Relativistic Aspects of Nuclear Physics ppt

Proceedings of the Sixth International Workshop on \t\elativistic rfAspects /\pclear (L/hysics ii * *"*»" v Editors T Kodama C E Aguiar H.-T Elze F Grassi YHama G Krein ^ \ ;^ ;*£ ^ | ^ - i World Scientific ' « , Proceedings of the Sixth International Workshop on Relativistic Aspects of Nuclear Physics Proceedings of the Sixth International Workshop on Relativistic Aspects of Nuclear Physics Caraguatatuba, Sao Paulo, Brazil 17-20 October 2000 Editors Takeshi Kodama Carlos Eduardo Aguiar Hans Thomas Elze Federal University of Rio de Janeiro, Brazil Frederique Grassi and Yogiro Hama University of Sao Paulo, Brazil Gastao Krein State University of Sao Paulo, Brazil V | b World Scientific wb London Singapore • New Jersey 'London • Hong Kong Published by World Scientific Publishing Co Pte Ltd P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataioguing-in-Publication Data A catalogue record for this book is available from the British Library RELATIVISTIC ASPECTS OF NUCLEAR PHYSICS RANP2000 Copyright © 2001 by World Scientific Publishing Co Pte Ltd All rights reserved This book or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA In this case permission to photocopy is not required from the publisher ISBN 981-02-4715-X Printed in Singapore by Uto-Print * ' Y*9 A* ""Sw s.™ '"•W**"-*^, m-:- •• • *'• v •II VII PREFACE It is our pleasure to present the Proceedings of the VI International Workshop on Relativistic Aspects of Nuclear Physics (RANP 2000) This time, the meeting took place in Tabatinga, a pleasant beach on the southern coast of Brazil, for the first time out of the city of Rio de Janeiro This series of workshops started in 1989, aiming to stimulate Brazilian scientific activities on Relativistic Nuclear Physics, especially among young researchers and graduate students The VI Workshop, held in October 2000, reflected the excitement created in the field by the start of operations of Brookhaven's Relativistic Heavy Ion Collider just four months earlier, in June The new frontiers of investigation opened by RHIC, among other topics, were actively discussed by the 100 participants of the Workshop, which came from all parts of Brazil and abroad RANP 2000 kept the format of the previous meetings, somewhat in the way between a specialist's workshop and an advanced graduate school The invited speakers did a remarkable job in presenting the most recent and important developments in Relativistic Nuclear Physics in a didactical manner They have also kindly contributed the manuscripts which form part of this volume Members of the organizing committee express their sincere thanks to those invited speakers who always warmly contributed to the success of the meeting In addition, many interesting contributed papers were presented in a poster session which are also included in the book Note that the number of contributed works increased steadily and this time we had more than twice compared to the earlier meetings of this series We are happy for this fact which shows the growth of the young researchers of the area in Brazil It is worth to mention that we had a really exciting round-table debate entitled, "QGP - Observed or not yet observed ? That is the question." In spite of the hottest discussion on a very controversial subject at the moment, the discussion leader transformed skillfully the fatal collision into a Happy-Hour, by the help of lubricating fluid, called "caipirinha" We regret that we failed to record this historically interesting debate As usual, Ms Dilza Barros again helped us the organization as Conference Secretary We thank her dedication and professional work The organization of RANP 2000 was supported from several Institutions to which we would like to express our thanks: CNPq, FAPESP, FAPERJ, CAPES, CLAF, PRONEX, CBPF, UFRJ, UERJ On April the 22nd of this year in Tokyo, Prof Mituo Taketani deceased He was not only one of the great leaders of modern Japanese physics but also left big footsteps in the Brazilian Physics community as is described in the article of Prof Afredo Marques included in this volume We thus dedicate this book to the memory of Prof M Taketani Prof Alfredo Marques, the ex-director of C B P F , has been an important member of the Brazil-Japan collaboration in Cosmic Ray Experiment, which discovered the well-known Centauro events IX CONTENTS Preface Mituo Taketani — In Memoriam Alfredo Marques vii Invited Talks First Physics Results from STAR John Harris Was a New Phase of Nuclear Matter Observed at CERN SPS ? Grazyna Odyniec 28 The Origin of the Highest Energy Cosmic Rays Angela V Olinto 38 Ultra-High Energy Cosmic Rays: Current Data and Propagation Scenarios Gustavo M Tanco 59 Imprints of Nonextensivity in Multiparticle Production Grzegorz Wilk and Z Wiodarczyk 78 Relics of the Cosmological Quark-Hadron Phase Transition Bikash Sinha 97 Hadronic Chiral Mean-Field Models at Extreme Temperatures and Densities Marcelo Chiapparini et al 112 Are High Energy Heavy Ion Collisions Similar to a Little Bang, or Just a Very Nice Firework? Edward V Shuryak 125 Hard Thermal Loops and QCD Thermodynamics J-P Blaizot 138 Optimized Perturbation Theory: Finite Temperature Applications Marcus B Pinto 147 Potential Gravitational Wave Sources and Laser Beam Interferometers Jose A F Pacheco 158 451 the quantity aw is the vacuum energy of the pion system The pion multiplicity distribution, P(N), can be derived from the density operator p by evaluating the expectation value P(N) = (N\p\N), (5) in the states \N) with definite number of pions, N We turn now to the system described by Eq.(2) The Hamiltonian (2) is rotationally invariant in the "isospin" space, so it preserves the "isospin" which is given by J V + !) = \ £ ( « t a - a]oi)2 = C ( ) ) (6) i.e., the Casimir operator of the group 0(3) In fact, the Hamiltonian (2) describes merely the isotropic three-dimensional anharmonic oscillator, so the technique of Refs.8 can be applied to obtain approximate solution at low energy in each isospin sector For this purpose, it is useful to introduce the operator of pair creation At and destruction A, i i which create (destruct) meson pairs with isospin = The operators At and A, together with the operator A0 that is related to the boson number, A° = \^(aU + aM), (8) i are closed under commutation algebra One has: [A,A] = 2A°, [A\A°\ = -A\ [A,A°] = A, (9) and form the algebra SU(1,1) The Hamiltonian of the self-interacting bosons can be expressed in terms of the generators of the SU(1,1) algebra: H = LJ[A° + \{2A° + A + A^ ] , A = Ac/w (10) The Casimir invariant of the algebra SU(1,1), Csu{i,i) = (A0)2 - (l/2)(AAt - At A) (11) 452 coincides, up to a c-number, with the Casimir operator of the 0(3) group (6), / ( / + 1) = l/4C 5t /(i,i) + c, (12) This allows one to use the conserved "isospin" quantity in the HolsteinPrimakoff representation for the pair operator SU(l,l)-algebra: A = f A y/z/2 + I + nb, = tfy/3/2 + I + n, n = tfb, N = 2A° - 3/2 = / + 2n (13) where boson operators tf and b rise and lower the number of isospin zero meson pairs in the system by one, [b,tf] — The total number of mesons N is the sum of the number of mesons with the stretched "isospin" and the doubled number of the isospin-zero pairs [cf the last eq (13)] While the first quantity is conserved by the interaction in (2), (10), the total effect of the interaction is the mixing of the states of different isospin-zero pairs within the same total isospin sector / Approximate elimination of the interaction can be done via unitary transformation8 One can introduce the new operators A*, A and A0 according to A0 = {l/A)[2(w + Cj^)A0-{Cj-w-l)(A A = 12 (1/4) \{w ' + u-^fA 12 + l2 + {w ' - u- ' ) ti ft)], - 2{w - Co'1)A0} , (14) with A = (A^y The tilded operators form the same SU(1,1) algebra (9) with the properties (13), the transformation (14) is in fact the finite rotation for the SU(1,1) group that is generated by the unitary operator U tfA% U = ee^-A\ = {l/2)lnu (15) If the constant (spin independent) value of the "rotation" parameter < is D used in (14), the transformation (14) can be interpreted as a Bogolyubov transformation for the meson operators of type a = ua + va}' The 0(3) 453 invariance in the "isospin" space allows one to employ broader class of transformations (14) using different values of Q = u)j in different isospin sectors The optimal choice for the wi is given by the solutions of the equation UJ] - &! = 4(5/2 + I)X, w/>l, (16) in each isospin sector, which allows one to reduce the Hamiltonian to the form H = Hdiag + ^Hint, w{(l/4) (3W/+W7 ) (7 + / ) + +2QIh [l + A, [3(n - 1) + / + 5/2]]} (17) and AHint is the off-diagonal correction (interaction between the new degrees of freedom) AHint = ww/A7 [A(hA + A*n) + (i+) + (A)2] , (18) which turns out to be suppressed, due to inequality A=A = - u)72 (19) < loTIr' w? 4(7 + 5/2) which follows from Eq.(16) Even for the case of the strong coupling, the resulting transformed Hamiltonian H is nearly linear, H w Hdiag ~ const(I) + 0,(1)A0, while the residual interaction is suppressed due to inequality (19) We demonstrate the appearance of the NBD for the boson multiplicities, starting from the case of zero temperature, T = In this case, the density operator is reduced to p-£7t|0>