Duality as Seen in Basis Light Front Quantization James P. Vary - PowerPoint PPT Presentation

Duality as Seen in Basis Light Front Quantization James P. Vary Iowa State University Ames, Iowa, USA Quark Hadron Duality Workshop: Probing the Transition from Free to Confined Quarks James Madison University September 23 – 25, 2018

Hot and/or dense quark-gluon matter Quark-gluon percolation QCD Resolution Hadron structure quark models Hadron-Nuclear interface ab initio Effective Field Theory CI Nuclear structure Nuclear reactions DFT Third Law of Progress in Theoretical collective Nuclear astrophysics Physics by Weinberg: and “ You may use any degrees of Applications of nuclear science freedom you like to describe a algebraic physical system, but if you use the models wrong ones, you’ll be sorry! ” Adapted from W. Nazarewicz

Sketch: hierarchy of strong interaction theories/scales/phenomena Effective Field Scale Range of Q Phenomena Theory QCD Chiral symmetry Q < m Planck Asymptotic freedom, pQCD restoration sQCD-Quark-Gluon Plasma Color glass condensate Hadron tomography, . . . Quark Clusters Chiral symmetry Q < (1 - 4) m N X > 1 staircase crossover transition EMC effect ~ (1 - 4) Λ QCD Q ~ m N Quark percolation ~ (1 - 4) m N Color conducting drops Deconfining fluctuations, . . Pionfull, Deltafull Chiral symmetry Q < m N Low-E Nucl. Struc/Reac’ns breaking 14 C anomalous lifetime Q ~ m π ~ Λ QCD ~ m N g A quenching Tetraneutron, . . . Pionless Chiral symmetry Q < m π ~ k F NN Scattering lengths breaking Stellar burning Q ~ 0.2 k F ~ Λ QCD ~ m N Halo nuclei Nuclear clusters, . . .

Effective Nucleon Interaction (Chiral Perturbation Theory) Chiral perturbation theory ( χ PT) allows for controlled power series expansion υ ⎛ ⎞ Expansion parameter : Q ⎜ ⎟ , Q − momentum transfer, ⎜ ⎟ Λ χ ⎝ ⎠ Λ χ ≈ 1 GeV , χ - symmetry breaking scale Within χ PT 2 π -NNN Low Energy Constants (LEC) are related to the NN-interaction LECs {c i }. C D C E Terms suggested within the Chiral Perturbation Theory Regularization is essential, which is also implicit within the Harmonic Oscillator (HO) wave function basis (see below) R. Machleidt and D.R. Entem, Phys. Rep. 503, 1 (2011); R. Machleidt, D. R. Entem, nucl-th/0503025 E. Epelbaum, H. Krebs, U.-G Meissner, Eur. Phys. J. A51, 53 (2015); Phys. Rev. Lett. 115, 122301 (2015)

Progressing to higher chiral order builds higher momentum components into the deuteron ground state wave function 2 ) Log 10 (| � gs LENPIC ( R = 1, �� = 20, N max = 120 ) Deuteron Ground State 10 1 4 k ( fm ) 1 2 3 10 - 1 Out[60]= Order 10 - 3 LO NLO N2LO 10 - 5 N3LO N4LO 10 - 7 Lesson : Physics at higher momentum scales (short distances) begins to have impact at higher order in the chiral EFT expansion R. Basili, W. Du, et al., in preparation

No-Core Configuration Interaction calculations Barrett, Navrátil, Vary, Ab initio no-core shell model , PPNP69, 131 (2013) Given a Hamiltonian operator p j ) 2 ( ⃗ p i − ⃗ ˆ � � � = + V ij + V ijk + . . . H 2 m A i<j i<j i<j<k solve the eigenvalue problem for wavefunction of A nucleons ˆ H Ψ ( r 1 , . . . , r A ) = λ Ψ ( r 1 , . . . , r A ) Expand wavefunction in basis states | Ψ ⟩ = � a i | Φ i ⟩ Expand eigenstates in basis states Diagonalize Hamiltonian matrix H ij = ⟨ Φ j | ˆ H | Φ i ⟩ No Core Full Configuration (NCFC) – All A nucleons treated equally No-Core CI: all A nucleons are treated the same Complete basis − → exact result In practice truncate basis study behavior of observables as function of truncation Progress in Ab Initio Techniques in Nuclear Physics, Feb. 2015, TRIUMF , Vancouver – p. 2/50

LENPIC NN + 3NFs at N 2 LO (arXiv: 1807.02848) -20 -120 + , 0) (0 + , 1) chiral EFT interaction with (0 + , 2) + , 0) (0 (1 semilocal regulator R = 1.0 fm -30 -140 + , 1) (2 - , 3/2) (3/2 -40 -160 Ground state energy (MeV) - , 1/2) (3/2 - , 1/2) -50 + , 0) (3/2 (0 -180 16 O + , 1) (0 + , 0) (3 -60 - , 1/2) (3/2 -70 p , T) (J + , 1) (1 2 LO 2 LO -80 LO, NLO, and N LO, NLO, and N 2 LO without 3N forces 2 LO without 3N forces N N + , 0) (0 -90 Expt. values Expt. values -100 7 Li 4 He 6 He 6 Li 8 He 8 Li 8 Be 9 Li 9 Be 10 Be 10 B 11 B 12 B 12 C

Is there a bridge between present-day chiral EFT and full QCD? Consider Light-front Hamiltonian approach to chiral Effec8ve Field Theory that is rela8vis8c and incorporates nucleon finite size effects. � Light-Front Wave Func8ons (LFWFs): 1. possess boost invariance 2. Provide access to experimental observables

Dirac’s forms of relativistic dynamics [Dirac, Rev. Mod. Phys. 21 , 392 1949] Dirac’s Forms of Relativistic Dynamics [Dirac, Rev.Mod.Phys. ’49] Instant form is the well-known form of dynamics starting with x 0 = t = 0 K i = M 0 i , J i = 12 ε ijk M jk , ε ijk = (+1,-1,0) for (cyclic, anti-cyclic, repeated) indeces Front form defines QCD on the light front (LF) x + , t + z = 0 . Front form defines relativistic dynamics on the light front (LF): x + = x 0 +x 3 = t+z = 0 P ± , P 0 ± P 3 , ~ P ⊥ , ( P 1 , P 2 ) , x ± , x 0 ± x 3 , ~ x ⊥ , ( x 1 , x 2 ) , E i = M + i , E + = M + − , F i = M − i , K i = M 0 i , J i = 1 2 ✏ ijk M jk . instant form front form point form x + , x 0 + x 3 √ t = x 0 ⌧ , time variable t 2 − ~ x 2 − a 2 quantization surface P − , P 0 − P 3 P µ H = P 0 Hamiltonian P, ~ ~ P ⊥ , P + , ~ ~ J, ~ ~ J − E ⊥ , E + , J z J K kinematical ~ ~ ~ F ⊥ , P − K, P 0 P, P 0 dynamical p 0 = p − = ( ~ p µ = mv µ ( v 2 = 1 ) dispersion p 2 + m 2 p p 2 ⊥ + m 2 ) /p + ~ relation Adapted from talk by Yang Li

Discretized Light Cone Quantization Pauli & Brodsky c1985 Basis Light Front Quantization* φ   *  + + f α [ ] ∑ ( ) = ( ) a α ( ) a α Operator-valued x f α x x distribution function α { } satisfy usual (anti-) commutation rules. where a α  ( ) are arbitrary except for conditions: Furthermore, f α x  *  ∫ ( ) f α ' ( ) d 3 x = δ αα ' Orthonormal: f α x x  *  = δ 3  x −  ∑ ( ) f α ( ) ( ) Complete: f α x x ' x ' α  ( ) => Wide range of choices for and our initial choice is f a x ik + x − Ψ n , m ( ρ , ϕ ) = Ne  ik + x − f n , m ( ρ ) χ m ( ϕ ) ( ) = Ne f α x *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=4 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

BLFQ Symmetries & Constraints All J ≥ J z states ∑ = B Baryon number b i in one calculation i ∑ = Q Charge q i i ∑ ( m i + s i ) = J z Angular momentum projection (M-scheme) i Finite basis k i ∑ ∑ = = 1 Longitudinal momentum (Bjorken sum rule) x i regulators K i i ∑ (2 n i + m i + 1) ≤ N max Transverse mode regulator (2D HO) i ∑ ≤ L Longitudinal mode regulator (Jacobi) l i i Global Color Singlets (QCD) Light Front Gauge Optional Fock-Space Truncation Preserve transverse H → H + λ H CM boost invariance Can we develop a fully relativitistic Chiral EFT?

G. A. Miller, Phys. Rev. C 56, 2789 (1997); Weijie Du, et al., in prepara8on By Legendre transforma8on, with the constraint equa8on Note this light front Hamiltonian density Now solve for the mass spectra and LFWFs in the proton sector 1. includes only the processes up to one pion absorp8on/emission; 2. is consistent with the results in G. A. Miller, Phys. Rev. C 56, 2789 (1997)

Weijie Du, et al., Preliminary results for the proton pion-nucleon in prepara8on scajering states emerge pion-nucleon threshold lowest mass eigenstate renormalized to experiment proton charge radius Fock sector probabili8es vs Nmax increases with N max 0.66 Bare proton (p) n+π + p+π 0

Now move to higher momentum scales, shorter distances, where the substructure of the mesons and baryons plays an essen8al role

Light Front (LF) Hamiltonian Defined by its Elementary Vertices in LF Gauge QED & QCD QCD

_ Effective Hamiltonian in the qq sector