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Understanding the Strong Interaction: Lattice QCD & Chiral Extrapolation. Anthony W. Thomas. Workshop on Duality, Frascati June 6 th , 2005. Outline. Quantum Chromodynamics within the Standard Model - PowerPoint PPT Presentation
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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
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
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
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
QCD and the Origin of Mass
HOW does the rest of the proton mass arise?
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
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
Thomas Jefferson National Accelerator Facility
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Leinweber, Signal et al.
Lattice QCD Simulation of Vacuum Structure
Thomas Jefferson National Accelerator Facility
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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?
Thomas Jefferson National Accelerator Facility
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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 )
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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
Thomas Jefferson National Accelerator Facility
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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
»
»
Thomas Jefferson National Accelerator Facility
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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
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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
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Power Counting Regime
Leinweber, Thomas & Young, hep-lat/0501028
Ensure coefficients c0 , c2 , c4 all identical to 0.8 GeV fit
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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….
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Thomas Jefferson National Accelerator Facility
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
Thomas Jefferson National Accelerator Facility
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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
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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
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Thomas Jefferson National Accelerator Facility
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
Thomas Jefferson National Accelerator Facility
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• 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
Thomas Jefferson National Accelerator Facility
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•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
Thomas Jefferson National Accelerator Facility
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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
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Thomas Jefferson National Accelerator Facility
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Summary of Unitary Data Included in Fit
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Self-Energy Contributions
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FRR Mass well determined by data
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Analysis of pQQCD data from CP PACS
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2 Reduced by a Factor of 2
Thomas Jefferson National Accelerator Facility
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• 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?
Thomas Jefferson National Accelerator Facility
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target service vessel
beam line
magnet
detectors
G0 Experiment at Jefferson Lab
Thomas Jefferson National Accelerator Facility
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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
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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
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u valence
UniversalHere!
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Convergence LNA to NLNAEffect of Decuplet
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Leinweber et al., hep-lat/0406002
Check: Octet Magnetic Moments
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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)
Thomas Jefferson National Accelerator Facility
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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!
Thomas Jefferson National Accelerator Facility
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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)
Thomas Jefferson National Accelerator Facility
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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
Thomas Jefferson National Accelerator Facility
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Special Mentions……
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility