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

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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:

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Fit Results

b peaks

ISR(1S)

b ?

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First Observation of the b

• 19200±2000 events

10 significance!

Bkg. subtractedCont. bkg. subtracted

b

ISRb

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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