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 1 S 0 neutron-proton

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

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

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

7. PATH INTEGRALS

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

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

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

13. PATH INTEGRALS FOR FIELDS

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

15. QCD reduced to quadratures

16. probability distribution for U i algorithm 1. find {U i } 2. compute 1/(D Ui +m) 3. compute observable

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

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

19. The difference between E 2N and E N is our signal phase shift

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

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

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

23. CP-PACS K(e4) Improved statistics

24. Nucleon-nucleon

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

26. Chiral “extrapolation” no anchor at m p = 0 wild behavior of the scattering length with m q

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

28. If the minimum pion energy was larger m , the signal would be better  (-z) = -  (z) ?

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

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

31. ?

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

33. weighted fit: l pp = 3.3(6)(3) m p a 2 = -0.0426 (6)(3)(18) 1-loop – 2-loop w/o counterterm different weigths l pp K(e4): m p a 2 = -0.0454(31)(10)(8) theoretical c PT predicts discretization errors (a 2 ) ~ 1% (D. O’Connel, A. Walker-Loud, R. V. Water, J. Chen) Finite volume (e -m p L ) ~ 1% (P.B. & I. Sato)

34. 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

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