Advances in High Energy Physics
Volume 2020 (2020), Article ID 5847430, 6 pages
https://doi.org/10.1155/2020/5847430

Research Article

Boson Production via - and Pb-Pb Collisions at

Leonard S. Kisslinger¹ and Debasish Das²

¹Department of Physics, Carnegie Mellon University, Pittsburgh PA 15213, USA
²Saha Institute of Nuclear Physics, HBNI, 1/AF, Bidhannagar, Kolkata 700064, India

Correspondence should be addressed to Leonard S. Kisslinger; kissling@andrew.cmu.edu

Received 10 May 2020; Accepted 13 August 2020; Published 24 September 2020

Academic Editor: Grégory Moreau

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.

Abstract.

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.

1. Introduction

This is an extension of our recent work on heavy quark state production via Xe-Xe collisions at [1] and heavy quark state production in Pb-Pb collisions at [2]. More than three decades ago, and bosons were observed at CERN via proton-antiproton experiments at [3]. CMS experiments on electroweak boson production via relativistic heavy ion collisions (RHIC) are related to our present research [4].

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 [5]. 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 [5], they have little interaction with the nuclear medium and by ALICE experiments that measured boson production in Pb-Pb collisions [6] and in -Pb collisions [7, 8] at . The estimate of boson production via Pb-Pb collisions makes use of Ref [9], which was based estimates of heavy quark state production in - collisions [10]. 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 [11] except the quarks have a vertex with bosons rather than pions and there is no gluon- vertex. Also, it was shown [12] 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).

Figure 1: , a hybrid component, to .

2. Production in - Collisions with

The cross section for in terms of [10, 13], the quark distribution function, is

where is the rapidity, , and . We take in the present work, so .

For , the quark distribution functions [10, 13] are

Therefore, from equations (30), (2), and (3),

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.

Figure 2: , a standard component, to .

In Figure 1, production with the hybrid component of is shown.

Figure 3 shows the coupling processes needed for Figures 1 and 2.

(a)

(b)

Figure 3: (a) Gluon-quark coupling and (b) - coupling.

In Figure 3(a), the operator giving the gluon sigma coupling is

where and is the gluon field.

In Figure 3(b), with with as the component of the vector boson and defining [5], the coupling is [14]

As shown in Section 3.2, the term does not contribute to , so we define .

3. Decay to

In this section, we estimate the decay of to for both the standard and hybrid components of as shown in Figures 1 and 2.

3.1. Decay to via the Standard Component of

As in Ref [11], the correlator corresponding to Figure 2 is

where the quark propagator , is the mass of a charm quark (), , and [5]. Since is independent of color, .

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 ,

Therefore,

Using

one finds

with

3.2. Decay to via the Hybrid Component of

The two-point correlator for the hybrid -, corresponding to Figure 1, without the gluon- or quark- coupling is [12] (see equation (18))

The correlator , obtained from Figure 1, is

Note that [15] (with )

Therefore,

with

Note that , so the term in equation (21) vanishes. Therefore, from equation (21),

Since ,

As in equation (11), using , one obtains for the terms

For the terms in equation (22),

From equations (22), (25), and (26) and using , the terms in equation (22) are

Defining , with as the boson momentum, from equations (14), (22), (23), (24), (27), and (13),

From equations (5) and (20), taking the sum with ,

with the boson momentum , so as in our calculation.

4. Calculation of via Calculation of for

Carrying out the integrals for shown in equation (15), one obtains from equation (29) the values of , with , which from equation (5) is the cross section with the proton-proton , shown in Figure 4.

Figure 4: with .

Note that [5] 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 [10]) in the color octet model in Pb-Pb collisions is given by [9]

where is the number of binary collisions, is the nuclear modification factor, and is the total energy in Pb-Pb collisions.

From [2], . Therefore,

or is approximately 130 times the results shown in Figure 4.

6. Conclusions

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 [6] measure boson production via Pb-Pb collisions at at large rapidities.

Data Availability

All data for our article can be found in the references, especially Refs [4–6, 12, 15], as is stated in our article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

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.

References

L. S. Kisslinger and D. Das, “Heavy quark state production and suppression via Xe-Xe collisions at ,” https://arxiv.org/abs/1801.03826.

L. S. Kisslinger and D. Das, “Heavy quark state production in Pb-Pb collisions at ,” Journal of High Energy Physics, vol. 105, 2017.

UA1 Collaboration, G. Arnison, A. Astbury et al., “Experimental observation of lepton pairs of invariant mass around 95 GeV/c² at the CERN SPS collider,” Physics Letters B, vol. 126, no. 5, pp. 398–410, 1983.

CMS Collaboration, “Study of Z boson production in PbPb collisions at ,” Physical Review Letters, vol. 106, no. 21, article 212301, 2011.

Particle Data Group, “On the Particle Data Group evaluation of and branching ratios,” Physical Review D, vol. 98, article 030001, 2018.

ALICE Collaboration, “Measurement of Z 0-boson production at large rapidities in Pb–Pb collisions,” Physics Letters B, vol. 780, pp. 372–383, 2018.

ALICE Collaboration, “Z-boson production in p–Pb collisions at and Pb–Pb collisions at ,” https://arxiv.org/pdf/2005.11126.pdf.

ALICE collaboration, “W and Z boson production in p-Pb collisions at ,” Journal of High Energy Physics, vol. 2017, no. 2, p. 77, 2017.

L. S. Kisslinger, M. X. Liu, and P. McGaughey, “Heavy-quark-state production in A-A collisions at ,” Physical Review C, vol. 89, no. 2, article 024914, 2014.

L. S. Kisslinger, M. X. Liu, and P. McGaughey, “Heavy-quark-state production in p−p collisions,” Physical Review D, vol. 84, no. 11, p. 114020, 2011.

L. S. Kisslinger, Z. Li-juan, W.-x. Ma, and P. Shen, “Ψ(2S) decay to J/Ψ(1S) + 2π or J/Ψ(1S) + σ + 2π,” International Journal of Theoretical Physics, vol. 56, no. 3, pp. 942–947, 2017.

L. S. Kisslinger, “Mixed heavy quark hybrid mesons, decay puzzles, and RHIC,” Physical Review D, vol. 79, no. 11, p. 114026, 2009.

“CTEQ6,” http://hep.pa.msu.edu/cteq/public/cteq6.html.

D. Wackeroth and W. Hollik, “Electroweak radiative correc`tions to resonant charged gauge boson production,” Physical Review D, vol. 55, pp. 6788–6818, 1997.

L. S. Kisslinger, D. Parno, and S. Riordan, “Hybrid Charmonium and the Puzzle,” Advances in High Energy Physics, vol. 2008, Article ID 982341, 16 pages, 2008.