Baryon-Baryon Forces from Lattice QCD

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1 Baryon-Baryon Forces from Lattice QCD quarks nuclei 1 fm neutron stars Tetsuo Hatsuda (Univ. Tokyo) T(r)opical QCD Cairns, Oct.1, 2010 [1] Why 10 fmbb forces? [2] NN force from lattice QCD [3] YN, YY forces from lattice QCD [4] ccbar- N force, Q-Qbar from 10 km lattice QCD [5] Summary and Future

2 Baryon-Baryon Forces from Lattice QCD quarks nuclei 1 fm neutron stars 10 fm 10 km Tetsuo Hatsuda (Univ. Tokyo) T(r)opical QCD Cairns, Oct.1, 2010

3 NN phase shifts 2S+1 L J virtual state mid-range attraction short-range repulsion deuteron mid-range attraction short-range repulsion Nijmegen partial-wave analysis, Stoks et al., Phys.Rev. C48 (1993) 792

4 Phenomenological NN potentials

5 phenomenological potentials -- how many parameters? -- ~ 4500 np and pp scattering data (T lab < 300 MeV) NNN, YN, YY: data very limited high precision NN interactions # of parameters c 2 /dof CD Bonn (p space) 38 ~ 1 AV18 (r space) 40 ~1 EFT in N 3 LO (nπ+contact) 24 ~ (1-2) R. Machleidt, arxiv: [nucl-th]

6 Nuclear Force and Neutron Star NNN AV18+3NF (ρ max ~ 6ρ 0 ) PSR NN Neutron star binary Pressure balance Fermi pressure Nuclear force gravity

7 phenomenological potentials -- how many parameters? -- ~ 4500 np and pp scattering data (T lab < 300 MeV) NNN, YN, YY: data very limited high precision NN interactions # of parameters c 2 /dof CD Bonn (p space) 38 ~ 1 AV18 (r space) 40 ~1 EFT in N 3 LO (nπ+contact) 24 ~ (1-2) R. Machleidt, arxiv: [nucl-th] QCD : 4 parameters m u, m d, m s, Λ QCD

8 Multi-baryons from QCD 1. Phase shift formula Lüscher (1991) 2. Lattice scattering length Kuramashi et al. (1995), CP-PACS Coll. (2005) NPLQCD Coll. (2006-) 3. Lattice potential Aoki, Hatsuda, Ishii ((2006) HAL QCD Coll. (2008-) 4. Lattice nuclei Yamazaki, Kuramashi, Ukawa (2009) 5. Strong coupling nuclei de Forcrand et al. (2009) 6. Holographic nuclei Hashimoto et al. (2009-)

9 Multi-baryons from QCD Ask HAL! 1. Phase shift formula Lüscher (1991) 2. Lattice scattering length Kuramashi et al. (1995), CP-PACS Coll. (2005) NPLQCD Coll. (2006-) 3. Lattice potential Aoki, Hatsuda, Ishii ((2006) HAL QCD Coll. (2008-) 4. Lattice nuclei Yamazaki, Kuramashi, Ukawa (2009) 5. Strong coupling nuclei de Forcrand et al. (2009) 6. Holographic nuclei Hashimoto et al. (2009-) N. Ishii, T. Hatsuda (Tokyo) T. Doi, K. Sasaki, S. Aoki (Tsukuba) K. Murano (KEK), T. Inoue (Nihon) Y. Ikeda (RIKEN), H. Nemura (Tohoku)

10 Equal-time BS amplitude φ (r) in lattice QCD x J y + all possible combinations y J y space Imaginary time φ (r > R) phase shift : φ (r < R) potential : Lüscher, Nucl. Phys. B354 (1991) 531 Ishii, Aoki & Hatsuda, PRL 99 (2007)

11 non-local NN potential Aoki, Hatsuda & Ishii, Prog. Theor,Phys. 123 (2010) [arxiv: [hep-lat]], (i) Choose a composite operator: e.g. (ii) BS amplitude: (iii) half off-shell T-matrix: (iv) non-local potential: (v) derivative expansion: LO LO NLO NNLO Calculate observables : phase shifts, binding energies etc

12 Frequently Asked Questions [Q1] Operator dependence of the potential? [Q2] Energy dependence of the potential? [A1] (N(x), U(x,x )) is a combination to define observables remember, QM : (ψ, V) ~ (ψ, V ) observables QFT : (asymptotic field, vertices) observables local composite operator is a convenient choice to prove reduction formula Nishijima, Haag, Zimmermann (1958) [A2] U(x,x ) is E-independent by construction non-locality can be determined order by order in velocity expansion (c.f. ChPT)

13 a ~ 0.09 fm HAL QCD (lattice setup) Exploratory studies with quenched QCD plaquette gauge action + Wilson quark m π = MeV a = fm, L = 4.4 fm Toward real world with 2+1 flavor QCD (using PACS-CS configurations) (4.4 fm) Iwasaki gauge action + clover quark m π = MeV a = fm, L = 2.9 fm m π = 135 MeV & L = 5.8 fm in two years (2.9 fm)

14 Lattice NN potential Quenched QCD (m π =530MeV, L=4.4 fm) (2+1)-flavor QCD : Iawasaki+clover (m π =570MeV, L=2.9 fm) r [fm] Ishii, Aoki & Hatsuda, PRL 99 (2007) Ishii, Aoki & Hatsuda, arxive [hep-lat]

15 LO potentials : V C (r) & V T (r) mixing between 3 S 1 and 3 D 1 through the tensor force

16 Central & tensor potentials : V C (r) & V T (r) Aoki, Hatsuda & Ishii, [hep-lat] PTP 123 (2010) quenched QCD E ~ 0 MeV

17 Central & tensor potentials : V C (r) & V T (r) Aoki, Hatsuda & Ishii, [hep-lat] PTP 123 (2010) quenched QCD quenched E ~ QCD 0 MeV E ~ 0 MeV V c (r 0) ~ (log r) β /r 2, V T (r 0) 0 from operator product expansion (Aoki, Balog & Weisz, arxiv: )

18 Central & tensor potentials : V C (r) & V T (r) Aoki, Hatsuda & Ishii, [hep-lat] PTP 123 (2010) quenched QCD quenched E ~ QCD 0 MeV E ~ 0 MeV quenched QCD E ~ 0 MeV fit function V c (r 0) ~ (log r) β /r 2, V T (r 0) 0 Rapid quark-mass dependence of V T (r) from operator product expansion Evidence of the one-pion-exchange (Aoki, Balog & Weisz, arxiv: )

19 NNLO potential of O( 2 ): how large? PBC (T Lab ~0 MeV) APBC (T Lab ~100 MeV) Murano (HAL QCD Coll.)

20 NNLO potential of O( 2 ): how large? PBC (T Lab ~0 MeV) APBC (T Lab ~100 MeV) Murano (HAL QCD Coll.)

21 NNLO potential of O( 2 ): how large? PBC (T Lab ~0 MeV) APBC (T Lab ~100 MeV) 1 S 0 Murano (HAL QCD Coll.)

22 Phase shifts from V(r) in (2+1)-flavor QCD 3 S 1 V C eff (r) 3 S 1 phase shift from V C eff (r) 3 S 1 phase shift (exp.) deuteron not bound for m π 410 MeV 3 S 1 Ishii et al. (HAL QCD Coll.), arxiv: [hep-lat]

23 unitary regime NN scattering lengths in full QCD BS wave func. q 2 Luscher s formula Kuramashi Plot [hep-lat/ ] a 0 [fm] NN interaction 1 S 0 3 S 1 net attraction at low energy still far from unitary regime 1 S 0 3 S 1 V(r) : mild func. of m q a 0 : highly sensitive to m q [MeV]

24 Hyperon Core of Neutron Stars Radius ~ 10 km Mass ~ solar mass Central density ~ kg/cm 3 Hyperon matter Schaffner-Bielich, NP A804 (2008). Solid Crust Neutron Liquid Hyperon Matter?

25 ΛN interaction in (2+1)-flavor QCD LO potentials from BS wave function (2+1)-flavor, Iwasaki + clover L=2.9fm, a=0.09fm, 32 3 x64 Nemura et al. (HAL QCD Coll.) arxiv: [hep-lat] Scattering length from Lüscher s formula with k from BS wave function LO potentiald from BS wave function ΛN interaction repulsive core + attractive well net attraction at low energy

26 BB interactions in a SU(3) symmetric world x 1. First step to study YN, YY interactions not accessible in exp. 2. Origin of the short rang repulsion Six independent potentials in flavor-basis

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28 Equal-time BS amplitudes in the SU(3) limit 1 27 Iwasaki + clover (CP-PACS/JLQCD) L=1.9 fm, a=0.12 fm, 16 3 x32 m π =835 MeV, m B =1752 MeV Inoue et al. (HAL QCD Coll.) ArXiv: [hep-lat] Prog. Theor. Phys. (2010) in press. 8 s Pauli principle at work! 1 : allowed 27 : partially blocked 8 s : almost blocked J.E.T. Ribeiro, CFMC-E-6-78 (78,REC.NOV) (1978), See also, Oka, Shimizu, Yazaki, Nucl. Phys. A464 (1987) 700

29 NN BB potentials in flavor-basis ( 1 S 0 channel)

30 NN BB potentials in flavor-basis ( 1 S 0 channel)

31 NN BB potentials in flavor-basis ( 1 S 0 channel)

32

33 cc - N interaction no Pauli-blocking + QCD van der Walls attraction charmonium-nucleus bound state? Brodsky et al., PRL 64 (1990) 1011 Klein, Thomas and Tsushima, arxiv: [nucl-th] cc Quenched QCD: 32 3 x48, L = 3 fm (2+1)-flavor QCD on-going Kawanai & Sasaki, ArXiv: [hep-lat] η c -N BS wave function η c -N Potential

34 Q-Q potential in Coulomb gauge q bar Quenched QCD: Coulomb gauge L = 3.3 fm, a = fm Iida & Ikeda, in progress q t 0 Pseudo scalar channel Vector channel

35 Q-Q potential in Coulomb gauge q bar Quenched QCD: Coulomb gauge L = 3.3 fm, a = fm Iida & Ikeda, in progress q t 0 Pseudo scalar channel Pseudoscalar channel Vector channel Vector channel Coulomb + linear behavior from the BS amplitude

36 Summary: Current and Future Nuclear forces from LQCD (HAL QCD strategy) BS amplitude NN, YN, YY potentials observables Full QCD with m π =135 MeV is our ultimate goal current : PACS-CS config. (N f =2+1) with L=2.9fm & m p = MeV in 1-2 years: PACS-CS config. (N f =2+1) with L=5.8fm & m p = 135 MeV in 5 years: new full QCD config. on 10 Pflops machine at Kobe (2012-) On-going projects in HAL QCD Collaboration LS force NNN forces Imaginary nuclei (m q >> m q phys ) by LQCD potentials + exact few body calculation meson-baryon interactions (e.g. KN)

37 Advanced Institute for Computational Science (AICS) National Institute just started in Kobe (July 1, Pflops machine available from Offices Main gate Five Major projects Machine floor 1. Life and Medicine 2. New materials 3. Environment 4. Engineering 5. Particle, nuclear and astrophysics

38 Some Useful References NN force in quenched QCD: Ishii, Aoki & Hatsuda, Phys. Rev. Lett. 99 (2007) [nucl-th/ ]. Theoretical foundation of the HAL formalism: Aoki, Hatsuda & Ishii, Prog. Theo. Phys 123 (2010) [arxive: [hep-lat]]. YN force in quenched QCD: Nemura, Ishii, Aoki & Hatsuda, Phys. Lett. B673 (2009) 136 [arxiv: [nucl-th]]. SU(3) BB interaction in (2+1) QCD Inoue et al. (HAL QCD Coll.) arxiv: [hep-lat] Prog. Theor. Phys. (2010) in press. Lecture : Lattice QCD and Nuclear Physics S. Aoki, Les Houches Summer School [arxiv: [hep-lat]] Review : Nuclear Physics from Lattice QCD T. Hatsuda, talk at Lattice 2010, to appear in arxive soon.

39 Backup slides

40 velocity dependence of the potential (NNLO) NNLO PBC (E~0 MeV) APBC (E~46 MeV) 1 S 0 3 S 1-3 D 1 NNLO can be determined from φ (r) for different E NNLO is small at least up to E cm ~ 46 MeV (T lab ~ 100 MeV) quenched QCD m π = 529 MeV Murano et al. (HAL QCD Coll.)

41 V C (r) and V T (r) in full QCD (m π =570MeV, L=2.9 fm) Quenched QCD Full QCD

42 S=-2 system: XN interaction (I=1) J-PARC DAY-1 exp. : 12 C(K -,K + ) 12 Be X Nemura, Ishii, Aoki, T.H., Phys.Lett. B673, 136 (2009) quenched QCD m π =510 MeV 1. Repulsive core + attractive well 2. Large spin dependence 3. Overall attraction

43 V C [MeV] V C [MeV] S-wave N-K + (us bar ) interaction δ 0 [deg] I=0 I=0 (lat) I=1(lat) I=1 r [fm] I=1(exp) I=0(exp) p lab [MeV] r [fm] (2+1)-flavor full QCD CP-PACS/JLQCD configurations a=0.12 fm, L=1.93 fm m π =871 MeV Ikeda et al. (HAL QCD Coll.)