INSTITUTE FOR fflGH ENERGY PHYSICS ШЕР 90-92 TD A.A. Iikhoded Z° decays due to the three-boson interaction Submitted to Pkys. Lett. В Protvino 1990 ГОК 538.1.01 Abstract А.А. Iikhoded ft decays due to the three-boson interaction: ШЕР Preprint 90-92. — Protvino, 1990. — p. 16, refe. 17. The e*e~-annihilation reactions with the three-vector-boson interaction and a final state meson have been discussed The possibility of making use of these processes for the exploration of the three-vector-boson reactions was estimated for the mesons corre- sponding to the diagonal Cabibbo-Kobayashi-Maskawa matrix elements (1Г, д А, Д, Tt) at the present and planned luminosity of the LEPl collider (y/S~ 100 GeV). Аннотация A.A. Лиходед. Распады Z"-6oooHa, обусловленные трехбоооиныи взаимодействием : Препринт ИФВЭ 90-92. — Протвино, 1990. —16 с, бнблиогр.: 17. Рассмотрены реакции б+е'-анивгидяцни с трехбозонным взаимодействием и ме- ооноы в конечном состоянии. Дла случая обраоовашы мезонов, соответствующих диагональным элементам матрацы Кабнббо-Кобаяши-М&скава (iT,ft Д ,Д,/7), оце- нена вооможность использования данного класса реакций для изучения трехбооон- ното взаимодействия при существующей и возможной светнмостях коллайдера LEP1 (/5~ loo ) i — Institute for High Energy Physics, 1990. Introduction The main two aspects of the W-pair production in the reaction of e+e~- annihilation exist in the physics of today. The first one is a precise de- termination of the W mass and width, W-boson coupling constants with different quark flavours, i.e., the Cabibbo-Kobayashi-Maskawa matrix ele- ments. The precise measurement of the W mass is particularly important for testing the Standard Model at the loop level. Second, the reactions of the W-pair production provide the best opportunity to measure directly the three-vector-boson couplings 7WW, ZWW via s - channel in e+e~- annihilation and , as it is shown in [1] , [2], even a small deviation of these couplings from their guage theory values can lead to observable effects. However, because of the low LEP1 energy the detailed investigation of the three-vector-boson vertex is the LEP2 collider problem. Small cross- sections of e+e~ —* W~{l~v)W+(l+v) [3] processes, in fact, exclude such attempts at LEP1 with yfs ~100 GeV. The coupling constants measure- ment is also possible in e+e~ —* W(qq)W reactions, whose cross-sections are higher than those of processes with the leptonic modes of W-boson decay. Although the cross-sections of e+e~ —+ W{qq)W are too small [2] 6 (Г(г°-Уг+д-1/зЬ/з)/Г{г°->ц+»-) ~ 10" [3]), nevertheless, according to the recent proposals [4] on increasing the LEP luminosity, it seems possible to suggest a simple way for making the process of e+e~-annihilation with W-boson and quark-pair in the final state experimentally observable. The aim of this work is to investigate the quark-pair production processes with the subsequent hadronization of this pair into a meson (see Fig.l). Fig.l The cross-sections of the processes with the production of тг±,р±,Аг and (cs) - mesons, corresponding to the diagonal Cabibbo-Kobayashi- Maskawa matrix elements will be evaluated. As the estimates presented bellow are mainly of a demonstrative character, we will omit the small background (7- exchange, see Fig.2) and interference (jZ) terms at en- ergies near the Z°-resonance pole,« q Fig.2 1 Vertex of the WWV—interaction. The general form of the three-vector-boson interaction of two charged vector bosons with a neutral vector boson has been much spoken about in literature [1,5 and refs. therein]. In the momentum space the relevant WWV-vertices can be written as follows: Fig.3 аР = ГЛя-яУя - iyAw !~Я)Р (1) iw where V = "f,Z°. The form-factors ff introduced here are dimension- less functions of p2. In the first order in p2. these form-factors can be represented in the following form: Л = -V f! = 9^ + kv + Xy (2) /6 - fv 1 \ /7 = ~2Av > and the coupling constants gv/wv for 7-quant and Z°-boson are gww-r = —e , gwwz = —e • cot^w , (3) where e is the positron charge, в\у is the Weinberg angle. For coupling a charge vector boson with 7-quantum there exists a simple interpretation of parameters contained in (1): g7 defines the W charge, ky is generally termed the "anomalous" magnetic moment of W [6], A7 is connected [7] with the magnetic moment nw and the electric quadrupole moment Qw of W-boson. The fey and A7 constants at parity violating terms are connected with the electric dipole dw and magnetic quadrupole Qw moments of W-boson as Let us discuss the three-vector-boson interaction in the approximation of the Standard Model. As shown in [1], in the Standard Model there exist sufficiently rigorous restrictions on form-factors (2) /ft.) = 1 + O{a) /ft.) = O(a) , (6) /ft.) = 2 + O(a) both for 7-quantum and for Z°-boson. It is worth mentioning that the «-dependence of form-factors arises only at the terms of the order of a. These restrictions can be written as kv = l + O(a) , Xv = O(a) . (7) Thus, in the Standard Model the vertex of the three-vector-boson inter- action can be rewritten in the following form: • (8) In the calculations presented below expression (8) will be used to repre- sent the three-boson vertex in the momentum space. 2 W-pair production with final state meson. The W-pair production processes in the e+e -annihilation in resonance Z° mode with a final state meson are shown on the diagram Fig.4 4 .where C{ is a W-meson(Afj) coupling constant. Let us choose among the mesons produced after quark-pair hadronization the mesons cor- responding to the large Cabibbo-Kobayashi-Maskawa matrix elements \Vril = 0.9747±0.0011 [8], \Va\ > 0.66 [9] or \VC.\ = 0.88±0.10 [10]. (ud)-mesons Let us discuss the case with (ud)-mesons and perform evaluations for the тг-meson production process. The coupling constant of W* with 7ri /x (see Fig.5) is well known from the experiment [11] /, = 131.69 ± 0.15 MeV Fig.5 The matrix element of the process shown in Fig.6 Fig.6 can be written as - ft W" where g and 3 are the guage constants of the weak neutral and charged currents, фт is a pseudoscalar 7r-meson wave function normalized by unity, 2 \Vud\ = cos9c, eu is a polarization vector of on-shell W-boson, £ = sin dw Calculating the matrix element squared , summing over the initial and averaging over final particle polarizations one obtains dt ~ 64тг ' v 8\/2 (Aijs)? + A2(s)t where g = ~^~, Ai(s) are the functions of s obtained as a result of tracing ( the analytic forms of Ai are represented in Appendix A). The 2 numeric values of Ai(s,тпж, Mz, Mw) at s =(91.2 GeV) , Mz = 91.2 GeV, Mw = 81 GeV and mT = 0.14 GeV are shown bellow: GeV2 6 4 A2 = -1.667-10 GeV . (11) 11 6 A3 = 1.036 • 10 GeV The total cross-section * = Т%^ (12) Integration yields <T ~ 0.2 • 10"7nb ~ 0.2 • 10-40cm2 . (13) At the highest LEP1 luminosity ~ 5 • lO^cm'V"1 such a small cross- section makes this process unobservable. However, when detecting the final meson states other channels, for example, processes with the p, A\ and (cs)-mesons production can contribute. The coupling constant of p-meson with W can be obtained from the r-lepton decay. 9рФа , (14) Fig.7 where фа is the wave function of the vector p-meson and 2 др is the scalar parameter of m dimensionality. To determine gp one can note that in Fig.7 gp = /, where / is the value of the loop integral, and we can write шГ^Г ' (15) where 7 is a dimensionless parameter, which from a detailed e+e~-annihi- lation treatment is — = 2.36 ±0.18 . (16) 4тг Thus, 2 д р 2 dt 64x ' V 8^/2 f m p 2 2 2 (17) - M zf + M zT z)((ml - where Bt are analogous to A{ in (10) and B{ ~ A{ (see Appendix A): 2 2 Bx = -9.58 • 10 GeV 6 4 J2 = -1.68 10 GeV . (18) 11 6 B3 = 1.03 • 10 GeV Then the cross-section of />-meson production can easily be evaluated 111 p Making use of (16) and taking into account the p-meson mass, one obtains — 2-145 •CT(e+e-_jj»--.w(,)w) • (20) Similarly, one can evaluate the contribution from an axial Лх(1260)- meson. The ^iW^-constant can be obtained from the Weinberg sum rule applying it to the r —• vT + (2re + 1)тг decay [12] lAi Ip and taking into account the difference of A\- and p-meson masses, we get 9\ mAj = ^-.a{eU-^Zo^w(p)w) (21) ~ 0.79- (cs)- mesons The large (~1) matrix element |V^S| corresponds to (cs)-mesons and D*(1969) among them. The order of magnitude of the Df -mesons pro- duction cross-oection Fig.8 can be estimated in the same way as in the case with тг, А\ and />-inesons. Estimates of the pseudoscalar X^-meson constant were obtained from the QCD sum rules [13] fo, — 220 MeV and from the lattice calculations of UCLA [14] fD, = 234 ± 46 ± 55 MeV and ELC [15] fD, = 215 ± 17 MeV. Then the cross-section of the process shown in Fig.8 is 2 \Vc,\ fh.