The Roper resonance from spatially large interpolation fields The χ QCD Collaboration: Mingyang Sun (speaker), Keh-Fei Liu, Yi-Bo Yang, Ying Chen, Ming Gong, Terrence Draper, Raza Sabbir Sufian, Andrei Alexandru χ QCD
Motivation • Radial excitation of nucleon • Roper mass experimental value: 1440 MeV ( Γ ≈ 300 MeV) 3.0 Dynamical 2.5 M N H GeV L 2.0 Mathur H 3.2 fm L 1.5 Sasaki H 3.0 fm L Lasscock H 2.6 fm L Burch H 2.4 fm L Brommel H 2.4 fm L 1.0 Basak H 2.3 fm L Quenched Mahbub H 2.0 fm L 0.5 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 2 H GeV 2 L M Π Overlap Sequential Empirical Bayesian Ying Chen et al., arXiv:hep-lat/0405001 (2004) , 49 827 (2011) Keh-Fei Liu et al., arXiv:1403.6847 (2014) Huey-Wen Lin, CJP 2 χ QCD
a -1 =1.77GeV, m l a=0.005 Nucleon (coulomb) 2.6 Roper(coulomb) Roper (JLab) Roper (SEB) 2.4 CSSM exp. 2.2 2 M H (GeV) 1.8 1.6 1.4 1.2 1 0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 (GeV 2 ) m π Keh-Fei Liu et al., arXiv:1403.6847 (2014) 3 χ QCD
Ground State Elimination (GSE) method Consider two correlators 4 χ QCD
Lattices used • RBC/UKQCD 2+1 flavor domain wall 24 3 ⨉ 64, a ≈ 0.112 fm, m π = 330 MeV, with overlap fermion on top, 200 configurations • JLab 2+1 flavor anisotropic clover 24 3 ⨉ 128, a ≈ 0.123 fm, m π = 390 MeV, 760 configurations 5 χ QCD
Steps 1. Take two correlators C 1 , C 2 2. Fit for proton, note the fitting window 3. Take linear combination of the two correlators with parameter a : C = C 1 + aC 2 4. For each jackknife sample, fit C to zero in the proton fitting window to fix a 5. For each jackknife sample, fit C for mass of the 1st excited state. 6 χ QCD
Overlap on domain wall Coulomb wall source, Smeared source (RMS r point sink ≈ 1 fm), point sink 7 χ QCD
a -1 =1.77GeV, m l a=0.005 Nucleon (coulomb) 2.6 Roper(coulomb) Roper (JLab) Roper (SEB) 2.4 CSSM exp. GSE on overlap 2.2 2 M H (GeV) 1.8 1.6 1.4 1.2 1 0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 (GeV 2 ) m π 8 χ QCD
Anisotropic Clover Smeared source (RMS r ≈ Smeared source (RMS r ≈ 0.62 fm), point sink 1.1 fm), point sink 9 χ QCD
a -1 =1.77GeV, m l a=0.005 Nucleon (coulomb) 2.6 Roper(coulomb) Roper (JLab) Roper (SEB) 2.4 CSSM exp. GSE on overlap 2.2 GSE on clover (big src) 2 M H (GeV) 1.8 1.6 1.4 1.2 1 0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 (GeV 2 ) m π 10 χ QCD
Smeared source (RMS r ≈ Point source, point sink 0.32 fm), point sink 11 χ QCD
a -1 =1.77GeV, m l a=0.005 Nucleon (coulomb) 2.6 Roper(coulomb) Roper (JLab) Roper (SEB) 2.4 CSSM exp. GSE on overlap 2.2 GSE on clover (big src) GSE on clover (small src) 2 M H (GeV) 1.8 1.6 1.4 1.2 1 0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 (GeV 2 ) m π 12 χ QCD
Cause of Discrepency Size of operator. Source should cover node of roper wave function. ≈ 0.9 fm Ying Chen, Mod. Phys. Lett. A22 , 583 (2007) ≈ 0.5 fm ≈ 0.8 fm Dale S. Roberts et al. (CSSM), PRD 89 , 074501 (2014) 13 χ QCD
a -1 =1.77GeV, m l a=0.005 Nucleon (coulomb) 2.6 Roper(coulomb) Roper (JLab) Roper (SEB) 2.4 CSSM exp. GSE on overlap 2.2 GSE on clover (big src) GSE on clover (small src) 2 M H (GeV) 1.8 1.6 1.4 1.2 1 0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 (GeV 2 ) m π 14 χ QCD
π N, ππ N η N 0 π∆ Roper couples strongly to π N state. A(1357,-76) -100 ρ N Im (E) (MeV) B(1364,-105) “Meson cloud effect” -200 C(1820,-248) B. Juliá-Díaz et al., PRC 80 , 025207 (2009) -300 Naomichi Suzuki et al. PRL 104 , 042302 (2010) σ N 1400 1600 1800 Re (E) (MeV) RBC/UKQCD 48 3 ⨉ 96 domain wall w/ overlap 1.6 (1/2) - (1/2) + 1.4 m N +m π would-be m S11 1.2 eff (t)a 1 m N 0.8 0.6 0.4 0.2 0 2 4 6 8 10 12 14 t/a 1.19 GeV Sea m π ≈ 139 MeV M. Selim Mahbub et al., PRD 87 094506 (2013) Valence m π ≈ 208 MeV 15 χ QCD
Summary • We used GSE method to extract the mass of roper • The roper extracted is sensitive to the size of the operator. One needs a set of large sources. • We speculate that the π N state coupling to the 3-quark interpolation field is important. • Effective in terms of statistics • I invite you to try this method on your data. 16 χ QCD
Variation Method Most studies use this approach, with multiple smear sizes, and interpolation fields. Anisotropic clover 17 χ QCD
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