Nuclear Forces from Lattice QCD

Transcription

1 Nuclear forces and their impact on structure, reactions and astrophysics TALENT 13 Lecture on Nuclear Forces from Lattice QCD Zohreh Davoudi University of Washington

2 S-wave Luescher formula - a demonstration Π 3 S p L L Π p Cot 1 a p Cot 1 a

3 NN spectrum in coupled 3S1-3D1 channel E [MeV] L[fm] Based on hep-lat/

4 the s-wave and the d-wave is higher order in the ERE and first appears at the same order as the shape parameter [39]. Therefore, while the scattering length and effective range are purely s-wave, the shape parameter is contaminated by the d-wave admixture. The EMPs associated with the first excited states with P = are shown in fig. 6, and with P = 1 are shown in fig. 7. The correlation functions calculated on the L = 6.7 fm ensemble have Nucleon-nucleon scattering b E.6 b E b E 3S1 channel t b 1 16 t b 1 16 t b S1 degrees S1 degrees FIG. 6: The EMPs of the first excited states with P = in the 3S1 channel in the L = 3. fm, L = L, P L, P.5 fm and L = 6.7 fm ensembles, respectively. Twice the nucleon mass has been subtracted from L 3, P L 3, P L, P 1 L, P 1 L 3regions, P 1 L 3, P 1 the15energy. The dark (light) shaded correspond to the statistical uncertainty (statistical 15 Levinson's Theorem Levinson's Theorem Experimental Experimental and systematic uncertainties combined in quadrature) of the fit to the plateau over the indicated interval. time energies that are too close to, or straddle, the singularities of Lu scher s eigenvalue equation k mπ k mπ UNH-11-3 NT@UW-11-1 ICCUB UCB-NPAT-11- NT-LBNL-11-1 FIG. : The phase shift in the 3S1 channel. The left panel is a two-parameter fit to the ERE, while the right panel is ev a three-parameter fit to the ERE, as described in the text. The inner (outer) mπ M The I = ππ S-wave Scattering Phase from Lattice QCD shaded region corresponds to the statistical uncertainty (statistical and Shift systematic uncertainties hep-lat/ v1. Wednesday, July, 13 S.R. Beane, E. Chang, W. the Detmold, H.W. Lin, combined in quadrature) in two- and three-parameter ERE fit to results of T.C. theluu,lattice QCD 1, 3, 5 6 7

5 as a function of the pion mass. In the chiral regime one would expect that that γ d scales as m π as suggested by effective field theory [ 51]. However, at the heavy up and down quarkfine masses used tuning here, naiveand expectations naturalness based on the uncertainty from principle LQCD? suggest that the deuteron binding momentum, if natural, would scale roughly as the inverse of the range of the interaction. As the ratio of γ d to m π as a function of m π is not constant, but rather is falling, we conclude that pion exchange is no longer the only significant contribution to 3. the long-range component of the nuclear force, consistent with the meson spectrum found at these quark masses..3 While more precise calculations at these quark masses are desirable, and LQCD calculations at other light-quark masses and at other lattice spacings are required to make. definitive statements, the present calculations suggest that the deuteron remains unnatural 1 nf1 NPLQCD over a large range of light-quark masses. This would NPLQCD nf3.1 imply nf1 Yamazaki thatet al the unnaturalness of the nf Yamazaki et al deuteron binding energy at the Experiment physical point is a generic nf1feature NPLQCD of QCD with three light Experiment quarks and does not result from a fine-tuning of their masses. If subsequently confirmed, this would be a very minteresting Π MeV result. m Π MeV r 3 s1 a 3 s1 FIG. 1: The left panel shows the ratio of the scattering length to effective range in the 3 S 1 channel. The right panel shows the normalized deuteron.3 binding momentum versus the pion mass [, 11, 13, 1]. The black point denotes the experimental value. r 1 s a 1 s m Π MeV NPLQCD nf3 Experiment 1 Γd mπ Γnn mπ...1 nf1 NPLQCD nf1 Yamazaki et al nf Yamazaki et al nf1 NPLQCD m Π MeV FIG. 13: The left panel shows the ratio of the scattering length to effective range in the 1 S channel. The right panel shows the normalized di-neutron binding momentum versus the pion mass [, 11, 13, 1]. hep-lat/ v1.

6 Multi-nucleon systems s = 1 + s = 1 s = B [MeV] body 3-body -body d nn 3 He 3 nσ Λ H 3 Λ He 3 He Σ He H-dib nξ + Λ He ΛΛ He m π MeV hep-lat/16.519v, PRD 13.

7 Pion-pion scattering phase shifts degrees Hoogland et al '77 Cohen et al '73 Durosoy et al '73 Losty et al '7 NPLQCD '11 π + π + scattering m π 39MeV k GeV hep-lat/17.53v, PRD 1.

8 Hyperon-nucleon scattering 1 S nσ 3 S 1 nσ! (degrees) NSC97f Juelich ' EFT 3 5 p LAB (MeV)! (degrees) NSC97f Juelich ' EFT p LAB (MeV) m π 39MeV hep-lat/1.366, PRL 1.