(Towards) Baryon Resonances from Lattice QCD

Transcription

1 (Towards) Baryon Resonances from Lattice QCD Daniel Mohler Fermilab Theory Group Batavia, IL, USA Paphos, October 2013 Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

2 Outline 1 Recent developments and lattice basics 2 Extracting (excited) baryon levels Light and strange baryons Hybrid baryons Baryons with heavy quarks 3 A closer look at some puzzles J P = 1 2 Nucleons J P = The Roper resonance Recent results on the Λ(1405) 4 Towards extracting Hadron resonances J P = 1 2 Nucleons The (1232) from Lattice QCD 5 Conclusions and Outlook Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

3 Recent developments I: Ground state masses Light mesons and baryons Heavy mesons b b h b (2P) h b (1P) b2 b1 (2P) b0 b2 b0 b1 (1P) expt fix params postdcns predcns (1D) MESON MASS (GeV/c 2 ) c c c2 h c1 c J/ c0 B c B c B s B B * B * c c B * s B * B * c0 2 D s D Example from BMW,Dürr et al. Science 322 (2008) 0 Example from HPQCD, Dowdall et al. PRD (2012) (Most) ground states calculated with full control of systematic uncertainties This can be done for a wide variety of (ground state) observables K Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

4 Recent developments II Calculations at the physical pion mass and we are seeing more... (RBC,ETMC) PACS-CS Phys.Rev. D81 (2010) BMW Phys.Lett. B701 (2011) 265 MILC Phys.Rev. D87 (2013) First dynamical flavor simulations (ETMC, MILC) Effects from Isospin-breaking and (quenched) QED effects can be taken into account. Today I talk about: Progress in extracting a larger number of excited energy levels Progress towards extracting hadron resonances (and bound states) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

5 Recent developments II Calculations at the physical pion mass and we are seeing more... (RBC,ETMC) PACS-CS Phys.Rev. D81 (2010) BMW Phys.Lett. B701 (2011) 265 MILC Phys.Rev. D87 (2013) First dynamical flavor simulations (ETMC, MILC) Effects from Isospin-breaking and (quenched) QED effects can be taken into account. Today I talk about: Progress in extracting a larger number of excited energy levels Progress towards extracting hadron resonances (and bound states) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

6 Lattice systematics - a reminder For fully controlled systematic uncertainties one needs (at least): Continuum limit: a(g, m) 0 Need simulations at multiple different lattice spacings Thermodynamic limit: L (L a = const.) Hadron physics in a small box finite volume effects Typical volume fm Calculation at physical quark masses or extrapolation to the Chiral limit/physical pion mass: m m 0 (M π M π,exp ) Physical u, d quark masses small Simulation very expensive! Chiral Perturbation Theory (χpt) Lattice QCD Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

7 Excited states and baron signal to noise Euclidean space correlation functions: Ô2 (t)ô1(0) e ten < 0 Ô2 n >< n Ô1 0 > T n Ground state is dominant at large t Exited states appear as sub-leading exponentials Noisy background from limited statistics Baryon signal to noise (asymptotically): signal noise Z e Mnt Z e 3 2 mπt G. P. Lepage, TASI89 summer school, Boulder ASI 1989: (QCD161:T45:1989). Excited baryons are very difficult! exploratory results Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

8 Excited states and baron signal to noise Euclidean space correlation functions: Ô2 (t)ô1(0) e ten < 0 Ô2 n >< n Ô1 0 > T n Ground state is dominant at large t Exited states appear as sub-leading exponentials Noisy background from limited statistics Baryon signal to noise (asymptotically): signal noise Z e Mnt Z e 3 2 mπt G. P. Lepage, TASI89 summer school, Boulder ASI 1989: (QCD161:T45:1989). Excited baryons are very difficult! exploratory results Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

9 Excited baryon spectra: A large number of states Edwards, Dudek, Richards, Wallace, PRD (2011) Results for m π = 396 MeV (702, 524 MeV not shown) State-of-the-art methods yield a large number of states Higher spin states are unambiguously determined Dudek, Edwards, Mathur, Richards, PRD 77, (2008) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

10 Baryon spectra: Attempting a chiral extrapolation Engel, Lang, DM, Schäfer, PRD (2013) mass [GeV] J P =1/2 + J P =3/2 + J P =1/2 + J P =3/ N Λ Σ Ξ Ω N Λ Σ Ξ Ω mass [GeV] N Λ Σ Ξ Λ Σ Ξ Ω 0 0 Positive parity ground states are reliably extracted Excited states are high compared to experiment No indications of multiparticle states Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

11 Baryon spectra: Attempting a chiral extrapolation Engel, Lang, DM, Schäfer, PRD (2013) mass [GeV] J P =1/2 - J P =3/2 - J P =1/2 - J P =3/ N Λ Σ Ξ Ω N Λ Σ Ξ Ω mass [GeV] Λ 0 0 Λ Overall negative parity spectrum matches experiment well I will discuss in detail: There are some hints of multiparticle states Results for the Λ(1405) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

12 Hybrid Baryons from Lattice QCD J.J. Dudek and R. G. Edwards, PRD (2012) Observed operator overlap suggests chromomagnetic gluonic excitations of J PC = 1 + Only a small mixing with regular 3-quark states is observed Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

13 Hybrid excitations: Associated mass scale J.J. Dudek and R. G. Edwards, PRD (2012) Hybrid mesons have been calculated in J. J. Dudek, PRD (2011) Findings suggest a common mechanism for mesons and baryons Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

14 Charmed baryons on flavor lattices Briceño, Lin, Bolton, PRD 86, (2012) Calculation of positive parity charmed baryon ground states Heavy quark action with non-perturbatively tuned coefficients Full chiral and continuum extrapolation Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

15 Charmed baryons on flavor lattices Poster by C. Kallidonis Preliminary results from ETMC M (GeV) ETMC N f=2 w / CSW ETMC N f=2+1+1 Liu et al. Na et al. Briceno et al. M (GeV) ETMC N f=2 w / CSW ETMC N f=2+1+1 Na et al. Briceno et al Λ c Σ c Ξ c Ξ ' c Ω c Ξ cc Ω cc 2.5 Σ* c Ξ* c Ω* c Ξ* cc Ω* cc Ω ccc Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

16 Energy levels for negative parity Nucleons Experiment: Two low-lying resonances N (1535) and N (1650) These couple to Nπ in S-wave (and to Nη, ΛK, Nππ) Example lattice data: Mahbub et al. PRD (2013) mass [GeV] N 1/ m π [GeV ] Engel et al. PRD (2013) Beware: different scale setting schemes Data from these groups agrees reasonably well Do Engel et al. see the Nπ scattering state at low m π? Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

17 Energy levels for negative parity Nucleons II Alexandrou, Korzec, Koutsou, Leontiou, arxiv: Twisted Mass (this work) Clover (this work) CSSM BGR Experiment: N (1535) S wave: +N J P = mn [GeV] m 2 [GeV] Beware: different scale setting schemes Results suggest some coupling to S-wave πn Extent might depend on interpolators, smearing,... Unambiguous identification of scattering levels needed! Adelaide group just gave an update: arxiv: Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

18 J P = The Roper resonance PDG: M = 1430(10)MeV Γ MeV Different experiments claim vastly different widths Recent lattice data: Most collaborations see no clear Roper candidate Twisted Mass (this work) Clover (this work) CSSM JLAB BGR Experiment J P = mn [GeV] m 2 [GeV] Alexandrou et al. arxiv: Mahbub et. al. PRD (2013) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

19 The Roper resonance II - a renewed controversy New data from χqcd, K. F. Liu private communication 3.5 J P = m N (GeV) Experiment BGR JLAB Twisted Mass Clover QCD CSSM m 2 (GeV 2 ) Uses one ensemble with m π 331MeV; a = 1.73GeV 1 Differences in used sources but hard to reconcile with other results Nπ (P-wave) and Nππ (S-wave) with m val = m sea at 1800 MeV Highlights the need to properly identify (shifted!) scattering levels Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

20 The Λ(1405) and the low-lying Λ baryon spectrum (1) Menadue et al., PRL (2012) (2) Engel, Lang, Schäfer, PRD (2013) Analysis features: (1) Λ(1405) at almost physical Pion and Kaon mass; 2+1 flavor (2) Spectrum of J P = 1 ± 2, 3 ± 2 Λ baryons; 2 flavor ensembles A chiral and infinite volume extrapolation is performed (1) and (2) extract excited states and study singlet-octet mixing Expected situation from Döring et al. EPJ A47, 163 (2011): PDG: M = ± Γ = 50 ± 2 Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

21 The low-lying Λ baryon spectrum: Results I Menadue et al. PRL (2012) mass [GeV] L ~ 2.2 fm L /2 + 1/2-3/2 + 3/2-1/2 + 1/2-3/2 + 3/ Engel et al. PRD (2013) The results on the Λ(1405) from both groups agree well The Λ(1405) level is predominantly a singlet state The 1st and 2nd excitation are almost pure octet (My) Hope for the future: Investigation including relevant scattering states Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

22 Low-Lying baryons: Flavor structure Edwards, Mathur, Richard, Wallace, PRD (2013) 2200 N Λ 8 Σ 8 Ξ Λ 1 Σ 10 Ξ 10 Ω E (MeV) 1900 E (MeV) Depicts the dominant flavor structure for each state Consistent with other results on the Λ(1405) Flavor structure also studied in Engel et al. PRD (2013) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

23 The Lüscher method for elastic scattering M. Lüscher Commun. Math. Phys. 105 (1986) 153; Nucl. Phys. B 354 (1991) 531; Nucl. Phys. B 364 (1991) 237. E = E(p 1 ) + E(p 2 ) E = E(p 1 ) + E(p 2 ) + E E n (L) (2) (3) δ l m R ; Γ R or coupling g (1) Extract energy levels E n (L) in a finite box (2) The Lüscher formula relates this spectrum to the phase shift of the continuum scattering amplitude (3) Extract resonance parameters with some degree of modeling/approximation Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

24 Meson-meson scattering and the Lüscher method This method has recently been applied to several meson-meson channels. For reviews see DM, PoS LATTICE2012 (2012) 003; S. Prelovsek, arxiv: ; Impressive results for the ρ meson at m π 400MeV Dudek, Edwards, Thomas PRD (2013) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

25 Alternative: Transition amplitude method McNeile, Michael, Pennanen, PRD (2002) Considers the decay H A + B with M H M A + M B Extracts information on the coupling g HAB by determination of the transition amplitude x =< H AB > from the correlators C H AB (t) = t 1 he m Ht 1 xe E AB(t t 1 ) b and C H H, C AB AB. Conditions: M H M A + M B xt 1 ; generically true for large L Advantages Cheaper (computationally) than the Lüscher method Also applicable for masses M H < M A + M B, M H M A + M B Potential issue: Excited state contributions suppressed only weakly Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

26 Pion Nucleon scattering in J P = 1 2 Lang and Verducci, PRD (2013) Puzzle: Do we extract an energy level related to the N (1535) or do we see the Nπ threshold? To address this: Combined basis of 3-quark and Nπ interpolators Simulation at M π = 266 MeV, m N = 1068 MeV on a 2-flavor sea Expected energy levels for a single resonance with Γ r = 150MeV: m Π 266 MeV m N 1068 MeV m N 1670 MeV E mn mn mπ L Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

27 Pion Nucleon scattering in J P = 1 2 II E[GeV] Exp. N N, Nπ - - Spectrum using just 3-quark interpolators can be misleading Pattern using combined basis is very similar to experiment At physical masses problem is inelastic much harder Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

28 g πn from the transition amplitude method Alexandrou, Negele, Petschlies, Strelchenko, Tsapalis PRD (2013) For δ = (E π + E N ) E the ratio is evaluated using R(t) = C πn (t) C (t)c πn πn (t) f 1 (t) = A + Ba sinh(δt/2) sinh(aδ/2) f 2 (t) = A + Bt + (Ct 3 ) The transition amplitude B is determined and translated to the coupling g πn Calculation at m π 360 MeV with spatial extent L = 3.6fm and lattice spacing a = 0.12fm Some Wick contractions for the πn System have been neglected This yields aδ = 0.106(16) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

29 The (1232) from Lattice QCD - results Alexandrou et al. PRD (2013) 0.45 fit lattice data R(t) t/a This translates to g lat πn = 27.0(0.6)(1.5) Model-independent K matrix analysis of experiment data g lat πn = 28.6(0.3) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

30 The (1232) from Lattice QCD - results M.Petschlies, private communication R(t) π N, fit lattice data Σ * - π Λ, R 1, q ~ (+1,0,0) R 1, q ~ (-1,0,0) t/a This translates to g lat Σ πλ = 21.5(0.7)(1.1) For physical values this is an inelastic channel (πλ and πσ) Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

31 Conclusions and Outlook There has been much progress in extracting excited state energy levels from 3-quark interpolators Modern dynamic calculations at light quark masses make it necessary to disentangle scattering states from resonances/ bound states There are tools to study resonances on the lattice Studies of resonances are in their infancy Hopefully existing puzzles can be resolved when taking into account the scattering thresholds There are indications from the meson-spectrum that inclusion of scattering states helps Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

32 Conclusions and Outlook There has been much progress in extracting excited state energy levels from 3-quark interpolators Modern dynamic calculations at light quark masses make it necessary to disentangle scattering states from resonances/ bound states There are tools to study resonances on the lattice Studies of resonances are in their infancy Hopefully existing puzzles can be resolved when taking into account the scattering thresholds There are indications from the meson-spectrum that inclusion of scattering states helps Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

33 ... Thank you! Particular thanks also to my collaborators Georg Engel and C. B. Lang Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

34 ... Backup Slides Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27

35 Triply charmed baryons Padmanath, Edwards, Mathur, Peardon, arxiv: Excited states up to J P = 7 ± 2 Definite Spin assignment Dudek, Edwards, Mathur, Richards, PRD 77, (2008) Single volume, lattice spacing at a single pion mass m - 3/2 m ηc (GeV) /2 + 3/2 + 5/2 + 7/2 + 1/2-3/2-5/2-7/2 - Daniel Mohler (Fermilab) Baryon Resonances from Lattice QCD Paphos, October / 27