Using CDF and D0 to Understand the TevatronUsing CDF and D0 to Understand the Tevatron

Jean SlaughterDOE ReviewJuly 21, 2003

Using CDF and D0 Information – July 2003 -Slaughter 2

Three Ways to Use CDF and D0 DataThree Ways to Use CDF and D0 Data

Computed versus measured luminosity Cross check on instrumentation, *

Size of the luminous region versus z Information on lattice at interaction points,

emittances Use silicon vertex detectors for very accurate

determination Stan Lai, William Trischuk, U. of Toronto, et al Juan Estrada, Avdhesh Chandra, D0, et al

z of proton and anti-proton bunches Time of flight and Central Tracking Chamber in CDF Mathew Jones, U. of Penn.

Using CDF and D0 Information – July 2003 -Slaughter 3

Calculated LuminosityCalculated Luminosity

. (1) 

N = numbers of protons, anti-protons per bunch (109) B = number of bunches (36) f = revolution frequency (47.7 KHz)rr = relativistic factor, 1045 = interaction point (cm, assumed equal in x

and y).H = hourglass factor, function of l, bunch length,

*

= transverse emittances

*

*

5

2

610

l

yppxpp

rrpp HNfBN

L

Using CDF and D0 Information – July 2003 -Slaughter 4

Measured LuminosityMeasured Luminosity

CDF – CLC (Cherenkov Luminosity Counter)

D0 – system of scintillation counters

Accurate measurement crucial to experiments for cross section determination Goal is 5% systematic error, < 1% statistical error

Systematic difference between D0 and CDF Ratio is linear with luminosity 10% difference at 4.0 1031

Using CDF and D0 Information – July 2003 -Slaughter 5

Ratio of D0 to CDF LuminosityRatio of D0 to CDF Luminosity

Using CDF and D0 Information – July 2003 -Slaughter 6

Components to Calculated LuminosityComponents to Calculated Luminosity

Number of protons, anti-protons FBI (Fast Bunch Integrator) or SBD (Sampled Bunch

Display)

Transverse emittances SyncLite

Bunch lengths SBD

Using CDF and D0 Information – July 2003 -Slaughter 7

D0 Measured Luminosity versus Calculated D0 Measured Luminosity versus Calculated LuminosityLuminosity

Using CDF and D0 Information – July 2003 -Slaughter 8

CDF measured Luminosity versus Calculated CDF measured Luminosity versus Calculated LuminosityLuminosity

Using CDF and D0 Information – July 2003 -Slaughter 9

CDF RatioCDF Ratio

Using CDF and D0 Information – July 2003 -Slaughter 10

D0 RatioD0 Ratio

Using CDF and D0 Information – July 2003 -Slaughter 11

Use Silicon Detectors for Size of the Luminous Use Silicon Detectors for Size of the Luminous RegionRegion

*

20*2 )(

zz

eff

pbarp

pbarpeff

*=0.35 cm , =2E-7 cm*=0.40 cm , =2E-7 cm*=0.35 cm , =3E-7 cm

.

Nominal value has * = 0.35 cm.

Two methods 1. vertices 2. distance of closest approach for 2 track pairs

Using CDF and D0 Information – July 2003 -Slaughter 12

Given a distribution of vertexes (xi,yi ,zi) then observed width is:

σbeam = width of the luminous region

σvertex = error in the vertex position

Problem - estimate for σvertex is smaller than the real error in the vertex, so find k from the data doing a linear fit

Method 1 - Use VertexesMethod 1 - Use Vertexes

222vertexbeamobs

222vertexbeamobs k

Using CDF and D0 Information – July 2003 -Slaughter 13

CDF resultsCDF results

Using CDF and D0 Information – July 2003 -Slaughter 14

Using CDF and D0 Information – July 2003 -Slaughter 15

Results for X – D0Results for X – D0

Stores:

1. 2312

2. 2315

3. 2341

4. 2420

5. 2507

6. 2523

7. 2540

store store

store

emittance z at minimum size

z (cm)

sigma

Using CDF and D0 Information – July 2003 -Slaughter 16

Results for Y – D0Results for Y – D0

Stores:

1. 2312

2. 2315

3. 2341

4. 2420

5. 2507

6. 2523

7. 2540

store

store

store

z (cm)

sig

ma

emit

tanc

e

Z of minimum

beta*

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Comparing D0 pseudo-emittance with Tevatron Comparing D0 pseudo-emittance with Tevatron measurementsmeasurements

1.60E-07

1.80E-07

2.00E-07

2.20E-07

2.40E-07

2.60E-07

2.80E-07

3.00E-07

0 2 4 6 8

epsi

lon

(cm

)

Measured at TevatronUsing vertexes at DØ

store store

= (p pbar)/(p+ pbar),

p p

p pbar are average over h and v for p and pbar

Using CDF and D0 Information – July 2003 -Slaughter 18

Method 2 - Track Pairs Method 2 - Track Pairs

Use distance of closest approach (dca) parameter for pairs of tracks

This assumes a circular beam. If the beam is not circular the relation is a little more complicated. Do has done it both ways.

If you include uncorrelated measurement errors for this tracks, the equation does not change. The error terms cancel in the formula above.

)cos(

)sin()cos(

212

21

F

iii

dd

xyd

Using CDF and D0 Information – July 2003 -Slaughter 19

Distance of Closest Approach PlotsDistance of Closest Approach Plots

dca

Z (cm)

phi

dca

beam

siz

e (c

m)

Using CDF and D0 Information – July 2003 -Slaughter 20

Comparing Results – Beam PositionsComparing Results – Beam Positions

The beam position is the same, when measured with the two methods(vertexes in black and tracks in blue). All scales in cm.

z (cm) z (cm)

x position y position

Using CDF and D0 Information – July 2003 -Slaughter 21

Comparing Results- Sigma versus ZComparing Results- Sigma versus Z

Vertex method gives consistently a beam that is 3-5 um larger in width and with less curvature (larger *). Great cross check on systematics. Under investigation.

(vertexes in black and tracks in blue) All scales in cm.

Using CDF and D0 Information – July 2003 -Slaughter 22

SummarySummary

Comparison of measured and calculated luminosities agree within the erros Work to reduce the errors on each element in

calculated luminosity

Size of luminous regions Interplay between understanding experiment

tracking and understanding the Tevatron lattice and emittances

Current formula is simplistic Adding dN/dz, (the number of vertices as a function

of z) will help Need to revive the work on the length of p and pbar

bunches using the CDF time-of-flight and COT tracking