Hadrons@FAIR, FIAS June 26th, 2008

Hadrons@FAIR, FIAS

June 26th, 2008

and mesons in medium: theoretical aspects and

experimental information

Daniel Cabrera *

Departamento de Física Teórica II

Universidad Complutense, Madrid

* in collaboration with L.Tolós, A.Ramos and R. Rapp

OutlineOutline

Experimental information on and meson in-medium decays

Progress on theoretical work

- K, K : strangeness in hot and dense matter

- meson decays in medium

- selfenergy in nuclear matter

- - cloud beyond T approximation

and 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)

KEK-PS E325: p-A reaction + , e+e- decayM. Naruki et al. PRL 96, 092301 (2006)

KEK-PS E325: p-A reaction + e+e- decayR. Muto et al., NPA774 (2006) 723

CBELSA/TAPS Col.: nuclear photoproduction + 0 decay D. Trnka et al., PRL 94, 192303 (2005)

CLAS-g7 Col.: -A reaction + e+e- decayC. Djalali et al., Int.J.Mod.Phys.A22:380-387,2007; M.H. Wood et al., arXiv:0803.0492

CBELSA/TAPS Col.: nuclear photoproduction + A-dep. (nucl. transparency) M. Kotulla et al, PRL 100, 192302 (2008)

LEPS Col: nuclear f photoproduction + e+e- decay + A-dep.(transparency) T. Ishikawa et al., Phys. Lett. B608 (2005) 215

MV()/MV = 1 – k /0, k ≈ 0.10, ≈ 0

M / Mvac = - 0.04 /0

/ vac= 10 /0

M < 0 ?

= 130-150 MeV at 0 !!

>> vac !!

M ≈ 0 !!

D. Cabrera, A. Ramos and L. Tolós

KK, , KK in hot, dense matter and in hot, dense matter and meson decay meson decay

Kaon and anti-kaon

interactions with nucleons

KN and KN scattering in hot nuclear medium (I)

KN: smooth at low energies, no S=1 resonances

KN: strongly dominated by sub-thres. (1405)

PT + Unitarization in coupled channels for S-wave KN and KN scattering

Kernel for a Bethe-Salpeter equation

Algebraic solution: T = [1-VG]-1 V

Good description of l.e. scattering observables

dynamically generated

Lutz, Kolomeitsev

Oset, Ramos, Tolos

Oller, Meissner

Hosaka, Jido

…

S= -1: KN, , , K (I=0); KN, , , , K (I=1)

S=+1: KN (I=0,1)

Selfconsistent calculation of the

S-wave selfenergy

and K selfenergies

Pauli blocking

Mean-field potentials

KN and KN scattering in hot nuclear medium (II)

Lehmann rep. of retarded progagator at finite and T: Imag. Time Formalism (ITF)

K, anti-K selfenergy and spectral function

model at finite T and , S, V potentials for N and Y (Machleidt 89, Tsushima 03)

L. Tolós, A. Ramos, A. Polls, PRC 65, 054907 (2002); L. Tolós, A. Ramos, T. Mizutani, PRC 77, 015207 (2003)

T = [1-VG]-1 V, eff. interactioniWm → P0+i

fermionic

bosonic

KN and KN scattering in hot nuclear medium (III)

Higher waves: P-wave selfenergy

h, h and *h excitations *=* (1385)

Important source of renormalization in a nuclear medium

KNY from l.o. Lagrangian: 0+ meson and 1/2+ baryon octetsKlingl, Waas and Weise 98; Oset and Ramos 01; Tolos, Ramos, Oset 06

Finite-T calculation: (ITF)

in → q0+i

Pauli blocking on hyperons

Rel. baryon kinematics

Baryon potentials

Retarded property!

(vanishes at q0=0 !)

KN and KN scattering in hot nuclear medium (IV)

Pion selfenergy in hot/dense medium: (, channels)

NN-1, N-1, short range corr. (g’)

Rel. baryon kinematics

Energy-dependent width!

M. Urban, M. Buballa, R. Rapp, J. Wambach, NPA 673 (2000) 357

Finite-temperature Lindhard functions:

Retarded selfenergy OK quasiparticle peak broadens

collective excitations mix with mode

“melting” spectral function

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

Results (II): K selfenergy and spectral function, S vs S+P

P-wave YN-1

Results(III): K spectral function, T and dependence

0

0

Results (IV): K spectral function, T and dependence

0

0

Results(V): K nuclear optical potential

T = 100 MeV

Results(VI): Kaon nuclear optical potential

T = 100 MeV

meson selfenergy: vacuum case

Interested in the to KK coupling main decay channel in vacuum BR 85%

KK Lagrangian in vector representation

Gives rise to a selfenergy built from:

KK loop diagram

Kaon tadpole diagram

57.4

)(Imexp

g

gf

KK

J. Schechter et al. 1988

W. Weise et al. 1998

meson selfenergy: medium effects at finite T and

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)

meson: M. Urban et al. NPA 673 (2000) 357

width grows considerably with the density:

30 MeV, =0

F. Klingl, T. Waas and W. Weise,

Phys. Lett. B 431 (1998) 254;

E. Oset and A. Ramos,

Nucl. Phys. A 679 (2001) 616

Real part of selfenergy: very small

mass change: (-8) MeV at =0

meson selfenergy: nuclear matter results (T = 0)

D. Cabrera, M.J.Vicente Vacas, Phys. Rev. C 67 045203 (2003)

decay width in dense and (moderately) hot matter

Finite-T width duplicates at T = 100 MeV w.r.t. cold nuclear matter

Bose enhancement more effective for broad kaons (low energy modes)

Considerable broadening of spectral function

→ KK, stimulated decay (Bose enhancement)

interactions with the meson gas: → K K*

(Anti-)Baryonic effects: (on the kaon cloud) S=+1

KN → Y, KN → YM (finite B)

Kaons experience similar mechanisms as anti-Kaons

Sizable enhancement of reactivity

(Limit B → 0 : Kaon and antikaon selfenergies symmetrize)

D. Cabrera, A. Ramos, R. Rapp, L. Tolós, work in progress

decay width in dense and (moderately) hot matter

Further contributions (higher temperatures, lower :RHIC, LHC)

L. Alvarez-Ruso, V. Koch, PRC65 (2002); W. Smith, K. Haglin, PRC57 (1998)

R. Rapp, PRC63 (2001)

meson selfenergy in nuclear mattermeson selfenergy in nuclear matter

D. Cabrera, R. Rapp

meson in the medium: theoretical approaches

properties in a selfenergy approach

Medium effects on intermediate mesons:

3: plenty of phase space

: not open at the physical mass, only the low energy tail is explored (E 500 MeV, p 200 MeV)

spectral function enhanced in this region at finite nuclear density (2-cloud, -N*h)

decay is about 90% of (3)

(from () 3 and radiative decays)

P. Jain et al., Phys. Rev. D37 (1988) 3252; F. Klingl et al., Z. Phys. A356 (1996) 193

Gell-Mann, Sharp, Wagner


In-medium mechanisms (hadronic many-body approach)

meson-cloud interactions with the medium

N N

N N [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]

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 (-)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 and spectral functions

F. Riek et al., Nucl. Phys. A740 (2004) 287

• Sizable increase of decay width, V

• Dispersion in results for MV → ≈ (-200,+50) MeV

something not well understood


selfenergy from N scattering: T-approximation

Focus on building N scattering amplitude (elastic+inelastic)

On-going discussion: non-rel. approximations

: low density theorem → () ≈ TN

F. Klingl et al. (1997,99); F. Eichstaedt et al. (2007)

Im TN Cutkowsky rules

Re TN Dispersion relation

Pauli blocking on intermediate states

Dyson resummation of in-medium meson propagators!

Resonance contributions (N, , N*…)? P. Muelich et al., NPA780 (2006) 187

VACUUM PHYSICS

…

…

(Figures borrowed from F. Eichstaedt, Ph.D. thesis)


selfenergy from in-medium loop: density dependence

As a consequence ( meson at rest):

Clear non-linear dependence from very low densities…

D. Cabrera et al., Nucl. Phys. A705(2002) 90


selfenergy from in-medium loop: energy dependence

N*h: enhanced PS for decay

: very attracted (ph, h, g’) → peak explored

2-cloud: reshuffling of strength in S

plus dynamics of decay: q2cm

Strong E dependence of Im Re

-N*h (not incl.)

O(2) terms IMPORTANT

Conclusions

Kbar and K selfenergy, spectral function and nuclear optical potentials in hot and dense matter: coupled-channel U approach, (s+p)-wave interactions

Medium effects (full calculation in ITF): Pauli blocking; mean field baryon potentials; , K, Kbar selfenergies → Selfconsistent evaluation

Temperature effects:

Kbar: further diss. of (1405), low energy strength from YN-1 exct., decreased attraction, enhanced width

Kaon: broadened spectral function (phase space)

meson: sizable medium (baryon density) effects from kaon cloud. Increased reactivity at finite temperatures (effective Bose enhancement, broader K, Kbar)

meson: theoretical approaches (hadronic many-body) need review validity of some approximations → T

Full meson spectral functions (, ) required, O(2) effects important

Backup slides

Analyticity tests: Energy Weighted Sum Rules (EWSRs)

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

A. Polls, A. Ramos, J. Ventura, S. Amari, W.H. Dickhoff,PRC49 (1994)

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

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

in → q0+i ≈ q0 + EN(p)

S-wave selfenergy from T-matrix in Imaginary Time Formalism

selfenergy from N scattering: T-approximation


selfenergy selfenergy


Some example where T- does not work…

Kaon-nucleon and the (1405)

KN repulsive at very low → rapidly turns attractive

E. Oset and A. Ramos, Nucl. Phys. A 671 (2000) 481


Work in progress: (D. Cabrera + R. Rapp, in preparation)

All diagrams fromN N

N N [N

• Resonances in baryonic lines

• Mass change: = () – (=0)

irreducible

resummation

selfenergy

selfenergy

some Vert. Corr.

Things to consider:

Rescattering in N (BS equation)

effects are important

Self-consistent G-matrix approach?

F. Klingl et al. (1997,99); F. Eichstaedt et al. (2007)

CBELSA/TAPS Col.: nuclear photoproduction + 0 decay


0 decay: much suppressed for meson (10-2) no overlap

Sizable enhancement of spectrum below M

Effect vanishes when increasing p cuts

Width dominated by exp. resolution ( < 55 MeV at estimated = 0.60)

- BUU transport with M = -16% at

P. Mühlich et al., Eur. Phys. J. A20 (2004) 499

-Monte Carlo simulation (A → 0 X) with rescaled bckgnd from elem. reaction

M. Kaskulov et al., Eur. Phys. J. A31(2007) 245

D. Trnka et al., PRL 94, 192303 (2005)

M. Kotulla, nucl-ex/0609012

M. Kaskulov et al. Eur. Phys. J. A31 (2007) 245

M. Kotulla, nucl-ex/0609012


KEK-PS E325: p-A reaction + e+e- decay

Yield excess below , mass: MV()/MV = 1 – k /0, k ≈ 0.10 from fit

(k = 0.10-0.22, Hatsuda, Lee, Shiomi ‘95)

No broadening is assumed

Actually, broadening is NOT favoured in the analysis!!

M. Naruki et al. PRL 96, 092301 (2006)


KEK-PS E325: p-A reaction + e+e- decayR. Muto et al., NPA774 (2006) 723

<1.25 (Slow) R. Muto, QM 2005

M / Mvac = - 0.04 /0

/ vac= 10 /0

Recent analysis:

*K+K- / vacK+K- = 1 + /0

= 1.4 ± 1.1 ± 2.1F.Sakuma et al. PRL 98 (2007) 152302


CLAS-g7 Col.: -A reaction + e+e- decayC. Djalali et al., Int.J.Mod.Phys.A22:380-387,2007

No mass modification Mass modification a la HL, k = 0.16

CONCLUSION:

k = 0.2 ± 0.2

Waiting for and results…

Problems:

Long lifetime: decays outside the nuclear medium

is produced with high P

Kinematical cuts to isolate small-P eventspoor statistics

Distortion in K+K- distribution (Coulomb interaction may bind K- in nucleus)

P. Muhlich, T. Falter, C. Greiner, J. Lehr, M. Post and U. Mosel,

Phys. Rev. C 67 (2003) 024605

Experimental information on 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

A K+K-X : LEPS, T. Ishikawa et al., Phys. Lett. B608 (2005) 215

Medium effects on the mass or decay width of the meson are difficult to observe

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Hadrons@FAIR, FIAS June 26th, 2008