Modeling of associated tw single top production including the interference with t t diagrams

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1 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 Modeling of associaed W single op producion including he inerference wih diagrams Edward oos,,, Viacheslav unichev,, Lev Dudko,, Igor Myagkov,, and Maxim Perfilov, Lomonosov Moscow Sae Universiy, Skoelsyn Insiue of Nuclear Physics (SINP MSU), (), Leninskie gory, SP-, Moscow 999, Russian Federaion Faculy of Physics M.V.Lomonosov Moscow Sae Universiy Leninskie ory, Moscow 999, Russian Federaion Asrac. he associaed W single op producion channel is one of he main mechanism of he elecroweak producion of op quarks a he LHC. Correc simulaion of he SM predicion for his process is one of he imporan asks in he SM measuremens and SM searches. One of he difficulies o simulae i correcly is a significan conriuion of he inerference erms wih he pair op quark producion. In his aricle auhors compare mos popular simulaion schemes for W producion wih simulaion of he complee se of diagrams and propose new scheme o simulae inerference erms wihou negaive weighs of he evens. Inroducion Elecroweak op quark producion is one of he mos promising opic o search for New Physics. hese are unique processes o measure some of he SM parameers. here are hree differen producion channels. hey are classified using he opology of diagrams which include W-oson [] as -channel, s-channel and associaed W producion. he associaive W channel ecomes imporan a he LHC and requires proper simulaion. he correc simulaion of he W process is difficul due o he well known prolem []-[8] ha a NLO level W diagrams inerfere wih pair op quark producion diagrams. he op quark pair producion has more han en imes larger cross secion han he associaed W producion and inerference is an imporan par in case of he precise measuremens of W process. here are differen approaches o simulae associaed W producion wih differen advanages and disadvanages. I is also possile o simulae complee se of ree level diagrams including pair op quark producion and inerference erms. In he nex secions we discuss differen popular approaches, simulaion of he complee se of Feynman diagrams and new scheme proposed oos@heory.sinp.msu.ru unichev@heory.sinp.msu.ru dudko@sinp.msu.ru imyagkov@cern.ch maxim.perfilov@cern.ch he Auhors, pulished y EDP Sciences. his is an open access aricle disriued under he erms of he Creaive Commons Ariuion License 4. (hp://creaivecommons.org/licenses/y/4./).

2 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 diagr. diagr. diagr. diagr.4 diagr.5 diagr.6 diagr.7 diagr.8 Figure : Diagrams for he process gg W. in his aricle which we call conac ineracions (CI) scheme. he CI scheme solves numer of simulaion prolems. hese schemes were implemened in CompHEP [9, ] package and he necessary simulaions have een performed. he resuls are presened in he nex secions. Modeling approaches he main LO conriuion o he W process comes from suprocesses wih -quark in he iniial sae. A NLO level his conriuion yields from gluon collisions and leads o he process gg W which includes 8 diagrams. he corresponding diagrams are presened in Fig.. Simulaion of all hese diagrams is he mos precise approach o model his process. However, par of hese diagrams correspond o he pair op quark producion wih significanly lager cross secion han he oher diagrams wih single op quark producion. I is possile o disinguish doule resonan diagrams wih pair op quark producion and single resonan diagrams wih single op quark producion. In addiional, here is significan inerference eween doule and single resonan diagrams. Accurae simulaion of he associaed W elecroweak single op quark producion have o ake ino accoun no only single resonan diagrams, u also he negaive inerference erms wih pair op quark producion. Differen approximae schemes have een developed o properly model W channel of single op quark producion. Diagram Removal. he mos simple recipe is o remove all Feynman diagrams wih pair op quark producion, diagrams - in Fig. Such approach is called Diagram Removal () scheme [,, 7]. In his approach he inerference of single resonan diagrams (diagrams 4-8 in Fig. ) and doule resonan diagrams (diagrams - in Fig. ) are no aken ino accoun. Diagram Suracion. More sophisicaed approach called Diagram Suracion [, 7] akes ino accoun inerference erms. his mehod implies removing only squared doule resonan diagrams

3 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 diagr. diagr. diagr. diagr.4 diagr.5 diagr.6 diagr.7 diagr.8 diagr.9 diagr. diagr. diagr. diagr. diagr.4 diagr.5 Figure : Squared single resonan diagrams for he process gg W. during he modeling. he remaining diagrams are shown in Fig. for he single resonan conriuion and in Fig. for he inerference eween single and doule resonan conriuions. his approach allows o reain all of anicipaed single op quark producion properies in he W verex. On he oher hand his suse of diagrams also inroduces exra singulariies from an uncoupled op quark decaying ino W oson and quark in eiher par of squared diagrams. his effec can e clearly oserved in a disriuion of invarian mass of sysem of W oson and quark, and leads o negaive weighs of he significan par of he simulaed evens. ac ineracions scheme. An improvemen can e done o previous scheme in order o ge rid of descried singulariies. hese singulariies can e excluded enirely y replacing op quark decaying ino W oson and quark y a single conac ineracion in he doule resonan par of he squared inerference diagrams in Fig.. In his case he disriuion of invarian mass of W and urns up o e single-op-like while keeping all inerference in place wihou negaive conriuion. scheme. Modeling he complee se of diagrams is he mos precise approach. For he SM measuremens his is no very ineresing approach since for he mos of he SM measuremens one

4 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 diagr. diagr. diagr. diagr.4 diagr.5 diagr.6 diagr.7 diagr.8 diagr.9 diagr. diagr. diagr. diagr. diagr.4 Figure : Squared inerference diagrams of single and doule resonan conriuions for he process gg W. needs o separae op quark single elecroweak producion mode and pair producion mode in srong ineracions. In he full modeling scheme, which will e referenced as a scheme, differen erms conriue in oal cross secion. hese are (as shown in Fig. ) resonan paired producion diagrams, resonan single op producion diagrams, and heir inerfere erms. o reain all single op-sensiive ineracions, inerference erms need o e sudied as well as resonan single op erms. Comparison In he previous secion we discuss differen schemes o simulae W wih differen conriuions. In his secion we compare he common kinemaic disriuions achieved in differen schemes. Figures 4-7 give a vision of differen impacs of paricular schemes. Since he cross secions are significanly differen for doule resonan and single resonan conriuions each curve is normilised o is inegral (oal cross secion for his conriuion) for he Figs he curves for,, conac ineracions approaches, full scheme and pair op quark producion are shown on he plos. he curve for 4

5 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 he inerference erm eween paired and single producion processes is shown on he plos as well. he ransverse momena and pseudorapidiy of he, W, are shown in Figs. 4-6 and Figs. 8-. he vecor sum of W oson and -quark ransverse momena and is pseudorapidiy is shown in Fig. 7 and Fig.. he significan difference eween simulaion approaches is visile in he shapes of -quark and W sysem disriuions. he angular disriuions are show in Figs. -5. he cosine of angle eween W and momena in he laoraory res frame and in W res frame are shown in Figs. and Figs. correspondingly. he cosine of angle eween and quarks momena are shown in Figs. 4 and Figs. 5 correspondingly. Angular disriuions demonsrae significan difference of and CI schemes from oher simulaion approaches. his is reasonale, since he and DI schemes akes ino accoun he inerference erms. he differenial cross secion of invarian mass of W oson and -quark is shown in Fig. 6. he disriuion of invarian mass of W oson and -quark for he inerference erm is presened in Fig. 7. (), p/ev /σ dσ/dp..5 In (), p/ev /σ dσ/dp In p () p () Figure 4: ransverse momenum of op quark Figure 5: ransverse momenum of quark. (W), p/ev /σ dσ/dp In (W), p/ev /σ dσ/dp..5 In p (W) p (W) Figure 6: ransverse momenum of W oson Figure 7: ransverse momenum of sysem of W oson and quark. 4 Kinemaic separaion Kinemaic separaion of doule and single resonan conriuions is also possile [, ]. Such approach akes ino accoun inerference erms, i is gauge invarian and avoids negaive weighs of he evens. In his secion we compare simulaion in differen approximae schemes wih he simulaion of complee se of diagrams. For he calculaions we exclude phase space region 45 < M W < ev which corresponds o he second op quark pole. In his way he cross secions for all schemes are comparale. he correc simulaion should correspond o single resonan diagrams wih inerference erm, and off-shell conriuion for he doule resonan diagrams. Simulaion of he complee se 5

6 4 4 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 /σ dσ/dη(), p/ev /σ dσ/dη(), p/ev η() 4 4 η() Figure 8: Pseudorapidiy of op quark. Figure 9: Pseudorapidiy of quark. /σ dσ/dη(w), p/ev /σ dσ/dη(w), p/ev 4 4 η(w) 4 4 η(w) Figure : Pseudorapidiy of W oson. Figure : Pseudorapidiy of sysem of W oson and quark. /σ dσ/dcos(w,), p/ev, p/ev W /σ dσ/dcos(w,) cos(w,) W cos(w,) Figure : Cosine eween W oson and op quark. Figure : Cosine eween W oson and op quark in res frame of W and. /σ dσ/dcos(,), p/ev, p/ev W /σ dσ/dcos(,) cos(,) W cos(,) Figure 4: Cosine eween op quark and quark. Figure 5: Cosine eween op quark and quark in res frame of W and. 6

7 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 dσ/dm(w), p/ev dσ/dm(w), p/ev In.5..5 M(W) M(W) Figure 6: Invarian mass of W oson and quark, no inerference erm. Figure 7: Invarian mass of W oson and quark, only inerference erm. of diagrams ( scheme ) is mos accurae way o model his process in his phase space region. Kinemaic disriuions in Figs. 8-7 demonsrae he difference eween,, CI schemes and full scheme. he conriuion of he negaive inerference is also shown as well as pure doule resonan conriuion. scheme should reproduce only single resonan conriuion. scheme have o ake ino accoun single resonan conriuion and negaive inerference. CI scheme is designed o reproduce kinemaics of he single resonan conriuion wih inerference erm, u wihou negaive evens. Doule resonan conriuion reproduces only pair op quark producion. scheme reproduces all conriuions, single resonan, doule resonan and heir inerference. (), p/ev dσ/dp ac Inerference (), p/ev dσ/dp.5.4 ac Inerference p () p () Figure 8: ransverse momenum of op quark wih excluded region 45 < M W < ev Figure 9: ransverse momenum of quark wih excluded region 45 < M W < ev. 5 clusion Presened echniques allow differen approaches o simulae W producion and may e useful for differen paricular analyses. However, only modeling of he complee se of Feynman diagrams reains correc disriuions of kinemaic variales. he Diagram Removal scheme discards all inerference erms which are significan par of single op quark producion processes. he Diagram Suracion scheme provides es differeniaion in angular disriuions and could e useful for separaion of single op quark producion, u inroduces negaive weighs for he significan par of he evens and arely can e used in he analysis. he improved ac ineracion scheme does no have evens wih negaive weighs and shows lile difference from Diagram suracion scheme for he angular disriuions, hus could e used for effecive simulaion and separaion of single op quark producion process. 7

8 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584 (W), p/ev dσ/dp.5. ac Inerference (W), p/ev dσ/dp ac Inerference p (W) p (W) Figure : ransverse momenum of W oson wih excluded region 45 < M W < ev Figure : ransverse momenum of sysem of W oson and quark wih excluded region 45 < M W < ev. dσ/dη(), p/ev ac Inerference dσ/dη(), p/ev ac Inerference 4 4 η() 4 4 η() Figure : Pseudorapidiy of op quark wih excluded region 45 < M W < ev. Figure : Pseudorapidiy of quark wih excluded region 45 < M W < ev. dσ/dη(w), p/ev 4 ac Inerference dσ/dη(w), p/ev ac Inerference 4 4 η(w) 4 4 η(w) Figure 4: Pseudorapidiy of W oson wih excluded region 45 < M W < ev. Figure 5: Pseudorapidiy of sysem of W oson and quark wih excluded region 45 < M W < ev. Kinemaic cu ased approach, as shown in Secion 4 is generally less sensiive o elecroweak properies since imporan par of phase space is discarded and he impac from paired op quark producion is no reduced enirely. Noneheless, such approach akes ino accoun all necessary conriuions and gives a more sale resul ecause i uses purely gauge invarian kinemaic reducion procedure. Kinemaic separaion does no have negaive weighs of he evens and can e used in he searches for he deviaions from he SM. 8

9 EPJ We of ferences 58, 4 (7) QFHEP 7 DOI:.5/epjconf/7584, p/ev W dσ/dcos(,) ac Inerference, p/ev W dσ/dcos(w,) ac Inerference cos(,) W W cos(w,) Figure 6: Cosine eween op quark and quark in res frame of W and wih excluded region 45 < M W < ev. Figure 7: Cosine eween W oson and op quark in res frame of W and wih excluded region 45 < M W < ev. Acknowledgmens he work was suppored y gran 6--8 of Russian Science Foundaion. References [] S. S. D. Willenrock and D. A. Dicus, Phys. Rev. D 4, 55 (986). doi:./physrevd.4.55 [] A. S. elyaev, E. E. oos and L. V. Dudko, Phys. Rev. D 59, 75 (999) doi:./physrevd [hep-ph/986]. []. M. P. ai, Phys. Rev. D 6, 4 (999) doi:./physrevd.6.4 [hepph/9995]. [4] S. Zhu, Phys. Le. 54, 8 () Erraum: [Phys. Le. 57, 5 ()] doi:.6/s7-69()95-4,.6/s7-69()44-6 [hep-ph/969]. [5] J. M. Campell and F. ramonano, Nucl. Phys. 76, 9 (5) doi:.6/j.nuclphys [hep-ph/5689]. [6]. P. Kersevan and I. Hinchliffe, JHEP 69, (6) doi:.88/6-678/6/9/ [hep-ph/668]. [7] S. Frixione, E. Laenen, P. Moylinski,. R. Weer and C. D. Whie, JHEP 87, 9 (8) doi:.88/6-678/8/7/9 [arxiv:85.67 [hep-ph]]. [8] C. D. Whie, S. Frixione, E. Laenen and F. Maloni, JHEP 9, 74 (9) doi:.88/6-678/9//74 [arxiv:98.6 [hep-ph]]. [9] E. oos e al. [CompHEP Collaoraion], Nucl. Insrum. Meh. A 54, 5 (4) doi:.6/j.nima [hep-ph/4]. [] E. oos e al., PoS ACA 8, 8 (8) [arxiv: [hep-ph]]. 9