Bottom Quark and J/Production at CDF

Thomas J. LeCompte

High Energy Physics DivisionArgonne National Laboratory

For the CDF Collaboration

2

Outline

“Theoretical” Outline– Theoretical motivation & early ideas on

quarkonium production– Description of the Experiment– Measuring Inclusive J/ production– Theoretical motivation for measuring the b

cross-section– Measurements at lower energy– Measuring J/’s from b quark decays– Theoretical Post-dictions– New Charmonium Results on the X(3872)– Summary

“Experimental” Outline– Theoretical Ramblings– A Digression– The Data– More theoretical ramblings– A Second Digression– More Data– Going too fast through the last 10

or 15 slides

3

An Introduction To Charmonium

3 GeV

3.8 GeV

J/

(2S) or ’

3S1

3S1

3P2

3P1

3P0

2

1

0

Charmonium is a bound stateof a charmed quark andantiquark. It is “almostnonrelativistic”: ~ 0.4:Hence the hydrogen atom-likespectrum

Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist.

States can make radiative (E1) transitions to the other column.

Mas

s

thresholdDD

4

Review: Quantum Numbers

JS L12

Total Angular Momentum

Orbital Angular Momentum

Spin Angular Momentum

13/ SJ

Means: Quark Spin=1 (3 = 2 x 1 + 1) Quark Orbital Ang. Mom. = 0 Total J/ Spin = 1

1PCJMeans: Total J/ Spin = 1 Parity is Odd Charge Conjugation is Odd

5

Early Thinking on J/’s

The J/ is extremely narrow: about 87 keV: Why?

Consider the possible strong decays

– Open charm? Nope – kinematically blocked

– Light quarks? Not directly – the J/ doesn’t contain any

– Two gluons? No• Reason 1: Quantum Mechanics

(Yang-Landau Theorem) – “a spin-odd particle cannot decay to two identical massless spin-1 particles”

• Reason 2: Violates charge conjugation symmetry

– Three gluons? Allowed, but suppressed

• In fact, electromagnetic decays compete with the strong decays!

• About 30% of the decays are electromagnetic/radiative

The direct production rate should be tiny

– If J/ → gg is forbidden, so is gg → J/

Hadroproduction through ’s (followed by → J/ + ) would be allowed

– This is the dominant source of J/’s.

The (2S) rate should be really, really tiny

– it can’t come from decay– All (2S) must be from the decay

b → (2S) + X

OZ

I Rul

eC

olor Singlet M

odel

6

Why this is utter nonsense

Theoretically:

– The same Yang-Landau Theorem prevents 1 production via gg interactions – but that didn’t seem to bother anybody

Experimentally– At fixed target energies, there is

roughly the same ratio N((2S))/N(J/) as at colliders

• This is true even at fixed target energies below b threshold!

– At all energies, roughly 40% (not 100%) of J/’s come from decays

We should have known better. This model should have beendead on arrival; it was only the absence of alternatives that keptit going as long as it did.

The field was in denial.

7

How Bad Was This Model?

CDF Data (20 pb-1) publishedin PRL79, 572 (1997)

J/ is a factor ~10 higher than predictions– That’s less bad by comparison

(2S) is a factor ~100 higher than predictions

Even astronomers wouldcall this disagreement!

8

The Color Octet Model

It’s fairly clear that the CSM is missing some source of J/’s– By the rate, it appears to be the dominant source

Consider the addition of two SU(3) (color) octets– 8+8 = 1 + 8 + 8 + 10 + 10bar + 27– This allows 8+8 = 8: i.e. two gluons can be in a color octet state– This is analogous to the three-gluon vertex

Think of this as a two-step process– 1. The charm-anticharm pair is produced in a color octet state– 2. The octet state radiates a gluon, and

becomes colorless

gSPgg 138

23

The J/

This gets us our third gluon painlessly.

Instead of ggg → J/, we have → J/ + g

This is analogous to production:instead of a singlet radiating a photonthere is an octet “” radiating a gluon.

Other octet states also contribute

9

No Free Lunch

The Color Octet Model gives us a third gluon “for free”

– Because it’s soft, there is little penalty for an extra power of s

– For exactly the same reason, the matrix element for the coupling between the octet c-cbar and the J/ + gluon is non-perturbative

• It must be fit from experiment

All is not lost

– There are only a small number of non-perturbative parameters

– While they have to be fit from experiment, they have to be consistent across different measurements

– There is at least one other prediction – J/’s show a large spin-alignment at large pT

Strictly speaking, the COM accommodates a largecross section – it doesn’t predict it.

10

Fitting COM Parameters

A consistent set of COM parameters can predict reproduceboth the measured J/ and (2S) cross-sections

A major success of the model!

11

Theoretical Summary &Experimental Strategy

Color singlet prediction of 3S1 charmonium production is low by orders of magnitude

– Other models can explain this, but not really predict it

– Collider measurements see only the top ~6% or so (in pT) of the cross-section

NLO production of bottom quarks is also low by a factor of 2 or 3

– More details on this later in the talk

– A substantial (10-20%) source of J/’s is from b decay

– Collider measurements see only the top ~10% or so (in pT) of the cross-section

Experimental plan: measure both cross-sections at ALL pT’s using the decay J/ → – This will settle the issue of the b cross-sections

– Experiment will be ahead of theory for the J/ and (2S).

12

The CDF Detector: All you need to know

Central Muon (CMU) detectors:2304 wire chambers

Central Calorimeter:For this analysis, it’s usedas passive steel, lead andplastic absorbers (4.7)

Open cell tracker: wireChamber in 1.5T magneticfield (COT)

Silicon vertex detector(SVX) – five layers forPrecision track measurementBeams-eye view of CDF

13

The CDF Detector:More Than You Need To Know

Silicon Vertex Detector being installed

CDF rolling into the collision hall

(uphill both ways)

14

Triggering in Words

Triggering is the key to hadron collider physics

– You can’t analyze an event you didn’t trigger on (and thus record)

– Collision rate (when this data was taken) is ~106 Hz

– Event recording rate is ~100 Hz

– Need to reject 99.99% of events CDF Uses a 3 Level Trigger

– Level 1:• Identify muon “stubs” (short tracks in the muon chambers)• Identify tracks in the transverse plane in the COT tracker with the XFT

– XFT = eXtremely Fast Tracker

– Level 2:• At the time this data was taken, Level 2 was in auto-accept mode for muons

– Level 3: • A fast version of offline reconstruction is done• Tracks are required to have a good r-match to the stubs• Tracks are required to have a coarse r-z match to the stubs

– We don’t match east-going muons with west-going tracks• Certain kinematic cuts are made

15

Triggering In Pictures

Two stubs in the muon chambers

Two tracks in the XFTpT > 1.5 GeV

A good match between them (nominally 5 degrees)

Leve

l 3

Mass between 2.6-4.0 GeVOpposite chargeGood match in r- planeFair match in r-z plane

Leve

l 1

(This event can’t really be a J/ – it’s shown for illustrative purposes only)

16

Measuring the Cross-Section

Ingredients– Number of J/’s– Integrated Luminosity– Detector Acceptance– Detector & Trigger Efficiency

• Product of several sub-efficiencies: Level-1 trigger, Level-3 trigger, tracking and muon reconstruction

A

JN

L)/(

I will attack the denominator first

17

Luminosity

We used 39.7 ± 2.7 pb-1 of data in this measurement– At the time we started, this was the largest single contiguous chunk of data

with common trigger conditions (February-October 2002)– Even this is broken into two pieces

• 24 pb-1 taken with () < 129o required in the trigger

– Kills low pT J/’s (oops!)

• 15 pb-1 taken with this cut removed– Uncertainty is due to uncertainties at every step of the chain

• Connecting our luminosity counter response to the total inelastic cross-section

• Connecting the total inelastic cross-section to the total elastic cross-section (strictly speaking, the imaginary part of the forward scattering amplitude)

• Connecting the total elastic cross-section to the QED Coloumb part of the elastic cross-section, which is calculable

• Theoretical extrapolation between 1800 GeV (where many of the measurements have been taken) and 1960 GeV (the Run II energy)

• After all this, ± 5.9% is what we end up with

18

Level 1 Trigger Efficiency

We also have a one-muon trigger with somewhat different requirements than the dimuon trigger

J/ events that pass this trigger have an unbiased second leg

We see how often this second leg does pass the trigger vs. pT

Note that this efficiency is for events that pass all subsequent analysis cuts

19

Other Efficiencies

The Level 3 and online muon reconstruction code is identical – so the efficiencies are 100% correlated

– Inefficiencies vary with pT and average 1.4 ± 1.0%

– Inefficiencies are due to events failing the tight (3) track-stub matching• Failing muons either

– have an early wide-angle scatter as the enter the absorber– scatter more often than typical muons

– Efficiency is determined by relaxing this requirement and counting the J/’s that have one leg fail

Offline Tracking Efficiency– Measured by embedding Monte Carlo tracks in data events and extracting

them again– Efficiency is 99.6% (+0.4%, -0.9%)– Results are consistent with W → e events that come in on a trackless trigger

The Level 3 Tracking efficiency is measured like the L1 efficiency– One unbiased leg

– Efficiency is 99.7 ± 0.1 ± 0.2%

20

Acceptance Calculation

Use a Monte Carlo with just the J/ tracks

– Any confusion with the rest of the event has been taken out already in the tracking efficiency

Apply the same geometric requirements to the MC as in the data

– Dead region near z=0 in the central tracker excluded

– Inefficient muon wedge (HV problems with field shaping) excluded

– Minor trigger error with one trigger card modeled and included

21

Is that bump at low pT real?

~zero pThigh pT

low pT

The threshold for a muon to penetrate the steelis 1.44 GeV, and the threshold to pass the triggeris 1.5 GeV – both close to ½ the J/ mass.

At rest, both muons are above threshold.At high pT, both muons are above threshold.With just a little boost, though, one muonis usually below threshold and ranges out.

22

Acceptance vs. rapidity

Our acceptance in rapidity is driven by the length of the muon chambers (± 0.6 units)

There is almost no correlation between acceptance in pT and in y.

We calculate the acceptance in 2-D bins of pT and y anyway.

23

Acceptance vs. J/ “polarization”

J/’s are always produced unpolarized (<Sz> = 0)

They can, however, have “alignment” or “tensor polarization”

– i.e. the density matrix is not equally populated

– (<Sz2> > 0)

– Gives a 1+ cos2() distribution– Symmetry of the J/ decay is a

function of , so alignment affects the acceptance

• Affects when the softer muon ranges out

We use = 0.15 ± 0.3– Mix of prompt and bottom J/’s– This corresponds to a 5-10%

effect on the acceptanceRun I Data

24

J/ Signal

We have hundreds of thousands of events; we will not be statisticslimited except at the very highestpT bins.

Raw pT spectrum

25

J/ yield in selected pT bins

pT < 250 MeV (lowest bin) 5.0 < pT < 5.5 GeV 12 < pT < 14 GeV

Yield is fit in each bin, corrected for acceptance and efficiency,and the cross-section bin-by-bin is calculated.

There is very little feeddown from bin to bin (because the resolution is good and our bins are narrow) but we do correct for it.

26

Systematic Uncertainties

p T d

epen

dent

p T

inde

pend

ent

The pT dependentterms tend to belargest at very smalltransverse momenta:The first few bins.

Polarization/Alignment 2 to 5%J/Psi spectrum 0 to 5%Detector Material 0.4 to 5%Fitting Technique -0.3 to +9%Momentum Scale -0.3 to +0.7%Luminosity 6.0%Reconstruction Efficiency 2.8%Muon Simulation 1%Data Quality Selection 1%L1 Trigger Efficiency 1.5%

Combined: about 7% systematic uncertainty

27

The J/ Cross-Section

nb1240)/( 3528

JBF (for |y| < 0.6)

28

The J/ cross-sectionin terms of pT

2

Results are in excellent agreement with Run I, where there is overlap (pT > 4 GeV)

(both in normalization and shape)

29

Sherman, set the Wayback Machine for 1989.

Turning to b production…

But First, A Little History

30

Ancient History: The Stone Age (1989)

P. Nason, S. Dawson and R.K. Ellis calculated the heavy flavor cross-section and found it to be in agreement with UA1 measurements at 630 GeV. – See Nucl. Phys.

B327, 49

31

Understanding the x-axis:pT(min)

Ideally, one would like to measure the differential cross-section d/dpT.

– Allows comparison with theory in magnitude and shape of the cross-section.

If this is difficult, one could quote just the total cross-section.

– Many experiments are insensitive to the cross-section below a pT threshold.

– It makes no sense to quote the total cross-section if you have no acceptance to anything below (e.g.) 10 GeV, where the bulk of the cross-section is.

– To deal with this, experiments quote the cross-section at a certain pT(min): the point where 90% of the b’s lie above.

• This 90% is pure convention – we could have picked some other number• We had to pick something, so we follow the UA1 convention

32

Ancient History:The Bronze Age (1992)

At DPF92, CDF reported bottom quark cross-sections a factor of at least two greater than theory.

This was at a center of mass energy of 1800 GeV.

33

A Jump Ahead to 1997

More recent CDF measurements show the same difficulty – the theory underpredicts the data by the same factor

This problem is not going away

Note that we measure only the high pT tail of the cross-section

– Most b’s were invisible to us.

34

Commentary on measuring the top 10% of something

Just how important could the other 90%

be anyway?

35

Questions one might ask

Is the cross-section rising with center-of-mass energy faster than we expect?

– If we take the measurements at face value, that’s what we would conclude

– Not a completely crazy idea• the NLO contributions are larger at 1800 GeV than 630 GeV• The scale dependence of the calculation is worse at NLO than LO

– This is due to a numerical accident, but was not widely known at this time– Large NNLO contributions might produce additional growth with center-of-mass

energy

Did (at least) one experiment get the measurement wrong?

Is something wrong with our theoretical models?

– Extra b sources? (ANL group)

– Fragmentation? (P. Nason et al.)

Is there anything we can do to put the experimental result on a more solid footing?

36

The Enlightenment (1995-6)

In the winter of 1995-6, we ran for 9 days at 630 GeV to address this question.

– We estimated 50 to 100 b’s at the lower energy, depending on whether this factor of 2 was real or not.

– Not many, but enough to measure a factor of 2

At the same time, we could collect jets and photons and do other QCD measurements

– Several Ph.D. theses have resulted from these measurements, and they were important in untangling the high ET jet excess

– Eleven papers were published by CDF and D0 based on this data

– This run was proposed and largely executed by ~6 people

37

The Dark Ages: 1995-2000 &The Renaissance: 2001-2002

Work beyond the preliminary stages stopped – the CDF upgrade expanded to consume all available time

– 4 Lehman reviews

– $3.6 million dollars

– 15 change requests

– innumerable monthly reports

– Yellowing scintillator• Not yellow like Coors beer• Yellow like a lemon

– shady vendors

– squabbling collaborators…

Only when the upgrade was behind us did this start moving again – see Phys.Rev.D66:032002,2002

And this was just the muon upgrade!

38

The Measurement: Some Key Ideas

We measure a ratio of cross-sections because it is both theoretically better determined and experimentally more certain

– Theory uncertainty is 10-15% rather than a factor of 2 or more

This measurement is statistically limited by the number of bottom events collected at 630 GeV

– Complications to improve understanding of other aspects like acceptance or efficiency will make a minimal impact on the final answer

We took pains to make the 1800 GeV sample as similar to the 630 GeV sample as possible.

– We rejected larger samples with more differences – for example, we could have used a sample that used an earlier version of our silicon detector, but we didn’t.

– Every event is taken within 3 weeks of the 630 GeV run• Much of this sample is taken from the period at 1800 GeV where we tested

the 630 GeV trigger table

39

Luminosity and Datasets

Run I CDF used a three tier trigger. For this analysis, we required– Level 1: a 6 GeV muon “stub” in the central muon chambers, plus at least 2

hits in the corresponding outer chamber– Level 2: that stub matched to a 4.7 GeV r- track– Level 3: a 4.5 GeV muon with good matching to both the inner and outer muon

chambers

Offline, we required– A 5 GeV muon with a good match between the track and the muon stub

These are the same requirements for both 630 and 1800 GeV

Integrated luminosity:– At 1800 GeV: 1932 nb-1

– At 630 GeV: 582 nb-1

40

Finding Beautiful Hadrons

Start with a beautiful muon– I will spare you the details

Find all the tracks with pT above 1 GeV and m(h) < 5.3 GeV in a cone of R < 1 around the muon

Select the highest pT track

Find the vertex of that track and the muon

Perform quality cuts– Again, I’ll spare you the details

Count the excess of events with the vertex forward of the interaction point vs. behind the interaction point

Interaction Point

Lxy

muon

hadron

The Goldilocks Principle:

Inclusive semileptonic decays are too impure. Exclusive decays are too rare. These are just right.

41

Counting b’s at 1800 GeV

3083 events ahead of the primary vertex (by at least 250 m)

1527 events behind

Yield is 1556 ± 68 bottom events

Lifetime (as a check) is 1.4 ± 0.1ps

42

Counting b’s at 630 GeV

383 events ahead of the primary vertex (by at least 250 m)

200 events behind

Yield is 183 ± 24

– You don’t get many b’s in a short, low energy run

Lifetime is 1.4 ± 0.3 ps

43

Cross-Section Ratio

We can put it all together to find the cross-section ratio

Comparison with NDE predictions and MRS-A’ parton densities is good

– Other PDF’s (MRSA, CTEQ 6M) give essentially the same prediction

012.024.171.)1800(

)630(

75.10

75.10

T

T

pb

pb

44

Comparison with UA1

We take the CDF measured b cross-section at 1800 GeV, multiply it by the derived ratio, and place the cross-section obtained on the UA1 plot.

It shows– We are a factor of ~2 higher

than NLO QCD• How could it be

otherwise?– We have smaller error bars

than UA1• This is the best single

measurement of the b cross section at these energies!

45

Summary of 630 GeV Run

CDF is marginally consistent with UA1– Reject UA1 at 90% confidence level– Fail to reject UA1 at 95% confidence level

The CDF central value is above theoretical predictions by a similar factor at 630 GeV as at 1800 GeV

There is no indication as to why this is– But we can exclude the cross section growing with center of mass energy

Precision measurements are possible in heavy flavor production experiments– Uncertainties of ~15%, not factors of 2

It’s a heckuva lot of fun to propose and run your own small experiment– And 11 papers out of 9 days of running is not too shabby…

46

Back to 1960 GeV:The b cross-section using J/s

Basic strategy:– We know the J/ cross-section– We know the branching fraction of b’s to J/’s (about 1.1%)– If we can measure the fraction of J/’s from b’s, we’re one multiplication and

one division away from the b quark cross-section Lifetime is the key

– B hadrons live ~1.5 ps– We can use the SVX (silicon vertex detector) to identify J/’s that were not

produced at the primary vertex – these must be from b decay. Complications

– The most probable decay time is zero: some b’s are identified as non-b’s– Our measurement is not perfect: some non-b’s are identified as b’s.– Slowly moving b hadrons don’t get very far before they decay

• Separation power is poor at low pT

47

Two acceptance complications

For us to separate prompt and non-prompt b’s accurately, we need to impose tight silicon requirements

– No more than one hit missed

– At least three hits

– Avoid “bad regions” – e.g. crossing silicon barrels

– Since we have some dead silicon ladders, these requirements may sculpt the acceptance (only about 1 in 3 J/’s have both muons pass these criteria)

• Events where we can measure the b fraction may not be representative of unbiased J/’s.

– We checked this, and the acceptance ratio (good silicon/total) is flat in pT(J/)

The spin alignment parameter is different for b’s and inclusive J/’s

– This means the acceptance is different • We have to (and do) correct for this: it’s a ~10% effect• For prompt J/’s we use our Run I measurement• For b’s, we take the (better & more recent) BaBar measurement and boost into our

frame– This is not entirely trivial, since BaBar measures this in the (4S) frame

– (BaBar) = -0.09 ± 0.10

48

Choice of Separation Variable

Variables of Interest

– Rxy

• The transverse flight distance• Has the best separation power

– Lxy

• The transverse flight distance dotted into the unit momentum vector

• Differs from Rxy by cos()

• A signed quantity

– Pseudo-c• Lxy boosted to B rest frame based on average

boost derived from MC

• Differs from Lxy by a known multiplicative constant

– c• The true B lifetime

• Differs from Rxy by an unknown multiplicative constant

+ +p(y)

p(B)

Rxy

Lxy

We use Lxy/pT: we trade statisticalseparation power for better control over systematics. The “/pT”corrects for the Lorentz boost

49

A word on b decay kinematics

Above 2 GeV, <pT(b)> is proportional to <pT ()>

Below 1.5 GeV, <pT(b)> is more or less constant

– This is because <pT()> is driven largely by the b decay kinematics, not by the b production dynamics

The <Rxy> distribution looks like this as well (it has to)

The <Lxy> distribution looks qualitatively like this

Once we get to J/’s of pT < 1.7 GeV or so, we are probing b’s down to pT’s of 0.

50

Fitting the B fraction

Prompt component

– Resolution function is determined from the zero-lifetime component

– Double-Gaussian with some small tails at large negative lifetime

B component

– Exponential convolved with the resolution function determined from the prompt component

Sidebands

– We assume the background under the J/ mass peak is modeled by the weighted average of the sidebands

– Note that there are B’s (double semileptonic decays) in the sidebands

51

Fitting bin-by-bin

1.25 < pT < 1.5 GeV (lowest bin) 5.0 < pT < 5.5 GeV 10 < pT < 12 GeV

9.7 ± 1.0 % b’s 14.3 ± 0.5 % b’s 27.9 ± 1.0 % b’s

52

Table of Systematic Uncertainties

Source UncertaintyResolution function model 0.5-8%MC production spectrum 2-7%MC decay spectrum 0.5-3%Inclusive b-hadron lifetime 0.5-4%Background fit model 0-2 %Fit bias 0-2 %Inclusive J/psi cross-section (I) 5-11%Inclusive J/psi cross-section (II) 6.9%

pT dependent

pT independent

Again, the systematics are largest in the low pT bins

53

The Fraction of J/’s from b’s

The trend is clear

– High transverse momentum means a larger beauty component

“Flattening out” at low pT is because the J/ pT is dominated by B decay kinematics, not pT(B)

54

Why is our lowest bin at 1.25 GeV?

The fit has problems converging down here– It’s bitten by four factors at once:

• The b fraction is small: about 9%• The J/ acceptance (and therefore yield) is small

– At 1 GeV, acceptance is 20% of what it is at 2 GeV• The variable Lxy (=Rxy cos() ) loses separation power

– Not because the flight distance is small– Because the J/ flight direction is no longer aligned along the b

flight direction– B’s are being miscategorized as prompt

• The sideband subtraction becomes less certain:– We lose the left sideband

However, we have already reached pT(b) = 0 at 1.25 GeV

– Pushing lower improves the precision of our measurement, but

– it does not improve the pT reach!

55

The J/-from-b Cross-section

We almost get to the turnover at low pT.

This is what we considerthe primary measurementand should be used tocompare with theory – points are uncorrelated

Approximately 80%of the cross-sectionis measured.

56

Unfolding the Spectrum

We know the region of J/ pT will be populated by a B of a given pT

– From Monte Carlo– Nothing mysterious – this is the measured (CLEO,

BaBar, Belle) pT distribution plus a Lorentz boost

We can use this to find the parent B-hadron spectrum that gives rise to the measured J/ spectrum

– We use an iterative method– Process converges after 2-3 passes. We use 10

passes.– The bins in the B-hadron spectrum will be

correlated.

57

The B-hadron Cross-Section

nbBFyHpp b6.24.24.05.24)6.0||,(

58

…and in terms of pT2

Note that even at pT = 0the deconvolution resultis free of artifacts.

59

Does this Agree with Run I?

The J/ inclusive cross-section matches to within a few percent where we have overlap (pT > 5 GeV)

– Run I: 17.4 ± 0.1 ± 2.7 nb

– Run II: 16.88 ± 0.12 ± ~2 nb The b fraction is the same to within a few percent We can put in and take out the appropriate branching fractions, and

convert this to a B+ cross-section

– Run IA: 2.7 ± 0.6 nb

– Run 1B: 3.6 ± 0.6 nb This measurement 2.75 ± 0.20 nb

One would expect from center of mass energy the cross-section to be ~10% higher than Run I. It’s 15% lower (but consistent within uncertainties)

60

More on Run I Comparisons

One would expect from center of mass energy the cross-section to be ~10% higher than Run I. It’s 15% lower (but consistent within uncertainties)

B cross-section J/ cross-section

61

The Total Cross-Section

We can correct this to (b):– Remove the 5.88% J/ branching fraction to mu pairs– Remove the 1.16% b-hadron (inclusive) branching fraction

to J/ + X– Correct to ±1.0 units of rapidity vs. ±0.6– Divide by two to get the single flavor b cross-section

b 1.49.34.04.29

NLO QCD predicts 20-40 b

62

What Does this All Mean?

Experimentally:

– The high pT 10% or so of the b cross-section agrees with past measurements: a factor of 2-3 above theory

– The total cross-section agrees with theory

– Conclusion: the pT spectrum is stiffer (shifted to higher transverse momenta) than predicted

Theoretically:

– “Theory” is a fixed order calculation (NLO)

– At LO, you have only 2 → 2 processes

– At NLO, you add gluon radiation to those 2 → 2 processes• Simplistic model: one b gets its transverse momentum increased, the other one gets

its transverse momentum decreased. Because there is a steeply falling spectrum, this produces a net stiffening of the spectrum.

– At NLO, you also add new processes – gluon splitting, flavor excitation• These processes double the cross-section• The stiffening effect in the 2 → 2 processes doesn’t kick in until NNLO

– It may not be crazy to think that the spectrum predicted at NLO will be softer than that predicted by NNLO

63

Detailed comparison with theory

Agreement with modern theory is substantially better

– No more factor of 2

Experimental uncertainties are now ~3x smaller than theoretical uncertainties

Theory: Cacciari, Frixione, Mangano, Nason & Ridolfi hep-ph/0312132

64

Theoretical Developments

PDF’s have changed– About a 20% effect

Calculations now available to NLL– About a 20% effect

Fragmentation functions have changed– remember, pQCD predicts quark

production, but experiments measure hadron production

– Fragmentation cannot change the total cross section, but does change the spectrum

– About a 20-50% effect

Fro

m M

. M

angano

All these pull in the same direction, so the agreement is now substantially better than in the past.

65

The Joy of X: X(3872)

At Lepton-Photon 2003, Belle announced a new charmonium state seen in B decays

– You don’t get a new charmonium state every day– Much less an unpredicted one!

(2S)

m(J/ +-) - m(J/)

Belle304M B’s

Eve

nts/

10 M

eV

?

Blow-up of right-hand peak

66

More Joy of X

With a speed uncharacteristic of hadron colliders, both CDF and D0 confirmed this particle

– Also, they identified that it is produced both promptly and in B decays

D0

67

What is the cause of all the X-Citement?

Charmonium?– It has to have the right quantum numbers to decay to and

– It has to have the wrong quantum numbers to decay to a pair of D-mesons

Some Options are:– hc: (1P1) – mass too low: should be near the center of mass of the ’s, or 3525 GeV

– First radial excitation h’c: 1P1(2P) – okay, so where is the regular hc then?

– 2: (3D2): potential models predict this around 3790 MeV

• Why the peak in the wrong spot?

• Should also decay to 1 + : not observed

• Prediction exists for the m() spectrum – agreement not great

– h3c: (1F3): potential models predict this around 4000 MeV

• Again, why is the peak in the wrong spot?• No quantitative prediction exists for the m() spectrum, but since the two pions are

in a relative l = 2 state, the centrifugal barrier will favor a large m().

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Dipion Mass X-perimental Results

Belle shows the dipion mass distribution to be peaked at high m() for the (2S).

This was explained by Brown and Cahn (1975) as a consequence of chiral symmetry.

I find the paper somewhat difficult to follow: “by theorists, for theorists.”

Belle’s measurement of m() is peaked at large mass.

CDF confirms this qualitatively.

Obscure and under-noticed m() prediction by Yan.Note the D-wave is not so prominent at high mass.

BelleBelle

69

X-otic possibilities

No charmonium states seem to match the data– If it’s charmonium, there’s something we don’t understand also going on

– This may be related to the state’s proximity to DD* threshold

Could this be a bound state of a D and an anti-D*?– Naturally explains the mass – just under threshold

– We know hadrons bind – we’re made of bound hadrons!• Not only are there nuclei in QCD, there are “hypernuclei”

– The high m() may be from the decay + • But watch out – the kinematics are such that any high mass enhancement

looks like a

– There may be precedent with a kaon anti-kaon bound state in the f0(980) and it’s isotriplet partner the a0(980)

• These are 0++ states that fit poorly into the meson nonet

• The f0 is narrow on the low mass side, where it decays to , but wide on the high mass side, where it decays to KK

• Other, more advanced arguments: c.f. Jaffe and Weinstein

– Expected quantum numbers: 1++ Hot Off The Presses: angular distributions from CDF: the acceptable fits are 1++ and 2-+

A new kind ofstrongly interacting matter?

70

Summary

We have a measurement of the J/ cross-section at all pT

– The cross-sections violently contradict the Color Singlet Model– The cross-sections are self-consistent with the Color Octet Model– The spin-alignment data agrees poorly with the COM

• This measurement is being repeated with the larger Run II dataset

At DPF92, it was asked “why is CDF’s b cross-section so high?”

– Twelve years later we have an answer: “It isn’t – just the high pT tail is high”

– Theory now explains the data quantitatively at both 630 and 1800 GeV

30 years after its discovery, charmonium still has the potential to surprise us – what is this X?

– D-D* molecule seems to fit many of the observed properties

71

Backup Slides

72

J/ Spin Alignment, Run I vs. Run II

Agreement between Run I and Run II is poor, and not well understood. Agreement between flipped sign Run I and Run II is better, but still not good.

73

Accelerator Operations at 630 GeV

The Good News: the Tevatron had to operate at 630 GeV to get to 1800 GeV The Bad News: Tevatron collisions at 630 GeV had not been attempted

before. Recall the Luminosity Equation:

)(2

)()(*

pp

pNpNf

L

74

Going to 630 GeV

= (normalized)/6– The Luminosity drops by a factor 630/1800 = 0.35

We have a choice with *

– We can either run the focusing magnets at their nominal current• That keeps * the same.• That requires more beam tuning, since it’s a new Tevatron lattice

– Or we can keep the accelerator lattice the same by running them at 35% of their nominal current

• This lowers * to 0.35 of its nominal• But it keeps the operating point the same – machine comes on

faster• We chose this deliberately (however, there is some evidence

things were better than this) The net effect is a factor of ~10 loss in luminosity

75

Implications

The luminosity is an order of magnitude lower at 630 GeV.

– 9 days at 630 GeV = 1 day at 1800 GeV The cross-section is a factor of ~6 lower at 630 GeV

– So now we have an equivalent of four hours worth of 1800 GeV data

We need to grab every b decay that we can

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The CDF Detector

This analysis uses only trackingand central muon detectors

77

Events Behind the Primary Vertex

When we subtract the events behind the primary, we are subtracting mostly background, but possibly some signal.

What happens if a real b hadron gets reconstructed behind the primary vertex?– So long as the fraction of times when this happens is the same at both

energies, the ratio measurement is unaffected– Several Monte Carlos were run

• All show that this ratio to be small (few %)• There is some variation between MC’s on this exact number• All show this effect to be the same at both energies

It turns out that if you don’t even try to subtract the background, the result changes by less than ½

– We could have done this analysis from trigger rates– (But we didn’t know this until after we did the work)

Because of all of this, we believe this is not a problem.

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Quality Cuts

Muon– Detected in inner and outer

central muon detectors• Behind ~5 and ~8 of steel

– Good match between extrapolated track and detected muon

– pT > 5 GeV

– At least 3 hits (of 4) on the silicon track

Hadron

– pT > 1 GeV

– At least 3 hits on the silicon track

Combination– Vertex P(2) > 1%– 1.5 < m(h) < 5.3 GeV

• Consistent with bottom• Rejects charm

– |Lxy| > 250 m

– If the highest pT track does not make a combination passing these cuts, the event is rejected.

• If one tries another track instead, the results change only minimally. Most of the added events are at short life-time

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Elements of the Cross-Section Ratio

Luminosity ratio Acceptance ratio Yield ratio Efficiency ratio (e.g. detector aging) is taken to be unity

1800630630

63018001800

)(

)(

)1800(

)630(

bNAL

bNAL

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Relative Luminosity Determination

The total cross-section is different at the two energies, and we correct for that

– Some of the 1800 GeV data was taken with the 630 GeV trigger table (as a test run), and this fools our luminosity calculation into thinking it was really taken at 630 GeV. We correct for this.

The 1800 GeV data is dynamically prescaled

– Effective prescale is 3.07 ± 0.07• Determined by seeing how many 12 GeV muons pass the

prescaled trigger • Agrees with prescale bookkeeping within uncertainties

L(630)/L(1800) = 0.926 ± 0.058

– This includes only those uncertainties that do NOT cancel in the ratio

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Acceptance Calculation

Part I: Monte Carlo

– Generate 10,000,000 b’s with our fast Monte Carlo

– Minimum b pT of 6.75 GeV

– Fragment with Peterson ( = 0.006)

– Decay with CLEO’s Monte Carlo (QQ Version 9.0)• No decays are forced to muons• Allows us to keep muons from charm daughters (5-18%)

– Simulate with our parametric simulator

– Count b’s passing cuts, with negative Lxy subtracted off

Results

– 1800 GeV: 4045 ± 67 pass

– 630 GeV: 2850 ± 56 pass

82

Acceptance Calculation II

Part II: We want to quote the cross-section above pT(min)

– That’s the point which 90% of our b’s are above

– It works out to 10.75 GeV

– This adds an additional acceptance correction of 1.282 ± 0.007• The uncertainty is from varying the b mass and scale

Part III: Beam Profile:

– The silicon acceptance is not the same at the two energies• The beam is wider and more off-center at 630 GeV• These two effects partially cancel

– This imposes an additional 0.817 ± 0.014 correction

– Calculated by counting high pT muons in and out of the SVX

A(630)/A(1800) = 0.738 ± 0.023

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Do we agree with UA1?

Under the assumption that we agree:

– The probability that we would get a result at least as high as we got is 1 in 16

– The probability that we would get a result at least as discrepant is 1 in 8

– Both calculations assume that the systematic uncertainties are Gaussian (which is almost certainly not true)

Paper statement: “…our measurement [is] above the UA1 value, but not so far above that the measurements would be inconsistent at the 95% confidence level”

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The Trouble With Gluons

Remember, we know that J/ → gg is forbidden

– J/ is a 3S1 (1--) state

– Violates charge conjugation parity• Left side is C odd, right is C even

– If that isn’t bad enough, spin-statistics forces the amplitude to be zero

That means gg → J/ is also forbidden ggg → J/ requires a 3-body collision

– Infinitesimal rateThere seems to be no mechanismthat allows gluons to fuse intoa 3S1 state like the J/

85

What about Color Evaporation?

Basic idea: – charm-anticharm pairs are produced

in a color octet state– These quarks emit one or more gluons in the process of forming a

colorless charmonium meson– No attempt to understand this microscopic behavior in detail is

made• Many theorists find this unsatisfying

Predictions?– Not many – most of the information gets washed out during the

color evaporation• Many experimentalists find this unsatisfying

– Relative yields of different charmonium states goes as ~(2J+1)• This actually agrees rather well with the data

– Small or zero spin-alignment parameter

The red-headed stepchild of quarkonium production theories