HPC-LEAP EUROPEAN JOINT DOCTORATES Scattering from the lattice: - - PowerPoint PPT Presentation

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HPC-LEAP EUROPEAN JOINT DOCTORATES Scattering from the lattice: - - PowerPoint PPT Presentation

Jan 20, 2023 318 likes •670 views

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 - N study study - N study

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SLIDE 1

Srijit Paul

HPC-LEAP

EUROPEAN JOINT DOCTORATES

Scattering from the lattice: applications to phenomenology and beyond. Dublin, May 14, 2018

Srijit Paul s.paul@hpc-leap.eu 1/20

1/20

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SLIDE 2

Overview

Aspects of π-N study ππ study π-N study Expected Outcomes π − N results

Srijit Paul s.paul@hpc-leap.eu 2/20

2/20

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SLIDE 3

section 1

Aspects of π-N study ππ study π-N study Expected Outcomes π − N results

Srijit Paul s.paul@hpc-leap.eu 3/20

3/20

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SLIDE 4

ππ Calculation

Gauge Ensemble Setup

  • Nf = 2 + 1 Clover fermions.
  • isotropic lattice.(323 × 96)
  • mπL = 5.865(32)
  • mπ is low enough: ρ is

unstable. a(fm) L(fm) mπ(MeV) mK(MeV) Nconfig 0.11403(77) 3.649(25) 317 530 1041

  • 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])

Srijit Paul s.paul@hpc-leap.eu 4/20

4/20

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SLIDE 5

ππ Calculation

Gauge Ensemble Setup

  • Nf = 2 + 1 Clover fermions.
  • isotropic lattice.(323 × 96)
  • mπL = 5.865(32)
  • mπ is low enough: ρ is

unstable. a(fm) L(fm) mπ(MeV) mK(MeV) Nconfig 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])

Srijit Paul s.paul@hpc-leap.eu 4/20

4/20

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SLIDE 6

ππ Calculation

Our results in modern context

ρ meson mass comparison

150 200 250 300 350 400 450 m (MeV) 700 800 900 1000 1100 m (MeV) Guo_et_al Bulava_et_al RQCD HadSpec Pellisier HadSpec PACS-CS Lang_et_al ETMC CP-PACS Fu Physical Nf=2 Nf=2+1 Nf=2+1

Srijit Paul s.paul@hpc-leap.eu 5/20

5/20

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SLIDE 7

ππ Calculation

Our results in modern context

ρ meson mass comparison

150 200 250 300 350 400 450 m (MeV) 700 800 900 1000 1100 m (MeV) Our result Guo_et_al Bulava_et_al RQCD HadSpec Pellisier HadSpec PACS-CS Lang_et_al ETMC CP-PACS Fu Physical Nf=2 Nf=2+1 Nf=2+1

Srijit Paul s.paul@hpc-leap.eu 5/20

5/20

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SLIDE 8

Our results in modern context

gρ−ππ coupling comparison

150 200 250 300 350 400 450 m (MeV) 5.0 5.5 6.0 6.5 7.0 7.5 g Guo_et_al Bulava_et_al RQCD HadSpec Pellisier HadSpec PACS-CS Lang_et_al ETMC CP-PACS Fu Physical Nf=2 Nf=2+1 Nf=2+1

Srijit Paul s.paul@hpc-leap.eu 6/20

6/20

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SLIDE 9

Our results in modern context

gρ−ππ coupling comparison

150 200 250 300 350 400 450 m (MeV) 5.0 5.5 6.0 6.5 7.0 7.5 g Our result Guo_et_al Bulava_et_al RQCD HadSpec Pellisier HadSpec PACS-CS Lang_et_al ETMC CP-PACS Fu Physical Nf=2 Nf=2+1 Nf=2+1

Srijit Paul s.paul@hpc-leap.eu 6/20

6/20

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SLIDE 10

section 2

Aspects of π-N study ππ study π-N study Expected Outcomes π − N results

Srijit Paul s.paul@hpc-leap.eu 7/20

7/20

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SLIDE 11

Brief History

  • First calculation setup using Lüscher method, and some

unpublished results.(mπ ≈ 250 MeV)

[Goeckler(2012), Mohler(2012)]

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)]

Srijit Paul s.paul@hpc-leap.eu 8/20

8/20

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SLIDE 12

Brief History

  • First calculation setup using Lüscher method, and some

unpublished results.(mπ ≈ 250 MeV)

[Goeckler(2012), Mohler(2012)]

  • Determination of ∆-resonance parameters, using Transfer

Matrix, Michael-McNeile method.(mπ ≈ 360 MeV)

[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)]

Srijit Paul s.paul@hpc-leap.eu 8/20

8/20

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SLIDE 13

Brief History

  • First calculation setup using Lüscher method, and some

unpublished results.(mπ ≈ 250 MeV)

[Goeckler(2012), Mohler(2012)]

  • Determination of ∆-resonance parameters, using Transfer

Matrix, Michael-McNeile method.(mπ ≈ 360 MeV)

[Alexandrou(2013)]

  • Pion-Nucleon Scattering in Lattice QCD, using Lüscher
  • method. (mπ ≈ 266 MeV)

[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)]

Srijit Paul s.paul@hpc-leap.eu 8/20

8/20

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SLIDE 14

Brief History

  • First calculation setup using Lüscher method, and some

unpublished results.(mπ ≈ 250 MeV)

[Goeckler(2012), Mohler(2012)]

  • Determination of ∆-resonance parameters, using Transfer

Matrix, Michael-McNeile method.(mπ ≈ 360 MeV)

[Alexandrou(2013)]

  • Pion-Nucleon Scattering in Lattice QCD, using Lüscher
  • method. (mπ ≈ 266 MeV)

[Verduci Thesis(2014)]

  • Study of decuplet baryon-resonance parameters, using

Transfer Matrix, Michael-McNeile method.(mπ ≈ 180 MeV)

[Alexandrou(2016)]

Elastic p-wave resonance, using Lüscher method, with distillation.( )

[Andersen(2017)]

Srijit Paul s.paul@hpc-leap.eu 8/20

8/20

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SLIDE 15

Brief History

  • First calculation setup using Lüscher method, and some

unpublished results.(mπ ≈ 250 MeV)

[Goeckler(2012), Mohler(2012)]

  • Determination of ∆-resonance parameters, using Transfer

Matrix, Michael-McNeile method.(mπ ≈ 360 MeV)

[Alexandrou(2013)]

  • Pion-Nucleon Scattering in Lattice QCD, using Lüscher
  • method. (mπ ≈ 266 MeV)

[Verduci Thesis(2014)]

  • Study of decuplet baryon-resonance parameters, using

Transfer Matrix, Michael-McNeile method.(mπ ≈ 180 MeV)

[Alexandrou(2016)]

  • Elastic I = 3/2 p-wave resonance, using Lüscher method, with

distillation.(mπ ≈ 280 MeV)

[Andersen(2017)]

Srijit Paul s.paul@hpc-leap.eu 8/20

8/20

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SLIDE 16

π-N Calculation

Lüscher Analysis

Quantization condition For Baryons

det( M ∆

Jlµ,J′l′µ′ − δJJ′δll′δµµ′ cot δJl ) = 0

[Goeckler(2012)] where

Srijit Paul s.paul@hpc-leap.eu 9/20

9/20

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SLIDE 17

π-N Calculation

Lüscher Analysis

Quantization condition For Baryons

det( M ∆

Jlµ,J′l′µ′ − δJJ′δll′δµµ′ cot δJl ) = 0

[Goeckler(2012)] M ∆

Jlµ,J′l′µ′ =

∑

m,σ m′,σ′

⟨ lm, 1 2σ

  • Jµ

⟩ ⟨ l′m′, 1 2σ′

  • J′µ′

⟩ M ∆

lm,l′m′

where M ∆

lm,l′m′ = (−1)lγ−l

π3/2

l+l′

∑

j=|l−l′| j

∑

s=−j

ij qj+1 Zjs(1, q2) Clm,js,l′m′

Srijit Paul s.paul@hpc-leap.eu 9/20

9/20

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SLIDE 18

π-N Calculation

Common Problems

  • The exponential degradation in the S-n ratio.
  • The additional valence quark ⇑ Wick contractions, ⇑

computational and storage costs.

Srijit Paul s.paul@hpc-leap.eu 10/20

10/20

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SLIDE 19

π-N Calculation

Gauge Ensemble Setup

  • Nf = 2 + 1 Clover fermions.
  • isotropic lattice.(243 × 48)
  • mπL = 3.6
  • mπ is low enough: ∆ is

unstable. a(fm) L(fm) mπ(MeV) mN(GeV) Nconfig 0.116 2.8 254(1) 1.072(7) 600

Srijit Paul s.paul@hpc-leap.eu 11/20

11/20

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SLIDE 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]

Srijit Paul s.paul@hpc-leap.eu 12/20

12/20

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SLIDE 21

Wick contractions

∆ Nπ ∆ u(uΓiu) u(uΓiu) Nπ

Srijit Paul s.paul@hpc-leap.eu 13/20

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Wick contractions

∆ πN ∆ u(uΓiu) u(uΓiu) ¯ dγ5u u(uΓid) u(uΓiu) πN ¯ dγ5u u(uΓid) u(uΓiu)

Srijit Paul s.paul@hpc-leap.eu 13/20

13/20

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SLIDE 23

Nπ − Nπ contraction

πN πN ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid) ¯ dγ5u u(uΓid)

Srijit Paul s.paul@hpc-leap.eu 14/20

14/20

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SLIDE 24

Nπ − Nπ contraction

Srijit Paul s.paul@hpc-leap.eu 14/20

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SLIDE 25

Nπ − Nπ contraction

Srijit Paul s.paul@hpc-leap.eu 14/20

14/20

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SLIDE 26

Nπ − Nπ contraction

Srijit Paul s.paul@hpc-leap.eu 14/20

14/20

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Delta and Nucleon Interpolators

χN1(x) = ϵabc

[

uT

a (x) Cγ5 db(x)

]

uc(x) , (1) χN2(x) = ϵabc

[

uT

a (x) C db(x)

]

γ5uc(x) , (2) χN3(x) = ϵabc

[

uT

a (x) Cγ5 γt db(x)

]

uc(x) (3) (4) (5) (6)

Srijit Paul s.paul@hpc-leap.eu 15/20

15/20

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SLIDE 28

Delta and Nucleon Interpolators

χN1(x) = ϵabc

[

uT

a (x) Cγ5 db(x)

]

uc(x) , (1) χN2(x) = ϵabc

[

uT

a (x) C db(x)

]

γ5uc(x) , (2) χN3(x) = ϵabc

[

uT

a (x) Cγ5 γt db(x)

]

uc(x) (3) χ∆1(x) = ϵabc

[

uT

a (x) Cγµ ub(x)

]

uc(x) (4) χ∆2(x) = ϵabc

[

uT

a (x) Cγµγt ub(x)

]

uc(x) , (5) χ∆3(x) = ϵabc

[

uT

a (x) Cγµγtγ5 ub(x)

]

γ5uc(x) (6)

Srijit Paul s.paul@hpc-leap.eu 15/20

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SLIDE 29

Pion energy spectrum

Srijit Paul s.paul@hpc-leap.eu 16/20

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Proton energy spectrum

Srijit Paul s.paul@hpc-leap.eu 17/20

17/20

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SLIDE 31

section 3

Aspects of π-N study ππ study π-N study Expected Outcomes π − N results

Srijit Paul s.paul@hpc-leap.eu 18/20

18/20

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SLIDE 32

π-N status and results

  • Correlation functions have been computed for each Irrep.
  • To do a GEVP on the correlation matrices for each Irrep.
  • Using the Lüscher quantization condition, we need to extract

to the scattering phase shifts for irrep and moving frame.

  • Using the Breit Wigner parametrization of the decay width, we

need to extract the mass of ∆(1232) and the g∆−Nπ

  • Using the Briceno-Hansen-Walker-Loud formalism for extract

scattering matrix elements of Nπ → Nγ.

Srijit Paul s.paul@hpc-leap.eu 19/20

19/20

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SLIDE 33

Thank you

Srijit Paul s.paul@hpc-leap.eu 20/20

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