Study of Trilinear Gauge Boson Couplings ZZZ, ZZγ and Zγγ

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1 DELPHI Collaboration DELPHI - CONF March, Study of Trilinear Gauge Boson Couplings, γ and γγ Preliminary P.Bambade, LAL, Orsay G.Borissov CERN C.Matteuzzi, V.Verzi Dipartimento di Fisica, Università di Milano and INFN sez.milano, Italy J. Rehn Inst. fur Exper. Kernphysik, Karlsruhe I. van Vulpen NIKHEF, Amsterdam M. Witek INP, Krakow Abstract Trilinear neutral gauge boson couplings, γ and γγ have been studied with the DELPHI detector, using data at energies between 89 and 8 GeV. Limits are derived on these couplings from an analysis of the reactions e + e γf f with f = q or ν and of the reactions e + e f ff f using all the visible channels except τ + τ q q, τ + τ ν ν and l + l l + l.

2 Introduction This note describes a measurement of the neutral triple gauge boson couplings, γ and γγ by DELPHI using LEP data taken between 997 and at energies between 89 and 8 GeV. The neutral coupling sector is probed by means of the reactions e + e γ and e + e. As shown in figure, within the Standard Model (SM) these processes receive contributions from the t-channel exchange of an electron. The same figure shows new physics contributions that come from the s-channel exchange of a virtual γ or, leading to γ or production via a triple vector boson coupling with subsequent decay of the in the final state. e + /γ e + /γ e + /γ + + V= * /γ * e - e - e - Figure : Feynman diagrams for the production of two on-shell gauge bosons and γ. The first two on the left represent the Standard Model contribution, while the third one involves an anomalous interaction among three neutral gauge bosons. The parametrization of the, γ and γγ vertex functions used here follows that suggested in []. There are twelve independent anomalous couplings. Calling V the exchanged boson (V =, γ), one has the couplings fi V (i =,) for final state and h V i (i =,, ) for γ final state. The couplings f V, h V and h V are CP-violating and f V, h V and hv are CP-conserving. When the final photon is on-shell, the γ production contributes to the f fγ final state. The differential cross-section for this process in presence of anomalous couplings has been calculated using code [] with vertex factors modified by a factor i according to the correction suggested in []. The kinematic region with high photon energy and large photon polar angle is sensitive to the anomalous couplings. In this region, the anomalous interactions give rise to a change in the total rate and to an enhancement of the production of longitudinally polarized bosons []. The differential cross-section for the process e + e f ff f with anomalous couplings has been calculated using code from the generator DELTGC []. The visible four-fermion final states receive contributions from both and γ production when the final photon is virtual. Therefore one can use this process to derive limits also on h V i couplings. However, due to the higher e + e f fγ cross-section, the sensitivity is much better when the photon is on-shell. In the following the four-fermion production is considered only in the kinematic region that maximizes the sensitivity to diagrams [6, 7]. The total cross-section is very sensitive to the anomalous couplings and the sensitivity strongly increases with s. Large interference between SM and anomalous am-

3 plitudes arises for CP-conserving couplings (expecially for f ) when one considers the differential cross-section dσ/d cos θ, where θ is the production angle with respect to the beam axis []. Compared to [] and [6, 7], the analyses presented in this note include the data collected in the year at energies ranging up to s 8 GeV corresponding to an integrated luminosity of about pb. Moreover, the analysis of the final state is improved in sensitivity because the measurement of the anomalous fi V couplings is based on a maximum likelihood fit to dσ/d cos θ. Selection of events Events were recorded in the DELPHI detector. Detailed descriptions of the DELPHI components can be found in [8] and the description of its performance, as well as of the trigger system and of the luminosity monitor, can be found in [9].. γ final state Events with only a very energetic photon in the final state were searched for in the region covered by the HPC, the barrel electromagnetic calorimeter of DELPHI, in the range < θ γ < where θ γ is the polar angle of the photon. The selection criteria and the data samples obtained at s from 89 to GeV are described in []. Table shows the results of the selection of events from the data collected in the year. The experimental signature of γ events where the decays into jets of particles is an energetic and well isolated photon recoiling against a hadronic system. Events with this topology, and where the photon has an energy greater than GeV and is produced in the region < θ γ <, have been selected at energies ranging from 89 GeV to 8 GeV. For ν νγ channel, the selection criteria and the results obtained at s ranging from 89 to GeV are described in [] while the results at higher energies are shown in table. The expected number of q qγ events has been calculated with PYTHIA relying on JETSET 7. [] for quark fragmentation while the expected number of ν νγ events has been computed with KORAL []. The total numbers of observed (expected) events used in this note are 96 (98.8) and 8 (6.) in the ν νγ and q qγ channels, respectively. Channel L(pb ) < s > N DAT A N MC efficiency(%) purity(%) ν νγ ±.7 q qγ ±. 97. ±. Table : Results of the selection of ν νγ and q qγ events collected in the year.. final state The same events selected by DELPHI to measure the cross-section are used here. A detailed description is reported in [7]. The measurement of the anomalous couplings has been done using all the visible channels except τ + τ q q, τ + τ ν ν and l + l l + l.

4 The qqqq process represents 9% of the final states and produces four or more jets in the final state. After a four-jet preselection, in order to discriminate the signal from the large background from W W and qq(γ) processes, a probability corresponding to production has been calculated. This probability is based on invariant mass information, on the b-tag probability per jet and on topological information. The process e + e l + l q q has a branching ratio of.7 %. High efficiency and high purity are attainable with a cut-based analysis thanks to the clear experimental signature given by the two leptons typically well isolated from all other particles. The decay mode ν νq q represents 8% of the final states. The signature of this decay mode is a pair of rather acoplanar jets with visible and recoil masses compatible with the mass. The most difficult backgrounds arise from single resonant W eν e processes, from W W processes where one of the W bosons decays into τν τ, and from q q events accompanied by energetic isolated photons escaping detection. The selection of events is done using a combined discriminant variable obtained with an Iterative Discriminant Analysis program (IDA) []. Finally the final state l + l ν ν has a branching ratio of.7%, and has been selected with a sequential cut-based analysis. Results on anomalous couplings Values of the neutral triple gauge boson coupling parameters h V i (V = /γ, i =,,, ), were derived from the data in the channel e + e ν νγ by comparing the observed number of events with the number predicted from the total cross-section for this process, and in the channel e + e qqγ by comparing the observed distribution of the decay angle α of the in its rest frame with predictions derived from the differential distribution dσ/d cos α. The definition and reconstruction of α are described in [] and its distribution for the full data sample collected between 998 and is compared to Standard Model expectations, in figure. The same figure shows the expected distributions for h γ = ±. obtained by reweighting [] events generated under the Standard Model hypothesis with the inclusion of the full detector simulation. The results of the fit of each h V i coupling are shown in table. These results have been obtained by combining the likelihoods for both q qγ and ν νγ channels and for the different centre-of-mass energies. In the fit to each coupling parameter, the value of the others were put to zero, their Standard Model value. Figure shows the combined likelihoods. In performing -parameter fits to the couplings, a total of 8 combinations (h V i, h V i ) are possible for the 8 couplings considered. Despite this large number of pairs, there are essentially only three situations that are conceptually different and they are described in []; they correspond to different regimes of interference between the two anomalous terms and the Standard Model term in the production amplitude. The unexcluded regions at the 9% and 68% of confidence level are shown in figure for the pairs (h, h ), (h, h ), (h γ, h γ ) and (h γ, h γ ), in the upper part of figure for the pairs (h, hγ ) (h, hγ ), and in the lower part of figure for the pairs (h, h γ ) (h, h γ ), corresponding to examples of the three different situations. Several sources of systematic effects have been studied for data at s ranging from 89 to GeV []. They have not yet been evaluated for data collected in, but their effect is expected to be similar to that estimated at lower energies: h syst / h stat %

5 for couplings h, h, h, h, h γ and h γ, and h syst / h stat % for h γ and h γ. The neutral triple gauge boson coupling parameters fi V (V = /γ, i =, ), have been measured by means of an extended maximum likelihood fit of the production angle (cos θ ) distribution for the channels selected with cut-based analyses (q ql + l and l + l ν ν). For q qq q (q qν ν) channels, in order to benefit from the performance of the analysis to distinguish the signal from the large background, the cos θ distribution has been fitted simultaneously to the probability (IDA output variable) distribution. The reconstruction of θ is free from ambiguity for all channels, except for q qq q where the indistinguibility of the jets leads to wrong pairing. The combination with the minimum value of the χ obtained on application to the event of a C kinematic fit has been retained. Figure shows the cos θ distributions for the full data sample and the Standard Model expectations. For illustrative purposes, only q qq q and q qν ν candidates in a high purity region are shown. Using the information of the production angle differential cross-section improves the sensitivity with respect to the analysis described in [6]. Also the correct dependence of the efficiency and purity on the anomalous couplings has been taken into account in this updated analysis. It was obtained by reweighting [] events generated within the Standard Model hypothesis, including all the detector effects. Figure shows the distributions obtained with this technique for f = ±.. The preliminary results of the single parameter fit of fi V couplings, obtained combining all channels and energies, are shown in table. The corresponding likelihoods are reported in figure 6, together with the unexcluded regions for -parameter fits for pairs (f, f γ ) and (f, f γ ). Systematic effects are expected from both experimental and theoretical sources but they have not yet been evaluated. Vertex Coup. 68% C.L. 9% C.L. f. +.. [.9, +.] f [., +.69] f γ [.6, +.8] f γ [.9, +.6] γ h [.,.] h [.,.] h [.,.7] h [.,.8] h γ [.,.] γγ h γ [.86,.87] h γ [.,.] h γ. +.. [.,.8] Table : Preliminary results of fits of the neutral trilinear gauge coupling parameters fi V and h V i at the 68% and 9% confidence intervals. In the fit to each coupling parameter, the other couplings were set to their Standard Model value. The errors shown are statistical only.

6 Conclusions The neutral triple gauge boson coupling parameters h V i (i =,, V = γ/) and f V i (i =,, V = γ/), have been measured studying the production of two neutral gauge bosons (γ, ). No deviation from the expectations of the Standard Model was found. Acknowledgements We are grateful to our DELPHI colleagues in the TGC and -fermion working group for useful discussions. References [] K.Hagiwara, K.Hikasa, R.D.Peccei, D.eppenfeld, Nucl. Phys. B8 (987) [] U. Baur and E. Berger, Phys. Rev. D7 (99) 889. [] G.J. Gounaris, J. Layssac and F.M. Renard, Phys. Rev. D6, 7 (). [] DELPHI Collaboration, Measurement of Trilinear Gauge Boson Couplings γ and γγ between 89 and GeV, DELPHI -8 CONF 7 (). [] V.V. Kostyukhin, V.F. Obraztsov and O.P. Yushchenko, DELTGC - A program for four-fermion calculations, DELPHI 99- PHYS 86 (999). [6] DELPHI Collaboration, Phys. Lett. B97 () 99. DELPHI Collaboration, Update of production measurement in e + e interactions using data at 9- GeV, DELPHI - CONF (). [7] DELPHI Collaboration, DELPHI - CONF 6. [8] DELPHI Collaboration, P.Aarnio et al., Nucl. Instr. Meth. A (99) [9] DELPHI Collaboration, P.Abreu et al., Nucl. Instr. Meth. A78 (996) 7 [] T.Sjöstrand, PYTHIA.7 / JETSET 7., CERN-TH 7/9 (99). [] S. Jadach et al., Comp. Phys. Comm. 79 (99). [] T.G.M. Malmgren, Comp. Phys. Comm. 6 (997) ; T.G.M. Malmgren and K.E. Johansson, Nucl. Inst. Meth. (998) 8. [] G.K. Fanourakis, D. Fassouliotis and S.S. Tzamarias, Nucl. Inst. Meth. A (998) 6.

7 DELP HI (P RELIMINARY ) Entries/. 7 7 γ DATA qqγ back h γ = +. h γ = cosα * Entries/. 6 DATA qqqq qqll qqνν llνν back f = cosθ f = -. Figure : Upper plot: distribution of the decay angle of the in its rest frame in hadronic γ events. Lower plot: distribution of the polar angle in events. In both cases, all the data selected at different centre-of-mass energies are included, except for q qq q and q qν ν channels where only candidates in high purity region have been considered. 6

8 DELP HI qqγ + ννγ (P RELIMINARY ) -log(l) h -log(l) h h h h h -log(l) h γ -log(l) h γ h γ h γ h h Figure : Likelihoods ( log L) obtained for the single parameter fits in the e + e ννγ and e + e qqγ channels. In the fits, the values of the other couplings were fixed to zero, their Standard Model values. 7

9 9% 68% h h γ DELPHI qqγ+ννγ (PRELIMINARY) h. h h γ h h γ h γ Figure : The regions accepted at the 9% (external contour) and at 68% confidence level (internal contour) for pairs of couplings whose amplitudes interfere strongly. The fits were made combining the measurements for qqγ and ννγ channels and for the different centre-of-mass energies. The points represent the Standard Model expectations for these couplings. 8

10 γ h.6. DELPHI qqγ+ννγ (PRELIMINARY) γ h.. 9% 68% γ h h. γ h h h h Figure : The regions accepted at the 9% (external contour) and at 68% confidence level (internal contour) for pairs of couplings (h γ i,h i ). The fits were made combining the measurements for qqγ and ννγ channels and for the different centre-of-mass energies. The points represent the Standard Model expectations for these couplings. 9

11 DELPHI (PRELIMINARY) -Log(L) f f γ -Log(L) f f γ f γ. -.. f V 9% 68% f γ. -.. f V 9% 68% SM SM f f Figure 6: Upper figures show the likelihoods ( log L) obtained for the single parameter fits to the fi V couplings. Lower figures show the regions accepted at the 9% (external contour) and at 68% confidence level (internal contour) for pairs of couplings with the same CP behaviour. The likelihoods have been obtained combining the measurements performed in all channels at the different centre-of-mass energies.