Testing the conjecture of partial chiral symmetry restoration: - PowerPoint PPT Presentation

Testing the conjecture of partial chiral symmetry restoration: meson-nucleus potentials and the search for mesic states Volker Metag II. Physikalisches Institut *funded by the DFG within SFB/TR16 56th. Int. Winter Meeting on Nuclear Physics Bormio, Italy, Jan. 22-26, 2018 1

bound systems bound by gravitation earth-moon system 2

bound systems bound by gravitation electromagnetic interaction e - ������� atom � �� ��� earth-moon system 2

bound systems bound by gravitation electromagnetic interaction e - ������� atom � �� ��� earth-moon system π - ,K - ������� π - ,K - - atoms � �� ��� 2

bound systems � ����,���������)� bound by strong gravitation electromagnetic interaction interaction e - η ’ mesic state ������� atom � �� ��� earth-moon system π - ,K - ������� π - ,K - - atoms � �� ��� 2

bound systems � ����,���������)� bound by strong gravitation electromagnetic interaction interaction e - η ’ mesic state ������� atom ⬄ � �� ��� earth-moon system meson - nucleus π - ,K - interaction attractive? repulsive? ������� → meson-nucleus potential π - ,K - - atoms � �� ��� 2

outline ◆ introduction: meson-nucleus interactions ◆ methods for determining meson-nucleus potentials ◆ ◆ potential parameters for K + ,K 0 ,K - , η , η ’ ω , Φ - A interaction ◆ ◆ search for meson-nucleus bound states ◆ summary & outlook 3

symmetry breaking in the hadronic sector MeV/c 2 1000 M=958 MeV/c 2 nonet of 750 pseudoscalar η M=548 MeV/c 2 500 K M=498 MeV/c 2 mesons 250 π M=140 MeV/c 2 0 4

symmetry breaking in the hadronic sector MeV/c 2 1000 M=958 MeV/c 2 nonet of 750 pseudoscalar η M=548 MeV/c 2 500 K M=498 MeV/c 2 mesons 250 π M=140 MeV/c 2 0 V. Bernard, R.L. Jaffe, U.-G. Meissner, NPB 308 (1988) 753 S. Klimt, M. Lutz, U. Vogel, W Weise, NPA 516 (1990) 429 Mass [GeV] mass as a result of η ’ 1000 η 0 symmetry breaking 800 η 600 SU(3) L x SU(3) R K 400 Goldstone bosons π 200 π , K, η 0 , η 8 π , K, η 8 0 SU(3) F spontaneous breaking U(1) A 0 U(3) L x U(3) R m u ≈ 2.3 MeV breaking breaking 0 m d ≈ 4.8 MeV 0 0 m i = 0 m i = 0 0 m s ≈ 95 MeV symmetry breaking 4

symmetry breaking in the hadronic sector MeV/c 2 1000 M=958 MeV/c 2 nonet of 750 pseudoscalar η M=548 MeV/c 2 500 K M=498 MeV/c 2 mesons 250 π M=140 MeV/c 2 0 V. Bernard, R.L. Jaffe, U.-G. Meissner, NPB 308 (1988) 753 S. Klimt, M. Lutz, U. Vogel, W Weise, NPA 516 (1990) 429 Mass [GeV] mass as a result of η ’ 1000 η 0 symmetry breaking 800 η 600 SU(3) L x SU(3) R K 400 partial restoration of Goldstone bosons π 200 chiral symmetry π , K, η 0 , η 8 π , K, η 8 0 SU(3) F predicted to occur spontaneous breaking U(1) A 0 U(3) L x U(3) R m u ≈ 2.3 MeV in a nucleus ⟹ impact breaking breaking 0 m d ≈ 4.8 MeV 0 0 m i = 0 m i = 0 0 m s ≈ 95 MeV on meson masses ?? symmetry breaking partial symmetry restoration 4

Predictions for in-medium mass changes η , η ’ K + , K - ρ , ω , Φ NJL-model RMF-approach QCD sum rules H. Nagahiro et al., T. Hatsuda, S. Lee J.Schaffner-Bielich et al., PRC 74 (2006) 045203 PRC46 (1992)R34 Nucl. Phys. A625 (1997) 325 SU(3) SU(2) Δ m ρ ( ρ 0 ) ≈ - (80-160) MeV Δ m η ’ ( ρ 0 ) ≈ -150 MeV Δ m K+ ( ρ 0 ) ≈ +30 MeV Δ m ω ( ρ 0 ) ≈ - (80-160) MeV Δ m η ( ρ 0 ) ≈ +20 MeV Δ m K- ( ρ 0 ) ≈ -100 MeV Δ m Φ ( ρ 0 ) ≈ -(20-30) MeV 5

Predictions for in-medium broadening ω Φ unitary coupled channel chiral-SU(3) effective Lagrangian model effective field theory P . Gubler, W. Weise P . Mühlich et al., PLB 751 (2015) 396 NPA 780 (2006) 187 Γ ω ( ρ = ρ 0 ) ≈ 60 MeV Γ Φ ( ρ = ρ 0 ) ≈ 45 MeV in the nuclear medium: mesons removed by inelastic reactions → shorter lifetime → larger in-medium width 6

meson-nucleus potential H. Nagahiro, S. Hirenzaki, PRL 94 (2005) 232503 U(r) = V(r) + i W(r) attractive ? absorption repulsive ? W(r) = - Γ 0 /2 ⋅ ρ (r)/ ρ 0 V(r) = Δ m( ρ 0 ) ⋅ ρ (r)/ ρ 0 = -1/2 ⋅ hc ⋅ ρ (r) ⋅ σ inel ⋅ β 7

meson-nucleus potential H. Nagahiro, S. Hirenzaki, PRL 94 (2005) 232503 U(r) = V(r) + i W(r) attractive ? absorption repulsive ? W(r) = - Γ 0 /2 ⋅ ρ (r)/ ρ 0 V(r) = Δ m( ρ 0 ) ⋅ ρ (r)/ ρ 0 = -1/2 ⋅ hc ⋅ ρ (r) ⋅ σ inel ⋅ β line shape analysis ⦁ transparency ratio measurement ⦁ excitation function σ γ A →η ’X ⦁ T A = momentum distribution A ⋅ σ γ N →η ’X ⦁ meson-nucleus bound states ⦁ D. Cabrera et al., NPA733 (2004)130 7

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function σ m V=0 γ N E thr E γ 8

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function σ m σ m attractive V=0 V=0 γ N E thr E γ E γ attractive interaction → mass drop → lower threshold → larger phase space → larger cross section 8

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function σ m σ m σ m attractive attractive V=0 V=0 V=0 repulsive γ N E thr E γ E γ E γ attractive interaction → mass drop → lower threshold → larger phase space → larger cross section repulsive interaction → mass increase → higher threshold → smaller phase space → smaller cross section 8

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function momentum distribution σ m σ m σ m d σ m attractive attractive dp m V=0 V=0 V=0 V=0 repulsive γ N E thr E γ E γ E γ p m attractive interaction → mass drop → lower threshold → larger phase space → larger cross section repulsive interaction → mass increase → higher threshold → smaller phase space → smaller cross section 8

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function momentum distribution σ m σ m σ m d σ m d σ m attractive attractive dp m dp m V=0 V=0 V=0 V=0 V=0 repulsive repulsive γ N E thr E γ E γ E γ p m p m attractive interaction → mass drop → repulsive interaction → extra kick → lower threshold → larger phase space → shift to higher momenta larger cross section repulsive interaction → mass increase → higher threshold → smaller phase space → smaller cross section 8

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function momentum distribution σ m σ m σ m d σ m d σ m d σ m attractive attractive attractive dp m dp m dp m V=0 V=0 V=0 V=0 V=0 V=0 repulsive repulsive repulsive γ N E thr E γ E γ E γ p m p m p m attractive interaction → mass drop → repulsive interaction → extra kick → lower threshold → larger phase space → shift to higher momenta larger cross section attractive interaction → repulsive interaction → mass increase → meson slowed down → higher threshold → smaller phase space → shift to lower momenta smaller cross section 8

Determining the real part of the meson-nucleus potential from excitation functions and momentum distributions sensitive to nuclear density at the production point excitation function momentum distribution σ m σ m σ m d σ m d σ m d σ m attractive attractive attractive dp m dp m dp m V=0 V=0 V=0 V=0 V=0 V=0 repulsive repulsive repulsive γ N E thr E γ E γ E γ p m p m p m attractive interaction → mass drop → repulsive interaction → extra kick → lower threshold → larger phase space → shift to higher momenta larger cross section attractive interaction → repulsive interaction → mass increase → meson slowed down → higher threshold → smaller phase space → shift to lower momenta smaller cross section quantitative analysis requires transport model or collision model calculations 8

Determining the imaginary part of the meson-nucleus potential from transparency ratio measurements η ’ T A = σ γ A →η ’X D. Cabrera et al., γ A ⋅ σ γ N →η ’X NPA733 (2004)130 π η ’ transport model calculation: GiBUU collision model calculation E. Ya. Paryev, J. Phys.G 40 (2013)025201 P . Mühlich and U. Mosel, NPA 773 (2006) 156 γ A →ω X at E γ =1.5 GeV γ A →η ’X at E γ =1.9 GeV 1.1 1.0 E γ =1.9 GeV 0.9 σ inel [mb] 0.8 C T A 6 Γ 0 =37 MeV 8 0.7 10 11.5 13 0.6 15 17 0.5 0 20 40 60 80 100 120 140 160 180 200 220 240 260 A W( ρ = ρ 0 ) = - Γ /2 ( ρ = ρ 0 ) -1/2 ⋅ hc ⋅ ρ 0 ⋅ σ inel ⋅ β = 9