A New Measurement of eta_b(1S) From Upsilon(3S) Radiative Decay at CLEO

0.37 MB·English

by  Sean Dobbs

h ¡
A New Measurement of (1S) From (3S) Radiative Decay
b
at CLEO
Sean Dobbs (for the CLEO Collaboration)
NorthwesternUniversity,Evanston,IL60208,USA
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0 Abstract. UsingCLEOdata,wereportontheconfirmationoftheh b(1S0)groundstateofbottomoniumintheradiativedecay
2 ¡ (3S)→gh b.WedetermineitsmasstobeM(h b)=9391.8±6.6±2.1MeV,whichcorrespondstothehyperfinesplitting
D Mhf(1S)=68.5±6.6±2.0MeV,andthebranchingfractionB(¡ (3S)→gh b)=(7.1±1.8±1.1)×10−4.Theseresults
n agreewiththosepreviouslyreportedbyBaBar.
a
J Keywords: BottomoniumSpectroscopy,Upsilons,Quarkonia
PACS: 14.40.Pq,12.38.Qk,13.25.Gv
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INTRODUCTION
]
x
e Bottomonium ((cid:12)bb¯(cid:11)) is the preferred system for the study of the qq¯ interaction. Theoretical calculations for bot-
- (cid:12)
p tomoniumaregenerallymorereliablethanforotherqq¯systemsduetothesmallrelativisticcorrections(v/c≈0.1).
e However,muchaboutthespectrumofbottomoniumstatesremainsunknown.Althoughpotentialmodelspredict∼26
h
bottomoniumstatestoliebelowtheBBthreshold(asillustratedinFig.1),only10ofthemhadbeenidentifiedsince
[
thediscoveryofbottomoniumin1977[1]until2008.Mostimportantly,thegroundstateh b(11S0),hadnotbeeniden-
1 tified,despitemanysearchesbyCUSB[2]andCLEO[3]atCESR,andALPEH[4]andDELPHI[5]atLEP,among
v others.
8 ThissituationchangedinJuly2008,whentheBaBarCollaborationannouncedthediscoveryofh (1S)intheirdata
b
3 for109million¡ (3S)[6, 7] in theradiativedecay¡ (3S)→gh (1S),witha significanceof>10s ,asillustratedin
2 b
2 Fig.2.WenotethatthesmallpeakatEg ≈920MeVduetotheradiativetransitiontoh b(1S)isnotvisibleuntilthe
. large smooth backgroundis subtracted. BaBar’s success is due not simply due to their large data set, more than an
1
orderofmagnitudelargerthanpreviouslycollectedatCLEO,butalsodueafactor3greaterbackgroundsuppression
0
bytheuseofacutonthe“thrustangle”.Thethrustangleisdefinedastheanglebetweenthesignaltransitionphoton
0
1 candidateandthethrustaxisoftherestoftheevent[8].
v: BaBar’sdiscoveryofh b isexcitingandlikeallsuchclaims,needstobeconfirmedbyanindependentexperiment.
WereportonsuchameasurementatCLEO.
i
X
r
a ANALYSISOF CLEO DATA
At CLEO we have an 18 times smaller data set than BaBar (5.9Mcomparedto 109M),so severalimprovementsin
analysis procedure were needed in order to identify the h signal. The three main improvementswere: performing
b
a detailed study of the background parameterization; obtaining accurate parameterizations of the photon peak line
shapes;andusingthepowerofthe thrustangleto separatesignalandbackgroundto performa jointanalysisof the
fulldatainthreebinsofthethrustangle.
InFig.2,weshowtheinclusiveenergyspectraforisolatedelectromagneticshowersinCLEO¡ (3S)and¡ (2S)data,
aftercontributionsfromp 0→gg havebeenrejected.Threefeaturesareimmediatelyvisiblefromthesespectra.One,
thespectraaredominatedbyalarger,smoothlyvaryingbackgroundfromotherbottomoniumdecaysanddecaysfrom
e+e− →g ∗ →lighter hadrons. Two, the visible peaks come from the unresolved transitions c (2P,1P)→g ¡ (1S),
bJ
J=0,1,2.Lastly,thepeaksfrome+e−→gISR¡ (1S)and¡ (3S,2S)→gh b(1S)(withEg(h b)≈600MeVfor¡ (2S)
andEg(h b)≈920MeVfor¡ (3S))areexpectedtobemorethananorderofmagnitudeweakerthanthe c bJ(2P,1P)
peaks,andtheyresideonthehighenergytailsofc (2P,1P).
bJ
FIGURE1. Spectrumof thebound bottomonium (bb¯)states. TheM1 transitionsfromthe¡ (n3S1) statestotheh b(11S0) are
indicatedbyredarrowsforthetransitionsreportedinthispaper.
·· 110033
05 GeV )05 GeV ) 550000 (a) 5 GeV) 5 GeV) 110088000000000000 (b)
Entries / ( 0.0Entries / ( 0.0 234234000000000000 Entries/ (0.00Entries/ (0.00246246000000000000000000
110000 00
--22000000
00
00..55 00..66 00..77 00..88 00..99 11 11..11 00..55 00..66 00..77 00..88 00..99 11 11..11
EEgg ((GGeeVV)) EEgg ((GGeeVV))
FIGURE2. BaBarresultsfortheobservationofh [6].(Left)Theobservedinclusivephotonspctrum.(Right)Thebackground
b
subtractedphotonspectrum.Thepeaks,fromlefttoright,arefromc bJ,¡ (1S)ISR,andh b.
PhotonLineShapes:Photonlineshapesincrystalcalorimeters,likethoseusedbyCLEO,aregenerallyparame-
terizedintermsoftheCrystalBallfunction.ThisfunctioncombinesaGaussian(widths ),withalow-energypower
lawtail(parametersa andn).Knowingtheshapeofthelowenergytailisespeciallyimportantforthec peaks,since
bJ
theyareimportantin determingtheshapeof thebackgroundatthe energyof thesmallh signal.These parameters
b
must be determined by fitting a background-freephoton peak. In our analysis we use two independentmethods. In
one method, we use the observed shape of photons from a given energy from radiative Bhabha events, and in the
otherweusetheshapeofphotonsfromtheexcusivedecaysc (2P,1P)→g ¡ (1S), ¡ (1S)→l+l−.Bothmethodsgive
b1
consistentresults,andoncetheparametersaredetermined,theyarefixedinsubsequentanalyses.
ISR Peak:All the parametersof the ISR photonpeakfrom¡ (nS)→g ¡ (1S)were fixed. Theyield of the ISR
ISR
peakwasestimatedbyextrapolatingtheobservedyieldinCLEOdatatakenat¡ (4S),andwasthenfixedtothisvalue.
Background:We find that fitting the smooth backgroundis the most crucialcomponentin determingthe results
for the weak h peak. We made severalhundredbackgroundfits to the data in each of three binsof |cosq |, using
b T
exponentialpolynomialsof various orders (2,3,4), in various energy regions(500–1340MeV), and with linear and
logarithmicbinningofthedata.Wefoundthatmanyofthesefitthedataacceptably,andtookasourfinalresultsthe
averageofEg(h b),B(¡ (nS)→gh b),andsignificanceforallthegoodfits(CL>10%).Ther.m.s.variationofthese
fitswasthentakenasameasureofthesystematicuncertaintyintheresultsfromthissource,±1MeVinEg,±10%in
B(h ),and±0.4s insignificance.
b
· 103 ·103
V V
0 Me400 U (3S) DATA 0 Me500 U (2S) DATA
unts/1330500 U (2Sfi) c bJ(1P) unts/1400 c bJ(1P)
o o
C250 C
300
200
150 c (2P) 200
bJ
100
100
50
0 400 600 800 1000 1200 0 400 600 800 1000 1200
Inclusive E(g ) (MeV) Inclusive E(g ) (MeV)
FIGURE3. CLEOinclusivephotonspectrafor(left)¡ (3S)decay,and(right)¡ (2S),illustratingthebroadfeaturesdescribedin
thetext.
FIGURE4. (Left)Thrustangle|cosq T|distributionfor¡ (3S)dataintheexpectedh bsignalregion,andtheexpecteddistribution
fortheh signalfromMCsimulations.(Right)Inclusivephotonspectraforthedatainthethreethrustangleregions,illustrating
b
theirdifferentsignal/backgroundratios.
JointAnalysisinThreeBinsof|cosq |:AsFig.4(left)shows,thedistributionofthrustangle(|cosq |)forthe
T T
background-dominateddata is strongly peaked in the forward direction, but for the transition photon to the h , the
b
distributionis expectedto be uniform.Thishappensbecausethe transition photonis uncorrelatedwith the particles
produced by the decay of the h , whereas the background photons tend to be correlated with the other particles
b
producedintheunderlyingevent.Wethereforedefinethreedifferentregionsof|cosq |:regionI(|cosq |=0−0.3),
T T
regionII(|cosq |=0.3−0.7),andregionIII(|cosq |=0.7−1.0)).Fig.4(right)illustratesthedifferentlevelsof
T T
signalandbackgroundinthethreeregions.
Unlike BaBar, we do notreject eventsin the |cosq |>0.7 region.Instead, we simultaneouslyfit the spectra for
T
each of the three regions, which lets each region contribute to the total result weighted by its individual signal-to-
background. We call this method the “joint fit”. We have analyzed our data by the joint fit method, and also with
|cosq |<0.7,forcomparisonwithBaBar’smethod.Wefindthatthejointfitmethodenhancesthesignificanceofthe
T
h identificationby∼1s .
b
JOINTFITRESULTS
We show a representative fit for the three bins of thrust angle in Fig. 5. The results of the fit are: N(h ) =
b
2311±546counts,Eg(h b)=918.6±6.0(stat)MeV,whichcorrespondstothehyperfinesplittingof68.5±6.6MeV,
B(¡ (3S)→gh )=(7.1±1.8(stat))×10−4,andsignificance4.1s .
b
AlthoughwefixG (h )=10MeV,becausethewidthofh isunknownwefindthatthebranchingfractiondepends
b b
ontheassumedh widthlinearlyasB(¡ (3S)→gh )×104=5.8+0.13(G (h )inMeV).Ourresultsaredominated
b b b
FIGURE5. Backgroundsubtractedspectraandrepresentativefitresultfor¡ (3S)→gh b(1S).Theh b(1S)peakisclearlyvisible
in|cosq T|regionIandII.
FIGURE6. Backgroundsubtractedspectraandrepresentativefitresultfor¡ (2S)→gh b(1S).Thedashedlinecorrespondstothe
90%CLupperlimitgiveninthetext.Theh b(1S)isnotseeninanyofthethreeregionsof|cosq T|.
TABLE1. Systematicuncertaintiesinmeasurementof¡ (3S)→gh b
photonenergyandbranchingfractions.
Uncertaintyin
Source EEEggg (MeV) B(((¡¡¡ (((333SSS)))→→→ggghhh bbb)))
Background(fn,range,binning) ±1.0 ±10%
PhotonEnergyCalibration ±1.2 —
PhotonEnergyResolution ±0.3 ±2%
CBandc bJ(2P)Parameters ±0.7 ±8%
ISRYield ±0.4 ±3%
PhotonReconstruction — ±2%
N(¡ (3S)) — ±2%
MCEfficiency — ±7%
Total ±1.8 ±15%
TABLE 2. Summary of h b resultsfrom CLEOand BaBar for hyperfine splitting D Mhf(1S)bb¯ and
branchingratio,andcomparisonwiththeoreticalpredictions.
D Mhf(1S)bb¯,(MeV) B(¡ (nS)→gh b)×104 significance
¡ (3S)→gh b (CLEO)[9] 68.5±6.6±2.0 7.1±1.8±1.1 4s
(BaBar)[6] 71.4+3.1±2.7 4.8±0.5±0.6 ≥10s
−2.3
¡ (2S)→gh b (CLEO)[9] — <8.4(90%CL) —
(BaBar)[7] 66.1+4.9±2.0 3.9±1.1+1.1 3.0s
−4.8 −0.9
Lattice(UKQCD+HPQCD)[10] 61±14
(TWQCD)[11] 70±5
(Ehrman)[12] 37±8
pQCD(various) 35−100 0.05−25(¡ (3S))
0.05−15(¡ (2S))
bytheirstatisticaluncertainties;thesystematicuncertaintiesweredeterminedconservativelyandaregiveninTable1.
Wefurthernotethatalthoughwequoteanuncertaintyinphotonenergycalibrationof±1.2MeV,theenergiesofthe
ISRpeakandthec (2P)centroidagreewiththeirexpectedenergieswithin±0.3MeV.
bJ
The analysis method described for ¡ (3S) was also used for our ¡ (2S) data. Because the background near the
expected¡ (2S)→gh b(1S)signal(Eg ≈610MeV)isapproximately6timeshigherthanthecorresponding¡ (3S)(see
Fig.3)transition,noevidencefortheexcitationofh wasobservedinany|cosq | bin,asillustratedin Fig.6.The
b T
jointanalysisledtoanupperlimitofB(¡ (2S)→gh )<8.4×10−4,at90%confidencelevel.
b
We summarize our results and compare them to BaBar’s results in Table 2. Both results are in agreement. In
Table2wealsolistthetheoreticalpredictionsforhyperfinesplittingandbranchingratio.Thevariouspotentialmodel
predictionsvaryoverawiderange.Latticecalculationsforthehyperfinesplittingarealsogiven[10,11,12],which
generallyagreewiththeexperimentalresults.
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