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Diffractive proton scattering at high energies – the TOTEM experiment at LHC, CERN, Geneva

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Diffractive scattering of protons is realized at small values of four momentum transfer squared t , i.e., when the majority of particles is scattered at very small angles in forward direction. In contrast to deep inelastic scattering their dynamical characteristics are only weakly energy dependent.

From the theoretical point of view the diffractive collisions represent the most complex problem as the usual perturbative methods can be hardly applied to their description.
 This is valid especiallly for the elastic scattering when the elastic hadronic amplitude is to be specified phenomenologically. The influence of Coulomb scattering should be taken into account in this case, too. The hitherto interference method proposed by West and Yennie may be applied only in the case of constant phase of the hadronic amplitude; consistent description of complete elastic scattering (with general t dependence of hadronic phase) may be formulated with the help of the eikonal method proposed in Refs. [1,2]. This method not only substitutes the previous approach, but also enables one to determine the values of the mean square of impact parameter, which characterize the range of forces responsible for total, elastic and complete inelastic scattering, directly from the elastic scattering data [3]. This has opened the discussion whether the elastic hadron scattering can be interpreted as central or peripheral process.
 The research in the framework of the project is realized in two directions. On the one hand we directly participate in the solution and analysis of TOTEM experiment results, while on the other hand we are studying some problems from the elementary particle physics theory that concern the interactions of hadrons.
 The aim of the TOTEM experiment (<a href="http://totem.web.cern.ch/Totem/">http://totem.web.cern.ch/Totem/</a>) in the LHC collider at CERN is to investigate the diffractive proton scattering at energies up to 14 TeV [4]. The scattered particles in the collisions of this kind remain mainly in the pipes of the collider and for their detection the edgeless silicon detectors located in the so called „Roman pots“, which constitute the parts of vacuum system of the LHC collider, are needed. The Roman pots are positioned symmetrically on both the sides of the interaction point at distances of 147 m and 220 m and when detecting particles, they should be brought as near as possible to the axis of the beam. The vacuum parts of the Roman pots had been produced by the Vacuum Praha company. The other produced particles are detected by T1 and T2 telescopes located again symmetrically on both sides of the interaction point inside the CMS experiment facilities and also by the CMS experiment own detectors. The T1 telescopes are constructed as cathode strip chambers and the T2 telescopes as gas electron multiplers GEM. 
 In the first phase the TOTEM experiment will study the elastic scattering of protons primarily in the region of very small momentum transfer; this will be utilised in determining the total hadron cross section and LHC luminosity [5]. The scattering in the region of larger values of |t| will be studied later so as to specify with the highest possible precision the elastic hadron amplitude, average values of impact parameters and profile functions directly from measured data. Last but not least, the TOTEM experiment will investigate individually some diffractive production channels and, together with the CMS experiment, other diffractive production processes.
 As to the theoretical part of the project, two items are being investigated:
 a)&nbsp;The probability model of elastic proton scattering is being further developed. It is based on two simple assumptions: 
<ol>
<li>
the proton is assumed to exist in different internal states that exhibit different external dimensions and the collision of two protons can be described as a superposition of channels corresponding to different combinations of such states;</li>
<li>each elastic channel (j) is characterized for each value of impact parameter b by the probability Pjel(b)&nbsp;=&nbsp;Pjtot(b).Pjrat(b) where the last two factors representing the total probability of a collision and the ratio of elastic and total probabilities may be considered as monotone functions in the interval (0, bjmax) where bjmax corresponds to the highest impact parameter with non-zero value of Pjtot(b). </li> 
</ol>
 The preliminary application to experimental data has shown that the individual parameters bjmax and the probabilities Pjtot(b) and Pjrat(b) may be established from the standard elastic data [6,7]. 
 b)&nbsp;Problems concerning the Einstein-Bohr controversy and the fundamentals of quantum theory are being formulated in more detail. We claim that two unjustified statements have been used in deciding this dispute and correct them: the assumption employed in deriving the Bell inequalities does not correspond (in contrast to prevailing opinion) to the theory with hidden variables, but only to classical physics. Furthermore, both quantum alternatives (Copenhagen and hidden variables) may lead, in contradiction to the statement of Belinfante, to the same predictions [8-11]. The consequences following from our solution of this controversy under new conditions will be presented and analyzed to a greater detail.

Important publications:
[1] V. Kundrát, M. Lokajíček: Z. Phys. C63 (1994) 619 [2] V. Kundrát, M. Lokajíček, D. Krupa: Phys. Lett. B544 (2002) 132 
[3] V. Kundrát, M. Lokajíček, I. Vrkoč: Phys. Lett. B656 (2007) 182 
[4] G. Anelli,..., J. Kašpar, V. Kundrát, M. Lokajíček, et al.: „The TOTEM experiment at the 
 CERN Large Hadron Collider“, 2008 JINST 3 S08007 
[5] J. Kašpar, V. Kundrát, M. Lokajíček: Contemporary models of elastic nucleon scattering 
 and their predictions for LHC; arXiv:0912.0112 [hep-ph] 
[6] V. Kundrát, M. Lokajíček: Optical theorem and Elastic Nucleon Scattering; Proceedings
 of the 13th International Conference on Elastic & Diffractive Scattering, CERN, 29th 
 June – 3rd July, 2009 
[7] V. Kundrát, M. Lokajíček: Elastic pp scattering and the internal structure of colliding 
 proton; arXiv:0909.3199 [hep-ph] 
[8] M.V. Lokajíček: Quantum theory without logical paradoxes; Concepts of Physics VI 
 (2009), No. 4, 581-604; see also /arxiv:09050140[quant-ph] 
[9] M.V. Lokajíček: Hidden-variable theory versus Copenhagen quantum mechanics; 
 Frontiers of Fundamental and Computational Physics - Proc. of the Ninth International 
 Symposium, January 2008, Udine and Trieste, edited by Sidharth B.G. et al., 
 Conference Proceedings, No. 1018, American Institute of Physics, 2008, pp. 40-45. 
[10] M.V. Lokajíček: Physical theory of the twentieth century and contemporary philosophy; 
 Concepts of Physics 4 (2007), No.2, 317-339; see also /arxiv/quant-ph/0611069 
[11] M.V. Lokajíček: Schrödinger equation, classical physics and Copenhagen quantum 
 mechanics; New Advances in Physics 1 (2007), No. 1, 69-77; see also /arxiv/quant-
 ph/0611176

Researchers: 
 Jan Kašpar, Vojtěch Kundrát, Miloš Lokajíček Snr, Jiří Procházka

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