unbinnedttingmethodhasbeenusedinordertoeliminateanyinueneofbinningeets,
whih an be large inthe ase of statistially small samples. The t urve in the left plot
inFig. 4.6isomposedfromathirdorder polynomialand aGaussian. The position ofthe
Gausspeakis 1528MeV with awidth of8MeV.
M( π + π - p) [ GeV ]
M=1527 ± 2.3(stat) MeV
whih an deayinto pK
S
and whih arenotinluded inthePythia6 event generator. In
order to onrm this possible explanation, thefollowing t proedure hasbeenused. The
t funtion for the measured invariant mass of the pK
S
system has been onstruted as
a sumof polynomial funtion, six onvoluted funtions of the Breit-Wigner funtion with
Gaussian andoneGaussian funtion. Thepolynomialparametershave beenobtainedfrom
a t of the simulated bakground and have been xed. The widths and positions of six
Breit-Wigner funtionshavebeenxedto thePDG [79 ℄values ofthe
. Thefollowingsix
+
were inluded: M =1480MeV with = 55MeV, M =1560MeV with =47MeV,
M =1580MeV with =13MeV,M =1620MeV with =100MeV M =1660MeV with
= 100MeV and M = 1670MeV with = 60MeV. The amplitudes of these have been
usedasfreeparametersofthet. However, anextra,unknownresonanemustbe inluded
inaddition to thesix
, inorder to desribe shape ofthe spetrum. The Gaussfuntion
ts the nominal role of a hitherto unknown resonane. As an be seen from the left box
of Fig. 4.6, suha onstruted funtion an very well desribe theshape of thespetrum.
The resonane represented by the Gaussian ould be an indiation of a new narrow state
deaying into pK
S
. Thet resultstoa massof1527MeVwiththeFWHM22MeV forthis
new state.
The amount of statistis ofobserved events with a pK
S
systemin the nal state
is rather poor, although the data over three years has been used for analysis. Due to
low statistis, the signiane of the observed peak ould a besubjet of disussion. Two
approahes have beenused inorder to estimatethesigniane. Therstexpression isthe
nave estimator N 2
s
= p
N 2
s
. The orresponding result is listed in Table 4.1. The seond,
more preise approah is using the ratio N
s
=ÆN
S
, where all orrelated unertainties from
thet areaountedforin ÆN
s .
4.2 The
State
Thestandardmodelshows that every partile hasan antipartile,for whih eah
additive quantum number has the negative of the value it has for the \normal" matter
partile. Ifweassumetheonditionthatourmeasuredpeakisrealandthat +
pentaquark
exists, then the harge onjugate anti-partile
has to exist as well. An analysis was
performedwiththegoalofndingsuhanantipartile. Thesamedatasamplewasanalyzed
+
+
mass FWHM N
2
s
N 2
b
nave Total sgnif.
[MeV℄ [MeV℄ in2 in 2 signif. N
s ÆN
s
Ia)
1527:02:32:1 2252 74 145 6.1 7818 4.3IIa)
1527:02:52:1 2452 79 158 6.3 8320 4.2Ib)
1528:02:62:1 1952 56 144 4.7 5916 3.7IIb)
1527:83:02:1 2052 52 155 4.2 5416 3.4Table 4.1: Mass and width values obtained by dierent t proedures of the pK
s
system
and theirsystemati and statistial errors. RowIa) isbased onthe t using thesimulated
bakgroundmodeland
s. IntheaseofrowIb),bakgroundisttedsimplybya
polyno-mial. RowsIIa)andIIb)areusingsamebakgroundmodelsasIa)andIb)respetively,but
dierent mass reonstrution expressions that are expeted to result in better resolution.
Numberofsignalandbakgroundeventsin2 areaareinolumnmarked asN 2
s
andN 2
b .
the hadron identied as a proton previously bymeans of the RICH, the harge had to be
negative. Sine the antiproton ould notome from a deay with but an originate
from thedeayof the
to p +
,the utinequation (4.12) was hanged to
jM
p
+ 1116jMeV<6MeV (4.16)
The resultant spetrum is shown in Fig. 4.7. The statistis obtained were abouta fator
ofve smallerthanintheaseofthe +
spetrumandthereforeitisnotpossibleto judge
theexistene ornon existene of state.
Non-observation of thepeakinpK
S
ouldbeonsistent with existeneof +
. As
willbeshownlaterintheanalysisof(1520)insetion4.6,theprodutionofantibaryonsis
suppressed. Thesuppression isdueto limitedreationphasespae forantipartile
produ-tion. Inorder to obeybaryon onservation law, anew baryon hasto beprodued together
with its antibaryon, while baryoni states an be produed from the nuleon target by
additional reation hannels. The suppression fator betweenbaryon and antibaryon with
similar masseslike +
is aboutfator 14,assumingthatthesuppression fatoris thesame
for (1520) and +
. Using the number of observed +
and this suppression fator, we
obtain thattheexpetednumberof is4or5,dependingon themethodusedforthet
of thepK
s
massspetrum.
)[GeV]
- p π π +
M(
1.45 1.5 1.55 1.6 1.65 1.7
(8 MeV) ⁄ Events
0 2 4 6 8 10 12 14 16 18
Figure4.7: TheinvariantmassdistributionofthepK
S
system. Thestatistis aretoosmall
foranystatement aboutexistene of state,.
4.3 Four Track Events Analysis
In the work [83 ℄, a possible prodution mehanism of the +
in the HERMES
experiment has been disussed. With a deuterium target, the most likely reations are
onsideredto be
p!
K 0
+
; (4.17)
or
n!K +
: (4.18)
Unfortunately,thereisnodiretaesstoonrmthesehypothesesbeauseoftheHERMES
aeptane. Dueto thesmallopeningangleoftheHERMESspetrometer,thedetetion of
all fourpartilesis unlikely. Intherst analysiswerequired three traks,whihhad to be
oppositely harged pions and a proton. The numberof statistis obtainedwas ratherlow.
Ifwe requiredan additional fourth trak, thestatistis would drop even more. A
partile-typeplotforthefourthtrakdetetedtogetherwithK
S
pevents, afterapplyingallanalysis
uts, is shown in Fig. 4.8. It is learly seen that we an notfully reonstrut all partiles
from the onsidered reation hannels due to the small number of K whih are deteted
as a fourth trak. On the other hand we an use the fourth trak to redue bakground.
Thereareother hannelswherefromK ouldoriginate. The mainontributiontotheK
Events
0 50 100 150 200 250 300
K - K +
π +
π
-Figure4.8: The distribution ofpartile type ofthe fourthtrak.
statistis ould be from
!K
L K
S
(4.19)
and
K
!
K
S
(4.20)
We ouldnotrejet eventsoriginating frombeauseitwouldbeneessaryto reonstrut
K
L
but ina priniple is possible redution of bakground from K
. The plot of invariant
massof thesystemof theK
S and
isshownin Fig. 4.9. The statistis arelow butthe
regionaround892MeV(whihismassoftheK
)isovered. Inthenextstep,thefollowing
utwas applied inorderto onstrut anew invariant massspetrumoftheK
S
p systemin
whih thefourthpartile hasto bedeteted,identiedas apionandinwhihtheinvariant
massof theK
S
systeman notbe interpretable as K
:
jM
K
S
0:892j>0:075GeV: (4.21)
Furthermore,thepionfromthefourthtrakouldbeadeayprodutofa. Therefore,the
invariant massofnegatively harged pionsand protonshasbeenalulated anduts(4.12)
appliedagain. TheresultingspetrumoftheK
S
psysteminvariantmassshowsalearpeak
at a mass of 1530MeV (see Fig. 4.10). The signal to bakground ratio is improved, but
total statistis aresigniantly lower. The estimate ofthe signiane of thepeak is3.5
)[GeV]
K S
π M(
0.6 0.7 0.8 0.9 1 1.1 1.2
(15 MeV) ⁄ Events
0 5 10 15 20 25
Figure 4.9: Invariant massspetrum of the system K
S
. The spetrum is generated from
events where three traks of standard +
uts are aompanied by fourth trak whih is
identied as pion.