Averaging of the inelastic cross sections measured by the CDF and the E811 experiments.

Transcription

1 Fermilab-FN-074 Averagg of the elastic cross sections measured by the CDF and the E8 experiments. S. Klimenko *, J. Konigsberg *, T.M. Liss * University of Florida, Gaesville University of Illois, Urbana-Champaign. Introduction To facilitate the comparison of CDF and D0 cross section measurements Run II, the collaborations have agreed to use a common pp elastic cross section for lumosity normalization. For this purpose, we present here an average of the CDF and E8 measurements of this quantity.. Total and elastic cross-sections Both CDF and E8 measured the total cross-section for pp collisions at.8 TeV usg the lumosity dependent method [,] b N 6 ( ) el tot = π ÿ c + ρ Nel + N, where N el is the rate of elastic and N is the rate of elastic pp scatterg events. The slope b is defed from the measurement of the elastic scatterg differential cross section at low four-momentum transfer (t) dn el b = t 0 N el dt and it is exactly the same for both experiments (see Table ). For the slope the E8 experiment used the average of the CDF and the E70 [3] measurements with the error domated by the CDF measurement. Therefore when comparg the CDF and E8 measurements, which has been discussed also [4], the b uncertaty should be excluded. The elastic cross-section is b N 6 ( ) el N = π ÿ c. ( ) + ρ Nel + N Introducg the ratio of the elastic and elastic rates R=N /N el, we can re-write the elastic cross-section as b R = 6 π( ÿ c). ( ) + ρ + R The E70 experiment was a predecessor to E8 and also measured the pp cross-sections. The E8 measurement is more precise and many ways supercedes the E70 result. Therefore only E8 is cluded the average presented here.

2 3. Measured values In both experiments the measured quantities are the number of elastic and elastic events. Table shows the slope b, the number of elastic and elastic events and their ratio R. CDF E8 N el 7869 ± K ± 3.5K N 4098 ± K ± 57.K R 3.06 ± ± 0.3 b 6.98 ± ± 0. Table. Input numbers for the elastic cross-section. In comparg the two experiments we should ignore the uncertaty of the slope b and compare the measured values of R only. The values of R and therefore all derived crosssections disagree at a level of 3.6 standard deviations. To localize the source of disagreement we look at how the elastic rates were measured. The elastic rate was measured as a sum of the double-arm rate N (cocidence of two detectors measurg elastic rates the p and p directions) and the sgle-arm rate N. We could normalize all rates by N el : N N x =, y =, R = x + y. N el N el The measurement of the N el and N rates was similar both experiments and the measurement of N was the most straightforward one. However the measurement of the rate N was quite different. CDF estimated the rate of the sgle diffractive (SD) process by measurg the cocidence rate of the p elastic detector with the opposite elastic detector (sgle diffractive rate). After applyg the selection cuts this rate had a small background, however considerable acceptance and detection efficiency corrections were needed to obta the sgle diffractive rate. To avoid double countg, the double-arm sgle diffractive events were subtracted from the total number of the sgle diffractive events, which gives the estimation of the N rate (309±503 events). The small contribution of the sgle-arm events from the non-diffractive processes (0.6%) was added to the N rate as a simulation-calculated correction. Therefore the corrected number of the sgle-arm events is 33403±50. The E8 experiment measured the exclusive sgle-arm rate usg the elastic detectors, which should be quite efficient for the sgle diffractive events. But the background from losses was large (~93%). To obta the 3% error quoted on the number of sgle-arm elastic events, it required the measurement of the background with uncertaty better than %, which is a non-trivial task. The measurement of the sgle-arm rate was done durg a special run with missg bunches. Therefore order to use it the analysis, fact, the ratio of the sgle-arm and double-arm rates was measured: r = 0.30 ± A small correction to this number due to the fal

3 acceptance is δ=0.007±0.006 []. The total number of the sgle-arm events was estimated as N = N ( r + δ ). Table shows the x and y values measured by the CDF and E8 experiments CDF E8 x.638 ± ± 0.03 y 0.44 ± ± 0.5 Table. The x and y ratios measured by the CDF and the E8. The x values are a very good agreement, but the y values disagree. This may lead to the conclusion that E8 has a factor of two more sgle diffractive events, possibly as a result of the large background subtraction. However, it is not valid to make direct comparison of the x and y values because they have different expectation values. The CDF and E8 elastic detectors had very different acceptances for the two-side events: ε ( CDF) 98.7%, ε ( E8) = ±.0%. The E8 sgle-arm rate had a lot of non-diffractive events missed by the two-side elastic trigger and the CDF N rate was due to the sgle diffractive process only. Therefore order to check if the E8 elastic rates are consistent with the CDF rates the acceptance corrections should be taken to account. For more accurate comparison, the non-diffractive and diffractive (e.g. SD) rates for both experiments should be estimated. It s straightforward for CDF. For the E8 experiment the rates are ε N nd = N / ε, N sd = N ( r + δ ). ε There should be a few percent correction for the N sd (E8) rate to account for the doublearm SD events, which we ignore at this moment. Table 3 shows the rates and their ratios to the elastic rate. CDF E8 N nd 0300 ± K ± 34.9K N sd 3778 ± K ± 36.3K N nd /N el.58± ±0.069 N sd /N el 0.480± ±0.07 N sd /N nd 0.86± ±0.04 Table 3. The x and y ratios measured by the CDF and the E8. At this time we have a remarkable agreement between the CDF and the E8 for the ratio of sgle diffractive and non-diffractive events N sd /N nd. So both experiments see the same fraction of the sgle diffractive events. At the same time there is the discrepancy of 4.4 standard deviations between the ratios of the non-diffractive elastic and elastic events. Similarly, the ratio for the sgle diffractive rate is also greater for the E8, but the errors are large and the SD ratios are compatible. So it is possible that the source of the CDF/E8 discrepancy is the measurement of the elastic rates.

4 Regardless on what is the source of the CDF and E8 disagreement, correct measurement of elastic and/or elastic rates will lead to a discrepancy measured values of R. Therefore to combe the CDF and E8 measurements we average the ratio of elastic and elastic rates. 4. Averagg of the CDF and E8 measurements. To fd the mean value of the elastic cross-section we should average the R measurements, which are not compatible. To average these non-compatible measurements we follow the PDG prescription [5]: Fd the average of two experiments usg the standard approach: R = Fd the average error usg the standard approach: = Calculate χ : 3. Scale the error to get χ = : = 0.. R At the first approximation, ignorg the correlation between the slope b and R,the elastic cross-section relative error is R = b R δ + R = (3.8%) ÿ. b R + R Fally the average elastic cross-section (at s =.8TeV )is ( + ρ ) = 60.4 ±.3 mb, which is.% below the CDF measurement and 5.8% above the E8 measurement. Now let s take to account the correlation between the slope b and the ratios R. The elastic rate is the raw n el rate measured each experiment divided by its acceptance Nel = nel /( exp( btm ) exp( btmax )), where ( tm, tmax ) is a range of t used by CDF ( 0.04 < t < 0. 9) and E8 ( < t < ). Both measurements depend on the slope b and, fact, they are anti-correlated. Namely, if we crease b by one standard deviation (.5%), the CDF value of R creases by ~% and the E8 value decreases by ~%. The covariance matrix cov(r i,r j ) is α C, = α where ( ) is the standard deviation of the ratio R ( R ) for the CDF (E8) measurement and the coefficient α is estimated to be The average value of the ratio R is R = fr + ( f ) R, where the weight f α f = + α can be found by mimization of the variance of R T var( R ) = FCF, F = ( f, f ).

5 The same result can be obtaed by mimization of the likelihood L = log( p( R, R, R,, ), where p is the probability distribution function of two correlated Gaussian variables ( R R ) ( R R) ( R R ) ( R R ) p = exp α + π α ( α ) Assumg that the standard deviations, are given by the errors listed Table,the average value of R is R = 3.0 ± 0.06, which is very close to the number obtaed above. Calculatg the χ χ = i, j ( R R ) C ( R R ) =.; ( i, j =,) i ij j and applyg the same procedure for the scalg of the error of R, the average R value and the elastic cross-section are R = 3.0 ± 0.0, ( + ρ ) = 60.3 ±.3mb. Fally, usg the ρ value of 0.35 the average elastic cross-section at s =.8 TeV is = 59.3 ±.3 mb.. 5. Inelastic cross-section at s = 960 GeV In Run-II the Tevatron center of mass energy is.96 TeV. There is no measurement of the pp scatterg cross-sections at this energy. Therefore the extrapolated value of the elastic cross-section is used for the lumosity measurements. Theory predicts [6,7] that the elastic cross-section creases with energy as ln s and the diffraction cross-section creases as ln s. The total cross-section is a mixture of the elastic and elastic processes, where the elastic cross-section creases more rapidly with energy. The energy dependence of obtaed from the best fit of the experimental data (cludg cosmic tot. rays data) is ln s [8], which is consistent with the expectations. However the E70 and E8 measurements favor the lns dependence. Table 6 shows the value of the elastic cross-section at.96 TeV and its relative variation for all three options. (.96TeV) δ /,% ln(s) 60.0 ±.3. ln (s) 60.7 ±.3.3 ln. (s) 60.8 ±.3.6 Table 6. Extrapolated elastic cross-section at.96 GeV. The last column is the fractional change relative to the cross section at.8 TeV. Actually the E8 error is underestimated, because the error of the slope b is ignored the R ratio.

6 Assumg the ln s energy dependence of the elastic cross-section and assigng an additional % systematic error due to uncertaty the energy dependence the elastic cross-section at.96 TeV is (.96TeV ) = 60.7 ± Acknowledgments We thank the members of the CDF, E70 and E8 experiments that participated the cross section measurements. Specifically we thank P. Giromi and C. Avila for very helpful discussions. We also thank H. Schellman and M. Begel for their participation and collaboration this effort. 7. References. F. Abe et al., Phys. Rev. D50, 5550, (994). C. Avila et al., Phys. Lett. B445, 49 (999) 3. N.A. Amos et al. Phys.Rev.Let, 68, 433, (99) 4. M.Albrow et al. CDF/PUB/CDF/PUBLIC/4844, January 6, Particle Data Group, Phys. Rev. D66, 0 (00) 6. A. Capella et al. Zeit. Phys. C3 (980) A. Capella et al. Phys. Reports 36 (994) 5 8. C. Augier et al. Phys. Lett. B35 (993) 503