ab initio Hamiltonian approach to nuclear physics - Departamento

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					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
             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?
                                                            DOE investments:
                                                            ~60 cpu-centuries
                                                            during calendar „09

Jaguar               Franklin           Blue Gene/p                Atlas
Theory of strong interactions

                                    Big Bang
            EFT                & Stellar Reactions
Chiral Effective Field Theory

                                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

                NN: AV18, CD-Bonn, Nijmegen, . . .             Need
                                                           Improved NNN
                NNN: Tucson-Melbourne, UIX, IL7, . . .

               Chiral EFT (Idaho)                           Need
                                                    Fully derived/coded
 Consistent      NN: N3LO                                  N3LO
EW operators
                 NNN: N2LO
                 4N: predicted & needed for consistent N3LO

               Inverse Scattering                              Need
                  NN: JISP16                              Consistent NNN
                The Nuclear Many-Body Problem

  The many-body Schroedinger equation for bound states consists
of 2( Z ) 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)

             All work to preserve and exploit symmetries
     Extensions of each to scattering/reactions are well-underway
           They have different advantages and limitations
                       No Core Shell Model
             A large sparse matrix eigenvalue problem
                            H  Trel  VNN  V3N  
                            H i  E i i
                            i   An n

                                   n 0

                            Diagonalize     m H n 
•   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,mj,z)]
                              n  [a  a ]n 0
                              n 1,2,...,1010 or more!
•   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
  Experiment-Theory comparison

  RMS(Total E) 0.739 MeV (2%)
 RMS(Excit‟n E) 0.336 MeV (1%)

GTexp 2.161 vs GTthy 2.198(7) (2%)
HH+EFT*: Vaintraub, Barnea & Gazit,

        Solid - JISP16 (bare)
         Dotted - Extrap. B



      P. Maris, A. Shirokov and J.P. Vary, ArXiv 0911.2281
                   How good is ab initio theory
            for predicting large scale collective motion?

                            Quantum rotator

        J 2 J(J  1)   2
                                    20MeV
  EJ      
        2I       2I
     E4 20
              3.33
     E2     6
   Experiment  3.17
Theory(N max  10)  3.54

                                Dimension = 8x109
                    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

                                                                                     P. Navratil, V.G. Gueorguiev,
                                                                                     J. P. Vary, W. E. Ormand
                                                                                     and A. Nogga,
                                                                                     PRL 99, 042501(2007);
                                                                                     ArXiV: nucl-th 0701038.

Extensions and work in progress
•   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 0708.3754)
•   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, 063613(2007); ArXiv 0706.4123) 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)
      RMS Eabs (45 states) = 1.5 MeV
      RMS Eex (32 states) = 0.7 MeV
P. Maris, J.P. Vary and A. Shirokov, Phys. Rev. C. 79, 014308(2009), ArXiv:0808.3420
Descriptive Science

Predictive Science
                             Proton-Dripping Fluorine-14
  First principles quantum solution for yet-to-be-measured unstable nucleus 14F

 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 ~ 2x109
 Solution takes ~ 2.5 hours on 30,000 cores (Cray XT4 Jaguar at ORNL)


 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 0911.2281
  Ab initio Nuclear Structure

Ab initio Quantum Field Theory
               Light cone coordinates and generators

                                                          
M  P P0  P P1  (P  P )(P0  P )  P P  KE
  2    0            1        0

  Equal time

          Discretized Light Cone Quantization (c1985)

                   Basis Light Front Quantization

           x    f x a  f * x a 


          where a  satisfy usual (anti-) commutation rules.
          Furthermore, f x  are arbitrary except for conditions

          Orthonormal:               f x f x d x  

          Complete:                  f x f x'   x  x'
                                               *        3


     => Wide range of choices for f a x and our initial choice is

      f x  Ne     ik  x 
                                   n,m (, )  Ne     ik  x 
                                                                       f n,m ()  m ( )
      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, ArXiv:0905:1411
                                      knm   k x   f nm   
                                      APBC :  L  x   L
                                                   1 i  kx   

                                       k x       eL
                                      k  1 2 , n  1, m  0



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

 bi  B

 (m i  s i )  J z

 ki  K
i                               Finite basis regulators
 2ni  | m i | 1  N m ax

Global Color Singlets (QCD)
Light Front Gauge
Optional - Fock space cutoffs
         Hamiltonian for “cavity mode” QCD in the chiral limit

              Why interesting - cavity modes of AdS/QCD

H  H 0  H int
Massless partons in a 2D harmonic trap solved in basis functions
commensurate with the trap :
                 2M 0  1
H 0  2M 0 PC           2ni  | m i | 1
                   K i xi
with  defining the confining scale as well as the basis function scale.
Initially, we study this toy model of harmonically trapped partons in the
chiral limit on the light front. Note   Kxi  k i and BC' s will be specified.
    Nucleon radial excitations

j             M   EXP
                                 M BLFQ
              M   0              M BLFQ

1             1.53               2 1.41

2             1.82
                               3 1.73

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

      Solve the finite many- body problem:
      H i  E i i
      and form the density matrix
      (E)                  i   i
               i E i  E 

      Statistical Mechanical Observables:
      O 
      Tr  (E)  Total number of states in MCE E
      (E)   (E)
       (E)  Density of states at E
      S(E,V )  k ln((E))
      1 S           S       E 
             ; P  T  ; CV   
      T E           V E     T 
E       2ni  | mi | 1
   i   xi
   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 = Nmax
Distribution of multi-parton states by Fock-space sector


                         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
  Non-interacting QED cavity mode with zero net charge
               Photon distribution functions

                   Labels: Nmax = Kmax ~ Q

       “Weak” coupling:                                   “Strong” coupling:
Equal weight to low-lying states                       Equal weight to all 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, 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

                          Jun Li, PhD Thesis 2009, Iowa State University
Elementary vertices in LF gauge

      QED & QCD

    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
          Cavity mode QED          H. Honkanen, et al., to be published
          gQED= [4
          lepton & lepton-photon Fock space only
                                                                  k photon    m e

                                  Schwinger perturbative result

                                                    Next steps
                                      Increase basis space size
                                      Remove cavity
                                      Evaluate form factors
             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
               Collaborators on BLFQ
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

                     Thank You!

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