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Forward - Backward Multiplicity in High Energy Collisions

Forward - Backward Multiplicity in High Energy Collisions. Speaker: Lai Weichang National University of Singapore. Introduction. Introduction. In our work, we attempt to determine the forward-backward multiplicity correlation in high-energy hadron-hadron collisions.

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Forward - Backward Multiplicity in High Energy Collisions

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  1. Forward - Backward Multiplicity in High Energy Collisions Speaker: Lai Weichang National University of Singapore

  2. Introduction

  3. Introduction • In our work, we attempt to determine the forward-backward multiplicity correlation in high-energy hadron-hadron collisions. • Colliding proton proton and proton anti-proton. • Done by choosing a probability distribution to predict the number of forward and backward particles formed.

  4. Contents • Review • Chow-Yang Model • Negative Binomial Distribution (NBD) • Cluster Model • Generalized Multiplicity Distribution (GMD) • Results • Discussions on cluster size r for GMD • Comparing plots of GMD and NBD • Correlation Strength b

  5. Review

  6. Review:Chou-Yang Model • In 1984 T.T. Chou and C.N. Yang suggested that for high energy collisions, the distribution with respect to the charge asymmetry is a binomial. (for a given number of particles produced, n) • [ at fixed ] = • Relation observed in 1984 by Chou and Yang in experiment. - T.T. Chou, C.N. Yang: Phys Lett. B135 (1984)

  7. Review:Chou-Yang Model • used to satisfy the simple formula that T.T. Chou and C.N. Yang observed of collisions at 540 Gev • Forward-backward multiplicity distribution separate into two components - T.T. Chou, C.N. Yang: Phys Lett. B135 (1984)

  8. Review:Chou-Yang Model • More explicitly, = Mean charges multiplicity = KNO scaling function = Normalization Constant

  9. Review:Negative Binomial Distribution • NBD gives better parameterization of multiplicity distribution, rewrite as - S.L. Lim, C.H. Oh et al.: Z. Phys. C 43 (1989) 621

  10. Review:Negative Binomial Distribution • Average backward multiplicity at fixed forward multiplicity: • Experimentally, a linear correlation of the type: • Plot - S. Uhlig et la.: Nucl. Phys B132 (1978) 15- UA5 Coll. K. Alpgard et. al.: Phys. Lett. 123B (1983) 361- UA5 Coll. R.E. Ansorge et. al.: Z. Phys. C 27 (1988)191

  11. Review:Negative Binomial Distribution • Observed for various energy • Collider energy fits well, disagreements exist in ISR energies - S. Uhlig et la.: Nucl. Phys B132 (1978) 15- UA5 Coll. K. Alpgard et. al.: Phys. Lett. 123B (1983) 361- UA5 Coll. R.E. Ansorge et. al.: Z. Phys. C 27 (1988)191

  12. Review:Cluster Model • Each cluster is assumed to fragment into 2 charged particles • Since this is only observed experimentally at 540 GeV, no reason for other energies to be the same. • Each cluster is assumed to fragment into exactly r charged particles besides neutrals. • Proposed that energy has a correlation with cluster size: [ at fixed n] = rn - S.L. Lim, C.H. Oh et. al.: Z. Phys. C 43 (1989) 621

  13. Review:Cluster Model • Rewrite NBD with cluster size r • r is adjusted to reproduce the experimental forward-backward correlation strength b of • re-plotted again - S.L. Lim, C.H. Oh et al.: Z. Phys. C 43 (1989) 621

  14. Review:Cluster Model - S.L. Lim, C.H. Oh et. al.: Z. Phys. C 43 (1989) 621 (r varied)

  15. Review:Cluster Model - S.L. Lim, C.H. Oh et. al.: Z. Phys. C 43 (1989) 621 - S. Uhlig et. la.: Nucl. Phys. B132 (1978) 15

  16. Review:Cluster Model (Finding r analytically) • Since • The slope b is a measure of correlation strength. • Indeed, it can be shown that b is equivalent to the statistical definition of the correlation coefficient. - UA5 Collaboration, K. Alpgard et. la.: Phys. Lett. B123 (1983) - S.L. Lim, C.H. Oh et. al.: Z. Phys. C 43 (1989) 621

  17. Review:Cluster Model (Finding r analytically) - S.L. Lim, C.H. Oh et. al.: Z. Phys. C 43 (1989) 621

  18. Generalized Multiplicity Distribution

  19. Generalized Multiplicity Distribution: • Interests in such studies has been revived since the data at the TeV region became available. • At high energy (900GeV), the NBD does not describe the data very well. • LHC will publish data this year. • The GMD is devised in NUS by Dr Chan and Prof Chew. • L.K. Chen, C.K. Chew et. al.: Z. Phys. C 76 (1997) 263 • T.Alexopoulos et. la.: Phys Lett. B 353 (1995) 155

  20. Generalized Multiplicity Distribution: • GMD is a convolution of NBD and FYD. • We use GMD for a better parameterization of the charged particle multiplicity distribution. • The physical meaning of k and can be explained • A.H. Chan, C.K. Chew: Phys. Rev. 41 (1989) 851

  21. Generalized Multiplicity Distribution: • In search of an even better parameterization of the multiplicity distribution, we rewrite as • Plot - S.L. Lim, C.H. Oh et al.: Z. Phys. C 43 (1989) 621

  22. Results

  23. Results:Discussions on cluster size r for GMD • Using the statistical definition of the correlation coefficient, • we calculate r for the GMD

  24. Results:Discussions on cluster size r for GMD • Ranges of mean cluster size r which would give correlation strength b equal to experimental values within the quoted experimental errors for collisions at CERN ISR and SppS Collider energies. • The r values derived from the NBD is compared to the GMD.

  25. Results:Discussions on cluster size r for GMD • In conclusion, the multiplicity correlations observed reveal the following features for 30 - 900 GeV: • Mean cluster size r correlates to energy as reported by Lim et. la. • Obeys relation • No significance difference between the cluster size r of NBD and GMD

  26. Results:Discussions on cluster size r for GMD • In conclusion, the multiplicity correlations observed review the following features for 1.8 - 14 TeV: • In 1995 E735 Collaboration produced some experimental results for r and b at 1.8 TeV • Using relation • We arrive at r = 2.60  0.35 for c.m.s energy of 1.8 TeV • This values compare favorably with experimental results from the E735 Collaboration for r = 2.62  0.12 - T.Alexopoulos et. la.: Phys Lett. B 353 (1995) 155

  27. Results:Discussions on cluster size r for GMD • In conclusion, the multiplicity correlations observed review the following features for 1.8 - 14 TeV: • Using relation • We predict the value of r = 3.300.41 for c.m.s energy of 14 TeV if the cluster size is a function of only energy. • Extrapolation to these energies may not be meaningful since the validities of the parameterization of , and becomes in doubt. • Cluster size may level off at higher energies. - T.Alexopoulos et. la.: Phys Lett. B 353 (1995) 155

  28. Results:Comparing plots of GMD and NBD • Plot • Compare the NBD with the GMD.

  29. Results:Comparing plots of GMD and NBD • GMD shown here as black line. Experimental result is shown as red. Green and blue are NBD with different r values. • Notice that the line plotted by using the GMD follows the curve of the data points at low nf values.

  30. Results:Comparing plots of GMD and NBD • GMD shown here as black line. Experimental result is shown as red. Green and blue are NBD with different r values. • Notice that the blue line plotted by using the NBD is almost indistinguishable from the distribution using the GMD

  31. Results: Correlation Strength b • a and b are calculated from linear fits of GMD plots shown previously. • Comparing between the linear forward-backward correlation parameters, experimental and calculated by using the NBD and GMD. - S.L. Lim, C.H. Oh et. al.: Z. Phys. C 43 (1989) 621 - S. Uhlig et. la.: Nucl. Phys. B132 (1978) 15

  32. Results: Correlation Strength b • In conclusion, the multiplicity correlations observed review the following features for the correlation strength b: • Our calculated b agrees well with those proposed previously by Lim et. la. • Using our results, we are able to propose the relation: • This values fall into the experimental results proposed by Alexopoulos et. la. - T.Alexopoulos et. la.: Phys Lett. B 353 (1995) 155

  33. Results:Correlation Strength b • In conclusion, the multiplicity correlations observed review the following features for the correlation strength b: • Our parameterization of b gives b = 0.980.19 at 14 TeV. • Agrees with the prediction of Chou and Yang that b saturates as energy approaches infinity. • T.T. Chou, C.N. Yang: Phys Lett. B135 (1984)

  34. Thank you

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