properties of the Λ 1405 measured at clas kei moriya ... at clas kei moriya reinhard schumacher...
TRANSCRIPT
— MENU 2010 —
Properties of theΛ(1405)
Measured at CLAS
Kei MoriyaReinhard Schumacher
March 31, 2010
Outline
1 IntroductionWhat is the Λ(1405)?Theory of the Λ(1405)
2 CLAS AnalysisSelecting Decay Channels of InterestRemoving Σ0(1385) and K ∗ BackgroundFit to Extract Λ(1405) Lineshape
3 ResultsΛ(1405) Lineshape ResultsΛ(1405) Cross Section ResultsΛ(1520) Cross Section ResultsΛ(1405),Λ(1520),Σ0(1385) Cross Section Comparison
4 Conclusion
K. Moriya (CMU) Λ(1405) lineshape May 2010 2 / 19
What is the Λ(1405)?
• **** resonance just below NK threshold
• JP = 12
−(experimentally unconfirmed)
• decays exclusively to (Σπ)0
• past experiments: the lineshape (= invariant Σπ mass distribution) isdistorted from a simple Breit-Wigner form
• what is the nature of this distorted lineshape?I “normal” qqq-baryon resonanceI dynamically generated resonance in
unitary coupled channel approach
K. Moriya (CMU) Λ(1405) lineshape May 2010 3 / 19
Chiral Unitary Coupled Channel Approach
dynamically generate Λ(1405)
( )J.C. Nacher et al.rPhysics Letters B 455 1999 55–6158
the Bethe–Salpeter equation, and diagrammatically
this is shown in Fig. 2.
The sum implicit in Fig. 2 is easily evaluated. The
t !g . matrix for the process with the j channel in thej
final state is given by means of the vector D sC Pj 1 j
QXas:j
e i s=q e! .!g .t s D q D G T , 8! ."j j l l l j2 # /2M4 f
l
where the on shell factorization of the strong ampli-w x w xtude found in 9 and in 22 for the related electro-
magnetic process has been used. Diagrams where the
photon couples to the mesons or baryons inside the
loops are largely suppressed at threshold. One can
see that the contribution from the photon attached to
the meson vanishes exactly at threshold. This can be
seen by noting that the loop involves a term of the3 ! . ! .type ePHd q q P f q ,q , with f q ,q a scalarL L L L
function. The integral is proportional to q and van-
ishes due to the Coulomb gauge constraint, ePqs0.
Similarly, for small values of the Kq momentum
one can prove that the corrections to the cross sec-! .2 ! qtion are of order krq k,q,K and photon mo-.menta respectively when compared to the dominant
! .terms of Eq. 8 . Analogously, the contribution from
the photon attached to the baryon is of the order of! 0 X0.k yk rq of the corresponding loops in Fig. 2and hence also negligible in the energy range consid-
ered here.! .The particular structure of Eq. 8 allows one to
obtain an easy formula for the invariant mass distri-
bution of the final j state, particularly suited to the
search of a resonance. We find
ds 1 1 MM 1js3 2dM 4 s MsyM2p! .I Ij
=—
2!g .< <t"" j
=l1r2 s,M 2 ,m2 l1r2 M 2 ,M 2 ,m2 ,! . ! .I K I j j
9! .
where M is the invariant mass of the j state, M , mI j j
! .the masses of the j state and l x, y, z the ordinary
Kallen function.¨In Fig. 3 we show dsrdM for the differentI
channels. While all coupled channels collaborate to
Fig. 2. Diagrammatic representation of the meson-baryon finalq ! .state interaction in the g p™K L 1405 process.
! .the built up of the L 1405 resonance, most of them
open up at higher energies and the resonance shape
is only visible in the pqSy, pySq, p 0S 0 channels.
The KN production occurs at energies slightly above
the resonance and the p 0L, with isospin one, onlyprovides a small background below the resonance.
It is interesting to see the different shapes of the
three pS channels. This can be understood in terms
of the isospin decomposition of the states
1 1 1q y< : < : < : < :p S sy 2,0 y 1,0 y 0,0 ,' ' '6 2 3
10! .1 1 1
y q< : < : < : < :p S sy 2,0 q 1,0 y 0,0 ,' ' '6 2 3
11! .1
20 0< : < : < :p S s 2,0 y 0,0 . 12( ! .3 '3Disregarding the Is2 contribution which is neg-
ligible, the cross sections for the three channels go
as:
22 21 1!1. !0. !0. !1.) q y< < < <T q T q Re T T ; p S ,! .2 3 '6
13! .2
2 21 1!1. !0. !0. !1.) y q< < < <T q T y Re T T ; p S ,! .2 3 '614! .
1 2!0. 0 0< <T ; p S . 15! .3
Apr-20-2009, NSTAR2009, Beijing R. A. Schumacher, Carnegie Mellon University 1
Chiral Unitary Model Prediction
!+"!
!0"0!!""
! Lineshape of “#(1405)” predicted to depend on "! decay channel
! J. C. Nacher, E. Oset, H. Toki, A. Ramos, Phys. Lett. B 455, 55 (1999).! Chiral Lagrangian + mB FSI
+ Channel Coupling! I(" !) = {0,1,2} – not in an
isospin eigenstate! I=2 contributions negligible! Interference between I=0
and I=1 amplitudes modifies mass distributions
# $ # $
# $ # $
# $
2 2(1) (0) (0) (1)* (2)
2 2(1) (0) (0) (1)* (2)
0 02(0) (2)
( ) 1 1 2Re
2 3 6
( ) 1 1 2Re
2 3 6
( ) 1
3
I
I
I
dT T T T O T
dM
dT T T T O T
dM
dT O T
dM
$ "
$ "
$ "
" !
! "
!% " " "
!% " ! "
!% "
!" Invariant Mass (GeV)
d$/d
MI (µ
b/G
ev) 1.7
p K
E GeV%
% "" !&
'
J. C. Nacher et al., Phys. Lett. B455, 55 (1999)
K. Moriya (CMU) Λ(1405) lineshape May 2010 4 / 19
Difference in Lineshape
!"#$%& '(#)%$*+,-./&+0$/.#1)#-(
!+"#
!0"0!#"$
! 2#(/3"%4/+-5+6%789:;<=4$/.#1)/.+)-+./4/(.+-(+"!./1%*+1"%((/&+
! >?+!?+@%1"/$A+B?+C3/)A+D?+E-F#A+G?+H%I-3A+0"*3?+2/))?+J+!""A+;;+78KKK<?! !"#$%& 2%L$%(L#%(+M+IJ NOP+
M+!"%((/&+!-Q4&#(L
! P7" !<+R+S:A8ATU+V (-)+#(+%(+#3-34#( /#L/(3)%)/
! PRT+1-()$#WQ)#-(3+(/L&#L#W&/
! P()/$5/$/(1/+W/)X//(+PR:+%(.+PR8+%I4&#)Q./3+I-.#5#/3+I%33+.#3)$#WQ)#-(3
& ' & '
& ' & '
& '
2 2(1) (0) (0) (1)* (2)
2 2(1) (0) (0) (1)* (2)
0 02
(0) (2)
( ) 1 1 2Re
2 3 6
( ) 1 1 2Re
2 3 6
( ) 1
3
I
I
I
dT T T T O T
dM
dT T T T O T
dM
dT O T
dM
( "
( "
( "
$ #
# $
!) $ $ $
!) $ # $
!) $
!" Invariant Mass (GeV)d(/d
MI(*
b/G
ev) 1.7
p K
E GeV+
+ "$, !
-
J. C. Nacher et al., Nucl. Phys. B455, 55
• difference in lineshapes is due to interference of isospin terms incalculation (T(I) represents amplitude of isospin I term)
• distortion of the lineshape is connected to underlying QCD amplitudesthat generate the Λ(1405)
• this analysis will measure all three Σπ channels
K. Moriya (CMU) Λ(1405) lineshape May 2010 5 / 19
Data From CLAS@JLab
• CLAS@Jefferson Lab
• liquid LH2 target
• γ + p→ K+ + Λ(1405)
• real unpolarized photonbeam
• Eγ < 3.84 GeV
• ∼ 20B total triggers
• measure charged particle
I ~p with driftchambers
I timing with TOFwalls
K. Moriya (CMU) Λ(1405) lineshape May 2010 6 / 19
Data From CLAS@JLab
• CLAS@Jefferson Lab
• liquid LH2 target
• γ + p→ K+ + Λ(1405)
• real unpolarized photonbeam
• Eγ < 3.84 GeV
• ∼ 20B total triggers
• measure charged particle
I ~p with driftchambers
I timing with TOFwalls
K. Moriya (CMU) Λ(1405) lineshape May 2010 6 / 19
Data From CLAS@JLab
• CLAS@Jefferson Lab
• liquid LH2 target
• γ + p→ K+ + Λ(1405)
• real unpolarized photonbeam
• Eγ < 3.84 GeV
• ∼ 20B total triggers
• measure charged particle
I ~p with driftchambers
I timing with TOFwalls
K. Moriya (CMU) Λ(1405) lineshape May 2010 6 / 19
Data From CLAS@JLab
• CLAS@Jefferson Lab
• liquid LH2 target
• γ + p→ K+ + Λ(1405)
• real unpolarized photonbeam
• Eγ < 3.84 GeV
• ∼ 20B total triggers
• measure charged particle
I ~p with driftchambers
I timing with TOFwalls
K. Moriya (CMU) Λ(1405) lineshape May 2010 6 / 19
Reaction of Interest
p!!(!0
, ")
52%
48%
100%
64%
!+!!
!0!
0
! + p p(!0)!!
(n)!+!!
K+
+ !(1405)
!!
!+
detected particles K+,p,π− K+,π+,π−
missing particle(s) (π0) (π0,γ) (n)
intermediate hyperon Λ Σ+ Σ0(→ γΛ) Σ+ Σ−
kinematic fit yes no yesreaction Σ(1385) Σ(1385), Λ(1405), Λ(1520)
K. Moriya (CMU) Λ(1405) lineshape May 2010 7 / 19
Reaction of Interest
p!!(!0
, ")
52%
48%
100%
64%
!+!!
!0!
0
! + p p(!0)!!
(n)!+!!
K+
+ !(1405)
!!
!+
33% each?(will be for pure
isospin 0)
detected particles K+,p,π− K+,π+,π−
missing particle(s) (π0) (π0,γ) (n)
intermediate hyperon Λ Σ+ Σ0(→ γΛ) Σ+ Σ−
kinematic fit yes no yesreaction Σ(1385) Σ(1385), Λ(1405), Λ(1520)
K. Moriya (CMU) Λ(1405) lineshape May 2010 7 / 19
Background
• Σ0(1385)→ ΣπI BR(Λπ0) = 88%� BR(Σ±π∓) = 6% each⇒ measure in Λπ0, scale down to each Σπ channel
I influence should be small due to branching ratio• K ∗Σ
I broad width – will overlap with signalI subtract off incoherently
)-π,+M(K0.6 0.7 0.8 0.9 1 1.1
)- π,+ ΣM
(
1.3
1.4
1.5
1.6
1.7
1.8
-110
1
10
Wbin: 3
2.150 <W< 2.250
only: 70414+Σdata kfit
K. Moriya (CMU) Λ(1405) lineshape May 2010 8 / 19
Background
• Σ0(1385)→ ΣπI BR(Λπ0) = 88%� BR(Σ±π∓) = 6% each⇒ measure in Λπ0, scale down to each Σπ channel
I influence should be small due to branching ratio• K ∗Σ
I broad width – will overlap with signalI subtract off incoherently
)-π,+M(K0.6 0.7 0.8 0.9 1 1.1
)- π,+ ΣM
(
1.3
1.4
1.5
1.6
1.7
1.8
-110
1
10
Wbin: 3
2.150 <W< 2.250
only: 70414+Σdata kfit
(1405)Λ
(1520)Λ
*0K
K. Moriya (CMU) Λ(1405) lineshape May 2010 8 / 19
Background
• Σ0(1385)→ ΣπI BR(Λπ0) = 88%� BR(Σ±π∓) = 6% each⇒ measure in Λπ0, scale down to each Σπ channel
I influence should be small due to branching ratio• K ∗Σ
I broad width – will overlap with signalI subtract off incoherently
)-π,+M(K0.6 0.7 0.8 0.9 1 1.1
)- π,+ ΣM
(
1.3
1.4
1.5
1.6
1.7
1.8
-110
1
10
Wbin: 3
2.150 <W< 2.250
only: 70414+Σdata kfit
(1405)Λ
(1520)Λ
*0Kkinematic boundary
K. Moriya (CMU) Λ(1405) lineshape May 2010 8 / 19
Σ(1385) is Fit in Λπ0 Channel (γ + p→ K+ + p + π− + π0)
)0π ΛM(1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65
coun
ts
0
20
40
60
80
100
120
140
160
180
200 Wbin: 2 anglebin: 17
2.050 <W< 2.150
<0.800CMK+θ0.700<cos
data
threshold0π Λ
example:1 energy and anglebin out of ∼ 150
• Σ(1385) is fit with templates of MC ofI Σ(1385) (non-relativistic Breit-Wigner)I K∗+Λ MC
• very good fit resultsK. Moriya (CMU) Λ(1405) lineshape May 2010 9 / 19
Σ(1385) is Fit in Λπ0 Channel (γ + p→ K+ + p + π− + π0)
)0π ΛM(1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65
coun
ts
0
20
40
60
80
100
120
140
160
180
200 Wbin: 2 anglebin: 17
2.050 <W< 2.150
<0.800CMK+θ0.700<cos
data
threshold0π Λ
(1385) MCΣexample:1 energy and anglebin out of ∼ 150
• Σ(1385) is fit with templates of MC ofI Σ(1385) (non-relativistic Breit-Wigner)I K∗+Λ MC
• very good fit resultsK. Moriya (CMU) Λ(1405) lineshape May 2010 9 / 19
Σ(1385) is Fit in Λπ0 Channel (γ + p→ K+ + p + π− + π0)
)0π ΛM(1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65
coun
ts
0
20
40
60
80
100
120
140
160
180
200 Wbin: 2 anglebin: 17
2.050 <W< 2.150
<0.800CMK+θ0.700<cos
data
threshold0π Λ
(1385) MCΣ MCΛ *+K example:
1 energy and anglebin out of ∼ 150
• Σ(1385) is fit with templates of MC ofI Σ(1385) (non-relativistic Breit-Wigner)I K∗+Λ MC
• very good fit resultsK. Moriya (CMU) Λ(1405) lineshape May 2010 9 / 19
Σ(1385) is Fit in Λπ0 Channel (γ + p→ K+ + p + π− + π0)
)0π ΛM(1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65
coun
ts
0
20
40
60
80
100
120
140
160
180
200 Wbin: 2 anglebin: 17
2.050 <W< 2.150
<0.800CMK+θ0.700<cos
data
threshold0π Λ
(1385) MCΣ MCΛ *+K
sum of MC/ndf: 1.602χ
example:1 energy and anglebin out of ∼ 150
• Σ(1385) is fit with templates of MC ofI Σ(1385) (non-relativistic Breit-Wigner)I K∗+Λ MC
• very good fit resultsK. Moriya (CMU) Λ(1405) lineshape May 2010 9 / 19
Σ(1385) Cross Section From Λπ0 Channel
c.m.K+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [c.
m.
K+
θdc
osσd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
5th order Legendre fit2.050<W<2.150
<1.994γ1.770<E
Preliminary
• scale by branching ratio and acceptance into each Σπ channel
• BR(Λπ) = 89% � BR(Σπ) = 11%
• Σ0π0 channel does not have Σ(1385)
K. Moriya (CMU) Λ(1405) lineshape May 2010 10 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ(1385) MCΣ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ(1385) MCΣ
(1405) MC ver.1Λ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ(1385) MCΣ
(1405) MC ver.1Λ(1520) MCΛ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ(1385) MCΣ
(1405) MC ver.1Λ(1520) MCΛ
+Σ *0K example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ(1385) MCΣ
(1405) MC ver.1Λ(1520) MCΛ
+Σ *0Ksum of MC
/ndf: 4.162χ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σ(1385) MCΣ
(1405) MC ver.1Λ(1520) MCΛ
+Σ *0Ksum of MC
/ndf: 2.092χ(1405) MC ver.2Λ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
100
200
300
400
500
600Wbin: 3 anglebin: 17
2.150 <W< 2.250<0.800CM
K+θ0.700<cosdata
0π p → +Σresidual
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K∗0
• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 11 / 19
Results of Lineshape
Invariant Mass [GeV]π Σ1.3 1.4 1.5
b/G
eV]
µ/d
M [
σd
0
0.5
1
1.5
2
2.5 <1.99γ1.77<E2.05<W<2.15
thresholdsπ Σ
weighted average-π +Σ0π 0Σ+π -Σ
PDG Breit-Wigner
Preliminary
• lineshapes do appear different for each Σπ decay mode
• Σ+π− decay mode has peak at highest mass, narrow than Σ−π+
• lineshapes are summed over acceptance region of CLAS
• difference is less prominent at higher energies
K. Moriya (CMU) Λ(1405) lineshape May 2010 12 / 19
Results of Lineshape
Invariant Mass [GeV]π Σ1.3 1.4 1.5
b/G
eV]
µ/d
M [
σd
0
0.2
0.4
0.6
0.8
1<2.73γ2.47<E
2.35<W<2.45
thresholdsπ Σ
weighted average-π +Σ0π 0Σ+π -Σ
PDG Breit-Wigner
Preliminary
• lineshapes do appear different for each Σπ decay mode
• Σ+π− decay mode has peak at highest mass, narrow than Σ−π+
• lineshapes are summed over acceptance region of CLAS
• difference is less prominent at higher energies
K. Moriya (CMU) Λ(1405) lineshape May 2010 12 / 19
Results of Lineshape
Invariant Mass [GeV]π Σ1.3 1.4 1.5
b/G
eV]
µ/d
M [
σd
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4<3.56γ3.27<E
2.65<W<2.75
thresholdsπ Σ
weighted average-π +Σ0π 0Σ+π -Σ
PDG Breit-Wigner
Preliminary
• lineshapes do appear different for each Σπ decay mode
• Σ+π− decay mode has peak at highest mass, narrow than Σ−π+
• lineshapes are summed over acceptance region of CLAS
• difference is less prominent at higher energies
K. Moriya (CMU) Λ(1405) lineshape May 2010 12 / 19
Theory Prediction From Chiral Unitary Approach
Apr-20-2009, NSTAR2009, Beijing R. A. Schumacher, Carnegie Mellon University 1
Chiral Unitary Model Prediction
!+"!
!0"0!!""
! Lineshape of “#(1405)” predicted to depend on "! decay channel
! J. C. Nacher, E. Oset, H. Toki, A. Ramos, Phys. Lett. B 455, 55 (1999).! Chiral Lagrangian + mB FSI
+ Channel Coupling! I(" !) = {0,1,2} – not in an
isospin eigenstate! I=2 contributions negligible! Interference between I=0
and I=1 amplitudes modifies mass distributions
# $ # $
# $ # $
# $
2 2(1) (0) (0) (1)* (2)
2 2(1) (0) (0) (1)* (2)
0 02(0) (2)
( ) 1 1 2Re
2 3 6
( ) 1 1 2Re
2 3 6
( ) 1
3
I
I
I
dT T T T O T
dM
dT T T T O T
dM
dT O T
dM
$ "
$ "
$ "
" !
! "
!% " " "
!% " ! "
!% "
!" Invariant Mass (GeV)
d$/d
MI (µ
b/G
ev) 1.7
p K
E GeV%
% "" !&
'
!"#$%& '(#)%$*+,-./&+0$/.#1)#-(
!+"#
!0"0!#"$
! 2#(/3"%4/+-5+6%789:;<=4$/.#1)/.+)-+./4/(.+-(+"!./1%*+1"%((/&+
! >?+!?+@%1"/$A+B?+C3/)A+D?+E-F#A+G?+H%I-3A+0"*3?+2/))?+J+!""A+;;+78KKK<?! !"#$%& 2%L$%(L#%(+M+IJ NOP+
M+!"%((/&+!-Q4&#(L
! P7" !<+R+S:A8ATU+V (-)+#(+%(+#3-34#( /#L/(3)%)/
! PRT+1-()$#WQ)#-(3+(/L&#L#W&/
! P()/$5/$/(1/+W/)X//(+PR:+%(.+PR8+%I4&#)Q./3+I-.#5#/3+I%33+.#3)$#WQ)#-(3
& ' & '
& ' & '
& '
2 2(1) (0) (0) (1)* (2)
2 2(1) (0) (0) (1)* (2)
0 02
(0) (2)
( ) 1 1 2Re
2 3 6
( ) 1 1 2Re
2 3 6
( ) 1
3
I
I
I
dT T T T O T
dM
dT T T T O T
dM
dT O T
dM
( "
( "
( "
$ #
# $
!) $ $ $
!) $ # $
!) $
!" Invariant Mass (GeV)
d(/d
MI(*
b/G
ev) 1.7
p K
E GeV+
+ "$, !
-
J. C. Nacher et al., Nucl. Phys. B455, 55
• Σ−π+ decay mode peaks at highest mass, most narrow
• difference in lineshapes is due to interference of isospin terms incalculation (T(I) represents amplitude of isospin I term)
• we have started trying fits to the resonance amplitudes
K. Moriya (CMU) Λ(1405) lineshape May 2010 13 / 19
Isospin Decomposition• Separate {!"#$, !%#%, !$#"} into I=0 and I=1
amplitude contributions(0) (0)
0ˆ{ } | |
IT T p# &
'( !
(1) (1)
1ˆ{ } | |
IT T p# &
'( !
2 2 2(0) (1) (0) (1)
01
1 1 2cos
3 2 6A T T T T
#)" $!
' " $ *
0 0
2 2(0)1
3A T
#!'
2 2 2(0) (1) (0) (1)
01
1 1 2cos
3 2 6A T T T T
#)$ "!
' " " *
+ ,2
2(0) (1) (2)
3 3 3 3 3 32
( )( , | 0,0) ( , |1,0) ( , | 2,0)
16 ( )
f
i
p mcdI I T I I T I I T
dm W p W# # #
- .
#! ! !
' " "!
0
(0,1,2) (0,1,2) 0
2 2
0
( )( ) ( )
m
T m gm m im q
/
/0
'$ $ 0
2 /q m/ '
0
0
( )( )
q mm
q0 ' 0
(2) (2)
2ˆ{ } | |
IT T p# &
'( !
!1#1phase space factor
Mass-dependent width
for relativistic Breit Wigner
K. Moriya (CMU) Λ(1405) lineshape May 2010 14 / 19
Isospin Decomposition
I=1 contributions
I=0 contribution
!" #
$
!# "
$
0 0
!$
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 15 / 19
Λ(1405) Differential Cross Section Results
c.m.K+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.05
0.1
0.15
0.2
0.25
<2.23γ1.99<E
2.15<W<2.25
Preliminary
Σ+π−Σ0π0
Σ−π+
total/3
• lines are fits with 6rd order Legendre polynomials
• clear turnover of Σ+π− channel at forward angles
• theory: contact term only, no angular dependence for interference
• experiment: able to see strong isospin AND angular interference effect
K. Moriya (CMU) Λ(1405) lineshape May 2010 16 / 19
Λ(1405) Differential Cross Section Results
c.m.K+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
<3.56γ3.27<E
2.65<W<2.75
Preliminary
Σ+π−Σ0π0
Σ−π+
total/3
• lines are fits with 6rd order Legendre polynomials
• clear turnover of Σ+π− channel at forward angles
• theory: contact term only, no angular dependence for interference
• experiment: able to see strong isospin AND angular interference effect
K. Moriya (CMU) Λ(1405) lineshape May 2010 16 / 19
Λ(1520) Differential Cross Section Comparison
]2 [GeV0t-t0 0.5 1 1.5 2 2.5
]-2
b/G
eVµ
[dtσd
0
0.2
0.4
0.6
0.8
1
1.2
<2.730γ
average: 2.474<Eπ Σ=2.440
γ average: E-p K
=2.503γ
average: E-p K=2.565
γ average: E-p K
=2.628γ
average: E-p K=2.690
γ average: E-p K
Preliminary
• binning is in t − tmin
• good agreement with pK− channel from CLAS (unpublished)— data provided by de Vita et al. (INFN Genova)K. Moriya (CMU) Λ(1405) lineshape May 2010 17 / 19
Comparison of Σ(1385)/Λ(1405)/Λ(1520) Cross Sections
c.m.K+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.2
0.4
0.6
0.8
1
1.2
<2.23γ1.99<E2.15<W<2.25
modesπ Σ(1405) sum of Λ
π Λ(1385) total from Σ
π Σ(1520) average of 3 Λ
Preliminary
• lines are fits with 5th order Legendre polynomials
K. Moriya (CMU) Λ(1405) lineshape May 2010 18 / 19
Comparison of Σ(1385)/Λ(1405)/Λ(1520) Cross Sections
c.m.K+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
<3.56γ3.27<E2.65<W<2.75
modesπ Σ(1405) sum of Λ
π Λ(1385) total from Σ
π Σ(1520) average of 3 Λ
Preliminary
• lines are fits with 5th order Legendre polynomials
K. Moriya (CMU) Λ(1405) lineshape May 2010 18 / 19
Conclusion
• difference in lineshapes observed
• difference in dσ/dcosθc.m.K+ behavior observed
• doing our own isospin decomposition of resonance amplitudes
• systematics under study
strong dynamical effects being observed for the Λ(1405)
hoping to finalize analysis soon
K. Moriya (CMU) Λ(1405) lineshape May 2010 19 / 19
effect of kinematic fit on resolution
example in 1 bin:• neutron combined with π± reconstructs Σ±
• project on each axis, select ±2σ, exclude other hyperon• diagonal band (K 0 from π+π−) is also excluded
(without kinematic fit)
,n)-!(2M1.2 1.4 1.6 1.8 2
,n)
+ !(2M
1.2
1.4
1.6
1.8
2 Wbin: 2 tbin: 182.050 <W< 2.150
-0.270<t<-0.135missing n: 26355
lines"2±nominal lines"2±kfit
+#
-#
K. Moriya (CMU) Λ(1405) lineshape May 2010 1 / 5
effect of kinematic fit on resolution
example in 1 bin:• neutron combined with π± reconstructs Σ±
• project on each axis, select ±2σ, exclude other hyperon• diagonal band (K 0 from π+π−) is also excluded
(with kinematic fit)
,n)-!(2M1.2 1.4 1.6 1.8 2
,n)
+ !(2M
1.2
1.4
1.6
1.8
2 Wbin: 2 tbin: 182.050 <W< 2.150
-0.270<t<-0.135CL(n)>1: 24408
lines"2±nominal lines"2±kfit
+#
-#
K. Moriya (CMU) Λ(1405) lineshape May 2010 1 / 5
Fit to Lineshape With MC Templates
Invariant Mass (GeV)π Σ1.3 1.4 1.5 1.6 1.7 1.8
coun
ts
0
50
100
150
200
250
300
350
400 Wbin: 3 anglebin: 172.150 <W< 2.250
<0.800CMK+θ0.700<cos
data
-π n → -Σ(1385) MCΣ(1405) MCΛ(1520) MCΛ
+Σ *0Ksum of MC
/ndf: 2.622χ
example:1 energy and anglebin out of ∼ 150
• subtract off Σ(1385), Λ(1520), K+Σ−π+ phase space• assigned the remaining contribution to the Λ(1405)
K. Moriya (CMU) Λ(1405) lineshape May 2010 2 / 5
Comparison of Lineshapes for Two Σ+Channels
Invariant Mass [GeV]π Σ1.3 1.4 1.5
b/G
eV]
µ/d
M [
σd
0
0.5
1
1.5
2
2.5<1.99γ1.77<E
2.05<W<2.15
-π 0π p → -π +Σ-π +π n → -π +Σ
weighted averagePDG Breit-Wigner
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 3 / 5
Comparison of Lineshapes for Two Σ+Channels
Invariant Mass [GeV]π Σ1.3 1.4 1.5
b/G
eV]
µ/d
M [
σd
0
0.2
0.4
0.6
0.8
1 <2.73γ2.47<E
2.35<W<2.45
-π 0π p → -π +Σ-π +π n → -π +Σ
weighted averagePDG Breit-Wigner
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 3 / 5
Comparison of Lineshapes for Two Σ+Channels
Invariant Mass [GeV]π Σ1.3 1.4 1.5
b/G
eV]
µ/d
M [
σd
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
<3.56γ3.27<E
2.65<W<2.75
-π 0π p → -π +Σ-π +π n → -π +Σ
weighted averagePDG Breit-Wigner
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 3 / 5
Λ(1405) Comparison of Two Σ+Channels
CMK+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.05
0.1
0.15
0.2
0.25
0.3
from fit to 6th Legendre2χ1.3221.4331.164
Wbin: 2
<1.99γ1.77<E
2.05<W<2.150π -π p → -π +Σ-π +π n → -π +Σ
-π +Σweighted
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 4 / 5
Λ(1405) Comparison of Two Σ+Channels
CMK+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
from fit to 6th Legendre2χ2.4621.0734.220
Wbin: 5
<2.73γ2.47<E
2.35<W<2.450π -π p → -π +Σ-π +π n → -π +Σ
-π +Σweighted
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 4 / 5
Λ(1405) Comparison of Two Σ+Channels
CMK+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
from fit to 6th Legendre2χ3.4792.8561.130
Wbin: 8
<3.56γ3.27<E
2.65<W<2.750π -π p → -π +Σ-π +π n → -π +Σ
-π +Σweighted
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 4 / 5
Λ(1520) Comparison of Two Σ+Channels
CMK+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.2
0.4
0.6
0.8
1 <1.99γ1.77<E
2.05<W<2.15
0π -π p → -π +Σ-π +π n → -π +Σ
-π +Σweighted
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 5 / 5
Λ(1520) Comparison of Two Σ+Channels
CMK+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
<2.73γ2.47<E
2.35<W<2.45
0π -π p → -π +Σ-π +π n → -π +Σ
-π +Σweighted
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 5 / 5
Λ(1520) Comparison of Two Σ+Channels
CMK+θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
b]µ [ θ
dcosσd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
<3.56γ3.27<E
2.65<W<2.75
0π -π p → -π +Σ-π +π n → -π +Σ
-π +Σweighted
Preliminary
K. Moriya (CMU) Λ(1405) lineshape May 2010 5 / 5