Chiral extrapolation of lattice QCD results

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1 Chiral extrapolation of lattice QCD results Ross Young CSSM, University of Adelaide MENU 2010, May 31 June College of William & Mary Williamsburg, VA, USA

2 Nucleon couples strongly to pions in QCD Goldberger-Treiman relation [1958]: In the chiral limit g πnn = g AM N Accurate to ~3% at physical point f π GMOR: m 2 π m q g πnn 13.3 g A M N f π 12.9

3 Nucleon couples strongly to pions in QCD Goldberger-Treiman relation [1958]: In the chiral limit g πnn = g AM N Accurate to ~3% at physical point f π GMOR: m 2 π m q g πnn 13.3 g A M N f π 12.9 Field-theoretic consequences for nucleon structure π N

4 Nucleon couples strongly to pions in QCD Goldberger-Treiman relation [1958]: In the chiral limit g πnn = g AM N Accurate to ~3% at physical point f π GMOR: m 2 π m q g πnn 13.3 g A M N f π 12.9 Field-theoretic consequences for nucleon structure π Nucleon properties exhibit nonanalytic expansion about chiral limit N eg. M LNA N 3 32π g 2 A f 2 π m 3 π

5 Lattice QCD: Entering the chiral regime BMW, Science 322, 1224 (2008) * Multiple lattice spacing * Multiple volumes * Variant strange-quark mass runs * mpi ~ 190 MeV Empirical chiral extrapolation

6 Chiral extrapolation Statistical average over many different fits (432 total fits) * 3 pion mass ranges * 2 scale setting procedures r X = m X m Ξ * 2 pion mass extrapolation strategies

7 Chiral extrapolation Statistical average over many different fits (432 total fits) * 3 pion mass ranges * 2 scale setting procedures r X = m X m Ξ * 2 pion mass extrapolation strategies

8 Chiral extrapolation Statistical average over many different fits (432 total fits) * 3 pion mass ranges * 2 scale setting procedures r X = m X m Ξ * 2 pion mass extrapolation strategies

9 Chiral extrapolation Statistical average over many different fits (432 total fits) * 3 pion mass ranges * 2 scale setting procedures r X = m X m Ξ * 2 pion mass extrapolation strategies Chiral r N = r ref N + α N r 2 π + α N r 3 π + β N [ r 2 K (r ref K )2]

10 Chiral extrapolation Statistical average over many different fits (432 total fits) * 3 pion mass ranges * 2 scale setting procedures r X = m X m Ξ * 2 pion mass extrapolation strategies Chiral r N = r ref N + α N r 2 π + α N r 3 π + β N [ r 2 K (r ref K )2] Taylor r ref π r N = r ref N = 1 2 (rmax π + α N + r phys π ) [ r 2 π (r ref π ) 2] + α N [ r 2 π (r ref π ) 2] 2 + βn [ r 2 K (r ref K )2]

11 Chiral extrapolation Statistical average over many different fits (432 total fits) * 3 pion mass ranges * 2 scale setting procedures r X = m X m Ξ * 2 pion mass extrapolation strategies Chiral r N = r ref N + α N r 2 π + α N r 3 π + β N [ r 2 K (r ref K )2] Taylor r ref π r N = r ref N = 1 2 (rmax π + α N + r phys π ) [ r 2 π (r ref π ) 2] + α N [ r 2 π (r ref π ) 2] 2 + βn [ r 2 K (r ref K )2]

12 Chiral fit Expectation of QCD MN LNA 3 32π g 2 A f 2 π m 3 π ( 5.6 GeV 2 )m 3 π ( MN M Ξ ) LNA ( 5.4 GeV 2 )m 3 π Lightest cut on lattice results α N 4.5(3.2)(0.5) GeV 2

13 Chiral fit Expectation of QCD MN LNA 3 32π g 2 A f 2 π m 3 π ( 5.6 GeV 2 )m 3 π ( MN M Ξ ) LNA ( 5.4 GeV 2 )m 3 π LHPC, PRL(2006) Lightest cut on lattice results α N 4.5(3.2)(0.5) GeV 2

14 Statistical challenges 1.6 Baryon signal-to-noise degradation Signal Noise exp { (M N 3 } 2 m π)t NPLQCD MB GeV PACS-CS, PRD(2009) m Π 2 GeV 2

15 Statistical challenges 1.6 Baryon signal-to-noise degradation Signal Noise exp { (M N 3 } 2 m π)t NPLQCD Structure properties can be rapidly varying r 2 V 1 2 (4πf π ) 2 (5g2 A + 1) log m π µ MB GeV PACS-CS, PRD(2009) m Π 2 GeV 2 Zanotti, PoS(2008)

16 Chiral effective field theory offers a method to dramatically reduce statistical uncertainties Can correlate seemingly uncorrelated observables

17 SU(3) Chiral Expansion I heard that the SU(3) chiral expansion is bad for baryons... Consider octet baryon magnetic moments

18 SU(3) Chiral Expansion I heard that the SU(3) chiral expansion is bad for baryons... Consider octet baryon magnetic moments SU(3) symmetry: related by just 2 parameters Coleman & Glashow, PRL(1961)

19 SU(3) Chiral Expansion I heard that the SU(3) chiral expansion is bad for baryons... Consider octet baryon magnetic moments SU(3) symmetry: related by just 2 parameters Leading nonanalytic chiral corrections lessen agreement with experiment Coleman & Glashow, PRL(1961) Caldi & Pagels, PRD(1974)

20 SU(3) Chiral Expansion I heard that the SU(3) chiral expansion is bad for baryons... Consider octet baryon magnetic moments SU(3) symmetry: related by just 2 parameters Leading nonanalytic chiral corrections lessen agreement with experiment Covariant IR formalism: no improvement Coleman & Glashow, PRL(1961) Caldi & Pagels, PRD(1974) Kubis & Meissner, EPJC(2001)

21 SU(3) Chiral Expansion I heard that the SU(3) chiral expansion is bad for baryons... Consider octet baryon magnetic moments SU(3) symmetry: related by just 2 parameters Leading nonanalytic chiral corrections lessen agreement with experiment Covariant IR formalism: no improvement Long distance regularisation: perturbative loop corrections Coleman & Glashow, PRL(1961) Caldi & Pagels, PRD(1974) Kubis & Meissner, EPJC(2001) Donoghue et al., PRD(1999)

22 SU(3) Chiral Expansion I heard that the SU(3) chiral expansion is bad for baryons... Consider octet baryon magnetic moments SU(3) symmetry: related by just 2 parameters Leading nonanalytic chiral corrections lessen agreement with experiment Covariant IR formalism: no improvement Long distance regularisation: perturbative loop corrections Extended-on-mass-shell (EOMS): improved expansion Coleman & Glashow, PRL(1961) Caldi & Pagels, PRD(1974) Kubis & Meissner, EPJC(2001) Donoghue et al., PRD(1999) Geng et al., PRL(2008)

23 One loop correction Geng et al., PRL(2008) No loop: CG Evolve meson masses from 0 to physical

24 SU(3) for lattice QCD Fits to octet and decuplet baryon masses in EOMS w/expt. Martin-Camalich et al., arxiv:

25 Finite-range regularisation (FRR) Strange-quark 1.6 mass correction mb GeV Ξ Σ Λ m latt s 1.3m phys s Not included in fit Accurate prediction of heavier simulation data Reliable correction for lattice simulation quark mass 1.0 N Lattice Experiment Fit extrapolation Lattice: LHPC, PRD(2009) m Π 2 GeV 2 RDY & Thomas, PRD(2010)

26 PACS-CS fits PACS-CS: 2+1-flavour simulation; different action discretization to LHPC mb GeV Prediction of fit Ξ Σ Λ N Lattice Experiment Fit extrapolation PACS-CS, PRD(2009) Correction in strange quark mass demonstrated to be reliable against numerical simulation As for LHPC, excellent agreement with observed spectrum m Π 2 GeV 2 PACS-CS have an additional run with a different strange quark mass RDY & Thomas, PRD(2010)

27 Predict PACS-CS from LHPC 0.10 Fit LHPC Data PACS CS Data PACS CS m q 23.0 m q 15.6 m q 8.97 m q 8.32 m q 4.74 m s 1.41 m s 1.33 m s 1.35 m s 1.19 m s 1.33 Discretization errors appear at 1 2% level

28 Strange-quark mass dependence mb GeV Strange quark extrapolation at physical pion mass m K 2 GeV 2

29 Quantifying uncertainties Nucleon Mass (GeV) Source MeV LHPC PACS-CS Dipole Sharp Discretisation ± ± Extrapolated baryon masses and fit parameters (LECs) in agreement Regulator Small dependence on choice of regulator similarly for other functional forms (monopole, Gaussian) Statistical 23.6 Discretisation 4.2 Model 3.1 Regulator 2.1 f π F D C (5%) 0.7 (15%) 1.3 (15%) 1.3 (15%) (15%) 0.4

30 Baryon Sigma Terms σ Bq = m q M B M B m q σ Bl σ Bs N Λ Σ Ξ 0.050(9)(1)(3) 0.028(4)(1)(2) (27)(1)(17) (10)(0)(4) 0.033(16)(4)(2) 0.144(15)(10)(2) 0.187(15)(3)(4) 0.244(15)(12)(2) ΣNs GeV NK GL YT BM Σ Nl GeV GW Preliminary: for illustration TF πn Sigma Term (Expt): GL: Gasser & Leutwyler (1991) GW: Pavan et al. (2001) Octet Masses & Breaking: Gasser (1981) NK: Nelson & Kaplan (1987) BM: Borasoy & Meissner (1997) 3-flavour Lattice QCD: YT: Young & Thomas (2009) TF: Toussaint & Freeman (2009) We determine precisely both the light and strange quark sigma terms

31 Spin-independent neutralino cross sections Ellis, Olive & Savage, PRD(2008) * Constrained Minimal Supersymmetric Standard Model (CMSSM) * Neutralino as dark matter candidate * Scalar contact interaction σ p SI f p 2 L SI = i α 3i χχ q i q i f p M p = q=u,d,s f p TG =1 α 3q σ pq + 2 m q 27 f p TG q=u,d,s σ pq q=c,b,t α 3q m q Trace anomaly: Shifman, Vainstein & Zakharov, PLB(1978) Uncertainty dominated by knowledge of light-quark sigma terms

32 Updated cross sections for benchmark models Model C Ellis, Olive & Savage Strong dependence on sigma term from poorly known strangeness Giedt, Thomas & RDY, PRL(2009) Tremendous advance in precision from new lattice QCD results Nuclear physics & lattice QCD can help discriminate supersymmetry scenarios

33 Remarks Lattice calculations are reaching the physical pion mass as we speak Remains a strong need for chiral approaches to extract the most physics Expansions should not be limited by the worst way of formulating SU(3) can be used effectively for baryons