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Nucleon Axial and Nucleon-to-Delta Axial Transition Form Factors from Lattice QCD

Nucleon Axial and Nucleon-to-Delta Axial Transition Form Factors from Lattice QCD. A. Tsapalis Institute of Accelerating Systems and Applications University of Athens. in collaboration with C. Alexandrou (Univ. of Cyprus) G. Koutsou (Univ. of Cyprus) Th. Leontiou (Univ. of Cyprus)

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Nucleon Axial and Nucleon-to-Delta Axial Transition Form Factors from Lattice QCD

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  1. Nucleon Axial and Nucleon-to-Delta Axial Transition Form Factors from Lattice QCD A. Tsapalis Institute of Accelerating Systems and Applications University of Athens in collaboration with C. Alexandrou (Univ. of Cyprus) G. Koutsou (Univ. of Cyprus) Th. Leontiou (Univ. of Cyprus) J. W. Negele (MIT)

  2. outline • Nucleon Axial Form Factors GA and GP • PCAC and pion pole dominance • Nucleon-to-Delta Axial Transition FFs • Lattice Evaluation of the FFs • Results – Checking the Pion Pole dominance & Goldberger-Treiman (GT) relations in N-N & N-Δ • Conclusions arXiv:0706.3011, to appear in PRD

  3. Nucleon Axial Form Factors axial isovector current axial vector form factor induced pseudoscalar axial charge GA (0) = 1.2695 (29) from nuclear β decay GA (q2) – from neutrino scattering & pion electroproduction GP (q2) – from muon capture experiments • theoretically studied in chiral effective theories • pioneering lattice study in PRL 74 2172 (1995) (K.F. Liu, S.J. Dong, T. Draper, W. Wilcox) • recent study by LHPC+MILC , arXiv:0705.4295

  4. Pseudoscalar Form Factor & PCAC PCAC in hadron world Axial WT identity in QCD pseudoscalar current πΝΝ form factor defined via connected to πΝΝ strong coupling constant gπΝΝ= GπΝΝ(mπ2) PCAC

  5. Pion Pole dominance & GT relations Pion pole on RHS constraints the induced pseudoscalar and leads to Goldberger-Treiman relation at q2 = 0 satisfy to 5% accuracy also fixes the ratio from low energy πΝΝ dynamics

  6. Nucleonto Δ(1232) Axial Transition Form Factors Adler parameterization transverse part dominant FFs small ≈ 0 C5Aanalogous to GA (q2) C6Aanalogous to GP (q2) • not much known experimentally • electroproduction experiments at JLab will measure N to Δ parity violating asymmetry connected to C5A • theoretical arguments indicate that C3A, C4A are small

  7. Lattice study in PRL 98,052003 (2006) established smallness of C3A and C4A , predicted q2 dependence of dominant form factors C5A and C6A

  8. Pseudoscalar πΝΔ Form Factor & PCAC πΝΔ form factor defined via connected to πΝΔ strong coupling constant gπΝΔ= GπΝΔ(mπ2) PCAC Non-diagonal Goldberger-Treiman relation Pion pole dominance relates: ..and fixes the ratio

  9. X kinematics: Evaluating Form Factors from Lattice QCD • measure 3-point-functions of axial & pseudoscalar currents • form ratios where t- and Z- dependence cancels • determine the optimal linear combination of 3pts maximal number of momentum vectors contributein rotationally symmetric fashion

  10. X • all operators and momenta measured at small cost optimizing the measurement • sequential inversions through the sink • look for plateau in t1 / Smear source & sink quarks to damp • fast the excited states • only one sequential inversion for GA(Q2), GP(Q2), GπNN(Q2) • simultaneous overconstrained analysis of all data maximal accuracy for the form factors – Q2 dependence

  11. Lattice parameters Wilson NF = 0β=6.0 323x64 a=0.09 fm mπ = 0.56 GeV mπ = 0.49 GeV mπ = 0.41 GeV Wilson NF = 2β=5.6 a=0.08 fm 243x40 mπ = 0.69 GeV (TXL) 243x40 mπ = 0.51 GeV (TXL) 243x32 mπ = 0.38 GeV (DESY) Nucleon Axial Hybrid scheme MILC NF = 2 + 1 Domain Wall valence (L5=16) a=0.125 fm ams amu mπ + N-to-Δ Axial 0.05 0.030.59GeV 203x64 0.05 0.02 0.50 GeV 203x64 0.05 0.01 0.36 GeV 283x64

  12. Checking the parameters Volume (2.5fm)3 vs (3.5fm)3 Ground state dominance source-sink distance 11a vs 13a C5A(Q2), C6A(Q2), GπNΔ(Q2) plateaus for GπΝΝ GA(Q2), GP(Q2), GπNN(Q2) WilsonNF=0, 323x64, mπ=0.49 GeV NF=2, 243x40, mπ=0.69 GeV WilsonNF=0, 323x64, mπ=0.41GeV MILC(DWF)0.01/0.05, mπ=0.36 GeV 203x64 vs 283x64,

  13. Results (I) – Nucleon Axial Form Factors • dipole fit describes well GA mA >=1.5 GeV (solid / fit) mA=1.1 GeV (dotted / exp) • pion pole dominates Gp (dash) monopole fit (solid) Hybrid results from 0705.4295 LHPC & MILC (Hägler etal)

  14. Results (II) – N to Δ Axial Transition FFs • dipole fit describes well CA5 mA >=1.5 GeV (solid / fit) mA=1.28 GeV (dotted / exp) • pion pole dominates CA6 (dash: wilson) (dot: MILC) monopole fit (solid)

  15. Results (III) – Checking Ratios of GT relations pion pole dominance renormalization constants, fπ, mq cancel 1.63(1) 1.73(3) 1.60(2) weak Q2 and mq dependence

  16. Conclusions • momentum dependence of the NN & NΔ axial form factors is evaluated optimally in Lattice QCD • dipole dependence of GA and C5A is verified – requires larger axial mass at the 410 MeV pion lattices • monopole behavior of Gp and C6A is verified • unquenching effects are visible at low Q2 and mπ = 360 MeV in the Hybrid scheme (MILC+DWF) – GA approaches expected behavior • ratios of GT relations in NN & NΔ systems are satisfied – show very weak quark mass and Q2 dependence

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