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Hadron Spectra from Lattice QCD All-to-all Propagators in Lattice Hadron Spectrum Calculations John Bulava Background Distillation - An Exact All-to-all Method Variance- Reduced Stochastic LapH (VRSL) Spectral decomposition of two-point correlation functions: 〈0| O(t + t 0 ) O(t 0 ) |0〉 = ∑ n | 〈0| O(t 0 ) |n〉 | 2 exp[−E n t] Difficult (or impossible) to fit sub-leading exponentials, instead form a matrix of two-point correlators: C ij (t) = 〈0| O i (t + t 0 ) O j (t 0 ) |0〉 Define new operators Ω n (t) such that: 〈0| Ω a (t + t 0 ) Ω b (t 0 ) |0〉 = δ ab λ a (t) Fit λ n (t) with a single exponential to obtain E n John Bulava All-to-all Propagators in Lattice Hadron Spectrum Calculations
The Need For All-to-all Propagators All-to-all Propagators in Lattice Hadron Spectrum Calculations John Bulava Finite-volume stationary states are comprised of resonance states as well as scattering states. Some resonance states may have multi-particle content. Background Distillation - An Exact All-to-all Method Variance- Reduced Stochastic LapH (VRSL) 〈0|B(p = 0, t)B(p = 0, t 0 )|0〉 = (1) 1 ∑ V 2 〈0|ϕ B (x, t)ϕ B (y, t 0 )|0〉 x,y B(p, t)M(−p, t) = 1 ∑ V 2 ϕ B (x, t)ϕ M (y, t)e ip·(x−y) (2) x,y Sum over y can be eliminated in Eq. 1, but not in correlation functions containing the operator from Eq. 2. Solving Mφ = η for all y is not feasible. John Bulava All-to-all Propagators in Lattice Hadron Spectrum Calculations
Page 1 and 2: All-to-all Propagators in Lattice H
Page 3 and 4: Outline All-to-all Propagators in L
Page 5: Lattice QCD Background All-to-all P
Page 9 and 10: Outline All-to-all Propagators in L
Page 11 and 12: Volume Dependence All-to-all Propag
Page 13 and 14: It’s All About the Operators All-
Page 15 and 16: Nucleon (JB) and Delta (E. Engelson
Page 17 and 18: N f = 2 + 1 Results: I G = 1 − an
Page 19 and 20: Stochastic All-to-all All-to-all Pr
Page 21 and 22: VRSL vs. Conventional Dilution All-
Page 23 and 24: Same-Time (‘Disconnected’) Diag
Page 25 and 26: Disc. Term from σ Meson Correlator
Page 27 and 28: VRSL Conclusions All-to-all Propaga

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