# Presentation: 542003

## Bottom Quark and J/Production at CDF

*Thomas J. LeCompte*
- High Energy Physics DivisionArgonne National Laboratory
*For the CDF Collaboration*

## 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

## 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 “almost
- nonrelativistic”:  ~ 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.

- Mass

-  threshold

## Review: Quantum Numbers

***Review: Quantum Numbers***

- Total Angular Momentum

- Orbital Angular Momentum

- Spin Angular Momentum

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

- Means:
-    Total J/ Spin = 1
-    Parity is Odd
-    Charge Conjugation is Odd

## 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

- OZI Rule

- Color Singlet Model

## 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.

## 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!

## 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

- 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

## 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.

## Fitting COM Parameters

- A consistent set of COM parameters can predict reproduceboth the measured J/ and (2S) cross-sectionsA major success of the model!

## 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).

## The CDF Detector: All you need to know

- Central Muon (CMU) detectors:2304 wire chambers

- Central Calorimeter:
- For this analysis, it’s used
- as passive steel, lead and
- plastic absorbers (4.7)

- Open cell tracker: wire
- Chamber in 1.5T magneticfield (COT)

- Silicon vertex detector
- (SVX) – five layers for
- Precision track measurement

- Beams-eye view of CDF

## The CDF Detector:More Than You Need To Know

- Silicon Vertex Detector being installed

- CDF rolling into the collision hall

- (uphill both ways)

## 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*

## 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)

- Level 3

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

- Level 1

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

## 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*

- I will attack the denominator first

## 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 ****(****) < 129**o** 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*

## 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

## 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%

## 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

## Is that bump at low pT real?

- ~zero pT

- high pT

- low pT

- The threshold for a muon to penetrate the steel
- is 1.44 GeV, and the threshold to pass the triggeris 1.5 GeV – both close to 1⁄2 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 muon
- is usually below threshold and ranges out.

## 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.

## 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 acceptance

- Run I Data

## J/ Signal

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

- Raw pT spectrum

## 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.

## Systematic Uncertainties

- pT dependent

- pT independent

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

**Combined: about 7% systematic uncertainty**

## The J/ Cross-Section

- (for |y| < 0.6)

## The J/ cross-sectionin terms of pT2

- Results are in excellent agreement with Run I, where there is overlap (pT > 4 GeV)
- (both in normalization and shape)

## Turning to b production...

**Sherman, set the Wayback Machine for 1989.**

***Turning to b production...***

**But First, A Little History**

## 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

## Understanding the x-axis:pT(min)

- Ideally, one would like to measure the differential cross-section d/d*p**T*.
- 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 *p**T* 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 *p**T*(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*

## 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.

## 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.

## Commentary on measuring the top 10% of something

- Just how important could the other 90% be anyway?

## 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?

## 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 *E**T* jet excess
- Eleven papers were published by CDF and D0 based on this data
- This run was proposed and largely executed by ~6 people

## 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!

## 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*

## 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

## Finding Beautiful Hadrons

- Start with a beautiful muon
- I will spare you the details
- Find all the tracks with *p**T* above 1 GeV and *m*(*h*) < 5.3 GeV in a cone of R < 1 around the muon
- Select the highest *p**T* 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.

## 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

## 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

## 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

## 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!*

## 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...

## 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 p**T*

## 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

## 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 R**xy** by cos(****) *
*A *signed* quantity*
- Pseudo-c
*L**xy** boosted to B rest frame based on average boost derived from MC*
*Differs from L**xy** by a known multiplicative constant*
- c
*The true B lifetime*
*Differs from R**xy** by an *unknown* **multiplicative constant*

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

## 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.

## 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

## 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

## Table of Systematic Uncertainties

- pT dependent

- pT independent

- Again, the systematics are largest in the low pT bins

## 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)

## 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!

## 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.

## 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.

## The B-hadron Cross-Section

## ...and in terms of pT2

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

## 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)

## 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

## 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

- NLO QCD predicts 20-40 b

## 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

## 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

## 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

- From M. Mangano

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

## 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!

- Blow-up of right-hand peak

## 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

## 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(****).*

## 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.

- Belle

- Belle

## 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 f**0** 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?

## 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

## Backup Slides

## 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.

## 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:

## 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

## 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

## The CDF Detector

- This analysis uses only trackingand central muon detectors

## 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 1⁄2 
- 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.

## 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
*p**T* > 5 GeV
- At least 3 hits (of 4) on the silicon track
- Hadron
*p**T* > 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 *p**T* 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 *

## Elements of the Cross-Section Ratio

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

## 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

## Acceptance Calculation

- Part I: Monte Carlo
- Generate 10,000,000 *b*’s with our fast Monte Carlo
- Minimum *b* *p**T* 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

## Acceptance Calculation II

- Part II: We want to quote the cross-section above *p**T*(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 *p**T* muons in and out of the SVX
- A(630)/A(1800) = 0.738 ± 0.023

## 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”

## 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 rate

- There seems to be no mechanismthat allows  gluons to fuse intoa 3S1 state like the J/

## 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