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Hamiltonian Light Front Field Theory: Recent Progress and Tantalizing Prospects

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Hamiltonian Light Front Field Theory:

Recent Progress and Tantalizing Prospects

James P. Vary

Iowa State University

Light Cone 2011

Dallas, Texas

May 23 - 27, 2011

Fundamental theories, such as Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED)

promise great predictive power spanning phenomena on all scales from the microscopic to cosmic scales.

However, new non-perturbative tools are required to build bridges from one scale to the next. I will outline

recent theoretical and computational progress to build these bridges and provide illustrative results

for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches

that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries [1].

Regulating the theory with an external field that can be removed to obtain the continuum limit offers

additional advantages as we showed recently in an application to the anomalous magnetic moment

of the electron [2]. Recent progress capitalizes on algorithm and computer developments for setting up

and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 10 billion basis

states are now solved routinely in leadership-class computers for their low-lying eigenstates

and eigenfunctions.

This work was supported in part by US DOE Grant DE-FG02-87ER40371

[1] J. P. Vary, H. Honkanen, Jun Li, P. Maris, S. J. Brodsky, A. Harindranath, G. F. de Teramond,

P. Sternberg, E. G. Ng, C. Yang, “Hamiltonian light-front field theory in a basis function approach”,

Phys. Rev. C 81, 035205 (2010); arXiv nucl-th 0905.1411

[2] H. Honkanen, P. Maris, J. P. Vary and S. J. Brodsky, “Electron in a transverse harmonic cavity”,

Phys. Rev. Lett. 106, 061603 (2011); arXiv: 1008.0068

Ab initio nuclear physics - hierarchy of fundamental questions

- Can hadron structures and their interactions be derived from QCD?
- Can nuclei provide precision tests of the fundamental laws of nature?
- What controls nuclear saturation - 3-nucleon interactions?
- How does the nuclear shell model emerge from the underlying theory?
- What are the properties of nuclei with extreme neutron/proton ratios?

Blue Gene/p

Jaguar

Franklin/Hopper

Atlas

Nuclear

Structure

Bridging the nuclear physics scales

Applications in astrophysics,

defense, energy, and medicine

- D. Dean, JUSTIPEN Meeting, February 2009

http://extremecomputing.labworks.org/nuclearphysics/report.stmhttp://extremecomputing.labworks.org/nuclearphysics/report.stm

Effective Nucleon Interaction(Chiral Perturbation Theory)

Chiral perturbation theory (χPT) allows for controlled power series expansion

WithinχPT 2π-NNN Low Energy Constants (LEC) are related to the NN-interaction LECs {ci}.

CD

CE

Terms suggested within the

Chiral Perturbation Theory

Further renormalization is necessary

since momentum transfers still too high,

reaching ~ 0.6 GeV/c

R. Machleidt, D. R. Entem, nucl-th/0503025

A large sparse matrix eigenvalue problem

- Adopt realistic NN (and NNN) interaction(s) & renormalize as needed - retain induced many-body interactions: Chiral EFT interactions and JISP16
- Adopt the 3-D Harmonic Oscillator (HO) for the single-nucleon basis states, α, β,…
- Evaluate the nuclear Hamiltonian, H or renormalized Heff, in basis space of HO (Slater) determinants (manages the bookkeepping of anti-symmetrization)
- Diagonalize this sparse many-body H in its “m-scheme” basis where [α =(n,l,j,mj,τz)]
- Evaluate observables and compare with experiment

- Comments
- Straightforward but computationally demanding => new algorithms/computers
- Requires convergence assessments and extrapolation tools
- Achievable for nuclei up to A=16 (40) today with largest computers available

NOTE: No known limitations in principle on choice of

- Hamiltonian
- Basis space
- Renormalization scheme

Note additional predicted states!

Shown as dashed lines

P. Maris, P. Navratil, J. P. Vary, to be published

“Anomalous Long Lifetime of Carbon-14”

Objectives

Impact

3-nucleon forces suppress critical component

- Dimension of matrix solved for 8 lowest states ~ 1x109
- Solution takes ~ 6 hours on 215,000 cores on Cray XT5 Jaguar at ORNL
- “Scaling of ab initio nuclear physics calculations on multicore computer architectures," P. Maris, M. Sosonkina, J. P. Vary, E. G. Ng and C. Yang, 2010 Intern. Conf. on Computer Science, Procedia Computer Science 1, 97 (2010)

net decay rate

Is very small

- Solve the puzzle of the long but useful lifetime of 14C
- Determine the microscopic origin of the suppressed β-decay rate

- Establishes a major role for strong 3-nucleon forces in nuclei
- Verifies accuracy of ab initio microscopic nuclear theory
- Provides foundation for guiding DOE-supported experiments

Predictive Science

“Proton-Dripping Fluorine-14”

Objectives

Impact

P. Maris, A. Shirokov and J.P. Vary,

Phys. Rev. C 81 (2010) 021301(R)

- Dimension of matrix solved for 14 lowest states ~ 2x109
- Solution takes ~ 2.5 hours on 30,000 cores (Cray XT4 Jaguar at ORNL)
- “Scaling of ab-initio nuclear physics calculations on multicore computer architectures," P. Maris, M. Sosonkina, J. P. Vary, E. G. Ng and C. Yang, 2010 Intern. Conf. on Computer Science, Procedia Computer Science 1, 97 (2010)

Experiment confirms

our publishedpredictions!

V.Z. Goldberg et al.,

Phys. Lett. B 692, 307 (2010)

- Apply ab initio microscopic nuclear theory’s predictive power to major test case

- Deliver robust predictions important for improved energy sources
- Provide important guidance for DOE-supported experiments
- Compare with new experiment to improve theory of strong interactions

Recent noteworthy accomplishments of the

ab initio no core shell model (NCSM)

and no core full configuration (NCFC)

- Described the anomaly of the nearly vanishing quadrupole moment of 6Li
- Established need for NNN potentials to explain neutrino -12C cross sections
- Explained quenching of Gamow-Teller transitions (beta-decays) in light nuclei
- Obtained successful description of A=10-13 nuclei with chiral NN+NNN potentials
- Explained ground state spin of 10B by including chiral NNN potentials
- Developed/applied methods to extract phase shifts (J-matrix, external trap)
- Successful prediction of low-lying 14F spectrum (resonances) before experiment
- Explained the mystery of the anomalous long lifetime of 14C, useful for archeology

Some perspectives on Hamiltonian applications to LFQ

1+1 dimensional theories

DLCQ initiated many applications (Review: Brodsky, Pauli, Pinsky)

Spontaneous symmetry breaking (Chakrabarti, Martinovic, Harindranath,…)

Critical phenomena - e.g. kink condensation (Chakrabarti, …)

Zero modes, boundary conditions, regulators, …(Bassetto, McCartor,…)

QCD SU(3) color singlet structures (Hornbostel)

2+1 dimensional theories

QCD - Bloch and SRG Heff treatments (Chakrabarti, Harindranath)

3+1 dimensional theories

QED - LF wave equations (Hiller, Chabysheva, Brodsky, …)

QCD - Transverse lattice (Dalley, van de Sande, Chakrabarti,….)

SRG approach (Wilson, Glazek, Perry, … )

DIS - Q2 evolution (Zhang, Harindranath,…)

“Near” LFQ (Franke, Prokhvatilov, Paston, Pirner, Naus, Lenz, Moniz, .…)

Consistent quantization (D. Kulshreshtha, U. Kulshreshtha,…)

Renormalization/Reg’n (Ji, Bakker, Karmanov, Mathiot, Smirnov, Grange’, …)

DVCS (Brodsky, Mukherjee, Chakrabarti, …)

BLFQ (this talk)

QED - BLFQ approach (Zhao poster at this meeting)

Discretized Light Cone Quantization (c1985)

Basis Light Front Quantization*

Orthonormal:

Complete:

=> Wide range of choices for and our initial choice is

*J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond,

P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010). ArXiv:0905:1411

Set of transverse 2D HO modes for n=0

m=0

m=1

m=2

m=3

m=4

J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath,

G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010). ArXiv:0905:1411

- Enumerate Fock-space basis subject to symmetry constraints
- Evaluate/renormalize/store H in that basis
- Diagonalize (Lanczos)
- Iterate previous two steps for sector-dep. renormalization
- Evaluate observables using eigenvectors (LF amplitudes)
- Repeat previous 4 steps for new regulator(s)
- Extrapolate to infinite matrix limit – remove all regulators
- Compare with experiment or predict new experimental results

Above now achieved for QED test case – electron in a trap

H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky,

Phys. Rev. Lett. 106, 061603 (2011)

Improvements: trap independence, (m,e) renormalization, . . .

X. Zhao, P. Maris, J.P. Vary, S.J. Brodsky, poster at this meeting

Finite basis regulators

Non-interacting QED cavity mode with zero net charge

Photon distribution functions

Labels: Nmax = Kmax ~ Q

“Strong” coupling:

Equal weight to all states

“Weak” coupling:

Equal weight to low-lying states

J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath,

G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010). ArXiv:0905:1411

Comment based on Stan Glazek’s, Craig Roberts’

and Stan Brodsky’s presentations

Operator SRG (Glazek) appears to be a natural route

to obtain the effective (Q-dependent) qluon mass invoked

for the Dyson-Schwinger approach (Roberts)

If the “gluon condensate” indeed exists only within the

hadron and is representable by the gluon mean field,

as is consistent with LFQ approach,

then the mean field of the glue could be defined (derived?)

at a given Nmax ~ K ~ Q. We would then increase

the number of gluons until convergence is reached at

that scale Q.

That is, we adopt the scale Q as defining the border

between dynamical gluons and high momentum gluons

that define the gluon mean field.

For such calculations we initially retain one parameter

for the strength of the SRG mean field interaction Vmf

between pairs of constituent quarks and gluons.

**

*H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky, Phys. Rev. Lett. 106, 061603 (2011);

X. Zhao, H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky, poster at this meeting

** T. Heinzl, A. Ilderton and H. Marklund, Phys. Lett. B692, 250(2010); arXiv:1002.4018

Electron in a transverse

harmonic trap*

Invariant M2 spectra

*H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky,

Phys. Rev. Lett. 106, 061603 (2011);

X. Zhao, P. Maris, J.P. Vary, S.J. Brodsky,

poster at this meeting

Extended and Improved QED Calculations

- Xingbo Zhao, Heli Honkanen, Pieter Maris,
- James P. Vary and Stanley J. Brodsky – Poster Session
- Corrects some implementation errors
- Implements sector-dependent renormalization
- of mass and charge
- Decouples trap frequency from basis frequency
- to improve convergence
- Preliminary results lead to a puzzle in the electron
- anomalous magnetic moment => Spurious CM motion?
- 5. Working now on alternative setup with external
- field removed completely to verify Schwinger moment
- Stay tuned for the paper!

g-2 for Electron in Harmonic Trap

- δμ=(g-2)/2 vs. basis ω (at Ω=0.5MeV):
- δμ=(g-2)/2 vs. trap potential Ω:

Convergence reached at large ω or Nmax

δμ should be independent of the choice of basis in the limit of Nmax->∞

?

- Each point is the extrapolated result at Nmax->∞
- δμ decreases with the strength of trap potential
- Extrapolated value at Ω=0 larger than the result
- from perturbation theory
- Contribution from center-of-mass motion in
- truncated HO basis?
- Remove center-of-mass KE from Hamiltonian!

Derivation of all HQCD vertices in momentum

representation and HO basis spaces

(Harindranath, Honkanen, Zhao, Wiecki, Li)

Comprehensive notes under development (All)

Jun Li’s color singlet code transferred to Wiecki and is

undergoing verification tests.

Programming of additional QCD vertices under development

(Zhao, Wiecki, Li)

Commencing initial applications to quarkonia

Applications of LF amplitudes to experiment - DVCS

S.J. Brodsky, D. Chakrabarti, A. Harindranath, A. Mukherjee, and J.P. Vary,

Phys. Letts B641, 440 (2006); Phys. Rev. D75, 14003 (2007)

Hadron

Optics!

Key to graphs

x Bjorken variable

invariant longitudinal

impact parameter

invariant conjugate

longitudinal momentum

M++ Helicity non-flip DVCS amplitude

FS Fourier Spectrum

F2 DIS structure function

Applications of LF AdS/CFT amplitudes to experiment - DVCS

S.J. Brodsky, D. Chakrabarti, A. Harindranath, A. Mukherjee, and J.P. Vary,

Phys. Letts B641, 440 (2006); Phys. Rev. D75, 14003 (2007)

Ab initio approaches maximize predictive power

& represent a theoretical and computational physics challenge

Key issue

How to achieve the full physics potential of ab initio theory

Conclusions

We have entered an era of first principles, high precision,

many-body and quantum field theory for strongly interacting systems

Linking hadronic physics and the cosmos

through the Standard Model (and beyond) is well underway

and LFQ could play a leading role

Avaroth Harindranath, Saha Institute, Kolkota

Dipankar Chakarbarti, IIT, Kanpur

Asmita Mukherjee, IIT, Mumbai

Stan Brodsky, SLAC

Guy de Teramond, Costa Rica

Usha Kulshreshtha, Daya Kulshreshtha, University of Delhi

Xingbo Zhao, Pieter Maris, Jun Li, Paul Wiecki, Young Li

Heli Honkanen, University of Jyvaskyla

Esmond Ng, Chou Yang, Metin Aktulga, Philip Sternberg, Lawrence Berkeley Laboratory

Thank You!

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