Research Article | Open Access
Leonard S. Kisslinger, Debasish Das, " Boson Production via - and Pb-Pb Collisions at ", Advances in High Energy Physics, vol. 2020, Article ID 5847430, 6 pages, 2020. https://doi.org/10.1155/2020/5847430
Boson Production via - and Pb-Pb Collisions at
We estimate the production of bosons, with as the component of a vector boson, via - collisions using previous work on production in - collisions, with the new aspect being the creation of bosons via quark interactions. We then estimate the production of bosons via Pb-Pb collisions using modification factors from previous publications.
This is an extension of our recent work on heavy quark state production via Xe-Xe collisions at  and heavy quark state production in Pb-Pb collisions at . More than three decades ago, and bosons were observed at CERN via proton-antiproton experiments at . CMS experiments on electroweak boson production via relativistic heavy ion collisions (RHIC) are related to our present research .
As the photon is the quantum of electromagnetic interactions, a boson is a quantum of weak interactions with no electric charge. The boson with mass is a vector boson with quantum spin 1 . Therefore, a boson has three components, , with , 0, and 1.
Our present estimate of the production of bosons, via Pb-Pb collisions, is motivated by the fact that since bosons have only a weak interaction , they have little interaction with the nuclear medium and by ALICE experiments that measured boson production in Pb-Pb collisions  and in -Pb collisions [7, 8] at . The estimate of boson production via Pb-Pb collisions makes use of Ref , which was based estimates of heavy quark state production in - collisions . Note that when the final calculation and results are presented in Sections 3 and 4, the momentum , the momentum of the boson produced by Pb-Pb collisions at , and , a boson.
Our present work is also related to an estimate of to decay to mesons  except the quarks have a vertex with bosons rather than pions and there is no gluon- vertex. Also, it was shown  that the state is approximately a 50%-50% mixture of a standard charmonium and hybrid charmonium state: while is essentially a standard state , which we use in our estimate of boson production via . Having a hybrid component, , is important for boson production from decay as the active gluon component of produces a boson, as shown in Figure 1 (Section 2).
2. Production in - Collisions with
We use the following notation: with and defined below.
The normal component of decaying to with production via quark- coupling is shown in Figure 2.
In Figure 1, production with the hybrid component of is shown.
In Figure 3(a), the operator giving the gluon sigma coupling is where and is the gluon field.
As shown in Section 3.2, the term does not contribute to , so we define .
3. Decay to
3.1. Decay to via the Standard Component of
Thus, the correlator for decay to is
The trace in equation (9) is
Using the fact that the trace of an odd number of s vanishes and ,
Using one finds with
3.2. Decay to via the Hybrid Component of
The correlator , obtained from Figure 1, is
Note that  (with )
As in equation (11), using , one obtains for the terms
For the terms in equation (22),
4. Calculation of via Calculation of for
Note that  the units for a cross section are . As it is customary, we take .
5. Production in Pb-Pb Collisions with
The cross section for the production of a heavy quark state with helicity (for unpolarized collisions ) in the color octet model in Pb-Pb collisions is given by  where is the number of binary collisions, is the nuclear modification factor, and is the total energy in Pb-Pb collisions.
Using the relationship between the cross sections and shown in equation (30) and decay to for both the standard and hybrid components of , the cross section was estimated for and the boson momentum , as shown in the figure. This should be useful for the experimental measurement of boson production via Pb-Pb collisions at . For simplicity, we assumed that the , where with as the longitudinal momentum. Current experiments  measure boson production via Pb-Pb collisions at at large rapidities.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Author D. Das. acknowledges the facilities of Saha Institute of Nuclear Physics, Kolkata, India. Author L.S. Kisslinger acknowledges support in part as a visitor at the Los Alamos National Laboratory, Group P25. The authors thank Bijit Singha for helpful suggestions.
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Copyright © 2020 Leonard S. Kisslinger and Debasish Das. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.