We consider the possibility of experimental observation of flavor-diagonal
and helicity conserving contact terms in the four fermion reactions e^+ e^- ->
e^+ e^- \mu^+ \mu^- and e^- q -> e^- \mu^+ \mu^- q at LEP2 and HERA.Comment: LaTeX, 7 pages, 12 figures in LaTeX format, uses axodraw.sty. To
  appear in the Proc. of XI Workshop on Quantum Field Theory and High Energy
  Physics (QFTHEP'96, St.Petersburg, Russia, September 1996

Berends, F.

Dubinin, M.

English

arXiv

We consider the possibility of experimental observation of flavor-diago= nal and helicity conserving contact terms in the four fermion reactions e^+ e= ^- -> e^+ e^- \mu^+ \mu^- and e^- q -> e^- \mu^+ \mu^- q at LEP2 and HERA.We consider the possibility of experimental observation of flavor-diagonal and helicity conserving contact terms in the four fermion reactions e~+ e~- -> e~+ e~- \mu~+ \mu~- and e~- q -> e~- \mu~+ \mu~- q at LEP2 and HERA

Berends, Frits A.

CERN Document Server

arXiv:hep-ph/9702344v1  15 Feb 1997Contact interactions in the four-fermion processes at LEP2 and HERAF.BerendsCERNCH-1211 Geneva 23, SwitzerlandM.DubininInstitute of Nuclear Physics, Moscow State University119899 Moscow, RussiaAbstractWe consider the possibility of experimental observation of flavor-diagonal and helicity conservingcontact terms in the four fermion reactions e+e− → e+e−µ+µ− and e−q → e−µ+µ−q at LEP2 andHERA.1 IntroductionSpeculations about the composite nature of leptons and quarks have been developed during a long periodof time [1]. With the help of compositeness of fundamental fermions one could hope to inderstand anumber of principal features of the Standard Model scheme such as the structure of fermion generations,mass spectrum of fermions and the symmetry breaking scenario.A large number of phenomenological studies of the possibility to observe the sigatures of compositenessat the new generation of e+e−, ep and pp¯ colliders exist (see [2, 3, 4] and references therein). One canimagine a simplified picture when leptons and quarks consist of some pointlike particles (preons) boundby some new interaction (metacolor force) which is probably confining and become strong at some energyscale Λ. If at the new colliders the momentun transfer exceeds Λ, leptons and quarks would interactin a manner completely different from their pointlike low energy structure, showing directly the hardscattering processes of the constituents. At the energies less than Λ one could observe some indicationsto the constituent dynamics (residual effective interactions) and describe this regime in the framework ofsome effective lagrangian approach. This effective lagrangian is given by a Standard Model lagrangian andsome operators of higher dimension involving the fields of the SM. For instance, the simplest effective termof this type is given by dimension six four-fermion operator (ψγψ)(ψγψ) multiplied by g2/Λ2 giving theeffective term with correct dimension four. The strength of such nonrenormalisable effective interactionsis determined by a dimensionless coupling g and powers of the compositeness scale Λ.2 Distributions in the Standard Model with LL− contact termfor the process e+e− → e+e−µ+µ−2.1 Parametrization of contact interactionsWe are using helicity conserving contact interactions of the form [5]Lc =g22Λ2(ηLLψ¯LγµψLψ¯LγµψL + ηRRψ¯RγµψRψ¯RγµψR + 2ηLRψ¯RγµψRψ¯LγµψL) (1)where g2/4pi = 1, |η| = 1 and ψL,R = (1 ∓ γ5)ψ/2. In the case of positive η the first and second termsare denoted by LL+ and RR+, if η is negative they are denoted by LL− and RR− correspondingly[2]. Particular choice of ηi gives V V and AA (vector-vector and axial-axial) current interactions. Inthe following we choose the LL− contact term. No qualitative difference in the results appears if wechoose any other variant from the six possible. Previous analyses performed in [5, 6] for the reactionse+e− → e+e−, e+e− → µ+µ− showed that the effect of LL and RR terms is typically several timessmaller than the effect of V V , AA terms.1e1 e1AE2e2e2AE1 E1diagr.1e1 e1Ae2e2E2AE1 E1diagr.2e1 e1AE2e2e2XE1 E1diagr.1e1 e1Ae2e2E2XE1 E1diagr.2e1 e1XE2e2e2AE1 E1diagr.3e1 e1Xe2e2E2AE1 E1diagr.4e1e1e1X e2E2AE1E1diagr.1e1e1A E1e1E1Xe2E2diagr.2e1e1AE1e1E1X e2E2diagr.3e1 Xe2E2e1e1AE1E1diagr.4Figure 1: Subset of 10 t-channel diagrams for the process e+e− → e+e−µ+µ−. SM diagrams are in thefirst row, in the second and third rows the X-particle exchange corresponds to some contact interaction.2.2 Search strategies and kinematical cutsCareful analysis is necessary in the Standard Model W and Higgs boson production for the definitionof the signal versus the background in the four fermion final state [7]. Usually it is more difficult toseparate the small signal of new physics, strongly restricted by the data from independent experiments,in the exclusive multiparticle final state. One can propose two contact terms search strategies. In theframework of the first strategy we impose loose kinematical cuts on the four fermion final state, thenumber of identifiable events is large enough, the contribution of the contact term in addition to the SMdistribution is small, but the statistical error is also small and one can hope to observe a deviation fromthe SM cross section in the high statistics experiment. Especially interesting is the case if the interferenceof SM and LL− defined amplitudes is large. In the framework of the second strategy we impose stringentkinematical cuts, the number of events is very small, but the contribution of the contact term in additionto the SM distribution can be large and one can hope to observe large deviation in the experiment witha small number of events. Generally speaking it is difficult to say in advance what strategy would bebetter.For the first and second strategy we are using the following cuts:Set I (Loose cuts):muon pair mass cut M(µ+µ−) ≥ 30, 60, 85 GeV (three cases)final muon energy cut E ≥ 10 GeVfinal muon angle with the beams ϑ ≥ 10 degreesSet II (Strong cuts):muon pair mass cut M(µ+µ−) ≥ 30, 60, 85 GeV (three cases)electron pair mass cut M(e+e−) ≥ 3.16 GeVelectrons angular cut with the beam ϑ ≥ 10 degreesfinal lepton energy cut E ≥ 10 GeVSet I corresponds to ”no-tag” experiment when the forward and backward electrons at very small2σ(e+e− → e+e−µ+µ−), pb, set I (loose cuts)M(µµ) cut (GeV) 30 60 85SM 4.165 0.527 0.135SM+LL− 4.180 0.535 0.142deviation in % 0.4 1.5 4.9N , see (2) 62500 4400 400σ(e+e− → e+e−µ+µ−), pb, set II (strong cuts)M(µµ) cut (GeV) 30 60 85SM 1.4∗10−2 0.56∗10−2 0.24∗10−2SM+LL− 1.6∗10−2 0.66∗10−2 0.29∗10−2deviation in % 14 18 21N , see (2) 50 30 20Table 1:angles (less than 0.1 degree) in the dominant final state configuration are not detected.2.3 Total cross sections and distributionsIn the SM with LL− contact term 110 tree level diagrams for the process e+e− → e+e−µ+µ− can begenerated. In order to optimize the procedure of calculation we separate them into subsets. Each subsetcontains subgraph corresponding to (with in-(out-) particles taken on-shell) some gauge invariant processof lower order. Detailed description of this procedure can be found in [8]. We select the subset of twodiagrams with t-channel photons (multiperipheral diagrams) in the SM case and for the case of contactterms we add to them eight diagrams with one t-channel photon and one contact interaction vertex (10diagrams, see Fig.1). The contributions from these subsets are generally speaking not always dominantin the overall complete tree level set (under some conditions single resonant diagrams with Z boson ins-channel are not small), but usually about one order of magnitude larger than others.The calculation of multiperipheral amplitudes containing t-channel photons is known to be veryuntrivial [9], especially in the case when no cuts are imposed on final electrons (”no-tag” experiment,total rate is finite because me 6= 0) and gauge cancellations between diagrams are extremely strong. Weused CompHEP 3.2 [10] and tested the results by means of EXCALIBUR [11]. In CompHEP numericalstability of the double poles 1/t2 cancellation to single ones is preserved by using quadruple precision andspecial algorithms of phase space generation [12].At the compositeness scale Λ =1 TeV and the energy√s = 200 GeV total cross sections in pb for theprocess e+e− → e+e−µ+µ− are shown in Table 1.We used a very rough criteria (similar to criteria accepted in [6]) that the number of events N neededto observe the δσ/σ fractional deviation from the SM cross section can be estimated by using the relationδσσ∼ 1√N(2)i.e. N is of order inverse fractional deviation squared. It follows from the Table that at the optimisticLEP2 integrated luminosity 500 pb−1 the effect of Λ = 1 TeV LL− contact term cannot be observed inthe total rate. For instance, 21% effect in the case M(µ+µ−) ≥ 85 GeV, set II, requires the identificationof 20 events while at LEP II luminosity we have only one event per year.As usual in this sitiation, we inspected the influence of contact terms on the shape of various distri-butions, hoping that in the distributions the effect could be much more pronounced if some phase spaceregion is controlled strongly by contact interaction dynamics. We calculated and compared distributionsover muon pair invariant mass dσ/dMµµ¯, muon angle dσ/dϑµ, muon transverse momentum dσ/dpt µ,and muon energy dσ/dEµ. In this set of distributions for all cases the LL− term effect looks like ratheruniform background not changing significantly in the whole physical region of the process. For instance,we show the distributions over muon angle in Fig.2. Their forward- backward structure is of course3completely different from the central structure of 2 → 2 body reaction e+e− → µ+µ− [5, 6] (whereonly partial wave with angular momentum zero contributes), but the shape of 2 → 4 body distributione+e− → e+e−µ+µ− with contact term is similar to standard distribution.ϑµ[Deg]dσ/dϑµ; [pb/Deg]e+e− − > e+e−µ+µ−0.00 50.0 100. 150. 180.5.00E − 63.32E − 61.50E − 52.50E − 5ϑµ[Deg]dσ/dϑµ; [pb/Deg]e+e− − > e+e−µ+µ−0.00 50.0 100. 150. 180.5.00E − 63.15E − 61.50E − 52.50E − 53.05E − 5Figure 2: Left figure - dσ/dϑµ, Standard Model, set II; right figure - dσ/dϑµ, SM+LL− contact term(Λ = 1 TeV, set II)We calculated also the fractional deviations dσLL−/dσSM for the cases of loose (set I) and strong(set II) cuts. The accuracy of our Monte Carlo (MC) calculation of the total rate is around 0.5%. Theaccuracy of distributions is quite satisfactory for the most important regions of the phase space (severalpercent in one bin). The error in the ratio of distributions is of course more sensitive to these statisticalmistakes. Fig.3 shows that the accuracy of our MC is not sufficient to show the 0.4% effect in the ratio(dσLL−/dM)/(dσSM/dM) for the case of loose cuts. Of course for practical purpose we do not need soprecise calculation in so far as at LEP2 only 2000 events could be observed while 60000 are necessary (seeTable 1). The effect of contact term could be clearly separated (Fig. 4) in the same ratio for the case ofstrong cuts (set II), but here we need the luminosity of order 104 pb−1 for experimental observation.3 Distributions in the Standard Model with LL− contact termfor the process e−p→ e−µ+µ−XIn the case of deep inelastic scattering we are using the MRS parametrization of proton structure functions[13], developed on the basis of latest experimental data from HERA. Available parametrizations of protonstructure functions can be used at the Q2 scale sufficiently large, so the calculations for the processe−q → e−µ+µ−q were performed applying |Q| = 3 GeV cut for the momentum transferred from theconstituent quark. Muon energy cut is equal to 10 GeV and we used 30 GeV for the muon pair invariantmass cut. For HERA ep collider the energy√s = 314 GeV, the electron-positron center of mass systemis moving in the laboratory system with the rapidity y = 1.654 and the integrated luminosity at presenttime is several pb−1.initial state eu ed eu¯ ed¯ es, es¯ ec, ec¯ totalSM 35.88 3.24 1.16 0.52 0.46 0.50 41.76SM+LL− 36.19 3.25 1.17 0.52 0.47 0.50 42.10Table 2: Total cross sections (fb) for partonic spieces in the process e−p → e−µ+µ−X , q = u, d, s, c,M(µ+µ−) ≥ 30 GeV, Λ = 1 TeV.4e+e−− > e+e−µ+µ−50 100 150 200Mµµ[GeV ]0.00.511.52.0dσLL−/dσSMe+e−− > e+e−µ+µ−50 100 150ϑµ[Deg]0.800.901.001.101.20dσLL−/dσSMFigure 3: Left figure - ratio dσLL−/dσSM for the muon pair invariant mass, Λ = 1 TeV, set I; right figure- ratio dσLL−/dσSM for the muon pair angle, Λ = 1 TeV, set I. The error of Monte Carlo calculation inthe ratio is indicated.e+e−− > e+e−µ+µ−90 120 150 180Mµµ[GeV ]0.81.01.21.41.6dσLL−/dσSMe+e−− > e+e−µ+µ−0.0 50 100 150ϑµ[Deg]0.511.52.0dσLL−/dσSMFigure 4: Left figure - ratio dσLL−/dσSM for the muon pair invariant mass, Λ = 1 TeV, set II, rightfigure - ratio dσLL−/dσSM for the muon angle, Λ = 1 TeV, set II. The error of Monte Carlo calculationin the ratio is indicated.Total cross sections for valence and sea quarks are shown in Table 2. Similar to e+e− case with loosecuts (set I), the contribution of the contact term in ep scattering is very small. According to criteria (2)in order to observe the deviation in total rate of order 1% it is necessary to identify approximately 104events, while even at upgraded high luminosity HERA (L ∼ 102 pb−1) it would be possible to observeof order 101 events. We show the fractional deviations of the muon pair invariant mass distribution andmuon angle distribution in Fig.5. In the distributions the effect is also practically unobservable.4 ConclusionWe calculated the effect of LL− contact term in the four-fermion channel e+e− → e+e−µ+µ− at theenergy 200 GeV. Search strategies with loose and strong cuts imposed on the final state were considered.5e−p− > e−µ+µ−X30 60 90 120Mµµ[Gev]0.81.01.21.4dσLL−/sσSMe−p− > e−µ+µ−X30 60 90 120ϑµ[Deg]0.800.901.001.101.20dσLL−/dσSMFigure 5: Left figure - ratio dσLL−/dσSM for the muon pair invariant mass, Λ = 1 TeV; right figure -ratio dσLL−/dσSM for the muon angle, Λ = 1 TeV.In the case of loose cuts (set I) at the compositeness scale 1 TeV the difference in the total ratesis around 1%. It would be hardly possible to observe the deviations from the SM in the distibutions.In the case of strong cuts (set II) the effect of contact terms is much more pronounced and is of order20% in the total rate and could be clearly observed in the distributions, but the number of events atLEP2 luminosity of several hundred pb−1 is too small. Separation of the contact term is possible at theintegrated luminosity of order 10 fb−1.The deviation from the SM distributions caused by contact terms is rather uniform and in all casesconsidered it looks like some bias of constant level in the whole physical region. At the compositenessscale 4 TeV the difference of SM and SM+LL− distributions in the same four fermionic channel decreasesapproximately by one order of magnitude.σtot (pb) deviation in deviation inSM σtot dσ/dcosϑµe+e− → µ+µ− 3.0 about 300% up to 300%e+e− → e+e−µ+µ−, set I 4.2 0.4% negligiblee+e− → e+e−µ+µ−, set II 2*10−2 15% up to 50%Table 3: Typical deviations in the total rate and muon angular distribution of the reactions e+e− → µ+µ−and e+e− → e+e−µ+µ− caused by LL− contact term at the energy √s = 200 GeV and compositenessscale Λ = 1 TeV. Muon pair mass Mµµ ≥ 30 GeV in the case of set I,II.We calculated also the ”four-fermion” channel e−q → e−µ+µ−q at the energy of HERA √s = 314GeV. The effect of the contact term in the total rate at the compositeness scale 1 TeV is about 1%.Again, it would be hardly possible to observe any deviations from the SM distributions.Four-fermion channel considered by us does not show new critical advantages over the possibilities ofthe compositeness search considered earlier [2]. We compare the magnitude of the effect for the reactionse+e− → µ+µ− and e+e− → e+e−µ+µ− in Table 3. The discovery potential of four-fermion reactions iscritically dependent from the collider luminosity.AcknowledgementThe research of M.D. was partially supported by RFBR 96-02-19773a, St-Pb. grant 95-0-6.4-38 andINTAS 93-1180ext.References6[1] J.C. Pati, A. Salam, J. Strathdee, Phys.Lett. 59B (1975) 265H. Terazawa, Phys.Rev. D22 (1980) 184H. Harari, N. Seiberg, Phys.Lett. 98B (1981) 269M. Peskin, in: Proc. of the 1981 Int.Symposium on Lepton and Photon Interactions, Bonn, 1981[2] in: J. Ellis, R. Peccei editors, Physics at LEP, CERN report 86-02, vol.II, 1986[3] R.J. Cashmore et.al., Phys.Reports 122 (1985) 276[4] E. Eichten, J. Hinchliffe, K. Lane, C. Quigg, Rev.Mod.Phys. 56 (1984) 579[5] E. Eichten, K. Lane, M. Peskin, Phys.Rev.Lett. 50 (1983) 811[6] B. Schrempp, F. Schrempp, N. Wermes, D. Zeppenfeld, Nucl.Phys. B296 (1988) 1[7] E.Accomando, A.Ballestrero, G.Passarino, Nucl.Phys. B476 (1996) 3 (hep-ph/9604326)T.Ishikawa, Y.Kurihara, M.Skrzypek, Z.Was, hep-ph/9702249; G.Passarino, hep-ph/9611248[8] Standard Model Processes, in: G.Altarelli, T. Sjoestrand, F. Zwirner editors, Physics at LEP2,CERN report 96-01, 1996, vol.I, p.207 (hep-ph/9601224)E. Boos, M. Sachwitz, H.J. Schreiber, S. Shichanin, Z.Phys. C64 (1994) 391[9] J.A.M. Vermaseren, Nucl.Phys. B229 (1983) 347[10] E. Boos, M. Dubinin, V. Ilyin, A. Pukhov, V. Savrin, preprint INP MSU 94-36/358, 1994 (hep-ph/9503280)Event generators for WW physics, in: G.Altarelli, T.Sjoestrand, F.Zwirner editors, Physics at LEP2,CERN report 96-01, 1996, vol.II, p.3[11] F.A. Berends, R. Kleiss, R. Pittau, Nucl.Phys. B424 (1994) 308, B426 (1994) 344[12] V. Ilyin, A. Kovalenko, A. Pukhov, Int.J.Mod.Phys. C7 (1996) 761 (hep-ph/9612479)[13] A.D. Martin, W.J. Stirling, R.G. Roberts, Phys.Rev. D51 (1995) 47567

Contact interactions in the four-fermion processes at LEP2 and HERA

Abstract

Similar works

Full text

Available Versions

CERN Document Server