X hyperons in the nuclear medium described by - PowerPoint PPT Presentation

X hyperons in the nuclear medium described 光学模光学模型ポテンシャルにおける by the chiral NLO interactions M. Kohno, RCNP Osaka University ◼ It is basic to obtain a better description of baryon-baryon interactions in the strangeness sector to understand strangeness physics ◼ Various potentials since 1970s ➢ Boson exchange picture: Nijmegen group [NHC-D, NHC-F, NSC89, NSC97, ESC04, ESC08, ESC16], Jülich YN(2005), ⋯ ➢ Quark picture: SU6 quark model by Kyoto-Niigata group [fss2] ⚫ role of Pauli forbidden state: strong repulsion in the S N 3 S 1 T=3/2 channel ⚫ role of antisymmetric spin-orbit component: small Λ spin-orbit splitting ◼ Recent development: construction in chiral effective field theory

Construction of baryon-baryon interactions in ChEFT B-B interactions in the strangeness sector by the Jülich-Bonn-München group ◼ 𝑇 = −1 ◼ LO [Polinder, Haidenbauer, and Meißner, Nucl. Phys. A 779 , 244 (2006)], NLO13, ➢ NLO19 [Haidenbauer, Meißner, and Nogga, arXiv:1906.11681] 𝑇 = −2 ◼ ➢ LO [Polinder, Haidenbauer, and Meißner, Phys. Lett. B653, 29 (2016)], NLO [Petschauer, Kaiser, Haidenbauer, Meißner, and Weise, Phys. Rev. C 93 , 014001 (2016)], Updated version [Haidenbauer and Meißner, Euro.Phys.J. A 55 , 23 (2019)] which is used in the present calculations. NLO diagrams [ 𝜌, 𝐿, and 𝜃 exchanges in SU(3) ] Parameters are determined by SU(3) symmetry and (scarce) two-body data. ◼ It is important to examine the predictions of the interaction for X properties in ◼ the nuclear medium and compare them with (yet scarce) experimental data.

XN phase shifts: NLO ChEFT and HAL-QCD ◼ It is interesting to see that ChEFT NLO potential and HAL-QCD potential (by T. Inoue†) yield similar XN phase shifts in all s-waves. † Takashi Inoue for HAL QCD Collaboration, AIP Conference Proceedings 2130, 020002 (2019) [ https://doi.org/10.1063/1.5118370 ]

Recent experiments concerning the 𝑇 = −2 sector Experimental data is scarce. ◼ ➢ Potential parameters are not well controlled. Recent ( K - , K + ) experiments at KEK ◼ (1) Emulsion experiments ➢ Double L hypernuclei, most likely ΛΛ 11 Be with ΔB ΛΛ = 1.87 ± 0.37 MeV [Ekawa et al ., PTEP 2019, 021D02 (2019)] ΔB ΛΛ = − ΛΛ V ΛΛ 𝐵 − (positive rearrangement effect, ∼ 1 MeV) ➢ Deeply bound ( 4.38 ± 0.28 MeV) state of X - – 14 N ( X - + 14 N → 10 Be + Λ 5 He ) Λ [Nakazawa et al ., PTEP 2015, 033D02 (2015)] (2) X production ( K - , K + ) inclusive spectrum on 12 C (Cross sections are not available yet) ➢ Peak position and its dependence on the momentum transfer (namely, K + scattering angle) depend on the X optical potential. ➢ Cross sections around the threshold are sensitive to the X potential.

X potential in nuclear matter: the lowest order Brueckner theory The cutoff scale ~550 MeV of ChEFT is not so soft to use the interactions in a ◼ perturbative scheme. The high-momentum components are treated by the Bethe-Goldstone ◼ equation (Lowest-order Brueckner theory) 𝑅 𝐻 XN ｰ XN = 𝑊 XN − XN + ෍ 𝑊 𝐻 𝐶 1 𝐶 2 − XN XN −𝐶 1 𝐶 2 𝜕 − 𝑢 𝐶 1 − 𝑢 𝐶 2 − 𝑉 𝐶 1 − 𝑉 𝐶 2 𝐶 1 𝐶 2 N X N X X N X N X N 𝑊 𝑊 B 1 B 2 G = + G X N X N X N Continuous prescription: potentials 𝑉 𝑂 , 𝑉 Λ , 𝑉 Σ in intermediate propagators ◼ are prepared by ChEFT NN, Λ N and Σ N interactions including 3BF effects. 𝑉 Ξ = σ 𝑂 X 𝑂 𝐻 XN ｰ XN X 𝑂 X single-particle potential ◼

X Potentials in nuclear matter real part imaginary part The weak attractive contribution ◼ comes from the baryon channel ( ΣΣ ) coupling in the T=0 3 S 1 state. Imaginary potential (from the ΛΛ ◼ coupling) is small at low momenta. Without baryon channel coupling, k-dependence is ◼ weak （ no meson-exchange XN → NX process ） .

X Potentials in pure neutron matter real part imaginary part Dose X - hyperon appear in high-density neutron star matter? ◼ X - potential with ChEFT is repulsive in pure neutron matter at higher ◼ densities.

X Potential in finite nuclei: local-density approximation ◼ Use local-density approximation （ LDA ） to convert the potential in NM into the potential in a finite nucleus. −1 ] local Fermi momentum [fm 12 C 0.2 ➢ Density distribution of a nucleus 𝜍(𝑠) 1.5 normal density density [fm −3 ] local Fermi momentum 1 0.1 𝑙 𝐺 𝑠 = 3𝜌 2 𝜍(𝑠)/2 1/3  (r) k F (r) 0.5 ➢ X potential 𝑉 X 𝑂𝑁 (𝐹, 𝑙 𝐺 ) in NM 0 0 0 2 4 6 as a function of 𝐹 (or 𝑙 ) r [fm] X potential in a finite nucleus 𝑉 X (𝐹, 𝑙 𝐺 (𝑠)) ➢ To correct the finite range effect, introduce a Gaussian form factor with the range 𝛾 = 1 fm (improve LDA). 𝑉 X 𝑠; 𝐹 = ( 𝜌𝛾) −3 න 𝑒𝒔 𝑓 − 𝒔−𝒔 ′ 2 /𝛾 2 𝑉 X (𝐹, 𝑙 𝐺 (𝑠′)) The reliability of the improved LDA is checked by comparing the ◼ potential with a more sophisticated folding procedure.

𝑉 X 𝑠; 𝐹 in 12 C and 14 N improved LDA improved LDA 12 C 14 N 10 10 E E U X (r;E) [MeV] U X (r;E) [MeV] 100 MeV 200 MeV 150 MeV 150 MeV 100 MeV 100 MeV 0 0 E E 50 MeV 50 MeV 20 MeV 20 MeV 0 MeV 0 MeV −10 −10 0 2 4 6 0 2 4 6 r [fm] r [fm] Weakly attractive at low energies, mainly due to the X N- SS ◼ coupling in T=1 3 S 1 state. The attractive potential lowers s and p Coulomb bound levels. ◼ The potential becomes repulsive with increasing the energy. ◼

Bound states provided by 𝑉 X 𝑠; 𝐹 𝑎𝑓 2 𝑠 2 𝑎𝑓 2 3 𝑠 for 𝑠 > 𝑆 𝐷 , 𝑆 𝐷 = 1.15𝐵 1/3 Coulomb: 𝑊 𝐷 𝑠 = − 2 − for 𝑠 < 𝑆 𝐷 , − 2 2𝑆 𝐷 2𝑆 𝐷 X  X - X  X - E=0 pure E=0 E=0 pure E=0 MeV Coul. MeV Exp. MeV Coul. MeV Exp. 0 0 0d 0d 0d 0d 0p 0p candidates depending on the residual nuclei 0p 0p −1 0s −1 0s 0s 0s −2 −2 MeV MeV −3 −3 −4 −4 0s X bound states X bound states −5 12 C −5 14 N in in 0s with U X (r,E) with U X (r,E) −6 −6 Exp. Data: Aoki et al ., Exp. Data: Nakazawa et al ., Phys. Lett. B355, 45 (1995) PTEP 2015, 033D02 (2015)

Summary in the first half ◼ X potentials are calculated in nuclear matter, using the NLO baryon-baryon interactions in chiral effective field theory, in the framework of lowest-order Brueckner theory ➢ N, L, and S potentials in the propagators of the G-matrix equation are prepared by the ChEFT interactions with including the effects of 3-body forces. ◼ The X potential in NM is converted to the potential in finite nuclei by improved LDA method. ➢ X bound states in 12 C and 14 N are evaluated. ➢ Shallow bound states are reasonable in view of the recent emulsion data. ◼ It is straightforward to study X bound states in heavier nuclei. ◼ Further experimental data should help to lessen the uncertainties in the parametrization of the interaction in 𝑇 = −2 . M. Kohno, “ X hyperons in the nuclear medium described by chiral NLO interactions“, Phys. Rev. C100, 024313 (2019)

X production ( K - , K + ) inclusive spectrum ◼ K + inclusive spectra of ( K - , K + ) X production reaction on nuclei provide information on X optical potential as well as X bound states. ➢ Experimental data of new 12 C( K - , K + ) measurements at KEK is being analyzed. ◼ 9 Be( K - , K + ) and 12 C( K - , K + ) spectra are calculated, using a semiclassical distorted wave method. ◼ Data of previous experiment at BNL [Khaustov et al., Phys. Rev. C61, 054603 (2000)] was used to deduce the attractive X potential with the strength of 14 MeV in a W-S shape. ◼ 𝑊 = −14 MeV has been a canonical value, but not conclusive.

DWBA description of X production ( K - , K + ) inclusive process 𝜀(𝑋 − 𝜗 Ξ + 𝜗 ℎ ) 𝐿 + 𝐿 − 𝑤 𝑔,𝑞,𝑗,ℎ Ξ ℎ 𝑒 2 𝜏 2 𝑒𝑋𝑒Ω = 𝜕 𝑗,𝑠𝑓𝑒 𝜕 𝑔,𝑠𝑓𝑒 𝑞 𝑗 1 − 𝜚 Ξ − 𝑤 𝑔,𝑞,𝑗,ℎ 𝜓 𝐿 − + 𝜚 ℎ ෍ 𝜓 𝐿 + 𝜀(𝑋 − 𝜗 Ξ + 𝜗 ℎ ) 2𝜌 2 𝑞 𝑔 4𝜕 𝑗 𝜕 𝑔 Ξ,ℎ − ： distorted waves are evaluated by OMP ｓ in a 𝑢𝜍 approximation + , 𝜓 𝐿 + ◼ 𝜓 𝐿 − ◼ 𝑤 𝑔,𝑞,𝑗,ℎ ： elementary amplitude ◼ Calculations by the semi-classical distorted wave (SCDW) method. ➢ Proton Fermi motion and angle dependence of the elementary amplitude are taken into account.