On the equivalence between the impact parameter and transverse momentum space formalisms for the Drell-Yan process

1981 ◽  
Vol 14 (6) ◽  
pp. 1457-1467 ◽  
Author(s):  
H F Jones ◽  
J Wyndham
2020 ◽  
Vol 35 (38) ◽  
pp. 2050314
Author(s):  
M. L. Nekrasov

We show that Gribov diffusion of the partons in the impact parameter plane, which leads to the square-root-of-logarithmic growth of the transverse size of the hadrons, can occur only simultaneously with a similar diffusion in the transverse-momentum space. At the same time, a restriction of the partons in the transverse momenta entails an increase in their propagation in the impact parameter plane. Ultimately this leads to a logarithmic growth of the transverse size of hadrons at asymptotically high energies.


Author(s):  
H. J. Bhabha

In a recent paper I developed a method for calculating the probability of the creation of an electron pair in the collision of two charged particles moving with a relative velocity very near that of light. I showed there that under certain conditions it is legitimate to treat one of the colliding particles, say the heavier one of charge Z2 and rest mass M2, which we shall call the particle 2, as fixed at the origin of coordinates, and the other, of charge Z1 and rest mass M1, which we shall call the particle 1, as moving classically along a straight line with uniform velocity V in the direction of the z-axis, passing the other particle 2 at a minimum distance of approach (impact parameter) b. I developed expressions (given by (18) to (22) of A) giving the probability of the transition of an electron from an initial state of negative energy E0 and momentum p0 lying in an element of momentum space dp0 to a final state of energy E and momentum p lying in an element of momentum space dp, under the combined perturbing influence of the two colliding particles when they pass at a minimum distance b. The initial state of the electron, left vacant after the transition, appears as a positron of momentum p+ = − p0. To get the differential effective cross-section for the creation of the above pair, we must integrate this probability over all values of the impact parameter b, and this integration can be performed easily as shown in A. The final result can be written as a sum of a finite number of doubly infinite integrals (A, (24)). The purpose of this paper is to carry through the evaluation of these integrals for certain special cases, and to consider the effects of screening. The results have already been communicated in A.


2007 ◽  
Vol 16 (07n08) ◽  
pp. 2029-2034
Author(s):  
SONG ZHANG ◽  
G. L. MA ◽  
Y. G. MA ◽  
X. Z. CAI ◽  
J. H. CHEN

It has been observed a “Mach-like” structure of di-hadron azimuthal correlations in Au + Au central collisions at [Formula: see text] in the framework of a multi-phase transport model (AMPT) with both partonic and hadronic interactions. In this paper, we will show centrality, transverse momentum (pT) and pseudorapidity (η) dependences of “Mach-like” structure. The splitting parameter D, i.e. half distance between two splitting peaks on away side, decreases with the impact parameter b (corresponding to centrality) and slightly increases with transverse momentum of associated hadrons [Formula: see text], which from string melting AMPT version is consistent with experimental results. And the splitting parameter D is flat in mid-pseudorapidity region and rapidly decreases with the increasing of high-|η assoc |.


2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hongxi Xing ◽  
Cheng Zhang ◽  
Jian Zhou ◽  
Ya-Jin Zhou

Abstract We present a detailed study of vector meson photoproduction in ultraperipheral heavy ion collisions (UPCs). Using the dipole model, we develop a framework for the joint impact parameter and transverse momentum dependent cross sections. We compute the unpolarized cross section and cos 2ϕ azimuthal angular correlation for ρ0 photoproduction with ϕ defined as the angle between the ρ0’s transverse momentum and its decay product pion meson’s transverse momentum. Our result on unpolarized coherent differential cross section gives excellent description to the STAR experimental data. A first compari- son between theoretical calculation and experimental measurement on the cos 2ϕ azimuthal asymmetry, which results from the linearly polarized photons, is performed and reasonable agreement is reached. We find out the characteristic diffractive patterns at both RHIC and LHC energies and predict the impact parameter dependent cos 2ϕ azimuthal asymmetries for ρ0 photoproduction by considering UPCs and peripheral collisions. The future experimental measurements at RHIC and LHC relevant to our calculations will provide a tool to rigorously investigate the coherent and incoherent production of vector meson in UPCs, as well as to probe the nuclear structure in heavy ion collisions.


2019 ◽  
Vol 34 (32) ◽  
pp. 1950259 ◽  
Author(s):  
S. M. Troshin ◽  
N. E. Tyurin

We comment briefly on relations between the elastic and inelastic cross-sections valid for the shadow and reflective modes of the elastic scattering. Those are based on the unitarity arguments. It is shown that the redistribution of the probabilities of the elastic and inelastic interactions (the form of the inelastic overlap function becomes peripheral) under the reflective scattering mode can lead to increasing ratio of [Formula: see text] at the LHC energies. In the shadow scattering mode, the mechanism of this increase is a different one, since the impact parameter dependence of the inelastic interactions probability is central in this mode. A short notice is also given on the slope parameter and the leading contributions to its energy dependence in both modes.


2011 ◽  
Vol 20 (08) ◽  
pp. 1735-1754 ◽  
Author(s):  
M. MOHERY ◽  
M. ARAFA

The present paper deals with the interactions of 22 Ne and 28 Si nuclei at (4.1–4.5)A GeV /c with emulsion. Some characteristics of the compound multiplicity nc given by the sum of the number of shower particles ns and grey particles ng have been investigated. The present experimental data are compared with the corresponding ones calculated according to modified cascade evaporation model (MCEM). The results reveal that the compound multiplicity distributions for these two reactions are consistent with the corresponding ones of MCEM data. It can also be seen that the peak of these distributions shifts towards a higher value of nc with increasing projectile mass. It may further be seen that the compound multiplicity distributions becomes broader with increasing target size and its width increases with the size of the projectile nucleus. In addition, it has been found that the MCEM can describe the compound multiplicity characteristics of the different projectile, target and the correlation between different emitted particles. The values of average compound multiplicity increase with increasing mass of the projectile. Furthermore, it is observed that while the value of 〈nc〉 depends on the mass number of the projectile Ap and the target mass number At, the value of the ratio 〈nc〉/D(nc) seems to be independent of Ap and At. The impact parameter is found to affect the shape of the compound multiplicity distribution. Finally, the dependence of the average compound multiplicity on the numbers of grey and black particles, and the sum of them, is obvious. The values of the slope have been found to be independent of the projectile nucleus.


2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1091-1093 ◽  
Author(s):  
TIMOTHY K. NELSON

The CDF Layer 00 detector consists of single-sided silicon sensors assembled on the beampipe, forming the innermost of eight silicon layers in the CDF detector for Run II of the Fermilab Tevatron. Radiation tolerant p-in-n silicon with 25(50) μm implant(readout) pitch are mounted on a lightweight, cooled support structure and connect to electronics outside the tracking volume via long, fine-pitch cables. Layer 00 will significantly improve the impact parameter resolution and enhance the longevity of the silicon system, benefitting a large portion of the physics program for Run II.


An experiment is described in which pairs of water drops of different size were caused to collide during free fall at a velocity equal to the difference of their terminal velocities in still air. The collision parameters of trajectory, drop size, and drop charge were controlled with precision, and impacts of a particular kind could be reproduced indefinitely. By using synchronized flash photography, well in excess of 30000 measurements were taken from more than 10000 frames of film of the resulting behaviour of the water-drop pairs. Data are discussed in terms of an impact parameter, X which defines the relative trajectory of the drops in the centre-of-mass frame, and three energy parameters e C , e R and e T which delineate the properties electrostatic energy, rotational energy, and total energy of the two-drop system before impact. Input parameters were confined to values appropriate to natural rainfall. After collision four basic types of rotation occurred, the particular kind of rotation depending upon X , e C , e R and e T . Measured rates of rotation were compared with that to be expected from a simple model of inelastic collision between solid spheres and showed a marked resemblance. Distributions of mass after collision were compared with a model based upon a bimodal Gaussian distribution to good effect. In addition, frequency distributions of the number of drop products resulting from a given collision were prepared showing the controlling influence of the impact parameter, X , and the effect of varying drop charge. Relations were also established between statistical values for the coalescence efficiency of a given drop pair and the input parameters; however, while all results were consistent and reproducible, the effect of drop charge could not be demonstrated by a simple model.


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