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

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

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......

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

PATH INTEGRALS

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

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

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

Typical paths

PATH INTEGRALS FOR FIELDS

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

QCD reduced to quadratures

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

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

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

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

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

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

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

CP-PACS K(e4) Improved statistics

Nucleon-nucleon

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

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

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

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

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

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

?

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

weighted fit: l pp = 3.3(6)(3) m p a 2 = (6)(3)(18) 1-loop – 2-loop w/o counterterm different weigths l pp K(e4): m p a 2 = (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)

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

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