Combinatorial background subtraction for e+e- signals

It is common to use the formula 2*sqrt(N++ N--) to model the combinatorial background when studying e+e- signals, e.g. for J/psi and Upsilon analyses.  We can obtain this formula in the following way.

Assume we have an event in which there are Nsig particles that decay into e+e- pairs.  Since each decay generates one + and one - particle, the total number of unlike sign combinations we can make is N+- = Nsig². To obtain the total number of pairs that are just random combinations, we subtract the number of pairs that came from a real decay.  So we have

N+-_comb=Nsig²-Nsig=Nsig(Nsig-1)

For the number of like-sign combinations, for example for the ++ combinations, there will be a total of (Nsig-1) pairs that can be made by the first positron, then (Nsig-2) that can be made by the second positron, and so on.  So the total number of ++ combinations will be

N++ = (Nsig-1) + (Nsig - 2) + ... + (Nsig - (Nsig-1)) + (Nsig-Nsig)

Where there are Nsig terms. Factoring, we get:

N++ = Nsig² - (1+2+...+Nsig) = Nsig² - (Nsig(Nsig+1))/2 = (Nsig² - Nsig)/2=Nsig(Nsig-1)/2

Similarly,

N-- = Nsig(Nsig-1)/2

If there are no acceptance effects, either the N++ or the N-- combinations can be used to model the combinatorial background by simply multiplying them by 2.  The geometric average also works:

2*sqrt(N++ N--) = 2*Nsig(Nsig-1)/sqrt(4) = Nsig(Nsig-1) = N+-_comb.

The geometric average can also work for cases where there are acceptance differences, with the addition of a multiplicative correction factor R to take the relative acceptance of ++ and -- pairs into account. So the geometric average is for the case R=1 (similar acceptance for ++ and --).

Estimating Acceptance Uncertainty due to unknown Upsilon Polarization

The acceptance of Upsilon decays depends on the polarization of the Upsilon.  We do not have enough statistics to measure the polarization.  It is also not clear even at higher energies if there is a definite pattern: there are discrepancies between CDF and D0 about the polarization of the 1S.  The 2S and 3S show different polarizations trends than the 1S. So for the purposes of the paper, we will estimate the uncertainty due to the unknown Upsilon polarization using two extremes: fully transverse and fully longitudinal polarization.  This is likely an overestimate, but the effect is not the dominant source of uncertainty, so for the paper it is good enough.

There are simulations of the expected acceptance for the unpolarized, longitudinal and transverse cases done by Thomas:

http://www.star.bnl.gov/protected/heavy/ullrich/ups-pol.pdf

Using the pT dependence of the acceptance for the three cases (see page 9 of the PDF) we must then apply it to our measured upsilons.  We do this by obtaining the pT distribution of the unlike sign pairs (after subtracting the like-sign combinatorial background) in the Upsilon mass region and with |y|<0.5.  This is shown below as the black data points.

The data points are fit with a function of the form A p_T²  exp(-p_T/T), shown as the solid black line (fit result: A=18.0 +/- 8.3, T = 1.36 +/- 0.16 GeV/c).  We then apply the correction for the three cases, shown in the histograms (with narrow line width).  The black is the correction for the unpolarized case (default), the red is for the longitudinal and the blue is for the transverse case.  The raw yield can be obtained by integrating the histogram or the function.  These give 89.7 (histo) and 89.9 (fit), which given the size of the errors is a reasonable fit.  We can obtain the acceptance corrected  yield (we ignore all other corrections here) by integrating the histograms, which give:

• Unpol: 158.9 counts
• Trans: 156.4 counts
• Longi: 163.6 counts

We estimate from this that fully transverse Upsilons should have a yield lower by -1.6% and fully longitudinal Upsilons should have a higher yield by 2.9%.  We use this as a systematic uncertainty in the acceptance correction. 

In addition, the geometrical acceptance can vary in the real data due to masked towers which are not accounted for in the simulation.  We estimate that this variation is of order 25 towers (which is used in the 2007 and 2008 runs as the number of towers allowed to be dynamically masked). This adds 25/4800 = 0.5% to the uncertainty in the geometrical acceptance.

Estimating Drell-Yan contribution from NLO calculation.

Ramona calculated the cross section for DY at NLO and sent the data points to us.  These were first shown in the RHIC II Science Workshop, April 2005, in her Quarkonium talk and her Drell-Yan (and Open heavy flavor) talk.

The total cross section (integral of all mass points in the region |y|<5) is 19.6 nb (Need to check if there is an additional normalization with Ramona, but the cross section found by PHENIX using Pythia is 42 nb with 100% error bar, so a 19.6 nb cross section is certainly consistent with this). She also gave us the data in the region |y|<1, where the cross section is 5.24 nb. The cross section as a function of invariant mass in the region |y|<1 is shown below.

The black curve includes a multiplication with an error function (as we did for the b-bbar case) and normalized such that the ratio between the blue and the black line is 8.5% at 10 GeV/c to account for the efficiency and acceptance found in embedding for the Upsilon 1s.  The expected counts in the region 8-11 are 20 +/- 3, where the error is given by varying the parameters of the error function within its uncertainty.  The actual uncertainty is likely bigger than this if we take into account the overall normalization uncertainty in the calculation.

I asked Ramona for the numbers in the region |y|<0.5, since that is what we use in STAR.  The corresponding plot is below.

 The integral of the data points gives 2.5 nb.  The integral of the data between 7.875 and 11.125 GeV/c2 is 42.30 pb.  The data is parameterized by the function shown in blue.  The integral of the function in the same region gives 42.25 pb, so it is quite close to the calculation.  In the region 8<m<11 GeV/c2, the integral of the funciton is 38.6 pb.  The expected counts with this calculation are 25 for both triggers.

Response to PRD referee comments on Upsilon Paper

First Round of Referee Responses

Click here for second round.

-------------------------------------------------------------------------
> Report of Referee A:
> -------------------------------------------------------------------------
>
> This is really a well-written paper. It was a pleasure to read, and I
> have only relatively minor comments.

We thank the reviewer for careful reading of our paper and for providing
useful feedback. We are pleased to know that the reviewer finds the
paper to be well written. We have incorporated all the comments into a
new version of the draft.

> Page 3: Although there aren't published pp upsilon cross sections there
> is a published R_AA and an ee mass spectrum shown in E. Atomssa's QM09
> proceedings. This should be referenced.

We are aware of the PHENIX results from
E. Atomssa, Nucl.Phys.A830:331C-334C,2009
and three other relevant QM proceedings:
P. Djawotho, J.Phys.G34:S947-950,2007
D. Das, J.Phys.G35:104153,2008
H. Liu, Nucl.Phys.A830:235C-238C,2009
However, it is STAR's policy to not reference our own preliminary data on the manuscript we submit for publication on a given topic, and by extension not to reference other preliminary experimental data on the same topic either.

>
> Page 4, end of section A: Quote trigger efficiency.
>

The end of Section A now reads:
"We find that 25% of the Upsilons produced at
midrapidity have both daughters in the BEMC acceptance and at least one
of them can fire the L0 trigger. The details of the HTTP
trigger efficiency and acceptance are discussed in Sec. IV"

> Figure 1: You should either quote L0 threshold in terms of pt, or plot
> vs. Et. Caption should say L0 HT Trigger II threshold.

We changed the figure to plot vs. E_T, which is the quantity that is
measured by the calorimeter. For the electrons in the analysis, the
difference between p_T and E_T is negligible, so the histograms in
Figure 1 are essentially unchanged. We changed the caption as suggested.

>
> Figures 3-6 would benefit from inclusion of a scaled minimum bias spectrum
> to demonstrate the rejection factor of the trigger.

We agree that it is useful to quote the rejection factor of the trigger.
We prefer to do so in the text. We added to the description of Figure
3 the following sentence: "The rejection factor achieved with Trigger
II, defined as the number of minimum bias events counted by the trigger scalers
divided by the number events where the upsilon trigger was issued, was
found to be 1.8 x 10⁵."

>
> Figure 9: There should be some explanation of the peak at E/p = 2.7
>

We investigated this peak, and we traced it to a double counting error.
The problem arose due to the fact that the figure was generated from
a pairwise Ntuple, i.e. one in which each row represented a pair of
electrons (both like-sign and unlike-sign pairs included), each with a
value of E and p, instead of a single electron Ntuple. We had plotted
the value of E/p for the electron candidate which matched all possible
high-towers in the event. The majority of events have only one candidate
pair, so there were relatively few cases where there was double
counting. We note that for pairwise quantities such as opening angle and
invariant mass, each entry in the Ntuple is still different. However,
the case that generated the peak at E/p = 2.7 in the figure was traced
to one event that had one candidate positron track, with its
corresponding high-tower, which was paired with several other electron
and positron candidates. Each of these entries has a different invariant
mass, but the same E/p for the first element of the pair. So its entry
in Figure 9, which happened to be at E/p=2.7, was repeated several times
in the histogram. The code to generate the data histogram in Figure 9
has now been corrected to guarantee that the E/p distribution is made
out of unique track-cluster positron candidates. The figure in the paper
has been updated. The new histogram shows about 5 counts in that
region. As a way to gauge the effect the double counting had on the
E/p=1 area of the figure, there were about 130 counts in the figure at
the E/p=1 peak position in the case with the double-counting error, and
there are about 120 counts in the peak after removing the
double-counting. The fix leads to an improved match between the data
histogram and the Monte Carlo simulations. We therefore leave the
efficiency calculation, which is based on the Monte Carlo Upsilon
events, unchanged. The pairwise invariant mass distribution from which
the main results of the paper are obtained is unaffected by this. We
thank the reviewer for calling our attention to this peak, which allowed
us to find and correct this error.

>
> -------------------------------------------------------------------------
> Report of Referee B:
> -------------------------------------------------------------------------
>
> The paper reports the first measurement of the upsilon (Y) cross-section
> in pp collisions at 200 GeV. This is a key piece of information, both
> in the context of the RHIC nucleus-nucleus research program and in its
> own right. The paper is rather well organized, the figures are well
> prepared and explained, and the introduction and conclusion are clearly
> written. However, in my opinion the paper is not publishable in its
> present form: some issues, which I enumerate below, should be addressed
> by the authors before that.
>
> The main problems I found with the paper have to do with the estimate
> of the errors. There are two issues:
>
> The first: the main result is obtained by integrating the counts above
> the like-sign background between 8 and 11 GeV in figure 10, quoted to
> give 75+-20 (bottom part of table III). This corresponds the sum Y +
> continuum. Now to get the Y yield, one needs to subtract an estimated
> contribution from the continuum. Independent of how this has been
> estimated, the subtraction can only introduce an additional absolute
> error. Starting from the systematic error on the counts above background,
> the error on the estimated Y yield should therefore increase, whereas
> in the table it goes down from 20 to 18.

Thanks for bringing this issue to our attention. It is true that when
subtracting two independently measured numbers, the statistical
uncertainty in the result of the subtraction can only be larger than the
absolute errors of the two numbers, i.e. if C = A - B, and error(A) and
error(B) are the corresponding errors, then the statistical error on C
would be sqrt(error(B)²+error(A)²) which would yield a larger absolute
error than either error(A) or error(B). However, the extraction of the
Upsilon yield in the analysis needs an estimate of the continuum
contribution, but the key difference is that it is not obtained by an
independent measurement. The two quantities, namely the Upsilon yield
and the continuum yield, are obtained ultimately from the same source:
the unlike sign dielectron distribution, after the subtraction of the
like-sign combinatorial background. This fact causes an
anti-correlation between the two yields, the larger the continuum yield,
the smaller the Upsilon yield. So one cannot treat the subtraction of
the continuum yield and the Upsilon yield as the case for independent
measurements. This is why in the paper we discuss that an advantage of
using the fit includes taking automatically into account the correlation
between the continuum and the Upsilon yield. So the error that is
quoted in Table III for all the "Upsilon counts", i.e. the Fitting
Results, the Bin-by-bin Counting, and the Single bin counting, is quoted
by applying the percent error on the Upsilon yield obtained from the
fitting method, which is the best way to take the anti-correlation
between the continuum yield and the Upsilon yield into account. We will
expand on this in section VI.C, to help clarify this point. We thank the referee for
alerting us.

>
> The second issue is somewhat related: the error on the counts (18/54, or
> 33%) is propagated to the cross section (38/114) as statistical error,
> and a systematic error obtained as quadratic sum of the systematic
> uncertainties listed in Table IV is quoted separately. The uncertainty on
> the subtraction of the continuum contribution (not present in Table IV),
> has completely disappeared, in spite of being identified in the text as
> "the major contribution to the systematic uncertainty" (page 14, 4 lines
> from the bottom).
>
> This is particularly puzzling, since the contribution of the continuum
> is even evaluated in the paper itself (and with an error). This whole
> part needs to be either fixed or, in case I have misunderstood what the
> authors did, substantially clarified.

We agree that this can be clarified. The error on the counts (18/54, or
33%) includes two contributions:
1) The (purely statistical) error on the unlike-sign minus like sign
subtraction, which is 20/75 or 26%, as per Table III.
2) The additional error from the continuum contribution, which we
discuss in the previous comment, and is not just a statistical sum of
the 26% statistical error and the error on the continuum, rather it must
include the anti-correlation of the continuum yield and the Upsilon
yield. The fit procedure takes this into account, and we arrive at the
combined 33% error.

The question then arises how to quote the statistical and systematic
uncertainties. One difficulty we faced is that the subtraction of the
continuum contribution is not cleanly separated between statistical and
systematic uncertainties. On the one hand, the continuum yield of 22
counts can be varied within the 1-sigma contours to be as low as 14 and
as large as 60 counts (taking the range of the DY variation from Fig.
12). This uncertainty is dominated by the statistical errors of the
dielectron invariant mass distribution from Fig. 11. Therefore, the
dominant uncertainty in the continuum subtraction procedure is
statistical, not systematic. To put it another way, if we had much
larger statistics, the uncertainty in the fit would be much reduced
also. On the other hand, there is certainly a model-dependent component
in the subtraction of the continuum, which is traditionally a systematic
uncertainty. We chose to represent the combined 33% percent error as a
statistical uncertainty because a systematic variation in the results
would have if we were to choose, say, a different model for the continuum
contribution, is smaller compared to the variation allowed by the
statistical errors in the invariant mass distribution. In other words,
the reason we included the continuum subtraction uncertainty together in
the quote of the statistical error was that its size in the current
analysis ultimately comes from the statistical precision of our
invariant mass spectrum. We agree that this is not clear in the text,
given that we list this uncertainty among all the other systematic
uncertainties, and we have modified the text to clarify this. Perhaps a
more appropriate way to characterize the 33% error is that it includes
the "statistical and fitting error", to highlight the fact that in
addition to the purely statistical errors that can be calculated from
the N++, N-- and N+- counting statistics, this error includes the
continuum subtraction error, which is based on a fit that takes into
account the statistical error on the invariant mass spectrum, and the
important anti-correlation between the continuum yield and the Upsilon
yield. We have added an explanation of these items in the updated draft of
the paper, in Sec VI.C.

>
> There are a few other issues which in my opinion should be dealt with
> before the paper is fit for publication:
>
> - in the abstract, it is stated that the Color Singlet Model (CSM)
> calculations underestimate the Y cross-section. Given that the discrepancy
> is only 2 sigma or so, such a statement is not warranted. "Seems to
> disfavour", could perhaps be used, if the authors really insist in making
> such a point (which, however, would be rather lame). The statement that
> CSM calculations underestimate the cross-section is also made in the
> conclusion. There, it is even commented, immediately after, that the
> discrepancy is only a 2 sigma effect, resulting in two contradicting
> statements back-to-back.

Our aim was mainly to be descriptive. To clarify our intent, the use of
"underestimate" is in the sense that if we move our datum point lower by the
1-sigma error of our measurement and this value is higher than the top
end of the CSM calculation. We quantify this by saying that the
size of the effect is about 2-sigma. We think that the concise statement
"understimate by 2sigma" objectively summarizes the observation, without
need to use more subjective statements, and we modified
the text in the abstract and conclusion accordingly.

>
> - on page 6 it is stated that the Trigger II cuts were calculated offline
> for Trigger I data. However, it is not clear if exactly the same trigger
> condition was applied offline on the recorded values of the original
> trigger input data or the selection was recalculated based on offline
> information. This point should be clarified.

Agreed. We have added the sentence: "The exact same trigger condition was
applied offline on the recorded values of the original trigger input data."

>
> - on page 7 it is said that PYTHIA + Y events were embedded in zero-bias
> events with a realistic distribution of vertex position. Given that
> zero-bias events are triggered on the bunch crossing, and do not
> necessarily contain a collision (and even less a reconstructed vertex),
> it is not clear what the authors mean.

We do not know if the statement that was unclear is how the realsitic
vertex distribution was obtained or if the issue pertained to where the analyzed collision comes from.
We will try to clarify both instances. The referee has correctly understood
that the zero-bias events do not necessarily contain a collision.
That is why the PYTHIA simulated event is needed. The zero-bias events
will contain additional effects such as out of time pile-up in the Time
Projection Chamber, etc. In other words, they will contain aspects of
the data-taking environment which are not captured by the PYTHIA events.
That is what is mentioned in the text:

"These zero-bias events do not always have a collision in the given
bunch crossing, but they include all the detec-
tor effects and pileup from out-of-time collisions. When
combined with simulated events, they provide the most
realistic environment to study the detector e±ciency and
acceptance."

The simulated events referred to in this text are the PYTHIA events, and
it is the simulated PYTHIA event, together with the Upsilon, that
provides the collision event to be studied for purposes of acceptance
and efficiency. In order to help clarify our meaning, we have also added
statements to point out that the dominant contribution to the TPC occupancy
is from out of time pileup.
Regarding the realistic distribution of vertices,
this is obtained from the upsilon triggered events (not from the zero-bias events, which
have no collision and typically do not have a found vertex, as the referee correctly
interpreted). We have added a statement to point this out and hopefully this will make
the meaning clear.

>
> - on page 13 the authors state that they have parametrized the
> contribution of the bbar contribution to the continuum based on a PYTHIA
> simulation. PYTHIA performs a leading order + parton shower calculation,
> while the di-electon invariant mass distribution, is sensitive to
> next-to-leading order effects via the angular correlation of the the two
> produced b quarks. Has the maginuted of this been evaluated by comparing
> PYTHIA results with those of a NLO calculation?
>

We did not do so for this paper. This is one source of systematic
uncertainty in the continuum contribution, as discussed in the previous
remarks. For this paper, the statistics in the dielectron invariant
mass distribution are such that the variation in the shape of the b-bbar
continuum between LO and NLO would not contribute a significant
variation to the Upsilon yield. This can be seen in Fig. 12, where the
fit of the continuum allows for a removal of the b-bbar yield entirely,
as long as the Drell-Yan contribution is kept. We expect to make such
comparisons with the increased statistics available in the run 2009
data, and look forward to including NLO results in the next analysis.

> - on page 13 the trigger response is emulated using a turn-on function
> parametrised from the like-sign data. Has this been cross-checked with a
> simulation? If yes, what was the result? If not, why?

We did not cross check the trigger response on the continuum with a
simulation, because a variation of the turn-on function parameters gave
a negligible variation on the extracted yields, so it was not deemed
necessary. We did use a simulation of the trigger response on simulated
Upsilons (see Fig. 6, dashed histogram).

>
> Finally, I would like to draw the attention of the authors on a few less
> important points:
>
> - on page 6 the authors repeat twice, practically with the same words,
> that the trigger rate is dominated by di-jet events with two back-to-back
> pi0 (once at the top and once near the bottom of the right-side column).

We have changed the second occurrence to avoid repetitiveness.

>
> - all the information of Table I is also contained in Table 4; why is
> Table I needed?

We agree that all the information in Table I is contained in Table 4
(except for the last row, which shows the combined efficiency for the
1S+2S+3S), so it could be removed. We have included it for convenience
only: Table I helps in the discussion of the acceptance and
efficiencies, and gives the combined overall correction factors, whereas
the Table IV helps in the discussion of the systematic uncertainties of
each item.

>
> - in table IV, the second column says "%", which is true for the
> individual values of various contributions to the systematic uncertainty,
> but not for the combined value at the bottom, which instead is given
> in picobarn.

Agreed. We have added the pb units for the Combined error at the bottom of the
table.

>
> - in the introduction (firts column, 6 lines from the bottom) the authors
> write that the observation of suppression of Y would "strongly imply"
> deconfinement. This is a funny expression: admitting that such an
> observation would imply deconfinement (which some people may not be
> prepared to do), what's the use of the adverb "strongly"? Something
> either does or does not imply something else, without degrees.

We agree that the use of "imply" does not need degrees, and we also
agree that some people might not be prepared to admit that such an
observation would imply deconfinement. We do think that such an
observation would carry substantial weight, so we have rephrased that
part to "An observation of suppression of Upsilon
production in heavy-ions relative to p+p would be a strong argument
in support of Debye screening and therefore of
deconfinement"

We thank the referee for the care in reading the manuscript and for all
the suggestions.

Second Round of Referee Responses

> I think the paper is now much improved. However,
> there is still one point (# 2) on which I would like to hear an
> explanation from the authors before approving the paper, and a
> couple of points (# 6 and 7) that I suggest the authors should
> still address.
> Main issues:
> 1) (errors on subtraction of continuum contribution)
> I think the way this is now treated in the paper is adequate
> 2) (where did the subtraction error go?)
> I also agree that the best way to estimate the error is
> to perform the fit, as is now explicitly discussed in the paper.
> Still, I am surprised, that the additional error introduced by
> the subtraction of the continuum appears to be negligible
> (the error is still 20). In the first version of the paper there
> was a sentence – now removed – stating that the uncertainty
> on the subtraction of the continuum contribution was one
> of the main sources of systematic uncertainty!
> -> I would at least like to hear an explanation about
> what that sentence
> meant (four lines from the bottom of page 14)

Response:
Regarding the size of the error:
The referee is correct in observing that the error before
and after subtraction is 20, but it is important to note
that the percentage error is different. Using the numbers
from the single bin counting, we get
75.3 +/- 19.7 for the N+- - 2*sqrt(N++ * N--),
i.e. the like-sign subtracted unlike-sign signal. The purely
statistical uncertainty is 19.7/75.3 = 26%. When we perform
the fit, we obtain the component of this signal that is due
to Upsilons and the component that is due to the Drell-Yan and
b-bbar continuum, but as we discussed in our previous response,
the yields have an anti-correlation, and therefore there is no
reason why the error in the Upsilon yield should be larger in
magnitude than the error of the like-sign subtracted unlike-sign
signal. However, one must note that the _percent_ error does,
in fact, increase. The fit result for the upsilon yield alone
is 59.2 +\- 19.8, so the error is indeed the same as for the
like-sign subtracted unlike-sign signal, but the percent error
is now larger: 33%. In other words, the continuum subtraction
increases the percent error in the measurement, as it should.
Note that if we one had done the (incorrect) procedure of adding
errors in quadrature, using an error of 14.3 counts for the
continuum yield and an error of 19.7 counts for the
background-subtracted unlike-sign signal, the error on the
Upsilon yield would be 24 counts. This is a relative error of 40%, which
is larger than the 33% we quote. This illustrates the effect
of the anti-correlation.

Regarding the removal of the sentence about the continuum
subtraction contribution to the systematic uncertainty:
During this discussion of the continuum subtraction and
the estimation of the errors, we decided to remove the
sentence because, as we now state in the paper, the continuum
subtraction uncertainty done via the fit is currently
dominated by the statistical error bars of the data in Fig. 11,
and is therefore not a systematic uncertainty. A systematic
uncertainty in the continuum subtraction would be estimated,
for example, by studying the effect on the Upsilon yield that
a change from the Leading-Order PYTHIA b-bbar spectrum we use
to a NLO b-bbar spectrum, or to a different Drell-Yan parameterization.
As discussed in the response to point 6), a complete
removal of the b-bbar spectrum, a situation allowed by the fit provided
the Drell-Yan yield is increased, produces a negligible
change in the Upsilon yield. Hence, systematic variations
in the continuum do not currently produce observable changes
in the Upsilon yield. Varying the continuum yield
of a given model within the statistical error bars does, and
this uncertainty is therefore statisitcal. Therefore, we removed the
sentence stating that the continuum subtraction is one
of the dominant sources of systematic uncertainty because
in the reexamination of that uncertainty triggered by the
referee's comments, we concluded that it is more appropriate
to consider it as statistical, not systematic, in nature.
We have thus replaced that sentence, and in its stead
describe the uncertainty in the cross
section as "stat. + fit", to draw attention to the fact that
this uncertainty includes the continuum subtraction uncertainty
obtained from the fit to the data. The statements in the paper
in this respect read (page 14, left column):

It should be noted that
with the statistics of the present analysis, we find that the
allowed range of variation of the continuum yield in the fit is
still dominated by the statistical error bars of the invariant mass
distribution, and so the size of the 33% uncertainty is mainly
statistical in nature. However, we prefer to denote
the uncertainty as “stat. + fit” to clarify that it includes the estimate of the anticorrelation
between the Upsilon and continuum yields obtained
by the fitting method. A systematic uncertainty due to
the continuum subtraction can be estimated by varying
the model used to produce the continuum contribution
from b-¯b. These variations produce a negligible change in
the extracted yield with the current statistics.

We have added our response to point 6) (b-bbar correlation systematics)
to this part of the paper, as it pertains to this point.

> Other issues:
> 3) (two sigma effect)
> OK
> 4) (Trigger II cuts)
> OK
> 5) (embedding)
> OK
> 6) (b-bbar correlation)
> I suggest adding in the paper a comment along the lines of what
> you say in your reply
> 7) (trigger response simulation)
> I suggest saying so explicitly in the paper

Both responses have been added to the text of the paper.
See page 13, end of col. 1, (point 7) and page 14, second column (point 6).

> Less important points:
> 8) (repetition)
> OK
> 9) (Table I vs Table IV)
> OK…
> 10) (% in last line of Table IV)
> OK
> 11) (“strongly imply”)
> OK

We thank the referee for the care in reading the manuscript, and look forward to
converging on these last items.

Upsilon Analysis in Au+Au 2007

Paper Title: Observation of Upsilon mesons in Au+Au collisions at sqrt(s_NN) = 200 GeV

Target Journal: PRC

PAs: Rosi Reed, Debasish Das, Haidong Liu, Pibero Djawotho, Thomas Ullrich and Manuel Calderón de la Barca Sánchez.

Figures.

Links.

Rosi Reed's Upsilon-related presentations.

Abstract:

We report on a measurement of the dielectron mass spectrum from 7 to 15 GeV/c² at midrapidity in Au+Au collisions at √s_NN = 200 GeV. The main contributions to the spectrum in this range are the ϒ(1S+2S+3S) states as well as the Drell Yan and b-bbar continuum. We compare the ϒ yield to the measured cross-section measured in p+p, scaled by the number of binary collisions, to obtain a nuclear modification factor of R_AA (1S+2S+3S) = 0.92 +/- 0.37 (stat.) ⁺⁰ _-0.14 (syst.).  The measured yield, which is dominated by the ϒ(1S) state, is consistent with no suppression within the available statistics. 

Conclusion:
We report on a measurement of the dielectron mass spectrum near the ϒ mass region with the STAR detector. Our result opens a new era of bottomonium studies in heavy-ion collisions.  The yield of ϒ(1S+2S+3S) states in 0-60% central Au+Au collisions is found to be 83 +/- 17 (stat) +/- X (syst). Given a cross-section of ϒ in p+p of 114 pb, we find that the nuclear modification factor R_AA for ϒ(1S+2S+3S) → e+e is 0.92 +/- 0.37 (stat.) ⁺⁰ _-0.14 (syst.). Our measured yield is dominated by the ϒ(1S), so our result indicates that this state shows little suppression in Au+Au collisions at RHIC energies.  We see a slight indication of suppression in the 0-10% most central collisions, but more statistics are needed to make definite conclusions.  Lattice QCD results on quarkonium suppression due to color screening indicate that the ϒ(1S) state survives to ~4Tc, so the observed yield places a model-dependent upper limit on the temperature reached in Au+Au collisions at RHIC.

Figures:

Figure 1a: The black histogram shows the η−φ radial distance R = √(Δη)2+(Δφ)2 where Δη and Δφ are the differences in η−φ between the candidate electron tracks in the TPC and the centroid of the triggered cluster in the BEMC.

Figure 1b: The E/p distribution for towers between 6.0 < E < 7.0 GeV, and tracks which have satisfied the conditions R < 0.04 and -2.0 < nσelectron < 3.0.  An electron should leave all of its energy in the calorimeter, so we would expect this distribution to be a Gaussian centered about 1. The Energy measurment includes contributions from the underlying-event, which is high in Au+Au collisions, shifting the E/p peak to values greater than 1. The tail at high E/p results from pi0 events, as the Upsilon trigger also selects dijet events.

Figure 4: Invariant mass spectrum for unlike-sign (closed circles) and like-sign (line histogram) electron pairs. The like-sign spectra were combined as B = 2√N++N--.

Figure 5: The solid circles depict the invariant-mass spectrum after subtraction of the like-sign combinatorial background. The fit (solid line: functional form; dashed histogram: integral in each bin) includes contributions from the ϒ states, as well as Drell-Yan and b-bbar. The ϒs are represented in the fit by three Crystal-Ball functions. The dot-dashed curve illustrates the Drell-Yan and b-bbar continuum as extracted in the fit.

Upsilon Analysis in d+Au 2008

Upsilon yield and nuclear modification factor in d+Au collisions at sqrt(s)=200 GeV.

PAs: Anthony Kesich, and Manuel Calderon de la Barca Sanchez.

• Dataset QA
  • Trigger ID, runs
    
    • Trigger ID = 210601
      • ZDC East signal + BEMC HT at 18 (Et>4.3 GeV) + L2 Upsilon
      • Total Sampled Luminosity: 32.66 nb^-1; 1.216 Mevents
        • http://www.star.bnl.gov/protected/common/common2008/trigger2008/lum_pertriggerid_dau2008.txt
    •  
  • Run by Run QA
  • Integrated Luminosity estimate
  • Systematic Uncertainty
• Acceptance (Check with Kurt Hill)
  • Raw pT, y distribution of Upsilon
  • Accepted pT, y distribution of Upsilons
  • Acceptance
  • Raw pT, eta distribution of e+,e- daughters
  • Accepted pT, eta distribution of e+,e- daughters
  • Comparison plots between single-electron embedding, Upsilon embedding
• L0 Trigger
  • DSM-ADC Distribution (data, i.e. mainly background)
  • DSM-ADC Distribution (Embedding) For accepted Upsilons, before and after L0 trigger selection
  • Systematic Uncertainty (Estimate of possible calibration and resolution systematic offsets).
  • "highest electron/positron Et" distribution from embedding (Accepted Upsilons, before and after L0 trigger selection)
• L2 Trigger
  • E1 Cluster Et distribution (data, i.e. mainly background)
  • E1 Cluster Et distribution (embedding, L0 triggered, before and after all L2 trigger cuts)
  • L2 pair opening angle (cos theta) data (i.e.  mainly background)
  • L2 pair opening angle (cos theta) embedding. Needs map of (phi,eta)_MC to (phi,eta)_L2 from single electron embedding. Then a map from r1=(phi,eta, R_emc) to r1=(x,y,z) so that one can do cos(theta^L2) = r1.dot(r2)/(r1.mag()*r2.mag()). Plot cos theta distribution for L0 triggered events, before and after all L2 trigger cuts. (Kurt)
  • L2 pair invariant mass from data (i.e. mainly background)
  • L2 pair invariant mass from embedding. Needs simulation as for cos(theta), so that one can do m^2 = 2 * E1 * E2 * (1 - cos(theta)) where E1 and E2 are the L2 cluster energies. Plot the invariant mass distribution fro L0 triggered events, before and after all L2 trigger cuts. (Check with Kurt)
• PID
  • dE/dx
    • dE/dx vs p for the Upsilon triggered data
    • nsigma_dE/dx calibration of means and sigmas (done by C. Powell for his J/Psi work)
    • Cut optimization (Maximization of electron effective signal)
    • Final cuts for use in data analysis
  • E/p
    • E/p distributions for various p bins
    • Study of E calibration and resolution between data and embedding (for L0 Trigger systematic uncertainty)
    • Resolution and comparison with embedding (for cut efficiency estimation)
• Yield extraction
  • Invariant mass distributions
    • Unlike-sign and Like-sign inv. mass
    • Like-sign subtracted inv. mass
    • Crystal-Ball shapes from embedding/simulation. Crystal-ball parameters to be used in fit
  • Fit to Like-sign subtracted inv. mass, using CB, DY, b-bbar
    • Contour plot (1sigma and 2sigma) of b-bbar cross section vs. DY cross section
    • Upsilon yield estimation and stat. + fit error
• Cross section calculation.
  • Yield, dN/dy
  • Integrated luminosity (for 1/N_events, where N_events were the total events sampled by the L0 trigger)
  • Efficiency (Numbers for each state, and cross-section-branching-ratio-weighted average)
  • Uncertainty
  • pt Distribution (invariant, i.e. 1/N_event 1/2pi, 1/pt dN/dpt dy) in |y|<0.5 vs pt) This might need one to do the CB, DY, bbbar fit in pt bins.
• Nuclear Modification Factor
  • Estimation of <Npart> for the dataset, and uncertainty.
  • Putting it all together: dN/dy in dAu, Npart, Luminosity (N_events), divided by the pp numbers (dsigma/dy, sigma_pp)
  • Plot of R_dAu vs y, comparison with theory
  • Plot of R_dAu vs Npart, together with Au+Au
  • Plot of R_dAu vs pt.  Try to do together with Au+Au (minbias, maybe in centrality bins, but maybe not enough stats)

Upsilon Analysis in p+p 2009

Upsilon cross-section in p+p collisions at sqrt(s_NN) = 200 GeV, 2009 data.

PAs: Kurt Hill, Andrew Peterson, Gregory Wimsatt, Anthony Kesich, Rosi Reed, Manuel Calderon de la Barca Sanchez.

• Dataset QA (Andrew Peterson)
  • Trigger ID, runs
  • Run by Run QA
  • Integrated Luminosity estimate
  • Systematic Uncertainty
• Acceptance (Kurt Hill)
  • Raw pT, y distribution of Upsilon
  • Accepted pT, y distribution of Upsilons
  • Acceptance
  • Raw pT, eta distribution of e+,e- daughters
  • Accepted pT, eta distribution of e+,e- daughters
  • Comparison plots between single-electron embedding, Upsilon embedding
• L0 Trigger
  • DSM-ADC Distribution (data, i.e. mainly background) (Drew)
  • DSM-ADC Distribution (Embedding) For accepted Upsilons, before and after L0 trigger selection
  • Systematic Uncertainty (Estimate of possible calibration and resolution systematic offsets).
  • "highest electron/positron Et" distribution from embedding (Accepted Upsilons, before and after L0 trigger selection)
• L2 Trigger
  • E1 Cluster Et distribution (data, i.e. mainly background)
  • E1 Cluster Et distribution (embedding, L0 triggered, before and after all L2 trigger cuts)
  • L2 pair opening angle (cos theta) data (i.e.  mainly background)
  • L2 pair opening angle (cos theta) embedding. Needs map of (phi,eta)_MC to (phi,eta)_L2 from single electron embedding. Then a map from r1=(phi,eta, R_emc) to r1=(x,y,z) so that one can do cos(theta^L2) = r1.dot(r2)/(r1.mag()*r2.mag()). Plot cos theta distribution for L0 triggered events, before and after all L2 trigger cuts. (Kurt)
  • L2 pair invariant mass from data (i.e. mainly background)
  • L2 pair invariant mass from embedding. Needs simulation as for cos(theta), so that one can do m^2 = 2 * E1 * E2 * (1 - cos(theta)) where E1 and E2 are the L2 cluster energies. Plot the invariant mass distribution fro L0 triggered events, before and after all L2 trigger cuts. (Kurt)
• PID (Greg)
  • dE/dx
    • dE/dx vs p for the Upsilon triggered data
    • nsigma_dE/dx calibration of means and sigmas
    • Cut optimization (Maximization of electron effective signal)
    • Final cuts for use in data analysis
  • E/p
    • E/p distributions for various p bins
    • Study of E calibration and resolution between data and embedding (for L0 Trigger systematic uncertainty)
    • Resolution and comparison with embedding (for cut efficiency estimation) (Kurt and Greg)
• Yield extraction
  • Invariant mass distributions
    • Unlike-sign and Like-sign inv. mass (Drew)
    • Like-sign subtracted inv. mass (Drew)
    • Crystal-Ball shapes from embedding/simulation. (Kurt) Crystal-ball parameters to be used in fit (Drew)
  • Fit to Like-sign subtracted inv. mass, using CB, DY, b-bbar.
    • Contour plot (1sigma and 2sigma) of b-bbar cross section vs. DY cross section. (Drew)
    • Upsilon yield estimation and stat. + fit error. (Drew)
  • (2S+3S)/1S (Drew)
• p_T Spectra (Drew)
• Cross section calculation.
  • Yield
  • Integrated luminosity
  • Efficiency (Numbers for each state, and cross-section-branching-ratio-weighted average)
  • Uncertainty
• h+/h- Corrections

Upsilon Paper: pp, d+Au, Au+Au

 Page to collect the information for the Upsilon paper based on the analysis of

• 2008 dAu
• 2009 pp
• 2010, 2011 AuAu

Anthony (4/24):

in data, the electrons were selected via 0<nSigE<3, R<0.02. For pt<5, we fit to 0<adc<303. For pt>5, 303<adc<1000.

In embedding, the only selections are the p range, R<0.02, and eleAcceptTrack. The embedding pt distro was reweighted to match the data.

Anthony (4/5): Added new Raa plot with comparison to strickland's supression models

Anthony (4/4): I attached some dAu cross section plots on this page. The eps versions are on nuclear. The cross sections are as follows:

all: 25.9±4.0 nb

0-2: 1.8±1.7 nb

2-4: 10.9±2.9 nb

4-6. 5.2±5.3 nb

6-8: 0.57±0.59 nb

I expect the cross sections to change once I get new efficiences from embedding, but not by a whole lot.

Drew (4/6): Got Kurt's new lineshapes, efficiencies, and double-ERF parameters today. Uploading the fits to them. I'm not sure I believe the fits...

Bin-by-Bin Counting Cross Section by pT (GeV/c):

|y|<1.0 all: 134.6 ± 10.6 pb

0-2: 27.6 ± 6.3 pb
2-4: 39.1 ± 5.8 pb
4-6: 19.9 ± 3.8 pb
6-8: 13.6 ± 5.1 pb

|y|<0.5 all: 119.2 ± 12.4 pb

0-2: 23.8 ± 6.8 pb
2-4: 35.9 ± 7.4 pb
4-6: 19.0 ± 4.5 pb
6-8: 14.2 ± 4.6 pb

The double ERF is a turn-off from the L2 trigger's mass cut. Kurt used the form: ( {erf*[(m-p1)/p2]+1}*{erf*[(p3-m)/p4]+1} )/2, but I used /4 in the actual fit because each ERF can be at most 2. By fits are also half a bin shifted from Tony's, we'll need to agree on it at some point. The |y|<1 are divided by 2 units in rapidity, and the |y|<0.5 by 1 unit.

Using Pythia 8 to get b-bbar -> e+e-

We used Pythia 8 to produce b-bbar events. First we used the default Pythia 8. Macro for running with default parameters is here. We then used the STAR Heavy Flavor tune v1.1 for Pythia 8.  The macro for running with the STAR HF tune is here.

The cross-sections reported by Pythia (numbers after 5M events) using the default parameters:

  *-------  PYTHIA Event and Cross Section Statistics  -------------------------------------------------------------*
 |                                                                                                                 |
 | Subprocess                                    Code |            Number of events       |      sigma +- delta    |
 |                                                    |       Tried   Selected   Accepted |     (estimated) (mb)   |
 |                                                    |                                   |                        |
 |-----------------------------------------------------------------------------------------------------------------|
 |                                                    |                                   |                        |
 | g g -> b bbar                                  123 |    19262606    4198826    4198275 |   6.971e-04  1.854e-07 |
 | q qbar -> b bbar                               124 |     3126270     801174     800981 |   1.331e-04  8.216e-08 |
 |                                                    |                                   |                        |
 | sum                                                |    22388876    5000000    4999256 |   8.303e-04  2.028e-07 |
 |                                                                                                                 |
 *-------  End PYTHIA Event and Cross Section Statistics ----------------------------------------------------------*

So gg initiated subprocess has a 0.697 ub cross section and the q-qbar initiated subprocess has a 0.133 ub cross section. The sum for both subprocesses pp -> b bbar is 0.830 ub. 

Using the STAR HF Tune, the cross section statistics reported by Pythia change to the following:

 *-------  PYTHIA Event and Cross Section Statistics  -------------------------------------------------------------*
 |                                                                                                                 |
 | Subprocess                                    Code |            Number of events       |      sigma +- delta    |
 |                                                    |       Tried   Selected   Accepted |     (estimated) (mb)   |
 |                                                    |                                   |                        |
 |-----------------------------------------------------------------------------------------------------------------|
 |                                                    |                                   |                        |
 | g g -> b bbar                                  123 |    31956918    4520459    4520459 |   9.247e-04  2.542e-07 |
 | q qbar -> b bbar                               124 |     2259563     479541     479541 |   9.817e-05  8.544e-08 |
 |                                                    |                                   |                        |
 | sum                                                |    34216481    5000000    5000000 |   1.023e-03  2.682e-07 |
 |                                                                                                                 |
 *-------  End PYTHIA Event and Cross Section Statistics ----------------------------------------------------------*
 

The cross section increases to 1.023 ub with the STAR HF Tune v1.1.  The main changes to the default parameters are the reduction of the bottom quark mass from 4.8 (default) to 4.3 GeV/c², the change of PDF from CTEQ5L (default) to the LHAPDF set MRSTMCal.LHgrid, and the choice of renormalization and factorization scales.

The selection of e+e- in the final state is done by following the fragmentation of the b or bbar quark into a B meson or baryon, and then looking at its decay products to find an electron or positron.  The pT distribution of the genrated b quarks is shown below.

Fig. 1: Generated b quarks.

The <pT> of the b quarks is 3.3 GeV.  These then fragment into B mesons and baryons.  As an example, we plot here the B0 and B0-bar pT distribution, below.

Fig. 2:Pt distribution of B0 and B0-bar mesons.

The <pT> of the B mesons is 3.055 GeV/c, one can estimate the peak of the Z distribution (most of the momentum of the b quark is carried by the meson, so it should be close to 1) as 3.055/3.331=0.92.

After the beauty hadrons are produced, they can decay producing electrons and positrons.  We search for the e+e- daughters of the beauty hadrons, their pT distribution is shown below.

Fig. 3: pT distribution of the e+ e- daughters of the b quarks.

When an event has both an electron and positron from the b-bbar pair this can generate a trigger.  However, these are generated in all of phase space, and we mainly have acceptance at mid-rapidity.  The full rapidity distribution of the e+e- pairs is shown below:

Fig. 4: Rapidity distribution of the e+e- pairs from b decay.

The distribution is well approximated by a Gaussian with mean ~ 0 and width close to 1 (off by 4.3%).

We calculate the invariant mass. This is shown below:

Fig 6. Invariant mass spectrum of e-e+ pairs originating from b-bbar pairs.

The red histogram is for all e+e- pairs generated by Pythia.  The blue histogram is for pairs with |y_pair|<0.5, which is the region of interest. The distributions are fit to a function to parameterize the shape, shown in the black lines.  This is inspired by using a QCD tree-level power-law distribution multiplied with a phase-space factor in the numerator. The fit parameters for the blue line are:

• b = 1.59 +/- 0.06
• c = 27.6 +/- 5.8
• m0 = 29.7 +/- 7.8

Using the STAR HF Tune, the parameters are:

• b = 1.45 +/- 0.05
• c = 64.2 +/- 26.1
• m0 = 49.7 +/- 18.0

With the default parameters, in mass region 8 < m < 11 GeV/c² and for |y|<0.5 the Pythia prediction is for a cross section of 29.5 pb.

With the STAR HF Tune, in the same phase space region the Pythia prediciton is for a cross section of 46.9 pb.

One can calculate from the Pythia cross section, the STAR efficiency*acceptance and the integrated luminosity the expected yield in the region 8< m < 11 GeV/c². This gives 12 expected counts for trigger 137603, assuming the trigger doesn't affect the invariant mass shape.

However, tince the trigger has a turn-on region, we need to take this into account.  The turn on can be obtained by looking at the background counts in the real data.  By modeling the background with an error function of the form (erf((m-m0)/sigma)+1)/2 and multiplying by an exponential, we obtain the parameters m0=8.07 +/- 0.74 GeV/c² and sigma = 1.75 +/- 0.45 GeV/c². The fit to obtain the error function is shown below (it is one of the figures in the paper):

Fig. 7 Unlike-sign and like-sign invariant mass distributions from data. The like-sign is fit with and exponential multiplied by an erf.

We then need to apply this function to parameterize the turn-on region of the trigger to the b-bbar e+e- invariant mass spectrum.  We have one additional piece of information from the efficiency estimation: the overall acceptance * trigger efficiency * tracking efficiency and including additional PID cuts for the Upsilon(12) is 5.4%, we can use this to normalize the function after including the trigger turn-on so that at M=10 GeV/c2 it gives 5.4% of the yield before applying the trigger turn-on.  This way we take care of the trigger turn-on shape and the overall normalization given by the acceptance, efficiency, etc. obtained from the upsilon embedding.  This assumes that an e+e- pair with invariant mass identical to the upsilon will have identical efficiency and acceptance.  Using this, we estimate the yield in the region 8<m<11 including the trigger turn-on and acceptance and efficiency to be 19 counts from b-bbar in the Upsilon mass region in the entire dataset.

For the STAR HF Tune, the cross section is larger and the expected counts are larger:

Varying the Continuum Contribution to the Dielectron Mass Spectrum

Initial Normalization

The normalization to the Drell-Yan and b-bbar cross sections are given by the calculation from Ramona in the Drell-Yan case and by Pythia in the b-bbar case.  There is an uncertainty in the overall normalization of the contribution from these two sources to the dielectron continuum under the Upsilon peak.  We can do a fit to obtain the Upsilon yield with the normalization fixed.  This is shown below.

Fig. 1: Fit to the invariant mass spectrum.  The data points are in blue. The Drell-Yan curve is the dot-dashed line and the b-bbar is the dashed line.  The Red line is the sum of the Upsilon line shape (obtained from embedding for the 1S+2S+3S keeping their ratios according to the PDG values) plus the continuum contribution from DY+b-bbar.  The red histogram is the integral of the red line, which is what is used to compare to the data in the fit (we fit using the "i" option to use the integral of the function in each bin).

With the above fit, we obtain 64.3 counts after integrating the upsilon part (the yield of DY is 32.3 and the yield of b-bbar is 26.8, both are held fixed for the fit). This gives a cross section of 63.4/(1*0.054*9.6 pb-1) = 124 pb.  The efficiency estimate of 5.4% for the overall efficiency is still being checked though, given the E/p shape not being gaussian due to the trigger bias near the L0 threshold, so this can still change.

It is also possible to let the yield of the continuum vary and study if the chisquare/dof of the fit improves.  That way, we can not just assume a continuum yield, but actually measure it.  Since the yields of the DY and the b-bbar are very similar and given our statistics we can't really discriminate one from the other, we are mainly sensitive to the sum.  One way to study this is to keep their ratios fixed as in the plot above, but vary the overall yield of both of them  This adds one extra parameter to the fit to account for the total sum of the continuum yield.  We perform the fit in the region 5< m < 16 GeV/c2.

One issue is that the Crystal-Ball fit is a user defined function, and we use the integral of the function to fit, which seems to push ROOT to its limit in an interactive session with a macro interpreted on the fly.  This is alleviated somewhat by cleaning up the code to do the one-parameter fit in a compiled macro.  However, trying out the two-parameter fit directly seems to be too much for ROOT even in compiled mode and the code runs out of memory and seg-faults.  A (rather inelegant) way around this is to scale the continuum yield by hand, compile the macro each time and do the one-parameter fit. For each of those fits, one can obtain the chisquare/deg. of freedom.  This is shown in the plot below:

Fig. 2. Chisquare per degree of freedom as a function of the continuum yield (Drell-Yan + b-bbar).

We find a clear minimum, indicating that our data do have some sensitivity to the continuum yield.  The Rightmost point with 59.1 counts is the yield obtained directly from Pythia 8.108 and from Ramona's calculation.  Our data indicate that the yield is likely smaller by about a factor of 2, we obtain at the minimum a yield of 26.6 counts.  Since the yield of Upsilons is obtained from the same fit, our fitted Upsilon yield will increase with decreasing counts from the continuum.  This is shown below.

Fig. 3: Fitted yield of Upsilons for a given continuum yield.  The minimum found above is illustrated by the vertical line.

The corresponding plot with the fit at the minimum is shown below.

Fig. 4: Dielectron data with the curves for the DY and b-bbar at the yield which minimizes the chi-square.  In other words, the result of a (poor man's) two-parameter fit to find both the Upsilon yield and the Continuum yield.

The results of this fit give 14.5 counts for DY and 12.1 counts for b-bbar, i.e a factor 0.45 lower than the 32.3 counts for DY and the 26.8 counts for b-bbar is 26.8 obtained before.  Ramona's calculation for dsigma/dm |y|<1 gave 5.25 nb and the Pythia cross section b-bbar cross section times the BR into e+e- gives 6.5 nb, so our data indicate that we can decrease these by a factor 0.45 (or decrease one by essentially 100% and leave the other one unchanged).  The Upsilon yield in this case increases to 92.1 counts, which gives a cross section of 92.1/(1*0.054*9.6) = 178 pb.  So this has a large effect on the yield (92.1-64.338)/92.1 = 0.3, i.e. a 30% change in the yield (and hence in the cross section).  Note also that 178 pb is quite larger than our first estimate for the cross section.  This highlights the importance of getting the efficiency estimates right.