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Had had pec Briceo, Chakraborty, Edwards, Jo, Cheung , Moir, Thomas, - PowerPoint PPT Presentation

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Meson resonances and their couplings Had had pec Briceo, Chakraborty, Edwards, Jo, Cheung , Moir, Thomas, Moss Richards, Winter O Hara , Peardon, Tims , Ryan, Wilson Dudek, Johnson , Radhakrishnan Mathur Had pec Resonances in experiments

  1. Meson resonances and their couplings Had had pec Briceño, Chakraborty, Edwards, Joó, Cheung , Moir, Thomas, Moss Richards, Winter O Hara , Peardon, Tims , Ryan, Wilson Dudek, Johnson , Radhakrishnan Mathur Had pec

  2. Resonances in experiments π 1 p pion cloud confirmation production mechanism [couplings] experimental demands identification of prominent decay channels couplings to decay channels structural understanding theoretical demands

  3. Inspired by lattice 3000 2500 2000 exotics hybrid 1500 1000 500 Dudek, Edwards, Guo, Thomas (2013) C 2 pt. X ab ( t, P ) ⌘ h 0 |O b ( t, P ) O † a,n e − E n t Extracted from: a (0 , P ) | 0 i = Z b,n Z ∗ Had n …using distillation and a large number [10-30] of local ops, O b ∼ ¯ q Γ b q Similar calculations by had pec have inspired baryon searches in Had pec

  4. Approximations ππ , KK, ηη , πππ , . . . Ops. basis did not include multi-hadron ops: Incomplete spectrum Unstable nature of the states ignored Finite volume are not resonances Demand for formalism Spectrum does suggest where some resonance are 3000 2500 6 π 2000 5 π 4 π 1500 3 π 1000 2 π 500 not all thresholds shown not all threshold are expected to matter

  5. Spectroscopy formalism scattering FV spectrum resonance amplitudes E L = finite volume spec . det[ F − 1 ( E L , L ) + M ( E L )] = 0 L = finite volume F = known function M = scattering amp . Lüscher (1986, 1991) [elastic scalar bosons] Rummukainen & Gottlieb (1995) [moving elastic scalar bosons] Kim, Sachrajda, & Sharpe/Christ, Kim & Yamazaki (2005) [QFT derivation] Feng, Li, & Liu (2004) [inelastic scalar bosons] Hansen & Sharpe / RB & Davoudi (2012) [moving inelastic scalar bosons] RB (2014) [general 2-body result]

  6. Extracting the spectrum Use local and multi-hadron ops Evaluate all Wick contraction: distillation w ( n ) X Variationally optimize operators: Ω n = O b b b e.g., ππ isotriplet at rest, m π =236 MeV 0.20 0.15 #3 ~ ππ ¯ ψ Γ ψ #26 ~ 0.10 Wilson, RB, Dudek, Edwards & Thomas (2015) #1 ~ KK

  7. Isovector ππ scattering 180 150 120 90 60 30 0 400 500 600 700 800 900 1000 16 π E cm Dudek, Edwards & Thomas (2012) M 1 = Wilson, RB, Dudek, Edwards & Thomas (2015) p cot δ 1 − ip

  8. The ρ vs m π Lin et al. (2009) Dudek, Edwards, Guo & Thomas (2013) Dudek, Edwards & Thomas (2012) Wilson, RB, Dudek, Edwards & Thomas (2015) Bolton, RB & Wilson (2015)

  9. Isoscalar ππ scattering 1 0.5 0 -0.5 -1 -0.06 -0.03 0 0.03 0.06 0.09 0.12 16 π E cm M 0 = p cot δ 0 − ip RB, Dudek, Edwards, Wilson - PRL (2017)

  10. The σ /f 0 (500) vs m π 0 300 500 700 900 -100 -200 -300 800 600 400 200 0 150 200 250 300 350 400

  11. The σ /f 0 (500) vs m π 0 300 500 700 900 -100 -200 P HYSICAL 118 R EVIEW -300 L ETTERS PRL 118 (2), 020401–029901, 13 January 2017 (288 total pages) 13 J ANUARY 2017 Articles published week ending 800 600 400 200 0 150 200 250 300 350 400

  12. Coupled-channels systems Had had pec Four systems consider so far, all by Had pec K π , K η : Dudek, Edwards, Thomas, Wilson - PRL (2015) Wilson, Dudek, Edwards, Thomas - PRD (2015) ππ , KK: Wilson, RB, Dudek, Edwards - PRD (2015) πη , KK: Dudek, Edwards, Wilson - PRD (2016) D π , D η , D s K: Moir, Peardon, Ryan, Thomas, Wilson - JHEP (2016) πη , KK, and the a 0 (980) (b) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 / MeV 1000 1050 1100 1150 1200 1250 1300 m π =391 MeV

  13. Physics Plan for 2017/2018 Part 1 - meson-meson scattering κ + κ 0 Isoscalars at higher energies: ππ , KK, ηη a + a 0 a − 0 f 0 0 0 f 0 (980), f 2 (1270),… First complete study of the scalar nonet σ Continuation to lighter quark masses κ 0 κ − ¯ m π =236, 275, 325 MeV Quark-mass dependence of couplings π 1 First exotic resonance: π 1, J PC =1 -+ m π = 700 MeV πη ’ ρ and b 1 are stable only two-body decays: πη , πη ’, ρπ , b 1 π πη

  14. Resonant electroweak processes Production/decay mechanisms: p Resonance form factors experimentally challenging or impossible information about structure Shape, size, composition,… p

  15. Optimized three-point functions Vanilla 3pt. functions: n 0 ,i e � ( δ t � t ) E n e � tE n 0 h n |J | n 0 i L C 3 pt. i ! f J = h 0 |O f ( δ t ) J ( t ) O † X Z n,f Z ⇤ i (0) | 0 i L = n,n 0 w ( n ) X Instead, use optimized ops: Ω n = O b b b to obtain: C 3 pt. i → f J = h 0 | Ω f,n f ( δ t ) J ( t ) Ω † i,n i (0) | 0 i L = e − ( δ t − t ) E nf e − tE ni h n f |J | n i i L + · · · Benefits: } excited state contamination is suppressed Crucial for few-body/resonance physics access excited state matrix elements

  16. Form factors @ m π = 700 MeV ( everything is stable! ) Ground states… 0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 1.0 2.0 1.5 0.8 1.0 0.5 0.6 0 -0.5 0.4 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Excited states… 0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Shultz, Dudek, Edwards - PRD (2015)

  17. 1-to-2 formalism partial wave resonance FV spectrum amplitudes = electroweak matrix elements form factors amplitudes + p � � � � � � h 2 � J � 1 i L = FV matrix element � h 2 � 1 i L � J A R A � = R = known function A = electroweak amp . Lellouch & Lüscher (2000) [K-to- ππ at rest] Kim, Sachrajda, & Sharpe/Christ, Kim & Yamazaki (2005) [moving K-to- ππ ] … Hansen & Sharpe (2012) [D-to- ππ /KK] RB, Hansen Walker-Lou /RB & Hansen (2014-2015) [general 1-to-2 result]

  18. πγ *-to- ππ amplitude 6.0 4.0 2.0 0 2.0 2.1 2.2 2.3 2.4 2.5 elastic ππ amplitude 100 50 0 2.0 2.1 2.2 2.3 2.4 2.5 m π =391 MeV RB, Dudek, Edwards, Thomas, Shultz, Wilson - PRL (2015)

  19. Explanation ππ -to- ππ amplitude: ∼ i | g ρ , ππ | 2 ∼ s − s 0 πγ *-to- ππ amplitude: ∼ iF πρ g ρ , ππ ∼ s − s 0

  20. π -to- ρ form factor evaluated at the ρ - meson pole, (853(2)-i 12.4(6)/2) MeV 0.24 E cm = E ρ 0.16 stable ρ 0.08 unstable ρ 0 0 0.2 0.4 0.6 0.8 2.5 0 −2 . 5 0 0.2 0.4 0.6 0.8 Shultz, Dudek, & Edwards (2014) RB, Dudek, Edwards, Shultz, Thomas & Wilson - PRL (2015)

  21. Elastic form factors of composite states Formalism in place: partial wave FV spectrum amplitudes = electroweak two-to-two form factors amplitudes matrix elements + = one-body matrix elements + RB & Hansen (2016) necessary for: scattering states bound states resonances untested!

  22. Physics Plan for 2017/2018 Part 2 - matrix elements Quark-mass dependence of πγ *-to- ππ amplitude m π =236, 275, 325 MeV Test chiral anomaly First calculation of a form factor of a composite state ππγ *-to- ππ elastic ρ form factors m π =236 MeV

  23. Had had pec Had pec 1 0 300 500 700 900 0.5 -100 0 -200 -0.5 -1 -300 -0.06 -0.03 0 0.03 0.06 0.09 0.12 (b) 0.7 6.0 0.6 0.5 4.0 0.4 2.0 0.3 0.2 0 2.0 2.1 2.2 2.3 2.4 2.5 0.1 100 50 0 / MeV 1000 1050 1100 1150 1200 1250 1300 2.0 2.1 2.2 2.3 2.4 2.5

  24. Had had pec Had pec Wilson Chakraborty Dudek Edwards Moir Peardon Ryan Thomas Mathur Winter Joó Richards Students: Meson Spectrum Baryon Spectrum Scattering Electroweak Johnson, Radhakrishnan, Cheung , Moss , O Hara , Tims JHEP05 021 (2013) PRD91 094502 (2015) PRL118 022002 (2017) PRD93 114508 (2016) PRD88 094505 (2013) PRD90 074504 (2014) JHEP011 1610 (2016) PRL115 242001 (2015) JHEP07 126 (2011) PRD87 054506 (2013) PRD93 094506 (2016) PRD91 114501 (2015) Formalism PRD83 111502 (2011) PRD85 054016 (2012) PRD92 094502 (2015) PRD90 014511 (2014) PRD82 034508 (2010) PRD84 074508 (2011) PRD91 054008 (2015) PRD95 074510 (2017) Techniques PRL103 262001 (2009) PRL113 182001 (2014) PRD94 013008 (2016) PRD87 034505 (2013) PRD92 074509 (2015) PRD85 014507 (2012) PRD86 034031 (2012) PRD91 034501 (2015) PRD80 054506 (2009) PRD83 071504 (2011) PRD89 074507 (2014) PRD79 034502 (2009)

  26. The σ /f 0 (500) vs m π U χ PT - Nebreda & Peláez (2015) 800 600 400 200 0 150 200 250 300 350 400

  27. Spectroscopy formalism scattering FV spectrum resonance amplitudes E L = finite volume spec . det[ F − 1 ( E L , L ) + M ( E L )] = 0 L = finite volume F = known function M = scattering amp . Lüscher (1986, 1991) [elastic scalar bosons] Rummukainen & Gottlieb (1995) [moving elastic scalar bosons] Kim, Sachrajda, & Sharpe/Christ, Kim & Yamazaki (2005) [QFT derivation] Feng, Li, & Liu (2004) [inelastic scalar bosons] Hansen & Sharpe / RB & Davoudi (2012) [moving inelastic scalar bosons] RB (2014) [general 2-body result]

  28. 1-to-2 formalism partial wave resonance FV spectrum amplitudes = electroweak matrix elements form factors amplitudes + p � � � � � � h 2 � J � 1 i L = FV matrix element � h 2 � 1 i L � J A R A � = R = known function A = electroweak amp . Lellouch & Lüscher (2000) [K-to- ππ at rest] Kim, Sachrajda, & Sharpe/Christ, Kim & Yamazaki (2005) [moving K-to- ππ ] … RB, Hansen Walker-Lou /RB & Hansen (2014-2015) [general 1-to-2 result]

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