K d pS n reaction 201598 1 Shota Ohnishi Hokkaido Univ in collaboration with Yoichi Ikeda RIKEN Tetsuo Hyodo YITP Kyoto Univ Emiko Hiyama RIKEN Wolfram Weise ECTTUM ID: 793225
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Slide1
Signature of L(1405) in K-dpSn reaction
2015/9/8
1
Shota Ohnishi(Hokkaido Univ.)
in collaboration
with
Yoichi Ikeda (RIKEN)
Tetsuo
Hyodo
(YITP, Kyoto Univ.
)
Emiko
Hiyama
(RIKEN)
Wolfram Weise (ECT*/TUM)
Slide22015/9/8
2
K
bar
N
interaction
In order to understand the structure of
L
(1405),
precise determination of
K
bar
N-
pS
(
I
=0) interaction is necessary.
above
K
bar
N
threshold energy
:
-
K
-
p
cross section
at/just-below
KN
threshold energy:
- Branching ratio - kaonic atom(new data by SIDDHARTA)below the KbarN threshold energy: - So far, cannot perform pS elastic scattering experimentally - pS mass spectra from L(1405) production reactions (CLAS, LEPS, HADES, J-PARC)
experimental constraint
Planed
K
-
d
reaction at J-PARC (E31) is our target
Slide32015/9/83
J-PARC E31 experiment
http://j-parc.jp/researcher/Hadron/en/pac_0907/pdf/Noumi.pdf
pKlab.= 1GeVdetect forward neutronMissing mass distribution for p+S-/p0S0/p-S+L(1405) production via
the (
K
-
,n
) reaction on
deuteron target.
We can access below the
K
bar
N
threshold.
L
(1405) in K
barN channel
Jido
,
Oset
,
Sekihara
, EPJA42, 257(2009).
Slide4Strategy of this work2015/9/84Study the cross section for J-PARC
E31 with KbarNN-
pYN
Faddeev (AGS) approach based on chiral SU(3) dynamicsFull three-body calculation for KbarNN-pYN systems with relativistic kinematics and higher partial waves for 1GeV incident momentuminvestigate how the signal of L(1405) resonance appears on pS mass spectrumTwo-step: Jido, Oset, Sekihara, EPJA42, 257(2009). Miyagawa, Haidenbauer, PRC85,065201(2012). Yamagata-Sekihara,
Sekihara
,
Jido
, PTEP043D02(2013).
Faddeev
:
Miyagawa
(Next talk)
Slide5Meson-baryon potential based on chiral SU(3)Leading order of chiral perturbation theory: Weinberg-Tomozawa (WT) term
“energy-dependent” potentials
E; two body scattering energy
; determined by flavor SU(3) structure2015/9/85; baryon mass; meson mass
“energy-independent” potentials
Derive the potentials by matching with WT amplitude
f
: PS meson fields,
B
: baryon fields
Energy is fixed at threshold
We introduce phenomenological dipole form factor to regularize loop integrals
Cutoff parameters
L
are determined to reproduce the
K
-
p
cross section
Weinberg, PRL 17, 616 (1966).
Tomozawa
,
Nuov
.
Cim
. 46A, 707 (1966).
NG boson associated with spontaneous breaking of chiral SU(3)
symmetry
Slide6cutoff (model parameters)We determine the cutoff parameters to reproduce K-p cross sections. 2015/9/8
6
Slide7KbarN amplitude and scattering length (output)2015/9/87
SIDDHARTA
xSU
(3) NLOE-dep.E-indep.
Ikeda,
Hyodo
, Weise
NPA
881 (2012) 98.
Slide8L
Alt-Grassberger-Sandhas(AGS) eq.
:
X
ij
;
quasi two-body amplitude
K
-
d ->
pS
n
reaction
2015/9/8
8
=
+
X
t
g
L
L
+
X
t
g
L
L
+
X
t
g
L
L
X
t
g
L
L
Slide92015/9/8
9
pS
invariant mass spectrumFor E-dep. model, signature of L(1405) appears on pS invariant mass spectrum around the binding energy of L(1405)For E-indep. model, signature of L(1405) is weak, and cusp appears at pS threshold
L
Slide102015/9/810pS invariant mass spectrum
For E-dep. model, signature of
L
(1405) appears on pS invariant mass spectrum around the binding energy of L(1405)For E-indep. model, signature of L(1405) is weak, and cusp appears at pS thresholdBump appears above the KbarN threshold
L
Slide11Angular dependence2015/9/811KN threshold cusp is enhanced in forward angle
Channel dependence is also large in forward angle
L
q
;
n
angle in C.M.
Slide12Angular dependence2015/9/812KN threshold cusp is enhanced in forward angle
Channel dependence is also large in forward angle
bump above K
barN threshold energy is enhanced in q=0
L
q
;
n
angle in C.M.
Slide13SummaryWe investigate how the signature of the L(1405) appears in K-d scattering reaction.How the signatures appear depends on the two-body interaction models.
The production reaction would be used to distinguish dynamical model of
L(1405).Channel dependence of the cross section is large
We would also obtain the information on I=1 KbarN-pS interactions from K-d scattering.Bump appears above the KN threshold, and it is enhanced in q=02015/9/813
Slide14Future workImprove the two-body interaction modelHigher order of chiral perturbationHigher partial waveCutoff parameters dependenceCompare with forthcoming J-PARC E312015/9/8
14
Slide15Backup slides2015/9/815
Slide16L
Alt-Grassberger-Sandhas(AGS) eq.
:
X
ij
;
quasi two-body amplitude
K
-
d ->
pS
n
reaction
2015/9/8
16
=
+
X
t
g
L
L
+
X
t
g
L
L
+
X
t
g
L
L
X
t
g
L
L
Slide17Contribution of each amplitude2015/9/817
X
YK,d
component is dominant
X
t
g
L
L
Slide18Bump structure above KN threshold2015/9/818
One- and two-step
One-step
Slide19Bump structure above KN threshold
2015/9/8
19
One- and two-stepOne-step
Two-step
Slide20cutoff dependenceWe determine the cutoff parameters to reproduce K-p cross sections.
2015/9/8
20
SIDDHARTA
Slide21cutoff dependence2015/9/821
Preliminary
Slide22Partial wave decomposition2015/9/822S- and d-wave components are dominant in low-energy region
p-wave component is also large around
KN threshold energy
Slide23Angular dependence2015/9/823KN threshold cusp is enhanced in forward angle
Channel dependence is also large in forward angle
bump above K
barN threshold energy is enhanced in q=0
L
q
;
n
angle in C.M.
Slide24Contribution of each amplitude2015/9/824
X
YK,d
component is dominant
X
t
g
L
L
Slide25Model of b
aryon-baryon interaction
Nijimegen93
NN potential
Y
N potential
Torres,
Dalitz
,
Deloff
, PLB 174, 213 (1986)
2015/9/8
25
CD-Bonn
q (MeV)
q
2
f
2
(1/MeV)
Julich’04
Slide26Coupled channel equation for Faddeev eq.
separable 2-body Interaction;
Alt-Grassberger-Sandhas(AGS) eq.
: Xij;quasi two-body amplitude
X
ij
X
nj
Z
ij
Z
in
t
n
=
+
i
j
i
j
i
j
n
2015/9/8
26
Slide27Singularity of particle exchange interactionmethods to handle moon shape singularity numerically
point method
moon shape singularity
Z-diagram
2015/9/8
27
L.
Schlessinger
, PR 167, 1411(1968)
Kamada, Koike,
Glökle
, PTP 109, 869(2003)
Slide28Point methodL. Schlessinger, PR 167, 1411(1968)
evaluate X at finite
e
i
X at
e
=0
continued
fraction
Kamada, Koike,
Glökle
, PTP 109, 869(2003)
2015/9/8
28