Understanding the Strong Interaction: Lattice QCD & Chiral Extrapolation

1. Understanding the Strong Interaction:Lattice QCD & Chiral Extrapolation Anthony W. Thomas Workshop on Duality, Frascati June 6th , 2005

2. Outline • Quantum Chromodynamics within the Standard Model • Lattice QCD : there are problems ) new opportunities!(and, by the way, some things CAN be calculated ACCURATELY) • MN , M , QQCD QCD pQQCD, M ; N , GMs • Modeling Hadron Structure • Tests of Physics Beyond the Standard Model

3. QCD and the Origin of Mass HOW does the rest of the proton mass arise?

4. Inclusion of Pion Cloud Precise computations at Physical Pion Mass Advances in Lattice QCD Actions with exact chiral symmetry Advances in high-performance computing From D. Richards

5. Lattice QCD Simulation of Vacuum Structure Leinweber, Signal et al.

6. Formal Chiral Expansion Formal expansion of Hadron mass: MN = c0 + c2 m2 + cLNA m3+ c4 m4 + cNLNA m4 ln m + c6 m6 + ….. • Another branch cut • from N!! N • higher order in m • hence “next-to-leading” • non-analytic (NLNA) • cNLNA MODEL INEPENDENT Mass in chiral limit First (hence “leading”) non-analytic term ~ mq3/2 (LNA) Source: N ! N ! N cLNA MODEL INDEPENDENT No term linear in m(in FULL QCD…… there is in QQCD) Convergence?

7. Relevance for Lattice data Knowing χ PT , fit with: α + β m2 + γ m3(dashed curve) Best fit with γ as in χ P T Problem: γ = - 0.76 c.f. model independent value -5.6 !! ( From: Leinweber et al., Phys. Rev., D61 (2000) 074502 )

8. The Solution There is another SCALE in the problem - not natural in (e.g.) dim-regulatedχPT Λ~ 1 / Size of Source of Goldstone Bosons ~ 400 – 500 MeV IF Pion Compton wavelength issmaller than source…..( m≥ 0.4 – 0.5 GeV ; mq ≥ 50-60 MeV)ALL hadron properties are smooth, slowly varying (with mq )and Constituent Quark like ! (Pion loops suppressed like (Λ / m)n ) WHERE EXPANSION FAILS: NEW, EFFECTIVE DEGREE OF FREEDOM TAKES OVER

9. Behavior of Hadron Masses with m From: Leinweber et al., Phys. Rev., D61 (2000) 074502 3M » Point of inflection at opening of N channel Lattice data fromCP-PACS & UKQCD 2M » BUT how model dependent is the extrapolation to the physical point?

10. Extrapolation of Masses At “large m” preserve observed linear (constituent-quark-like) behaviour: MH ~ m2 As m~ 0 : ensure LNA & NLNA behaviour: (BUTmust die as (Λ / m )2 for m> Λ) Hence use: MH = a0 + a2 m2+ a4 m4 + LNA(m ,Λ)+ NLNA(m,Λ) • Evaluate self-energies with form factor , “finite range regulator”, FRR, with » 1/Size of Hadron

11. χ’al Extrapolation Under Control whenCoefficients Known – e.g. for the nucleon FRR give same answer to <<1% systematic error! Leinweber et al., PRL 92 (2004) 242002

12. Power Counting Regime Ensure coefficients c0 , c2 , c4 all identical to 0.8 GeV fit Leinweber, Thomas & Young, hep-lat/0501028

13. Its NOT exp(- m L) that matters! By the way…. We must have m (L/2 – R)>>1 with R » 0.8 fm Thomas et al., hep-lat/0502002

14. InitialStudy 1998: Used Cloudy Bag Model • mq = 6 MeV at physical point • scales with m2 • CBM created in 1979 to restore chiral symmetry to MIT bag…. Leinweber, Lu & Thomas, Phys Rev D60 (1999) 034014

15. Early Fit to Lattice Data for μp and μn μp(n) = μ0 / (1 ± α / μ0 m+ β m2 ) : fit 0 and β to lattice data. Thus: μp = μ0 – α m + …… ; α = 4.4 μN -GeV-1 (from χ PT) At physical quark mass: μp = 2.85 ± 0.22 μN μn = -1.90 ± 0.15 μN (purely statistical errors) p ~ 1 / M (~ 1 / m2) n (Leinweber et al., Phys. Rev. D60 (1999) 034014; /// Hemmert & Weise: nucl-th/0204005 and Pascalutsa, Holstein… 2004)

16. Strong Evidence for QQCD Chiral Behaviour proton • ! N ! opposite Sign in QQCD + New data Zanotti et al. (CSSM): 1 Teraflop, FLIC action (nucl-th/0308083)

17. Not a Problem but a Bonus! Hadron properties ‘t Hooft: extremely valuable constraints NC - | 3 Physical region mq » 5 MeV 1 Adds a third dimension to our knowledge of QCD mq

18. Towards a New Quark Model • Traditionally Constituent Quark Models for light quarks OMIT effects of Goldstone boson loops! • OR assume they are included in effective parameters • Simply not tenable any longer ! • Pion loops:  MN» 300 MeV /// value for  M • LNA term in n: n =  m» 0.6 N is 1/3rd of physical n! • LNA term in <r2>p is » 1 fm 2 at mphys • LNA terms depend on hadron and can ONLY come from Goldstone loops

19. Chiral Extrapolation Connects CQM to Physical Data • Calculate CQM magnetic moments at M (strange) +/- 20 MeV (use exact SU(6) symmetry) • Use Pade approximant to extrapolate to physical quark mass Cloet et al., Phys. Rev. C65 (2002) 062201

20. Reconstruction of PDF versus xBjorken Need some phenomenology, take usual form: N x a ( 1 – x )b (1 + c √x + d x) Fit “N, a, b, d” to moments : m≥ 0.5 GeV:~ CQM Detmold, Melnitchouk & Thomas

22. Summary of Unitary Data Included in Fit

23. Self-Energy Contributions

24. FRR Mass well determined by data

25. Analysis of pQQCD  data from CP PACS

26. 2 Reduced by a Factor of 2

27. Role of heavy flavors in the nucleon? • Matter we see in the Universe is made of u and d quarks • Great interest in role of strangeness in dense matter • BUT what about “normal” hadrons?? A large “hidden strangeness” component in the proton? • Claim strange quarks ) >20% of Mp ? • Spin crisis )» 10% of spin of proton ? • WHAT ABOUT THE MAGNETIC MOMENT OF THE PROTON?

28. G0 Experiment at Jefferson Lab magnet beam line detectors target service vessel

29. Lattice View of Magnetic Moments with Charge Symmetry p = 2/3 up -1/3 dp + ON n = -1/3 up +2/3 dp + ON 2p +n = up +3 ON CS (and p + 2n = dp + 3 ON ) + = 2/3 u – 1/3 s + O - = -1/3 u -1/3 s + O + - - = u HENCE: ON = 1/3 [ 2p + n - ( up / u ) (+ - -) ] OR ON = 1/3 [ n + 2p – ( un / u ) (0 - -) ] Just these ratios from Lattice QCD

30. upvalence : QQCD Data Corrected for Full QCD Chiral Coeff’s a0 + a2 m2 + a4 m4 +  ‘al loops c.f. CQM 2/3 940/540 » 1.18 New lattice data from Zanotti et al. ; Chiral analysis Leinweber et al.

31. uvalence Universal Here!

32. Convergence LNA to NLNAEffect of Decuplet

33. Check: Octet Magnetic Moments Leinweber et al., hep-lat/0406002

34. State of the ART Magnetic Moments

35. Accurate Final Result for GMs Highly non-trivial that intersection lies on constraint line! 1.10±0.03 1.25±0.12 Yields :GM s = -0.046 ± 0.019 µN Leinweber et al., hep-lat/0406002

36. Accurate Final Result for GMs Precise new data expected from Happex and G0 (at Jlab) within 1-2 years Highly non-trivial that intersection lies on constraint line! 1.10±0.03 Yields :GM s = -0.046 ± 0.019 µN 1.25±0.12 Leinweber et al., hep-lat/0406002 Direct lattice QCD computation of strange loop is CRUCIAL (& challenging)

37. Conclusions • Wonderful synergy between experimental advances at • Jlab and progress using Lattice QCD to solve QCD • Study of hadron properties as function of mq using data from lattice QCD is extremely valuable….. • (major qualitative advance in understanding) • + TEST BEYOND STANDARD MODEL • Inclusion of model independent constraints of  PT • to get to physical quark mass is essential • FRR PT resolves problem of convergence • Insight enables: accurate, controlled extrapolation • of all hadronic observables…. • ( e.g. mH , H , GMs, <r2>ch , G E,G M, <x n>……..)

38. Special Mentions……