First measurement of the pi+pi- atom lifetime

Physics Le e s B 619 (2005) 50–60
www.else ie .com/loca e/physle b
Fi s measu emen o he π+π−a om li e ime
B. Ade ap,L.A anasye l,1, M. Benayoune, A. Benelliq,Z.Be kab, V. B ekho skikho,
G. Ca agheo gheopolm, T. Cechakb, M. Chibak, S. Cons an inescum, C. De aza,
D. D eossig, D. D ija da, A. Duda e l,I.E angeloud, M. Fe o-Luzzia, M.V. Gallasp,a,
J. Ge nd b,R.Giacomichg, P. Giano i ,D.Goldinq,F.Gómezp,A.Go ino,
O. Go chako l,C.Gua aldo , M. Hans oula,R.Hosekb, M. Iliescu ,m, V. Ka pukhinl,
J. Klusonb, M. Kobayashih, P. Kokkasd, V. Koma o l,V.K uglo l, L. K uglo al,
A. Kuliko l, A. Kup so l, I. Ku ochkino, K.-I. Ku odal,A.Lambe og,A.Lana oa, ,
V. Lapshino,R.Lednickyc,P.Le us ee, P. Le i Sand i , A. Lopez Ague ap,
V. Luche ini ,T.Makij,N.Man hosd, I. Manuilo o, L. Mon ane a, J.-L. Na jouxe,
L. Nemeno a,l, M. Niki inl, T. Núñez Pa dop,K.Okadai, V. Olche skiil,A.Pazosp,
M. Pen iam,A.Penzog, J.-M. Pe eaua,C.Pe ascu ,m,M.Plóp, T. Pon am,D.Popm,
G.F. Rappazzog, A. Rod iguez Fe nandezp,A.Rome op, A. Ryazan se o,V.Rykalino,
C. San ama inap,q,a, J. Sabo idop, J. Schache , Ch.P. Schue zq,A.Sido o o,
J. Smolikc,F.Takeu chii, A. Ta aso l,L.Tausche q, M.J. Toba p,S.T uso n,
V. U kin l, O. Vázquez Docep, P. Vázquezp,S.Vlachosq,V.Yazko n, Y. Yoshimu ah,
M. Zhabi skyl,P.Z elo l
aCERN, Gene a, Swi ze land
bCzech Technical Uni e si y, P ague, Czech Republic
cIns i u e o Physics ACSR, P ague, Czech Republic
dIoannina Uni e si y, Ioannina, G eece
eLPNHE des Uni e si es Pa is VI/VII, IN2P3-CNRS, F ance
INFN, Labo a o i Nazionali di F asca i, F asca i, I aly
gINFN, T ies e and T ies e Uni e si y, T ies e, I aly
hKEK, Tsukuba, Japan
iKyo o Sangyo Uni e si y, Kyo o, Japan
jUOEH-Kyushu, Japan
kTokyo Me opoli an Uni e si y, Japan
lJINR, Dubna, Russia
mIFIN-HH, Na ional Ins i u e o Physics and Nuclea Enginee ing, Bucha es , Romania
nSkobel sin Ins i u e o Nuclea Physics o Moscow S a e Uni e si y, Moscow, Russia
oIHEP, P o ino, Russia
pSan iago de Compos ela Uni e si y, Spain
qBasel Uni e si y, Swi ze land
Be n Uni e si y, Swi ze land
0370-2693 2005 Else ie B.V.
doi:10.1016/j.physle b.2005.05.045
Open access unde CC BY license.
B. Ade a e al. / Physics Le e s B 619 (2005) 50–60 51
Recei ed 22 Ap il 2005; accep ed 18 May 2005
A ailable online 31 May 2005
Edi o : M. Dose
Abs ac
The goal o he DIRAC expe imen a CERN (PS212) is o measu e he π+π−a om li e ime wi h 10% p ecision. Such a
measu emen would yield a p ecision o 5% on he alue o he S-wa e ππ sca e ing leng hs combina ion |a0−a2|. Based on
pa o he collec ed da a we p esen a i s esul on he li e ime, τ=[2.91+0.49
−0.62]×10−15 s, and discuss he majo sys ema ic
e o s. This li e ime co esponds o |a0−a2|=0.264+0.033
−0.020m−1
π.
2005 Else ie B.V.
PACS: 36.10.-k; 32.70.Cs; 25.80.E; 25.80.Gn; 29.30.Aj
Keywo ds: DIRAC expe imen ; Elemen a y a om; Pionium a om; Pion sca e ing
1. In oduc ion
The aim o he DIRAC expe imen a CERN [1] is
o measu e he li e ime o pionium, an a om consis -
ing o a π+and a π−meson (A2π). The li e ime is
domina ed by he cha ge-exchange sca e ing p ocess
(π+π−→π0π0)2and is hus ela ed o he ele an
sca e ing leng hs [4]. The pa ial decay wid h o he
a omic g ound s a e (p incipal quan um numbe n=1,
o bi al quan um numbe l=0) is [2,5–9]
(1)Γ1S=1
τ1S
=2
9α3p|a0−a2|2(1+δ)
wi h τ1S he li e ime o he a omic g ound s a e, α
he ine-s uc u e cons an , p he π0momen um in
he a omic es ame, and a0and a2 he S-wa e ππ
sca e ing leng hs o isospin 0 and 2, espec i ely.
The e m δaccoun s o QED and QCD co ec ions
[6–9]. I is a known quan i y (δ=(5.8±1.2)×10−2)
ensu ing a 1% accu acy o Eq. (1) [8]. A measu e-
men o he li e ime he e o e allows o ob ain in a
model-independen way he alue o |a0−a2|.Theππ
sca e ing leng hs a0,a2ha e been calcula ed wi hin
he amewo k o s anda d chi al pe u ba ion heo y
[10] wi h a p ecision be e han 2.5% [11] (a0=
E-mail add esses: leonid.a anase[email p o ec ed],
a anase[email p o ec ed]. u (L. A anasye ).
1PH Di ision, CERN, CH 1211 Gene a 23, Swi ze land.
2Annihila ion in o wo pho ons amoun s o ≈0.3% [2,3] and is
neglec ed he e.
0.220 ±0.005, a2=−0.0444 ±0.0010, a0−a2=
0.265 ±0.004 in uni s o in e se pion mass) and lead
o he p edic ion τ1S=(2.9±0.1)×10−15 s. The
gene alized chi al pe u ba ion heo y hough allows
o la ge a- alues [12]. Model independen measu e-
men s o a0ha e been done using Ke4decays [13,14].
Opposi ely cha ged pions eme ging om a high
ene gy p o on–nucleus collision may be ei he p o-
duced di ec ly o s em om s ong decays (“sho -
li ed” sou ces) and elec omagne ic o weak decays
(“long-li ed” sou ces) o in e media e had ons. Pion
pai s om “sho -li ed” sou ces unde go Coulomb i-
nal s a e in e ac ion and may o m a oms. The egion
o p oduc ion being small as compa ed o he Boh
adius o he a om and neglec ing s ong inal s a e
in e ac ion, he c oss sec ion σn
A o p oduc ion o
a oms wi h p incipal quan um numbe nis ela ed o
he inclusi e p oduc ion c oss sec ion o pion pai s
om “sho li ed” sou ces wi hou Coulomb co ela-
ion (σ0
s)[15]
(2)
dσn
A
dpA=(2π)3EA
MA
ΨC
n ∗=0

2d2σ0
s
dp+dp−



p+=p−
wi h pA,EAand MA he momen um, ene gy and mass
o he a om in he lab ame, espec i ely, and p+,
p− he momen a o he cha ged pions. The squa e o
he Coulomb a omic wa e unc ion o ze o dis ance
 ∗be ween hem in he c.m. sys em is |ΨC
n(0)|2=
p3
B/πn3, whe e pB=mπα/2 is he Boh momen um
Open access unde CC BY license.
52 B. Ade a e al. / Physics Le e s B 619 (2005) 50–60
o he pions and mπ he pion mass. The p oduc ion o
a oms occu s only in S-s a es [15].
Final s a e in e ac ion also ans o ms he “unphys-
ical” c oss sec ion σ0
sin o a eal one o Coulomb
co ela ed pai s, σC[16,17]:
(3)
d2σC
dp+dp−
=
ΨC
−
k∗ ∗

2d2σ0
s
dp+dp−
,
whe e ΨC
−
k∗( ∗)is he con inuum wa e unc ion and
2
k∗≡qwi h qbeing he ela i e momen um o he
π+and π−in he c.m. sys em.3|ΨC
−
k∗( ∗)|2de-
sc ibes he Coulomb co ela ion and a ∗=0 coin-
cides wi h he Gamo –Somme eld ac o AC(q) wi h
q=|q|[17]:
(4)AC(q) =2πmπα/q
1−exp(−2πmπα/q).
Fo low q,0⩽q⩽q0,Eqs.(2)–(4) ela e he num-
be o p oduced A2πa oms, NA, o he numbe o
Coulomb co ela ed pion pai s, NCC [18]
NA
NCC =σ o
A
σ o
C|q⩽q0
=(2παmπ)3
π
∞
n=11
n3
q0
0AC(q) d3q
(5)=k h(q0).
Eq. (5) de ines he heo e ical k- ac o . Th oughou he
Le e we will use
(6)q0=2MeV/c and k h(q0)=0.615.
In o de o accoun o he ini e size o he pion p o-
duc ion egion and o he wo-pion inal s a e s ong
in e ac ion, he squa es o he Coulomb wa e unc-
ions in Eqs. (2) and (3) mus be subs i u ed by he
squa e o he comple e wa e unc ions, a e aged o e
he dis ance  ∗and he addi ional con ibu ions om
π0π0→A2πas well as π0π0→π+π−[17].I
should be no iced ha hese co ec ions essen ially
cancel in he k- ac o (Eq. (5)) and lead o a co ec-
ion o only a ac ion o a pe cen . Thus ini e size
co ec ions can sa ely be neglec ed o k h.
Once p oduced, he A2πa oms p opaga e wi h el-
a i is ic eloci y (a e age Lo en z ac o ¯γ≈17 in
ou case) and, be o e hey decay, in e ac wi h a -
ge a oms, whe eby hey become exci ed/deexci ed o
3Fo he sake o cla i y we use he symbol Q o he expe imen-
ally econs uc ed and q o he physical ela i e momen um.
Fig. 1. Rela i e momen um dis ibu ions (q,qL) o a omic π+π−
pai s a he poin o b eak-up and a he exi o he a ge . No e ha
qLis almos no a ec ed by mul iple sca e ing in he a ge .
b eak up. The π+π−pai s om b eak-up (a omic
pai s) exhibi speci ic kinema ical ea u es which al-
low o iden i y hem expe imen ally [15], namely e y
low ela i e momen um qand qL( he componen o
qpa allel o he o al momen um p++p−)asshown
in Fig. 1. A e b eak-up, he a omic pai a e ses he
a ge and o some ex en loses hese ea u es by mul-
iple sca e ing, essen ially in he ans e se di ec ion,
while qLis almos no a ec ed. This is one eason o
conside ing dis ibu ions in QLas well as in Qwhen
analyzing he da a.
Exci a ion/deexci a ion and b eak-up o he a om
a e compe ing wi h i s decay. Sol ing he anspo
equa ions wi h he c oss sec ions o exci a ion and
b eak-up, [20–31] leads o a a ge -speci ic ela ion
be ween b eak-up p obabili y and li e ime which is
es ima ed o be accu a e a he 1% le el [22,32,33].
Measu ing he b eak-up p obabili y hus allows o de-
e mine he li e ime o pionium [15].
The i s obse a ion o he A2πa om [34] has al-
lowed o se a lowe limi on i s li e ime [18,19] o
τ>1.8×10−15 s (90% CL). In his Le e we p esen
a de e mina ion o he li e ime o he A2πa om, based
on a la ge sample o da a aken in 2001 wi h Ni a ge s.
B. Ade a e al. / Physics Le e s B 619 (2005) 50–60 53
Fig. 2. Schema ic op iew o he DIRAC spec ome e . Ups eam o he magne : a ge , mic os ip gas chambe s (MSGC), scin illa ing ibe
de ec o s (SFD), ioniza ion hodoscopes (IH) and i on shielding. Downs eam o he magne : d i chambe s (DC), e ical and ho izon al
scin illa ion hodoscopes (VH, HH), gas Che enko coun e s (Ch), p eshowe de ec o s (PSh) and, behind he i on abso be , muon de ec o s
(Mu).
2. The DIRAC expe imen
The DIRAC expe imen uses a magne ic double-
a m spec ome e a he CERN 24 GeV/c ex ac ed
p o on beam T8. De ails on he se -up may be ound
in [35]. Since i s s a -up, DIRAC has accumula ed
abou 15000 a omic pai s. The da a used o his wo k
we e aken wi h wo Ni oils, one o 94 µm hickness
(76% o he π+π−da a), and one o 98 µm hick-
ness (24% o he da a). An ex ensi e desc ip ion o he
DIRAC se -up, da a selec ion, acking, Mon e Ca lo
p ocedu es, signal ex ac ion and a i s high s a is ics
demons a ion o he easibili y o he li e ime mea-
su emen , based on he Ni da a o 2001, ha e been
published in [36].
The se -up and he de ini ions o de ec o ac onyms
a e shown in Fig. 2. The main selec ion c i e ia and
pe o mance pa ame e s [36] a e ecalled in he ol-
lowing.
Pai s o opposi ely cha ged pions a e selec ed by
means o Che enko , p eshowe and muon coun e s.
Th ough he measu emen o he ime di e ence be-
ween he e ical hodoscope signals o he wo a ms,
ime co ela ed (p omp ) e en s (σ =185 ps) can be
dis inguished om acciden al e en s (see [36]). The
esolu ion o he h ee componen s o he ela i e mo-
men um Qo wo acks, ans e se and pa allel o
he c.m. ligh di ec ion, Qx,Qyand QL, is abou
0.5 MeV/c o Q⩽4MeV/c. Due o cha ge com-
bina o ials and ine iciencies o he SFD, he dis ib-
u ions o he ans e se componen s ha e subs an ial
ails, which he longi udinal componen does no ex-
hibi [37]. This is ye ano he eason o analyzing bo h
Qand QLdis ibu ions.
Da a we e analyzed wi h he help o he DIRAC
analysis so wa e package ARIANE [39].
The acking p ocedu es equi e he wo acks ei-
he o ha e a common e ex in he a ge plane
(“V- acking”) o o o igina e om he in e sec o
he beam wi h he a ge (“T- acking”). In he ol-
lowing we limi ou sel es o quo ing esul s ob ained
wi h T- acking. Resul s ob ained wi h V- acking do
no show signi ican di e ences, as will be shown
la e .
The ollowing cu s and condi ions a e applied (see
[36]):
•a leas one ack candida e pe a m wi h a con i-
dence le el be e han 1% and a dis ance o he beam
spo in he a ge smalle han 1.5 cm in xand y;
•“p omp ” e en s a e de ined by he ime di e -
ence o he e ical hodoscopes in he wo a ms o he
spec ome e o | |⩽0.5ns;
•“acciden al” e en s a e de ined by ime in e als
−15 ⩽ ⩽−5 ns and 7 ⩽ ⩽17 ns, de e mined
by he ead-ou ea u es o he SFD de ec o ( ime de-
penden me ging o adjacen hi s) and exclusion o
co ela ed π−ppai s. [36];
54 B. Ade a e al. / Physics Le e s B 619 (2005) 50–60
•p o ons in “p omp ” e en s a e ejec ed by ime-
o - ligh in he e ical hodoscopes o momen a o
he posi i e pa icle below 4 GeV/c. Posi i e pa icles
wi h highe momen a a e ejec ed;
•e±and µ±a e ejec ed by app op ia e cu s on
he Che enko , he p eshowe and he muon coun e
in o ma ion;
•cu s in he ans e se and longi udinal compo-
nen s o Qa e QT⩽4MeV/c and |QL|<15 MeV/c.
The QTcu p ese es 98% o he a omic signal. The
QLcu p ese es da a ou side he signal egion o
de ining he backg ound;
•only e en s wi h a mos wo p eselec ed hi s pe
SFD plane a e accep ed. This p o ides he cleanes
possible e en pa e n.
3. Analysis
The spec ome e including he a ge is ully simu-
la ed by GEANT-DIRAC [38], a GEANT3-based sim-
ula ion code. The de ec o s, including ead-ou , ine i-
ciency, noise and digi aliza ion a e simula ed and im-
plemen ed in he DIRAC analysis code ARIANE [39].
The igge s a e ully simula ed as well.
The simula ed da a se s o di e en e en ypes can
he e o e be econs uc ed wi h exac ly he same p o-
cedu es and cu s as used o expe imen al da a.
The di e en e en ypes a e gene a ed acco ding
o he unde lying physics.
A omic pai s. A oms a e gene a ed acco ding o
Eq. (2) using measu ed o al momen um dis ibu ions
o sho -li ed pai s. The a omic π+π−pai s a e gen-
e a ed acco ding o he p obabili ies and kinema ics
desc ibed by he e olu ion o he a om while p opa-
ga ing h ough he a ge and by he b eak-up p ocess
(see [40]). These π+π−pai s, s a ing om hei spa-
ial p oduc ion poin , a e hen p opaga ed h ough he
emaining pa o he a ge and he ull spec ome-
e using GEANT-DIRAC. Recons uc ion o he ack
pai s using he ully simula ed de ec o s and igge s
leads o he a omic pai dis ibu ion dnMC
A/dQ.
Coulomb co ela ed π+π−pai s (CC-back-
g ound). The e en s a e gene a ed acco ding o
Eqs. (3), (4) using measu ed o al momen um dis-
ibu ions o sho -li ed pai s. The gene a ed q-dis-
ibu ions a e assumed o ollow phase space modi-
ied by he Coulomb co ela ion unc ion (Eq. (4)),
dNgen
CC /dq ∝q2×AC(q). P ocessing hem wi h
GEANT-DIRAC and hen analyzing hem using he
ull de ec o and igge simula ion leads o he Cou-
lomb co ela ed dis ibu ion dNMC
CC /dQ.
Non-co ela ed π+π−pai s (NC-backg ound).
π+π−pai s, whe e a leas one pion o igina es om
he decay o a “long-li ed” sou ce (e.g., elec omag-
ne ically o weakly decaying mesons o ba yons) do
no unde go any inal s a e in e ac ions. Thus hey a e
gene a ed acco ding o dNgen
NC /dq ∝q2, using sligh ly
so e momen um dis ibu ions han o sho -li ed
sou ces (di e ence ob ained om FRITIOF-6). The
Mon e Ca lo dis ibu ion dNMC
NC /dQ is ob ained as
abo e.
Acciden al π+π−pai s (acc-backg ound).π+π−
pai s, whe e he wo pions o igina e om wo di e en
p o on–nucleus in e ac ions, a e gene a ed acco ding
o dNgen
acc /dq ∝q2, using measu ed momen um dis i-
bu ions. The Mon e Ca lo dis ibu ion dNMC
acc /dQ is
ob ained as abo e.
All he Mon e Ca lo dis ibu ions a e no malized,
Qmax
0(dNMC
i/dQ)dQ =NMC
i,i=CC,NC,acc, wi h
s a is ics abou 5 o 10 imes highe han he expe i-
men al da a; simila ly o a omic pai s (nMC
A).
The measu ed p omp dis ibu ions a e app oxi-
ma ed by app op ia e shape unc ions. The unc ions
o a omic pai s, FA(Q), and o he backg ounds,
FB(Q), (analogously o QL) a e de ined as
FA(Q) =n ec
A
nMC
A
dnMC
A
dQ ,
(7)
FB(Q) =N ec
CC
NMC
CC
dNMC
CC
dQ +N ec
NC
NMC
NC
dNMC
NC
dQ
+ωaccNp
NMC
acc
dNMC
acc
dQ
wi h n ec
A,N ec
CC,N ec
NC he econs uc ed numbe o
a omic pai s, Coulomb- and non-co ela ed back-
g ound, espec i ely, and ωacc he ac ion o acciden-
al backg ound ou o all p omp e en s Np . Analyz-
ing he ime dis ibu ion measu ed wi h he e ical
hodoscopes (see [36]) we ind ωacc =7.1% (7.7%) o
he 94 µm (98 µm) da a se s [36,37] and keep i ixed
when i ing. The χ2 unc ion o Q(analogously o

B. Ade a e al. / Physics Le e s B 619 (2005) 50–60 55
Fig. 3. Top: expe imen al Qand QLdis ibu ions a e sub ac ion o he p omp acciden al backg ound, and i ed Mon e Ca lo backg ounds
(do ed lines). The peak a Q=4 MeV/c is due o he cu QT⩽4 MeV/c. Bo om: esiduals a e backg ound sub ac ion. The do ed lines
ep esen he expec ed a omic signal shape. The bin-wid h is 0.25 MeV/c.
QL) o minimize is
(8)
χ2=
νmax

νmin
dNp
dQ Qν−([FA(Q) +FB(Q)]Q)ν2
dNp
dQ Qν+(σA)2
ν+(σB)2
ν
wi h Q he bin wid h and σA,σB he s a is ical e -
o s o he Mon e Ca lo shape unc ions, which a e
much smalle han ha o he measu emen . The i
pa ame e s a e n ec
A,N ec
CC,N ec
NC (see Eq. (7)). As a
cons ain he o al numbe o measu ed p omp e en s
is es ic ed by he condi ion Np (1−ωacc)=N ec
CC +
N ec
NC +n ec
A. The measu ed dis ibu ions as well as he
backg ound a e shown in Fig. 3 ( op).
The da a aken wi h 94 and98 µm hick a ge s we e
analyzed sepa a ely. The o al numbe o e en s in he
p omp window is Np =471290.
Fi s , we de e mine he backg ound composi ion by
minimizing Eq. (8) ou side o he a omic pai signal
egion, i.e., o Q>4MeV/c and QL>2MeV/c.
Fo his pu pose we equi e n ec
A=0. As a cons ain ,
he backg ound pa ame e s N ec
CC and N ec
NC ep esen -
ing he o al numbe o CC- and NC-e en s, ha e o
be he same o Qand QL. Then, wi h he pa a-
me e s ound, he backg ound is sub ac ed om he
measu ed p omp dis ibu ion, esul ing in he esid-
ual spec a. Fo he signal egion, de ined by he cu s
Q=4MeV/c and QL=2MeV/c, we ob ain he o-
al numbe o a omic pai s, n esidual
Aand o Coulomb
co ela ed backg ound e en s, Nsig
CC. Resul s o i s o
Qand QL oge he a e shown in Table 1.
CC-backg ound and NC- o acc-backg ounds a e
dis inguishable due o hei di e en shapes, mos p o-
nounced in he QLdis ibu ions (see Fig. 3, op).
Acciden al and NC-backg ound shapes a e almos
iden ical o Qand ully iden ical o QL(uni o m
dis ibu ions). Thus, he e o s in de e mining he ac-
ciden al backg ound ωacc a e abso bed in i ing he
NC backg ound. The co ela ion coe icien be ween
CC and NC backg ound is −99%. This s ong co ela-
ion leads o equal e o s o N ec
CC and N ec
NC. The CC-
backg ound is de e mined wi h a p ecision be e han
1%. No e ha he di e ence be ween all p omp e en s
and he backg ound is Np −N ec
CC −N ec
NC −ωaccNp =
6590, hence e y close o he numbe o esidual
a omic pai s (n esidual
A) as expec ed. This ela ion is
alsousedas a s ic cons ain o i s ou side o hesig-
56 B. Ade a e al. / Physics Le e s B 619 (2005) 50–60
Table 1
Fi esul s (94 and 98 µm a ge s oge he , backg ound shapes om Mon e Ca lo (MC)) o he pa ame e s N ec
CC ( o al numbe o CC-e en s),
N ec
NC ( o al numbe o NC-e en s) and n ec
A(a omic pai s) and deduced esul s o he numbe o a omic pai s om he esiduals (n esidual
A)and
he numbe o CC-backg ound e en s in he signal egion (Nsig
CC). MC-a: backg ound i excluding he signal egion. MC-b: i o he en i e
momen um ange including Mon e Ca lo shape o a omic pai s (“shape i ”). The cu s we e a Qcu =4 MeV/c and QL,cu =2 MeV/c.Q
and QL-dis ibu ions we e i ed oge he . The no malized χ2we e 0.9 o MC-a and MC-b
N ec
CC N ec
NC n esidual
An ec
ANsig
CC
MC-a Q374022 ±3969 56538 6518 ±373 106500 ±1130
QLsame same 6509 ±330 82289 ±873
MC-b Q374282 ±3561 56213 6530 ±294 106549 ±1014
QLsame same same 82345 ±783
nal egion (>), N>
p −N ec>
CC −N ec>
NC −(ωaccNp )>=0
and, hence, he i equi es only one ee pa ame e ,
N ec>
CC .
Second, he a omic pai signal may be di ec ly
ob ained by minimizing Eq. (8) o e he ull ange
and including he Mon e Ca lo shape dis ibu ion FA
(“shape i ”). The signal s eng h has o be he same
o Qand QL. The esul o he signal s eng h n ec
A
as well as he CC-backg ound below he cu s, Nsig
CC,
a e shown in Table 1. The e o s a e de e mined by
MINOS [41].
The consis ency be ween he analysis in Qwi h he
one in QLes ablishes he co ec ness o he QT econ-
s uc ion. A 2D i in he a iables (QL,Q
T) con i ms
he esul s o Table 1.
4. B eak-up p obabili y
In o de o deduce he b eak-up p obabili y, Pb =
nA/NA, he o al numbe o a omic pai s nAand he
o al numbe o p oduced A2πa oms, NA,ha e obe
known. None o he wo numbe s is di ec ly measu ed.
The p ocedu e o ob aining he wo quan i ies equi es
econs uc ion e iciencies and is as ollows.
Numbe o a omic pai s. Using he gene a o o
a omic pai s a la ge numbe o e en s, ngen
A, is gene -
a ed in a p ede ined la ge spa ial accep ance window
Ωgen, p opaga ed h ough GEANT-DIRAC including
he a ge and econs uc ed along he s anda d p oce-
du es. The o al numbe o econs uc ed Mon e Ca lo
a omic pai s below an a bi a y cu in Q,nMC- ec
A(Q ⩽
Qcu )de ines he econs uc ion e iciency o a omic
pai s cu
A=nMC- ec
A(Q ⩽Qcu )/ngen
A. The o al num-
be o a omic pai s is ob ained om he measu ed pai s
by nA=n ec
A(Q ⩽Qcu )/cu
A.
Numbe o p oduced A2πa oms.He eweuse he
known ela ion be ween p oduced a oms and Coulomb
co ela ed π+π−pai s (CC-backg ound) o Eq. (5).
Using he gene a o o CC pai s, Ngen
CC e en s, o
which Ngen
CC (q ⩽q0)(see Eq. (6))ha eqbelow
q0, a e gene a ed in o he same accep ance window
Ωgen as o a omic pai s and p ocessed analogously
o he pa ag aph abo e o p o ide he numbe o
econs uc ed CC-e en s below he same a bi a y
cu in Qas o a omic pai s, NMC- ec
CC (Q ⩽Qcu ).
These CC-e en s a e ela ed o he o iginally gene -
a ed CC-e en s below q0 h ough cu
CC =NMC- ec
CC (Q ⩽
Qcu )/Ngen
CC (q ⩽q0). The numbe o p oduced a oms
hus is NA=k h(q0)N ec
CC(Q ⩽Qcu )/cu
CC (see
Eq. (6)).
The b eak-up p obabili y Pb hus becomes
Pb =nA
NA=n ec
A(Q ⩽Qcu )
k(Qcu )N ec
CC(Q ⩽Qcu )wi h
(9)k(Qcu )=k h(q0)cu
A
cu
CC
.
In Table 2 he k- ac o s a e lis ed o di e en cu s
in Qand QL o he wo a ge hicknesses (94 and
98 µm) and he weigh ed a e age o he wo, co e-
sponding o hei ela i e abundances in he Ni da a
o 2001. The accu acy is o he o de o one pa pe
housand and is due o Mon e Ca lo s a is ics.
Wi h he k- ac o s o Table 2 and he measu emen s
lis ed in Table 1, he b eak-up p obabili ies o Table 3
a e ob ained. The simul aneous i o Qand QLwi h
he a omic shape esul s in a single alue.
B. Ade a e al. / Physics Le e s B 619 (2005) 50–60 57
Table 2
k(Qcu ) ac o s as a unc ion o cu s in Qand QL o he 94 and 98 µm hick Ni a ge s, and he weigh ed a e age o he wo o a ela i e
abundance o 76% (94 µm) and 24% (98 µm)
k94 µm k98 µm ka e age
Qcu =2 MeV/c 0.5535 ±0.0007 0.5478 ±0.0007 0.5521 ±0.0007
Qcu =3 MeV/c 0.2565 ±0.0003 0.2556 ±0.0003 0.2563 ±0.0003
Qcu =4 MeV/c 0.1384 ±0.0002 0.1383 ±0.0002 0.1384 ±0.0002
QL,cu =1 MeV/c 0.3054 ±0.0004 0.3044 ±0.0003 0.3050 ±0.0004
QL,cu =2 MeV/c 0.1774 ±0.0002 0.1776 ±0.0002 0.1774 ±0.0002
Table 3
B eak-up p obabili ies o he combined Ni 2001 da a, based on he
esul s o Table 1 and he k- ac o s o Table 2 o he cu s Qcu =
4 MeV/c and QL,cu =2 MeV/c. E o s a e s a is ical
n esidual
An ec
ANsig
CC Pb
Q6518 ±373 106500 ±1130 0.442 ±0.026
QL6509 ±330 82289 ±873 0.445 ±0.023
Q&QL6530 ±294 106549 ±1004 0.447 ±0.023
The b eak-up p obabili ies om Qand QLag ee
wi hin a ac ion o a pe cen . The alues om shape
i and om backg ound i a e in pe ec ag eemen
(see Table 1). We adop he a omic shape i alue o
Pb =0.447 ±0.023s a , because he i co e s he ull
Q,QL ange and includes co ela ions be ween n ec
A
and Nsig
CC.
Analyzing he da a wi h h ee allowed hi candi-
da es in he SFD sea ch window ins ead o wo, e-
sul s in mo e a omic pai s (see Re . [36], T- acking).
The b eak-up p obabili ies ob ained a e 0.440±0.024
and 0.430 ±0.021 o Qand QL, espec i ely. They
a e no in disag eemen wi h he adop ed alue o
0.447. Despi e he la ge s a is ics, he accu acy is no
imp o ed, due o addi ional backg ound. This back-
g ound o igina es om addi ional eal hi s in he up-
s eam de ec o s o om elec onic noise and c oss-
alk. This has been simula ed and leads essen ially o
a educed econs uc ion e iciency bu no o a de e-
io a ion o he econs uc ion quali y. The addi ional
sou ces o sys ema ic unce ain ies lead us no o con-
side his s a egy o analysis u he on.
V- acking p o ides a sligh ly di e en da a sam-
ple, di e en k- ac o s and di e en signal s eng hs
and CC-backg ound. The b eak-up p obabili y, how-
e e , does no change signi ican ly and is PV- acking
b =
0.453±0.025s a , only 0.3σo om he adop ed alue
0.447.
The b eak-up p obabili y has o be co ec ed o
he impu i ies o he a ge s. Thus, he 94 µm hick
a ge has a pu i y o only 98.4%, while he 98 µm
hick a ge is 99.98% pu e. The impu i ies (C, Mg,
Si, S, Fe, Cu) being mos ly o smalle a omic num-
be han Ni lead ( o he weigh ed a e age o bo h
a ge s) o a educ ion o he b eak-up p obabili y o
1.1% as compa ed o pu e Ni, assuming a li e ime o
3 s. The e o e, he measu ed b eak-up p obabili y has
o be inc eased by 0.005 in o de o co espond o pu e
Ni. The inal esul is
(10)Pb =0.452 ±0.023s a .
5. Sys ema ic e o s
Sys ema ic e o s may occu h ough he analy-
sis p ocedu es and h ough physical p ocesses which
a e no pe ec ly unde con ol. We in es iga e i s
p ocedu e-induced e o s.
The b eak-up p obabili y will change, i he a io
N ec
CC/N ec
NC depends on he i ange. I so, he Mon e
Ca lo dis ibu ions do no p ope ly ep oduce he mea-
su ed dis ibu ions and he amoun o CC-backg ound
may no be cons an . In Fig. 4 he dependence is shown
o he i s in Q,QLand bo h oge he . The a io is ea-
sonably cons an wi hin e o s, wi h he smalles e o s
o a i ange o Q=QL=15 MeV/c. A his poin
he di e ence be ween Qand QL i s leads o a di e -
ence in b eak-up p obabili y o P CC
b =0.023.
Consis ency o he p ocedu e equi es ha he
b eak-up p obabili y does no depend on Qcu .In
Fig. 5 he dependence on he cu is shown o b eak-up
p obabili ies deduced om n esidual
A. The e is a sys-
ema ic e ec which, howe e , le els o o la ge cu
momen a. This dependence indica es ha he shape o
he a omic pai signal as ob ained om Mon e Ca lo
58 B. Ade a e al. / Physics Le e s B 619 (2005) 50–60
Fig. 4. Ra io o CC-backg ound o e NC-backg ound as a unc ion
o i ange.
(and used o he k- ac o de e mina ion) is no in pe -
ec ag eemen wi h he esidual shape. This may be
due o sys ema ics in he a omic pai shape di ec ly
and/o in econs uc ed CC-backg ound o small el-
a i e momen a. The mo e he signal is con ained in
he cu , he mo e he Pb alues s abilize. As a con-
sequence, we chose a cu ha con ains he ull signal
(see Eq. (10)). This a gumen is also ue o sha pe
cu s in QT han he one om he e en selec ion. Cu
momen a beyond he maximum cu o Fig. 5 would
only es backg ound, as he signal would no change
anymo e.
To in es iga e whe he he a omic pai signal shape
is he cause o he abo e cu dependence, we s udied
wo ex eme models o a om b eak-up: b eak-up only
om he 1S-s a e and b eak-up only om highly ex-
ci ed s a es. The wo ex emes esul in a di e ence in
b eak-up p obabili y o P shape
b =0.008.
Sou ces o sys ema ic e o s may also a ise om
unce ain ies in he genuine physical p ocess. We ha e
in es iga ed possible unce ain ies in mul iple sca e -
ing as simula ed by GEANT by changing he sca -
e ing angle in he GEANT simula ion by ±5%. As
a esul , he b eak-up p obabili y changes by 0.002
pe one pe cen change o mul iple sca e ing angle.
Fig. 5. Pb as a unc ion o cu momen um o Qand QL.
In ac we ha e measu ed he mul iple sca e ing o
all sca e e s (ups eam de ec o s, acuum windows,
a ge ) and ound na owe angula dis ibu ions han
expec ed om he s anda d GEANT model [42].This,
howe e , may be due also o e o s in de e mining he
hickness and ma e ial composi ion o he ups eam
de ec o s. Based on hese s udies we conse a i ely
a ibu e a maximum e o o +5% and −10% o mul-
iple sca e ing.
Ano he sou ce o unce ain y may be due o he
p esence o un ecognized K+K−and ¯pp pai s ha
would ul ill all selec ion c i e ia [43]. Such pai s may
be as abundan as 0.5% and 0.15%, espec i ely, o
π+π−pai s as es ima ed o K+K−wi h FRITIOF-
64and o ¯pp om ime-o - ligh measu emen s in a
na ow momen um in e al wi h DIRAC da a. Thei
mass ende s he Coulomb co ela ion much mo e
peaked a low Q han o pions, which leads o a
change in e ec i e π+π−Coulomb backg ound a
small Q, hus o a smalle a omic pai signal and he e-
o e o a dec ease o b eak-up p obabili y. The e ec
leads o a change o P ¯
KK, ¯pp
b =−0.04. We do no
4FRITIOF-6 ep oduces well p oduc ion c oss sec ions and mo-
men um dis ibu ions o 24 GeV/c p o on in e ac ions.