Muhammad Ajaz PhD Scholar, 50th Course: WHAT WE WOULD LIKE LHC TO GIVE US June 27, 2012

Outlines Abstract Motivation The Method Main goal The Experiment Results from pC- & dC- interaction Discussions Conclusion 2

Abstract we studied nuclear transparency effect using p 12 C- & d 12 C- A GeV/c. half angle (θ ½ ) technique is used which divide the emitted particles in two groups (incone/outcone) depending on their polar angle in the lab. frame. The behavior of average characteristics of the incone and the outcone protons &  ∓ - mesons are studied separately as a function of the number of identified protons (N p ) in an event The transparency observed is divided into three groups: leading effect; cascade effect; and medium effect. Analyses of the results shows that coherent interactions of grouped nucleons could be the reason for the last group of transparency. 3

4 Motivation So study of the Nuclear Transparency in hA & AA collisions at high energies could help to extract the information on new phases of the strongly interacting matter as well as the QCD critical point.

Nuclear Transparency (theoretically) T vs. R based on the parameterization of Bethe from 200—800 MeV [H. A. Bethe, Phys. Rev.57, p. 1125(1940).] r o effective reduced nuclear radius, the reduced wavelength of the incident particle, z and Z the charge of the incident particle and the target nucleus, respectively T is the transparency 5

Nuclear Transparency (experimentally) 6 ratio of nuclear cross section per nucleon to that on a free nucleon. A. Leksanov et al., PRL 87, (2001). ratio of cross section for (e, e ’ p) scattering measured in nuclear target to the cross section for (e, e ’ p) in PWIA K. Garrow et al., Phy. Rev. C 66 (2002) Ratio of the experimental charge normalized yield divided by the charge normalized Monte Carlo equivalent yield of target A to that of 1 H B. Clasie et al., PRL 99, (2007). Sometimes, due to lack of appropriate pp data, which enables to calculate R AA, a ratio of central to peripheral spectra is used (R cp ), on the premise that ultra peripheral events look very like elementary collisions. F. Antinori et al., Physics Letters B 623 (2005) 17–25 Ratio of the average characteristics of hadrons in nucleon-nucleus or nucleus-nucleus collisions as a function of number of protons (N p ) in an event to that of N p = 2 transparency in an experiment could be defined as an effect at which the characteristics of hA and AA collisions don’t depend on a number of identified protons (N p ). because N p is connected to the baryon density of matter

 We define  1/2 from NN interaction at 4.2 A GeV/c which divide the particle multiplicity in two equal parts  half angle (  1/2 =25 o : 5 o, 10 o, 15 o, 20 o, 25 o ):  Half angle gives incone and outcone  particles with  <  1/2 incone particles  particles with  >  1/2 outcone particle half angle (  1/2 ) Technique 7

NTNT at high energies using half angle (θ ½ ) P.L. Jain, M.Kazuno, G.Thomas, B.Girard.Phys.Rev.Lett. 33,660,1974; J.I. Cohen, E.M. Friedlander et al. Lett.Nuovo Cim.,9,337,1974; A.I. Anoshin et al. Sov. Journal of Nucl. Phys., 27, 5, p ,

 Different mechanisms could be reason of the nuclear transparency effect  [Y. Afek et, al., THC11NI0N - PH ] I. particle-nucleus collisions is a multistep process 1. Intranuclear Cascade Models, 2. Leading particle Cascade Models, 3. Energy Flux Cascade Models, 4. Multiperipheral Regge Type Models, 6. and various types of Statistical and Hydrodynamical Models II. particle-nucleus collisions is a single step process F.C. Roesler and C.B.A. McCusker, Nuovo Cimento 10, 127 (1953). W. Heitler and C.H. Terreaux, Proc. Phys. Soc. London A66, 929 (1953). S.Z. Belenkij and L.D. Landau, Nuovo Cimento 3, 15 (1956). D.S. Narayan and K.V.L. Sarma, Prog, of Theor. Phys. 31, 93 (1964). L.D. Landau in "Collected Papers of L.D. Landau, Pergamon Press London 1965 (Editor D. Ter Harr). A.M. Baldin, Proceedings of the VI Int. Conf. on High Energy Physics. A. Dar, MIT Preprint 1972 (unpublished). K. Gottfried, in "High Energy Physics and Nuclear Structure" North Holland Publ. Com (Editor G. Tibell). A. Dar, Proceeding of the ICTP Topical Meeting on High Energy Reactions Involving Nuclei, Trieste 1974 (Editor L. Bertocci). A.Z. Patashinskii, JETP Lett. 19, 338 (1974). G.Berlad, A. Dar and G. Eilam, Phys. Rev. D13, 161 (1976). F. Takagi, Nuovo Cimento Lett. 14, 559 (1975). S. Fredriksson, Nucl. Phys. B (to be published) [A.M. Baldin, Proceedings of the VI Int. Conf. on High Energy Physics and Nuclear Structure, Santa Fe, June 1975 and references therein.] 9

Main goal looking for the transparency effect of nuclear matter To understand whether the effect connects with the first category of models or with second ones. To reach the goal we used “half angle” technique for lightest nuclear system at relativistic energiessystem 10

Nuclear Transparency Effect  We have studied the average characteristics of the secondary charged particles produced in p 12 C- and d 12 C-interactions at 4.2 A GeV /c as a function of N p ;  Experimental Data , and of protons (incone and outcone) , and of π + (incone and outcone) , and of π - (incone and outcone)  CASCADE Model , and of protons (incone and outcone) , and of π + (incone and outcone) , and of π - (incone and outcone)  Fitting to get quantitative results 11

EXPERIMENTAL DATA 12

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p vs N p 14 pCdC The effect is suppressed for Cascade Model as compared with experiment. It can be explained with some mixture of the fast  + -mesons among these protons in the experiment. The fast  + -mesons could appear as a result of proton exchange reactions when leader proton transform to neutron and fast positive pions through the reactions p  n +  +

15 p vs N p pC dC

pC p vs N p 1. This type of transparency is connected to leading effect Leading particles are projectiles which could give some part of their energy during interaction. The particles will have maximum energy in an event and would be identified in an experiment as incone particles due to their high energy /low angle. Due to their high energy they passes very fast through the medium. That is why medium seems transparent to them. 16

17  - vs N p pCdC

18  - vs N p pC dC We support that these fast and small angle mesons could be connected with leader nucleons too. They could appear as a result of charge exchange reactions for the leader nucleon n  p +  - and p  n +  +. It confirmed with the comparison of pC and dC-data. In pC the difference between model and experimental data become smaller compare with dC-data due to absent neutron. This type of transparency may be connected to cascade effect only.

π - vs N p pCdC 19

π - vs N p pC dC 20 Not describe by the cascade model and it could not be consider as a leader effect because the behavior is observed for the outer cone π - - and π + -mesons (low energy secondary particles with large angle). We consider the result as some signal on appearance of the transparency which could be connected with some particular properties of the medium. Because the average momentum and average transverse momentum of these particles don’t depend on the number of identified protons.

21 pC  0.26 dC  0.28 R~1/ pion radiation area (R) could be defined ~ GeV/c the value of R~ fm The carbon nucleus radius is roughly R c = R p A 1/3  1.83 fm (here R p ~ 0.8 fm) The diameter of carbon nucleus becomes 3.67 which is the same as that of the out cone pions radiation area. Discussions

22 The second category included all models that assume that particle-nucleus collisions is a single step process where a few nucleons (or partons) in the nucleus interact collectively with the incident particle. In such models the effective center of mass energy available for the production of particles is approximately given by s eff  2m eff P lab, Where m eff is the mass of the system that interacts collectively with the incident particle, its value is of the order of a few times the mass of a single nucleon. P lab is a momentum for the incident particles.

23 Using expression from CTM [Y. Afek, A. Dar and G. Eilam THC11NI0N - PH - 76 –87] for the average multiplicity of secondary charged particles ( Np ) as a function of the number of fast protons N p, we can get roughly the number of protons in tube (i p ). The expression: ip and pp are the multiplicity of the secondary charged particles produced in tube with i p protons and in pp- interactions respectively so i p ~ 3.0  0.4 in pC and 3.1  0.3 in dC

CONCLUSION 24 5.We observed several cases for which behaviors of, and didn’t depend on the N p – some signals on appearance of nuclear transparency effect. 6.The signals were characterized in three groups of transparency: I.Transparency due to leading effect : projectile gives some part of its energy during interaction and could save other essential part of its energy. The particle will have maximum energy in an event, very fast passes the medium, cannot interact more and that is why medium seems transparent for it. II.Cascade Transparency because data coming from the code could satisfactorily describes the effects. III.Transparency due to medium effect. and which could not be explained as a result of leading effect and as a result of cascade mechanism. Analyses of the result shows that the collective interaction of grouped nucleons could be the reason of observed transparency.

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