from / production data and in-medium properties Shuntaro Sakai - PowerPoint PPT Presentation

Study of η ′ 𝑂 interaction from η/η ′ production data and in-medium η′ properties Shuntaro Sakai (Institute of Theoretical Physics, CAS (Beijing,China))

Introduction - O rigin of the η’ mass Anomaly-induced coupling ← U A (1) anomaly and chiral symmetry breaking (3flavor) Witten(1979),’t Hooft (1986),… Pisarski-Wilzek(1984), Kunihiro-Hatsuda(1988), Cohen (1996), Lee- Hatsuda (1996),…  Chiral restoration in nuclear medium (reduction of order parameter of chiral symmetry breaking) In- medium η’ as a probe of chiral symmetry in nuclear medium - η’ mass in finite density Costa-Ruivo-Kalinovsky(2003), Kwon-Lee-Morita-Wolf(2012), Fejos-Hosaka (2017)… - η’ -nucleus system Tsushima(2000),Nagahiro-Hirenzaki(2005),Nagahiro-Takizawa-Hirenzaki (2006),Jido-Nagahiro-Hirenzaki (2012), Tanaka et al . (2016),Metag-Naova-Paryev (2017),… η’ -nucleon interaction = basic information Borasoy (2000), Bass-Thomas (2006), Oset-Ramos (2011), S.S.-Jido(2013), Moskal(2000), Czerwinski et al .(2014) ,… s-wave η’p scattering length from pp  ppη’  Study of η’ -few nucleon system: Sekihara-Fujioka-Ishikawa(2018) for η’d

Recent data on η/η′ photoproduction η ′ 𝑞 threshold effect A2 Collaboration at MAMI, PRL118(2017)212001

- η′ photoproduction from proton -- Comparison with phase space Data: A2 Collaboration at MAMI, PRL118(2017)212001 Phase space Near-threshold enhancement ■ N(1895) contribution: PRL118(2017)212001[A2 Collaboration], PLB785(2018)626[Anisovich et al.]

from latest PDG [PRD98,030001(2018)] Broad resonance @ η ′ 𝑞 threshold(=1896MeV) - πN  πN: PRC89(2014)045205[ Svarc et al .] - γp  K *Λ: PLB771(2017)142[CLAS Collab.] - γp and π p  KΛ : EPJA53(2017)242[Anisovivh et al .] - Multichannel: PRL119(2017)062004[Anisovich et al .]

- η photoproduction from proton MAID analysis: A2MAMI, PRL118(2017)212001 Partial-wave analysis: Anisovich et al , arxiv:1803.06814 Threshold effect -- Threshold effect: Flatte parametrization or K-matrix approach Partial-wave analysis  s-wave η ′ 𝑞 scattering length Anisovich et al ., arxiv:1803.06814

Threshold cusp  A simple t matrix with channel coupling: (κ: real and positive)

Information on 𝜽 ′ 𝒒 amplitude ( 𝑁𝐶 can be η ′ 𝑞, η𝑞, π𝑞 , 𝐿Λ , 𝐿Σ , ω𝑞 ,…) Extraction of the η ′ 𝑞 amplitude □ η ′ 𝑞 scattering length □ η ′ -optical potential from η/η′ -photoproduction data -- Focus on η ′ 𝑞 -threshold behavior  Focus on the η ′ 𝑞 -threshold region (~100MeV around η ′ 𝑞 threshold)

Setup 〇 Final-State Interaction = + +… ~1.7GeV -- for channel coupling effect ( π𝑞 , 𝐿Λ , 𝐿Σ , ω𝑞 ) ※ Resonance is not assumed in η ( ’ ) p amplitude

: polynomial of 𝑡 -- with for η𝑞 and η′𝑞 -- --- to take account of other channels ( π𝑞 , 𝐿Λ , 𝐿Σ , ω𝑞 ,…) Fit η/η′ -photoproduction data in (Δ <70MeV) Fit parameter -- Interaction kernel of η (′) 𝑞 -- η (′) 𝑞 production amplitude from photon

Constraint on scattering amplitude 〇 Optical theorem can happen Restriction a large number

A simple test: fit γ𝑞 → η ′ 𝑞 data with η ′ 𝑞 FSI () with  phase space  fit η ′ 𝑞 -threshold Data: A2MAMI, PRL118(2017)212001 0 Flip sign below η ′ 𝑞 threshold

A simple test: fit γ𝑞 → η ′ 𝑞 data with η ′ 𝑞 FSI with 𝑁𝐶 = η ′ 𝑞 would be responsible for the enhancement

Results of γ𝑞 → η (′) 𝑞 fitting γ𝑞 → η𝑞 data: A2MAMI, PRL118(2017)212001 and CLAS, PRC80(2009)045213 γ𝑞 → η ′ 𝑞 data : A2MAMI, PRL118(2017)212001 Fit Δ varied (n max =1) Δ=50 -70MeV

η ′ 𝑞 scattering amplitude Δ varied (n max =1) 0 (Δ=60MeV) η ′ 𝑞 -threshold Flip sign below η ′ 𝑞 threshold 𝑞𝑞 → 𝑞𝑞η′ [Czerwinski et al ., PRL113, 062004(2014)] -- pole~(1877- 63i)MeV(Δ=60MeV) 〇 Too far away from real axis… ※ Error of parameters: ~10% Anisovich et al ., arxiv:1803.06814

Results of γ𝑞 → η (′) 𝑞 fitting : polynomial of 𝑡 -- Fit (Δ=60MeV fixed) n max varied

η ′ 𝑞 scattering amplitude n max varied (Δ=60MeV) 0 η ′ 𝑞 -threshold

Δ varied (Δ=30MeV)

η ′ -optical potential @ ρ = ρ 0 Δ varied (n max =1)

η ′ -optical potential @ ρ = ρ 0 n max varied (Δ=60MeV)

Δ varied

Summary • Analysis of η/η ′ photoproduction data with η (′) 𝑞 Final-State Interaction • Threshold effect Reproduced • Near-threshold enhancement in γ𝑞 → η ′ 𝑞 by η (′) 𝑞 FSI well • Cusp of γ𝑞 → η𝑞 cross section @ η ′ 𝑞 thr. • For s-wave η ′ 𝑞 scattering length, +some uncertainties… • Contribution from broad resonance @1880MeV? ~N(1895)? -- Similar result to other analyses -- Too far away from real axis: large uncertainties… • η ′ -optical potential from η ′ 𝑞 amplitude with 𝑢ρ approximation • Magnitude: O(10) MeV @ρ=ρ 0 (typical hadronic scale) • Characteristic energy dependence near η ′ 𝑞 threshold