Srijit Paul HPC-LEAP EUROPEAN JOINT DOCTORATES Scattering from the lattice: applications to phenomenology and beyond. Dublin, May 14, 2018 1 / 20 Srijit Paul s.paul@hpc-leap.eu 1/20
Overview Aspects of π - N study ππ study π - N study Expected Outcomes π − N results 2 / 20 Srijit Paul s.paul@hpc-leap.eu 2/20
section 1 Aspects of π - N study ππ study π - N study Expected Outcomes π − N results 3 / 20 Srijit Paul s.paul@hpc-leap.eu 3/20
-wave scattering and the resonance from lattice QCD authored by C. Alexandrou, L. Leskovec, S. Meinel, J. Negele, S. Paul, M. Petschlies, A. Pochinsky, G. Rendon, S. Syritsyn.(arXiv:1704.05439v2 [hep-lat]) ππ Calculation Gauge Ensemble Setup • N f = 2 + 1 Clover fermions. • m π L = 5 . 865(32) • isotropic lattice.( 32 3 × 96 ) • m π is low enough: ρ is unstable. a (fm) L(fm) m π (MeV) m K (MeV) N config 0 . 11403(77) 3 . 649(25) 317 530 1041 4 / 20 Srijit Paul s.paul@hpc-leap.eu 4/20
ππ Calculation Gauge Ensemble Setup • N f = 2 + 1 Clover fermions. • m π L = 5 . 865(32) • isotropic lattice.( 32 3 × 96 ) • m π is low enough: ρ is unstable. a (fm) L(fm) m π (MeV) m K (MeV) N config 0 . 11403(77) 3 . 649(25) 317 530 1041 P -wave ππ scattering and the ρ resonance from lattice QCD authored by C. Alexandrou, L. Leskovec, S. Meinel, J. Negele, S. Paul, M. Petschlies, A. Pochinsky, G. Rendon, S. Syritsyn.(arXiv:1704.05439v2 [hep-lat]) 4 / 20 Srijit Paul s.paul@hpc-leap.eu 4/20
ππ Calculation Our results in modern context ρ meson mass comparison N f =2 1100 N f =2+1 N f =2+1 Guo_et_al 1000 Bulava_et_al RQCD m (MeV) HadSpec 900 Pellisier HadSpec PACS-CS 800 Lang_et_al ETMC CP-PACS 700 Fu Physical 150 200 250 300 350 400 450 m (MeV) 5 / 20 Srijit Paul s.paul@hpc-leap.eu 5/20
ππ Calculation Our results in modern context ρ meson mass comparison N f =2 1100 N f =2+1 N f =2+1 Our result Guo_et_al 1000 Bulava_et_al RQCD m (MeV) HadSpec 900 Pellisier HadSpec PACS-CS 800 Lang_et_al ETMC CP-PACS 700 Fu 150 200 250 300 350 400 450 Physical m (MeV) 5 / 20 Srijit Paul s.paul@hpc-leap.eu 5/20
Our results in modern context g ρ − ππ coupling comparison 7.5 N f =2 N f =2+1 N f =2+1 7.0 Guo_et_al Bulava_et_al 6.5 RQCD HadSpec 6.0 Pellisier g HadSpec PACS-CS 5.5 Lang_et_al ETMC 5.0 CP-PACS Fu Physical 150 200 250 300 350 400 450 m (MeV) 6 / 20 Srijit Paul s.paul@hpc-leap.eu 6/20
Our results in modern context g ρ − ππ coupling comparison N f =2 7.5 N f =2+1 N f =2+1 7.0 Our result Guo_et_al Bulava_et_al 6.5 RQCD HadSpec 6.0 Pellisier g HadSpec 5.5 PACS-CS Lang_et_al ETMC 5.0 CP-PACS Fu 150 200 250 300 350 400 450 Physical m (MeV) 6 / 20 Srijit Paul s.paul@hpc-leap.eu 6/20
section 2 Aspects of π - N study ππ study π - N study Expected Outcomes π − N results 7 / 20 Srijit Paul s.paul@hpc-leap.eu 7/20
Determination of -resonance parameters, using Transfer Matrix, Michael-McNeile method.( ) [Alexandrou(2013)] Pion-Nucleon Scattering in Lattice QCD, using Lüscher method. ( ) [Verduci Thesis(2014)] Study of decuplet baryon-resonance parameters, using Transfer Matrix, Michael-McNeile method.( ) [Alexandrou(2016)] Elastic p-wave resonance, using Lüscher method, with distillation.( ) [Andersen(2017)] Brief History • First calculation setup using Lüscher method, and some unpublished results.( m π ≈ 250 MeV ) [Goeckler(2012), Mohler(2012)] 8 / 20 Srijit Paul s.paul@hpc-leap.eu 8/20
Pion-Nucleon Scattering in Lattice QCD, using Lüscher method. ( ) [Verduci Thesis(2014)] Study of decuplet baryon-resonance parameters, using Transfer Matrix, Michael-McNeile method.( ) [Alexandrou(2016)] Elastic p-wave resonance, using Lüscher method, with distillation.( ) [Andersen(2017)] Brief History • First calculation setup using Lüscher method, and some unpublished results.( m π ≈ 250 MeV ) [Goeckler(2012), Mohler(2012)] • Determination of ∆ -resonance parameters, using Transfer Matrix, Michael-McNeile method.( m π ≈ 360 MeV ) [Alexandrou(2013)] 8 / 20 Srijit Paul s.paul@hpc-leap.eu 8/20
Study of decuplet baryon-resonance parameters, using Transfer Matrix, Michael-McNeile method.( ) [Alexandrou(2016)] Elastic p-wave resonance, using Lüscher method, with distillation.( ) [Andersen(2017)] Brief History • First calculation setup using Lüscher method, and some unpublished results.( m π ≈ 250 MeV ) [Goeckler(2012), Mohler(2012)] • Determination of ∆ -resonance parameters, using Transfer Matrix, Michael-McNeile method.( m π ≈ 360 MeV ) [Alexandrou(2013)] • Pion-Nucleon Scattering in Lattice QCD, using Lüscher method. ( m π ≈ 266 MeV ) [Verduci Thesis(2014)] 8 / 20 Srijit Paul s.paul@hpc-leap.eu 8/20
Elastic p-wave resonance, using Lüscher method, with distillation.( ) [Andersen(2017)] Brief History • First calculation setup using Lüscher method, and some unpublished results.( m π ≈ 250 MeV ) [Goeckler(2012), Mohler(2012)] • Determination of ∆ -resonance parameters, using Transfer Matrix, Michael-McNeile method.( m π ≈ 360 MeV ) [Alexandrou(2013)] • Pion-Nucleon Scattering in Lattice QCD, using Lüscher method. ( m π ≈ 266 MeV ) [Verduci Thesis(2014)] • Study of decuplet baryon-resonance parameters, using Transfer Matrix, Michael-McNeile method.( m π ≈ 180 MeV ) [Alexandrou(2016)] 8 / 20 Srijit Paul s.paul@hpc-leap.eu 8/20
Brief History • First calculation setup using Lüscher method, and some unpublished results.( m π ≈ 250 MeV ) [Goeckler(2012), Mohler(2012)] • Determination of ∆ -resonance parameters, using Transfer Matrix, Michael-McNeile method.( m π ≈ 360 MeV ) [Alexandrou(2013)] • Pion-Nucleon Scattering in Lattice QCD, using Lüscher method. ( m π ≈ 266 MeV ) [Verduci Thesis(2014)] • Study of decuplet baryon-resonance parameters, using Transfer Matrix, Michael-McNeile method.( m π ≈ 180 MeV ) [Alexandrou(2016)] • Elastic I = 3 / 2 p-wave resonance, using Lüscher method, with distillation.( m π ≈ 280 MeV ) [Andersen(2017)] 8 / 20 Srijit Paul s.paul@hpc-leap.eu 8/20
where π - N Calculation Lüscher Analysis Quantization condition For Baryons Jlµ,J ′ l ′ µ ′ − δ JJ ′ δ ll ′ δ µµ ′ cot δ Jl ) = 0 det( M ∆ [Goeckler(2012)] 9 / 20 Srijit Paul s.paul@hpc-leap.eu 9/20
π - N Calculation Lüscher Analysis Quantization condition For Baryons Jlµ,J ′ l ′ µ ′ − δ JJ ′ δ ll ′ δ µµ ′ cot δ Jl ) = 0 det( M ∆ [Goeckler(2012)] ⟨ lm, 1 � ⟩ ⟨ l ′ m ′ , 1 � ⟩ M ∆ ∑ 2 σ ′ � J ′ µ ′ M ∆ � � Jlµ,J ′ l ′ µ ′ = 2 σ � Jµ � � lm,l ′ m ′ m,σ m ′ ,σ ′ where l + l ′ j lm,l ′ m ′ = ( − 1) l γ − l i j ∑ ∑ M ∆ Z js (1 , q 2 ) C lm,js,l ′ m ′ π 3 / 2 q j +1 j = | l − l ′ | s = − j 9 / 20 Srijit Paul s.paul@hpc-leap.eu 9/20
π - N Calculation Common Problems • The exponential degradation in the S-n ratio. • The additional valence quark ⇑ Wick contractions, ⇑ computational and storage costs. 10 / 20 Srijit Paul s.paul@hpc-leap.eu 10/20
π - N Calculation Gauge Ensemble Setup • N f = 2 + 1 Clover fermions. • m π L = 3 . 6 • isotropic lattice.( 24 3 × 48 ) • m π is low enough: ∆ is unstable. a (fm) L(fm) m π (MeV) m N (GeV) N config 0 . 116 2 . 8 254(1) 1 . 072(7) 600 11 / 20 Srijit Paul s.paul@hpc-leap.eu 11/20
π - N Calculation Lattice setup for scattering Specific Problem • Mixing of S and D wave channel to the ∆(1232) channel [Addressed in Goeckler 2012, Roper 1965] 12 / 20 Srijit Paul s.paul@hpc-leap.eu 12/20
Wick contractions ∆ Nπ u ( u Γ i u ) u ( u Γ i u ) ∆ Nπ 13 / 20 Srijit Paul s.paul@hpc-leap.eu 13/20
Wick contractions ∆ πN ¯ dγ 5 u u ( u Γ i u ) u ( u Γ i u ) u ( u Γ i u ) u ( u Γ i d ) ∆ ¯ dγ 5 u u ( u Γ i u ) u ( u Γ i d ) πN 13 / 20 Srijit Paul s.paul@hpc-leap.eu 13/20
Nπ − Nπ contraction πN ¯ ¯ ¯ ¯ dγ 5 u dγ 5 u dγ 5 u dγ 5 u u ( u Γ i d ) u ( u Γ i d ) u ( u Γ i d ) u ( u Γ i d ) πN ¯ ¯ ¯ ¯ dγ 5 u dγ 5 u dγ 5 u dγ 5 u u ( u Γ i d ) u ( u Γ i d ) u ( u Γ i d ) u ( u Γ i d ) 14 / 20 Srijit Paul s.paul@hpc-leap.eu 14/20
Nπ − Nπ contraction 14 / 20 Srijit Paul s.paul@hpc-leap.eu 14/20
Nπ − Nπ contraction 14 / 20 Srijit Paul s.paul@hpc-leap.eu 14/20
Nπ − Nπ contraction 14 / 20 Srijit Paul s.paul@hpc-leap.eu 14/20
(4) (5) (6) Delta and Nucleon Interpolators [ ] u T (1) χ N 1 ( x ) = ϵ abc a ( x ) Cγ 5 d b ( x ) u c ( x ) , [ ] u T (2) χ N 2 ( x ) = ϵ abc a ( x ) C d b ( x ) γ 5 u c ( x ) , [ ] u T (3) χ N 3 ( x ) = ϵ abc a ( x ) Cγ 5 γ t d b ( x ) u c ( x ) 15 / 20 Srijit Paul s.paul@hpc-leap.eu 15/20
Delta and Nucleon Interpolators [ ] u T (1) χ N 1 ( x ) = ϵ abc a ( x ) Cγ 5 d b ( x ) u c ( x ) , [ ] u T (2) χ N 2 ( x ) = ϵ abc a ( x ) C d b ( x ) γ 5 u c ( x ) , [ ] u T (3) χ N 3 ( x ) = ϵ abc a ( x ) Cγ 5 γ t d b ( x ) u c ( x ) [ ] u T (4) χ ∆1 ( x ) = ϵ abc a ( x ) Cγ µ u b ( x ) u c ( x ) [ ] u T χ ∆2 ( x ) = ϵ abc a ( x ) Cγ µ γ t u b ( x ) u c ( x ) , (5) [ ] u T χ ∆3 ( x ) = ϵ abc a ( x ) Cγ µ γ t γ 5 u b ( x ) γ 5 u c ( x ) (6) 15 / 20 Srijit Paul s.paul@hpc-leap.eu 15/20
Pion energy spectrum 16 / 20 Srijit Paul s.paul@hpc-leap.eu 16/20
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