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at BABAR
M. Davier
To cite this version:
M. Davier. Study of e
+
e
−
collisions with a hard initial state photon at BABAR. Tau Lepton Physics
Study of e +
e ollisions with a hard initial state photon at BABAR
Mi helDavier
a
E-mail: davierlal.in2p3.fr
a
Laboratoiredel'A elerateurLineaire,IN2P3/CNRS-UniversitedeParis-Sud,
BP34,91898Orsay,Fran e
Astudyofseveral3-and4-bodyhadroni nalstates(
+ 0 , + + ,K + K + andK + K K + K )
a ompaniedbyahardphotonispresented. These statesareprodu edfrome
+
e ollisionsatthe .m. energy
nearthe(4S)resonan eusinga90fb
1
datasample olle tedwiththeBABAR dete toratthePEP-II ollider.
The invariant mass of the hadroni nal state determinesthe virtual photon energy, so that the data an be
omparedwithdire te
+
e rossse tions. Crossse tionshavebeenobtainedfromthresholdupto4.5 GeVwith
systemati errorsat the5% level. The a ura yofthe results is omparable withthe bestdire te
+
e results
overall,but a hievesamu hbetter pre ision in1.4-2.5GeV region where dataare sparse. In additionto light
mesonspe tros opythesedata anbeusedtoimprovethedeterminationofR{theratioofe
+ e !hadrons ross se tiontoe + e ! +
{andtherebytoimpa ttheunderstandingofthere ent(g 2)measurementthrough
abetterevaluationofthehadroni va uumpolarization ontribution.TheISRte hniquealsogivesa esstoJ=
produ tionandallowsonetomeasurebran hingratiosinto3-and4-body nalstatesaboveatalevelofpre ision
thatistypi allybetterthanthatobtainedinthe ombinedearlier measurements.
1. Introdu tion
The possibility of using the initial state
ra-diation (ISR) of hard photons at B-fa tories to
study hadroni nal state produ tion at lower
e +
e .m. energies has been dis ussed
previ-ously [1-3℄. The interest in this kind of study
has been in reasing be ause of the dis repan y
betweenthemeasuredmuon g 2valueandthe
predi tionwithintheStandardModel[4,5℄,where
thehadroni va uumpolarization ontributionis
evaluated using data from e
+
e experiments at
low energies. The study of ISR events at
B-fa tories anprovide independentmeasurements
ofhadroni rossse tionsaswellas ontributeto
hadroni spe tros opy.
TheISR rossse tionforaparti ular nalstate
f dependsone + e rossse tion f (s)andis ob-tainedfrom: d(s;x) dx =W(s;x) f (s(1 x)); (1) where x = 2E = p s, E
is the energy of the
ISR photonin thenominal .m. frame with
to-tal energy
p
s,and s
0
=s(1 x) isthesquareof
W(s;x)des ribestheenergyspe trumofthe
vir-tual photons and an be al ulated with better
than 1% a ura y [1-3℄. ISR photons are
pro-du ed at allangles relative to the ollision axis.
TheBABARa eptan efor su h photonsat
rela-tivelylargeangles(typi ally20-144
Æ
inthe
labo-ratoryframe)isaround10-15%:
An advantagederiving from the use of ISRis
that theentire rangeof e e tive ollisionenergy
iss annedinoneexperiment. Thisavoidsthe
rel-ativenormalizationun ertaintieswhi h anarise
when data from di erent experiments are
om-bined. Adisadvantageisthattheinvariantmass
resolution is alimit whenstudying narrow
reso-nan es.
A omprehensive program is under way at
BABAR to measure all hadroni pro esses in the
fewGeVrange. Whilethe
+
hannelrequires
moresystemati studiesinordertorea hthe
in-teresting1%(orbetter)level,someresultsare
al-ready available for2-and 3-bodypro esseswith
lower ross se tions. They are presented in this
ontribution.
de- f J= (s)= 12 2 ee B f m J= s W(s;x); (2) withx=1 m 2 J=
=s,isproportionaltothe
prod-u t ee B f or B ee B f where and B ee , B f
are the total width and bran hing fra tions
of J= into e
+
e andf. The invariantmass of
the nal parti les determinestheposition ofthe
J= peakandadete tormassresolution8MeV
an be a hieved by using a kinemati t.
Pre-liminarystudiesofsomeparti ularISRpro esses
havebeenperformed(seeRef.[6-8℄)showinggood
BABARdete tor[9℄eÆ ien yandparti le
identi - ation apabilityforthesetypesofevents. Signal
and ba kgroundISRpro essesaresimulated
us-ingMonteCarlo(MC)eventgeneratorsbasedon
omputer odes des ribed in Ref. [10-13℄. Also
simulated were generi ba kground from
quark-antiquark and pro esses using JETSET [14℄
andKORALB[15℄pa kages.
2. Three-body nal state:
+
0
Theinitialsele tionofe
+ e ! + 0
an-didates requires that all the nal parti les are
dete ted inside a du ial volume. One of the
photonsisrequiredtohaveanenergyinthe .m.
frameabove3GeV.Twoofthetra ksmust
origi-natefromtheintera tionpoint,haveatransverse
momentum above 100 MeV/ with no kaon-ID
andbeinthegoodregionofdete tora eptan e.
Thephotonwithgreatest .m. energyisassumed
to be the ISR photon. The remaining photons
arepairedtoform andidate
0
s. Akinemati t
isapplied tothesele tedevent,imposingenergy
and momentum onservation, and onstraining
the andidate
0
invariant mass. Analysis
de-tails anbefound in Ref. [8℄. The 3 invariant
massdistributionoftheeventsafterba kground
subtra tion was t with a sum of ex itation
urves des ribing !(782); (1020);!(1420) and
!(1650)resonan es. Relativephasesfor !(1420)
and !(1650) are xed at 0 and . The
result-ing parameters obtained from the t (Fig. 1,
2
=dof=146=148)arethefollowing:
B !ee B !3 = (6:700:060:27)10 5 (3) B ! 0 ee B ! 0 3 = (0:820:050:06)10 6 M ! 0 = (13502020)MeV/ 2 ! 0 = (4507070)MeV/ 2 B ! 00 ee B ! 00 3 = (1:30:10:1)10 6 M ! 00 = (1660102) MeV/ 2 ! 00 = (2303020)MeV/ 2 (4)
The tted masses and widths of the !
0 and
! 00
mesons are model dependent but
neverthe-less anbe omparedwiththeestimatesofthese
parameters by the PDG [16℄: M ! 0 = 1400 1450MeV/ 2 , ! 0 =180 250MeV/ 2 , M ! 00 = 1670 30MeV/ 2 , ! 00 = 315 35MeV/ 2 .
The PDG data are based on small data
sam-ples for e + e ! ! 0 ;! 00 ! 3; ! [21,20,23℄, pp!! 0 0 !! 0 0 0 [17℄,and p!! 00 n!
!n [18℄ rea tions. We presenta new
measure-ment of the !
0
and !
00
parameters based on a
signi antly largerdata sample for the e
+ e ! ! 0 ;! 00
! 3 rea tion. From the measured
val-ues of B(V ! e + e )B(V ! 3), the ele troni widthsof! 0 and! 00 anbeestimated. Assuming that B(! 0 !3)1and B(! 00 !3)0:5we derivethat (! 0 !e + e )370eVand (! 00 ! e +
e )570eV.Thelargevaluesofthesewidths,
omparable with (! ! e
+
e ) 600 eV, are
in disagreement with expe tations of the quark
model,whi hpredi tsatleastoneorderof
magni-tudelowervaluesfortheele troni widthsforthe
ex itedmesonstates(see,forexample,Ref.[19℄).
Thee + e ! + 0
rossse tioninthe
1.05-3.0 GeV=
2
regionis presentedin Fig.2. Itis in
agreementwiththe SNDdata [20℄,but itshows
alargedis repan ywiththeDM-2[21℄
measure-ment.
It is interestingto plug these new resultsinto
the dispersion integral yielding the
orrespond-ingva uumpolarization ontributiontothemuon
anomalous magneti moment. In order to
om-pare withprevious al ulations[4℄usingexisting
data,theenergyinterval1.055to1.8GeVis
ho-sen. The urrentvalue[4℄is
M
3
π
(GeV/c
2
)
events/(2.5 MeV/c
2
)
0
500
1000
1500
0.8
0.9
1.0
M
3
π
(GeV/c
2
)
events/(25 MeV/c
2
)
0
100
200
300
1.2
1.4
1.6
1.8
Figure1. Theba kground-subtra ted3massspe trumformassesbetween0.70and1.05 GeV=
2 (left)
andformassesfrom 1.05to1.80 GeV=
2
(right). The urvesaretheresultofthe t.
M
3
π
(GeV/c
2
)
Cross section (nb)
0
2
4
6
8
1.5
2
2.5
3
Figure2. Thee + e ! + 0rossse tionmeasuredinthiswork( lled ir les),bySND(open ir les),
0
10
20
30
1000
1500
2000
ND
CMD
SND
DM1
GG2
DM2
CMD2
CMD2
BaBar
E
C.M.
(MeV)
σ
(e
+
e
-
→
2
π
+
2
π
-
) (nb)
Figure3. Thee + e ! + + rossse tionobtainedfromISRatBABAR in omparisonwith
existinge
+
e data.
whilethenewestimateusingonlythenewBABAR
data yields a larger and more pre ise
ontribu-tion, a had =(3:310:13 exp 0:03 rad )10 10 (6)
3. Four-body nal states:
+ + , K + K + and K + K K + K
Event andidates were required to have four
good hargedtra ksand ahardphotonassumed
tobefromISR.Hadronidenti ationinBABAR is
used to separate harged pions from kaons and
identify the di erent
+ + , K + K + andK + K K +
K nal statesisdes ribed.
Fig-ure3presentstheobtainede
+ e ! + +
ross se tion in omparison with all existing
e +
e data. The estimated systemati error is
about5%.
Againwe anexaminetheimpa tofthesenew
resultsonthe al ulationofhadroni va uum
po-larization. Thehadroni ontributionto(g 2)
fromthe
+
+
hannel[4℄,evaluatedusing
+ a had;ee = (14:210:87 exp 0:23 rad )10 10 (7) a had; = (12:350:96 exp 0:40 SU2 )10 10 (8)
The evaluation is less pre ise in this hannel
sin eitisbasedonthemeasurementofthe
spe -tral fun tion inthe !
3
0
de aymode,
in-volvingthere onstru tionofthree
0
de ays.
Evaluating the same ontribution with the
BABAR datain thisenergyrangegives
a had =(12:950:64 exp 0:13 rad )10 10 (9)
whi hshowsthepotentialofISRmeasurements.
Figure 4 shows the obtained ross se tions
for K + K + and K + K K + K nal states.
Thesystemati normalizationerrorsare15%and
25%, omingessentiallyfromtheun ertaintiesin
thedynami susedintheMonteCarloevent
gen-erators. respe tively.
4. Three- and four-bodyJ= de ays
TheinvariantmassofthreepionsfromJ=
de- ays is shown in Fig. 5(top). From about 900
events after ba kground subtra tion the
follow-ingprodu t anbedetermined:
(J= !e
+
e )B(J= !3)=(12258)eV(10)
Thesystemati errorin ludestheun ertaintieson
thedete tioneÆ ien y,theintegratedluminosity,
andtheradiative orre tion. Usingthe (J= !
e +
e )measurementobtainedbyBABAR[7℄from
the study of e
+
e ! J= with J= !
+
,
theJ= !3bran hingfra tionis al ulatedto
be
B(J= !3)=(2:180:19)% (11)
whi hisinsubstantialdisagreement(3)with
the world average value [16℄ of (1:470:13)%,
but agrees withthere entresult fromBES [22℄:
B(J= !3)=(2:100:12)%.
Figure 5 shows the J= and (2S) signals
( ontaining27020and 62025observedevents
respe tively) in the four- harged-tra k invariant
massspe trum. Thelattersignaloriginatesfrom
the pro ess (2S)!J=
+
!
+
0
2
4
6
1
2
3
4
- DM1
- BaBar ISR
E
C.M.
(GeV)
σ
(K
+
K
-
π
+
π
-
) (nb)
0
0.05
0.1
0.15
0.2
2
3
4
E
C.M.
(GeV)
σ
(K
+
K
-
K
+
K
-
) (nb)
Figure 4. Thee + e !K + K + (left)and K + K K +K (right) ross se tionsobtainedfrom ISR
atBABAR in omparisonwithe
+ e data.
M
3
π
(GeV/c
2
)
events/(2.5 MeV/c
2
)
0
25
50
75
100
2.9
3
3.1
3.2
3.3
0
100
200
3
3.5
4
4.5
m(
π
+
π
-
π
+
π
-
) (GeV/c
2
)
Events/0.01 GeV/c
2
Figure 5. The signalsfrom J= and (2S) in 3(left)and 4(right) nalstates. Theshaded regionat
thelatter orrespondsto (2S)!J=
+
,withJ= !
+
0
25
50
75
100
3
3.05
3.1
3.15
3.2
m(K
+
K
-
π
+
π
-
) (GeV/c
2
)
Events/0.0067 GeV/c
0
5
10
15
3
3.05
3.1
3.15
3.2
m(K
+
K
-
K
+
K
-
) (GeV/c
2
)
Events/0.005 GeV/c
Figure6. Thesignalsfrom J= de aysintoK
+ K + (left)andK + K K +
K (right) nal states.
pairof hargedparti les(shadedhistogram)tobe
onsistent with the J= mass. By using
dete -tion eÆ ien y from simulation and the e e tive
ISRluminositythefollowingprodu tshavebeen
obtained: B J= !4 J= ee =(19:51:41:3)eV, B (2S)!J= + B J= !2 (2S)ee = (45:01:82:2) eV.
Using the world averages value for (J= !
e + e ), (2S)!e + e and B J= !2 wederivethe valuesB J= !4 =(3:700:270:36)10 3 and B (2S)!J= + =0.3610.0150.037. Figure6
shows the J= signals in the K
+ K + and K + K K +
K nal states, where 23319 and
38.56.7eventshavebeenobservedrespe tively.
Usingthedete tioneÆ ien yobtainedfrom
sim-ulation andthe e e tive ISRluminosity the
fol-lowingprodu tshavebeenobtained:
B J= !2K2 J= ee = (32:92:72:7)eV(12) B J= !4K J= ee = (3:60:60:5)eV(13) (14)
Usingtheworldaveragevaluefor (J= !e
+
e )
wederivetherelativede ayrates
B = (6:250:500:62)10 3 (15) B J= !4K = (6:91:21:1)10 4 (16) 5. Con lusion
A numberof ISR pro esseshavebeenstudied
with a 90 fb
1
data sample in the BABAR
de-te tor, utilizing the ex ellent dete tor eÆ ien y
and parti le identi ation apabilities of the
de-te tor. The e + e ! + 0 , and preliminary + + , K + K + , K + K K + K ross
se tions overtheentire massrangefrom
thresh-old to 4.5 GeV in the e
+
e .m. system with
systemati normalization errors that are similar
to those a hived by thebest e
+
e experiments
over amu h smaller mass region. Radiative
re-turntotheJ= resonan eallowsonetomeasurea
numberofbran hingfra tions signi antlymore
pre isely thanearlierdeterminations.
REFERENCES
1. A.B.Arbuzovetal.,JHEP9812(1998)9.
2. S. Binner, J.H. Kuhn, K. Melnikov,Phys.
Lett.B 459(1999)279.
3. M. Benayoun et al., Mod. Phys. Lett. A 14
(1999)2605.
Z. Zhang, Eur. Phys. J. C 27 (2003) 497;
Eur.Phys. J. C 31(2003)503.
5. M.Davier,Thehadroni ontribution to(g
2)
,these pro eedings.
6. E.P.Solodov,hep-ex/0107027.
7. BABARCollaboration,B.Aubertetal.,Phys.
Rev.D 69(2004)011103.
8. BABARCollaboration,B. Aubert et al.,
hep-ex/0408078,a eptedbyPhys. Rev.D.
9. BABARCollaboration,B.Aubertetal.,Nu l.
Inst.Meth. A479(2002)1.
10. H.Czyz and J.H.Kuhn, Eur. Phys. J. C 18
(2000)497.
11. A.B.Arbuzovetal., JHEP9710(1997)1.
12. M. Ca o, H. Czyz, E. Remiddi, Nuo. Cim.
110A (1997)515;Phys. Lett. B 327(1994)
369.
13. E. Barberio, B.vanEijkand Z.Was,Comp.
Phys. Comm.66(1991)115.
14. T.Sjostrand,Comp. Phys. Comm.82(1994)
74.
15. S. Jada hand Z. Was, Comp. Phys. Comm.
85(1995)453.
16. ReviewofParti lePhysi s,S.Eidelmanetal.,
Phys. Lett.B 592(2004)1.
17. CrystalBarrelCollaboration,A.V.Anisovi h
etal.,Phys. Lett.B 485(2000)341.
18. E852Collaboration,P. Eugenioet al., Phys.
Lett.B 497(2001)190.
19. S. Godfrey and N. Isgur, Phys. Rev. D 32
(1985)189.
20. SND Collaboration, M.N. A hasov et al.,
Phys. Rev.D 66(2002)032001.
21. DM2 Collaboration, A. Antonelli et al., Z.
Phys. C 56(1992)15.
22. BESCollaboration,J.Z.Baietal.,Phys.Rev.
D 70(2004)012005.
23. CMD-2 Collaboration, R.R. Akhmetshin et
