# Presentation: 664927

## Hadron Structure from Lattice QCD

**Hadron Structure from Lattice QCD**

-  DWF Valence on a Asqtad light sea
* ** *Nucleon Properties:
-  Form Factors
-  Momentum and Spin Fraction
-  GPDs
-  Pion Form Factor
-  Radiative transitions - Hybrid meson decays

- Robert Edwards
- Jefferson Lab

## LHP Collaboration

- Dru Renner* **University of Arizona*
- Richard Brower, James Osborn *Boston University*
- Rebecca Irwin, Michael Ramsey-Musolf *CalTech*
- Robert Edwards, David Richards *JLab*
- Bojan Bistrovic, Jonathan Bratt, Patrick Dreher, Oliver Jahn, John Negele, Kostas Orginos, Andrew Pochinsky, Dmitry Sigaev* **MIT*
- Matthias Burkardt, Michael Engelhardt  *New Mexico State University*
- George Fleming *Yale *
- Constantia Alexandrou, Antonios Tsapalis Cyprus, Wolfram Schroers *DESY**, *Philippe de Forcrand *EHT-Zurich*,* *Philipp Hägler *Vrije Universiteit*

## SciDAC Initiative

- DOE Scientific Discovery through Advanced Computing Initiative: develop software/hardware infrastructure for next generation computers
- U.S. Lattice QCD Collaboration consists of 64 senior scientists. Research closely coupled to DOE’s experimental program:
- Weak Decays of Strongly Interacting Particles
- Babar (SLAC)
- Tevatron B-Meson program (FNAL)
- CLEO-c program
- Quark-Gluon Plasma
- RHIC (BNL)
- Structure and Interactions of Hadrons
- Bates,  BNL,  FNAL,  JLab,  SLAC
- The JLab-MIT led LQCD Hadron Physics Collaboration includes 25 theorists from 14 institutions.
- Evolved into USQCD Collaboration

## Lattice QCD Hardware

- JLab SciDAC Clusters:
- 2002: 128 singles, 0.1 TFlops†
- 2003: 256 singles, 0.37 TFlops†
- 2004: 384 singles, 0.65 TFlops†
-      2005-9: more to come...
**First teraflops LQCD machine to achieve $1 per MFlops!**
**† ****Sustained performance on lattice QCD code**
- Other resources: BNL QCDOC and FNAL Cluster

## State of the Art

** ****Current resources enable us to begin exploiting these advances in full QCD**
** ****Employ computationally efficient full QCD lattices generated by MILC Collaboration using “staggered” fermions for sea quarks**
** ****Employ ****DWF**** for valence quarks**
** ****Pion masses down to less than 300 MeV to yield**
** ****Moments of GPD’s and PDF’s**
** ****Elastic form factors**
** ****Resonance spectrum of baryons and mesons**
** ****Approach requires introducing multiplicity of pions and approximation to fermion determinant**

**Next step:**** fully consistent treatment of chiral symmetry for both sea and valence quarks**

## Onward to light pion masses....

**Flavor-non-singlet momentum fraction in nucleon.**

**Detmold *****et al*****, PRL87, 172001 (2001**)

- Achievable precision limited by lightest pion mass

-  Exact chiral symmetry at Finite Spacing *a*
-  Domain-wall fermions (DWF)  in five dimensions

**Expt value**

## Partially Quenched Chiral Perturbation Theory

- Full QCD expensive!
- Leverage off cheap(er) valence calcs
- Correct low-energy constants, *in principle*
- Must be in domain of validity
- Extend partially quenched PT to include O(a) terms
- Mixed actions

- Bär, Rupak, Shoresh, 2002, 2003

## Hybrid Lattice Action

**Hybrid Lattice Action**

- MILC Asqtad lattices – staggered sea quarks
- Conventional DWF valence quarks (L5=16) computed on HYP-smeared lattices
- Parameter matching – tune DWF pion to match Asqtad Goldstone pion mass m
- a = 0.125 fm, two volumes at lightest pion mass

- PRD64, 034504

## “Decay” in Quenched Approximation

- Dramatic behavior in isotriplet scalar particle a0!intermediate state
- Loss of positivity of a0 propagator from missing bubble insertions
- Quenched a0 has double pole in PT
- Also appears in m0

- Bardeen, Duncan, Eichten, Thacker, 2000

## Partially Quenched Singularity 

- Non-positivity of a0 correlator
- (Partially) Quenched singularity (still) present at m, valencea = m, seaa
- Suggests not single *staggered* pion in chiral loops – taste breaking not neglible
- Need complete partial PT
- Vary valence and sea masses
- Theory under development...

## DIS and GPD’s for Nucleons

**DIS and GPD’s for Nucleons**

- Measures light-cone correlation functions

-  DIS gives diagonal matrix element

-   DVCS gives off-diagonal matrix element

## Moments of Structure Functions and GPD’s

**Moments of Structure Functions and GPD’s**

- Generates tower of twist-two operators
- Expand *O(x) *around light-cone
- Diagonal matrix element
- Off-diagonal matrix element

**p**

**q**

## Moments.....

- GPDs and GFFs are related through Mellin Transformation:
- Generalized Form Factors related to familiar quantities

## Renormalization of Operators

- One-loop renormalization of operators in boosted perturbation theory:

- HYP Constants close to unity

- B. Bistrovic, PhD Thesis, MIT 2005

## Anatomy of a Matrix Element Calculation

- Jf,iy : Current with desired quantum numbers of state A,B
- Normalize:
- Compute ratio:
- Need propagator from t ! tf

- Want |h 0|Jy|ni|2 » n,0 for best plateau

## Example plateau: gA 

- Time plot of current insertion:  Nucleon source, t=10,    nucleon sink, t=20

## Nucleon Isovector F1 (or A10) Form Factor

- Charge radii h r2ipch and h r2inch
- Dirac charge radius h r2iu-dch using *dipole ansatz* and  Q2 · 1 GeV2
- Chiral extrap. Using LNA and LA terms and finite-range regulator (PRL 86, 5011)
- Best fit:   1⁄4 740 MeV
- As the pion mass approaches the physical value, the size  approaches the correct value

## Nucleon Isovector F1 at Higher Q^2

- Breit frame at m 1⁄4 600 MeV
- Need more statistics as Q2 increases
- Both polarization transfer experiments and lattice data consistent with dipole *ansatz* up to 4 GeV2

## Nucleon Isovector F1 and F2

- F1

- F2

## Nucleon Axial Charge gA in a Finite Volume

- gA strongly suppressed by finite volume when  m L < 4
- hep-lat/0409161 (QCDSF), m = 717 MeV, curve is  LO  PT finite volume correction

## Axial Form Factor

- Axial charge: **g****A**** = ****h**** 1 ****i******** u - ******** d**** = ****Ã****u-d****10****(0)**

- Fu-dA(Q2)=Ãu-d10(Q2)

## Tensor Charge:  gT = h 1 i u- d = Au-dT 10(0)

## Momentum Fraction: h x iu-d = Au-d20(0)

## Polarized Momentum Fraction: h xi u -  d= Ãu-d20(0)

## Transverse Quark Distributions

**Transverse Quark Distributions**

- Higher moments An0 weight
-  x » 1
- Slope of An0 decreases as n increases
- Burkardt

## Pion Electromagnetic Form Factor: F(Q2) 

- Transition between perturbative and non-perturbative aspects of QCD
- Asymptotic normalization determined (?)
- Small Q2, vector-meson dominance provides faithful description
- Free of disconnected contributions – *straightforward lattice calculation*

## Pion Form Factor: Experimental Results

- Existing data fit VMD monopole formulae too well. Where’s perturbative QCD?
- Because of simple valence structure, argued that PQCD should apply to lower Q2 than other hadrons
- PQCD calc. far off.
- Experimental interpretation problematic – must extrapolate to the pion pole
- Use lattice QCD!

## Pion Form Factor –III

** ****Pion Form factor over Q****2**** commensurate with experiment**
** ****Pion GPDs and transition form factors**

## Rho!Pion Transition Form-Factor

- Electro-disintegration of deuteron intensively studied
- Isovector exchange currents identified
- Isoscalar exchange currents not clear
-  h (pf)|J|k(pi)i » 2 V(Q2) pf pI / (m+m)
- Extracted coupling rough agreement to expt
- Need higher Q2 to discern VMD
- First lattice calc!

- Maris-Tandy (2002)

## Photo-couplings and Transition FF: H !  M

- Photo-couplings between hybrid and conventional mesons need to be calculated!
- GlueX proposal to produce hybrid mesons using real photons supported by flux-tube model calculations
-  No suppression of conventional-hybrid photo-couplings for hybrids near 2 GeV

**Close and Dudek, PRL91, 142001 (2003); PRD 69 034010 (2004)**** **

** ****Investigate and attempt to verify prediction using **
**        ****lattice QCD**

## First tests:  V! S +   in Charmonium

- Many new techniques: test using conventional mesons
- Chiral fermions at charm scale – automatic O(a) improvement
- Quenched anisotropic lattices – as = 0.1fm, at = 0.033 fm
- Extraction of excited transition form-factors

- Time plateaus: C1

- E1

## First results:  V ! S +  in Charmonium

*****

**Dudek, Edwards, Richards, *****Lattice 2005***

**Lattice calculation of E****1**** transition form factor**
**Extrapolate using quark-model wavefunc**

##  V ! P +  in Charmonium

*****

**Dudek, Edwards, Richards, *****Lattice 2005***

**Lattice calculation of  ****V****!**** P**** transition form factor**
**Extrapolate using quark-model wavefunc**

- Q2 (GeV2)

- V(Q^2)

- exp

## Conclusions and Perspective

- Use of hybrid Asqtad/DWF calculation providing entry into pion-cloud regime for range of physical quantities – spectrum, nucleon and meson form factors and transition form factors, moments of PDF’s and GPD’s...
- Computations being extended both to smaller values of lattice spacing (a=0.9, 0.6 fm), and to lighter m  = 250 MeV – reveal effects of pion cloud.
- Disconnected diagrams, transition form factors...