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Meson exchange K+N interaction and K+-nucleus cross sections
N U C L EAR PHYSICS A
Nuclear Physics A553 (1993) 599c-602c North-H01hmd, Amsterdam
Meson Exchange K+-N Interaction and K+-Nucleus Cross Sections P. Wyborny, K. Holinde, F. Osterfeld and J. Speth l n s t i t u t fiir Kernphysik der Forschungsanlage Jiilich (KFA) D-5170 Jiilich, West Germany Abstract A meson exchange model for the K+-nucleon interaction is presented, which is based on a full coupled-channel (KN,K*N,KA) treatment including the direct K*N and K A interactions based likewise on meson exchange. This microscopic model, which provides a good description of K+N elastic and pion production data, is then used to calculate K+-2d and K+-12C cross sections. Characteristic discrepancies to the empirical d a t a are found, which are similar to those obtained when starting from the empirical K+N amplitude. Rough agreement resuhs if the masses of the vector mesons ,.v,p in the K+N interaction are reduced by 4t.7cin 12C, which is considerably smaller than suggested b.v recent estimates. I;ossible reasons are discussed. 1. T h e K + - N i n t e r a c t i o n m o d e l The diagrams used in our coupled-channel model are shown in fig. 1.
,K N
.... ~ 6J,p K
K, NI
o)
NI
!K
All All
c)
iK
c0~O la,
,K i)
qiK
. . . . ~l
,
~'Pll,/,
N/
g)
,r,
IK*
, A . ,~.
rr N
U
f)
I
d)
LI
NI
,,K
II
K*,, A , ~
... / . CO,p1 I
e)
',K b)
NL ~i N/
,K
IN
,,
N
h)
,K
K•
,
J)
Fig. 1: Diagrams included in our coupled-channel model. 0375-9474/93/$06.00 @ 1993 - Elsevier Science Publishers B.V. All rights reserved.
600c
P. Wyborny et al. I K+-N interaction and K+-nucleus cross sections
Vertex coupling constants are constrained by SU(3) symmetry. As for the cutoff parameters iu monopole-type form factors, they are taken in case of non-strange vertices from the Bonn N-N model [1]; for strange vertices, they are adjusted to the K+-N observables. Compared to a former model [2], we now make the following extensions, which are essential for a realistic description ofpion production data: First, we take into accouat the width of the A and K*, evaluated in a generalized Lee model, see fig. li and fig. lj. Second, we include the direct KA and K*N interactions (fig 1 d,g,h). Fig. 2 shows the dramatic improvement provided by the direct KA interaction for the inelastic KN--- KA cross section. The solid line is our prediction; the dotted line represents the result if the direct KA interaction (fig. ld) is omitted.
12
t 4J
"I
C ratio
%
'7'!
0! plab in Gc',:/c Fig. 2: Inelastic K N ~
plab in GeV//c
K A cross scct~,m.
Experimental results ore taken k o m
[3].
Fig. 3: 7btal cross section ratio R. Experimental ~ s n l t s are from [4].
2. K+-12C s c a t t e r i n g
The present I( + N model provides a good overall description of the K+N data, both below and above pion production thresht~ld. It should therefore be a reliable starting poinl fear microscopic nuclear structure calculations. In a next step: we have calculated the h~tal cross section of K+-I2c scattering, using tile lowest-order optical potential in an averaged tp factorisation and including Pauli-blocking effects [5]. Fig. 3 (solid K÷_12 C
line) shows the resulting ratio R
=
~
as function of the kaon lab momentum,
[ol
in comparison with experiment. As expected and similar to calculations starting from the empirical K+N amplitude (phase shifts), the predicted ratio shnws some shadowing, which is however in distinct disagreement with the data. They apparently show
P. Wyborny et al. I K÷-N interaction and K'-nucleus cross sections
601c
antishadowing. In this connection it is interesting to note that one of our former K+N models led in fact to good agreement with the data [6]. However, that model did not describe all K+N observables quantitatively. Namely, in the relevant energy range, it did r~t reproduce the almost isotropic behavior of the differential K+p --* K+p cross section. The reason is the nonvanishing p-wave contribution to d # / d ~ generated by that model. We stress however that the empirical p-waves
(Pl 2*J
= PI1;P13) are quite large in
order to reproduce the sizable polarisation in that energy range; nevertheless, isotropic behavior of d ~ / d f t is obtained since 2~(p13) + ~(PII) ~ 0, a condition which is much better reproduced in our extended K+N model. The persistent discrepancy between empirical K+-nucleus scattering data and optical model calculations based on a realistic free K+N amplitude apparently calls for unconventional medium effects. Brown et al. [7] suggest to reduce the mass of vector mesons (w, p) in the medium, in proportion to the nuclear density. Indeed, with a 10% reduction in the nuclear interior they obtained the required enhancement of the K+-12C cross sections, under the assumption that the K+ N interaction is completely due to w, p exchange. In our model, the vector meson exchange is considerably larger since it has to balance the additional attraction partly arising from the coupled-channel processes, which, a'-. stressed before, are required for a realistic description of pion production. Theiefore it is not surprising that in our model the cross section enhancement generated by a 10e~ reduction of vector meson masses is much t o . large, see fig.3 (dash-dot line). (For simplicity we have taken the reduction to be constant throughout the nuclear volume. We expect that the deviation from the gaussian shape used in [7] does not alter our qualitative arguments.) In fact, as fig. 3 (dashed line) shows, a 4% decrease turns out to be sufficient. Note that a considerable part of the enhancement arises from pwaves, since a change of vector meson masses in the medium removes the aforementioned delicate balance of those waves in free K+N scattering. This is demonstrated by the dotted line in fig. 3, which shows the result obtained if the 10% mass reduction is done in the S I I phase shift only. Of course, our results depend on the assumption that the strong phenomenological repulsion needed to describe the K+N data is completely due to oJ-exchange. This is not necessarily correct. In fact, it has been shown in [8] that such an interpretation leads to difficulties in the K - N system. Namely, K - N data seem to require that genuine
602c
p. Wyborny et al. / K÷-N interaction and I~.nucleus cross sectimt~
~0-exchange has the much weaker SU(3) coupling, and tha~. the additional repulsion in K+N behaves differently under G-parity transformation. Indeed, applying the mass reduction to the SU(3) part of w-exchange only, a somewhat larger reduction (about 6~) is needed; however, in this case the energy dependence is slightly deteriorated. Thus the problem of a consistent description of K+N and K+-nucleus data is intimately connected to the question about the nature of tile short-range repulsion in hadronie systems. REFERENCES [1] R. Machleidt, K. lIolinde and Ch. Elster, Phys. Rep. 149 (1987) 1. [2] R. Biittgen, K. tlolinde, A. Miiller-Groeling, J. Speth and P. Wyborny, Nucl. Phys. A506 (1990) 586 [3] R. \V. Bland et al. Nucl. Phys. BI3 (1969) 595. [.t] J. Aister et al. Proceedings of the International Symposium of llyp~rnuclear aped Strange |)article Physics / Shimoda (Japan) 1991; to be published in Nucl. Phys. A [5] P. Wyborny, Spezielle Berichle der Kernforschungsanlage Jfilich, JiiI-Spez-186 (1988). [6] P. Wyborn.v F. Osterfeld and J. Speth, c,mtributed paper to PANIC XII (1990)session IV-7 [7] G. F. Brown, C. B. Dover. P. L. Siegel and W. Weise, I'h.vs. Rev. 1.ell. 60 (1988) 2733. [8] A. Miiller-Groeling, K. lloli,de a,d .1. Speth, Nucl. Phys. A513 (1990) 557.
Nuclear Physics A553 (1993) 599c-602c North-H01hmd, Amsterdam
Meson Exchange K+-N Interaction and K+-Nucleus Cross Sections P. Wyborny, K. Holinde, F. Osterfeld and J. Speth l n s t i t u t fiir Kernphysik der Forschungsanlage Jiilich (KFA) D-5170 Jiilich, West Germany Abstract A meson exchange model for the K+-nucleon interaction is presented, which is based on a full coupled-channel (KN,K*N,KA) treatment including the direct K*N and K A interactions based likewise on meson exchange. This microscopic model, which provides a good description of K+N elastic and pion production data, is then used to calculate K+-2d and K+-12C cross sections. Characteristic discrepancies to the empirical d a t a are found, which are similar to those obtained when starting from the empirical K+N amplitude. Rough agreement resuhs if the masses of the vector mesons ,.v,p in the K+N interaction are reduced by 4t.7cin 12C, which is considerably smaller than suggested b.v recent estimates. I;ossible reasons are discussed. 1. T h e K + - N i n t e r a c t i o n m o d e l The diagrams used in our coupled-channel model are shown in fig. 1.
,K N
.... ~ 6J,p K
K, NI
o)
NI
!K
All All
c)
iK
c0~O la,
,K i)
qiK
. . . . ~l
,
~'Pll,/,
N/
g)
,r,
IK*
, A . ,~.
rr N
U
f)
I
d)
LI
NI
,,K
II
K*,, A , ~
... / . CO,p1 I
e)
',K b)
NL ~i N/
,K
IN
,,
N
h)
,K
K•
,
J)
Fig. 1: Diagrams included in our coupled-channel model. 0375-9474/93/$06.00 @ 1993 - Elsevier Science Publishers B.V. All rights reserved.
600c
P. Wyborny et al. I K+-N interaction and K+-nucleus cross sections
Vertex coupling constants are constrained by SU(3) symmetry. As for the cutoff parameters iu monopole-type form factors, they are taken in case of non-strange vertices from the Bonn N-N model [1]; for strange vertices, they are adjusted to the K+-N observables. Compared to a former model [2], we now make the following extensions, which are essential for a realistic description ofpion production data: First, we take into accouat the width of the A and K*, evaluated in a generalized Lee model, see fig. li and fig. lj. Second, we include the direct KA and K*N interactions (fig 1 d,g,h). Fig. 2 shows the dramatic improvement provided by the direct KA interaction for the inelastic KN--- KA cross section. The solid line is our prediction; the dotted line represents the result if the direct KA interaction (fig. ld) is omitted.
12
t 4J
"I
C ratio
%
'7'!
0! plab in Gc',:/c Fig. 2: Inelastic K N ~
plab in GeV//c
K A cross scct~,m.
Experimental results ore taken k o m
[3].
Fig. 3: 7btal cross section ratio R. Experimental ~ s n l t s are from [4].
2. K+-12C s c a t t e r i n g
The present I( + N model provides a good overall description of the K+N data, both below and above pion production thresht~ld. It should therefore be a reliable starting poinl fear microscopic nuclear structure calculations. In a next step: we have calculated the h~tal cross section of K+-I2c scattering, using tile lowest-order optical potential in an averaged tp factorisation and including Pauli-blocking effects [5]. Fig. 3 (solid K÷_12 C
line) shows the resulting ratio R
=
~
as function of the kaon lab momentum,
[ol
in comparison with experiment. As expected and similar to calculations starting from the empirical K+N amplitude (phase shifts), the predicted ratio shnws some shadowing, which is however in distinct disagreement with the data. They apparently show
P. Wyborny et al. I K÷-N interaction and K'-nucleus cross sections
601c
antishadowing. In this connection it is interesting to note that one of our former K+N models led in fact to good agreement with the data [6]. However, that model did not describe all K+N observables quantitatively. Namely, in the relevant energy range, it did r~t reproduce the almost isotropic behavior of the differential K+p --* K+p cross section. The reason is the nonvanishing p-wave contribution to d # / d ~ generated by that model. We stress however that the empirical p-waves
(Pl 2*J
= PI1;P13) are quite large in
order to reproduce the sizable polarisation in that energy range; nevertheless, isotropic behavior of d ~ / d f t is obtained since 2~(p13) + ~(PII) ~ 0, a condition which is much better reproduced in our extended K+N model. The persistent discrepancy between empirical K+-nucleus scattering data and optical model calculations based on a realistic free K+N amplitude apparently calls for unconventional medium effects. Brown et al. [7] suggest to reduce the mass of vector mesons (w, p) in the medium, in proportion to the nuclear density. Indeed, with a 10% reduction in the nuclear interior they obtained the required enhancement of the K+-12C cross sections, under the assumption that the K+ N interaction is completely due to w, p exchange. In our model, the vector meson exchange is considerably larger since it has to balance the additional attraction partly arising from the coupled-channel processes, which, a'-. stressed before, are required for a realistic description of pion production. Theiefore it is not surprising that in our model the cross section enhancement generated by a 10e~ reduction of vector meson masses is much t o . large, see fig.3 (dash-dot line). (For simplicity we have taken the reduction to be constant throughout the nuclear volume. We expect that the deviation from the gaussian shape used in [7] does not alter our qualitative arguments.) In fact, as fig. 3 (dashed line) shows, a 4% decrease turns out to be sufficient. Note that a considerable part of the enhancement arises from pwaves, since a change of vector meson masses in the medium removes the aforementioned delicate balance of those waves in free K+N scattering. This is demonstrated by the dotted line in fig. 3, which shows the result obtained if the 10% mass reduction is done in the S I I phase shift only. Of course, our results depend on the assumption that the strong phenomenological repulsion needed to describe the K+N data is completely due to oJ-exchange. This is not necessarily correct. In fact, it has been shown in [8] that such an interpretation leads to difficulties in the K - N system. Namely, K - N data seem to require that genuine
602c
p. Wyborny et al. / K÷-N interaction and I~.nucleus cross sectimt~
~0-exchange has the much weaker SU(3) coupling, and tha~. the additional repulsion in K+N behaves differently under G-parity transformation. Indeed, applying the mass reduction to the SU(3) part of w-exchange only, a somewhat larger reduction (about 6~) is needed; however, in this case the energy dependence is slightly deteriorated. Thus the problem of a consistent description of K+N and K+-nucleus data is intimately connected to the question about the nature of tile short-range repulsion in hadronie systems. REFERENCES [1] R. Machleidt, K. lIolinde and Ch. Elster, Phys. Rep. 149 (1987) 1. [2] R. Biittgen, K. tlolinde, A. Miiller-Groeling, J. Speth and P. Wyborny, Nucl. Phys. A506 (1990) 586 [3] R. \V. Bland et al. Nucl. Phys. BI3 (1969) 595. [.t] J. Aister et al. Proceedings of the International Symposium of llyp~rnuclear aped Strange |)article Physics / Shimoda (Japan) 1991; to be published in Nucl. Phys. A [5] P. Wyborny, Spezielle Berichle der Kernforschungsanlage Jfilich, JiiI-Spez-186 (1988). [6] P. Wyborn.v F. Osterfeld and J. Speth, c,mtributed paper to PANIC XII (1990)session IV-7 [7] G. F. Brown, C. B. Dover. P. L. Siegel and W. Weise, I'h.vs. Rev. 1.ell. 60 (1988) 2733. [8] A. Miiller-Groeling, K. lloli,de a,d .1. Speth, Nucl. Phys. A513 (1990) 557.