hadron structure on the lattice - jefferson lab · pdf filehadron structure on the lattice...

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

First Know Thy SM: QCD

gluon field

quark field

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

§ Even just the vacuum of QCD is complicated

§ Direct QCD calculation is desired Lattice QCD

Difficulties at Low Energy

Classical QCD

010010101010 111010…

§ 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...

§ Computer power available for gaming in the 1980s:

§ Computer power available today:

§ Exciting progress during the last decade

§ 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

LQCD for Nuclear Physics

§ 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?

The Trouble with Nucleons

§ 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:

Noise falls as e− (3/2)mπ t

What you want: What you get:

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

HWL et al (HSC), 0911.3373

lΞ= mπ2 / 4mΞ

§ For example, single-baryon masses Lighter quark simulations require $$$

Extrapolations

a ≈ 0.123 fm

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

Work in progress...

Successful Examples

Charmed-Baryon Spectroscopy Raul Briceno, Huey-Wen Lin, Daniel Bolton Phys. Rev. D86 (2012), 094504

Successful Examples

Highly Excited States

2 3−

2 5−

Hybrid Baryons

Phys. Rev. D82, 014507 (2010)

Jozef Dudek, Robert Edwards, Phys. Rev. D85, 054016 (2012)

Properties of N*

§ 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

§ Structure function/distribution functions Deep inelastic scattering (DIS)

xnq, xnΔq, x

nδq , xng

Moments of Structure

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)

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

§ 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:

Hyak @ UW

7n @ JLab

Hopper @ NERSC

Sporades @ W&M

William Detmold (MIT)

HWL (U. of Washington)

Medium-Modification Project

§ We calculate

§ Contractions Examples from 3-π+ system

Pion Structure Function

§ We calculate

§ Wick contractions Use mixed-meson recursion relations

W. Detmold, B. Smigielski, Phys.Rev.D84:014508 (2011)

Treated as diff.

meson spices

§ We calculate

§ Wick contractions Examples from n-π+ system

§ Matrix elements extraction (naively)

§ xπ,N/x π,0 without thermal-state degrees of freedom tsep=T/2

Pion Momentum Fraction

pion medium

§ 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)

§ 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

Future Plans: Working on light nuclei

Form Factors § Structure function/distribution functions Deep inelastic scattering (DIS)

xnq, xnΔq, x

§ Form factors Elastic scattering

F1(Q2), F2(Q

2), GA(Q2), GP(Q2)

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

§ 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?

Higher-Q2 Form Factors

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

−log[C(t)/C(t+1)]

§ Solution: confront excited states directly and allow operators to couple to excited states

F1u−d F2

§ Phenomenological choice with dimensionless parameter

§ Nf = 2+1 anisotropic lattices, Mπ ≈ 450, 580, 875 MeV

High-Momentum Sources

HWL et al., arXiv: 1005.0799

§ 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

HWL, National Academies Press

Transverse Charge Density § Fourier transform using large-Q2 form factors to reveal

transverse charge densities in a polarized nucleon

§ 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)

§ Nf = 2+1 anisotropic lattices, Mπ ≈ 450, 580, 875 MeV

Nucleon Axial Form Factors

GAu−d(Q2)

Generalized Parton Distribution § Structure function/distribution functions Deep inelastic scattering (DIS)

xnq, xnΔq, x

§ 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

GA(Q2) = A~

10(Q2), GP(Q2) = B

10(Q2)

Nucleon spin A20(0), B20(0)

§ 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

GA(Q2) = A~

10(Q2), GP(Q2) = B

10(Q2)

Nucleon spin A20(0), B20(0)

Generalized Parton Distribution

§ 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

§ 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

Applications beyond QCD

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

LANSCE UCN

What You See/How You Look

LSM + LBSM

§ 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

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

T. Bhattacharya et al., Phys. Rev. D85 054512 (2012)

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

§ Tensor charge: the zeroth moment of the transversity gT = δu − δd

Experimentally, probed through SIDIS

(HERMES and COMPASS)

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

Including excited-states in the analysis is the way to go

In contrast, the single-state ansatz

Including excited-states in the analysis is the way to go

May still have an optimal tsep but won’t lose as much signal

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

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)

§ Given precision gS,T and OBSM, predict new-physics scales Nuclear Exp.

Model input

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

§ Given precision gS,T and OBSM, predict new-physics scales New UCN Exp.

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)

§ Given precision gS,T and OBSM, predict new-physics scales Precision LQCD input (mπ → 140 MeV, a→0)

New UCN Exp.

High-Energy Constraints

§ Constraints from high-energy experiments? LHC current bounds and near-term expectation

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

§ 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

Outlook

§ 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

hadron structure on the lattice - jefferson lab · pdf filehadron structure on the lattice...

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