First Observation of the Bottomonium Ground State
Chris West
SLAC National Accelerator Laboratory
Fermilab HEP SeminarApril 27, 2010
Outline
• Introduction
• Previous searches for the b
• Υ(3S) → b : first observation of b
• Υ(2S) → b : confirmation of b
• Combination of results
• Conclusions2
Introduction
Hyperfine Splitting in Hydrogen Atom
• Hyperfine splitting from Zeeman effect due to magnetic field of nucleus
Very small effect, proportional to 4(m/mp);Responsible for 21 cm line in microwave astronomy 4
Bottomonium• Bound state of b quark and b
antiquark
• The b is the ground state
– Last ground state of a quark-antiquark system to be observed
• Large mb → nonrelativistic system, small s
• Many transitions between states; allowed transitions restricted by symmetries
• Of interest in this study are the magnetic dipole transitions to the b and the Υ(1S)-b hyperfine mass splitting 5
Theoretical Tools
• Lattice QCD
• Effective field theories (EFTs)– Non-relativistic QCD (NRQCD)– Potential NRQCD (pNRQCD)
• Potential models
Simulation of action density of QCD vacuum in lattice QCD
6
Hyperfine Splitting in Bottomonium• Hyperfine splitting
– Mass difference between triplet and singlet states, m-mb
– QCD analog of hyperfine splitting in hydrogen
• Lattice (NRQCD): 61(4)(12)(6) MeV– Gray, et al., PRD 72, 094507
(HPQCD and UKQCD Collaborations)– Errors due to
• Statistical/fitting/discretization• Radiative corrections• Relativistic corrections
• Perturbative QCD– 44 ± 11 MeV (static QCD potential)
• S. Recksiegel and Y. Sumino, PLB 578, 369 (2004)
– 41 ± 11+8-9 (s) MeV (pNRQCD)
• Kniehl, et al. PRL 24, 242001
• Potential models– 35 – 100 MeV
NLL
NLO
LO
LL
Hyperfine splitting assuming
s ± 0.003
Kniehl, et al. PRL 24, 242001
Expected expt. precision
7
Hyperfine Splitting from Kniehl, et al.
Dependent only on fundamental parameters s and mb possibly useful
for extracting s
Leading log (LL)Leading
order (LO)
Next to leading log (NLL)
8
Branching Fraction Predictions
• Primarily calculated in potential models– Often neglecting relativistic corrections– Including relativistic corrections plagued with technical ambiguities
• Range of theoretical predictions:– (1-15)x10-4 for Υ(2S) → b
– (1-20)x10-4 for Υ(3S) → b
• Other methods:– Radiative transition rates calculated in lattice QCD only for charmonium
• No similar study done for bottomonium– No EFT-based calculations for transitions from excited states
9
Width of b
• q~ s
2|q(0)|2mq ~ s
5mq (q=c, b)
• b width smaller than c width of 26.5 MeV due to smaller s() at =mb versus mc
• Predictions range from 4-20 MeV
10
Previous Searches for the b
Previous Knowledge of b
12
Entry in PDG from 2002 to 2008
Previous Searches for the b
– In two-photon events at ALEPH, L3, and DELPHI, b
reconstructed in set of exclusive modes• Best limit on xBF from ALEPH (95% CL):
– < 48 eV (4 charged tracks), <132 eV (six charged tracks)– Assumes b) = 557 ± 85 eV
– CLEO III limit:• BF[(3S)b] < 4.3x10-4,• BF[(2S)b] < 5.1x10-4 @ 90% CL
– Unpublished CDF limit (at 95% CL): b
(|y|<0.6)∙BF(bJ/J/) ∙ BF(J/)2 < 2.6 pb
13
Search for Υ(3S) → b at BaBar
15
BaBar Calorimeter
Used in this analysis for measurement of photon energies
Composed of 6580 CsI(Tl) crystals16
17
Simulated event
Cluster in calorimeter consistent with EM shower, isolated from charged tracks and rest of event, inconsistent with being a 0 daughter, away from edges of calorimeter
b decays (through two gluons) have high track and cluster multiplicity
Analysis Overview• Decay 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 background
Expected signal position
Huge background! Blind analysis
19
Signal PDF
• Photon 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 non-relativistic Breit-Wigner 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
20
Background Sources• Non-peaking backgrounds
– udsc production– Generic ISR– Bottomonium decays
• Peaking backgrounds– Υ(3S)→ bJ(2P),
bJ(2P)→ Υ(1S) (J=0, 1, 2)
– e+e-→ ISRΥ(1S)
bISR(1S)
b ?
22
Background: e+e- → ISRΥ(1S)• Photon from ISR production of Υ(1S) peaks at 856 MeV
– Close to signal. Very important to model correctly!
• Yield fixed from off-resonance Υ(4S) data, adjusted for luminosity, cross-section and efficiency– Fitted yield: 35800±1600– Yield extrapolated to Υ(3S):
25200±1700• Yield could also be fixed
using Υ(3S) off-resonance data– Extrapolated yield consistent– Lower statistical precision
Off-resonance Υ(4S) data before Bkg. Subtraction
After Bkg Subtraction
23
Background: b(2P)→ Υ(1S)• Second transition in Υ(3S) → b(2P),
b(2P)→ Υ(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 function– Transition point and power law tail
parameter fixed to same value for each peak
– Means fixed to PDG values minus a common offset
– Ratio 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 excluded
Signal region
excluded
ISR (1S) PDF
Bkgd subtracted distributionbJ(2P)->(1S)J=0,1,2
24
Fit Strategy• b peak shape fixed, yield allowed to float
• ISR peak position and lineshape fixed; yield fixed from Υ(4S) off-resonance data
• Zero-width b shape fixed from MC, convolved with Breit-Wigner shape
• Non-peaking background modeled by empirical function:
25
Fit Results
b peaks
ISR(1S)
b ?
26
First Observation of the b
• 19200±2000 events
10 significance!
Bkg. subtractedCont. bkg. subtracted
b
ISRb
27
Observation of b in (3S) Sample
• b mass
• Hyperfine splitting
• Branching fraction
The implications of these values will be discussed later in the talk
28
Search for Υ(2S) → b at BaBar
• Confirmation of b in different dataset with signal peak at a different energy
• Improved absolute energy resolution at lower signal photon energies → better separation between peaks
• Ratio of branching fraction to b at Υ(2S) and Υ(3S) resonances a probe of nature of peak seen in Υ(3S) sample
Motivation for Υ(2S) Analysis
30
Event Selection• Use same selection as Υ(3S) analysis with re-optimized
|cosT| and E2 selections
– |cosT|<0.8
• Was 0.7 in Υ(3S) analysis• Due to lower continuum background fraction in Υ(2S) analysis
– E2 > 40 MeV and |m-m|<15 MeV
• Was E2 > 50 MeV in Υ(3S) analysis
• More combinatorial 0 background at E=614 MeV versus 921 MeV
• Hadronic event and photon selection criteria identical31
Sources of Background
Sources of Background
• Non-peaking background– udsc production – mainly 0
decays
– Generic ISR– Bottomonium decays– Modeled by exponential of 4th order polynomial
• Υ(2S)→ bJ(1P), bJ(1P)→ Υ(1S) (J =0, 1, 2)
• e+e- → Υ(1S)• Other Υ(2S) backgrounds
– ΥS ΥS absorbed into non-peaking component– ΥS ΥS ΥS ΥS
• The presence of these backgrounds is considered as a (small) systematic error
33
Background: Υ(2S) → b, b → Υ(1S)• Second transition in Υ(2S)→ b, b→ Υ(1S)• Three overlapping peaks:
– b0 E = 391.1 MeV– b1 E = 423.0 MeV– b2 E = 441.6 MeV
• Improved energy resolution → some technical issues become important
– Doppler broadening due to b CM
momentum non-negligible compared to Gaussian width: ~5 MeV compared to ~10 MeV
– Scaling widths from c states show that the width of the b peaks is negligible
• Relative rates fixed from control sample Υ(2S)→b, b Υ(1S) , Υ(1S)→
34
Background: e+e- → Υ(1S)
• Decided to float ISR yield in fit– Compared to Υ(3S) analysis, peaks better separated, toy studies show that it
is not necessary to fix ISR yield– Error on extrapolated ISR yield comparable to fitted ISR yield
• Estimated ISR yield used as consistency check– Use ISR yield from Υ(4S) off-peak data to estimate yield in on-Υ(2S) data– Estimated yield from Υ(4S) sample consistent with off-Υ(3S) and off-Υ(2S)
yields
Bkg. Subtracted(4S) off-resonance
35
Tests of Fit Procedure
37
Tests of Fit Procedure
• Fit to optimization sample
• Fit of full data sample with signal region excluded
• Toy studies using simulated datasets
38
Fit to Optimization Sample
• Test fit procedure on 1/10 optimization sample
• 2/ndof=94/93• ISR yield consistent with
expectation of 1423
b ISR b
38
39
Fit of Blinded Sample
• Fitted ISR yield of 15200+4200
-4000 consistent with expected yield of 16700– A 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
39
Fit Results
Fitted Spectrum and Residuals
b peaks
ISR(1S)b ?
41
Background-subtracted Spectrum
b ISR b
42
Zoomed Spectrum
b ISRb
43
Comparison with Υ(3S) Spectrum
Υ(2S) spectrum Υ(3S) spectrum
44
Fit Results
• b yield:
• Corrected b peak position:
• 2/ndof=115.1/93
45
Width Variations
• We 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
46
Yield and Peak Position Systematics
47
Branching Fraction SystematicsSelection efficiency
Branching fraction
48
Summary of Υ(2S) Results
• Branching fraction:
b mass:
• Hyperfine splitting:
• Hyperfine splitting consistent with result from Υ(3S) analysis:
49
Combined b mass
Ratio of branching fractions
Combination of Results
Consistent with lattice QCD calculation of HPQCD and UKQCD collaborations but 2 higher than pNRQCD calculation making
extraction of s problematic
Consistent with (large!) range of predictions from potential models ~ 0.3 – 0.7
50
Updated CLEO Analysis
After the BaBar b publications, CLEO updated their b analysis, including |cosT| information and ISR background.
They now find 4 evidence for the b; their results are consistent with those of
BaBar
|cosT|<0.3
0.3<|cosT|<0.7
|cosT|>0.7
51
• First observation of b in Υ(3S)b and confirmation in Υ(2S) sample– 10 significance in Υ(3S)– 3.0 significance in Υ(2S)
– Consistent value of mass extracted in two datasets
• Properties consistent with those expected of the b
Conclusions
52
Backup slides
The Standard Model
Three families: Identical Interaction, different masses
Electromagnetic StrongWeak
Forces carried by gauge bosons
54
• Quantum electrodynamics (QED) describes all electromagnetic phenomena
• QED calculations are done in perturbative expansions of ~1/137. These calculations are relatively straightforward because is small expansions converge– Photon is electrically uncharged
QED
55
QCD
• Quantum Chromodynamics (QCD) describes the interactions of quarks and gluons.
• QCD is responsible for quark-antiquark bound states
• It is complicated by– The large value of s
– The gluon carries a color charge
• At high energies s decreases, simplifying calculations
(GeV)
QEDWeak
QCD
56
PEP-II Storage Ring
The PEP-II storage ring collides 3.1 GeV e+ with 8.60 GeV or 8.05 GeV e- to produce (3S) and (2S) resonances, respectively
57
Discovery of Υ(1S)
Subtract nonpeaking background
The Υ(1S) – the first state containing a b quark – was discovered in 1977.
What was the status of its spin-singlet partner 30 years later?
pN X
58
Introduction to b• Υ(1S)-b mass splitting:
– 71±4 MeV from (3S) analysis
• Width of b
– q~ s
2|q(0)|2mq ~ s
5mq
– b width smaller than c width of 26.5 MeV due to smaller s()
– Predictions range from 4-20 MeV
• Branching fraction predictions:
– Υ(2S) → b ~ (1.4-15)x10-4
– Υ(2S) → A1~3x10-4 (assuming Υ(3S) signal is unmixed Higgs)
• 90% CL UL from CLEO:– 5.1x10-4 (assuming zero width)
59
Signal PDF
• Single Crystal Ball function convolved with a non-relativistic Breit-Wigner of width 10 MeV
• Fit truth-matched data to determine signal PDF and all reconstructed candidates passing cuts to find efficiency of = (35.8 ± 0.2) %
60
Alternate PDF in Υ(2S) Analysis
61
62
Optimization Procedure• Use ~10% of the Υ(2S) on-
resonance data sample for optimization– To avoid bias, this data is not
used in final fit
• Optimization uses signal MC and on-resonance data in the energy range 0.5< E<0.7 GeV
• Optimize for best S/√(B)• Optimization result
– E2 > 40 MeV (red line)
– |cosT|<0.8 (red points)
Summary of Fit Procedure• Binned 2
fit of region 270 < E < 800 MeV• All yields floating• Background parameters
– c1, c2, c3, and c4 floating• b parameters
– b1 and b2 Crystal Ball parameters, floating– b0 Crystal Ball parameter fixed to parameter of b2
– A, the Crystal Ball transition point, floating– N, the Crystal Ball power law parameter, fixed from MC– An energy scale offset, common to all peaks, floating– Ratio of bJ yields fixed from sample
• ISR parameters– All lineshape parameters fixed from MC
• b parameters– All Crystal Ball parameters fixed from MC– Width fixed to average of theoretical values, 10 MeV
63
• To search for possible fit bias, a series of studies with simulated datasets (“toy studies”) was performed
– Signal and background generated with expected yield using assumed PDFs
• Toy studies done with all combinations of– = 5, 10 MeV– Yield = 10k, 20k, 30k
– Floating and fixed ISR yield
• No significant biases seen• Used to determine best fit procedure regarding ISR
component– Due to separation of ISR and b peaks, not necessary to fix ISR
yield
Toy Studies
64
• ΥS ΥS (~ 2.3x105 events in fit region) absorbed into non-peaking component– ΥS ΥS ΥS ΥSnearly negligible: ~3k
events in fit region– Lower end of fit range chosen to avoid having to model
exclusive modes extensively
Other Background Sources
Lower bound of fit region Lower bound of fit region
Υ2S Υ1S Υ2S Υ1S
65
Control Sample
Control Sample
• Branching 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 sample– We choose to fix from control
sample
• Use sample of Υ(2S)→b,
b Υ(1S) , Υ(1S)→ events
• Model each peak as Crystal Ball plus Gaussian
Spectrum before cuts
soft hard
67
Control Sample
J=2 J=1 J=0
68
Additional PEP-II Photos
Background: Υ(2S) → b, b → Υ(1S)• Model each as a Crystal Ball function convolved with a flat-top to model Doppler Effect
– CB transition point, power law tail parameter fixed to same value for each peak
– Means fixed to PDG values minus a common offset
– Relative ratio of J=0 component fixed in fit, J=1 to J=2 ratio floating
– Crystal Ball function power law tail fixed from MC
– of b1 and b2 allowed to float
– of b0 fixed to of b2
• Allow a floating energy offset
b2 MC
70
|cosT| Distribution
71
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