understanding the strong interaction: lattice qcd & chiral extrapolation

Thomas Jefferson National Accelerator Facility

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy

Anthony W. Thomas

Understanding the Strong Interaction:Lattice QCD & Chiral Extrapolation

Workshop on Duality, FrascatiJune 6th , 2005



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



QCD and the Origin of Mass

HOW does the rest of the proton mass arise?



Advances in Lattice QCD

Precise computations at Physical Pion Mass

Actions with exact chiral symmetry

Advances in high-performance computing

Inclusion of Pion Cloud

From D. Richards



Leinweber, Signal et al.

Lattice QCD Simulation of Vacuum Structure



Formal Chiral Expansion

Formal expansion of Hadron mass:

MN = c0 + c2 m2 + cLNA m

3 + c4 m4

+ cNLNA m4 ln m + c6 m

6 + …..

Mass in chiral limit

No term linear in m

(in FULL QCD…… there is in QQCD)

First (hence “leading”)non-analytic term ~ mq

3/2

( LNA)Source: N ! N ! N

cLNA MODEL INDEPENDENT

Another branch cutfrom N ! ! N- higher order in m

- hence “next-to-leading” non-analytic (NLNA)

cNLNA MODEL INEPENDENT

Convergence?



Relevance for Lattice data

Knowing χ PT , fit with: α + β m2 + γ m

3 (dashed curve)

Problem: γ = - 0.76 c.f. model independent value -5.6 !!

Best fit with γ as in χ P T

( From: Leinweber et al., Phys. Rev., D61 (2000) 074502 )



The SolutionThere 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 ≥ 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



Lattice data fromCP-PACS & UKQCD

From: Leinweber et al., Phys. Rev., D61 (2000) 074502

Point ofinflection at opening of N channel

BUT how model dependent is the extrapolation to the physical point?

3M

2M

Behavior of Hadron Masses with m

»

»



Extrapolation of MassesAt “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 m2+ a4 m

4 + LNA(m ,Λ) + NLNA(m ,Λ)

• Evaluate self-energies with form factor , “finite range regulator”, FRR, with » 1/Size of Hadron



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



Power Counting Regime

Leinweber, Thomas & Young, hep-lat/0501028

Ensure coefficients c0 , c2 , c4 all identical to 0.8 GeV fit



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/0502002

By the way….



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) 034014



Early Fit to Lattice Data for μp and μnμp(n) = μ0 / (1 ± α / μ0 m

+ β m2 ) : 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)

(Leinweber et al., Phys. Rev. D60 (1999) 034014; /// Hemmert & Weise: nucl-th/0204005 and Pascalutsa, Holstein… 2004)

~ 1 / M (~ 1 / m2)

p

n



Strong Evidence for QQCD Chiral

Behaviour

New data Zanotti et al. (CSSM): 1 Teraflop, FLIC action (nucl-th/0308083)

proton

+

! N ! opposite Sign in QQCD



Not a Problem but a Bonus!

Hadronproperties

NC

3 1

‘t Hooft: extremely valuable constraints

mq

|

Physical regionmq » 5 MeV

-

Adds a third dimension to our knowledge of QCD



• 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

Towards a New Quark Model



•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

Chiral Extrapolation Connects CQM to Physical Data



Reconstruction of PDF versus xBjorkenNeed 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



Summary of Unitary Data Included in Fit



Self-Energy Contributions



FRR Mass well determined by data



Analysis of pQQCD data from CP PACS



2 Reduced by a Factor of 2



• 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?

Role of heavy flavors in the nucleon?

• Claim strange quarks ) >20% of Mp ?

• Spin crisis ) » 10% of spin of proton ?

• WHAT ABOUT THE MAGNETIC MOMENT OF THE PROTON?



target service vessel

beam line

magnet

detectors

G0 Experiment at Jefferson Lab



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

+ = 2/3 u – 1/3 s + O

- = -1/3 u -1/3 s + O

+ - - = u

(and p + 2n = dp + 3 ON )

HENCE: ON = 1/3 [ 2p + n - ( up / u ) (+ - -) ]

OR ON = 1/3 [ n + 2p – ( un / u ) (0 - -) ]

Just these ratios from Lattice QCD

CS



upvalence : QQCD Data Corrected

for Full QCD Chiral Coeff’s

New lattice data from Zanotti et al. ; Chiral analysis Leinweber et al.

c.f. CQM2/3 940/540

» 1.18

a0 + a2 m2 + a4 m

4 + ‘al loops



u valence

UniversalHere!



Convergence LNA to NLNAEffect of Decuplet



Leinweber et al., hep-lat/0406002

Check: Octet Magnetic Moments



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) -0.613 (4)

0 -1.16 (04) -1.26 (04) -1.28 (04) -1.25 (01)

- -0.65 (02) -0.68 (02) -0.70 (02) -0.651 (03)

up 1.66 (08) 1.85 (07) 1.85 (07) 1.81 (06)

u -0.51 (04) -0.58 (04) -0.58 (04) -0.60 (01)



Yields :GM s = -0.046 ± 0.019 µN

1.10±0.03

1.25±0.12

Leinweber et al., hep-lat/0406002

Accurate Final Result for GMs

Highly non-trivial that intersection lies on constraint line!



Yields :GM s = -0.046 ± 0.019 µN

1.10±0.03

1.25±0.12Leinweber et al., hep-lat/0406002

Accurate Final Result for GMs

Highly non-trivial that intersection lies on constraint line!

Precise new data expected from Happex and G0 (at Jlab) within 1-2 years

Direct lattice QCD computation of strange loop is CRUCIAL (& challenging)



Conclusions

• 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 , GM

s, <r2>ch , G E,G M, <x n>……..)

• Wonderful synergy between experimental advances at Jlab and progress using Lattice QCD to solve QCD



Special Mentions……

understanding the strong interaction: lattice qcd & chiral extrapolation

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