Non-Resonant Diagrams in Radiative Four-Fermion Processes

FR9700401

KEK-CP-015 KEK Preprint 94-46 LAPP-Exp.-94.09 June 1994 H

Non-resonant Diagrams in Radiative Four-fermion Processes

J. FUJIMOTO, T. ISHIKAWA, S. KAWABATA, Y. KURIHARA, Y. SHIMIZU and D. PERRET-GALLIX

Submitted to the Proceedings of Physics at LEP200 and Beyond, Teupitz/Brandenburg, Germany, April 10 -15,1994.

L.A.P.P. B.P. 110 F-74941 ANNECY-LE-VIEUX CEDEX • TELEPHONE 50.09.16.00+ • TELECOPIE 50 2794 95 National Laboratory for High Energy Physics, 1994 KEK Reports are available from: Technical Information & Library National Laboratory for High Energy Physics l-lOho,Tsukuba-shi Ibaraki-ken, 305 JAPAN Phone: 0298-64-1171 Telex: 3652-534 (Domestic) (0)3652-534 (International) Fax: 0298-64-4604 Cable: KEK OHO E-mail: LIBRARY®JPNKEKVX (Bitnet Address) [email protected] (Internet Address) Non-resonant diagrams in radiative four-fermion processes J. Fujimoto, T. Ishikawa, S. Kawabata, Y. Kurihara. Y. Shiniizu » and D. Perret-Gallixb * Miuanii-Tateya Collaboration. KEK, Japan bLAPP-IN2P3/CNRS, France

+ The complete tree level cross section for e c~ —» e~utud-y is computed and discussed in comparison with + + the cross sections for e e~ —• e~utud and e e~ —• udud. Event generators based on the GRACE package for the non-radiative and radiative case are presented. Special interest is brought to the effect of the non-resonant diagrams overlooked so far in other studies. Their contribution to the total cross section is presented for the LEP II energy range and for future linear colliders (-/a =500 GeV). Effects, at the W pair threshold, of order 3% {e~Ptui) and 27% (udud) are reported. Similar behaviour for the radiative case is shown. At -Ja = 500 GeV, the relative contribution of the non-resonant diagrams for the radiative channel reaches 42.5%.

1. Introduction processes, and they will contribute to the overall mass and width measurement uncertainties. Two years ago. a complete calculation of It has been recognized, since some time [3], two four-fermion final states in e+e~ collisions. + + that the radiative corrections in W pair produc- e e~ —» e~Deud and e e~ —» udud, was re- tion have to be included for a precise comparison ported at the Sotchi meeting [1]. It was shown with measurements at the e+e~ colliders. Initial that the non-resonant diagrams play an impor- state radiations (ISR) reduce the available center tant role below the W pair threshold (up to 27% of mass energy. Close to the W pair threshold, at \/s = 150 GeV) and exhibit a non-negligible ISR will, therefore, enhance the relative contri- effect at higher energy (7% at y/s = 190 GeV). bution of non-resonant diagrams. Final state ra- In these results, in addition to a set of exper- diative corrections will contribute to additional imental loose constraints, a cut on the 0 angle uncertainties on the mass reconstruction, unless of the outgoing electron was applied to cope with the photon is detected and properly accounted gauge violations appearing in the subset of 7 — W for in the mass reconstruction algorithm. How- diagrams. Below threshold, the non-resonant di- ever, photons coming from the intermediate W, agrams competing only with the off-shelluess of which can be mis takingly recognized as final state the resonant ones, their relative contribution be- bremsstrahlung. will introduce additional uncer- comes quite large. The non-resonant diagrams tainties. are dominated by t-channel 7 — W graphs in sim- ilarity with the well-known two-photon (7 - 7) Although a number of studies has been car- processes. Hence the cross section increases with ried out in these last years, including [4][5], we the energy and the contribution of non-resonant present, for the first time, the complete tree level processes keeps growing in contrast to that of res- computation of one of the radiative four-fermion onant diagrams which falls with the energy. This processes. This work can be used as a benchmark effect was confirmed at this workshop by the anal- for testing the validity of simplified and therefore ysis of selected final states based on a dedicated faster generators. four-fermion generator [2]. The non-resonant processes are essentially single W or no W production. Some examples of these type of diagrams 2. The GRACE system for the radiative case can be seen on Fig.lb,2. As The GRACE system [6] has been used to far as the W mass reconstruction is concerned, perform the very lengthy computations involved these diagrams should be counted as background in the study of most radiative processes. The GRACE package is a complete set of tools for d V,

e w (a) Figure 2. (Fig.l cont.) Some examples of diagrams from the radiative process e+e~ —» e V. e~Ptudy: Other non-resonant diagrams. W\ d u| the basic integration variables to regularize the u divergencies appearing in the integration of the T/ e e e > e matrix element. The best kinematics will give the best accuracy for a given computation time.

e v. e v. 3. Four-fermion production w\— d d 7 The results presented hereafter have been obtained using the following set of parameters: / e e

Mz = 91.1 GeV (b) Tz = 2.534 GeV a = 1/137 Figure 1. Some examples of diagrams from the l 2 + sin 9w = 1 - (M, V/M|) radiative process e e~ —• e~veudy. a) Resonant diagrams. b)Nou-resouant 7 — W diagrams. MW = 80 GeV mu = md = 0.1 GeV computing tree level processes. All the phases involved in a given computation are covered: The width of the W is taken from the Particle from the process definition (specification of the Data Table; IV = 2.25 GeV. The gauge boson initial and final particles) to the event genera- (W.Z) widths are assumed to be constant in the tor. It is composed essentially of three compo- calculation. Furthermore some realistic experi- nents: the diagram generator, the construction of mental cuts have been introduced: the matrix element based on helicity amplitude function from the CHANEL [7] library and the 6€ > 8, 20, 30, 40° 8 multi-dimensional phase space integration pack- 172° > 07, 0,,, > ° age BASES [8] associated with the event genera- £7 > 1 GeV, £e,,,, > 1 GeV tor SPRING [8]. Fermion masses are properly introduced in the helicity amplitudes. The particle width is intro- where 6e.6y and 6qq are angles measured from duced into the gauge boson propagators when the incident e~ beam and -Be.j,, are the energies the denominator can vanishes for positive squared of filial e~.q and q. respectively. The electron momentum transfer. A gauge iuvariance checking polar angle cut is introduced to avoid an undesir- program is automatically built by the system. able gauge violation for extremely forward direc- Only the kinematics for complex processes has tions [9] caused inevitably by the finite width of to be written by the user. The issue, here, is to W boson when the subset of 7 - W diagrams is figure out what is the best transform to apply to considered. 1.2 1 i; •_• •_!_' i The gauge iuvariance of the amplitude is a) checked numerically for a random selection of the 1.0 boson gauge parameters at several points in the phase space. The errors are within the preci- 0.B sion of numerical calculation (typically less than 12 O(10~ ) in double precision) when the W width 0.6 is turned off. Further gauge cancellations are 111' * 1111111 I I I I I t I M checked to confirm that the obtained cross sec- b) e+e"-»u3ud tions are stable against finite width. The pro- 1.0 nit, cedure is as follows: first extract the product of gauge boson propagators without width as an 0.8 overall factor of the whole amplitude. Then re- place them by those with finite width. As a result, 0.6 one is left with rigorously gauge invariant anipli- 1 1 1 tude[10]. For the resonant diagrams, this method 160 180 200 220 240 gives the same results as ordinally method. While VS (G«V) for the 7 - W diagrams, this gives 10% smaller results. Figure 4. Energy dependence of the relative contribution of resonant diagrams in a) e+e~ —• 0.6 + I • - L— T e~Peud and b) e e~ —» udud with 0C > 8° to 0.5 the full computation. 0.4 0.3 0.2 RMS • 0.1 and udud. Fig.3 shows the cross sections ver- 0.0 i..|..t..rr,r 4-f-rrf |fTH | 1 i i T; 1.5 B) «V-»UQUd ~ sus the center of mass energy around the W pair threshold. The solid line represents the case where all diagrams are included, the dashed line the contribution of the resonant diagrams only. In the udud channel, one can observe the onset of the Z resonant diagrams as a small shoulder starting around 2Mz- The behaviour below the 160 180 200 220 240 W pair threshold can be better seen in fig.4 where VS (G«V) the ratio of the three main resonant diagrams over the complete calculation is plotted for the same + Figure 3. Cross sections for a) e e —» e veud range of center of mass energy. In the e~ueud and b) e+e~ —» udud versus CM. energy with channel, the effect is of the order of ±3% around Be > 8°. The solid curves are for all diagrams v/5 = 160 GeV. while in udud it readies -28%. and dashed ones for three resonant graphs. The At the energy of future LC, 300 GeV. the contri- dotted line in a) is the contribution from the 7 — bution of non-resonant diagrams is quite signifi- W and Z — W processes. The estimates at 500 cant in e~vKud but is negligible in udud. GeV are indicated by arrows. Similarly to the 7 — 7 events, the non-resonant processes are predominantly peaked in the forward/backward direction. Fig.5 shows the be- 3.1. The non-radiative case haviour of the cross section versus the electron The contribution of the non-resonant diagrams polar angle cut. The non-resonant contribution has been considered for two filial states. c~veud vanishes as the cut is raised. 0.5 0.125 - 0.4 - 0.100 - 0.3 - 0.075 - 0.2 - 0.050 -

0.1 - 0.026 -

0.0 0.000 0 10 20 30 160 1B0 200 220 240 Electron out angla (d«gr«e) VS(G«V) + Figure 5. Electron angular cut dependence for Figure 6. Total cross section for e e —» e i>eudj e+e- _ e~Pevd (CM. energy = 180 GeV). Solid versus the CM. energy with 0e > 8°. The solid line: all diagrams, dashed line: three resonant line represents the complete cross section while diagrams and dotted line: 7 — W aud Z — W the dotted line the resonant term only. processes.

the order of 1 GeV is observed on the e~Pe in- 3.2. The radiative case variant mass due to final state radiation. In the covariant gauge, the GRACE package generates 752 diagrams when all the interactions 4. Conclusions are included, but actually 142 diagrams are used in the unitary gauge with Higgs-fermion coupling A complete calculation of the radiative four- + being set to 0. The full tree level computation fermion final state e e~ -* e~veudy has been requires, for a decent precision, some 100 hours performed, for the first time, using automatic on a HP 735 computer. Thanks to the vectoriza- Feynman diagram calculation techniques imple- tion of the integration package BASES, the most mented in the GRACE system. Comparison with extensive computation could be performed on the two non-radiative computations e~9eud and udud KEK vector processor within 1 hour. Fig.6 shows has been carried out. The contribution of the the contribution of the non-resonant terms in the non-resonant processes is large below threshold total cross section versus the CM. energy. The (at least for udud channel) which makes the W behaviour is similar to the non-radiative case. In mass determination from the excitation curve fig.7. one can see more clearly the contribution more difficult. At high energy, the contribu- of non-resonant diagrams similar to fig.4 for non- tion increases, reaching 46% (e~Deud) and 42.5% radiative case. {e~veudf) at fermions. The general shape is, ward direction. Furthermore the final state radia- as expected, a Breit-Wigner distribution. How- tive correction will introduce a shift in the mass ever some background coming from the onset of of the W unless the photon is properly taken into non-resonant processes can be seen. In addition, account in the algorithm of mass reconstruction. for the radiative process (fig.10), a mass shift of However, this last point may prove to be diffi- 0.11 • ' • • 1

Va-180 G«V) 0.10 - ( - • ^5

0.09 - x • 0.08 - ^ -

1 1 . . . . i.; 0.07 160 180 200 220 240 0 10 20 30 40 VS(G«V) Daotron out anfle + Figure 7. Energy dependence of the contribution Figure 8. Total cross section for e e —> e veudy + of non-resonant diagrams in e e~ —» e~Peudj versus the electron polar angle cuts in degree. with 0e > 8°. The ratio of contribution of reso- The solid line: all diagrams, the dashed line: resonant diagrams versus all diagrams is shown. nant diagrams, and the dotted line: resonant and 7 - W. cult as the photon may be produced either from REFERENCES the initial state, the intermediate charged boson or the final state fermious. Only this last class T. Ishikawa, T. Kaneko, S. Kawabata, Y. plays a role in the W mass determination. More Kurihara, Y. Shimizu and H. Tanaka, KEK detailed studies are needed to check if additional Preprint 92-210, 1992 and in the Proceedings kineniatical cuts can impro%'e the mass determi- of the 7th workshop on high energy physics nation. aud quantum Reid theory. Sotchi, Russia, However to quantify the actual relative contri- 1992. bution of radiative events in the total cross sec- M. Pittau, in these proceedings. tion, soft photon and one-loop contributions must M. Lemoine and M. Veltman. Nud. Phys. be taken into account. Large negative contribu- B164 (1980) 445 tions are expected, reducing, consequently, the H. Tanaka, T. Kaneko and Y. Shimizu, Coai- number of radiative events and softening the mass put. Phys. Coaitnun. 64(1991) 149. reconstruction problem. See related contributions in these proceedings. T. Ishikawa. T. Kaneko, K. Kato, S. Kawa- 5. Acknowledgements bata, Y. Shimizu and H. Tanaka. KEK Re- This work has taken place in the framework port 92-19, 1993, The Grace manual Ver. 1 of the KEK-LAPP collaboration supported in H. Tanaka. Comput. Phys. Cowniun. 58 part by the Ministry of Education, Science and (1990) 153 and see also [4]. Culture (Monbusho) under the Grant-in-Aid for 8 S. Kawabata. Comput. Phys. Conwiun. International Scientific Research Program No. 41(1986) 127. 04044158 in Japan and by le Centre National de 9 E.E. Boos et a/., Phys. Lett. B326(1994) 190. la Recherche Scieutifique (CNRS) and Tlnstitut 10 A.E. Pukhov and V.A. Ilyin, private commu- de Physique Nucleaire et Physique des Particules nication. (IN2P3) in France. •0 H 100 IN

Figure 9. Invariant mass for non-radiative process in solid line for the ud system and in dotted line for the e~ut system with 0e > 8°.

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Figure 10. Invariant mass for radiative process in solid line for the ud system and in dotted line for the e~i>e system with 6e > 8°.