First Observation of the Bottomonium Ground State
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First Observation of the Bottomonium Ground StateChris WestSLAC National Accelerator LaboratoryFermilab HEP Seminar April 27, 2010

Outline
Introduction Previous searches for the b (3S) b : first observation of b (2S) b : confirmation of b Combination of results Conclusions*

Introduction

Hyperfine Splitting in Hydrogen AtomHyperfine splitting from Zeeman effect due to magnetic field of nucleusVery small effect, proportional to a4(m/mp);Responsible for 21 cm line in microwave astronomy*

BottomoniumBound state of b quark and b antiquarkThe b is the ground stateLast ground state of a quarkantiquark system to be observedLarge mb nonrelativistic system, small asMany transitions between states; allowed transitions restricted by symmetriesOf interest in this study are the magnetic dipole transitions to the b and the (1S)b hyperfine mass splitting
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Theoretical ToolsLattice QCD
Effective field theories (EFTs)Nonrelativistic QCD (NRQCD)Potential NRQCD (pNRQCD)
Potential modelsSimulation of action density of QCD vacuum in lattice QCD*

Hyperfine Splitting in BottomoniumHyperfine splittingMass difference between triplet and singlet states, mmbQCD analog of hyperfine splitting in hydrogen
Lattice (NRQCD): 61(4)(12)(6) MeVGray, et al., PRD 72, 094507 (HPQCD and UKQCD Collaborations)Errors due toStatistical/fitting/discretizationRadiative correctionsRelativistic corrections
Perturbative QCD44 11 MeV (static QCD potential)S. Recksiegel and Y. Sumino, PLB 578, 369 (2004)41 11+89 (s) MeV (pNRQCD)Kniehl, et al. PRL 24, 242001
Potential models35 100 MeVNLLNLOLOLLHyperfine splitting assumings 0.003Kniehl, et al. PRL 24, 242001Expected expt. precision*

Hyperfine Splitting from Kniehl, et al.Dependent only on fundamental parameters as and mb possibly useful for extracting as Leading log (LL)Leading order (LO)Next to leading log (NLL)*

Branching Fraction PredictionsPrimarily calculated in potential modelsOften neglecting relativistic correctionsIncluding relativistic corrections plagued with technical ambiguities
Range of theoretical predictions:(115)x104 for (2S) b (120)x104 for (3S) b
Other methods:Radiative transition rates calculated in lattice QCD only for charmoniumNo similar study done for bottomoniumNo EFTbased calculations for transitions from excited states
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Width of b
q~ s2q(0)2mq ~ s5mq (q=c, b) b width smaller than c width of 26.5 MeV due to smaller s() at =mb versus mc Predictions range from 420 MeV
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Previous Searches for the b

Previous Knowledge of b*Entry in PDG from 2002 to 2008
 Previous Searches for the bIn twophoton events at ALEPH, L3, and DELPHI, b reconstructed in set of exclusive modesBest limit on xBF from ALEPH (95% CL): < 48 eV (4 charged tracks),

Search for (3S) b at BaBar

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BaBar CalorimeterUsed in this analysis for measurement of photon energies
Composed of 6580 CsI(Tl) crystals*

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Analysis OverviewDecay modes of b not known or predicted; analysis must remain as inclusive as possible
Two body decay: look for a bump in E distribution around
Reduce continuum/0 background with photon isolation cuts and 0 veto
Accurately model peaking backgroundExpected signal positionHuge background! Blind analysis*

Signal PDFPhoton peaks normally fit with Crystal Ball function: a Gaussian with a power law tail to model energy leakage
Signal probability density function (PDF) modeled with a single Crystal Ball function convolved with a nonrelativistic BreitWigner of width 10 MeV
Fit signal MC with all selection criteria imposed to determine signal PDF and efficiency of = (35.8 0.2) %
Crystal Ball Function*

SelectionEvent selection b expected to decay mainly via two gluons: high track multiplicity Event shape cut (ratio of second to zeroth FoxWolfram moments) to remove QED backgroundPhoton selectionIsolated from charged tracksShape consistent with that of EM showerPhoton in calorimeter barrelVeto consistent with being a 0 daughterCut on angle between and event thrust axis, TOptimize S/(B)S from signal MCB from onpeak data in ~1/10 of total data, excluded from final fit
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Background SourcesNonpeaking backgroundsudsc productionGeneric ISRBottomonium decays
Peaking backgrounds(3S) bJ(2P), bJ(2P) (1S) (J=0, 1, 2)e+e ISR(1S)
bISR(1S)b ?*

Background: e+e ISR(1S)Photon from ISR production of (1S) peaks at 856 MeVClose to signal. Very important to model correctly!Yield fixed from offresonance (4S) data, adjusted for luminosity, crosssection and efficiencyFitted yield: 358001600Yield extrapolated to (3S): 252001700Yield could also be fixed using (3S) offresonance dataExtrapolated yield consistentLower statistical precision
Offresonance (4S) data before Bkg. SubtractionAfter Bkg Subtraction*

Background: b(2P) (1S)Second transition in (3S) b(2P), b(2P) (1S)
Three overlapping peaks: b0(2P) E = 743 MeV b1(2P) E = 764 MeV b2(2P) E = 777 MeV
Model each as a Crystal Ball functionTransition point and power law tail parameter fixed to same value for each peakMeans fixed to PDG values minus a common offsetRatio of yields taken from PDG
Offset of 3.8 MeV observed in data used to correct energy scale of other peaks.
Shape fixed from full dataset with signal region excludedSignal regionexcludedISR (1S) PDFBkgd subtracted distributionbJ(2P)>(1S)J=0,1,2*

Fit Strategy b peak shape fixed, yield allowed to floatISR peak position and lineshape fixed; yield fixed from (4S) offresonance dataZerowidth b shape fixed from MC, convolved with BreitWigner shapeNonpeaking background modeled by empirical function:
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Fit Resultsb peaksISR(1S)b ?*

First Observation of the b192002000 events10 significance!Bkg. subtractedCont. bkg. subtracted bISRb*

Observation of b in (3S) Sample b mass
Hyperfine splitting
Branching fraction
The implications of these values will be discussed later in the talk*

Search for (2S) b at BaBar

Confirmation of hb in different dataset with signal peak at a different energyImproved absolute energy resolution at lower signal photon energies better separation between peaksRatio of branching fraction to hb at (2S) and (3S) resonances a probe of nature of peak seen in (3S) sampleMotivation for (2S) Analysis*

Event SelectionUse same selection as (3S) analysis with reoptimized cosT and E2 selectionscosT 40 MeV and mm 50 MeV in (3S) analysisMore combinatorial p0 background at Eg=614 MeV versus 921 MeVHadronic event and photon selection criteria identical*

Sources of Background

Sources of BackgroundNonpeaking backgroundudsc production mainly 0 decaysGeneric ISRBottomonium decaysModeled by exponential of 4th order polynomial (2S) bJ(1P), bJ(1P) (1S) (J =0, 1, 2)e+e (1S)Other (2S) backgrounds S S absorbed into nonpeaking component S S S S The presence of these backgrounds is considered as a (small) systematic error*

Background: (2S) b, b (1S)Second transition in (2S) b, b (1S)Three overlapping peaks: b0 E = 391.1 MeV b1 E = 423.0 MeV b2 E = 441.6 MeVImproved energy resolution some technical issues become importantDoppler broadening due to b CM momentum nonnegligible compared to Gaussian width: ~5 MeV compared to ~10 MeVScaling widths from c states show that the width of the b peaks is negligibleRelative rates fixed from control sample (2S)b, b (1S) , (1S)
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Background: e+e (1S)
Decided to float ISR yield in fitCompared to (3S) analysis, peaks better separated, toy studies show that it is not necessary to fix ISR yieldError on extrapolated ISR yield comparable to fitted ISR yieldEstimated ISR yield used as consistency checkUse ISR yield from (4S) offpeak data to estimate yield in on(2S) dataEstimated yield from (4S) sample consistent with off(3S) and off(2S) yields
Bkg. Subtracted
(4S) offresonance*

Tests of Fit Procedure

*Tests of Fit ProcedureFit to optimization sampleFit of full data sample with signal region excludedToy studies using simulated datasets

*Fit to Optimization SampleTest fit procedure on 1/10 optimization sample 2/ndof=94/93 ISR yield consistent with expectation of 1423
b ISRb*

*Fit of Blinded SampleFitted ISR yield of 15200+42004000 consistent with expected yield of 16700A check of the fitted background yield near the signal region
Residuals show no unexpected features in signal region
2/ndof=116.2/93
Blinded region
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Fit Results

Fitted Spectrum and Residualsb peaksISR(1S)b ?*

Backgroundsubtracted Spectrumb ISRb*

Zoomed Spectrumb ISRb*

Comparison with (3S) Spectrum(2S) spectrum(3S) spectrum*

Fit Results
b yield:
Corrected b peak position:
2/ndof=115.1/93*

Width VariationsWe decided before unblinding to use an b width of 10 MeV. Theoretical predictions vary between 4 and 20 MeV.Other widths not significantly favored by the data*

Yield and Peak Position Systematics*

Branching Fraction SystematicsSelection efficiencyBranching fraction*

Summary of (2S) Results
Branching fraction:
b mass:
Hyperfine splitting: Hyperfine splitting consistent with result from (3S) analysis:
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Combined hb mass
Ratio of branching fractions
Combination of ResultsConsistent with lattice QCD calculation of HPQCD and UKQCD collaborations but 2s higher than pNRQCD calculation making extraction of as problematicConsistent with (large!) range of predictions from potential models ~ 0.3 0.7*
 Updated CLEO AnalysisAfter the BaBar b publications, CLEO updated their b analysis, including cosT information and ISR background.They now find 4s evidence for the b; their results are consistent with those of BaBarcosT

First observation of b in (3S) b and confirmation in (2S) sample10s significance in (3S) 3.0s significance in (2S)Consistent value of mass extracted in two datasets
Properties consistent with those expected of the b
Conclusions*

Backup slides

The Standard ModelThree families: Identical Interaction, different massesForces carried by gauge bosons*

Quantum electrodynamics (QED) describes all electromagnetic phenomenaQED calculations are done in perturbative expansions of a~1/137. These calculations are relatively straightforward because a is small expansions convergePhoton is electrically uncharged
QED*

QCDQuantum Chromodynamics (QCD) describes the interactions of quarks and gluons. QCD is responsible for quarkantiquark bound statesIt is complicated byThe large value of asThe gluon carries a color chargeAt high energies as decreases, simplifying calculations(GeV)QEDWeakQCD*

PEPII Storage RingThe PEPII storage ring collides 3.1 GeV e+ with 8.60 GeV or 8.05 GeV e to produce (3S) and (2S) resonances, respectively*

Discovery of (1S)Subtract nonpeaking backgroundThe (1S) the first state containing a b quark was discovered in 1977.What was the status of its spinsinglet partner 30 years later?pN mm X*

Introduction to b (1S)b mass splitting:714 MeV from (3S) analysis
Width of b q~ s2q(0)2mq ~ s5mq b width smaller than c width of 26.5 MeV due to smaller s() Predictions range from 420 MeV
Branching fraction predictions: (2S) b ~ (1.415)x104 (2S) A1~3x104 (assuming (3S) signal is unmixed Higgs)
90% CL UL from CLEO:5.1x104 (assuming zero width)
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Signal PDF
Single Crystal Ball function convolved with a nonrelativistic BreitWigner of width 10 MeV
Fit truthmatched data to determine signal PDF and all reconstructed candidates passing cuts to find efficiency of = (35.8 0.2) %
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Alternate PDF in (2S) Analysis*
 *Optimization ProcedureUse ~10% of the (2S) onresonance data sample for optimizationTo avoid bias, this data is not used in final fitOptimization uses signal MC and onresonance data in the energy range 0.5< E 40 MeV (red line)cosT

Summary of Fit ProcedureBinned 2 fit of region 270 < E < 800 MeVAll yields floatingBackground parametersc1, c2, c3, and c4 floating b parameters b1 and b2 Crystal Ball parameters, floating b0 Crystal Ball parameter fixed to parameter of b2A, the Crystal Ball transition point, floatingN, the Crystal Ball power law parameter, fixed from MCAn energy scale offset, common to all peaks, floatingRatio of bJ yields fixed from sampleISR parametersAll lineshape parameters fixed from MC b parametersAll Crystal Ball parameters fixed from MCWidth fixed to average of theoretical values, 10 MeV*

To search for possible fit bias, a series of studies with simulated datasets (toy studies) was performedSignal and background generated with expected yield using assumed PDFsToy studies done with all combinations of = 5, 10 MeV Yield = 10k, 20k, 30kFloating and fixed ISR yieldNo significant biases seenUsed to determine best fit procedure regarding ISR componentDue to separation of ISR and b peaks, not necessary to fix ISR yieldToy Studies*

S S (~ 2.3x105 events in fit region) absorbed into nonpeaking component S S S Snearly negligible: ~3k events in fit region Lower end of fit range chosen to avoid having to model exclusive modes extensively
Other Background SourcesLower bound of fit regionLower bound of fit region2S 1S2S 1S*

Control Sample

Control SampleBranching fractions to and from b(1P) not as well known as b(2P)
Must either fit for relative rate in inclusive sample or fix from control sampleWe choose to fix from control sample
Use sample of (2S)b, b (1S) , (1S) events
Model each peak as Crystal Ball plus GaussianSpectrum before cutssoft hard *

Control SampleJ=2J=1J=0*

Additional PEPII Photos

Background: (2S) b, b (1S)Model each as a Crystal Ball function convolved with a flattop to model Doppler EffectCB transition point, power law tail parameter fixed to same value for each peakMeans fixed to PDG values minus a common offsetRelative ratio of J=0 component fixed in fit, J=1 to J=2 ratio floatingCrystal Ball function power law tail fixed from MC of b1 and b2 allowed to float of b0 fixed to of b2Allow a floating energy offset
b2 MC*

cosT Distribution*
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