Meson Properties at Finite Density from Meson-Nucleus Systems

Meson Properties at Finite Density from Meson Nucleus Systems Satoru Hirenzaki (Nara Womens University, Japan) 10 June 2015 * eta by d+d * Comments on phi data

Basic Motivation Symmetry Breaking Pattern and Meson Properties h’ h p … cf.) NJL model with KMT Schematic View of the PS meson mass spectrum Jido et al., PRC85(12)032201(R) Nagahiro et al., PRC (2013) 1000 800 UA(1) breaking (KMT term[1,2]) 600 UA(1)anomaly effect Meson mass [MeV] 400 200 massless [1] Kobayashi-Maskawa PTP44(70)1422 [2] G. ’t Hooft, PRD14(76)3432 ChS manifest dynamically broken dyn. & explicitly broken Costa et al.,PLB560(03)171, Nagahiro-Takizawa-Hirenzaki, PRC74(06)045203

Formation of η-4He by d + d reaction at COSY with H. Nagahiro (Nara Women’s Univ.) N. Ikeno (Tottori Univ.) D. Jido (Tokyo Metropolitan Univ)

hNN* system -No I=3/2 baryon contamination -Large coupling constant -no suppression at threshold (s-wave coupling) Doorway to N*(1535) eta-Nucleus system h-mesic nuclei properties of eta meson h meson h-N system • Strong Coupling to N*(1535), Motivation and our aim • h-N system … strongly couples to the N*(1535) resonance • h-mesic nuculei … doorway to in-medium N*(1535) • N*(1535) … a candidate of the chiral partner of nucleon • chiral symmetry for baryons ?

h-mesic nuclei Many works for h mesic nuclei from 1980’s • Theor. Liu, Haider, PRC34(1986)1845 Kohno, Tanabe, PLB231(1989)219; NPA519(1990)755 Garcia-Recio, Nieves, Inoue, Oset PLB550(02)47 C. Wilkin, T. Ueda, S. Wycech, …… • Exp. Chrien et al., PRL60(1988)2595 TAPS@MAMI (g + 3He  p0 + p + X) COSY-GEM (p + Al  3He + Mg-h) WASA-at-COSY (d + d  3He + p + p) JPARC (Itahashi, Fujioka…), …… Our works for eta-mesic nuclei • R.S. Hayano, S. Hirenzaki, A. Gillitzer, Eur. Phys. J. (99) • D.Jido, H.Nagahiro and S.Hirenzaki, Phys.Rev.C66, 045202, 2002. • H.Nagahiro, D.Jido, S.Hirenzaki, Phys.Rev.C68, 035205, 2003. • H.Nagahiro, D.Jido and S.Hirenzaki, Nucl.Phys.A761,92, 2005. • D.Jido, E.E.Kolomeitsev, H.Nagahiro, S.Hirenzaki, Nucl.Phys.A811:158, 2008. • H.Nagahiro, D.Jido, S.Hirenzaki, Phys.Rev.C80,025205, 2009.

A Theoretical Calculation for (discussions with P.Moskal, W. Krzemien, M. Skurzok) Some remarks • Momentum transfer ------- Large pd = 1.025 GeV/c, pa = ph= 0 at threshold in C.M. • Data of d d 4He h above threshold • Simple spectral structure is expected for light systems • It’s a few body system (2N+2N  4N + eta), but the momentum transfer is large. • NO SPECTATOR! All 4N participate to the formation reaction seriously for ‘the signal process’. • Results of experiments: • exclusive analysis for the final states, charge channels,,,

A Theoretical Calculation for Some remarks • Transition (h-production) part h High q transfer at each propagator Parameterize this part.

A Theoretical Calculation for Schematic picture d h Green function method a d with h-a optical potential s total s s(dd4Heh) data escape conversion Etot Etot threshold threshold

Green’s function method Ref. O.Morimatsu and K. Yazaki, NPA435(1985)727-737  

h d F(q) a d Scattering Amplitude F(q) ( f (r) : r-space representation)… Assumed to be Gaussian

A Theoretical Calculation for 3 parameters in this model • h-a optical potential • (used to calculate the eta Green’s function • V0, W0 • Potential Strength • at nuclear center • h production part dd 4Heh • F should include the information on • Deuterons and alpha particle structure and their overlap (fusion) • Nucleon - nucleon interaction for eta meson production • for high momentum transfer region.

A Theoretical Calculation for Exp. Data of dd4Heh Fig. taken from NFQCD10@YITP, 2010 slide by S. Schadmand R.Frascaria et al., Rhys.Rev.C50 (1994) 573, N. Wills et al., Phys. Lett. B 406 (1997) 14, A.Wronska et al., Eur. Phys. J. A 26, 421-428 (2005). This part can be compared with the escape part of Green’s function calculation. s s(dd4Heh) data • Some restrictions • to the model parameters. Etot threshold

Numerical Results (Ideal case) 8 stot [nb] 25 20 7 15 10 5 0 6 5 (V0,W0) = (−100, −10) MeV p0 = 500 MeV/c Arbitrary unit 4 3 2 1 0 −20 −15 −10 −5 0 5 10 15 Eh − mh [MeV]

~ ~ ~ ~ Numerical Results (Larger imaginary part ) 6 stot [nb] 25 5 20 15 10 5 4 0 Arbitrary unit (V0,W0) = (−100, −20) MeV p0 = 500 MeV/c 3 2 0 −20 −15 −10 −5 0 5 10 15 Eh − mh [MeV]

~ ~ ~ ~ Numerical Results (Larger imaginary part ) 12 stot [nb] 25 20 11 15 10 5 0 (V0,W0) = (−100, −40) MeV p0 = 500 MeV/c 10 Arbitrary unit 9 8 0 −20 −15 −10 −5 0 5 10 15 Eh − mh [MeV]

(V0 = -100 MeV) (W0= -5, -10, -20, -40 MeV) (p0 =500 MeV/c)

(V0 = -100 MeV) (W0= -5, -10, -20 MeV) (p0 =1000 MeV/c)

(V0 = -100, -50, -30 MeV) (W0= -20 MeV) (p0 =500 MeV/c)

(V0 = -100, -50 MeV) (W0= -20 MeV) (p0 =1000 MeV/c)

(V0 = -100 MeV) (W0= -10 MeV) (p0 =1000, 500, 400 MeV/c)

(V0 = -100 MeV) (W0= -20 MeV) (p0 =1000, 500 MeV/c)

In these cases, eta production data above threshold can not be reproduced. (V0 = -50 MeV) (W0= -5 MeV) (p0 =1000, 500 MeV/c)

Summary for d+d reaction ★ Formation of h mesic nucleus • d + d  (4He-h )  X (several channels) reaction • High momentum transfer (~1GeV/c) • h production data above threshold exist • Simple spectra are expected ★ A model calculation with Green’s function • It may provide an estimation and interpretation of the inclusive experimental data. • But for the comparison, backgrounds • from non-(eta + alpha) processes must be removed • (quasi-elastic pion production etc).

Summary for d+d reaction ★ Further studies = Better form for transition part = Exclusive treatment of the final particles * Evaluation of ImV for each channel * Implementation of the realistic meson self-energy * Independent treatment of the eta-alpha decay process could be fine (decay model different from formation part)

Vector mesons in nucleus = Transparency ratio and Invariant mass = with S. Tokunaga (Nara Women’s Univ.) J. Yamagata-Sekihara (Oshima National College of Maritime Technology) H. Nagahiro (Nara Women’s Univ.)

Summary Table -- Results by independent groups Mass shift: 3.4% Mass shift: no mention

meson • Isolated peak structure • Long life time • (selection of slow particle)

We consider here. • DATA by KEK E325, LEPS/SPring8, JPARC E16 • R. Muto et al., Phys. Rev. Lett. 98 (2007) 042501 • T. Ishikawa et al., Phys. Lett. B 608 (2005) 215-222 • T. Sawada, Doctor Thesis, Osaka University (2013) • Thoretical works from Hatsuda and Lee, importance and sensitivity to • S quark condensate.

Motivation / Interests * Determine the <N|sbar s|N> from in-medium * Importance of <N|sbar s|N> = How much is the strangeness component in nucleon (important for hadron structure studies.) = <N|sbar s|N> basic quantity for nuclear matter, which relate to various phenomena (KN sigma term => kaon condensattion in neutron star, etc ) = <N|sbar s|N> may complete SU(3) info. on condesates with SU(2) part info. by other data

* First of all, we need ‘Stable (consistent) interpretation of data’ * Then, we should check ‘How reliable is theoretical connection between in-medium phi property and condensate ? ’ * Mass shift is not mandatory. If, it is zero, it’s important to confirm how accurately 0.

Mass shift: 3.4% Mass shift: no mention

Goal for the first step • Describe ‘Transparency ratio (LEPS/SPring8)’ • and ‘Invariant Mass (KEK E325)’ in an unified manner. • * Find the consistent interpretation of the observables. • And deepen the understanding between observables • and meson propertes.

Formula of the transparency ratio -T. Ishikawa et al., Phys. Lett. B 608 (2005) 215-222-T. Sawada, Doctor Thesis, Osaka University (2013) Transparency ratio A : mass number : incident photon number : Flux loss of the incident photon : Flux loss of phi : path of the phi : phi momentum

3, Transparency Ratio–計算結果– Calculated Results

Formula for Invariant Mass • Unified treatment with Transparency 　→ Calcualte Invariant mass dist. by the same model parameters as the Transparency Decay phi number : Produced phi at (b, z0) : Number of phi at (b, z) : Num of Incident particles : Branching Ratio of phi in vacuum,

An Example Production at origin φの生成位置入射粒子 (φの飛距離) density Distance from production point

Phi meson decay number per unit length Phi meson decay number to e+e- channel

Target case Distance from production point

Target case Target case density Distance from production point

Target case Target case density Distance from production point Nuclear center Nuclear surface/ Outside

Phi meson decay number per unit length Phi meson decay number to e+e- channel Invariant mass distribution seen in e+e- decay channel phi production point phi mass in vacuum Full width in vacuum : φ中間子の生成位置 Parameter for mass shift C : φ中間子の質量変化の大きさを決めるパラメータ

Numerical Results – Invariant Mass of e+e- pair • Input data γ-distortion: proton-distortion:

proton-induced, target: , βγ=1.0 (KEK E325) Experimental energy resolution (~10.7MeV) is not taken into account.

γ-induced • , target: ,βγ=1.0

Larger initial distortion  Larger contribution of in-medium decay at forward directions. ( Meson is produced at early stage in Nucleus. ) Angular dependence of the mass shift contribution can be interesting (But large distortion of initial particles may break the target seriously before meson production.)

proton-induced, target: , βγ=0.5 (J-PARC E16) (Slow phi in large Nucleus) Simulation By S. Yokkaichi (Resolution 5 MeV)

Meson Properties at Finite Density from Meson-Nucleus Systems