactions, especially focusing on disconnected diagrams. We utilize innovative methods like deflation and eigenspectrum subtraction to study quark loop contributions, enhancing our understanding of strong interactions. Reach out for our recruitment packet to discover more about our research programs!

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Lattice QCD Research at Baylor: Exploring Disconnected Diagrams and Quantum Chromodynamics

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  1. Shameless Baylor Advertisement • Baylor’s Physics Department – 15 research-active faculty. Rank #18 in the percentage of faculty whose works are cited and #16 in dollars per research grant. • Faculty Scholarly Productivity from Academic Analytics is #71 (out of 177 programs) in the country. • Have active experimental research programs at FermiLab (CDF) and the LHC (CMS). • Ask me for a recruitment packet!

  2. Disconnected Diagrams and Lattice QCD • What is Lattice QCD? • Taming disconnected diagrams Collaborators: Victor Guerrero and Ron Morgan

  3. Quantum Chromodynamics (QCD)--- the fundamental theory of the strong interaction (quarks and gluons) Aspects of lattice QCD • 2 "Actions" - gluon and quark. • Does the "path integral" automatically via Monte Carlo simulation. • Degrees of freedom are the points in space, colors, spin and particle/anti-particle. • Lattice scale "a" set by renormalization group behavior. • Quark propagators are matrix inverses of the "mass matrix".

  4. Lattice Quantum Chromodynamics (QCD) Variables

  5. Example: quark-antiquark potential

  6. Example : as

  7. Example: hadron masses (Durr et al)

  8. Deflation and noise subtraction methods

  9. The HARD problem: quark loop Ugly gluon lines destruction creation

  10. Deflation basics Krylov subspace: Starting, residual vectors: q is poly of degree m or less that has value 1 at 0.

  11. Matrix: bidiagonal, diagonal is 0.1, 1, 2, 3, …1999, superdiagonal is all 1’sGMRES polynomial of degree 10

  12. GMRES polynomial of degree 100(close up view)

  13. GMRES polynomial of degree 150(close up view)

  14. Residual norm curve Matrix vector products

  15. NonHermitian deflation 2+1 CP-PACS 163 x 32 lattice, kappa=0.13980.

  16. Hermitian deflation: CG vs. D-CG (M+M) Getting M from M+M; 203 x 32 lattice, 1st rhs: Lan-DR(200,k).

  17. Hermitian deflation: CG vs. D-CG (5 M) Getting M from 5M; same 203 x 32 lattice

  18. Hermitian deflation: Minres vs. D-Minres (5 M) Using5 M to get M using D-Minres; same 203 x 32 lattice

  19. Subtraction basics • Noise matrices: • Variance: • Z(N) ( ) noise:

  20. Perturbative subtraction (PS) (Q = M-1): Should work best for small (large quark mass). • Eigenspectrum (ES) subtraction: Should work best for large(small quark mass). • Can also combine PS and ES methods

  21. 30x30 pseudolattice spectrum

  22. Eigenspectrum Subtraction (30x30 matrix) Noises ES=eigenspectrum subtraction, PE=perturbative subtraction, DS=direct sum (no subtraction).

  23. 500 x 500 bidiagonal matrix (eig: 0.1,1,2,3,...) Trace Error #subtracted eigenvalues

  24. 84 Wilson lattice spectrum at _critical Imag Real Figure 1: Plot of the low eigenspectrum of the 84 Wilson lattice at kcr= 0.15701 . Figure 1: Plot of the low eigenspectrum of the 84 Wilson lattice at kcr= 0.15701 .

  25. Noi 84 Lattice Results; =0.15701 Noises NS=no subtraction, PE=perturbative subtraction, #ev=no. of eigen. subtracted, PEc+#ev=corrected perturbative subtraction on #ev method.

  26. Summary • Deflation is a important new method in Lattice studies, which will become more important for smaller quark masses. Effective in a Hermitian or non-Hermitian context. • Eigenspectrum subtraction is helpful for disconnected diagrams at small quark masses. Extension to Fortran (larger lattices) is almost finished. • Thanks to Ron Morgan and Victor Guerrero for their invaluable contributions!

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