1. Workshop on Duality, Frascati
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. Advances in Lattice QCD
Inclusion of Pion Cloud
Actions with exact chiral symmetry
Precise computations at Physical Pion Mass
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 = c.f. model independent value -5.6 !!
( From: Leinweber et al., Phys. Rev., D61 (2000) )

8. The Solution There is another SCALE in the problem
- not natural in (e.g.) dim-regulated χPT
Λ ~ 1 / Size of Source of Goldstone Bosons ~ 400 – 500 MeV
IF Pion Compton wavelength is smaller than source… ( m ≥ 0.4 – 0.5 GeV ; mq ≥ 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) 3M
Point of
inflection
at opening
of N 
channel
Lattice data from CP-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:
( BUT must 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 when Coefficients Known – e. g
χ’al Extrapolation Under Control when Coefficients Known – e.g. for the nucleon
FRR give same
answer to <<1%
systematic error!
Leinweber et al., PRL 92 (2004)

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

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

14. Initial Study 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)

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 = ± 0.15 μN
(purely statistical errors) p
~ 1 / M (~ 1 / m2) n
(Leinweber et al., Phys. Rev. D60 (1999) ; /// Hemmert & Weise: nucl-th/ 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/ )

17. Not a Problem but a Bonus!
Hadron
properties
‘t Hooft: extremely
valuable constraints NC - |
Physical region
mq » 5 MeV 3 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)

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 NLNA Effect of Decuplet

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

34. State of the ART Magnetic Moments
QQCD
Valence
Full QCD
Expt. p
2.69 (16)
2.94 (15)
2.86 (15)
2.79 n
-1.72 (10)
-1.83 (10)
-1.91 (10)
-1.91 +
2.37 (11)
2.61 (10)
2.52 (10)
2.46 (10) -
-0.95 (05)
-1.08 (05)
-1.17 (05)
-1.16 (03) 
-0.57 (03)
-0.61 (03)
-0.63 (03)
(4) 0
-1.16 (04)
-1.26 (04)
-1.28 (04)
-1.25 (01) -
-0.65 (02)
-0.68 (02)
-0.70 (02)
(03) up
1.66 (08)
1.85 (07)
1.81 (06) u
-0.51 (04)
-0.58 (04)
-0.60 (01)

35. Leinweber et al., hep-lat/0406002
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 = ± µN
Leinweber et al., hep-lat/

36. Leinweber et al., hep-lat/0406002
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 = ± µN
1.25±0.12
Leinweber et al., hep-lat/
Direct lattice QCD computation of strange loop is CRUCIAL (& challenging)

37. Conclusions Inclusion of model independent constraints of  PT
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……