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Hadron Structure on the Lattice
Huey-Wen Lin University of Washington
Huey-Wen Lin — Jefferson Lab Seminar
Outline
§ Lattice gauge theory A brief introduction
§ Building a picture of hadrons Recent developments on
form factors, EMC effect, etc.
§ Applications beyond QCD Scalar and tensor contributions to neutron decays
Huey-Wen Lin — Jefferson Lab Seminar
Huey-Wen Lin — Jefferson Lab Seminar
First Know Thy SM: QCD
gluon field
quark field
a
L
t
x, y, z
αs(Q)
Strong Force and Lattice QCD § Quantum Chromodynamics (QCD) § The strong interactions of quarks and gluons (SU(3) gauge)
§ Lattice gauge theory
Huey-Wen Lin — Jefferson Lab Seminar
§ Even just the vacuum of QCD is complicated
§ Direct QCD calculation is desired Lattice QCD
Difficulties at Low Energy
Classical QCD
010010101010 111010…
Huey-Wen Lin — Jefferson Lab Seminar
§ Lattice gauge theory was proposed in the 1970s by Wilson Why haven’t we solved QCD yet?
§ Progress is limited by computational resources But assisted by advances in algorithms
It’s Straightforward, but...
Huey-Wen Lin — Jefferson Lab Seminar
§ Lattice gauge theory was proposed in the 1970s by Wilson Why haven’t we solved QCD yet?
§ Progress is limited by computational resources But assisted by advances in algorithms
§ Computer power available for gaming in the 1980s:
It’s Straightforward, but...
Huey-Wen Lin — Jefferson Lab Seminar
§ Lattice gauge theory was proposed in the 1970s by Wilson Why haven’t we solved QCD yet?
§ Progress is limited by computational resources But assisted by advances in algorithms
§ Computer power available today:
§ Exciting progress during the last decade
It’s Straightforward, but...
Huey-Wen Lin — Jefferson Lab Seminar
§ USQCD facilities: JLab, Fermilab, BNL
§ Non-lattice resources open to USQCD: ORNL, LLNL, ANL
§ NSF and worldwide increase in computer facilities
Computational Resources
XSEDE Kraken ALCF Mira
Huey-Wen Lin — Jefferson Lab Seminar
LQCD for Nuclear Physics
Huey-Wen Lin — Jefferson Lab Seminar
§ What is the spectrum of QCD? N* resonances and exotic mesons
§ What is the makeup of the nucleon? Quark, gluon and flavor-singlet sea-quark
contributions to nucleon structure
§ How does QCD bind (hyper)nuclei? Two- and three-body interactions
among baryons and mesons
Binding energy of an alpha particle
§ How do nature’s symmetries break? Why is there matter and not antimatter?
Advanced computing makes it possible!
Necessary when experiments are limited
§ From “quenched” to “dynamical” QCD vacuum
§ Gauge generation costs with the latest algorithms scale as Cost factor (estimation): a−(5–6), L5, Mπ
−(2–4)
§ Most major 2+1-flavor gauge ensembles: Mπ < 200 MeV Including ensembles at physical pion mass
§ Charm dynamics: 2+1+1-flavor gauge ensembles MILC (HISQ), ETMC (TMW)
§ Pion-mass extrapolation Mπ → (Mπ)phys
(Bonus products: Low-Energy Constants)
Are We There Yet?
Huey-Wen Lin — Jefferson Lab Seminar
The Trouble with Nucleons
Huey-Wen Lin — Jefferson Lab Seminar
§ Difficulties in Euclidean space § Exponentially worse signal-to-noise ratios Consider a baryon correlator C= O= qqq(t) q̄ q̄ q̄(0) Variance (noise squared) of C O†O− O2
Signal falls exponentially as e−mN t
What you want:
The Trouble with Nucleons
Huey-Wen Lin — Jefferson Lab Seminar
§ Difficulties in Euclidean space § Exponentially worse signal-to-noise ratios Consider a baryon correlator C= O= qqq(t) q̄ q̄ q̄(0) Variance (noise squared) of C O†O− O2
Signal falls exponentially as e−mN t
Noise falls as e− (3/2)mπ t
What you want: What you get:
The Trouble with Nucleons
Huey-Wen Lin — Jefferson Lab Seminar
§ Difficulties in Euclidean space § Exponentially worse signal-to-noise ratios Consider a baryon correlator C= O= qqq(t) q̄ q̄ q̄(0) Variance (noise squared) of C O†O− O2
Signal falls exponentially as e−mN t
Noise falls as e− (3/2)mπ t
Problem worsens with:
increasing baryon number
decreasing quark (pion) mass
What you want: What you get:
§ For example, single-baryon masses Lighter quark simulations require $$$
Extrapolations
a ≈ 0.123 fm
Huey-Wen Lin — Jefferson Lab Seminar
HWL et al (HSC), 0911.3373
lΞ= mπ2 / 4mΞ
2
§ For example, single-baryon masses Lighter quark simulations require $$$
Extrapolations
a ≈ 0.123 fm
Huey-Wen Lin — Jefferson Lab Seminar
HWL et al (HSC), 0911.3373
lΞ= mπ2 / 4mΞ
2 BMW Collaboration, Science (2008)
Mild lattice-spacing dependence
a≤ 0.125fm
§ Provide higher precision for known quantities
§ Make a lot of mass predictions
Work in progress...
Successful Examples
Huey-Wen Lin — Jefferson Lab Seminar
§ Provide higher precision for known quantities
§ Make a lot of mass predictions
Work in progress...
Successful Examples
Huey-Wen Lin — Jefferson Lab Seminar
Charmed-Baryon Spectroscopy Raul Briceno, Huey-Wen Lin, Daniel Bolton Phys. Rev. D86 (2012), 094504
§ Provide higher precision for known quantities
§ Make a lot of mass predictions
Successful Examples
Huey-Wen Lin — Jefferson Lab Seminar
Highly Excited States
1−
2 3+
2 5+
2 1+
2 3−
2 5−
2
Hybrid Baryons
M-M
N(M
eV)
Phys. Rev. D82, 014507 (2010)
Jozef Dudek, Robert Edwards, Phys. Rev. D85, 054016 (2012)
Properties of N*
Huey-Wen Lin — Jefferson Lab Seminar
§ For example, Roper-N transition form factors 2+1f anisotropic clover with Mπ ≈ 390, 450, 875 MeV (L = 3, 2.5, 2.5 fm)
HWL, 1108.2528; 1104.5072
Building a Picture of Hadrons
Huey-Wen Lin — Jefferson Lab Seminar
§ Structure function/distribution functions Deep inelastic scattering (DIS)
xnq, xnΔq, x
nδq , xng
Moments of Structure
Huey-Wen Lin — Jefferson Lab Seminar
Medium Modification § Parton structure function in nuclear medium
The famous EMC effect
Significant deviations between
heavy nuclei and deuterium
Many models:
pion enhancement
nucleon expansion
multiquark clusters
rescaling
shadowing
local correlations
…
§ No universal understanding
J. J. Aubert et al. Phys. Lett. 123, 275 (1983)
Huey-Wen Lin — Jefferson Lab Seminar
Medium Modification § Not only significant for heavy nuclei,
also important for light-nuclear systems J. Seely et al., Phys. Rev. Lett. 103, 202301 (2009)
Hall C E03-103
Huey-Wen Lin — Jefferson Lab Seminar
§ Interesting physics with multi-baryon systems Study with nonzero μB
notorious “sign” problem in Monte Carlo calculation
Add nucleons to the system
complicated quark contraction and noise/signal issue
Medium Modification
§ Take a step back and look at nonzero-isospin/multi-meson systems Many studies: “QCD at Finite Isospin Density”, Son & Stephanov
Gain insight and experience for how to deal with nuclear systems
Number of contractions: (A+Z)!× (2A−Z)! Triton: 2880 → 93
4He: 518400 → 1107
Signal Quality What you want: What you get:
Huey-Wen Lin — Jefferson Lab Seminar
Hyak @ UW
USQCD
7n @ JLab
Hopper @ NERSC
Sporades @ W&M
William Detmold (MIT)
HWL (U. of Washington)
Medium-Modification Project
Huey-Wen Lin — Jefferson Lab Seminar
§ We calculate
where
§ Contractions Examples from 3-π+ system
Pion Structure Function
Huey-Wen Lin — Jefferson Lab Seminar
§ We calculate
where
§ Wick contractions Use mixed-meson recursion relations
W. Detmold, B. Smigielski, Phys.Rev.D84:014508 (2011)
Pion Structure Function
Treated as diff.
meson spices
Huey-Wen Lin — Jefferson Lab Seminar
§ We calculate
where
§ Wick contractions Examples from n-π+ system
Pion Structure Function
§ Matrix elements extraction (naively)
,
Huey-Wen Lin — Jefferson Lab Seminar
§ xπ,N/x π,0 without thermal-state degrees of freedom tsep=T/2
Pion Momentum Fraction
pion medium
Huey-Wen Lin — Jefferson Lab Seminar
§ Significant for n-π+ system through amplitudes § For example, a=0.12 fm ensemble, T=64
Thermal Contamination
a = 0.12 fm, Mπ= 290 MeV, MπT = 11.6 a = 0.12 fm, Mπ= 490 MeV, MπT = 19.9
§ Matrix elements extraction for p=0 (in reality)
Huey-Wen Lin — Jefferson Lab Seminar
§ First lattice-QCD attempt to measure EMC effects Pion momentum fraction in pion medium
With mπ≈ 290–490 MeV, 2 lattice spacings
§ xπ,N/x π,0 with thermal-state degrees of freedom multiple tsep used
W. Detmold + HWL; and updated
Medium Modification
ρπ
Future Plans: Working on light nuclei
Huey-Wen Lin — Jefferson Lab Seminar
Form Factors § Structure function/distribution functions Deep inelastic scattering (DIS)
xnq, xnΔq, x
nδq
§ Form factors Elastic scattering
F1(Q2), F2(Q
2), GA(Q2), GP(Q2)
Huey-Wen Lin — Jefferson Lab Seminar
Higher-Q2 Form Factors
Q2 (GeV2 )
Recent progress on precision
data for proton up to
≈ 8.5 GeV2
Experimentally more
challenging for neutron
(more from JLab 12-GeV)
Little is known in the
axial form-factor channels
§ Higher-Q2 data will help us to understand hadrons and challenge QCD-based models
§ Electromagnetic probes are a common exp. approach
§ Nucleon form factors
Huey-Wen Lin — Jefferson Lab Seminar
§ At higher energies, perturbative QCD should work better
§ However, the range of validity is unclear…
§ For example, recent BaBar data for γ*γ→π0
Disagreement with pQCD
over a wide range:
4 GeV2 < Q2 < 40 GeV2
Nonperturbative QCD
will provide a direct test
Lattice QCD
Why Nonperturbative?
Huey-Wen Lin — Jefferson Lab Seminar
Higher-Q2 Form Factors
Huey-Wen Lin — Jefferson Lab Seminar
RBC/UKQCD Dirac FF LHPC, Q2 Fπ
§ Challenge for lattice-QCD calculations Typical Q2 range for nucleon form factors is < 3.0 GeV2
Higher-Q2 calculations suffer from poor noise-to-signal ratios
2+1 dynamical example:
§ Problem: traditional approach fails at large Q2
Simplify to a one-state problem JNJN = ΣnJ|n n|Je−En t
Nucleon “effective mass”
Source Selection
t
0 t
−log[C(t)/C(t+1)]
§ Solution: confront excited states directly and allow operators to couple to excited states
Huey-Wen Lin — Jefferson Lab Seminar
F1u−d F2
u−d
§ Phenomenological choice with dimensionless parameter
§ Nf = 2+1 anisotropic lattices, Mπ ≈ 450, 580, 875 MeV
High-Momentum Sources
HWL et al., arXiv: 1005.0799
Huey-Wen Lin — Jefferson Lab Seminar
§ 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
G. A. Miller, arXiv: 1002.0355
Transverse Charge Density
Huey-Wen Lin — Jefferson Lab Seminar
HWL, National Academies Press
Transverse Charge Density § Fourier transform using large-Q2 form factors to reveal
transverse charge densities in a polarized nucleon
Huey-Wen Lin — Jefferson Lab Seminar
§ Less is known about the pion form factor
New Proposal
Precision data up to ≈ 2.5 GeV2
Disagreement among model calculations at large Q2
Higher-Q2 Pion Form Factors
Q 2Fπ
Work in progress 12-GeV Project E12-06-101 (Huber and Gaskell)
Huey-Wen Lin — Jefferson Lab Seminar
§ Nf = 2+1 anisotropic lattices, Mπ ≈ 450, 580, 875 MeV
Nucleon Axial Form Factors
Huey-Wen Lin — Jefferson Lab Seminar
GAu−d(Q2)
Generalized Parton Distribution § Structure function/distribution functions Deep inelastic scattering (DIS)
xnq, xnΔq, x
nδq
§ Form factors Elastic scattering
F1(Q2), F2(Q
2), GA(Q2), GP(Q2)
§ Generalized Parton Distribution Deeply virtual Compton scattering (DVCS)
xn−1q = An0(0), xn−1Δq = A~
n0(0),
xnδq = ATn0(0)
F1(Q2) = A10(Q
2), F2(Q2) = B10(Q
2),
GA(Q2) = A~
10(Q2), GP(Q2) = B
~
10(Q2)
Nucleon spin A20(0), B20(0)
Huey-Wen Lin — Jefferson Lab Seminar
2)
§ Generalized Parton Distribution Deeply virtual Compton scattering (DVCS)
xn−1q = An0(0), xn−1Δq = A~
n0(0),
xnδq = ATn0(0)
F1(Q2) = A10(Q
2), F2(Q2) = B10(Q
2),
GA(Q2) = A~
10(Q2), GP(Q2) = B
~
10(Q2)
Nucleon spin A20(0), B20(0)
Generalized Parton Distribution
Huey-Wen Lin — Jefferson Lab Seminar
§ What is the makeup of the nucleon? The origin of the nucleon’s spin (the “spin crisis”)
For example, LHPC + QCDSF dynamical results
Mπ2 (GeV2)
Renormalized at 2 GeV
Origin of Proton Spin
ΔΣ: spin
L: orbital angular momentum
§ Ignore disconnected diagram § Gluon contribution estimated from sum rule
Huey-Wen Lin — Jefferson Lab Seminar
§ What is the makeup of the nucleon spin?
Origin of Proton Spin
§ Breakdown: ΔΣq= 50(2)%, Lq= 25(12)% (mostly DI), Jg= 25(8)%
§ Looking forward to χQCD (overlap/DWF), QCDSF (clover)
χQCD, 1203.6388 [hep-ph]
Mπ2 (GeV2)
Jtotal
Ju+d,CI
Jg
Ju/d
Js
Huey-Wen Lin — Jefferson Lab Seminar
Applications beyond QCD
Huey-Wen Lin — Jefferson Lab Seminar
Fermi Theory of Beta Decay § Four-fermion interaction explained beta decay before electroweak theory was proposed New operators in effective low-energy theories
§ Electroweak theory adds 3 vector bosons W and Z bosons directly detected later at CERN
~g2/Λ2
Λ≈mW≈ 80 GeV, mZ≈ 90 GeV
Huey-Wen Lin — Jefferson Lab Seminar
LHC
SLC
LANSCE UCN
What You See/How You Look
LSM + LBSM
LSM +
Huey-Wen Lin — Jefferson Lab Seminar
§ Neutron beta decay could be related to new interactions: the scalar and tensor
BSM Interactions
εS and εT are related to the masses of the new TeV-scale particles
… but the unknown coupling constants gS,T are needed
OBSM = fO(εS,T gS,T) Precision LQCD input
(mπ≈140 MeV, a→0)
εS,TΛS,T εS,TΛ−2
§ Given precision gS,T and OBSM, predict new-physics scales
Experiment
Huey-Wen Lin — Jefferson Lab Seminar
εS and εT Gives the scale of particles
mediating new forces
With exp’t precision of
|B1− b|BSM < 10−3
|b|BSM < 10−3
b = fb (εS,T gS,T) B1 = fB (εS,T gS,T)
UCNs by 2013 Precision LQCD input
(mπ≈140 MeV, a→0)
Physics Program § Given precision gS,T and b, B1,
we can predict possible new particles
Huey-Wen Lin — Jefferson Lab Seminar
T. Bhattacharya et al., Phys. Rev. D85 054512 (2012)
PNDME
Tanmoy Bhattacharya
Rajan Gupta HWL (PI)
Saul Cohen Anosh Joseph
Precision Neutron-Decay Matrix Elements (2011–) http://www.phys.washington.edu/users/hwlin/pndme/index.xhtml
Nf = 2+1+1
Lightest pion mass 220 MeV
amin = 0.06 fm
Physical pion mass planned
Huey-Wen Lin — Jefferson Lab Seminar
§ Tensor charge: the zeroth moment of the transversity gT = δu − δd
Experimentally, probed through SIDIS
(HERMES and COMPASS)
Huey-Wen Lin — Jefferson Lab Seminar
x
Model-dependent extractions
Combined with other experiments
M. Anselmino et al., Phys. Rev. D75, 054032 (2007)
gT(Q2=0.8 GeV2)=0.77+0.18 gT(Q2=0.8 GeV2)=0.77−0.24
Tensor and Scalar Charges
§ Trade off: signal-to-noise versus contamination Noise issue (P. Lepage; D. Kaplan)
Consider a baryon correlator C= O= qqq(t) q̄ q̄ q̄(0) Variance (noise squared) of C O†O− O2
Excited-State Contamination
What you want: What you get: Signal falls exponentially as
e−mNt
Noise falls as e−(3/2)mπ t
§ Difficulties in Euclidean space True ground state (nucleon in this case) at large Euclidean time
Huey-Wen Lin — Jefferson Lab Seminar
Excited-State Contamination
Including excited-states in the analysis is the way to go
In contrast, the single-state ansatz
Huey-Wen Lin — Jefferson Lab Seminar
Excited-State Contamination
Including excited-states in the analysis is the way to go
May still have an optimal tsep but won’t lose as much signal
Huey-Wen Lin — Jefferson Lab Seminar
gTLQCD=0.988(42)(?)
Tensor and Scalar Charges § Tensor charge: the zeroth moment of the transversity gT = δu−δd Experimentally, probed through SIDIS:
Model estimate: 0.8(4)
§ Scalar charge n|u−d|p Prior model estimate: 1gS0.25
gSLQCD=0.761(88)(?)
gT(Q2=0.8 GeV2)=0.77+0.18 gT(Q2=0.8 GeV2)=0.77−0.24
Huey-Wen Lin — Jefferson Lab Seminar
Combined with Experiments
Nuclear beta decays
0+ 0+ transitions
β asym in Gamow-Teller 60Co
polarization ratio between
Fermi and GT in 114In
positron polarization in
polarized 107In
β-ν correlation parameter a
OBSM = fO(εS,T gS,T)
εS,TΛS,T εS,TΛ−2
§ Given precision gS,T and OBSM, predict new-physics scales Nuclear Exp.
Model input
Huey-Wen Lin — Jefferson Lab Seminar
Combined with Experiments
LANL UCN neutron decay exp’t
Expect by 2013:
|B1− b|BSM < 10−3
|b|BSM < 10−3
Similar proposal at ORNL by 2015
OBSM = fO(εS,T gS,T) Model input
εS,TΛS,T εS,TΛ−2
§ Given precision gS,T and OBSM, predict new-physics scales New UCN Exp.
Huey-Wen Lin — Jefferson Lab Seminar
Combined with Experiments
LANL UCN neutron decay exp’t
Expect by 2013:
|B1− b|BSM < 10−3
|b|BSM < 10−3
Similar proposal at ORNL by 2015
OBSM = fO(εS,T gS,T)
εS,TΛS,T εS,TΛ−2
§ Given precision gS,T and OBSM, predict new-physics scales Precision LQCD input (mπ → 140 MeV, a→0)
New UCN Exp.
Huey-Wen Lin — Jefferson Lab Seminar
High-Energy Constraints
§ Constraints from high-energy experiments? LHC current bounds and near-term expectation
εS,TΛS,T εS,TΛ−2
Estimated though effective L
Looking at high transverse mass
in e ν + X channel
Compare with W background
Estimated 90% C.L. constraints on
HWL, 1112.2435; 1109.2542 T. Bhattacharya et al, 1110.6448
Huey-Wen Lin — Jefferson Lab Seminar
§ LQCD is building a picture of hadrons Revealed proton spin components, transverse distribution
New techniques for gluonic, disconnected and in-medium quantities
shine new light for more calculations
§ Applications of LQCD to probe beyond the Standard Model Opportunities combining high- (TeV) and low- (GeV) energies
Vital input when experiment is limited (e.g. gS)
§ Aim at high precision and understand/quote systematics!
Summary Exciting time to explore
Huey-Wen Lin — Jefferson Lab Seminar
Outlook
§ Welcome more ideas and discussions
Huey-Wen Lin — Jefferson Lab Seminar
§ Welcome more ideas and discussions
A wide variety of experiments of this type, including improved measurements of neutron beta decay, as well as searches for proton decay, neutron-antineutron oscillations, dark matter, and permanent electric dipole moments (EDMs) would benefit from
a renewed look at the QCD inputs required to set limits on models of BSM physics. Our plan is to collect a group of phenomenologists, lattice gauge theorists and a few key experimentalists, to discuss the constraints on theories probed by the experiments we consider and the manner in which these constraints are entwined with QCD physics, both perturbative and nonperturbative.
Outlook
Huey-Wen Lin — Jefferson Lab Seminar