Baryon-baryon interactions and the quest to constrain them by - PowerPoint PPT Presentation

Baryon-baryon interactions and the quest to constrain them by measuring correlation functions Johann Haidenbauer IAS & JCHP , Forschungszentrum Jülich, Germany YITP Workshop, Kyoto, March 25-29, 2019 Johann Haidenbauer Baryon-baryon interactions

Outline Introduction 1 Baryon-baryon interaction in chiral effective field theory 2 Strangeness S=-1 sector 3 Strangeness S=-2 sector 4 Three- and four-body systems 5 Hyperons in nuclear matter 6 Final-state interaction 7 Summary 8 Johann Haidenbauer Baryon-baryon interactions

Introduction BB interaction in chiral effective field theory Λ N and Σ N scattering → Role of SU(3) flavor symmetry Few-body systems with hyperons: 3 Λ H , 4 Λ H , 4 Λ He , ... → Role of three-body forces large charge symmetry breaking 4 Λ H ↔ 4 Λ He ( Λ , Σ ) hypernuclei and hyperons in nuclear matter → very small spin-orbit splitting: weak spin-orbit force existence of Ξ hypernuclei repulsive Σ nuclear potential implications for astrophysics → hyperon stars stability/size of neutron stars Johann Haidenbauer Baryon-baryon interactions

BB interaction in chiral effective field theory Baryon-baryon interaction in SU(3) χ EFT à la Weinberg (1990) Advantages: Power counting systematic improvement by going to higher order Possibility to derive two- and three-baryon forces and external current operators in a consistent way • degrees of freedom: octet baryons ( N , Λ , Σ , Ξ ), pseudoscalar mesons ( π , K , η ) • pseudoscalar-meson exchanges • contact terms – represent unresolved short-distance dynamics LO : NLO : LO: H. Polinder, J.H., U.-G. Meißner, NPA 779 (2006) 244 NLO: J.H., S. Petschauer, N. Kaiser, U.-G. Meißner, A. Nogga, W. Weise, NPA 915 (2013) 24 Johann Haidenbauer Baryon-baryon interactions

Structure of the potential ( � σ 1 · � q )( � σ 2 · � q ) V OBE 2 = − f B 1 B ′ 1 P f B 2 B ′ 2 P B 1 B 2 → B ′ 1 B ′ � q 2 + m 2 P f B 1 B ′ 1 P ... coupling constants fixed by standard SU(3) relations utilizing f NN π m P ... mass of the exchanged pseudoscalar meson SU ( 3 ) symmetry breaking due to the mass splitting of the ps mesons ( m π = 138.0 MeV, m K = 495.7 MeV, m η = 547.3 MeV) taken into account already at LO! (TBE ⇒ J.H. et al., NPA 915 (2013) 24) 2 = ˜ C α + C α ( p 2 + p ′ 2 ) V CT ( or C β pp ′ ) B 1 B 2 → B ′ 1 B ′ α = 1 S 0 , 3 S 1 , 3 S 1 − 3 D 1 β = 3 P 0 , 1 P 1 , 3 P 1 , 3 P 2 Johann Haidenbauer Baryon-baryon interactions

SU ( 3 ) structure of contact terms for BB SU ( 3 ) structure for scattering of two octet baryons → 8 ⊗ 8 = 1 ⊕ 8 a ⊕ 8 s ⊕ 10 ∗ ⊕ 10 ⊕ 27 BB interaction can be given in terms of LECs corresponding to the SU ( 3 ) f irreducible representations: C 1 , C 8 a , C 8 s , C 10 ∗ , C 10 , C 27 Channel I V α V β V β → α C 10 ∗ S = 0 NN → NN 0 – – β C 27 NN → NN 1 – – α � � � � α + C 8 s C 8 a β + C 10 ∗ 1 1 9 C 27 1 − C 8 sa S = − 1 Λ N → Λ N α 2 10 2 β � � � � 1 3 α + C 8 s 1 − C 8 a β + C 10 ∗ − C 27 − 3 C 8 sa Λ N → Σ N α β 2 10 2 C 8 sa � � � � α + 9 C 8 s C 8 a 1 1 C 27 1 β + C 10 ∗ 3 C 8 sa Σ N → Σ N α 2 10 2 β 3 C 27 C 10 Σ N → Σ N – α β 2 α = 1 S 0 , 3 P 0 , 3 P 1 , 3 P 2 , β = 3 S 1 , 3 S 1 − 3 D 1 , 1 P 1 No. of contact terms (LECs): limited by SU(3) symmetry LO : 6 [2 ( NN , ΞΞ ) + 3 ( YN , Ξ Y ) + 1 ( YY )] NLO: 22 [7 ( NN , ΞΞ ) + 11 ( YN , Ξ Y ) + 4 ( YY )] (No. of spin-isospin channels in NN + YN : 10 S = − 2 , − 3 , − 4: 27) Johann Haidenbauer Baryon-baryon interactions

SU(3) symmetry + breaking S. Petschauer, N. Kaiser, NPA 916 (2013) 1: example: 1 S 0 partial wave for pure { 27 } states C 27 + C 27 ( p 2 + p ′ 2 ) + 1 V I = 1 ˜ 2 C χ 1 ( m 2 K − m 2 = π ) NN C 27 + C 27 ( p 2 + p ′ 2 ) + 1 V I = 3 / 2 ˜ 4 C χ 1 ( m 2 K − m 2 = π ) Σ N C 27 + C 27 ( p 2 + p ′ 2 ) V I = 2 ˜ = ΣΣ C 27 + C 27 ( p 2 + p ′ 2 ) + 1 V I = 3 / 2 ˜ 4 C χ 2 ( m 2 K − m 2 = π ) ΞΣ C 27 + C 27 ( p 2 + p ′ 2 ) + 1 2 C χ V I = 1 ˜ 2 ( m 2 K − m 2 = π ) ΞΞ C χ 1 , C χ 2 , LECs that break SU(3) symmetry of LO contact terms Our strategy: impose SU(3) symmetry only for BB systems with same strangeness S { NN } or { Λ N , Σ N } or { ΛΛ , ΣΣ , Ξ N , ΛΣ } BB scattering for S = 0 to S = − 4: 6 C χ i s for 1 S 0 and 6 C χ i s for 3 S 1 → cannot be determined from presently available data Johann Haidenbauer Baryon-baryon interactions

Coupled channels Lippmann-Schwinger Equation T ν ′ ν, J V ν ′ ν, J ( p ′ , p ) ( p ′ , p ) = ρ ′ ρ ρ ′ ρ � ∞ dp ′′ p ′′ 2 2 µ ρ ′′ V ν ′ ν ′′ , J p 2 − p ′′ 2 + i η T ν ′′ ν, J � ( p ′ , p ′′ ) ( p ′′ , p ) + ρ ′ ρ ′′ ρ ′′ ρ ( 2 π ) 3 0 ρ ′′ ,ν ′′ ρ ′ , ρ = Λ N , Σ N ( ΛΛ , Ξ N , ΛΣ , ΣΣ ) LS equation is solved for particle channels (in momentum space) Coulomb interaction is included via the Vincent-Phatak method The potential in the LS equation is cut off with the regulator function: V ν ′ ν, J ( p ′ , p ) → f Λ ( p ′ ) V ν ′ ν, J f Λ ( p ) = e − ( p / Λ) 4 ( p ′ , p ) f Λ ( p ); ρ ′ ρ ρ ′ ρ consider values Λ = 550 - 700 MeV [LO] 500 - 650 MeV [NLO] Johann Haidenbauer Baryon-baryon interactions

YN integrated cross sections − p -> Λ n Λ p -> Λ p Λ p -> Λ p Σ 300 70 300 + n -> 0 p Σ <- Σ EFT LO EFT LO NLO 60 Sechi-Zorn et al. EFT LO 250 Jülich ’04 Kadyk et al. Kadyk et al. Engelmann et al. Alexander et al. Jülich ’04 Jülich ’04 Hauptman 50 200 200 40 σ (mb) σ (mb) σ (mb) 150 30 100 100 20 50 10 0 0 0 100 200 300 400 500 600 700 800 900 500 600 700 800 100 120 140 160 180 p lab (MeV/c) p lab (MeV/c) p lab (MeV/c) LO: H. Polinder, J.H., U.-G. Meißner, NPA 779 (2006) 244 NLO: J.H., S. Petschauer, et al., NPA 915 (2013) 24 Jülich ’04: J.H., U.-G. Meißner, PRC 72 (2005) 044005 Johann Haidenbauer Baryon-baryon interactions

YN integrated cross sections − p -> Σ 0 n − p -> Σ − p + p -> Σ + p Σ Σ Σ 500 300 250 EFT LO EFT LO NLO NLO 250 Jülich ’04 EFT LO Jülich ’04 400 NLO Eisele et al. 200 Eisele et al. Jülich ’04 Engelmann et al. 200 300 150 σ (mb) σ (mb) σ (mb) 150 200 100 100 100 50 50 0 0 0 100 120 140 160 180 100 120 140 160 180 100 120 140 160 180 p lab (MeV/c) p lab (MeV/c) p lab (MeV/c) LO: H. Polinder, J.H., U.-G. Meißner, NPA 779 (2006) 244 NLO: J.H., S. Petschauer, et al., NPA 915 (2013) 24 Jülich ’04: J.H., U.-G. Meißner, PRC 72 (2005) 044005 Johann Haidenbauer Baryon-baryon interactions

Λ p differential cross sections Λ p -> Λ p Λ p -> Λ p Λ p -> Λ p 50 50 3 p lab = 180-248 MeV/c p lab = 248-330 MeV/c Alexander (1968) Sechi-Zorn (1968) Jülich 04 Sechi-Zorn (1968) Sechi-Zorn (1968) NSC97f 40 40 LO600 LO600 d σ/ d Ω forward/backward ratio LO NLO600 NLO600 NLO J04 J04 NSC97f NSC97f 2 no. of events no. of events 30 30 20 20 1 10 10 0 0 0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 100 200 300 400 500 cos θ cos θ p lab (MeV/c) LO: H. Polinder, J.H., U.-G. Meißner, NPA 779 (2006) 244 NLO: J.H., S. Petschauer, et al., NPA 915 (2013) 24 Jülich ’04: J.H., U.-G. Meißner, PRC 72 (2005) 044005 Nijmegen NSC97f: T.A. Rijken et al., PRC 59 (1999) 21 Johann Haidenbauer Baryon-baryon interactions

YN differential cross sections − p -> Λ n − p -> Λ n − p -> Σ − p Σ Σ Σ 150 140 140 p lab = 160 MeV/c p lab = 160 MeV/c p lab = 135 MeV/c 120 120 100 100 100 d σ /dcos θ (mb) d σ /dcos θ (mb) d σ /dcos θ (mb) 80 80 60 60 50 40 40 20 20 0 0 0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 cos θ cos θ cos θ Johann Haidenbauer Baryon-baryon interactions

YN differential cross sections − p -> Σ − p + p -> Σ + p + p -> Σ + p Σ Σ Σ 60 100 70 p lab = 550 MeV/c p lab = 450 MeV/c p lab = 170 MeV/c 60 50 80 50 40 d σ /dcos θ (mb) d σ /dcos θ (mb) d σ /dcos θ (mb) 60 40 30 30 40 20 20 20 10 10 0 0 0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 cos θ cos θ cos θ Johann Haidenbauer Baryon-baryon interactions

YN scattering lengths [fm] experiment ∗ EFT LO EFT NLO Jülich ’04 NSC97f Λ [MeV] 550 · · · 700 500 · · · 650 a Λ p − 1 . 8 + 2 . 3 − 1 . 90 · · · − 1 . 91 − 2 . 90 · · · − 2 . 91 − 2 . 56 − 2 . 51 s − 4 . 2 a Λ p − 1 . 6 + 1 . 1 − 1 . 22 · · · − 1 . 23 − 1 . 51 · · · − 1 . 61 − 1 . 66 − 1 . 75 t − 0 . 8 a Σ + p − 2 . 24 · · · − 2 . 36 − 3 . 46 · · · − 3 . 60 − 4 . 71 − 4 . 35 s a Σ + p 0 . 60 · · · 0 . 70 0 . 48 · · · 0 . 49 0 . 29 − 0 . 25 t χ 2 ≈ 30 15 . 7 · · · 16 . 8 ≈ 22 16 . 7 ( 3 Λ H ) E B − 2 . 34 · · · − 2 . 36 − 2 . 30 · · · − 2 . 33 − 2 . 27 − 2 . 30 − 2 . 354 ( 50 ) ∗ G. Alexander et al., PR 173 (1968) 1452 Note: ( 3 Λ H ) E B is used as additional constraint in EFT and Jülich ’04 Λ p data alone do not allow to disentangle 1 S 0 (s) and 3 S 1 (t) contributions Johann Haidenbauer Baryon-baryon interactions