W-boson-loop versus ultraheavy-fermion-loop contributions to the processγγ→ZZ

Abstract

The computation of the cross section for yy + Z Z to one-loop order in the standard model with mHi,,. = 100 GeV shows that the W-loop contribution dominates the unpolarized cross section. A signal of a hypothetical fourth family of ultraheavy particles could be detected at energies below the fourth-family mass only if both final Z are longitudinal. The mass, however, could not be determined because the results are insensitive to its value. PACS number(s): 12.15.Ji, 12.15.Ff, 13.10.+q In the minimal standard electroweak model [l] the known fermions are grouped in three families and the neutrinos are treated as massless. However, no symmetry principle forbids massive Dirac neutrinos and/or other families. Experimental data fix the number of different light (m, << M z ) neutrinos to three [2], but allow a fourth family of leptons and quarks if it contains %early degenerate" multiplets of ultraheavy particles [3].The very high energy needed for direct production of these particles makes its potential detection difficult also a t future colliders. For this reason Chanowitz [4] has recently proposed to detect such hypothetical in the process yy + Z Z at energies much larger than the top quark mass, but yet lower than the mass of the fourth generation fermions. The idea is based on the fact that the contribution to the cross section of the light families is decreasing like 11s in this energy range, while the contribution of the fourth family with ultraheavy fermions is growing like s. The computation [4] is incomplete, because the Wloop contribution was neglected. The purpose of this Rapid Communication is to fill the gap in [4], calculating also the W-loop contribution to the amplitude in the context of the minimal standard model with one Higgsboson doublet [I]. Some of the Feynman diagrams with one loop contributing to yy + Z Z are shown in Fig. 1.They can be divided into four groups. The first contains graphs with one loop formed by the gauge bosons W * , the "would-be Goldstone bosons" q5* and the ghosts c*, -ci, but without any Higgs-boson line (first row in Fig. 1-84 graphs), the second with one W k , di, ci, loop and a Higgs-boson propagator in the s channel (second row-14 graphs), the third with one fermion loop and no Higgs-boson lines (third row-3 graphs), and the last with one fermion loop and a Higgs boson in the s channel (fourth row-1 graph). The complete set of Feynman diagrams belonging to the first group can be found in [5] (with ZZyy external lines instead of Zyyy). The graphs for the vertex H y y at one-loop order, which form, with the H propagator in the s channel and the vertex H Z 2 a t the tree level, the diagrams of the second group, can be found in [6]. The calculation was done in the 't HooftFeynman gauge. A computer package for symbolical calculation of Feynman graphs, written in SMP, was used to obtain analytic expressions of all the Feynman diagrams. The so-obtained expressions for some diagrams are very long. The first diagram shown in Fig. 1 alone has 608 terms, for example. Each ...

Decays $Z\toγγ$ and $Z\to gg$ in the Standard Model Extension

“…While motivated by specific scenarios in the context of string theory, 47,48 general relativity with spontaneous symmetry breaking, 49-52 a The exception is the ZZZZ vertex, which can be induced at the tree level via the interchange of a neutral Higgs boson. b Light by light scattering has been explored in diverse contexts in Refs., [5][6][7][8][9][10][11][12][13][14][15][16][17] works about the Zγγγ vertex can be found in Refs., [18][19][20][21] the ZZγγ vertex is studied in Refs., [22][23][24][25][26][27][28][29][30][31] and quartic neutral couplings among Z gauge bosons, photons, and gluons have been investigated in Refs. 32-37 c It is important to stress that the Landau-Yang's theorem is actually only applicable to on-shell particles.…”

Signals for low scale gravity in the processγγ→ZZ

“…Numerical calculations of the cross sections were also performed in Refs. [10,11]. More recently the helicity amplitudes were again derived as a background for a search for possible virtual supersymmetric particles 1 After this work was completed, we became aware of a paper [9] which included an approximate calculation of the Standard Model background and calculated the helicity amplitudes.…”

Decays Z → γγ and Z → gg in the Standard Model Extension

“…Once performed some algebraic manipulations, the expressions in Eqs. (24,25,26,27) can be rewritten as…”

“…b Light by light scattering has been explored in diverse contexts in Refs., [5][6][7][8][9][10][11][12][13][14][15][16][17] works about the Zγγγ vertex can be found in Refs., [18][19][20][21] the ZZγγ vertex is studied in Refs., [22][23][24][25][26][27][28][29][30][31] and quartic neutral couplings among Z gauge bosons, photons, and gluons have been investigated in Refs. 32-37 c It is important to stress that the Landau-Yang's theorem is actually only applicable to on-shell particles.…”