Table Of ContentEPJ manus
ript No.
(will be inserted by the editor)
pp
Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II)
8 6 2 6 6 6 5,2
9 S.AbdEl-Sa6mad ,R.Bilge6r ,K.-Th.B3rinkmann ,H7.Clement ,M.D2ietri
h ,E.D3,o1roshkevi
h4,S.Dshemu
h4adse ,
0 K. Ehrha3rdt , A. Erhardt4, W. Eyri
h2 , A. Filip2pi , H. Freie2sleben , M.4Frits
h 6, R. Geyer , A.2Gillitzer , 7
0 J. Hau(cid:27)e , D4. Hesselbart6h , R. Jaeke5l , B. Jakob ,4L. Kars
h , K.5Kilian , J. K4ress , E. Kuhlm4ann , S. Mar
el2lo,3,
2 S. Marwinski , R. Meier2, K. Möller , H3.P. Mors
h , L3. Naumann2, J. Ritman 3, E. Roderburg6, P. S
hönme3ier ,
n M. S
hulte-6Wissermann1, W. S
hr3oeder , F. S6tainzing , G.Y. Sun ,9J. Wä
hter , G.J. Wagner , M. Wagner ,
a U. Weidli
h , A. Wilms , S. Wirth , G. Zhang , and P. Zupranski
J 1
2 Ruhr-UniversitätBo
hum, Germany
5
3 Te
hnis
heUniversität Dresden, Germany
1
4 Friedri
h-Alexander-UniversitätErlangen-Nürnberg, Germany
] 5 Fors
hungszentrumJüli
h, Germany
x 6 Fors
hungszentrumRossendorf, Germany
e 7 Physikalis
hes Institut derUniversität Tübingen, Tübingen,Germany
l- 8 Universityof Torino and INFN,Sezione di Torino, Italy
c 9 Atomi
Energy AuthorityNRCCairo, Egypt
u Soltan Institute for Nu
lear Studies, Warsaw, Poland
n
(COSY-TOF Collaboration)
[
2 January 15, 2009
v
pp→dπ+ pp→npπ+ pp→ppπ0
9
Abstra
t. Thesingle-pionprodu
tionrea
tions , and weremeasuredata
8 Tp ≈
beammomentumof0.95GeV/
( 400 MeV)usingtheshortversionoftheCOSY-TOFspe
trometer.
1
The
entral
alorimeter provided parti
le identi(cid:28)
ation, energy determination and neutron dete
tion in
1
addition to time-of-(cid:29)ight and angle measurements from other dete
tor parts. Thus all pion produ
tion
.
7
hannelswenrepπre+
ordedwith1-4over
onstraints.Themainemphasisisputonthepresentationanddis
us-
0 sion of the
hannel, sin
e the results on the other
hannels have already been published previously.
8 Theptpoπt0al and di(cid:27)erential
ross se
tinopnπs+obtained are
ompared to theoreti
∆al
al
ulations. In
ontrast to
0
: the
hannelwe observe in the (3 cos
2hΘan+ne1l)a strong in(cid:29)uen
eofthe ex
itation. Inp∆arti
ular the
v pion angular distribution exhibits a dπ+ dependen
e, typi
al for a pure s-
hannel ex
itation
Xi andide1nDti2
aplntothatobservedinthe
hannel.Sin
ethelatter isupnndπe+rstoodbyas-
hannelresonan
e
in the partial wave, we dis
uss ananalogous s
enario for the
hannel.
r
a
PACS. 13.75.Cs (cid:21) 14.20.Gk (cid:21) 14.20.Pt (cid:21) 25.10.+s (cid:21) 25.40.Ep
∆
1 Introdu
tion
ate the presen
e ofsigni(cid:28)
ant produ
tionin a relative
p-wavealready
lose to threshold.
pp→pnπ+
Single-pion produ
tion in the
ollision between two nu- In this workwepresentourresultsforthe
leons is thought to be the simplest inelasti
pro
ess be-
hannel at th∆e same in
ident energy. We will show that
tween two baryons, nevertheless its understanding is still here, where produ
tion in relative s-wave is allowed,
far from being satisfa
tory - both from the theoreti
al indeed this produ
tion pro
ess is overwhelmingly domi-
and the experimental point of view. In a re
ent publi- nant and
hara
terizes the di(cid:27)erential observables in this
ation [1℄ (cid:21) in the following denoted by (I) (cid:21) we have
hannel.
presentepdpt→hepp(cid:28)πrs0t kinemati
ally
omplete measurement The rea
tion of interest here has been investigated in
for the
hanneTl a=t a beam momentum o∆f 0.95 thenear-thresholdregionalreadypreviouslybyaseriesof
p
GeV/
(
orrespondingto 397MeV).Although pro- measurementsatJINR[2℄,KEK[3,4℄,TRIUMF[5℄,CEL-
du
tion in a relative s-wave is prohibited in this rea
tion SIUS [6℄ and notably at IUCF [7,8,9,10℄, sin
e there ex-
hannel, wehaveseen that the angular distributions indi- perimentshavebeen
arriedoutbothwithpolarizedbeam
a andtarget.Inthesemeasurementsvery
losetothresThold
p
present address: Peking University it was already noted [7℄ that at beam energies of =
Corresponden
e to: H. Clement 320 MeV, i.e. only 20 MeV above threshold, an onset of
∆
email:
lementpit.physik.uni-tuebingen.de the ex
itation is seen in the pion angular distribution.
pp
2 S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II)
p ∆
N
dete
tor system
onsists of the so-
alled Quirl, a 3-layer
π
q s
intillator system 1081 mm downstream of the target (cid:21)
p
and in its peripheral part of the so-
alled Ring, also a 3-
N
layers
intillatorsystembuiltin adesignanalogoustothe
Quirl,however,withinnerandouterradiiof560and1540
N mm, respe
tively. Finally behind the Quirl a
alorimeter
p
∆ π was installed for identi(cid:28)
ation of
harged parti
les and of
neutrons as well as for measuring the energy of
harged
p parti
les. The
alorimeter
onsists of 84 hexagon-shaped
N s
intillatorblo
ksoflength450mm,whi
hsu(cid:30)
estostop
deuterons, protons and pions of energies up to 400, 300
and 160 MeV, respe
tively. The energy
alibration of the
Fig. 1. Graphs used for the theoreti
al
al
ulations. Top: t-
alorimeter was performed by dete
ting
osmi
muons.
hannelapproa
h(PWIA,dire
tpartonly),bottom:s-
hannel
approa
h.
2.2 Parti
le identi(cid:28)
ation and event re
onstru
tion
The latter
hanges from isotropi
at energies below 300
IntheexperimentthetriggerrequiredtwohitsintheQuirl
MeV to anisotropi
at 320 MeV suggesting there a 30 -
% ∆ and/or Ring asso
iated with two hits in the start dete
-
40
ontribution of the ex
itation. In the TRIUMF
tor. Tra
ks of
harged parti
les are re
onstru
ted from
measurements,whi
hwereperformedat beam energiesof
Tp straight-line (cid:28)ts to the hit dete
tor elements. They are
= 420 and 500 MeV, it was noti
ed thpapt→at tdhπe+se en- a
epted as good tra
ks, if they originate in the target
perpgi→esptnhπe+pion angular distributions of and and have a hit in ea
h dete
tor element the tra
k passes
rea
tions are not only very similar, but also
th◦rough.In this waythe angularresolutionisbetter than
very
losetotheangulardistributionexpe
tedfromapure
∆ 1 both in azimuthal and in polar angles. If there is an
ex
itation. In te1rDm2s opfppartial waves this means a pre- isolated hit in the
alorimeter with no asso
iated hits in
dominan
e of the partial wave at these energies
the pre
eding dete
tor elements, then this hit quali(cid:28)es as
as is in fa
t thepopu→t
omdπe+of the SAID [11℄ partial wave aneutron
andidate(further
riteriawill bedis
ussed be-
analysis for the rea
tion. Hen
e after presen-
low). In this
ase the angular resolution of the neutron
tation and dis
ussion of our data we will
onfront them
tra
k is g◦iven by the size of the hit
alorimeter blo
k, i.e.
withtheoreti
alt-
hannel
al
ulations(Fig.1,top)aswell
by 7 - 8 . By
onstru
tion of the
alorimeter a parti
le
as with s-
hannel
al
ulation1sD(2Fig. 1, bottom). The lat- will hit one or more
alorimeter blo
ks. The number of
ter a
ount for the striking partial wave dominan
e
blo
ks hit by a parti
ular parti
le is given by the tra
k
andassumeforsimpli
itythatallotherpartialwavesgive
re
onstru
tion. The total energy deposited by this parti-
negligible
ontributions.Inboth
asesanex
itationofthe
∆
le in the
alorimeter is then just the (
alibrated) sum of
resonan
e is assumed.
energiesdepositedinallblo
ksbelongingtotheparti
ular
tra
k.
In order to have maximum angular
overage by the
2 Experiment dete
torelements andtominimizethefra
tionof
harged
pions de
aying in (cid:29)ight before rea
hing the stop dete
-
2.1 Dete
tor setup tors,theshortversionoftheTOFspe
tromete◦r≤waΘsluasbed≤.
In◦this way a total polar angle
overage of 3
Sin
e the experimental setup has been dis
ussed in detail 49 was◦a
≤hieΘvleadb w≤ith◦the
entral
alorimeter
overingthe
alreadyin(I),wegivehereonlyashorta
ount.Themea- region 3 28 . For fast parti
les the energy res-
surementshavebeen
arriedoutattheJüli
hCoolerSyn- olution of the
alorimeter amounting to 4% is superior to
hrotronCOSYusingthetime-of-(cid:29)ightspe
trometerTOF that from time-of-(cid:29)ight measurements due to the short
atoneofitsexternalbeamlines.Attheentran
eofthede- path length. However, the time-of-(cid:29)ight resolution is still
∆E
te
torsystemthebeam-
ollimatedtoadiametersmaller mu
hbetterthanthe resolutionoftheQuirlelements.
2 ∆E
than 2 mm - hits the LH target, whi
h has a length of Hen
e, for parti
le identi(cid:28)
ation, instead of plotting
µm E
cal
4 mm, a diameter of 6 mm and 0.9 thi
k hostaphan versus , the un
orre
ted parti
le en∆eErgy∼d(ezp/oβs)i2ted in
foils as entran
e and exit windows. At a distan
e of 22 the
alorimeter,wezu=tili1ze the rela1t/ioβn2 E with
cal
mm downstream of the target the two layers of the start theparti
le
harge andplot versus ,where
β = v/c
dete
tor (ea
h
onsisting of 1 mm thi
k s
intillators
ut the parti
le velo
ity is derived from the time-of-
into 12 wedge-shaped se
tors) were pla
ed followed by a (cid:29)ight measurement.
two-plane (cid:28)ber hodos
ope (96 x 96 (cid:28)bers, 2 mm thi
k Byidentifyingandre
onstrduπ
+tinngptπh+etwo
phpaπrg0edtra
ks
ea
h ) at a distan
e of 165 mm from target. Whereas the of an event the exit
hannels , and
an be
startdete
tormainlysuppliesthestarttimesignalsforthe separated. Kinemati
ally th≈e9m◦aximum possible la≈bo3r2a◦-
time-of-(cid:29)ight (TOF) measurements, the (cid:28)ber hodos
ope tory (lab) polar angles are for deuterons and
primarily provides a good angular resolution for the de- forprotons(andneutrons).Hen
e86%oftheangular
ov-
te
ted parti
le tra
ks. In its
entral part the TOF-stop erage for protons and neutrons from single pion produ
-
pp
S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II) 3
tion arewithin the angulara
eptan
eofthe
alorimeter.
For
harged pions the angular
overage has been mu
h ]
b
lower withΘthlaibs s=etup,◦sin
e kinemati
ally they
an ex- µ
tend up to 180 . Hen
e within the angularπ
+over- [π 20
age of≈Qui%rl and Ring the angular a
eptan
e for has φp
been 40 only. Nevertheless most of the phase spa
e ∆
d
part ne
essary for a full
overage of the physi
s in sin-
/ 15
glepionprodu
tionhasbeen
overed(seebelow)bythese σ
d
measurements due to the
ir
umstan
e that the
enter-
of-mass (
◦m) angular distributions have to be symmetri
10
about 90 be
ause of identi
al
ollision partners in the
in
ident
hannel.
5
npπ+
2.3 Sele
tion of the
hannel
0
0 50 100 150
npπ+ ∆φ
The
hannel is sele
ted by identifying proton and
pπ
pioninthe
alorimeteroronlytheprotoninthe
alorime-
ter, when the se
ond
harged tra
k is in the Ring. In ad-
pπ MM
pπ
dition, the missi/ncg2 ≤ mMaMss ≤ has to m/ce2et the
on-
pπ
dition 900 MeV dπ+980 MeV . Also to ∆φ
suppress ba
kground from the
hannel - in parti
u- Fig. 2. Distribution of the pplapn→aritpynπa+ngle de(cid:28)ned in the
enter-of-masssystemforthe rea
tion.Dataofthis
lar when the deuteron brpeπa+ksup and appearsasa proton
work are shown by full
ir
les and phase spa
e by the shaded
in the
alorimeter - the tra
k is required to be non-
∆Φ area. Solid and dashed lines denote s-
hannel and t-
hannel
oplanar.Tothisendwedeterminethevariable ,whi
h
al
ulations, respe
tively, as dis
ussed in the text. For ease
is de(cid:28)ned as the proje
tion of the opening angle between
twotra
ksontothep∆laΦne≤no1r8m0◦altothebeamve
tor.That oexfp
eormimpeanritsaolntotthael
arol
suslastei
otniosnh.aTvheeb
eoennstnroarinmtal∆izΦed<to16th0◦e
waywehavealways . Thpeπa+
ordinghistogram fortheeliminationofeventsstemmingfromdeuteronbreakup
is displayed in Fig.2. We see that events stemmin◦g
180 is indi
atedbytheverti
al dash-dottedline.
fromdeuteronbreakupgiverisetoalargepeaknear .
In order to get rid◦ of these events we introdu
e the
on-
∆Φ < 160
straint∆Φ<170◦ . From Fig. 2 we see that in prini
ple over
onstraintsforthis
hannel.Correspondingkinemati
a
ut would already be su(cid:30)
ient to eliminate
(cid:28)ts were applied.
this ba
kground.However, in order to bepopn→thedπsa+fe side Theluminosityoftheexperimentwasdeterminedfrom
pp
and to have no per
eptible tails from the rea
-
the analysisof elasti
s
attering, see (I). All data have
tion in the (cid:28)nal data sample, we used the more rigorous
been e(cid:30)
ien
y
orre
ted by MC simulations of the de-
onstraint. From Fig. 2 we see that this
onstraint does
te
tor setup by using the CERN GEANT3 [12℄ dete
tor
1
not
ut away signi(cid:28)
ant pie
es of physi
s information .
simulation pa
kage, whi
h a
ounts both for ele
tromag-
Any extrapolation into the
ut region, be it by model or
neti
and hadroni
intera
tions of the eje
tiles with the
by phase spa
e, will introdu
e un
ertainties on the level
dete
tor materials.
of less than two per
ent.
Aside from this physi
s ba
kground due to deuteron
breakup we do not (cid:28)nd any sizable ba
kground in the
2.4 Un
ertainties
(cid:28)nal data sample, as has been
he
ked by
ontrol mea-
surements, where the target
ell was empty.
Furtheron,theneutron4-momentumisre
onstru
ted The (cid:28)nal data sample
ontains about 80000 good events,
fromthe 4-momentaofprotonandpionandit is
he
ked, i.e.thestatisti
alerrorsareontheper
entlevelandhen
e
Θ Φ
whether a
alorimeter blo
k in the
orresponding ( , ) of minor importan
e in
omparisonwith systemati
alun-
regionre
ordedahitwithoutanyadditionalentriesre
orded
ertainties.Onesour
eofsystemati
errorsarebeamalign-
in the pre
eding dete
tor elements of the Quirl. If these ment and quality. The requirement that the beam has to
onditionsaremet,aneutrontra
kisassumed. Thatway pass a 2 mm
ollimator without signi(cid:28)
ant halo assures
Θ Φ
nand naredeterminedbythelo
ationofthis
alorime- good alignment and quality of the beam. The alignment
ter blo
k. By this method we obtain a neutron dete
tion is also veri(cid:28)ed by the fa
t that the angular distributions
%
e(cid:30)
ien
y of 36 . Thus having only the neutron energy intheover◦all
enter-of-masssystemhavetobesymmetri
undetermined experimentallyweend upwith3kinemati
about 90 , see next se
tion. In addition polarized beam
measurementswith the identi
al dete
torsetup usedhere
1 we note that the data sample with the
ut ∆Φ < 170◦ also give no hint for noti
eable misalignments [13℄.
leads to results, whi
h are pra
ti
ally indistinguishable from A mu
h more severe sour
e for systemati
un
ertain-
those shown here ties
on
erns the a
eptan
e and e(cid:30)
ien
y
orre
tions of
pp
4 S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II)
lptahlreetredaanmtgaoe.mAoefsnttdhuiesm
ruersaas
netgdioean,bohofovwienettvheerere,dstne.toeTt
htthoisrem
ooevmaenrpssl,etttheheaa
tnogtmhue-- 2)]MeV/c 30 µΩb/sr] [ 60 a2 = 0.96(2)
ua
n
mepeatasunr
eed
oarnrgeu
tlaiornrehgaisontso. rFerloymontheextDraapliotzlatpiloontss idnitso- µb/( [Mpn20 σ /dd 40 a’2 = 0.79(2)
d
played in Fig. 4 we see that (cid:21) a
ording to all we know σ / 10 20
d
fromthisrea
tion(cid:21)theseunmeasuredregionsaretheones
with the lowest
ross se
tion. Hen
e systemati
errors in- 0 1880 1900 1920 0-1 -0.5 0 0.5 1
trodu
edbytheseextrapolationsoughttobeofminorim- Mpn [MeV/c2] cosθCπM
portan
e.Toquantifythisstatementwe
omparethedata
resultingfrom
orre
tionswithMCsimulations,whi
hare
based either on pure phapspe→span
peπo+r alternatively on a Fig. 3. Di(cid:27)erMential
ross se
tions in dependen
e on thΘeCinM-
model des
ription of the rea
tion. A model, variant mass pn (left) and the pion s
atterpinpg→anpgnleπ+π
whi
h is trimmed to des
ribe all essential features of the (right) in the
enter-of-mass system for the re-
data,is the appropriatetoolfora reliable a
eptan
eand a
tion. The full
ir
les show our data properly
orre
ted by
e(cid:30)
ien
y
orre
tionbyaMCsimulation,whi
hpassesthe a self-
onsistent MC simulation, i.e. using a rea
tion model,
eje
tiles from the rea
tion of interest through the virtual whi
h is in agreement with the (cid:28)nal data. The open
ir
les
dete
tor. It has the potential of providing a self
onsistent derive from MC simulations using just pure phase spa
e. The
pro
edureforthese
orre
tions.Contraryto this the pure phasespa
edistributionsforthedi(cid:27)erentialspe
traareshown
phase spa
e des
ription of the rea
tion is (cid:21) as we easily by the shaded area. Solid and dashed lines in the right (cid:28)ag2ure
anseefromtheexperimentalresultsdisplayedinFigs.2- show Legendre (cid:28)ts to the (cid:28)lled and open
ir
les yielding =
6 (cid:21)inadequate though
onvenient.It may serve,however, 0.96(2) and =0.79(2), respe
tively.
as a very
onservative estimate of the systemati
un
er-
tainties due to the a
eptan
e and e(cid:30)
ien
y
orre
tions.
As epxnamplesMwepndisplay in Fig. 3 our data for the invari- in (Ip).pI→t isdrπo+ughly a fa
tor of two smaller than that for
ant mass and forthσe(ΘpiCoMna)ngular distribution in the pp → pp
πh0annel and (cid:28)ve times larger than that
π
the
enter-of-mass system evaluated (properly) for the
hannel, see Table 1 in (I). For the
by use of a model, whi
h (cid:28)ts the (cid:28)nal data (solid
ir
les),
omparison with data at neighbouring energies [14,3,5,8℄
andalternativelybyuseofpurephasespa
e(open
ir
les), see dis
ussion in the next se
tion.
respe
tively. The use of the latter for the extrapolation Di(cid:27)erentialdistributionsareshowninFigs.3-6.Sin
e
into unmeasuredregionsbringsthe data,of
ourse,some- a 3-body system in the (cid:28)nal state has (cid:28)ve independent
what
loser to the phase spa
e predi
tions. However, de- variables, we
hoose to present the three invariant mass
M M M
spite the fa
t that phase spa
e and model predi
tions are spe
tra pn, pπ+ and nπ+ as well as the proton and
vastly di(cid:27)erent, the e(cid:27)e
t of the inadequate phase spa
e pion angular distributions in the overall
enter-of-mass
orre
tion on the data is still very moderate. A realisti
system (
ms). Be
ause of th0e◦l<imiΘtecdma≤
e9p0t◦an
e for pi-
upperlimitforsystemati
un
ertaintiesduetoa
eptan
e ons only the angular range π is
overed◦.
and e(cid:30)
ien
y
orre
tion will be mu
h smaller than the However, as pointed out above, due to the required 90
di(cid:27)eren
es between open and solid
ir
les in Fig. 3. As a symmetry of the angular distributions the full informa-
realisti
estimate for this kind of systemati
un
ertainties tion is
ontained in the data.
we
on
lude that they are within the size of the symbols, ppπ0
whi
h are used in Figs. 2 - 6 for displaying our experi- Ipnnπ
o+ntrast to the
hannel the Dalitz plots for
the
hannelarefarfrom being (cid:29)at(cid:21)seeFig.4.This
mental results. We note that the use of either t-
hannel
is also borne out in the proje
tions, the invariant mass
or s-
hannel
al
ulations in the MC simulations does not Mpπ+ Mnπ+
spe
tra and (see Fig. 5, top), whi
h peak at
lead to any noti
eable di(cid:27)eren
es in the a
eptan
e and
the highest kinemati
ally available masses. In
ontrast to
e(cid:30)
ien
y
orre
ted data. Mpn
these the spe
trum (Fig. 5, bottom) peaks at the
lowest masses. Note that the high-mass enhan
ement is
M M
pπ+ nπ+
similarin both and spe
tra. Thisisin agree-
3 Results
ment with the trend observed in bubble
hamber data at
T
p
= 432 MeV [4℄.
Duetotheidentityofthe
ollisionpartnersintheentran
e
hannel the angular distributions in the over◦all
enter-of- Whereas the proton angular distribution is
lose to
masssystemhavetobesymmetri
about90 ,i.e.thefull (cid:29)at, the pion angular distribut(i3ocnosis2Θstcrmon+g1ly) anisotropi
.
information about t0h◦e≤reaΘ
ctmion≤
9h0a◦nnels is
ontained al- Itis(cid:28)ttedverywellbyapure π+ distribution
readyintheinterval .Deviationsfromthis (solid line in Fig.3, right).
symmetryinthedataindi
atesystemati
un
ertaintiesin Our results are in good agreement with the results
the measurements. Hen
e we plot - where appropriate - from PROMICE/WASA [6℄T, w≈hi
harethe only other un-
p
the full angular range, in order to show the absen
e of polarizeddataavailableat 400MeV.Note,however,
major systemati
errors in our measurement. pp → thatthosemeasurementswere
arriedoutinaverylimited
pnπT+he total
rossTse=
ti4o0n0Mofe0V.47(2) mb for the phase spa
e region only. E.gc.o,s(tΘhecmp)io≥n angular distribu-
rea
tion at p has already been given tion was only measured for π+ 0.79.
pp
S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II) 5
M2pπ vs M2pn M2pπ vs M2nπ
18000 sr] sr]
16000 10000 b/ b/
42]/cGeV1.25 111024000000000 42]/cGeV1.25 68000000 µΩσ [ /dd 4600 a2 = 0.20(2) µΩσ [ /dd 4600 a2 = 0.96(2)
2 [Mπ+p1.2 68000000 2 [Mπ+p1.2 4000 20 20
4000
2000
2000
1.15 1.15
3.5 3.55 3.6 3.65 3.7 0 1.15 1.2 1.25 0 0-1 -0.5 0 0.5 1 0-1 -0.5 0 0.5 1
Mp2n [GeV2/c4] Mn2π+ [GeV2/c4] cosθCpM cosθCπM
M2pπ vs M2pn M2pπ vs M2nπ
4500
2500
4000 Fig.6.Angulardistributionsofprotpopns→(lepfnt)πa+ndpions(right)
422]/c [GeVMπ+p1.12.52 12233505050000000000 422]/c [GeVMπ+p1.12.52 112050000000 siopnufhltatthhsseei[s6s
℄pewbnaoyt
reekorb-paoyerfn-etmh
seaihrso
sshlwesasnyds(ebtrdeeymnaforufreolmalr.a
tSilhrioz
eleliedds,taonWdσAtdoStaAsoh/fePtrdheRailsO
intwMieoosInrCdk.e)EDnaaornttedae-
1000 500 s-
hannelandt-
hannel
al
ulations,respe
tively,asdis
ussed
500
1.15 1.15 in thetext.For ease of
omparison the
al
ulations have been
3.5 3.55 3.6 3.65 3.7 0 1.15 1.2 1.25 0 normalized to the experimental total
ross se
tion. Given are
Mp2n [GeV2/c4] Mn2π+ [GeV2/c4] alsotheLegendre
oe(cid:30)
ientsa2 fromaLegendre(cid:28)ta
ording
to eq. 2 in (I) tgether with statisti
al errors.
M2
Fig.4. Dalitzplotsfortheinvariantmass
ombinations pπ+
versus Mp2n (left) and Mp2π+ versus Mn2π+ (right) as obtained 2)]c 4 2)]c 4
pp→pnπ+ V/ V/
forthe rea
tion:dataareshownontopandtheMC Me 3 Me 3
s-
hannel
al
ulation (see text) at the bottom. Note that the b/( b/(
µ µ
plots for the data are e(cid:30)
ien
y but not a
eptan
e
orre
ted. [Mpp 2 M [π0p 2
Tohrenetrinsyadreevdiuateiotnostfhreomext
hluedeelldipbtie
a
mir-
huomleferreegnio
ne.attheupper σ /dd 1 σ /dd 1
0 1880 1900 1920 0 1080 1100 1120
2)]c 2)]c Mpp [MeV/c2] Mpπ0 [MeV/c2]
V/ V/
Me 20 Me 20
b/( b/(
µ µ
[dMπ+p10 dM [π+n10 mFiags.se7s.MDpip(cid:27)e(rleefntt)iaalnd
rMosspπs0e
(triiognhst)infordetpheenpdpe→n
eppoπn0inrevaa
rtiaionnt
σ /d σ /d (from (I)). Phase spa
e is shown by the shaded area. For the
explanationof the
urves see (I).
0 1080 1100 1120 0 1080 1100 1120
Mpπ+ [MeV/c2] Mnπ+ [MeV/c2]
4 Dis
ussion of Results
2)]c 30 ppπ0
eV/ 4.1 Comparison with the
hannel
M
µb/( 20 pnπ+ ppπ0
[Mpn For the
omparison of and
hannels we show
σ /d 10 on
e more resultspipnπ0Figs. 7 and 8, whi
h we obtained
d previously for the
hannel, see (I). pnπ+
0 1880 1900 1920 ppπT0he proton angular distributions both in and
M [MeV/c2]
hannelsare
losetoisotropi
(seeFigs.6and8,left).
pn
Theyneverthelessshowatenden
y ofopposite
urvature,
whi
h just may be some re(cid:29)e
tion of the very di(cid:27)erent
pion angular distributions in both
hannels. At these low
mFiags.se5s.MDpi(cid:27)ne,rMenptπia+l
arnodssMsen
πt+ionfsorinthdeeppepnd→enp
enπo+n irnevaa
rtiiaonnt. energies the pion angular distributions aredes
ribed
on-
Dataofthisworkareshownbyfull
ir
les andphasespa
e by venσie(nΘtlπcym0b)y∼th1e+Lae2ge∗n(d3rceosa2nθsπcam0tz−1)/2,
the shaded area. Solid and dashed lines denote s-
hannel and a2
where the parameter is (cid:28)tted to the data. This
t-
hannel
al
ulations, respe
tively, as dis
ussed in the text.
For ease of
omparison the
al
ulations have been normalized papnπsa0tz has also been used in (I) for the analysis of the
to theexperimental total
ross se
tion. a
2hannel(cid:21)seeeq. 2in (I). Other notationsrelatedto
our parameter are as follows: in the notation of Ref.
a2 =A2/A0
[5℄, Table III wehave , in the notationof Ref.
pp
6 S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II)
cosθ cosθ
sr] sr]
hannel,wedonot(cid:28)ndsu
habehaviorhere.Thepionan-
b/ a2 = -0.14(2) b/ a2 = -0.12(1) gular distributions stay essentially the same for di(cid:27)erent
µΩ [ 10 µΩ [ 10 q-regions. This again is in support of a single dominant
d d
σ / σ / me
hanism pro
eeding via a single partial wave.
d d
5 5 Whereas we (cid:28)nd good agreement in the anisotropy of
the pion angular distribution with the ones measured at
T
p
TRIUMF at = 420 and 500 MeV [5℄, we fa
e a pro-
0-1 -0.5 0 0.5 1 0-1 -0.5 0 0.5 1 founddis
repan
ywithIUCFresults[10℄.Therekinemat-
cosθCpM cosθCπM i
ally
omplete measurements with both polarized beam
T
p
and target are presented for = 325, 350, 375 and 400
MeVtogetherwithLegendrepolynomial(cid:28)ts,whi
hrepro-
Fig.8.Angulardistributionsofprotopnps→(lepftp)πa0ndpions(right) du
e the measured angular distributions of the polariza-
inthe
enter-of-masssystemforthe rea
tion (from tion observables. In Table II of Ref. [10℄ the
oe(cid:30)
ients
(I)). The solid
urves representLegendre (cid:28)ts, see (I). resulting from these (cid:28)ts are listed. This list also
ontains
b00 = a2/2
the anisotropy parameterσ(ΘCM) for the unpolarized
π
a2 =B/A di(cid:27)erential
ross se
tion . Sin
e that paper
on-
[8℄,TableVwehave a2 =2∗ba0n0dinthean0o0t=ati1onofRef.
entrates on the polaσr(izΘaCtiMon)observables, it does not di-
[10℄, Table II we have (sin
e pthpπer0e).
usstheunpolarized π datain anydepta+il.nItisjust
For the pion angular distribution in
aseao2f we noted that these have been dedu
ed from
oin
i-
(cid:28)nd a slightly
on
ave shape (Fig. 8, right; = -0.12), den
es. As a result of their Legendreanalysisthey obtain
pwnhπe+reas we get a strongly
ao2nvex shape in
ase of the a2=0.39(9)forTp=400MeV,avalue,whi
hislessthan
hannel (Fig. 6, right; p=pπ+00.96(2)). half of our value. The di(cid:27)eren
e amounts to six standard
A striking ∆di(cid:27)eren
e to the pn
πh+annel is the dom- deviations.Wefa
ehereperhapsasimilarproblemasdis-
ipnpaπn0
e of the∆ ex
itation in the
hannel. In the
ussed in (I) for thppe s→itupaptπio0n of the experimental data
hannel produ
tionin a s-waverelativeto the a
- with the rea
tion at the same beam energy
T
p
ompanying nu
leon is prohibited by quantum numbers. of = 400 MeV. There also a large dis
repan
y exists
∆ a2
However,asdemonstratedin(I),the produ
tioninrela- between the asymmetry parameter found in the IUCF
tivep-waveisallowedandindeed
ontributessigni(cid:28)
antly analysisand the one we found at COSY-TOF. Our result
to this
hannel alread∆y
lose to threshold. pnπ+ has meanwhile been
on(cid:28)rmed by CELSIUS/WASA data
The signature of produ
tion in the
hannel [15℄. In both these worksit has been shownthat previous
is seen in all di(cid:27)erential observables shown in Figs. 3 - 6. results (cid:21) like the one obtained at PROMICE/WASA [16℄
M
pn
The Mspe
trum (Fig. 5, botptpoπm0) is markedlydi(cid:27)erent (cid:21)su(cid:27)eredfrominsu(cid:30)
ientphasespa
e
overage
ombined
pp
from the spe
trum in the
hannel (Fig. 7, left). withinappropriateextrapolationsintotheunmeasuredre-
pn
Though the (cid:28)nal state intera
tion (FSI) is somewhat gions.
pp
larger than the FSI, it
annot a
ount for the huge
Wenotethefollowingsurprisingtrendintheresultsof
di(cid:27)eren
e between both spe
tra at low masses. It rather a2
M theIUCFanalyses
on
erningthe parameter.Inagree-
pπ+
is a re(cid:29)e
tion from the
omplementaryspe
tra and
M mentwithpreviousIUCFworkvery
losetothreshold[8℄,
nπ+, whi
h peak just at the highest available masses a2
M where a strong in
rease in the value with energy is ob-
(sFpeig
.tr5u,mtopob)sienr
voendtirnastthetoptphπe0m
hoarnenpehla(sFei-gs.p7a,
erilgihket).Tphπe0 sMerevVe,dre(asp2e=
ti0v,el0y.)1,2aavnadlu0e.3o1f aat2T=p 0=.3249(74), 2a9t9Tpan=d 332159
high-m∆ass enhan
ement in turn is most likely asso
iated MeV is reported in Ref. [10℄, Table II. Th∆is in
rease just
with ex
itation. re(cid:29)ep
pts→thenpinπ
+reasing importan
e of the T ex
itation in
p
the rea
tion. However, above = 325 MeV
a2
Ref. [10℄(see again Table II) (cid:28)nds that the parameter
4.2 Pion angular distribution nolongerin
reases,butrathersaturatesatavalueof0.39.
∆
This implies that the
ontribution also suddenly satu-
pnπ+ T ∆
The most s(t3rickoins2gΘfecmat+ur1e)in our data at p = 400 rates despite the fa
t the pole is still far from being
MeVisthe π+ dependen
eofthepionangular rea
hed at these energies. Also the Jüli
h model
al
ula-
distribution. It is exa
tly this dependen
e, whi
h is seen tions[17℄, whi
hareusedin Ref.[10℄ for
omparisonwith
πN ∆
in s
attering in pthpe→drπe+sonan
e region and whi
h is thepolarizat∆iondatapredi
t astronglyin
reasingimpor-
alsoobservedinthe rea
tionoveralargerange tan
e ofthe ex
itation at these beam energies(cid:21)asalso
of in
ident energies. We note that also the pion angular expe
ted intuitively.
T
p
distributions at = 420 anpdp5→00pMnπe+V, dedu
ed from InRef.[10℄thedis
repan
yTbetweentheir400MeVre-
p
in
lusivemeasurementsofthe rea
tioninRef. sult and the TRIUMF data at = 420 MeV [5℄ was not
[5℄ are basi
ally in a
ord with this dependen
e. dis
ussed. The TRIUMF measurements were performed
We also noptepπi0n passing, that in
ontrast to the sit- asasingle-armexperimentwithamagneti
spe
trometer,
uation in the
hannel, where we observe a strong whi
h measures a 3-body rea
tion only in
lusively. Su
h
dependen
e of the pion angular distribution on the rel- measurements are known to be very reliable for the de-
ative momentum q between the two nu
leons in the exit termination of single-parti
le angular distributions, sin
e
pp
S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II) 7
ht2
exa
tlythesamedete
torisusedfortheparti
ledete
tion
at all angles minimizing thus the problem of a
eptan
e
]
and e(cid:30)
ien
y
orre
tions. b
a2 m
Tosummarizethedis
ussionabout wefa
easevere s+t
[
Tpdpips
→=repn4a0pn0π
+MybeVetwfoerenbotthheItUheCpFpa→ndpCpOπ0SYre-aT
OtiFonreasnudltsthaet σ tot 10 t pnπ+
rea
tion.However,thereisgoodagreementof
ourresultforthe(cid:28)rstrea
tionwiththe
orrespondingone s
from CELSIUS/WASA and for the se
ond rea
tion with
the one obtained at TRIUMF. We (cid:28)nally note that the 1
a2
un
ertainty of quoted in Fig.6 onlyin
ludes the statis-
ti
al un
ertainties of the data. If we in
lude an estimate
dπ+
onsystemati
un
ertainties(asdis
ussedaboveinthese
-
tio∆na22.4≈), we end up with an estimated total un
ertainty 10-1 s
of 0.08. dπ+
Tphneπ
+losesimilarityintheangulardistributionsof
and
hannels is in agreement with the predi
tions
of Fäldt and Wilkin [18℄, a
ording to whi
h the meson 10-20 0.2 0.4 0.6 0.8 1 1.2 1.4
angular distributions
oin
ide
losely in bound state and
T [GeV]
breakup(
3hcaonsn2eΘlscmne+ar1t)hreshold. pp→dπ+ p
The π+ 1D2dependen
e in the rpep-
a
tion is due to the partial wave in the in
ident
hannel
ombinedwiththe
onstraintofap-wavepionrel-
ative to the deuteron in the exit
hannel. As kn1oDw2nPfrom Fig. 9p.pE→nedrgπy+dependen
eoftpopta→l
pronsπs+se
tionsfortherea
-
phaseshiftanalysesofthpispr→ea
dtπio+n[11,19℄this par- tions (squares) and (
ir
les). The (cid:28)lled
tialwavedominaTtes≈the rea
tionbasi
allyfrom symbolsdenoteresultsofthiswork,opensymbolsarefrom[14,
p
threshold up to 900 MeV. It is responsible for the 3,8℄. Dash-ddπo+tted anpdnπd+ashed lines represent s-
hannel
al
u-
resonan
e-like energy dependen
e of the total
ross se
- lationsfor and
hannels,respe
tively,normalizedto
T
tion and performs a perfe
t looping in the Argand dia- pthneπ+data at p = 400 MeV. The t-
hannel
al
ulation for the
gram[11℄. Thus this partialwavepossesIs(eJsPa)ll=fea1t(u2r+e)sto
hTann≥elisgivenbythedottedlineandnormalizedtothe
p
qualify for apsp-
hannel resonan
edwπi+th in dataat 1GeV,whereitisknowntoprovideareasonable
thein
identN∆
hannel,the (cid:28)nal
hannel and thein- des
ription.Thesolid
urvedepnpot→edpbnyπs++tisthein
oherent
termediate
hannel (cid:21) see also d1iDs
2uPssion in Ref. [27℄. sumof both pro
esses for the
hannel.
Fromppt→hedtoπt+al
ross se
tion of the partial wave in
the rea
tion [11℄ we see that the resonan
e en-
N∆
ergy is some 60 MeV below the≈nominal threshold, 4.4 Comparison to t- and s-
hannel
al
ulations
whereas the resonan
e width of 110 MeV
orresponds
∆
Finallywe
onfrontthedatawithsimpletheoreti
al
al
u-
to that of the resonan
e.
T
p lations a
ording to the graphsdepi
ted in Fig. 1. In this
Theexper(i3mceonst2aΘlocmbs+erv1a)tionthatupto =500MeV
essentiaplply→a pnπ+ π+ dependen
e is observed also wexipther
imomenptleaxlp
aapl
eurlaittiiosnnso,twohui
rhaaimretboe
yoomndpatrheeosu
orpdeatoaf
in the 1D2P rea
tion points to the predominan
e this work.We rather wantto use these
al
ulations in or-
of the partial wave in this rea
tion, too, as was
derextra
tthemainphysi
smessageresidinginthedata.
already noted in Ref. [5℄. From this also follows that the ∆
pn Sin
ewehaveseeninthedis
ussionabovethat ex
i-
likesyqsutaenmtuamt tshtaestee eIn(JerPg)ie=s i0s(p1r+e)f.erably in the deuteron- t1aDt2ionandde
ayisthedominantrea
tionme
hanismand
is by far the dominant partial wave at least in the
T
p
energy region = 400 - 500 MeV, we expli
itly negle
t
any non-resonant terms in the rea
tion pro
ess.
4.3 Total
ross se
tion We start with a (properly antisymmetrized) t-
hannel
approa
h in (cid:28)rst-order impulse approximation, whi
h is
pTphe→endeπr+gy deppepnd→enn
peπo+f the total
ross se
tions for the known to provide reasTona≥ble results for the angular dis-
p
ppa→ndpnπ+
hanTnelsisdisplayedin Fig.9. tributions at energies 1 GeV [20,21,22,23,24℄. For
p
Forthe
hannelat =400MeVthereareno our energy we show su
h a t-
hannel
al
ulation by the
experimental data to
ompare with. However, our result dashed lines in Figs. 2, 3, 5 and 6. We see that the pion
(cid:28)ts well to the trend given by the experimental results angular distribution is not reprodu
ed
orre
tly. The rea-
∆
[14,3,5,8℄ at neighbouring energies.In orderto dis
uss in sonforthisfailureissimple.Sin
einthisapproa
hthe is
the next se
tion the energy dependen
e in som1De2broader ex
itedbypionex
hangebetweenthetwo
ollidingnu
l∆e-
ontext with regard to the dominan
e of the partial ons,thereferen
eaxisforthepionde
ayoftheex
ited
wave,weplotinFig.9theenergyrangefromthresholdup resonan
e is the momentum transfer q and not the beam
T ∆
p
to = 1.5 GeV, i.e. overthe full region of ex
itation. axis. Note that the latter, however, is the referen
e axis
pp
8 S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II)
ht2
gooda
ount of the di(cid:27)erential distributions both for the
] invariant masses and for the parti
le emission anIg(leJsP. )=
b
m 1(2+M)ass(2.07GeV) andwidth(160MeV) ofthe
resonan
einthiss-
hannelansatzhavebeen
hosen
σ [tot 10 pnπ1D+2 SP40 dttoioomrneiponrfaontdh
uee
,pei.peth.→uepedntπoe+rTgprye≈da
e7tpi0eo0nndMienenV
teh.eTofhretahgteiwotnaoytoafwlte
hrseoims1sDusl2teaP
--
1D SP07
2 neouslyget a good des
ription fpopr→thepennπe+rgy dependen
e
s Tofpt≈hetotal
rossse
tionforthe rea
tionupto
1 600 MeV. If
ombined with the amplitude of the t-
hannelapproa
hweevenobtainareasonabledes
ription
of the total
ross se
tions up to the GeV region (Fig. 9).
dπ+
10-1 1D SP93
al
Fuilnaatilolynswfoer
tohmep1aDr2epinartFiaigl.w1a0veoiunrtshiemnppleπ+s-
hhaanNnnnNeell
2 s to the results opfpS→AIdDπ+[11℄ partial wave analyses of
s
at1teDri2ngand rea
tion. The imaginary part of
the partialwave,whi
h is obtained from the analysis
NN
10-20 0.2 0.4 0.6 0.8 1 1.2 1.4 of elasti
σisn
ealt(t1eDri2n)g, gives r1isDe2to the total inelasti
ross se
tion for the partial wave, whi
h
T [GeV]
p in turn is given by the sum of the pion-pprpod→u
ptpioπn0
ross
se
tionsi1nDt2his partialwave.Sin
e in the rea
-
tion the partial wave is highly suppressed due to the
∆
suppression of the ex
itation, we have in good approx-
Fig. 10. Energy dependen
e of total
rosspspe
→tiondsπa+s
al
u- imaσtipopn→npπ+(1D2)≈σinel(1D2)−σpp→dπ+(1D2)
lated with opupr→s-
phnanπn+el approa
h for the (dash- The thus derived results are shown in Fig. 10 for the
dotted)and (dashed
ureve)rea
tions,normalized NN
T
tothedatapointsfromthisexperimentat p=400MeV((cid:28)lled SAIDsolutionsSP07andSP40from s
atteringa1nDal2-
squareand
ir
le,respe
tively;seealsoFig.9).For
omparison yses together withdtπh+e SAID solution SP93 for the
tluhteiosnhsonrSptPπd0+a7sha-nddotStPed40a,nrdesdpoet
tteivdelliyn,efsorgitvheet1hDe2SApaIrDtia[1l1w℄asvoe- apnasratitazlwovaevrepirnedtih
ets the
1hDan2npela.rWt oefsetehethpapto→urdsπ-
+ha
nronsesl
inthe
hannel(seetext),w1hDe2reas thesolid
urveshdoπw+s se
tion at higher energies as expe
ted, sin
e we have as-
the SAID solution SP93 for the partial wave in the sumedfornspiπm+pli
itythatonlythispartialwave
ontributes.
hannel. For the
hannel the SP07 solution underpredi
ts
the
ross se
tion in the near-threshold region strongly,
Twhe≤reas the SP40 solution, whi
h is made for the region
p
400MeV,providesaproperenergydependen
e,how-
for angles in the
enter-of-mass frame. Sin
e the momen-
ever, is in the absolute s
ale substantially above the data
tum transfer varies in dependen
e of the nu
leon s
atter-
and the s-
hannel
al
ulation in this energy region. At
ing angles, whi
h are integrated over(i3nctohse2Θpiqon+an1g)ular
distribution, the
al
ulated intrinsi
π+ de- higher energies up to 800 MeV our
al
ulation is essen-
penden
einthet-
hannelapproa
happearstobesmeared tially between both solu1tDio2ns. This
omparison with the
SAID solutions for the partial wave shows that our
out in the
ms pion angular distribution.
simple model des
ription is not in severe
ontradi
tion to
In order to establish the beam dire
tion as the appro- the SAID results, where the large spread between both
NN
priate referen
e axis for the pion angular distribution in solutionspointstostillsubstantialambiguitiesinthe
the
al
ulation one either has to reiterate the pion ex-
partial wave analyses
on
erning the imaginary parts of
hanges and sum them up to in(cid:28)nity or simply make a partial waves.
s-
hannel ansatz. The l1aDtt2er is easily made by a Breit-
Wigner ansatz for the resonan
e (Fig. 1, bottom),
N∆
whi
hdisso
iatesintoa systemin relatives-wavefol-
∆
lowed by(t3hceods2eΘ
acymo+f1t)he resonan
e. This grants the 5 Summary
observed π+ dependen
eforthepionsaswell pp → pnπ+
asthedespirped→shdaπp+eoftheinvariantmassspe
tra.Tosim- We have pTres≈ented measurements of the re-
p
ulatethe rea
tionwithinthisansatzweimpose a
tion at 400 MeV. In this energy region they are
theHulthen wavefun
tion as
onditionforthepFpe→rmpinmπo+- the (cid:28)rst ex
lusive ones of solid statisti
s to
over most
mentumbetweenprotonandneutron.Forthe of the rea
tion phase spa
e. The di(cid:27)erential distributions
rea
tion we impose a FSI intera
tion of Migdal-Watson are
hara
terized by the overwhelming dominan
e of the
pn ∆
type [25,26℄ on the system. These
al
ulations (Tnor- ex
itation.Thepionppan→gudlaπr+distribution
oin
ideswith
p
malized to our results for the total
ross se
tions at = that observed in the 1D
h2aPnnel, whi
h in turn is
400MeV) areshownby the Dalitzplotsin Fig.4,bottom dominated by the resonating partiaplnwπa+ve. From
and by the solid lines in Figs. 2,3, 5 and 6. They give a this
oin
iden
e we
on
lude that also the
hannel
pp
S. AbdEl-Samadet al.: Single-Pion Produ
tion in Collisions at 0.95 GeV/
(II) 9
isdominatedbythesames-
hannelresonan
einthenear-
thresholdregion.The
orrelationbetweenboundstateand
breakup
hannelsisina
ordan
ewiththe predi
tionsby
Fäldt and Wilkin [18℄.
This work has been supported by BMBF, DFG (Europ. Gra-
duiertenkolleg683)andCOSY-FFE.Wea
knowledgevaluable
dis
ussions with R. A. Arndt, L. Alvarez-Ruso, D. Bugg, C.
Hanhart,M.Kaskulov,V.Kukulin,E.Oset,I.Strakovsky,W.
Weise and C. Wilkin.
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