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QUARKS, GLUONS AND NUCLEAR FORCES

QUARKS, GLUONS AND NUCLEAR FORCES. Paulo Bedaque University of Maryland, College Park. strong nuclear force: binds neutrons and protons into nuclei. Quantum Chromodynamics (QCD). What do we know ?. 1) NN phase shifts. 1 S 0 neutron-proton. What do we know ?.

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QUARKS, GLUONS AND NUCLEAR FORCES

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  1. QUARKS, GLUONS AND NUCLEAR FORCES Paulo Bedaque University of Maryland, College Park

  2. strong nuclear force: binds neutrons and protons into nuclei Quantum Chromodynamics (QCD)

  3. What do we know ? 1) NN phase shifts 1S0 neutron-proton

  4. What do we know ? 2) Several potentials that fit them pion exchange all kinds of things …

  5. What do we know ? 3) These potentials explain a lot but not everything • NNn, NNg, couplings few % on nd • NNN forces ~5% of nuclei binding • NY forces strangeness in neutron stars • ...

  6. Can we understand the nuclear forces (and NNN, NNn, …) from first principles ? LATTICE QCD

  7. PATH INTEGRALS

  8. Quantum mechanics reduced to quadratures operators numbers is as well (or ill) defined as

  9. Imaginary time (t it): just like stat mech probability distribution

  10. But I don’t live in imaginary time ! What can I do with imaginary time correlators ? lowest energy state w/ some overlap

  11. Typical paths

  12. PATH INTEGRALS FOR FIELDS

  13. Quantum Chromodynamics Q = spinor, 3 colors, 6 flavors = quarks U = SU(3) matrix = gluons

  14. QCD reduced to quadratures

  15. probability distribution for Ui • algorithm • find {Ui} • compute 1/(DUi+m) • compute observable

  16. Scattering through finite volumes: the Luscher method (Marinari, Hamber, Parisi, Rebbi) one particle Periodic boundary conditions: box is a torus Energy levels at

  17. Scattering through finite volumes: the Luscher method (Marinari, Hamber, Parisi, Rebbi) two particles known function Learn about the deuteron in boxes smaller than the deuteron

  18. The difference between E2N and EN is our signal phase shift

  19. The time to try it is now • Pion masses small enough for chiral extrapolation • No quenching • Volumes ~ (3 fm)3 • Improved actions • Good chiral symmetry • Software resources

  20. S. Beane, T. Luu, K. Orginos, E. Pallante, A. Parreno, M. Savage, A. Walker-Loud, …

  21. Gold platted scattering observable: I=2 pp K(e4) CP-PACS

  22. Improved statistics K(e4) CP-PACS

  23. Nucleon-nucleon

  24. Nucleon-nucleon “natural” |a| < 1 fm for 350 < mp < 600 MeV a=5.4 fm or 20 fm for mp=138 MeV is indeed fine tuned

  25. Chiral “extrapolation” • no anchor at mp= 0 • wild behavior of the scattering length with mq

  26. The crucial problem is the large statistical errors signal: 2 baryons error: 6 pions

  27. If the minimum pion energy was larger mp, the signal would be better p(-z) = -p(z) ?

  28. Parity orbifold (P.B. +Walker-Loud) parity reversed minimum pion energy is

  29. Parity orbifold: pinhole these points are related by parity minimum pion energy is

  30. ?

  31. Summary • Lattice QCD calculation of hadron interactions are doable • Meson-meson scattering can be computed with few % precision • There is a serious noise problem in baryon-baryon channels, new ideas are needed • New ideas exist ! We’ll find out how they work really soon

  32. weighted fit: lpp = 3.3(6)(3) different weigths mp a2 = -0.0426 (6)(3)(18) 1-loop – 2-loop w/o counterterm lpp K(e4): mp a2 = -0.0454(31)(10)(8) theoretical cPT predicts discretization errors (a2) ~ 1% (D. O’Connel, A. Walker-Loud, R. V. Water, J. Chen) Finite volume (e-mpL) ~ 1% (P.B. & I. Sato)

  33. Extracting physics from euclidean space : energies are "easy" some operator with quantum numbers of the pion, made of quarks and gluons, for instance: lowest energy state with the quantum numbers of the pion

  34. Solution 2: Aharonov-Bohm effect add a background magnetic potential coupled to baryon number with zero curl or or no coupling to local operators !

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