Mass dependence of inclusive nuclear photoproduction

D. Cabrera 1, L. Roca 1, E. Oset 1, H. Toki 2 and M.J. Vicente Vacas 1

International Workshop on “Chiral Restoration in Nuclear Medium”

(Chiral 05)

RIKEN, 15-17 Feb 2005

1 University of Valencia and IFIC

2 Research Center for Nuclear Physics, Osaka University

Motivation The meson is an appropriate probe for in-medium modification of

mesons and the possibility of a partial restoration of Chiral Symmetry in hadronic matter.

Isolated in the mass spectrum

Changes of properties comparatively larger than other mesons

properties in nuclear medium strongly related to the renormalization of kaon properties

Kaon selfenergy

Kaon condensation astrophysical implications

Experimental observation in principle easier

Variety of models, predict different kaon potentials

Good reproduction of data (K-atoms, HIC)

Experimental information from decayvaluable info on kaon selfenergy

Lines of workTheoretical calculations of properties

mass

Effective Lagrangian approach

Weise et al.; Kuwabara and Hatsuda; Song; Bhatttachayya et al.

QCD sum rules

Asakawa and Ko; Kampfer et al.

decay width

Dropping of meson masses

Bhattacharyya et al.; Ko et al.; Shuryak et al.; Panda et al.

Collisional broadening by -baryon and -meson interactions

Smith and Haglin; Alzarez-Ruso and Koch

Modification of decay channels ( selfenergy approach, kaon selfenergies)

Weise et al.; Ramos et al.

Sizable renormalization of width

and small mass shift in nuclear medium

Lines of work

Proposed reactions to test properties in nuclear medium

AA, pA collisions

-p n in nuclei

N N in nuclei

Experiments

KEK-PS

LEPS Near future...

HADES

CLAS

Purpose of this work

Calculate the meson selfenergy in nuclear medium from which M and can be obtained.

Apply the results to study recent experimental proposal to study properties in nuclear medium by means of nuclear inclusive photoproduction (,)

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

D. Cabrera, L. Roca, E. Oset, H. Toki and M.J. Vicente Vacas, Nucl. Phys. A 733 (2004) 130

OutlineOutline

Model for coupling to KK and selfenergy. Nuclear medium effects.

Results: mass and decay width in the nuclear medium.

Comparison with Experiment: study of nuclear inclusive photoproduction.

meson selfenergy in vacuum

Interested in the to KK coupling main decay channel in vacuum BR 85% (ignore other contributions).

KK Lagrangian in a gauge vector representation

Gives rise to a selfenergy built from:

KK loop diagram

Kaon tadpole diagram

57.4

)(Imexp

g

gf

KK

Nuclear medium effects

)()(qD

KK);,( 0

)(qqD

KK

We modify the kaon propagators with selfenergy accounting for interactions with the nuclear medium

);,( 0)(

qqKK

Kaon and anti-kaon interactions with nucleons are rather different we treat them separately

KN: smooth at low energies, since there are not S=1 resonancesWe use t aproximation

KN: strongly dominated by the excitation of sub-threshold (1405).

Chiral unitary model in coupled channels for S-wave KN scattering

0

2 13.0)(2

1

KnKpKK

mtt

Selfconsistent calculation of the S-wave selfenergy

and K selfenergies

Kaon selfenergy: S-wave

E. Oset and A. Ramos, Nucl. Phys. A 635 (1998) 99

Pauli blocking

Mean-field potentials

N. Kaiser, P.B. Siegel and W. Weise, Nucl. Phys. A 594 (1995) 325

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

Built from h, h and *h excitations, found to be an important source of renormalization in a nuclear medium.

KNY interaction from lowest order chiral Lagrangian coupling pseudoscalar meson and 1/2+ baryon octets.

),( )(~

2

1

),( )(~

2

3

),( )(~

2

1),(

**0*

0

222

222

222

qUqqfV

qUqqfV

qUqqfVq

pK

pK

pK

PK

);,();,( 00 qqqq PK

PK

Kaon selfenergy: P-wave

Klingl, Waas and Weise 98; Oset and Ramos 01

*=* (1385)

iq

qS

iq

qSdqqD KKKK

KK 0

)(

0

)(

0

0)(

);,();,( );,(

Kaon propagator:

decay channels which open in the medium due to K :

S-wave:

P-wave: YhK

YhKM

) ,(

);,();,( 0)(

0)(

qqDqqDKKKK

Use of spectral (Lehmann) representation for kaon, anti-akon propagator, guarantees crossing

meson selfenergy in the medium

Vertex corrections and gauge invariance

P- and S-wave kaon selfenergy insertions and realted vertex corrections:

(a) included by using the renormalized kaon & antikaon propagators

(b-d) generated by vertex corrections

Contact vertices: can be obtained by imposing W.I.

Herrmann, Friman and Noremberg 93; Chanfray and Schuck 93

Detailed analysis of necessary diagrams to satisfy gauge invariance in a non-realtivistic approximation of vertices involving baryons and baryon propagators

0 q

00

00

0

000

000

00000

jj

ii

q

q

q

( at rest in n.m.)

Vertex corrections and gauge invariance (II)

Results: mass and decay width in the nuclear medium

width grows considerably with the density: 30 MeV, =0

Sizeable energy dependence due to the K *h channel (thres. 940 MeV)

K S-wave: mildly attractive contribution, compensates partly K repulsion

K P-wave: small contribution from sizeable from and * excitations

Vertex corrections: further enhancement of the total width

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, attractive up to 1.1 GeV

mass change: (-8) MeV at =0

Results: mass and decay width in the nuclear medium (II)

Results from p-A reaction: KEK-PS E325, K. Ozawa et al., Nucl. Phys. A 698 (2002) 535c

Experimental information on properties in the nuclear medium

Several experimental proposals to observe changes in the properties in a nuclear medium:

HIC’s (p-A, A-A collisions)

-p N

N N

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

A K+K-X : LEPS, T. Ishikawa et al., nucl-ex/0411016

Medium effects on the mass or decay width of the meson are not observed

No need to cut phase space better statistics

A dependence of flux can be related to the decay width in the nuclear medium

But: Most of the produced ’s carry a high momentum

Extension of our model for finite P

Experiment:

Spring8/Osaka

(, ) with E [1.5-2.4] GeV

P 1.8 GeV

Proposal: observation of loss of flux due to nuclear effects and its A dependence

LEPS

Study of inclusive nuclear photoproduction

flux and decay width:

Pdt

PdP

dtv

dP

dl

dP

dt

dPVopt

Im

Im

2ImIm

2

Nuclear cross section for inclusive nuclear photoproduction:

survival probability

Absorption factor

Study of inclusive nuclear photoproduction

A dependence P dependence

Clear loss of flux: enhanced effect for small P and heavy nuclei

E = 1.6 GeV P 1000 MeV in fwd direction Pout 0.65 for 64Cu, and smaller for heavier nuclei

Inclusive nuclear photoproduction: results (II)

12C

64CuP = 2 GeV

P = 1.4 GeV

Other nuclear effects: Pauli blocking and Fermi motion

Pauli blocking of the final nucleon is important for high P (small momentum transfer)

photoproduction is forward peaked, thus actual effect is to be found somewhere in L < a few degrees

Inclusive nuclear photoproduction: results

64Cu

P = 2 GeV

L = 5 º

L = 0 º

Inclusive nuclear photoproduction: experimental results

T. Ishikawa et al., nucl-ex/0411016 LEPS Collaboration

Inclusive nuclear photoproduction: experimental results

Separation of the coherent photoproduction is important, particularly for light nuclei

Stronger effect than theoretically predicted, as seen in model independent results normalized to Li

Other possible sources of N interactions. Ex: 3, pion selfenergy!

LEPS Collaboration,

T. Ishikawa et al.,

nucl-ex/0411016

meson mass and decay width in a nuclear medium

Conclusions

decay width increases considerably in nuclear matter (6-8 free at 0)

Very small change in the mass

Experimental results from K+K- and dilepton spectra do not need in-medium mass change to fit the data

Inclusive nuclear photoproduction: A dependence

A dependence of loss of flux can be related to the in-medium decay width

Clear deviation from unity in the calculated survival probability indicates a loss of flux due to nuclear medium effects

Experimental results from the LEPS Collaboration find a reduction in the survival probability, stronger effect than calculated

spectral function in nuclear matter

3

D. Cabrera, E. Oset and M.J. Vicente Vacas, Nucl Phys. A705 (2002) 90

M(3) = 420 MeV

M() = 910 MeV

M(N* h ) 600 MeV

Antikaon spectral function for several nuclear densities

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