Hadronic Interactions and Nuclear Physics
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1 Williamsburg,VA LATT2008 7/2008 p. 1/35 Hadronic Interactions and Nuclear Physics Silas Beane University of New Hampshire
2 Williamsburg,VA LATT2008 7/2008 p. 2/35 Outline Motivation Signal/Noise Estimates MM MM...M MB BB The Future
3 Lattice QCD : So What?? Williamsburg,VA LATT2008 7/2008 p. 3/35
4 Williamsburg,VA LATT2008 7/2008 p. 3/35 Lattice QCD : So What?? Particle and Nuclear physics perspectives...
5 The particle physics perspective Williamsburg,VA LATT2008 7/2008 p. 4/35
6 Williamsburg,VA LATT2008 7/2008 p. 4/35 The particle physics perspective QCD is Background for beyond-the-standard-model physics (f K /f π, f Ds, B K,...)
7 The nuclear physics perspective Williamsburg,VA LATT2008 7/2008 p. 5/35
8 Williamsburg,VA LATT2008 7/2008 p. 5/35 The nuclear physics perspective Intrinsically interesting QCD physics! (Y N, Kπ, h πnn, nnn,...)
9 Williamsburg,VA LATT2008 7/2008 p. 6/35 The nuclear physics perspective Intrinsically interesting QCD physics! (Y N, Kπ, h πnn, nnn,...)
10 Williamsburg,VA LATT2008 7/2008 p. 7/35 NEOS p Σ interactions K + π Atoms Dirac collaboration interesting physics m π a 3/ a 0 : χpt p 2 - a 0 : χpt p 4 - a 0 : χpt p 6 fit A fit B fit C fit D Roy-Steiner (1-σ) χpt p 4 (1-σ) χpt p m π a 1/2
11 Williamsburg,VA LATT2008 7/2008 p. 7/35 NEOS p Σ interactions K + π Atoms Dirac collaboration interesting physics m π a 3/ a 0 : χpt p 2 - a 0 : χpt p 4 - a 0 : χpt p 6 fit A fit B fit C fit D Roy-Steiner (1-σ) χpt p 4 (1-σ) χpt p m π a 1/2 NPDgamma Experiment h πnn 0 O N (t) O π (τ 2 )Ow I=1 (τ 1 )ŌN(0) 0
12 Williamsburg,VA LATT2008 7/2008 p. 8/35 Signal/Noise Estimates Lepage (1989) Signal/Noise Estimates
13 Williamsburg,VA LATT2008 7/2008 p. 8/35 Signal/Noise Estimates Lepage (1989) PIONS : noise signal σ(t) θ(t) Signal/Noise Estimates e nm π t q`a2 A 2 0 NA0 e nm πt 1 N
14 Williamsburg,VA LATT2008 7/2008 p. 8/35 Signal/Noise Estimates Lepage (1989) PIONS : noise signal σ(t) θ(t) Signal/Noise Estimates e nm π t q`a2 A 2 0 NA0 e nm πt 1 N Noise independent of t!
15 Williamsburg,VA LATT2008 7/2008 p. 8/35 Signal/Noise Estimates Lepage (1989) PIONS : noise signal σ(t) θ(t) Signal/Noise Estimates e nm π t q`a2 A 2 0 NA0 e nm πt 1 N Noise independent of t! BARYONS : noise signal σ(t) θ(t) 1 N e (m p 3 2 m π)t
16 Williamsburg,VA LATT2008 7/2008 p. 8/35 Signal/Noise Estimates Lepage (1989) PIONS : noise signal σ(t) θ(t) Signal/Noise Estimates e nm π t q`a2 A 2 0 NA0 e nm πt 1 N Noise independent of t! BARYONS : noise signal σ(t) θ(t) 1 N e (m p 3 2 m π)t Exponential growth of noise!
17 Williamsburg,VA LATT2008 7/2008 p. 9/35 np ( 1 S 0 ) NPLQCD MILC/2064f21b676m010m050 signal/noise (Courtesy of Bedaque,Walker-Loud arxiv: )
18 Williamsburg,VA LATT2008 7/2008 p. 10/35 signal/noise Currently the main obstacle to lattice QCD calculations of nucleon and nuclear quantities is the signal/noise problem. Nuclear physics requires exponentially more resources than meson physics.
19 Williamsburg,VA LATT2008 7/2008 p. 10/35 signal/noise Currently the main obstacle to lattice QCD calculations of nucleon and nuclear quantities is the signal/noise problem. Nuclear physics requires exponentially more resources than meson physics. Theoretical fixes? z z 0 z L z L Orbifold boundary conditions z z 0 z L Bedaque,Walker-Loud/ arxiv:
20 Williamsburg,VA LATT2008 7/2008 p. 11/35 ππ Universal band tree (1966), one loop (1983), two loops (1996) Prediction (χpt + dispersion theory, 2001) l 4 from low energy theorem for scalar radius (2001) NPLQCD (2005, 2007) l 3 and l 4 from MILC (2004, 2006) l 3 from Del Debbio et al. (2006) l 3 and l 4 from ETM (2007) l 3 and l 4 from RBC/UKQCD (2007) l 3 and l 4 from PACS-CS (preliminary) Universal band tree (1966), one loop (1983), two loops (1996) Prediction (χpt + dispersion theory, 2001) E865 Ke4 (2003) isospin corrected DIRAC (2005) NA48 K3π (2006) NA48 Ke4 (preliminary) isospin corrected a a a a 0 0 (Courtesy of H. Leutwyler arxiv: )
21 Williamsburg,VA LATT2008 7/2008 p. 12/35 Hybrid of staggered sea quarks (MILC) and domain-wall valence quarks (LHPC+NPLQCD) (2+1) dynamical flavors Coarse lattices chopped from 64 to 32 with sources displaced in time and space Config Set Dimensions m π # configs # sources 2064f21b676m007m MeV f21b676m010m MeV f21b679m020m MeV f21b681m030m MeV f21b709m0062m MeV b coarse MILC fm bfine MILC 0.09 fm L 2.5 fm
22 Williamsburg,VA LATT2008 7/2008 p. 13/35 ππ-method E 0 (2, L) = 4π a ππ m π L 3 { 1 ( aππ ) ( aππ ) 2 [ I + I 2 J ] ( aππ ) 3 [ ] } + I 3 + 3IJ K + 8π2 3 a ππ r π L π L π L m π L 6 ππ + O ( L 7) I = lim Λ j i Λ X j i 0 1 i 2 4πΛ j = , J = X i 4 = , K = X i 0 i i 6 =
23 Williamsburg,VA LATT2008 7/2008 p. 14/35 0 ππ-bottom line -0.1 m π a ππ I= MA χ - PT (One Loop) χ - PT (Tree Level) CP-PACS (2004) (n f = 2) E 865 (2003) NPLQCD (MILC fine) NPLQCD (MILC coarse) m π / f π Savage/PAR-Mon-6pm
24 Williamsburg,VA LATT2008 7/2008 p. 15/35 Status of ππ χ - PT (Tree Level) NPLQCD (2007) E 865 (2003) NPLQCD (2005) MILC (2006)* MILC (2004)* CGL (2001) m π a I=2 ππ χpt (Tree Level) NPLQCD (2007) ± E 865 (2003) ± ± ± NPLQCD (2005) ± ± ± MILC (2006)* ± MILC (2004)* ± CGL (2001) ± m π a π+π+
25 Williamsburg,VA LATT2008 7/2008 p. 16/35 ππ Theoretical Developments ππ in χ-pt for Wilson lattice actions Buchoff/ arxiv: Aoki et al./ arxiv: /ps-b Wavefunction method for ππ phase shift Sasaki,Ishizuka/ arxiv: MM interactions from multi-m interactions NPLQCD/ arxiv: /par-tue-2:30pm
26 Williamsburg,VA LATT2008 7/2008 p. 17/35 m K + a K+K χ-pt (Tree Level) MILC coarse (b /= 0) MILC fine (b /= 0) physical point extrapolated with MAχ-PT KK m K + / f K+ m K + a K + K + = ± NPLQCD/arXiv : PAR-Mon-6pm
27 Williamsburg,VA LATT2008 7/2008 p. 18/35 meson-meson scattering 0 π + π + (Ι=2) 0 K + K + (I=1) m π a π +π χ - PT (Tree Level) Experiment NPLQCD (MILC coarse) CP-PACS m K a K+K χ-pt (Tree Level) NPLQCD (MILC coarse) physical line m π / f π m K / f K Mysterious disappearance of higher-order effects!
28 Williamsburg,VA LATT2008 7/2008 p. 19/35 MM...M n pions in a finite volume Detmold et al./ arxiv: , /par-tue-2:30pm Tan/ arxiv: E 0 (n, L) = 4π a ππ m π L 3 0 n A 2 1 I + π L aππ aππ 3 h + π L 0 1 aππ π L n A 8π2 a 3 ππ 2 m π L 6 r ππ + 2 ˆI2 + (2n 5)J I 3 (2n 7)IJ `5n i 2 41n + 63 ) K n 3 1 A η 3(L) L 6 + O `L 7 η 3 (L) = η 3 (µ) + 64π a ππ 4 m π (3 3 4π) log(l µ) 96 a 4 ππ (2Q + R) m π π2 dim reg /w MS : Q = , R =
29 Williamsburg,VA LATT2008 7/2008 p. 20/35 Three-body force NPLQCD/arXiv: , body Force mπ f L ΠΗ m Π f Π
30 Williamsburg,VA LATT2008 7/2008 p. 21/35 Pion condensate Μ I 1 m Π m Π 291 MeV Μ I 1 m Π m Π 352 MeV pion condensate n 2.5 fm 3 Ρ I n 2.5 fm 3 Ρ I Μ I 1 m Π 0.4 m Π 491 MeV Μ I 1 m Π m Π 591 MeV n 2.5 fm 3 Ρ I n 2.5 fm 3 Ρ I χ PT : ρ I = 1 2 f2 πµ I 1 m4 π µ 4 I!
31 Williamsburg,VA LATT2008 7/2008 p. 21/35 Pion condensate Μ I 1 m Π m Π 291 MeV Μ I 1 m Π m Π 352 MeV pion condensate n 2.5 fm 3 Ρ I n 2.5 fm 3 Ρ I Μ I 1 m Π 0.4 m Π 491 MeV Μ I 1 m Π m Π 591 MeV n 2.5 fm 3 Ρ I n 2.5 fm 3 Ρ I χ PT : ρ I = 1 2 f2 πµ I 1 m4 π µ 4 I! Three-body force is important!
32 Williamsburg,VA LATT2008 7/2008 p. 22/35 Μ K 1 m K Kaon condensate m Π 291 MeV m K 580 MeV NPLQCD/arXiv: Μ K 1 m K Kaon condensate m Π 352 MeV m K 597 MeV fm 3 Ρ K 2.5 fm 3 Ρ K Μ K 1 m K m Π 491 MeV m K 640 MeV Μ K 1 m K m Π 591 MeV m K 678 MeV fm 3 Ρ K 2.5 fm 3 Ρ K χ PT : ρ K = 1 2 f2 K µ K m4 K µ 3 K!
33 Williamsburg,VA LATT2008 7/2008 p. 22/35 Μ K 1 m K Kaon condensate m Π 291 MeV m K 580 MeV NPLQCD/arXiv: Μ K 1 m K Kaon condensate m Π 352 MeV m K 597 MeV fm 3 Ρ K 2.5 fm 3 Ρ K Μ K 1 m K m Π 491 MeV m K 640 MeV Μ K 1 m K m Π 591 MeV m K 678 MeV fm 3 Ρ K 2.5 fm 3 Ρ K χ PT : ρ K = 1 2 f2 K µ K m4 K µ 3 K! Why does χpt work so well??
34 Williamsburg,VA LATT2008 7/2008 p. 23/35 Meson-Baryon scattering Torok/PAR-Thu-8:50am Interesting phenomenology Important for baryon spectroscopy Juge/PAR-Tue-3:30pm
35 Williamsburg,VA LATT2008 7/2008 p. 23/35 Meson-Baryon scattering Torok/PAR-Thu-8:50am Interesting phenomenology Important for baryon spectroscopy Juge/PAR-Tue-3:30pm
36 Williamsburg,VA LATT2008 7/2008 p. 24/35 Baryon-Baryon scattering What should one calculate using lattice QCD? V NN (r) or δ NN (E)?
37 Williamsburg,VA LATT2008 7/2008 p. 24/35 Baryon-Baryon scattering What should one calculate using lattice QCD? V NN (r) or δ NN (E)? Historically nuclear physicists have used energy-independent potentials V NN (r) to fit NN phaseshifts with χ 2 /d.o.f. 1 over a wide range of (low) energies. V NN (r) = +
38 Williamsburg,VA LATT2008 7/2008 p. 24/35 Baryon-Baryon scattering What should one calculate using lattice QCD? V NN (r) or δ NN (E)? Historically nuclear physicists have used energy-independent potentials V NN (r) to fit NN phaseshifts with χ 2 /d.o.f. 1 over a wide range of (low) energies. V NN (r) = + = (χ 2 /d.o.f. 1)
39 V NN (k,k) [fm] Williamsburg,VA LATT2008 7/2008 p. 25/35 Baryon-Baryon scattering The modern viewpoint: Effective Field Theory S 0 Paris Bonn A Nijmegen I Nijmegen II Argonne v 18 CD Bonn Idaho A S 1 k [fm -1 ] (Courtesy of A. Schwenk et al. nucl-th/ )
40 V low k (k,k) [fm] Williamsburg,VA LATT2008 7/2008 p. 26/35 Use RG to integrate out Baryon-Baryon scattering = 4.1 fm -1 = 3.1 fm = 2.6 fm -1 = 2.1 fm k [fm -1 ] Argonne v 18 Paris CD Bonn Bonn A Idaho A Nijmegen I Nijmegen II
41 V low k (k,k) [fm] Williamsburg,VA LATT2008 7/2008 p. 26/35 Use RG to integrate out Baryon-Baryon scattering = 4.1 fm -1 = 3.1 fm = 2.6 fm -1 = 2.1 fm k [fm -1 ] Argonne v 18 Paris CD Bonn Bonn A Idaho A Nijmegen I Nijmegen II Bottom line: short distance part of V NN (r) not meaningful!
42 Williamsburg,VA LATT2008 7/2008 p. 27/35 Baryon-Baryon scattering Can one define and calculate V LATT BB (r)?
43 Williamsburg,VA LATT2008 7/2008 p. 27/35 Baryon-Baryon scattering Can one define and calculate V LATT BB (r)? NN: Aoki et al./ arxiv: /par-wed-3:50pm YN: Nemura et al./ arxiv: /par-wed-4:10pm Bethe-Salpeter wave function V LATT BB
44 Williamsburg,VA LATT2008 7/2008 p. 28/35 QQCD potentials V C (r) [MeV] np ( 1 S 0 ) pξ 0 ( 1 S 0 ) r [fm] m π =380MeV m π =529MeV m π =731MeV V (MeV) m π 368MeV m π 511MeV OPEP(α=0.36) r (fm) 1S Wilson quark action β = 5.7 b 0.137fm L 4.4fm
45 Williamsburg,VA LATT2008 7/2008 p. 29/35 PROBLEMS Detmold et al./ arxiv:hep-lat/ v1 Baryon-Baryon scattering
46 Williamsburg,VA LATT2008 7/2008 p. 29/35 PROBLEMS Detmold et al./ arxiv:hep-lat/ v1 Baryon-Baryon scattering V LAT T BB (r, E) Aoki/PAR-Wed-2:50pm
47 Williamsburg,VA LATT2008 7/2008 p. 29/35 PROBLEMS Detmold et al./ arxiv:hep-lat/ v1 Baryon-Baryon scattering V LAT T BB (r, E) Aoki/PAR-Wed-2:50pm V LAT T BB (r, E) δ LAT T BB (E)
48 Williamsburg,VA LATT2008 7/2008 p. 29/35 PROBLEMS Detmold et al./ arxiv:hep-lat/ v1 Baryon-Baryon scattering V LAT T BB (r, E) Aoki/PAR-Wed-2:50pm V LAT T BB (r, E) δ LAT T BB (E) V LAT T BB (r, E) δ LAT T BB (E )!!
49 Williamsburg,VA LATT2008 7/2008 p. 29/35 PROBLEMS Detmold et al./ arxiv:hep-lat/ v1 Baryon-Baryon scattering V LAT T BB (r, E) Aoki/PAR-Wed-2:50pm V LAT T BB (r, E) δ LAT T BB (E) V LAT T BB (r, E) δ LAT T BB (E )!! V LAT T BB (r, E, J) Aoki et al./in preparation V LAT T BB (r, E, J) r m 1 π V LAT T BB (r, E)??
50 Williamsburg,VA LATT2008 7/2008 p. 29/35 PROBLEMS Detmold et al./ arxiv:hep-lat/ v1 Baryon-Baryon scattering V LAT T BB (r, E) Aoki/PAR-Wed-2:50pm V LAT T BB (r, E) δ LAT T BB (E) V LAT T BB (r, E) δ LAT T BB (E )!! V LAT T BB (r, E, J) Aoki et al./in preparation V LAT T BB (r, E, J) r m 1 π V LAT T BB (r, E)?? QQCD : V LAT T NN (r) `M 0 α Φ m 2 π e m π r Dominates over Yukawa force!!
51 Williamsburg,VA LATT2008 7/2008 p. 30/35 Results: NN NN (singlet) a ( 1 S 0 ) [fm] NPLQCD (2006) (n f = 2+1) Aoki et al (2008) (n f = 0) Fukugita et al (1995) (n f = 0) m π [MeV]
52 Williamsburg,VA LATT2008 7/2008 p. 30/35 Results: NN NN (singlet) a ( 1 S 0 ) [fm] NPLQCD (2006) (n f = 2+1) Aoki et al (2008) (n f = 0) Fukugita et al (1995) (n f = 0) m π [MeV]
53 Williamsburg,VA LATT2008 7/2008 p. 31/35 Results: NN NN (triplet) a ( 3 S 1 ) [fm] NPLQCD (2006) (n f = 2+1) Aoki et al (2008) (n f = 0) Fukugita et al (1995) (n f = 0) m π [MeV]
54 Williamsburg,VA LATT2008 7/2008 p. 31/35 Results: NN NN (triplet) a ( 3 S 1 ) [fm] NPLQCD (2006) (n f = 2+1) Aoki et al (2008) (n f = 0) Fukugita et al (1995) (n f = 0) m π [MeV]
55 Williamsburg,VA LATT2008 7/2008 p. 32/35 Results: YN pξ 0 (QQCD) S 0 S a0 (fm) m π =0.135 GeV m π 2 (GeV 2 ) Nemura et al./ arxiv: /par-wed-4:10pm
56 Williamsburg,VA LATT2008 7/2008 p. 33/35 δ( k = 255 MeV ) (degrees) δ( k = 179 MeV ) (degrees) nλ ( 1 S 0 ) EFT 06 Juelich 04 Nijmegen NSC97f NPLQCD (2006) (n f = 2+1) m π (MeV) nσ ( 1 S 0 ) EFT 06 Juelich 04 Nijmegen NSC97f NPLQCD (2006) (n f = 2+1) m π (MeV) δ( k = 168 MeV ) (degrees) δ( k = 261 MeV ) (degrees) nλ ( 3 S 1 ) EFT 06 Juelich 04 Nijmegen NSC97f Results: YN NPLQCD (2006) (n f = 2+1) m π (MeV) nσ ( 3 S 1 ) EFT 06 Juelich 04 Nijmegen NSC97f NPLQCD (2006) (n f = 2+1) m π (MeV)
57 Williamsburg,VA LATT2008 7/2008 p. 34/35 The Future NN ( 3 S 1 ) b 0.125fm L 5fm 0.2 Tflop-years 2 Tflop-years 20 Tflop-years 4 a [fm] pion mass [MeV]
58 Williamsburg,VA LATT2008 7/2008 p. 35/35 Currently the main obstacle to lattice QCD calculations of nucleon and nuclear quantities is the signal/noise problem. Conclusion Nuclear physics requires exponentially more resources than meson physics. The advent of petascale computing will overcome this obstacle and allow the calculation of nuclear properties and interactions! The future is bright!
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