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Transverse momentum distribution of lepton-pairs in Drell-Yan process in an asymptotically free scalar field theory
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Transverse Momentum Distribution of Lepton-Pairs in Drell-Yan Process in an Asymptotically MIGUEL MEDINA-GARCIA, AND WU-KI Scalar Field Theory. PORTER W. JOHNSON. Department of Physics, Illinois Institute of Technology, Chicago, Illinois, 60616.
Free TUNG.
The transverse momentum dependence of the parton distribution function and the Drell-Yan cross section is studied in detail in the asymptotically free scalar field theory in six dimensions. In the context of the renormalization group approach of Collins. particular attention is devoted to the transition between the small q7 formula (due to multi-quanta effects) and the large qr formula (due to single hard quantum emission). The calculation represents a case study of the application of the renormalization group method and provides a guide to the corresponding study in QCD.
On
a Newtonian-like Formulation of Einstein’s F. REUSE. Dtpartement de Physique Thtorique,
Relativity Universite
and Relativistic Quantum Mechanics. de Geneve, 1211 Geneve 4. Switzerland.
In relativity, space-time is described by charts associating to each event four numbers (.Y’,.~~,x~..Y~) = (x, t) referring to a position and a time. These charts are related to each other by the transformations of the inhomogeneous orthochronous Lorentz group. The possible description of spacetime in relativity is discussed by charts associating to each event four numbers (q’, q2, q3. q4) = (q. r) in such a way that these charts are related to each other by transformations of the inhomogeneous Galilei group. Then r refers to a universal time and q refers to a position in a three-dimensional space supplied with the geometry of the Euclidean group. It is shown that such a description is obtained by measuring time according to the clocks of a privileged frame and by defining the unit length in an appropriate way. The above discussion is mainly motivated by considerations concerning quantum mechanics. Actually, universal time r permits a consistent quantization in relativity. Afterwards a model for the quantum relativistic spinless particle of mass m0 is formulated based on the assumption that the evolution is governed by the universal time r. Except for the choice of the Hamiltonian, this model is formulated analogously to the corresponding one in the nonrelativistic case; in particular there exists a position observable. Further we compare the above model with the usual relativistic formalisms. For the free particle case our model may be formulated such as to contain Wigner’s group theoretical approach to relativistic quantum mechanics. Further, the case of the particle interacting with an external electromagnetic field is discussed in detail and the model is finally compared with the usual Klein-Gordon formalism.
The H: Ion in an Intense Magnetic Field: Improved Adiabatic Approximations. J. C. LE Gur~rou. Laboratoire de Physique Theorique et Hautes Energies, Universite Paris VI, Tour 16 ler-&age, 75230 Paris Cedex 05, France: AND J. ZINN-JUSTIN. Service de Physique Theorique. Centre d’Ftudes Nucleaires de Saclay, 9 I 19 I Gif-sur-Yvette. France. The ground state binding energy of the H: ion in an intense magnetic field is studied. These calculations are based on improved forms of the adiabatic approximation. The binding energy, the equilibrium internuclear separation, and the zero point energies of nuclear vibrations both parallel and perpendicular to the magnetic field are calculated. Comparison of these results with those obtained from the static adiabatic approximation and from variational calculations. shows a substantial improvement.
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OF PAPERS
TO APPEAR
IN FUTURE
203
ISSUES
Transverse Momentum Distribution of Lepton-Pairs in Drell-Yan Process in an Asymptotically MIGUEL MEDINA-GARCIA, AND WU-KI Scalar Field Theory. PORTER W. JOHNSON. Department of Physics, Illinois Institute of Technology, Chicago, Illinois, 60616.
Free TUNG.
The transverse momentum dependence of the parton distribution function and the Drell-Yan cross section is studied in detail in the asymptotically free scalar field theory in six dimensions. In the context of the renormalization group approach of Collins. particular attention is devoted to the transition between the small q7 formula (due to multi-quanta effects) and the large qr formula (due to single hard quantum emission). The calculation represents a case study of the application of the renormalization group method and provides a guide to the corresponding study in QCD.
On
a Newtonian-like Formulation of Einstein’s F. REUSE. Dtpartement de Physique Thtorique,
Relativity Universite
and Relativistic Quantum Mechanics. de Geneve, 1211 Geneve 4. Switzerland.
In relativity, space-time is described by charts associating to each event four numbers (.Y’,.~~,x~..Y~) = (x, t) referring to a position and a time. These charts are related to each other by the transformations of the inhomogeneous orthochronous Lorentz group. The possible description of spacetime in relativity is discussed by charts associating to each event four numbers (q’, q2, q3. q4) = (q. r) in such a way that these charts are related to each other by transformations of the inhomogeneous Galilei group. Then r refers to a universal time and q refers to a position in a three-dimensional space supplied with the geometry of the Euclidean group. It is shown that such a description is obtained by measuring time according to the clocks of a privileged frame and by defining the unit length in an appropriate way. The above discussion is mainly motivated by considerations concerning quantum mechanics. Actually, universal time r permits a consistent quantization in relativity. Afterwards a model for the quantum relativistic spinless particle of mass m0 is formulated based on the assumption that the evolution is governed by the universal time r. Except for the choice of the Hamiltonian, this model is formulated analogously to the corresponding one in the nonrelativistic case; in particular there exists a position observable. Further we compare the above model with the usual relativistic formalisms. For the free particle case our model may be formulated such as to contain Wigner’s group theoretical approach to relativistic quantum mechanics. Further, the case of the particle interacting with an external electromagnetic field is discussed in detail and the model is finally compared with the usual Klein-Gordon formalism.
The H: Ion in an Intense Magnetic Field: Improved Adiabatic Approximations. J. C. LE Gur~rou. Laboratoire de Physique Theorique et Hautes Energies, Universite Paris VI, Tour 16 ler-&age, 75230 Paris Cedex 05, France: AND J. ZINN-JUSTIN. Service de Physique Theorique. Centre d’Ftudes Nucleaires de Saclay, 9 I 19 I Gif-sur-Yvette. France. The ground state binding energy of the H: ion in an intense magnetic field is studied. These calculations are based on improved forms of the adiabatic approximation. The binding energy, the equilibrium internuclear separation, and the zero point energies of nuclear vibrations both parallel and perpendicular to the magnetic field are calculated. Comparison of these results with those obtained from the static adiabatic approximation and from variational calculations. shows a substantial improvement.
Printed
in Belgium