Restless pions,, nuclear forces and statistical noise in lattice QCD. Paulo Bedaque U. of Maryland, College Park

Transcription

1 Restless pions,, nuclear forces and statistical noise in lattice QCD Paulo Bedaque U. of Maryland, College Park

2 What do we know? 1) NN phase shifts 1 S 0 neutron-proton

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

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

5 The theory of strong nuclear forces does not describe (yet) nuclear forces Matter of principle and matter of practice 0, 1 baryon 2 or more baryons hadron masses decay constants weak matrix elements pion scattering "exotic" particles NN phase shifts hyperon interactions pion-nucleon couplings electroweak exchange currents three-body forces

6 Scattering through finite volumes: the Luscher method (Marinari, Hamber, Parisi, Rebbi) one particle Periodic boundary conditions: box is a torus Energy levels at E n 2 n = + m L 2 2

7 Scattering through finite volumes: the Luscher method (Marinari, Hamber, Parisi, Rebbi) two particles 2 1 M EL M E cot δ ( E) = S 2 L 4 known function Learn about the deuteron in boxes smaller than the deuteron

8 d(de<0): unphysical region Twisted boundary conditions = Aharonov-Bohm

9 Gold-platted scattering observable: I=2 K(e4) CP-PACS m a m 3m m = 1+ log + l ( µ ) f 16 f µ 8(l 1 +l 2 )+2(l 3 -l 4 )

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

11 NEW m p a 2 = (42) K(e4): m p a 2 = (31)(10)(8) theoretical Other processes pk: m a m a 3/ 2 1/ 2 = ± ± = ± ±

12 Fitting two nucleons inside a box pions around the world are not much of a problem E = 1 L 3 drv ( r) = 1 dr V ( r) = 4 a L L ML L V ( ) ( ) ( ) ( 2 ) L r = V r + V r + L + V r + L + (P.B & I. Sato) realistic m p, L=5 fm ~ 10% error but hard to estimate MUCH smaller errors with larger m p

13 Nucleon-nucleon nucleon

14 Similarly for hyperons dibaryon? ΛΛ NΛ triplet

15 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

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

17 The crucial problem is the large statistical errors signal: error: σ 6 6 2Mt C( t) = < q ( t) q (0) > e 2 baryons m t ( t) =< q ( t) q ( t) q (0) q (0) > e 6 pions signal noise N e (2M 3 m ) t N

18 e -(2M (2M-3m)t current noise

19 signal noise N e (2E 3 E ) t N If the minimum pion energy was larger m, the signal would be better (-z) ) = -(z))?

20 Parity orbifold (P.B. +Walker-Loud) parity reversed ( z) ( z) = minimum minimum pion energy is E ( ) 2 2 m = + L

21 Parity orbifold: : pinhole these points are related by parity ( x, y, z) = ( x, y, z) minimum pion energy is E = + L 3 ( ) 2 2 m

22 Expected impact on noise parity orbifold? current noise e -(2M (2M-3m)t

23 In the case of the simpler mirror orbifold A ( x, y, z, t) = A ( x, y, z, t) 3 3 A ( x, y, z, t) = A ( x, y, z, t) 0,1,2 0,1,2 q( x, y, z, t) = q( x, y, z, t) q( x, y, z, t) = q( x, y, z, t) z z z = iγ γ 5 3 ( x, y, z, t) = ( x, y, z, t) N( x, y, z, t) = σ N( x, y, z, t) 3

24 [ ] 4 ( ) ( ) ( ) S = κ q γ r q q γ + r q + a q q + q q [ γ ] = 2 κ q ( + r) q + 2a q q z Not γ 5 hermitian

25 In the case of the simpler pinhole orbifold Ai ( r, t) = Ai ( r, t) A0 ( r, t) = A0 ( r, t) q( r, t) = q( r, t) q( r, t) = q( r, t) = γ 0 ( x, y, z, t) = ( x, y, z, t) N( x, y, z, t) = N( x, y, z, t)

26 Twisting only the valence quarks (Sachrajda&Villadoro Sachrajda&Villadoro,, P.B. & J. Chen) e Λ QCDL e m L dependence on sea b.c. exponentially suppressed e m L

27 Summary No nuclear physics on the lattice without new methods Anisotropic lattices, Luscher-Wolff and/or ORBIFOLDS A lot is hinging on this, it should be tried