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Hadrons@FAIR, FIAS June 26th, 2008

f and w mesons in medium: theoretical aspects and experimental information. Daniel Cabrera *. Departamento de F í sica Te ó rica II Universidad Complutense, Madrid. Hadrons@FAIR, FIAS June 26th, 2008. * in collaboration with L.Tol ó s, A.Ramos and R. Rapp.

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Hadrons@FAIR, FIAS June 26th, 2008

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  1. f and w mesons in medium: theoretical aspects and experimental information Daniel Cabrera * Departamento de Física Teórica II Universidad Complutense, Madrid Hadrons@FAIR, FIAS June 26th, 2008 * in collaboration with L.Tolós, A.Ramos and R. Rapp

  2. K,K: strangeness in hot and dense matter • f meson decays in medium • w selfenergy in nuclear matter • r-p cloud beyond Tr approximation Outline Experimental information on f and w meson in-medium decays Progress on theoretical work

  3. CLAS-g7 Col.: g-A reaction + r, w, f e+e- decay C. Djalali et al., Int.J.Mod.Phys.A22:380-387,2007; M.H. Wood et al., arXiv:0803.0492 f and w mesons in the medium: experimental information • HIC’s 28Si + 196Au: BNL-AGS E802, Y. Akiba et al., Phys. Rev. Lett. 96 (1996) 2021 • Au + Au: PHENIX Col., Adler et al., nucl-ex/0410012 (vacuum decays) MV(r)/MV = 1 – k r/r0, k ≈ 0.10, DG≈ 0 • KEK-PS E325: p-A reaction + r,w e+e- decay M. Naruki et al. PRL 96, 092301 (2006) DMf / Mfvac= - 0.04 r/r0 DGf / Gfvac= 10 r/r0 • KEK-PS E325: p-A reaction + f e+e- decay R. Muto et al., NPA774 (2006) 723 • CBELSA/TAPS Col.: nuclear w photoproduction + wp0g decay D. Trnka et al., PRL 94, 192303 (2005) DMw < 0 ? • CBELSA/TAPS Col.: nuclear w photoproduction + A-dep. (nucl. transparency) M. Kotulla et al, PRL 100, 192302 (2008) Gw = 130-150 MeV at r0!! Gf >> Gfvac!! • LEPS Col: nuclear f photoproduction + f e+e- decay + A-dep.(transparency) T. Ishikawa et al., Phys. Lett. B608 (2005) 215 DMr≈ 0 !!

  4. K, K in hot, dense matter and f meson decay D. Cabrera, A. Ramos and L. Tolós

  5. KN and KN scattering in hot nuclear medium (I) S= -1: KN, pS, hL, KX (I=0); KN, pL, pS, hS, KX (I=1) S=+1:KN (I=0,1) KN: smooth at low energies, no S=1 resonances KN: strongly dominated by sub-thres.L(1405) Kaon and anti-kaon interactions with nucleons cPT + Unitarization in coupled channels for S-wave KN and KN scattering Kernel for a Bethe-Salpeter equation Lutz, Kolomeitsev Oset, Ramos, Tolos Oller, Meissner Hosaka, Jido … • Algebraic solution: T = [1-VG]-1V • Good description of l.e. scattering observables • L(1405)dynamically generated

  6. KN and KN scattering in hot nuclear medium (II) Pauli blocking Mean-field potentials pand K selfenergies L. Tolós, A. Ramos, A. Polls, PRC 65, 054907 (2002); L. Tolós, A. Ramos, T. Mizutani, PRC 77, 015207 (2003) s-w model at finite T and r, S, V potentials for N and Y(Machleidt 89, Tsushima 03) Lehmann rep. of retarded progagator at finite r and T: Imag. Time Formalism (ITF) bosonic Selfconsistent calculation of the S-wave selfenergy fermionic iWm→ P0+ie T = [1-VG]-1V, eff. interaction K, anti-K selfenergy and spectral function

  7. KN and KN scattering in hot nuclear medium (III) Higher waves: P-wave selfenergy • Lh,ShandS*h excitations S*=S* (1385) • Important source of f renormalization in a nuclear medium • KNY from l.o. c Lagrangian: 0+ meson and 1/2+ baryon octets Klingl, Waas and Weise 98; Oset and Ramos 01; Tolos, Ramos, Oset 06 Finite-T calculation: (ITF) • Pauli blocking on hyperons • Rel. baryon kinematics • Baryon potentials • Retarded property! i wn→ q0+ie (vanishes at q0=0 !)

  8. KN and KN scattering in hot nuclear medium (IV) Pion selfenergy in hot/dense medium: (pL, pS channels) M. Urban, M. Buballa, R. Rapp, J. Wambach, NPA 673 (2000) 357 • NN-1, DN-1, short range corr. (g’) • Rel. baryon kinematics • Energy-dependent D width! Finite-temperature Lindhard functions: Retarded selfenergy OK • p quasiparticle peak broadens • collective excitations mix with p mode • “melting” spectral function

  9. Results (I): KN in-medium S-wave scattering amplitude

  10. Results (II): K selfenergy and spectral function, S vs S+P P-wave YN-1

  11. Results(III): K spectral function, T and r dependence r0 2r0

  12. Results (IV): K spectral function, T and r dependence r0 2r0

  13. Results(V): K nuclear optical potential T = 100 MeV

  14. Results(VI): Kaon nuclear optical potential T = 100 MeV

  15. f meson selfenergy: vacuum case • Interested in the f to KK couplingmain f decay channel in vacuum, BR 85% J. Schechter et al. 1988 W. Weise et al. 1998 fKK Lagrangian in vector representation • Gives rise to a f selfenergy built from: • KK loop diagram • Kaon tadpole diagram

  16. f meson selfenergy: medium effects at finite T and r Vacuum width: Thermal width: few MeV enhancement (C. Gale, J.I. Kapusta 1991) Decay width at finite temperature and nuclear density: (FAIR conditions) “Stimulated” (Bose enhanced) decay Diffusion term (low energy) r meson: M. Urban et al. NPA 673 (2000) 357

  17. f meson selfenergy: nuclear matter results (T = 0) • Real part of f selfenergy: very small • f mass change: (-8) MeV at r=r0 • f width grows considerably with the density: • Gf30 MeV, r=r0 D. Cabrera, M.J.Vicente Vacas, Phys. Rev. C 67 045203 (2003) F. Klingl, T. Waas and W. Weise, Phys. Lett. B 431 (1998) 254; E. Oset and A. Ramos, Nucl. Phys. A 679 (2001) 616

  18. f decay width in dense and (moderately) hot matter • Finite-Tf widthduplicates at T = 100 MeV w.r.t. cold nuclear matter • Bose enhancement more effective for broad kaons (low energy modes) • Considerable broadening of f spectral function

  19. f decay width in dense and (moderately) hot matter Further contributions (higher temperatures, lower m :RHIC, LHC) • f→ KK, stimulated decay (Bose enhancement) • f interactions with the meson gas: f p→ K K* • (Anti-)Baryonic effects: (on the kaon cloud) S=+1 • KN → Y, KN → YM(finite rB) L. Alvarez-Ruso, V. Koch, PRC65 (2002); W. Smith, K. Haglin, PRC57 (1998) R. Rapp, PRC63 (2001) Kaons experience similar mechanisms as anti-Kaons Sizable enhancement of f reactivity (LimitmB→ 0 : Kaon and antikaon selfenergies symmetrize) D. Cabrera, A. Ramos, R. Rapp, L. Tolós, work in progress

  20. w meson selfenergy in nuclear matter D. Cabrera, R. Rapp

  21. Medium effects on intermediate mesons: • 3p: plenty of phase space • rp: not open at the physical r mass, only the low energyrtail is explored (E  500 MeV, p  200 MeV) r spectral function enhanced in this region at finite nuclear density (2p-cloud, r-N*h) w meson in the medium: theoretical approaches w properties in a selfenergy approach Gell-Mann, Sharp, Wagner rp decay is about 90% of G(w3p) (from f (w)  3p and radiative decays) P. Jain et al., Phys. Rev. D37 (1988) 3252; F. Klingl et al., Z. Phys. A356 (1996) 193

  22. Sizable increase of w decay width, DGV • Dispersion in results for DMV → ≈ (-200,+50) MeV something not well understood w meson in the medium: theoretical approaches In-medium mechanisms (hadronic many-body approach) • w meson-cloud interactions with the medium • wN  pN • wN  rN [pp]N • Chiral SU(3) Lagrangian approach • F. Klingl et al., Nucl. Phys. A624 (1997) 527; A650 (1999) 299 • F. Eichstaedt et al., arXiv:0704.0154 [nuc-th] • w coupling to several Rh (sub-thres.) states • N*(1520)D13, N*(1650)S11, ... • P. Muelich et al., Nucl. Phys. A780 (2006) 187 • M. Lutz et al Nucl. Phys. A706 (2002) 431 • Isovector-isoscalar mixing (s-w) • K. Saito et al, Phys. Lett. B433 (1998) 243; 460 (1999) 17 • Gy. Wolf et al., Nucl. Phys. A640 (1998) 129 • O. Teodorescu et al., Phys. Rev. C63 (2001) 034903 • A. Dutt-Mazumder, Nucl. Phys. A713 (2003) 119 • Self-consistent r and w spectral functions • F. Riek et al., Nucl. Phys. A740 (2004) 287

  23. VACUUM PHYSICS w meson in the medium: theoretical approaches w selfenergy from wN scattering: T-r approximation • Focus on building wN scattering amplitude (elastic+inelastic) • On-going discussion: non-rel. approximations • Pw: low density theorem →Pw(r) ≈ TwNr • F. Klingl et al. (1997,99); F. Eichstaedt et al. (2007) ImTwNCutkowsky rules ReTwNDispersion relation … (Figures borrowed from F. Eichstaedt, Ph.D. thesis) … • Pauli blocking on intermediate states • Dyson resummation of in-medium meson propagators! • Resonance contributions (N, D, N*…)?P. Muelich et al., NPA780 (2006) 187

  24. w meson in the medium: theoretical approaches w selfenergy from in-medium pr loop: density dependence D. Cabrera et al., Nucl. Phys. A705(2002) 90 As a consequence (w meson at rest): Clear non-linear dependence from very low densities…

  25. r-N*h: enhanced PS for w decay • p: very attracted (ph, Dh, g’) → r peak explored • 2p-cloud: reshuffling of strength in Sr • plus dynamics of wrp decay: q2cm Strong E dependence of Im Pw Re Pw w meson in the medium: theoretical approaches w selfenergy from in-medium pr loop: energy dependence w-N*h (not incl.) O(r2) terms IMPORTANT

  26. Conclusions • Kbar and Kselfenergy, spectral function and nuclear optical potentials in hot and dense matter: coupled-channel cU approach, (s+p)-wave interactions • Medium effects (full calculation in ITF): Pauli blocking; mean field baryonpotentials; p, K, Kbar selfenergies→ Selfconsistent evaluation • Temperature effects: • Kbar: further diss. of L(1405), low energy strength from YN-1 exct., decreased attraction, enhanced width • Kaon: broadened spectral function (phase space) • f meson: sizable medium (baryon density) effects from kaon cloud. Increased reactivity at finite temperatures (effective Bose enhancement, broader K, Kbar) • w meson: theoretical approaches (hadronic many-body) need review validity of some approximations →Tr • Full meson spectral functions (r, p) required, O(r2) effects important

  27. Backup slides

  28. Analyticity tests: Energy Weighted Sum Rules (EWSRs) A. Polls, A. Ramos, J. Ventura, S. Amari, W.H. Dickhoff,PRC49 (1994) • Lehmann representation(“Cauchy’s theorem in a smart way”) • Exploit information of meson selfenergy at E = 0 and at high energy … … D. Cabrera, A. Polls, A. Ramos, L. Tolós, work in progress

  29. s-w model (Walecka-type) at finite temperature from DBHF calculation of nuclear matter properties at T=0

  30. P-wave selfenergy: non-relativistic “naive” extension vs full relativistic thermal calculation in ITF

  31. S-wave selfenergy from T-matrix in Imaginary Time Formalism i wn→ q0+ie w≈ q0 + EN(p)

  32. w meson in the medium: theoretical approaches w selfenergy from wN scattering: T-r approximation p selfenergy r selfenergy

  33. w meson in the medium: theoretical approaches Some example where T-rdoes not work… • Kaon-nucleon and the L(1405) • KN repulsive at very low r→ rapidly turns attractive E. Oset and A. Ramos, Nucl. Phys. A 671 (2000) 481

  34. w meson in the medium: theoretical approaches Work in progress: (D. Cabrera + R. Rapp, in preparation) • All diagrams from • wN  pN • wN  rN [pp]N • Resonances in baryonic lines • Mass change: DPw = Pw(r) – Pw(r=0) r selfenergy p selfenergy some Vert. Corr. irreducible resummation F. Klingl et al. (1997,99); F. Eichstaedt et al. (2007) Things to consider: • Rescattering in wN (BS equation) • O(r2) effects are important Self-consistentG-matrix approach?

  35. M. Kotulla, nucl-ex/0609012 M. Kotulla, nucl-ex/0609012 M. Kaskulov et al. Eur. Phys. J. A31 (2007) 245 w and f mesons in the medium: experimental information • CBELSA/TAPS Col.: nuclear w photoproduction + wp0g decay D. Trnka et al., PRL 94, 192303 (2005) • p0g decay: much suppressed for r meson (10-2) no overlap • Sizable enhancement of spectrum below Mw • Effect vanishes when increasing pw cuts • Width dominated by exp. resolution (Gw < 55 MeV at estimated r = 0.6r0) • - BUU transport with DMw = -16% at r0 • P. Mühlich et al., Eur. Phys. J. A20 (2004) 499 • Monte Carlo simulation (gA →p0gX) with rescaled bckgnd from elem. reaction • M. Kaskulov et al., Eur. Phys. J. A31(2007) 245

  36. w and f mesons in the medium: experimental information • KEK-PS E325: p-A reaction + w e+e- decay M. Naruki et al. PRL 96, 092301 (2006) • Yield excess below r, w mass: MV(r)/MV = 1 – k r/r0, k ≈ 0.10from fit • (k = 0.10-0.22, Hatsuda, Lee, Shiomi ‘95) • No broadening is assumed • Actually, broadening is NOT favoured in the analysis!!

  37. w and f mesons in the medium: experimental information • KEK-PS E325: p-A reaction + f e+e- decay R. Muto et al., NPA774 (2006) 723 DMf / Mfvac= - 0.04 r/r0 DGf / Gfvac= 10 r/r0 Recent analysis: G*K+K- / GvacK+K- = 1 + ar/r0 a = 1.4 ± 1.1 ± 2.1 F.Sakuma et al. PRL 98 (2007) 152302 bg<1.25 (Slow) R. Muto, QM 2005

  38. w and f mesons in the medium: experimental information C. Djalali et al., Int.J.Mod.Phys.A22:380-387,2007 • CLAS-g7 Col.: g-A reaction + r e+e- decay CONCLUSION: k = 0.2 ± 0.2 Waiting for w and f results… No mass modification Mass modification a la HL, k = 0.16

  39. Problems: • Long f lifetime:f decays outside the nuclear medium • f is produced with high Pf • Kinematical cuts to isolate small-Pf events poor statistics • Distortion in K+K- distribution (Coulomb interaction may bind K-in nucleus) Experimental information on f properties in the nuclear medium • Results from p-A reaction: KEK-PS E325, K. Ozawa et al., Nucl. Phys. A 698 (2002) 535c • HIC’s 28Si + 196Au: BNL-AGS E802, Y. Akiba et al., Phys. Rev. Lett. 96 (1996) 2021 • Au + Au: PHENIX Col., Adler et al., nucl-ex/0410012 • gAK+K-X: LEPS, T. Ishikawa et al., Phys. Lett. B608 (2005) 215 Medium effects on the mass or decay width of the f meson are difficult to observe P. Muhlich, T. Falter, C. Greiner, J. Lehr, M. Post and U. Mosel, Phys. Rev. C 67 (2003) 024605

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