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γp Anomalous produ tion of top quarks at CLIC+LHC based olliders ∗ Orhan Çak(cid:25)r Ankara University, Fa ulty of S ien es, Department of Physi s, 06100, Tandogan, Ankara, Turkey. The single produ tion of top quark due to (cid:29)avor hanging neutral urrent (FCNC) intera tion bW γp tcγ tuγ and its de ay to are studied at CLIC+LHC based olliders. We onsider both κc aκnud γ γ anomalous ouplings9..5The1a0n−o3m8a.l0ous 1h0a−r3m(up)γqpuarkanomalous√ soeupp=lin6g.4p8arameter L( =)1 a0n0 be−p1robed down to × ( × ) at a ollider with TeV and int fb . The (cid:29)avor hanging neutral urrent (FCNC) rea tions are known to be absent at tree level in the Standard Model (SM). Howteveqr,Vthey10 −an13nat1u0r−a1l0ly appear atq t=hec,oune-looVp l=evγel,gd,uZe to CKM mixing whi h leads to the bran hing 3 ratio BR( → )∼ − [1℄ where and . Extensions of the SM su h as supersymmetry 0 (SUSY) [2℄, exoti quarks (EXQ) [3℄,[4℄ and two-Higgsdoublet models (2HDM) [5℄ ould lead to an enhan ements of 0 su h transitions. In these models the top quark is predi ted to have large FCNC ouplings [6, 7℄. The approximate 2 ordersofthebran hingratiosforFCNCtopquarkde ayspredi tedwithinthesemodels[see[8℄andreferen estherein℄ n are given in Table I. a Duetothelargemass losetotheele troweaksymmetrybreakings aleand havingpoorlymeasured ouplings,the J topquarkisagood andidateforprobingnewphysi sbeyondtheSM.Thismotivatesthestudyofsingletopprodu tion 6 1 by FCNC ouplings at future olliders. The proed+ue −tion of top quarks via FCNC intera tions was extensively studied at hadron olliders[9, 10, 11, 1e2+,e1−3, 14, 15℄, at olliders[15, 16, 17, 18℄, and at lepton-hadron olliders[18, 19℄. 1 Additional option of linear olliders would be an ep ollider when linear ollider is onstru ted on the samepe v base as the proton ring. The ompa t linear ollider (CLIC) [20℄ at CERN an be onverted into CLIC+LHC 6 ollider. Photon olliders [21℄ are based on the Compton s attering of laser light on high energy ele trons in linear 1 olliders. The s atteredphotonshaveenergies loseto theenergyofthe initialele tronbeams. Then, it ispossibleto γp γp 1 onstru t TeV s ale ollider on the CLIC+LHC base. The main parameters of the CLIC+LHC based olliders 1 are given in Table II. 0 tcγ tuγ γp In this paper, single produ tionoftop quarksvia anomalous and ouplings at future CLIC+LHCbased 3 0 olliders has been studied. / If the FCNC ouplings of the top quark exist, they will a(cid:27)e t top quark produ tion and de ay at high energies. h Therefore, any possible deviations from SM predi tions will be an indi ation of new physi s. Top quark FCNC p ouplings an be parametrized in a model independent way by an e(cid:27)e tive Lagrangian - p e κq h L = ig Q γtσ kνqAµ e q µν Λ v: qX=u,c i g κq X + 2sinθ ecosθ t i ΛZσµνkν −γµ(vZq −aqZγ5) qZµ r q=u,c W W (cid:20) (cid:21) a X κq λa + ig gtσ kν qGµ+ . . s Λ µν 2 a H (1) q=u,c X kν σ =i(γ γ γ γ )/2 Λ Aµ µν µ ν ν µ wZhµere Giµs the momentum of the neutral gauge boson, − and is theκne,wκphysiκ s s ale. , γ Z g and arethe photon, Z-boson and gluon (cid:28)elds, respe tively. The anomalous ouplings ve de(cid:28)ne the tqγ tqZ tqg v a Z Z strengthofthe , and verti es,respe tively. Thetermsin luding and aretheanomalousnon-diagonal Z g g e s ouplings whi h are zero in the SM. and are the ele tromagneti and strong oupling onstants, respe tively. Q θ q W is the quark harge and is the Weinberg angle. Using the e(cid:27)e tive Lagrangian(1) it is straightforwardto obtain the FCNC de ay widths of top quark: κq 2 2 Γ(t qg)= g α m3 → Λ 3 s t (2) (cid:18) (cid:19) ∗ Ele troni address: o akirs ien e.ankara.edu.tr;URL:http://s ien e.ankara.edu.tr/-o akir 2 κq 2 2 Γ(t qγ)= γ αm3 → Λ 9 t (3) (cid:18) (cid:19) αm m2 2 κq 2 m2 κq m2 Γ(t qZ)= t 1 Z Z m2(2+ Z) 6vq Zm +(vq2+aq2)(2+ t ) → 4sin22θW (cid:18) − m2t (cid:19) "(cid:18) Λ (cid:19) t m2t − Z Λ t Z Z m2Z # (4) m m Z t where and are the masses of Z boson and top quark, respe tively. t u(c)γ t u(c)Z pp The CDF ollaboration performed a sear h for FCNC in the top quark de ays → and → in 1.8 ollisions at a entre of mass energy of TeV. They obtained upper limits at 95% on(cid:28)den e level (CL) on the bran hing ratios [22℄: BR(t uγ)+BR(t cγ)<0.032, → → BR(t uZ)+BR(t cZ)<0.33. → → e+e− tq A slightly better limit from the DELPHI experiments for the pro ess → is obtained on the top quark BR(t uZ)+BR(t cZ)<0.18 FCNC bran hing fra tion → κq < 0.52→ vq 2+[23a℄qas2su<m0in.3g2other FCNC ouplings to be zero. Note that the LEP2 gives a better limit for Z and | Z| | Z| than that given by the CDF. From the tqZ v 2+ a 2 < 0.15 low energy experiments a more stringent upper boundpon the ouplings | Z| | Z| an be found in [8℄. p tuγ tcγThe H1 Collaborationsear hedfortheprodu tionpro essκesuby onsidκecringboth oftheanomalousverti es and fromthefa tthatHERA hasmuκ qh<hi0g.h1e9rsensitivitytoκqγ<th0a.3n0t5o γ, dueto morefavorablepartondensity[24℄. The urrent limits from HERA are γ (ZEUS) and γ (H1) [25℄. In this study we de(cid:28)ne the bran hing ratio for FCNC de ay of top quark as Γ(t qV) BR(t qV)= → . → Γ(t qV) (5) → Λ = m = 175 α = 1/128Pα = α (m2) By onvention, we set t GeV and , s s t in our al ulations. The bran hing ratios t qg t qZ t qγ Λ=m =175 t BRof → , → and → areshowninFig. 1. Usingthee(cid:27)e tivelagrangian(1)withthes ale Γ(t bW) 1.4 GeV, and standard de ay widthκq <→0.28 κq≃<0.7G7eV, thesveqb2ra+n ahqin2gs< a0n.48be translated into the bounds on the top quark anomalous ouplings γ , Z and | Z| | Z| as seen in Fig. 1. t qZ κ The bran hings for → avreq d2e+noateqd2b=y κthe ontripbution from a 5-dimensional FCNC oupling or the 4- dimensional FCNC ouplings | Z| | Z| for an illustration. Here, we assume that only the relevant FCNC oupling is allowed to deviatepfrom its SM value at a time as the others are set to zero. tcγ tuγ Sin e we allow and anomalous intera tion in t(hκec)d2i+re (tκuto)2p quark produ tion we should also in lude this term in the de ay of top quark,whi h is proportional to γ γ and ontributes to the top quark de ay width. t bW One an see the e(cid:27)e t of additional hannel for top quark de ay, whi h de reases the → bran hing ratio and tcγ tuγ auses a noti eable deviation from the quadrati behavior. Assuming only the presen e of and ouplings top quark de ay width hanges a ording to [(κc)2+(κu)2]32 m2 Γt =Γt→bW "1+ γ Λ2 γ 9 (1−m2W/m2t)2(W1+2m2W/m2t)#. (6) t qV q = u,c V = γ,Z,g While the → ( and ) de ays will o ur in the presen e of the anomalous ouplings given t bW κ < 0.2 V in Eq. (1), they are smaller than the → de ay and they will have negligible bran hing ratios for Λ = m t bW t at . Given the existing upper bound of the anomalous oupling mentioned earlier [9℄, → will be the dominant de ay mtodeboWf t+he tolp+νqbuark. Sin e the leptoni de ay hannel of W boson has a lear signature, here we onsider only the → → de ay for our signal. The total ross se tion for dire t top quark produ tion is given by 0.83 1 dx τ tˆ+ dσˆ σ = f (x,Q2)f ( ) dtˆ Zτ Zτ/0.83 x q γ x Ztˆ− dtˆ (7) min 3 where tˆ- = (m2t −sˆ), tˆ+ = 0 and τmin = m2t/s. The fγ(y) is the spe trum of photons s attered ba kward from tγhqe inttera btWion+of laser photon with the high energy ele trons [28℄. The di(cid:27)erential ross se tion for the subpro ess → → is given by dσˆ κq 2 πα2 V 2 = γ | tb| sˆ3+sˆ2tˆ (m2 +2m2)sˆ2 (2m2 +m2+m2)sˆtˆ dtˆ Λ 9m2 2θ sˆ[(sˆ m2)2+m2Γ2] − w b − w t b (cid:18) (cid:19) wsin w − t t t +(m4+2m2m2 +2m2m2)sˆ+(m2m2+(cid:2)2m2m2)tˆ m2m2m2 2m2m4 b b w t w b t t w − b t w− t w (8) (cid:3) Inthis study, the anomalousintera tionvertfi e(sx,aQre2)implQem2e=ntmed2intotheCALtCqγHEP [25℄ pa kagewiththeparton distributionfun tionlibraryCTEQ5M[26℄for q at t. TheFCNC ouplings anbeprobeddire tly γp γu t γc t at olliders through the top quark produ tion subprto essbeWs+ →l+νabnd → . The diagram for the FCNC top quark produ tion me hanism and its subsequent de ay → → are shown in Fig. 2. ep The ross se tions for anomalous top quark produ tion at three options of olliders with the enter of mass √sep =2.64 3.74 6.48 energies , and TeV are given in Tables III, III and V, respe tively. From these tables it is easy tuγ tcγ to see that the ontribution from anomalous oupling is largerthan that from oupling. b We sear h for the signal in dete tor through the presen e of one -tagged jet, one isolated lepton and missing p b T transverse momentum. The transverse momentum distribution of (cid:28)nal state parti les are given in Fig. 3. The p T quark distribution hasapeak aroundthe halfmassoftopquark. A smallshift ba kwardsdue to themassof(cid:28)nal p W T state parti les is seen. The spe trum of the ele tron (or positron) mainly distributed at the half mass of the p T boson. In Fig. 4 we present the psep,νe,b t>ru1m0of (cid:28)nal state parti les for the relevant ba kground. We apply initial kinemati uts T GeV for the experimental obserpvea,νti>on2o0f the signapl.bT>he5s0e uts redu e the signal ross se tion by 5% and ba kground by 45%. More stringent uts T GeV and T GeV lead to a redu tionηeo,νn,bth<e s2i.g5nal ross se tion about 50% and ba kground about808%5%. The rapidity uts9a0r%e more e(cid:27)e tive su h that | | redu es the signal ross se tion by a fa tor about and ba kground by . In order to enhan e the signal to the ba kground, we want to make uts on the invariant mass of (cid:28)nal parti les m M t lνb whi h should be sharply peaked at for the signal. To determine the invariant mass , one should re onstru t p =p +p +p t l ν b . Theneutrinoisnotobservedbutitstransversemomentum anbededu edfromthemissingtransverse m = W mmoment(upm+. Tph)e2longitudinal omponent of the neutrino momentum is determined by the W-mass onstraint lν l ν = , and is given by p χpl p2(χ2 p2 p2 ) m2 pν = L± l − Tl Tν , χ= W +pl pν L p2 2 T · T (9) p Tl p p L T and and refer to the longitudinal and transverse momenta, respe tively. We hose the solution whi h would lνb best re onstru t the mass of the top quarκkc. Theκiunvariant mass distributions of system for thpel,νt,bhr>ee2o0ptions of anomalous intera tion vertex parameters γ and γ are shown in Fig.κ5cwherκeuwe apply the uts T GeV. We an determine the minimum value of the anomalous ouplings γ or γ by using the signal and ba kground γp events at olliders. Assuming the Poisson statisti s the number of signal events required for dis overy of a signal 95% at the on(cid:28)den e level is S 3 √S+B ≥ (10) S B (S,B)=σ BR L ǫ ǫ w int where and arede(cid:28)ned a ordingto the number ofevents al ulation × × × , where is the 1% L BR int w overalldete tion e(cid:30) ien y of forthis hannel. isthe integratedluminosity forone workingyear,and is W the bran hing ratio for leptoni de ay of the boson. Sin e the harm and up quarks are in the initial state, theκirc ontrκibuutions to dire t top quark produ tion an not bedistinguished. The plotsofthedis overylimit when both γ and γ areassumedto be nonzeroareshownin Figs. 6 and 7. tuγ tcγ u We (cid:28)nd that ross se tion is more sensitive to than due to the more favorable quark density in proton. Fro1m00Fig−.16one anseethatlarger entertocfγmtausγsenergyimprovesthesensitivity. Assumingtheintegratedluminosity of fb one anprobetheanomalous ( ) ouplingsdowntothevalueof0.0095(0.008)whenthes aleofthe γp smax 5.9 intΛera tion is set to the top quark m(amss/aΛt)a2CLIC+LHC based ollider with γp ≃ BTeRV. Foqrγothe5r h1o0i− e5s of the results an be res aled by t . These limits orrespond to the brapn hing ratio → ≈ × . In the SM extension wOith(1e0x−o5t)i quarks[3℄,[4℄ and supersymmetri models with R-parittqyγviolation [2℄, this bran hing ratio an be aslow as . If these models arethe only sour e for the anomalous ouplings, our al ulations 4 γp therefore indi ate that future improvements at the CLIC+LHC based olliders will be needed to make this a dete tible signal unless LO and NLO orre tionsfurther enhan e the ontributions. Inprin iple,there anbetheoverlappingbetweenthedire ttopquarkprodu tionandthephotonorgluonsplitting qq¯ u c diagrams where photon (gluon) splits into a pair, and and/or ombines with the gluon (photon) to produ e a top quark. Care must be taken with these pro esses to avoid the double ounting. In the dire t produ tion due to tcγ tuγ anomalous and/or ouplings, initial state parti les are assumed to be massless, and thus we may ignore the e(cid:27)e ts of the double ounting problem. In on lusion, the anomalous ouplings an be large in a spe i(cid:28) model. 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[21℄ V.TelnovandH.Burkhardt,"CLIC3TeVPhotonColliderOption",CERN-SL-2002-013,CLICNote508,Geneva,(2002). [22℄ CDF Collaboration, F. Abe et al.,Phys.Rev. Lett. 80 (1998) 2525. [23℄ DELPHICollaboration, P. Abreu et al.,Phys. Lett. B446 (1999) 62. [24℄ H1Collaboration, (cid:16)Sear h for single top produ tionin ep ollisions at HERA(cid:17), ontributed paper 516, LP2001, Rome. [25℄ S. Dusini, Nu l. Phys.B (Pro . Suppl.),109B, 262 (2002). [26℄ A. Pukhovet al.,hep-ph/9908288 (1999). [27℄ CTEQ Collaboration, H. L. Lai et al.,Eur. Phys.J. C12, 375 (2000). [28℄ I.F. Ginzburget al.,Nu l.Instr. and Meth. 205, 47 (1983). Table I: Bran hing ratios for FCNC top quarkde ays as predi tedwithin the SM and theSM extensions. BR(t qg) BR(t qγ) BR(t qZ) → → → −10 −12 −13 SM 10 10 10 −5 −7 −6 2HDM 10−5 10−6 10−6 SUSY 10 10 10 −3 −5 −2 EXQ 10 10 10 5 γp Table II: The mainparameters of theoptions of CLIC+LHC based olliders. CLIC+LHC Ee(TeV) Ep(TeV) √sep(TeV) √smγpax(TeV) Lep ≃Lγp(×1032 m−2s−1) Option1 0.25 7 2.64 2.41 1-100 Option2 0.50 7 3.74 3.41 1-100 Option3 1.50 7 6.48 5.90 1-100 γp bWX γp √sep =2.64 Table III: The ross se tion for thepro ess → at a CLIC+LHC based ollider with TeV. Λ=m κu t γ σ (pb) 0 0.01 0.05 0.1 0.2 0.3 0.4 4.95 10−2 1.92 10−1 3.61 100 1.43 101 5.69 101 1.28 102 2.82 102 0 × × × × × × × 1.16 10−1 3.08 10−1 3.73 100 1.44 101 5.70 101 1.28 102 2.82 102 0.01 × × × × × × × 1.70 100 2.08 100 5.50 100 1.62 101 5.88 101 1.29 102 2.84 102 0.05 × × × × × × × κc 6.67 100 6.86 100 1.03 101 2.09 101 6.36 101 1.35 102 2.88 102 γ 0.1 × × × × × × × 2.65 101 2.67 101 6.68 101 8.43 101 1.54 102 2.69 102 4.34 102 0.2 × × × × × × × 5.95 101 1.37 102 1.43 102 1.60 102 2.30 102 3.46 102 5.10 102 0.3 × × × × × × × 1.06 102 2.43 102 2.49 102 2.66 102 3.36 102 4.52 102 6.16 102 0.4 × × × × × × × γp bWX γp √sep =6.48 Table V: The ross se tion for thepro ess → at a CLIC+LHC based ollider with TeV. Λ=m κu t γ σ (pb) 0 0.01 0.05 0.1 0.2 0.3 0.4 2.45 10−1 6.33 10−1 9.95 100 3.91 101 1.55 102 3.50 102 6.21 102 0 × × × × × × × 5.16 10−1 1.15 100 1.05 101 3.96 101 1.55 102 3.50 102 6.21 102 0.01 × × × × × × × 6.95 100 7.58 100 1.69 101 4.60 101 1.62 102 3.57 102 6.28 102 0.05 × × × × × × × κc 2.71 101 2.77 101 3.70 101 6.62 101 1.82 102 3.77 102 6.48 102 γ 0.1 × × × × × × × 1.07 102 1.08 102 1.17 102 1.46 102 2.62 102 4.57 102 7.28 102 0.2 × × × × × × × 2.42 102 2.43 102 2.52 102 2.81 102 3.97 102 5.92 102 8.63 102 0.3 × × × × × × × 4.29 102 4.29 102 4.39 102 4.68 102 5.84 102 7.79 102 1.05 103 0.4 × × × × × × × γp bWX γp √sep =3.74 Table IV: The ross se tion for thepro ess → at a CLIC+LHC based ollider with TeV. Λ=m κu t γ σ (pb) 0 0.01 0.05 0.1 0.2 0.3 0.4 8.12 10−2 2.59 10−1 4.52 100 1.78 101 7.11 101 1.59 102 2.84 102 0 × × × × × × × 1.84 10−1 4.43 10−1 4.70 100 1.79 101 7.13 101 1.59 102 2.84 102 0.01 × × × × × × × 2.63 100 2.89 100 7.15 100 2.04 101 7.37 101 1.62 102 2.87 102 0.05 × × × × × × × κc 1.03 101 1.05 101 1.48 101 2.81 101 8.14 101 1.69 102 2.94 102 γ 0.1 × × × × × × × 4.10 101 4.12 101 4.55 101 5.88 101 1.12 102 2.00 102 3.25 102 0.2 × × × × × × × 9.22 101 9.24 101 9.67 101 1.10 102 1.63 102 102 3.76 102 0.3 × × × × × 2.51× × 1.64 102 1.64 102 1.68 102 1.82 102 2.35 102 3.23 102 4.48 102 0.4 × × × × × × × 6 0 10 -1 10 -2 10 t→gq R t→Zq(4) B t→Zq(5) -3 t→ γq 10 Λ=m t -4 10 -5 10 -2 -1 0 10 10 10 κ κ. Figure 1: Bran hing ratios depending on the anomalous oupling Only the relevant FCNC oupling is allowed to deviate t qZ from its SM value at a time as the others are set to zero. The bran hings → are onsidered in two ases as explained in thetext. γ W+ t u,c b γp Figure 2: Feynmangraph for anomalous top quarkprodu tion in ollision. 7 0.2 b ν 0.18 e + e 0.16 0.14 Λ = m t V) κq = 0.1 e 0.12 γ G b/ p 0.1 ( T p d 0.08 σ/ d 0.06 0.04 0.02 0 0 20 40 60 80 100 120 140 p (GeV) T b e+ µ+ p T Figure 3: The transverse momentum distribution of -quark, lepton ( or ), and the missing from the FCNC top γp √s = 3.74 Λ = mt κprqo=du0 .t1ion at a ollider based on CLIC+LHC with ep TeV for the s ale and the anomalous oupling γ . b ν e -4 10 + e ) V e G b/ p ( T p d -5 σ/ 10 d -6 10 20 40 60 80 100 120 140 160 p (GeV) T b e+ µ+ p ep e+νbX T Figure4: Thetransversemomentumdistributionof -quark,lepton( or ),andthemissing forthepro ess → γp √s =3.74 at a ollider with ep TeV. 8 0.6 κc=κu=0.1 γ γ 0.5 κγc=0,κγu=0.1 κc=0.1,κu=0 γ γ V) 0.4 e G b/ p ( 0.3 b ν e M d σ/ 0.2 d 0.1 0 150 155 160 165 170 175 180 185 190 195 200 Meνb(GeV) Figure 5: Meνb distributions for the utpeT,ν,b >20 GeV at theγp ollider with √sep =3.74TeV. -1 10 √s=2.65 TeV -1 L =10 fb √s=3.74 TeV int √s=6.48 TeV uκγ 10-2 -3 10 -3 -2 -1 10 10 10 κc γ κc κu L=10 -1 Λ=mt Figure 6: Dis overylimits for and for ea h of the olliders onsidered at fb , for . 9 -1 1 fb 10-1 √s=6.48 TeV 10 fb-1 -1 100 fb u κγ -2 10 -3 10 -3 -2 -1 10 10 10 κc γ κc κu γp √s=6.48 Figure7: Dis overylimitsfor and at CLIC+LHCbased olliders at TeVforthreedi(cid:27)erentluminosityand Λ=m t .