ab initio Hamiltonian approach to nuclear physics and to light-front field theory James P. Vary Iowa State University High Energy Physics in the LHC Era HEP-2010 Valparaiso, Chile January 4-8, 2010

Ab initio nuclear physics - fundamental questions  Can we develop a predictive theory from QCD to nuclear reactions  What controls nuclear saturation?  How does the nuclear shell model emerge from the underlying theory?  What are the properties of nuclei with extreme neutron/proton ratios?  Can nuclei provide precision tests of the fundamental laws of nature? JaguarFranklin Blue Gene/p Atlas DOE investments: ~60 cpu-centuries during calendar ‘09

QCD Theory of strong interactions  EFT Chiral Effective Field Theory Big Bang Nucleosynthesis & Stellar Reactions r,s processes & Supernovae

Fundamental Challenges for a Successful Theory  What is the Hamiltonian  How to renormalize in a Hamiltonian framework  How to solve for non-perturbative observables  How to take the continuum limit (IR -> 0, UV-> ) Focii of the both the Nuclear Many-Body and Light-Front QCD communities!

Realistic NN & NNN interactions High quality fits to 2- & 3- body data Meson-exchange NN: AV18, CD-Bonn, Nijmegen,... NNN: Tucson-Melbourne, UIX, IL7,... Chiral EFT (Idaho) NN: N3LO NNN: N2LO 4N: predicted & needed for consistent N3LO Inverse Scattering NN: JISP16 Need Improved NNN Need Fully derived/coded N3LO Need JISP40 Consistent NNN Need Consistent EW operators

The Nuclear Many-Body Problem The many-body Schroedinger equation for bound states consists of 2( ) coupled second-order differential equations in 3A coordinates using strong (NN & NNN) and electromagnetic interactions. Successful Ab initio quantum many-body approaches Stochastic approach in coordinate space Greens Function Monte Carlo (GFMC) Hamiltonian matrix in basis function space No Core Shell Model (NCSM) Cluster hierarchy in basis function space Coupled Cluster (CC) Comments All work to preserve and exploit symmetries Extensions of each to scattering/reactions are well-underway They have different advantages and limitations

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, , ,… Evaluate the nuclear Hamiltonian, H, 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 [  =(n,l,j,m j,  z )] 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 No Core Shell Model A large sparse matrix eigenvalue problem

Experiment-Theory comparison RMS(Total E) MeV (2%) RMS(Excit’n E) MeV (1%) GT exp vs GT thy 2.198(7) (2%) HH+EFT*: Vaintraub, Barnea & Gazit, PRC79,065501(2009);arXiv Solid - JISP16 (bare) Dotted - Extrap. B P. Maris, A. Shirokov and J.P. Vary, ArXiv ,0 3,0 0,1 2,0 2,1 1,0

How good is ab initio theory for predicting large scale collective motion? Quantum rotator 12 C Dimension = 8x10 9 E4E4 E2E2

ab initio NCSM with  EFT Interactions Only method capable to apply the  EFT NN+NNN interactions to all p-shell nuclei Importance of NNN interactions for describing nuclear structure and transition rates Better determination of the NNN force itself, feedback to  EFT (LLNL, OSU, MSU, TRIUMF) Implement Vlowk & SRG renormalizations (Bogner, Furnstahl, Maris, Perry, Schwenk & Vary, NPA 801, 21(2008); ArXiv ) Response to external fields - bridges to DFT/DME/EDF (SciDAC/UNEDF) - Axially symmetric quadratic external fields - in progress - Triaxial and spin-dependent external fields - planning process Cold trapped atoms (Stetcu, Barrett, van Kolck & Vary, PRA 76, (2007); ArXiv ) and applications to other fields of physics (e.g. quantum field theory) Effective interactions with a core (Lisetsky, Barrett, Navratil, Stetcu, Vary) Nuclear reactions & scattering (Forssen, Navratil, Quaglioni, Shirokov, Mazur, Vary) Extensions and work in progress P. Navratil, V.G. Gueorguiev, J. P. Vary, W. E. Ormand and A. Nogga, PRL 99, (2007); ArXiV: nucl-th

P. Maris, J.P. Vary and A. Shirokov, Phys. Rev. C. 79, (2009), ArXiv: RMS E abs (45 states) = 1.5 MeV RMS E ex (32 states) = 0.7 MeV

Descriptive Science Predictive Science

Proton-Dripping Fluorine-14 First principles quantum solution for yet-to-be-measured unstable nucleus 14 F  Apply ab initio microscopic nuclear theory’s predictive power to major test case  Robust predictions important for improved energy sources  Providing important guidance for DOE-supported experiments  Comparison with new experiment will improve theory of strong interactions  Dimension of matrix solved for 14 lowest states ~ 2x10 9  Solution takes ~ 2.5 hours on 30,000 cores (Cray XT4 Jaguar at ORNL) Predictions: Binding energy: 72 ± 4 MeV indicating that Fluorine-14 will emit (drip) one proton to produce more stable Oxygen-13. Predicted spectrum (Extrapolation B) for Fluorine-14 which is nearly identical with predicted spectrum of its “mirror” nucleus Boron-14. Experimental data exist only for Boron-14 (far right column). P. Maris, A. M. Shirokov and J. P. Vary, PRC, Rapid Comm., accepted, nucl-th

Ab initio Nuclear Structure Ab initio Quantum Field Theory

x0x0 x1x1 H=P 0 P1P1 Light cone coordinates and generators Equal time

Discretized Light Cone Quantization (c1985) Basis Light Front Quantization => Wide range of choices for and our initial choice is Orthonormal: Complete:

Set of transverse 2D HO modes for n=0 m=0m=1m=2 m=3m=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, ArXiv:0905:1411

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, ArXiv:0905:1411

Symmetries & Constraints Finite basis regulators

Hamiltonian for “cavity mode” QCD in the chiral limit Why interesting - cavity modes of AdS/QCD 

j Nucleon radial excitations

Quantum statistical mechanics of trapped systems in BLFQ: Microcanonical Ensemble (MCE) Develop along the following path: Select the trap shape (transverse 2D HO) Select the basis functions (BLFQ) Enumerate the many-parton basis in unperturbed energy order dictated by the trap - obeying all symmetries Count the number of states in each energy interval that corresponds to the experimental resolution = > state density Evaluate Entropy, Temperature, Pressure, Heat Capacity, Gibbs Free Energy, Helmholtz Free Energy,... Note: With interactions, we will remove the trap and examine mass spectra and other observables.

Microcanonical Ensemble (MCE) for Trapped Partons

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, ArXiv:0905:1411

Cavity mode QED with no net charge & K = N max Distribution of multi-parton states by Fock-space sector K=Nmax 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, ArXiv:0905:1411

“Weak” coupling: Equal weight to low-lying states “Strong” coupling: Equal weight to all states Non-interacting QED cavity mode with zero net charge Photon distribution functions Labels: N max = K max ~ Q 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, ArXiv:0905:1411

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, ArXiv:0905:1411

without color with color but no restriction with color and space-spin degeneracy Jun Li, PhD Thesis 2009, Iowa State University

QED & QCD QCD Elementary vertices in LF gauge

Renormalization in BLFQ => Analyze divergences  Are matrix elements finite - No => counterterms  Are eigenstates convergent as regulators removed? Examine behavior of off-diagonal matrix elements of the vertex for the spin-flip case: As a function of the 2D HO principal quantum number, n. Second order perturbation theory gives log divergence if such a matrix element goes as 1/Sqrt(n+1) 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, ArXiv:0905:1411

Next steps  Increase basis space size  Remove cavity  Evaluate form factors H. Honkanen, et al., to be published Cavity mode QED M 0 =m e =0.511 M j =1/2 g QED = [4   lepton & lepton-photon Fock space only Preliminary Schwinger perturbative result

QFT Application - Status  Progress in line with Ken Wilson’s advice = adopt MBT advances  Exact treatment of all symmetries is challenging but doable  Important progress in managing IR and UV cutoff dependences  Connections with results of AdS/QCD assist intuition  Advances in algorithms and computer technology crucial  First results with interaction terms in QED - anomalous moments  Community effort welcome to advance the field dramatically Collaborations - See Individual Slides

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 Pieter Maris, Jun Li, Heli Honkanen, Iowa State University Esmond Ng, Chou Yang, Philip Sternberg, Lawrence Berkeley National Laboratory Collaborators on BLFQ Thank You!