hadron form factors at large momentum transfer from ... · lhpc, dirac ff rbc/ukqcd dirac ff lhpc,...
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Hadron Form Factors at Large Momentum Transfer
from Lattice QCD
Huey-Wen LinUniversity of Washington
1Huey-Wen Lin — Exclusive 2010
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Outline
§ Why Higher-Q2 form factors?Talks at this workshop: G. Huber, K. de Jager…
§ The tool = Lattice Gauge Theory
Ph. Hagler (Tue), B. Musch (Fri)
§ Lattice Form Factor Calculations What’s been done in the past What’s new in this talk Some results (nucleon and pion)
§ Summary and Outlook
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a
L
t
x, y, z
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Conventional Calculation
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LHPC, Dirac FF RBC/UKQCDDirac FF
LHPC, Q2Fπ
§ Higher-Q2 calculations suffer from poor noise-to-signal ratios
§ Challenge for lattice-QCD calculations Typical Q2 range for nucleon form factors is < 3.0 GeV2
Examples from 2+1f cases
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§ Problem: traditional approach Study hadron properties by looking at 2-point function
JNJN = ΣnJ|n n|Je−En t
Conventional Calculation
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t
0 t
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§ Problem: traditional approach Study hadron properties by looking at 2-point function
JNJN = ΣnJ|n n|Je−En t
Simplify to a one-state problem
Nucleon “effective mass”
Conventional Calculation
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t
0 t
−log[C(t)/C(t+1)]
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§ Problem: traditional approach Simplify to one-state problem
Conventional Calculation
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tsrc tsnk
t
3pt correlator
pi,f = (2π/L) ni,f a−1
q = pf −pi
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Example of Σ @ 600 MeV pion
§ Problem: traditional approach Simplify to one-state problem
Conventional Calculation
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tsrc tsnk
t
3pt correlator
pi,f = (2π/L) ni,f a−1
q = pf −pi
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§ Solution: confront excited states directly andallow operators to couple to excited states
§ Problem: traditional approach fails at large Q2
Conventional Calculation
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Actions§ Nf=2+1 anisotropic clover fermions
§ Renormalized anisotropy as/at=3.5§ Better resolution in temporal directionCorrelators have time-dependent form Ae−Et
§ as≈0.1227(8) fm (using mΩ) R. Edwards, B. Joo, HWL, Phys. Rev. D 78, 014505 (2008)
HWL et al., Phys. Rev. D 79, 034502 (2009)
2+1f : u/d + s
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x, y, z
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§ Nf = 2+1 anisotropic clover vacuum structure (Mπ ≈ 380 MeV)
Dynamical Anisotropic Lattices
http://www.phys.washington.edu/users/hwlin/visQCD.html
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§ Consider multiple-state 3pt correlators…
Form Factors
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Wanted
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§ “Variational method” for better determined Z’s and E’s
§ Consider multiple-state 3pt correlators…
Form Factors
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§ “Variational method” for better determined Z’s and E’s
§ n = n′ = 0 gives us nucleon
Matrix Element
and solve linear equations for form factors
§ Consider multiple-state 3pt correlators…
Form Factors
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Q2(GeV2)
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§ n = n′ = 0 gives us nucleon
ME
and solve linear equations
for form factors
§ The form factors are buried in the amplitudes
F2(0)
Consistency Checks
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GEp GM
p
GEn
GMn
(GeV2)HWL et al., arXiv: 1005.0799; HWL et al. [0810.5141]
Our Results§ Nf= 0 anisotropic lattices, Mπ≈ 480, 720, 1080 MeV
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(GeV2)HWL et al., arXiv: 1005.0799; HWL et al. [0810.5141]
§ Nf= 2+1 anisotropic lattices, Mπ≈ 450, 580, 875 MeV
GEp GM
p
GEn
GMn
Our Results
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F1u−d F2
u−d
§ Phenomenological choice with dimensionless parameter
§ Nf= 2+1 anisotropic lattices, Mπ≈ 450, 580, 875 MeV
Parametrization
HWL et al., arXiv: 1005.0799
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§ Infinite-momentum frame
§ How does high-Q2 affect charge density?
Red band uses
lattice data ≤ 2.0 GeV2
Blue band uses
lattice data ≤ 4.0 GeV2
HWL et al., arXiv: 1005.0799
G. A. Miller, arXiv: 1002.0355
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Transverse Charge Density
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Transverse Charge Density
HWL et al., arXiv: 1005.0799
Proton
§ Transverse charge density in infinite-momentum frameG. A. Miller, arXiv: 1002.0355
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by (f
m)
bx (fm)
b (fm)
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Neutron
Transverse Charge Density
HWL et al., arXiv: 1005.0799
b (fm)
§ Transverse charge density in infinite-momentum frameG. A. Miller, arXiv: 1002.0355
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by (f
m)
bx (fm)
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Transverse Magnetization Density
Magnetization density
Proton
§ Magnetization density in infinite-momentum frame
§ φ = π/2
G. A. Miller, arXiv: 1002.0355
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by (f
m)
bx (fm)
b (fm)
HWL et al., arXiv: 1005.0799
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Transverse Magnetization Density
Magnetization density
HWL et al., arXiv: 1005.0799
Neutron
§ Magnetization density in infinite-momentum frame
§ φ = π/2
G. A. Miller, arXiv: 1002.0355
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b (fm)
by (f
m)
bx (fm)
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§ Nf= 2+1 anisotropic lattices, Mπ≈ 450, 580, 875 MeV
Nucleon Axial Form Factors
Preliminary
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GAu−d(Q2)
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§ Nf= 2+1 anisotropic lattices, Mπ≈ 875, 1350 MeV
Pion Form Factors
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G.M. Huber et al., Phys.Rev.C78:045203,2008.
Preliminary
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§ Disconnected contribution O(10−2) for EM form factor Small for most of the form factors but
could be significant for neutron electric form factor
§ To get larger momentum, we use O(ap) ≈ 1Rome was not built in a day…
Methodology for improving a traditional lattice calculation
§ Possible future improvement Step-scaling through
multiple lattice spacings and volumes
Higher momentum transfer
Miscellany
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Exploratory study of large momentum transfer on the lattice
§ A Novel Strategy
Include operators that couple to high-momentum and excited states
Explicitly analyze excited states to get better ground-state signal
§ What We Show
Demonstrated results for heavier pions
Transverse densities
§ Future Work
Smaller src-snk separation for better signal
Extend to other hadrons or isotropic lattices
Multiple lattice spacings to study/reduce systematic error
Summary
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