Some features of a program 'eett6f' for top quark pair production and decay
into six fermions at linear colliders are discussed. Lowest order standard
model predictions for cross sections of some six fermion channels and for the
top quark decay width are confronted with the predictions obtained within a
model with an anomalous Wtb coupling. The question of wether non doubly
resonant background can easily be reduced by imposing kinematical cuts is
addressed.Comment: 10 pages, 8 figures, presented at the Cracow Epiphany Conference on
  Heavy Flavors,Cracow, Poland, January 3--6, 200

Kolodziej, Karol

Acta Physica Polonica B

English

arXiv

Some features of a program e e tt6 f for top quark pair production and
decay into six fermions at linear colliders are discussed. Lowest order standard
model predictions for cross sections of some six fermion channels and
for the top quark decay width are confronted with the predictions obtained
within a model with an anomalous Wtb coupling. The question of whether
non doubly resonant background can easily be reduced by imposing kinematical
cuts is addressed

Kołodziej, Karol

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Studying top quark pair production at a linear collider with a program eett6f  Author: Karol Kołodziej   Citation style: Kołodziej Karol. (2003). Studying top quark pair production at a linear collider with a program eett6f. "Acta Physica Polonica. B" (2003, no. 9, s. 4511-4520). STUDYING T O P  QUARK PA IR  P R O D U C T IO N  AT A LIN EA R CO LLID ER W IT H  A PR O G R A M  e e tt6 f  * **K a r o l  K o ł o d z i e jInstitute of Physics, University of Silesia Uniwersytecka 4, 40-007 Katowice, Poland E-mail: kolodzieQ us.edu.pl(Received April 23, 2003)Some features of a program e e tt6 f  for top quark pair production and decay into six fermions at linear colliders are discussed. Lowest order stan­dard model predictions for cross sections of some six fermion channels and for the top quark decay width are confronted with the predictions obtained within a model with an anomalous W tb  coupling. The question of whether non doubly resonant background can easily be reduced by imposing kine­matical cuts is addressed.PACS numbers: 12.15. y. 13.40.Ks, 14.65.Ha1. In tro d u ctio nAs a top quark is the heaviest m atter particle ever observed, with mass close to  the energy scale of the electroweak sym m etry breaking, investiga­tion of its physical properties may give hints towards understanding physics beyond the Stnadard Model at higher energy scales. Therefore precise mea­surements, at a level of a few per mille, of the top quark properties and interactions will most certainly belong to  the research program  of any fu­ture e+ e-  linear collider [1]. In order to  m atch th a t high precision level of the m easurements, theoretical predictions should include radiative corrections.As it has been shown in [2] and will be illustrated later in this lecture, effects caused by the off-shellness of the t t  pair and off-resonance contribu­tions may be im portant too, especially for measurements a t the centre of* Presented a t th e  Cracow Epiphany Conference on Heavy Flavors, Cracow, Poland, January  3-6, 2003.** Work supported in p art by the Polish S tate Com m ittee for Scientific Research (KBN) under contract No. 2 P03B 045 23 and by European Commission’s 5-th Framework contract HPRN-CT-2000-00149.(4511)mass system (c.m.s.) energies much above the t t  threshold. As the t- and f-quark of the reactione+ e“ —> i t  (1)almost immediately decay, predom inantly into b W + and b W ~ ,  with the W ± boson decaying into a fermion pair, what one actually observes are 6 fermion reactions of the forme+ e-  b f j { b f 2f l  (2)where f \  =  ve, i+, vT,u ,c ,  /2 =  e~, p ~ ,  r ~ , d , s  and /{, f 2 are the corre­sponding weak isospin partners, /{ =  e~, p ~ ,  r ~ , d , s ,  f 2 =  ve, vT,u ,c .  For example, a pure electroweak (EW) reactione+e“ &i+p+6p“ i+ (3)in unitary  gauge receives contributions from 452 Feynman diagrams, ne­glecting the Higgs boson couplings to  fermions lighter than  b, while there are only two ‘signal’ diagrams contributing to  reaction (2) in the double resonance approximatione+ e-  t * f  -> b f j [ b f 2f> (4)at the same time.In the present lecture, some features of the updated version of a computer program  eett6f [2] th a t allows for computing cross sections of reactions (2) to  the lowest order of the standard  model (SM), with a complete set ofthe Feynman diagrams, w ill be discussed. The question of whether the nondoubly resonant background can easily be reduced by imposing kinematical cuts w ill be addressed. Moreover, lowest order SM predictions for some six fermion channels of (2) and for the 3 particle top quark decay w idth w ill be confronted with the predictions obtained within a model with an anomalous W tb  coupling.2. A  programA com puter program eett6f for calculating cross sections of 6 fermion reactions (2) relevant for a ii-pair production and decay at c.m.s. energies typical for linear colliders has been w ritten in FORTRAN 90 [3]. The program consists of 50 files including a makefile, all stored in one working directory. The user should specify the physical input param eters in a module inprm s . f  and select a number of options in the main program  csee6 f . f . The options allow, among others, for calculation of the cross sections while switching on and off different subsets of the Feynman diagrams. It is also possible tocalculate cross sections in two different narrow width approximations, for tt- quarks, or lff± -bosons. The program allows for taking into account both the EW  and QCD lowest order contributions. Version 1 of the program  allows for calculating both  the to ta l and differential cross sections of (2) at tree level of SM. Some anomalous effects beyond the SM th a t will be discussed later have been already implemented in the program. The program  can be used as the Monte Carlo (MC) generator of unweighted events as well.M atrix elements are calculated with the helicitv am plitude m ethod de­scribed in [4]. Phase space integrations are performed with the MC m ethod.The most relevant peaks of the m atrix  element squared, related to  the Breit-W igner shape of the W, Z ,  Higgs and top quark resonances, and to the exchange of a massless photon, or gluon have to be m apped away. As it is not possible to hnd out a single param etrization of the 14-dimensional phase space which would allow to cover the whole resonance structure of the integrand, the program utilizes a multichannel MC approach.Constant widths of unstable particles: the massive electroweak vector bosons, the Higgs boson and the top quark, are introduced through the complex mass param etersM 2 =  m l  -  im \  I \  . V  =  W ,Z ,  (5)M jj  =  m 2H -  i m Hr H, M t =  m t -  i r t / 2,which replace masses in the corresponding propagators,=  - - Y W 1 ' (6)A " (,)  =  Y m I ’ SAq)  =  T W 'Propagators of a photon and a gluon are taken in the Feynman gauge.The EW  mixing param eter may be dehned either real or complex,sin2 6\v  =  1 -  - y - ,  or sin2 6\v  =  1 -  ~77T- V )T il ryT iW 2Performing substitution (6) both in the s- and ¿-channel Feynman diagrams and taking the complex electroweak mixing param eter of Eq. (7) leads to fulhlment of the W ard identities. As light fermion masses are not neglected, cross sections can be calculated without any kinem atical cuts.A number of checks of the program  eett6f have been performed. The reader is referred to [3] for details.In the present version of the program, an anomalous W tb  coupling has been implemented. The model describing departures of the W tb  interactionfrom the SM, caused by new fundam ental interactions at high energies, can be specified in term s of the low energy effective Lagrangian containing terms of dimension 6 [5]L  =m \\-W f b Y i f f P -  +  f t P + ) t  -dl,W F b a '11' ( f f  P -  +  / 2+ P+)t h.c. (8)In Eq. (8), P±  are chirality projectors given by P± =  (1 ± 75) /2 , =i fydryv _  jV jH )  / 2, the anomalous couplings f f "  and f 2 are assumed to be real, and should be regarded as an effective vector field. The SM W tb  coupling is reproduced with / 7  =  f 2 =  f 2 =  0 and equal to the real Cabibbo-Kobayashi-Maskawa m atrix element Vjfc- According to  the present experimental data, Vjfc '1S ver7 close to 1 [6] and / 7  is strongly constrained by the CLEO b —> s j  d a ta  which give /j* ~  0 [7]. The couplings f 2 and f 2 are at present only weakly constrained, see e.g. [8].3. N um erical resultsIn the present section, a sample of numerical results obtained with the current version of eett6f will be presented. The physical input param eters th a t are used are the same as in [2].The energy dependence of the to ta l cross sections of (3) is shown in figure 1. The full lowest order cross section a  is plotted with the solid line, the signal cross section 07*t* with the dotted line, and the cross section in the narrow top w idth approximation, 0 7 , with the dashed line. A comparison of the solid and dotted  lines shows the effects of the off resonance background contributions to  reaction (3), and a comparison of the dotted and dashed lines shows the effect of the off-mass-shell production of the i f -pair. Both effects are substantial, especially a t higher energies. Therefore they should be taken into account in the future analysis of data.The question arises, whether those big off resonance effects and back­ground contributions can easily be reduced by imposing cuts. This issue will be preliminarily addressed below for one specific channel of reaction (2) by imposing the following cuts th a t are usually used in literature6(1, beam) >  5°, 6(q, beam) > 5°,6(1,1') > 5°, 6(1,q ) >  5°,Ei > 10 GeV, E q >  10 GeV,m(q,q ')>  10 GeV, (9)where q, I denote quark and charged lepton, respectively.y /a  (G eV )Fig. 1. Total cross sections of e+e-  —¥ bu^p+bp~P^ as functions of the c.m.s. energy.Results for three differential cross sections: invariant mass distribu­tion of a kfc-quark  triple and energy distributions of a 6-quark and p + of e+ e-  —> bisflp +bdu a t the c.m.s. energy of 500 GeV with cuts (9) have been compared against the corresponding results without cuts in Figs. 2-4. The solid histograms in Figs. 2-4 show the lowest order SM results obtained with the complete set of the Feynman diagrams, the dotted  histograms show the contribution of the two t t  signal diagrams and the dashed histograms have been obtained in the narrow top w idth approximation. The dotted histogram s in Fig. 2 cannot be distinguished from the solid ones.By comparing the plots on the left and right hand side of Figs. 2-4, one sees th a t, with cuts (9), the background and off resonance contributions are reduced to  a similar extent as the top pair production signal itself. Of course, this somewhat naive analysis does not preclude existence of a set of cuts th a t would keep intensity of the signal and reduced the background at the same time, bu t finding this suitable set need not be a completely simple task  a t all.e e t6 f  gives also a possibility of looking at effects of the anomalous W tb  coupling defined by Eq. (8) th a t have been implemented in the program. Figs. 5 and 6 illustrate how the possible existence of an anomalous couplingmay change angular and energy distributions of i-quark decay products in the rest frame of the top. The solid histograms show the SM results, whilerriMu (GeV) m hlitl (GeV)Fig. 2. Invariant mass distributions of a fedu-quark triple at f fs  = 500 GeV without cuts (left) and with cuts (right).Fig. 3. Energy distributions of a fe-quark at f fs  = 500 GeV without cuts and with cuts.the dotted histograms represent results in presence of the anomalous W tb  coupling with /% =  1, /£*” =  =  0 and =  0.1, both in Fig. 5 and 6. InFig. 5, the well known fact from the literature th a t angular distribution of the charged lepton resulting from the decay t  —> bg+vp is the most efficient analyzer of the top-quark spin [9] is recollected. Solid histogram s in Fig. 5 clearly show proportionality of the angular distribution of g + to (1 +  cos#) if the spin of the decaying top-quark points in the positive direction of the quantization axis (spin up) and to  (1 — cos#) if the spin of the decaying top-quark points in the negative direction of the quantization axis (spin down).Fig. 4. Energy distributions of a p + at f f s  = 500 GeV without cuts and with cuts.cos OpFig. 5. Angular distributions of a top quark decay products in the top rest frame.The angular and energy distributions of a 6-quark and p + resulting from the decay of i-quark produced in e+ e-  annihilation at yfs =  360 GeV are plotted in Figs. 7 and 8. Again the solid histogram s show SM results while the dotted, dashed and dashed-dotted  histogram s represent results in pres­ence of the anomalous W tb  coupling. One sees th a t the flat histogram s of Fig. 5 corresponding to  decay of the unpolarized top quark have developed a slope due to  the Lorentz boost from the rest frame of i-quark to the c.m.s. of e+ e- . Similarly, how the Lorentz boost changes the energy distributionsE  (GeV)Fig. 6. Energy distributions of a top quark decay products in the top rest frame.Fig. 7. Angular distributions of a fe-quark (left) and p+ (right) at f f s  = 360 GeV.of the top decay products is illustrated in Fig. 8. It is interesting to  note, how the relatively big effects arising if only a single anomalous coupling is nonzero, i.e. =  0.1 and f 2 =  0 (dotted histogram s), or /% =  0 and ¡2  =  0.1 (dashed histogram s), are reduced by interference, if fi) =  0.1 and f f )  = 0.1 (dashed-dotted histograms).Fig. 8. Energy distributions of a 6-quark (left) and p + (right) at y/s = 360 GeV.4. S um m ary and o u tlo o kTop quark pair production and decay into 6 fermions in e+ e“ annihilation at c.m.s. energies typical for linear colliders can be theoretically studied to the lowest order of SM with a program eett6f . A sample of results on selected channels of reaction (2) have been presented. It has been shown th a t, although the two t i  signal diagrams dom inate to ta l cross sections even at c.m.s. energies much above the t i  threshold, the effects related to  off- mass-shell production of the t i -pair and the off resonance background may be relevant for the analysis of future precision data. It has been illustrated th a t these effects are not reduced by imposing typical cuts given by (9). Some extensions of the SM have been implemented in the program and results illustrating effects of the nonstandard W tb  coupling Eq. (8) have been shown.Work towards completing im plem entation of all the channels of (2) pos­sible in the SM is underway. In order to  m atch high precision of future experiments it is also required to implement higher order effects. As it is not feasible to  calculate radiative corrections to the full set of Feynman di­agrams th a t contribute to any specific channel of (2), it would be desirable to  include higher order effects a t least to the two signal diagrams. This ap­proach would be justified by the fact th a t the to ta l cross section of reactions(2) is dom inated by the doubly resonant signal. Work in this direction is planned in collaboration with the Zeuthen-Bielefeld group [10].REFERENCES[1] TESLA Technical Design Report, Part III: Physics at an e+e Linear Collider, edited by R.-D. Heuer, D. Miller, F. Richard, P.M. Zerwas, DESY 2001-011, ECFA 2001-209, TESLA Report 2001-23, TESLA-FEL 2001-05, March 2001, hep-ph/0106315; T. Abe et al, American Linear Collider Working Group Collaboration, SLAC-R-570, Resource book for Snowmass 2001; K. Abe et al., hep-ph/0109166.[2] K. Kołodziej, Eur. Phys. J. C23, 471 (2002); A. Biernacik, K. Kołodziej, Nucl. Phys. B  (Proc. Suppl) 116, 33 (2003), hep-ph/0210405.(3] K. Kołodziej, Comput. Phys. Commun. 151, 339 (2003), hep-ph/0210199.(4] K. Kołodziej, M. Zralek, Phys. Rev. D43, 3619 (1991); F. Jegerlehner, K. Kołodziej, Eur. Phys. J. C12, 77 (2000).[5j G.L. Kane, G.A. Ladinsky, C.-P. Yuan, Phys. Rev. D45, 124, (1992);E. Boos, M. Dubinin, M.Sachwitz, H.J. Schreiber, Eur. Phys. J. C16, 269 (2000); B. Grzadkowski, Z. Hioki, Phys. Lett. B476, 87 (2000).[6j K. Hagiwara et al, Phys. Rev. D 66, 010001 (2002).(7] M. Alam, et.al, CLEO Collaboration, Phys. Rev. Lett. 74, 2885 (1995).(8] K. Whisnant, J.M. Yang, B.-L. Young, X. Zhang, Phys. Rev. D56, 467 (1997).[9j M. Jeżabek, J.H. Kühn, Nucl. Phys. B320, 20 (1989).(10] J. Fleischer, A. Leike, T. Riemann, A. Werthenbach, hep-ph/0302259.

Studying top quark pair production at a linear collider with a program eett6f

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Studying top quark pair production at a linear collider with a program 'eett6f'

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