Measuring anomalous Wtbcouplings at e p collider. Phys. J. C (2015) 75:577 DOI...

Eur. Phys. J. C (2015) 75:577DOI 10.1140/epjc/s10052-015-3776-z

Regular Article - Theoretical Physics

Measuring anomalous Wtb couplings at e p collider

Sukanta Dutta1,a, Ashok Goyal2,b, Mukesh Kumar3,c, Bruce Mellado4,d

1 SGTB Khalsa College, University of Delhi, Delhi 110007, India2 Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India3 National Institute for Theoretical Physics, School of Physics, School of Physics and Mandelstam Institute for Theoretical Physics,

University of the Witwatersrand, Johannesburg, South Africa4 University of the Witwatersrand, Private Bag 3, Wits, 2050 Johannesburg, South Africa

Received: 2 August 2015 / Accepted: 5 November 2015 / Published online: 7 December 2015 The Author(s) 2015. This article is published with open access at Springerlink.com

Abstract We study the accuracy with which the lowestorderCP conserving anomalous Wtb couplings in the singletop-quark production at the proposed large hadron electroncollider can be probed. The one-dimensional distribution ofvarious kinematic observables at the parton level MC andtheir asymmetries arising due to the presence of anomalouscouplings both in the hadronic and leptonicW decay is exam-ined. We find that at 95 % CL the anomalous coupling associ-ated with the left-handed vector current can be measured at anaccuracy of the order of 102103, while those associatedwith the right-handed vector and left- as well as right-handedtensor currents have a sensitivity at the order of 101102for the systematic uncertainty varying between 101 % at anintegrated luminosity of 100 fb1. A comprehensive analy-sis of the combined covariance matrix derived from all one-dimensional distributions of kinematical observables is usedto compute the errors in the anomalous couplings.

1 Introduction

The top quark provides an excellent opportunity for the studyof the electroweak symmetry breaking mechanism as well asit provides a glimpse of new physics (NP) beyond the stan-dard model (SM). The top quark decays almost exclusivelyin the t bW+-channel.

The cosine of the angle between the momentum direction of thecharged lepton from the W-boson decay and the reversed momentumdirection of the b quark from top-quark decay, both boosted into theW-boson rest frame.

a e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]

The kinematic distributions of its decayed particles fromthe top quark provide the information about the Wtb vertexand associated new physics potentiality with the top-quarkproduction mechanism.

Within the SM, the Wtb vertex is purely left-handed, andits amplitude is given by the CabibboKobayashiMaskawa(CKM) matrix element Vtb, related to the weak interactionbetween a top and a b-quark and assuming |Vtd |2 +|Vts |2 |Vtb|2. The most general, lowest dimension, CP conserving,Lagrangian for the Wtb vertex is given by [13]

LWtb = g2

[W t

(Vtb fL

1 PL + f R1 PR)b

12mW

W t( f L2 PL + f R2 PR)b

]+ h.c. (1)

where f L1 1 + f L1 , W = W W, PL ,R =12 (1 5) are left- and right-handed projection operators, = i/2 ( ) and g = e/ sin W . In SM|Vtb| f L1 1, all other couplings f L2 , f R1 , f R2 vanish at treelevel. Their non-vanishing values are generated at the one-loop level [4].

Wtb anomalous couplings fi are constrained from fla-vor physics. The magnitudes of the right-handed vector andtensor couplings can be indirectly constrained from the mea-sured branching ratio of the b s process. Current 95 %CL bounds based on the CLEO data give

f R1 4.0103at the 2- level [57]. The branching ratio (BR) BR(b s ) is computed by neglecting the | fi |2 terms in the matrixelement squared and assuming only one anomalous couplingto be non-zero at a time. The upper and lower limits for|Vtb| f L1 , f R1 , f L2 , and f R2 obtained from the B decays are0.13 |Vtb| f L1 0.03, 0.0007 f R1 0.0025,0.0015 f L2 0.0004, and 0.15 f R2 0.57,respectively [8]. If more than one coupling are taken non-zero simultaneously, their magnitudes in principle are notbound by b s alone and the limits can be very dif-

123

http://crossmark.crossref.org/dialog/?doi=10.1140/epjc/s10052-015-3776-z&domain=pdfmailto:[email protected]:[email protected]:[email protected]:[email protected]

577 Page 2 of 19 Eur. Phys. J. C (2015) 75 :577

ferent. Combining the analysis on Bd,s = Bd,s mixing andB Xsl+l, the authors of Ref. [9] constrained the Wtbcouplings within an effective field theory framework.

The sensitivity of anomalous Wtb couplings can also bemeasured from the W helicity distributions arising fromtop decays to their dominant Wb mode in the top pair pro-duction processes [10]. It can also be measured from theobserved single top quark production cross section throughW -boson exchange and has both linear and quadratic termsin the effective couplings. Although the single top productionin the SM is comparable to the t t pair production, it is quitechallenging to make the extraction due to the considerablebackgrounds at the Tevatron [11,12] and the LHC [13,14].D with 5.4 fb1 data reported a combined analysis of Wboson helicity studies and the single top-quark productioncross section exclusively through the Wtb vertex. This setsupper limits on the anomalous Wtb couplings at 95 % CLviz.

f L2 0.224, f R1 0.548, f R2 0.347 (givenin Table 1 of Ref. [15]). The sensitivities of the anomalousWtb couplings on the cross section of the associated tWproduction are also studied at LHC through p collisionsat

s =14 TeV for various luminosities and acceptance cri-

teria [16]. The study of the coefficients of dimension sixoperators affecting Wtb couplings from electroweak preci-sion measurements [17,18] suggest that the upper limits onthese couplings are one order of magnitude weaker than thoseobtained directly from the helicity fraction study of the topdecay at NLO QCD [19].

The sensitivity of the effective couplings in (1) can be stud-ied through one-dimensional distributions of the kinematicobservables. These distributions manifest a certain amountof associated asymmetry depending on the specific Lorentzstructure, which can then be used as a discriminator to con-strain these anomalous couplings. Based on the associatedasymmetries generated from the measured angular distribu-tions of cos defined in [20], the ATLAS collaboration [21]set limits on the single anomalous couplings at 95 % CL tobe 0.44 Re( f R1 ) 0.48, 0.24 Re( f L2 ) 0.21,and 0.49 Re( f R2 ) 0.15. A combined constraint on theanomalous couplings from CMS and ATLAS [22,23] showsthe sensitivity of these couplings with respect to the helicityfraction in the top quark decays. The constraints on the Wtbvertex based on the angular asymmetries constructed fromATLAS data and the t-channel single top cross section inCMS have been analyzed in [24]. The projected sensitivityof all anomalous top couplings has also been studied in Ref.[25].

The effects of the anomalous coupling on the angular dis-tributions of the b-quark and + have been studied in thee+e linear collider with one specific semileptonic channelin the double resonance approximation for the t and t pro-duction [2629]. A preliminary study of the sensitivity ofWtb anomalous couplings on the single top-quark produc-

tion cross section in e p collision for TESLA + HERA andLHC+CLIC energies has been performed in [30].

Recently a deep inelastic electronnucleon scatteringfacility has been proposed at the LHC, known as LHeC. Itis proposed that an electron beam of 60 GeV will collidewith 7 TeV proton beam simultaneous to the existing protonproton collision experiments at the LHC [3133]. The LHeCis expected to test the rich electroweak physics with preci-sion. There has been some work on the physics goals of thecollider [3136]. The working group involved in the synergybetween the LHC and the LHeC brought out an excellentreport showing the inter-dependencies of the physics reachand goals of both these colliders [37]. The LHeC is goingto provide an unprecedented platform for studying the singletop-quark production as this has an advantage over the LHCand the Tevatron in terms of providing (a) a clean environ-ment with suppressed background from strong interactioninitiated processes, and (b) a kinematic reach for leptonnucleon scattering at a cm energy around 1.3 TeV [3843].

Thus it is worthwhile to study the single top-quark produc-tion and probe the Wtb anomalous couplings at the LHeC.

In Sect. 2 we analyze and study the single antitop-quarkproduction and potential backgrounds, their yield, the choiceof selection cuts, and the kinematic distributions at the LHeC.We introduce kinematic asymmetries as estimators in Sect. 3,provide the exclusion contours based on a bin analysis ofthe distributions involving kinematic observables, and finally,using the method of optimal variables, we give error corre-lation matrices and exclusion contours with 1 % luminosityuncertainty. We discuss the impact of the luminosity uncer-tainty on the measurement of the couplings and their correla-tions. A summary and analysis of our observations are givenin Sect. 4.

2 Single antitop-quark production

In hadron colliders, the SM single top-quark productionat leading order is studied through three disparate non-interfering modes via the s-, t-, and Wt-channels, respec-tively; details can be found in [44]. The t-channel throughcharge current (CC) interactions dominates over all the otherproduction mechanisms. In the LHeC we can study the sin-gle top-quark production only through t-channel processeb et + X as shown in Fig. 1. In sharp contrast tothe LHC the absence of pile-up and underlying event effectsat the LHeC, high rates of single antitop production areexpected to provide a better insight on Wtb anomalous cou-plings. The sensitivity of the Wtb couplings is also investi-gated through the sub-dominant associated tW production inRefs. [45,46].

We have implemented Wtb effective couplings corre-sponding to both chiral vector and tensor structures given

123

Eur. Phys. J. C (2015) 75 :577 Page 3 of 19 577

1 2

Fig. 1 Single antitop-quark production through charge current at thee p collider. The blobs at vertices 1 and 2 show the effective W t bcouplings, which includes the SM contribution. Further W decays intothe hadronic mode via light quarks ( j u, d, c, s) or the leptonic mode(l e, ) with missing energy

by the Lagrangian (1) in MadGraph/MadEvent [47] usingFeynRules [48]. The partonic cross sections are convolutedwith CTEQ6L1 parton distribution functions (PDFs) keep-ing the factorization and renormalization scale F = R =mt = 172.5 GeV. The mass of the b-quark, mb = 4.7 GeV,and the W boson,mW= 80.399 GeV, are based on assumingthe SM value for |Vtb| f L1 = 1.

The total top decay width, which is is one of the fundamen-tal properties of top physics, is measured with precision fromthe partial decay width (t W b) in the t-channel of thesingle top-quark production. The effect of anomalous Wtbcouplings in evaluating the decay width of the antitop quarkis consistently taken into account throughout our analysis forthe signal cross section.

Considering the five flavor constituents of a proton westudy the 2 2 process e p et+X and probe the accu-racy with which the anomalous couplings can be measured.The variation of the cross section of the single top productionin SM is studied with respect to the center of mass energyand electron energy in Fig. 2 and we find agreement with theearlier results given in [30]. We also show the effect of takingan 80 % beam polarization for electron, which results in theenhancement of the SM single top production cross sectionas the cross section scales as (1+ Pe), Pe being the degreeof polarization of the electron.

We also depict the varying contribution of the 2 3process e p t e b from the four flavor proton where thegluon splits into b, b and b participates in the interaction,while the b quark is produced in the final state as a spectatorquark. This process is, however, suppressed in comparisonto the 2 2 process e p t e. This signal can be vetoedout by demanding the exclusion of two b jets. We do notconsider this process for our analysis.

For the rest of the analysis we compute all cross sectionsfor the proposed LHeC with Ee = 60 GeV and Ep = 7TeV as per recommendations given in the LHeC conceptualdesign report [31]. The total events are estimated with anintegrated luminosity L = 100 fb1.

The new physics effect can arise either at the productionvertex of the antitop in the process e p te bWeor at the decay vertex. Figure 3 depicts the interplay of theinterference terms for the left-handed current and shows the

Fig. 2 Single antitop-quark production cross section at the LHeC withthe variation of electron energy Ee and fixed proton energy Ep = 7 TeV.The top two curves depict the cross section for e p e t from the80 % polarized and unpolarized e beam, respectively. The third and thefifth curve correspond to the branching of the unpolarized cross sectioninto hadronic and leptonic decay modes of W. The first and the thirdcurve from the below correspond to the cross section for e p t e bbranching to the leptonic and hadronic decay modes ofW, respectively

Fig. 3 Variation of the single antitop-quark production cross sectionwith the effective Wtb couplings (taking one anomalous coupling at atime with SM) at the production and decay vertices, for fixed Ep =7 TeV and Ee = 60 GeV

variation of the cross section with respect to the variation inthe anomalous couplings.

The stronger dependence of the cross section on theanomalous coupling f L1 is because of the identical Lorentzstructure associated with the SM and f L1 , and accord-ingly the constructive (destructive) interference becomespronounced for positive (negative)

f L1 . Therefore thecross section of the left-handed vector current mediated pro-cess varies as [(1 + f L1 ) |Vtb|]2. On the other hand, theright-handed current mediated processes vary as

f Ri 2 fori = 1, 2 and are therefore sub-dominant even in the pres-

123


Fig. 4 The variation of the helicity fractions F, F0, and F+ as defined in the text with the anomalous coupling fi

ence of a large f Ri because of the non-SM structure of the

current.We estimate and study the W helicity distributions aris-

ing from NP effects. The W polarization distribution dis-tinguishes the contribution of anomalous couplings. Westudy the behavior of the helicity fractions of the W interms of ratios of the number of events F = N/N ,F+ = N+/N , and F0 = N0/N where N, N+, and N0are the left, right, and longitudinally polarized W eventsand N = N+ + N + N0.

We vary the coupling and study its effect through the vari-ation of these ratios in Fig. 4. We observe that:

(a) The F and F+ corresponding to the positive and nega-tive polarizedW s show an opposite trend to the variationof all effective couplings except |Vtb| f L1 .

(b) The helicity fractions Fi associated with the left-handedtensor current is most sensitive as it interferes with theSM and has a larger momentum dependence. The right-handed vector chiral current shows an appreciable sen-sitivity w.r.t. the Fi helicity distribution.

The helicity fractions F and F0 are also sensitive tothe change in the coefficient of the right-handed tensorcurrent.

The helicity fractions are recently measured in the topquark pair events decaying leptonically and semileptonicallywith

s = 8 TeV at CMS detector in LHC with an integrated

luminosity of 5 fb1 [49,50]. Constraints obtained on F andF0 are found to be consistent with SM but observations haveleft F+ unconstrained.

Helicity fractions are studied through the reconstructedtops/antitops in the experiment. Therefore the sensitivitiesof these helicity fractions are subjected to systematic uncer-tainties arising from the reconstruction algorithm efficiencyand the determination of the angular distribution of all thedecay products of the top/antitop. However, one can over-come the above shortcomings with large statistics e.g. in LHCand improving the reconstruction of the most extreme binsin the angular distribution [51]. Moreover, it is better stud-ied in hadron colliders where tops/antitops are dominantlyproduced through strong interaction vertices for which the

123


Table 1 Cross section of all background processes in pb for thehadronic channel with selection cuts. The effective background crosssection eff is computed in the fifth column by multiplying the b/b tag-

ging efficiency and/or faking probability 1/10 and 1/100 correspondingto final state charm/anti-charm and light jets j u, u, d, d, s, s, g,respectively

No. Background process pT j,b 20 GeV j 5,

|b| 2.5 E,b 0.4R j,b/j 0.4 ET 25

E, j 0.4m j1 j2 mW 22 GeV

eff

1 e p eWb without antitop line 7.5 103 6.8 103 4.5 103 2.7 1032 e p e j j j 4.2 100 3.6 100 2.4 100 7.2 1023 e p ecj j and e p ec j j 1.5 100 1.2 100 8.6 101 8.6 1024 e p ecc j 5.8 102 5.0 102 3.2 102 6.7 1035 e p ebb j 2.5 102 2.2 102 5.6 103 1.3 1036 e p ce (c W s) 2.5 102 2.2 102 1.5 102 1.5 104

Wtb anomalous coupling would only depend on the decayvertices of tops/antitops.

In this article, we proceed to extract more informationon the sensitivity of anomalous couplings through a one-dimensional distribution of the kinematic variables in thefollowing section.

Finally we analyze the antitop through the hadronic andleptonic decay modes of the W s. Henceforth, we have mul-tiplied the cross section (for processes having b or b as thefinal state) with b, b tagging efficiency b = 0.6.

2.1 Sensitivity in the hadronic mode

In order to study the sensitivity of the anomalous couplingsintroduced in Eq. (1), we examine the process e p te, (t Wb,W j j), j u, d, c, s at the LHeCand its potential backgrounds. We impose standard selectioncuts as follows:

(i) Minimum transverse momentum for jets, b-antiquarkpTb, j 20 GeV, pTj,l 25 GeV and minimum missingtransverse energy /ET 25 GeV.

(ii) The pseudo-rapidity region for leptons and b-antiquarkb,l is taken to be 2.5, however, for jets j 5.(iii) Isolation cuts for lighter, heavy quarks and leptons

require Ri j 0.4 where i, j leptons, jets andb antiquark.In addition, we impose the following cuts to reduce thebackground:

(iv) The difference of azimuthal angle between missingenergy /ET and jets, leptons, and b-antiquark should be 0.4.

(v) To further reduce the background in the hadronic chan-nel we reconstruct W from di-jets assuming the jetenergy resolution E = 0.6E . In this setup the di-jet invariant mass resolution around the W mass isapproximately 7 %. Thus a mass window around 28 %(4 times of this resolution at 2 level) of the W mass

22 GeV is taken into consideration and hence the di-jet invariant mass is allowed to satisfy |m j1 j2 mW | 22 GeV.

The cross section of the background processes and the effectof these selection cuts are given in Table 1. The effectivecross section given in the fifth column is calculated aftermultiplying the bb tagging efficiency of 0.6. The b or b fakingprobability is taken to be 1/100 for u, d, s quarks, antiquarks,and 1/10 for c, c quarks.

We observe that:

(a) The dominant background process is e p ec/c( j j)where j u, u, d, d, s, s, g. The effective irreduciblecross section of this background after imposing all cutsis 0.1 pb. The other dominant background is e p e j j j , which along with the first one constitutes almost94 % of the total irreducible background 169 fb.

(b) the cross section of e p eWb is dominated bydiagrams wherein the Wb is generated from antitopquarks. However, after multiplying with the appropriatebranching ratio for the hadronic mode of W the crosssection is reduced to the order of 103 pb. We have alsofound that the potential background due to mis-taggingof one of the double b, b events arising from the processto e p e jbb is negligibly small.

To probe the effect of these cuts on the yield, we study allkinematic distributions in SM, other non-top backgroundsand compare them with contributions from the new physicscases with the representative value of the effective couplingat 0.5. The analysis is summarized in Table 2 and the overallfiducial efficiencies of additional cuts are presented. The sig-nificance S/

S + B gives the sensitivity of the cross section

corresponding to these representative values. The yield of thebackground processes mentioned in Table 1 is computed bytaking the appropriate weight factor due to mis-tagging ortagging of light quarks and b quark, respectively.

123


Table 2 Yield with selection cuts in the hadronic channel correspond-ing to the chosen anomalous coupling value of 0.5 at integrated luminos-ity L = 100 fb1. The yields corresponding to SM+i Bkgi signify

the total cumulative events of the SM and all backgrounds after takinginto account the b, b faking/tagging efficiency. Yields corresponding toall anomalous couplings include the SM top background

Event selection pT j,b 20 GeV j 5,

|b| 2.5 R j,b/j 0.4 ET 25E, j 0.4E,b 0.4

m j1 j2 mW 22 GeV Fiducialefficiency (%) S/S + B

SM 3.2 104 2.3 104 2.2 104 66.7 SM+

i Bkgi 6.5 104 5.0 104 4.0 104 61.5

|Vtb| f L1 = 0.5 7.3 104 5.0 104 5.0 104 68.0 1.92f R1 = 0.5 4.6 104 3.2 104 3.2 104 69.7 1.43f L2 = 0.5 4.9 104 3.6 104 3.6 104 73.2 1.55f L2 = 0.5 3.4 104 2.3 104 2.3 104 69.6 1.40f R2 = 0.5 5.7 104 4.1 104 4.1 104 72.3 1.69

The characteristics of the highest pT jet j1, the final stateb, and the missing transverse energy /ET are likely to bearthe signature of the Wtb couplings at the production/decayvertex. We reconstruct the W from jets at the final states tostudy the azimuthal angle separation between W and b, andthe missing energy /ET . We study one-dimensional distribu-tions of the azimuthal angle (the angle between the planes)/ET , j1 , /ET , b, /ET ,W , and b,W along with thecos b j1 and b j1 , where all angles are defined in the labframe. Figure 5 exhibits these distributions. To study the dis-tribution profile and shape variation, all histograms are nor-malized to unity and are drawn for an anomalous couplingrepresentative value of 0.5. The normalized distributions cor-responding to |Vtb| f L1 = 0.5 are identical to that of theSM. However, on consideration of the backgrounds the dis-tribution profile of the kinematical variable generated from|Vtb| f L1 = 0.5 shows distortion when compared to thatof pure SM. The SM+

Bkgi distributions are drawn after

summing the bin-wise contribution from each backgroundprocess with the appropriate factor as mentioned earlier.

In most of the distributions the new physics couplingsplay a significant role and a clear distinction has been seen inthe profiles with respect to the combined effect SM and back-grounds. We observe from Fig. 5 that the contribution of left-and right-handed tensorial Lorentz structures are distinguish-able in most distributions. The distributions corresponding to(a) azimuthal angle between missing energy and highest pTjet j1 and (b) the cosine of the angle between massive b quarkand j1 show a noticeable difference in the profile with respectto the right-handed tensor chiral current.

2.2 Sensitivity in the leptonic mode

Similarly we study the yield of the leptonic decay mode ofW through the process e p te, (t Wb, W ll), l e, at the LHeC. We impose as the standardselection cuts the same as those given in Sect. 2.1. The effectsof these selection cuts are given in Table 3. The effective cross

section is given in the fourth column of this table. In generalall backgrounds processes are sub-dominant. Reading Table3, we observe that:

(a) processes with a charged lepton, /ET and light jets, wherethe light jets can fake a b jet of the signal becomes negli-gibly small once they are screened through the selectioncuts and multiplied by the appropriate faking probabilityfactor.

(b) Background processes with two charged leptons whereone of them vanishes in the beam pipe is negligible afterthe imposition of the selection cuts.

The fiducial efficiencies due to the additional cuts are com-puted for the representative value of the couplings at 0.5corresponding to the coefficient of the different chiral andLorentz structures as given in Eq. (1). They are shown alongwith the significance in Table 4.

In the leptonic mode the final state charged lepton alongwith b shows the characteristic features of the anomalouscouplings. Further we study the sensitivity of the couplingsthrough one-dimensional distributions corresponding to theazimuthal angle /ET , l1 , /ET , b, along with the polar anglecos bl1 and the difference of the pseudo-rapidities bl1between b and the charged lepton with highest pT , desig-nated as l1. Figure 6 depicts these distributions. As men-tioned before all normalized distributions corresponding to|Vtb| f L1 = 0.5 are identical to that of SM single top pro-duction. We observe that f L2 shows a distinguishable profileover the others. However, the distribution /ET l is sensitiveto all anomalous couplings.

3 Estimators and 2 analysis

3.1 Angular asymmetries from histograms

We construct the asymmetry from the distribution of thekinematic observables in both the hadronic and the leptonic

123


Fig. 5 Normalized distributions of /ET j1 , /ET b, /ET W , b W ,cos b j1 , and b j1 for the hadronic decay mode of W

, correspond-ing to SM and an anomalous coupling of 0.5. Here j1 is the highest pT

jet. The normalized distribution corresponding to |Vtb| f L1 = 0.5 isidentical to that of the SM. All kinematic observables are measured inthe lab frame

modes. These asymmetries can be sensitive discriminatorsin distinguishing the contributions from the different Lorentzstructures due to their characteristic momentum dependence.We study the angular asymmetries with respect to the polarangle cos i j , the rapidity difference i j , and the azimuthal

angle difference i j , where i, j may be any partons (includ-ing the b-antiquark), charged lepton, or missing energy. Theassociated asymmetries Ai j , Ai j , and Ai j are definedas

123


Table 3 Cross section of all background processes in pb for the leptonicchannel with selection cuts. The effective background cross section effis computed in the fourth column by multiplying b/b tagging efficiencyand/or faking probability 1/10 and 1/100 corresponding to final state

charm/anti-charm and light jets j u, u, d, d, s, s, g, respectively.The background processes with two charged leptons are taken into con-sideration where one gets lost in the beam pipe

No. Background process pT j,b,l 20 GeV,R j,b/j 0.4, ET 25 j 5, b,l 2.5

E, j 0.4E,b 0.4E,l 0.4

eff

1 e p lle j 1.5 101 1.4 101 1.4 1032 e p llec and e p llec 6.6 103 6.1 103 6.1 1043 e p lleb and e p lleb without top line 3.6 103 3.2 103 1.9 1034 e p ell c 1.5 102 6.9 103 6.9 1045 e p ell j 1.2 101 5.5 102 5.5 104

Table 4 Yield with selection cuts in the leptonic channel correspondingto the chosen anomalous coupling value of 0.5 at integrated luminosityL = 100 fb1. The yields corresponding to SM+i Bkgi signify the

total cumulative events of the SM and all backgrounds after taking intoaccount the appropriate b, b faking/tagging efficiency

Event selection pT j,b 20 GeV j 5,

|b| 2.5 R j,b/j 0.4 ET 25E, j 0.4E,b 0.4E,l 0.4

Fiducialefficiency (%)

S/S + B

SM 1.2 104 1.1 104 92.0 SM+

i Bkgi 1.3 104 1.2 104 92.0

|Vtb| f L1 = 0.5 2.7 104 2.5 104 92.6 1.55f R1 = 0.5 1.7 104 1.6 104 94.1 1.23f L2 = 0.5 1.9 104 1.7 104 89.5 1.27f L2 = 0.5 1.1 104 1.0 104 90.9 0.95f R2 = 0.5 2.2 104 2.0 104 90.9 1.38

Ai j =N A+ (cos i j > 0) N A(cos i j < 0)N A+ (cos i j > 0) + N A(cos i j < 0)

, (2)

Ai j =N A+(i j > 0) N A(i j < 0)N A+(i j > 0) + N A(i j < 0)

, (3)

Ai j =N A+ (i j > 2 ) N A(i j < 2 )N A+ (i j > 2 ) + N A(i j < 2 )

, (4)

with 0 i j . The asymmetry A and its statisticalerror for N A+ and N A events where N =

(N A+ + N A

) = L is calculated by using the following definition based on thebinomial distribution:

A = a a, where a = NA+ N A

N A+ + N Aand

a =

1 a2L ; ( = cos i j ,i j ,i j ). (5)

Here (e p t, t Wb) BR(W j j/ l)b is the total cross section in the respective chan-nel after imposing selection cuts and b = 0.6 is the b/btagging efficiency.

Based on the one-dimensional histograms given in Figs. 5and 6, we look for the asymmetry within a distribution gen-

erated due to the interplay of the SM, background channelsand a given anomalous coupling for two distinct hadronic andleptonic modes of W decay. Any large deviation from thecombined asymmetry due to SM and background processeswould then imply that the associated kinematic observableis an optimal variable in determining the sensitivity of thegiven anomalous coupling. We provide these asymmetriesconstructed from the distributions in Tables 5 and 6 for thehadronic and leptonic channels, respectively, a representa-tive value of the anomalous coupling of 0.5. Any asymmetrywith respect to the distributions corresponding to |Vtb| f L1is identical to the one in SM.

The asymmetries shown in Tables 5 and 6 are good esti-mators for preliminary studies. They give a handle for judg-ing the ability of the measured observable to distinguish thecontribution from an anomalous term in the Lagrangian. Weobserve in Table 5 that the couplings are sensitive in magni-tude as well as in sign of the asymmetry generated by cos b j1distribution. But they may not be sensitive enough for thecouplings which are one order of magnitude smaller than therepresentative value. In fact, the whole distribution is essen-tially divided into two halves, which correspond to only twobins with large bin widths.

123


Fig. 6 Normalized distributions of /ET l1 , /ET b, cos b l1 , andb l1 for leptonic decay mode of W

corresponding to SM and ananomalous coupling of 0.5. Here l1 is the highest pT charged lepton.

The normalized distribution corresponding to |Vtb| f L1 = 0.5 isidentical to that of the SM. All kinematic observables are measured inthe lab frame

Table 5 Asymmetries and its error associated with the kinematic distributions in Fig. 5 at an integrated luminosity L = 100 fb1. These asymmetriesare computed for a representative value of the anomalous coupling 0.5 along with SM

A/ET j1 A/ET bA/ET W

AW b Ab j1A b j1

SM+

i Bkgi 0.532 0.003 0.282 0.005 0.503 0.004 0.799 0.003 0.023 0.001 0.712 0.003f R1 = +0.5 0.327 0.004 0.231 0.004 0.564 0.004 0.778 0.003 0.0005 0.004 0.806 0.003f L2 = 0.5 0.528 0.004 0.082 0.004 0.716 0.003 0.748 0.003 0.196 0.004 0.868 0.002f L2 = +0.5 0.390 0.005 0.269 0.004 0.585 0.004 0.683 0.004 0.106 0.005 0.795 0.003f R2 = +0.5 0.330 0.004 0.363 0.004 0.566 0.003 0.656 0.003 0.197 0.004 0.823 0.002

Table 6 Asymmetries and its error associated with the kinematic distributions in Fig. 6 at an integrated luminosity L = 100 fb1. These asymmetriesare computed for a representative value of the anomalous coupling 0.5 along with SM and all background processes

A/ET l1 A/ET bAbl1

Abl1

SM +

i Bkgi 0.384 0.004 0.710 0.003 0.551 0.006 0.765 0.007f R1 = +0.5 0.484 0.004 0.702 0.003 0.332 0.006 0.821 0.003f L2 = 0.5 0.526 0.004 0.620 0.003 0.410 0.006 0.831 0.002f L2 = +0.5 0.353 0.005 0.812 0.003 0.392 0.007 0.850 0.003f R2 = +0.5 0.424 0.004 0.684 0.003 0.507 0.005 0.809 0.003

123


3.2 Exclusion contours from bin analysis

In this subsection the sensitivities of the couplings areobtained through a 2 analysis, where we compute the sum ofthe variance of the events over all bins. Thus more bin infor-mation is likely to yield a better sensitivity than the asymme-tries which are generated essentially by dividing the wholedistribution into two equal bins.

To make the analysis more effective we switch on twoeffective anomalous couplings at a time with SM and allpossible background processes with the same final states.The 2 becomes a function of the two effective anomalouscouplings fi , f j , and it is defined as

2( fi , f j ) =N

k=1

(N expk N thk

(fi , f j

)N expk

)2(6)

where N thk ( fi , f j ) and N expk are the total number of eventspredicted by the theory involving fi , f j , and measured in theexperiment for the kth bin. N expk is the combined statisticaland systematic error sys in measuring the events for the kthbin. If all the coefficients fi are small, then the experimentalresult in the kth bin should be approximated by the SM andbackground prediction as

N expk N SMk +i

NBkgik = N SM+

i Bkgik . (7)

The error N SMk can be defined as

N SM+

Bkgik =

N SM+

i Bkgi

k

(1 + 2sys N SM+

i Bkgi

k

).

(8)

The 2 analysis due to un-correlated systematic uncertaintiesis studied for the three representative values of sys of 1, 5,and 10 %, respectively.

The analysis is performed for both hadronic and leptonicobservables which depend on the distributions shown in Figs.5 and 6. Using this definition of 2 in Eq. (6), we drawthe exclusion contours on the six different two-dimensionalplanes defined by the anomalous couplings |Vtb| f L1 , f R1 ,f L2 , and f

R2 . 68.3 and 95 % CL. Exclusion contours for the

hadronic and leptonic channels are shown in Figs. 7, 8, 9, and10, respectively. For each pair of the couplings, the effectof the overall systematic uncertainty (including luminositymeasurement error, etc.) is sketched for the three represen-tative values of Sys = 1, 5, and10 %.

On examination of the exclusion contours in both decaymodes we find that:

(a) The sensitivity of measuring all anomalous couplings areaffected by the systematic uncertainty Sys.

(b) The sensitivity of |Vtb| f L1 at 95 % CL is of the 5 103 and 3 102 with systematic error of 1 and

10 %, respectively. The order of the sensitivity for otheranomalous couplings varies as 102101 at 95 % CLwith Sys varying between 0.01 to 0.1.

3.3 Errors and correlations

In order to constrain the anomalousWtb couplings further weadopt the method of optimal observables [5258] by using thefull information from the distribution of kinematic observ-ables. This technique of estimating the equivalent maximumlikelihood estimator has been used in the experimental anal-ysis to compute the expected efficiencies in extracting theanomalous couplings from the experimental data [5964]. Bythis method, all the anomalous couplings fi , having differentshape profiles from each other, can be constrained simulta-neously. For a given integrated luminosity L , the statisticalerrors in the fi and the correlations of the errors among theanomalous coupling measurement can be obtained from 2,which is a function of all anomalous couplings. Redefiningthe 2 of Eq. (6) in terms of the two anomalous couplingsand the covariance matrix V we have

2( fi , f j ) = 2min +i, j

( fi fi )[V1

]i j

( f j f j ). (9)

A total of ten inverse covariant matrices V1 can be gen-erated from six and four distinct distributions of kinematicobservables in hadronic and leptonic modes, respectively,using the approximation (7).

If the SM prediction along with all dominant backgroundsgives a reasonably good description of the data in most of thephase space region, then the statistical errors fi of fi andtheir correlations are determined solely in terms of the thesesix covariance matrices V as

fi fi = fi = Vii , i j = Vi j/

Vii Vj j . (10)

i j gives the correlation coefficient between two distinctanomalous couplings fi and f j and gives the absolute errorfor a given anomalous coupling fi = f j . fi gives the uncer-tainty with which these couplings will be measured at theLHeC. fi is the expected mean value in SM, which is zerofor all anomalous couplings fi .

Subsequently, an optimal analysis with an integrated lumi-nosity L = 100 fb1 is made after combining all kinematicobservables in both the hadronic and the leptonic modes,respectively.

The inverse of the covariance matrix V1i j is generatedfrom the one-dimensional histogram of each sensitive kine-matic observable and the corresponding respective correla-tion matrix is computed. We combine all inverse covariantmatrices to compute the combined 2 in the hadronic andleptonic modes separately.

123


Fig. 7 68.3 % CL exclusion contours on the plane of |Vtb| f L1 f R1 ,|Vtb| f L1 f L2 , |Vtb| f L1 f R2 , f R1 f L2 , f R1 f R2 , and f L2 f R2 ,and based on a combined bin analysis of all kinematic observables in thehadronic decay mode of W. A 2 analysis is performed by taking into

account the deviation from SM and background process with the sys-tematic error of 1, 5, and 10 %, respectively, at an integrated luminosityof L = 100 fb1

123


Fig. 8 95 % CL exclusion contours on the plane of |Vtb| f L1 f R1 ,|Vtb| f L1 f L2 , |Vtb| f L1 f R2 , f R1 f L2 , f R1 f R2 , and f L2 f R2 ,and based on a combined bin analysis of all kinematic observables in thehadronic decay mode of W. A 2 analysis is performed by taking into


123


Fig. 9 68.3 % CL exclusion contours on the plane of |Vtb| f L1 f R1 ,|Vtb| f L1 f L2 , |Vtb| f L1 f R2 , f R1 f L2 , f R1 f R2 , and f L2 f R2and based on a combined bin analysis of all kinematic observables in theleptonic decay mode of W. A 2 analysis is performed by taking into


123


Fig. 10 95 % CL exclusion contours on the plane of |Vtb| f L1 f R1 ,|Vtb| f L1 f L2 , |Vtb| f L1 f R2 , f R1 f L2 , f R1 f R2 , and f L2 f R2and based on a combined bin analysis of all kinematic observables in theleptonic decay mode of W. A 2 analysis is performed by taking into


123


The combined 2 reads

2comb.( fi , f j ) n

k=12mink

=k

i, j

( fi fi )[V1]ki j ( f j f j ). (11)

Here k number of distributions corresponding to the kine-matic observables. n = 6 and 4 for hadronic and leptonicchannels, respectively.

We thus provide the accuracy with which anomalous cou-plings can be measured from each of these distributions.The correlation matrices and the absolute errors in each andevery couplings in the hadronic and leptonic modes are givenbelow:

|Vtb| f L1 = 4.5 104f R1 = 7.2 104f L2 = 4.7 104f R2 = 3.2 104

1

0.07 10.04 0.07 10.03 0.006 0.02 1

;

(a) hadronic mode (12)

|Vtb| f L1 = 4.6 104f R1 = 7.2 104f L2 = 8.3 104f R2 = 4.3 104

1

0.02 10.05 0.06 10.01 0.09 0.07 1

;

(b) leptonic mode (13)

Until now we have considered the hadronic and leptonicmodes of single antitop production at the LHeC to be twodifferent probes for measuring these anomalous couplings.We now combine the observations from both channels interms of the combined inverse covariance matrix. The globalerrors and correlations from the corresponding global com-bined covariance matrix are then given as

|Vtb| f L1 = 3.2 104f R1 = 4.6 104f L2 = 4.2 104f R2 = 2.6 104

1

0.05 10.04 0.06 10.02 0.03 0.04 1

.

(14)

It is worthwhile to mention that we have not yet consideredany systematic error in the covariance analysis. On compar-ing the errors given in Eqs. (13a) and (13b) corresponding tothe hadronic and leptonic modes, respectively, and the errorsfor the global combined analysis in Eq. (14) with those inSect. 3.2, we find that the sensitivity of |Vtb| f L1 and oth-ers are found to have increased by one and two orders ofmagnitude, respectively.

We have computed all the errors and their correlationsbased on 60 % b tagging efficiency b along with 10 % and1 % b faking probability by charm and light jets, respectively.

One can, however, take these parameters in the 2 analysisexplicitly rather than as an overall multiplying factor in therespective cross sections. Since we consider processes withthe same final states (same number of b, b) for the signalas well as the dominant SM top background, the optimalanalysis shows that the sensitivity of the errors in the mea-surement of these couplings will scale as 1/

b for a given

luminosity and 2. Assuming the measured luminosity to bethe true luminosity, the accuracy with which the anomalouscouplings are measured scales as 1/

L .

3.3.1 Luminosity error

An error in the measurement of luminosity is, however, likelyto affect the measurements of some effective couplings. Itis thus instructive to study the impact of the uncertainty inthe luminosity measurement on the sensitivity of anomalousWtb couplings. The true luminosity L can be estimated as

L L, = 1 , (15)

where L is the measured mean value, and is its one uncertainty. With the inclusion of the luminosity uncertaintythe 2comb. definition given in (9) is modified to

2comb.( fi , f j ) 2comb.( fi , f j , )

m

k=1

ni=0

nj=0

( fi fi )[V1]ki j ( f j f j ) +(

k 1k

)2.

(16)

Here [V1]ki j is now a (n+1) (n+1) matrix with f0 = 1. The luminosity uncertainty k is the same forall kinematic observables at a given collision energy. Heren 0, 1, 2, 3, 4, corresponding to the luminosity factor and four anomalous couplings.m = 6 (4), correspond to thenumber of kinematic observables for the hadronic (leptonic)mode.

It is straightforward to integrate out the f0 = 1 depen-dence and obtain the probability distribution of the param-eters f1 to fn in the presence of the luminosity uncertainty.|Vtb| f L1 is the only coupling whose weight function is iden-tical to the SM distribution at tree level. The other effectivecouplings get the SM contribution at the one-loop level andit is thus likely that the statistical errors dominate over thesystematics. Therefore the errors coming from the luminos-ity uncertainty can be safely neglected for the other threecouplings, namely f R1 , f

L2 , and f

R2 . The impact of the lumi-

nosity uncertainty can thus be accounted for algebraically byusing the 2 functions written in terms of f L1 . We redefineour 2comb. function by

123


2comb.( fi , f j , )

= 2comb.(

f L1 f L1 = f L1 +1

2

)+

(1

)2

=m

k=1

ni=0

nj=0

f i [V1]ki j f j +(

k 1k

)2(17)

where f L1 = f L1 + ( 1)/2 and f i fi (for i = 1).

The luminosity uncertainty in the 2comb. function inEq. (17) can be factored out as

2comb. =[ 1eff

+ eff R]2

+ 2comb., where

{eff}2 = 12

+ 14

[V1]11; R = 12

4a=1

fa [V1]1a .

(18)

The new 2comb. is the reduced combined 2 function, which

can be re-written as

2comb. = 2comb. (eff)2 R2. (19)

The reduced 2 function can now be used to study the con-straints on the effective couplings in the presence of the lumi-nosity uncertainty. It is worth mentioning that the correlationsbetween the |Vtb| f L1 with other couplings are affected dueto the presence of the second term in Eq. (19). Following theoptimal analysis by incorporating the luminosity uncertaintyand the reduced 2comb., we get a 4 4 covariance matrix.The modified correlation matrices based on the combinedstudy of the six and four kinematical distributions from thehadronic and leptonic modes, respectively, at an integratedluminosity of L = 100 fb1 can now be computed for differ-ent luminosity uncertainty factor . We give the spectrum ofthree correlation matrices corresponding to the three choicesfor = at 1, 5, and 10 %, respectively:

|Vtb| f L1 = 5.0 103f R1 = 4.7 104f L2 = 4.2 104f R2 = 2.6 104

1

0.003 10.003 0.068 10.002 0.032 0.041 1

;

(a) = 1 % (20)|Vtb| f L1 = 2.5 102f R1 = 4.6 104f L2 = 4.2 104f R2 = 2.6 104

1

0 1

0 0.068 10 0.032 0.041 1

;

(b) = 5 % (21)

|Vtb| f L1 = 5.0 102f R1 = 4.6 104f L2 = 4.2 104f R2 = 2.6 104

1

0 1

0 0.068 10 0.032 0.041 1

;

(c) = 10 %. (22)It is observed from Eqs. (20), (21), and (22) that the sensi-

tivities of all couplings except for |Vtb| f L1 remain the sameas before, given in (14). The sensitivity of |Vtb| f L1 , whichhas the same weight function as SM, is, however, reduced byone order of magnitude, 103, corresponding to a luminos-ity uncertainty of 1 %. The error in |Vtb| f L1 is now compa-rable to that obtained in the bin analysis with 1 % systematicerror. Following the same suite of bin analysis the sensitivityfurther worsens by an order of magnitude of 102 withincreased luminosity uncertainty at 510 % uncertainty. Onthe assumption that the statistical error might dominate overthe systematics in the determination of all other couplings,we observe that they are not affected due to the varying as mentioned in the definition of 2comb. This is in sharp con-trast to that observed in the bin analysis where all couplingsare affected by the systematic uncertainty. The correlationsof f R1 , f

L2 , and f

R2 with |Vtb| f L1 are drastically reduced

for = 0.01 and finally becomes vanishingly small for = 0.05 and = 0.10. However, the correlationsamong f R1 , f

L2 , and f

R2 remain the same as given in Eq. (14).

As an illustration, we study the variation in the total errormeasurement of |Vtb| f L1 based on this optimal analysiswith a fixed luminosity uncertainty . In Fig. 11, the vari-ation of the total error in the estimation of |Vtb| f L1 , withthe luminosity for a given is shown. Thus the error in the

Fig. 11 Variation of the total error of |Vtb| f L1 with the luminosity fora given luminosity uncertainty of 1, 5, and 10 %, corresponding to thekinematical distributions from hadronic, leptonic, and combined decaymodes of W, respectively,

123


anomalous coupling not only depends on the high magnitudeof the luminosity, but also on its measured value.

4 Observations and discussion

An attempt has been made to study and investigate the sen-sitivity of the measurement of anomalous Wtb couplingsassociated with the left or right vector and tensor chiral cur-rents. The LHeC, being comparatively clean with respect topp and p p colliders, provides an excellent environment tostudy the electroweak production of single antitop. We ana-lyze the effect of anomalous couplings in the Wtb vertex byexamining its one-dimensional distributions.

4.1 Observations

We summarize our results as follows:

(i) It is found that the asymmetries of the kinematic vari-ables constructed from respective one-dimensional dis-tributions can discriminate the effect of non-SM con-tribution through new vector and tensor chiral currentsexcept for |Vtb| f L1 , as shown in Tables 5 and 6, foranomalous couplings are of the order of 101. Theasymmetry study suggests the distribution of the cosineof the angle between the tagged b quark and the highestpT jet j1 in the hadronic decay mode of W to be themost sensitive observable.

(ii) We have conducted a 2 analysis based on the differ-ential events of all kinematic variables for hadronic andleptonic modes in the SM and background channels.This gives the exclusion contours on the anomalouscouplings plane. Contours at 68 and 95 % are providedfor both hadronic and leptonic decay modes of W inFigs. 7, 9, 8, and 10, respectively. The sensitivity of|Vtb| f L1 at 95 % CL is found to be of the order of 103102 with the corresponding variation of 110 % in the systematic error (which includes the lumi-nosity error). The order of the sensitivity for the otheranomalous couplings varies between 102101 at95 % CL We find that the sensitivity of the anomalouscouplings can be increased with the increase in the lumi-nosity as the coupling scales as 1/

L for a given 2.

Thus for 1 ab1 the sensitivities of all fi s are going tobe roughly improved by a factor of 0.31. Similarly,for a given integrated true luminosity and 2, an n foldincrease in the b-tagging efficiency would increase thesensitivity of the anomalous couplings by 1/

n.

(iii) Adopting the technique of the optimal observable, wefound that the global combined error sensitivity of allcouplings is of the order of 104 in the absence ofany systematic uncertainty.

(iv) Finally, we have extended our optimal analysis toinclude the luminosity uncertainty factor in addition tofour anomalous couplings. The increasing luminosityerror reduces the sensitivity of |Vtb| f L1 and its corre-lation with other couplings. On combining the resultsfrom both hadronic and leptonic modes and errors withluminosity uncertainty at 1 % we find that the errorsensitivity of |Vtb| f L1 103 becomes comparableto that observed in the bin analysis. The sensitivity isfurther reduced to 102 for a luminosity uncertaintygreater than 5 %. However, the sensitivities of all othercouplings are unchanged at 104.

4.2 Comparison and analysis

We compare our results with those quoted in the joint reportTOPLHCNOTE [22,23], based on the recent experimentaldata at

s = 7 TeV and an integrated luminosity of 35

pb1 to 2.2 fb1. They found the sensitivity of Re( f R2 ) =0.100.06(stat.)++0.070.08(syst.). Performing the analysis forthe LHeC with Ep = 7 TeV, Ee = 60 GeV, and an integratedluminosity of 100 fb1, we find the upper limit on anomalouscoupling

f R2 0.011 and 0.01 for the hadronic and leptonicmodes, respectively.

Alternatively, one constrains the CtW /2, a coefficient ofthe dimension six operator OtW = (q I t)W I thatcontributes to the Wtb anomalous coupling. By translatingthe upper bound on the f R2 on the upper limit of the coef-ficient corresponding to the dimension six operator, we findCtW /2 0.13 TeV2.

However, the limit from low energy electroweak precisiondata on the above operator is much stronger, CtW /2 0.4 1.2 TeV2 [17] than the present LHC bound and tilldate it provides the benchmark upper limit on the coefficientfor this operator. Electroweak precision data also constrainsthe other coefficient,CbW /2 1113, associated with thedimension six operator ObW = (q I b)W I . Translat-ing the upper bound from the coefficient f L2 , we find that theproposed LHeC will improve the bound to a level of 102as is evident from Eq. (22). Recently, a detailed study of thetop anomalous couplings for LHC at 14 TeV with 10 fb1data [25] has been done. One has computed the effect of theanomalous couplings at both production and decay verticesinto the full t-channel matrix element of the single top-quarkproduction and illustrated that the one sigma contours onthe plane of the anomalous couplings lie within the orderof magnitude 101. Therefore, the accuracy with whichthese couplings are measured at LHC can be improved uponin the proposed LHeC, as shown in Figs. 7, 8, 9, and 10 fromthe bin analysis.

At present a stringent upper bound on the magnitude of theanomalous couplings exists from the low energy B physics

123


experiments as mentioned in the introduction and given inRefs. [59]. On comparing with these limits we find that theLHeC might be able to measure these anomalous couplingsat the same level of accuracy or even can do better with a highluminosity facility having a luminosity uncertainty 12 %.

The single top-quark production process at ILC is real-ized through e+ + e t + b + e + e , which issub-dominant in comparison to the top pair production pro-cess e+ + e t + t . Therefore, the sensitivity anal-ysis of Wtb anomalous couplings at ILC has been per-formed in the top pair production processes followed by theirdecay in hadronic, semileptonic, and leptonic decay modes[6569]. Boos et al. [68] have simulated the observablesforwardbackward asymmetry, the spinspin asymmetry ofthe top/antitop decay products, and the asymmetry of thelepton energy spectrum for their analysis of Wtb couplingsand found that the 2 exclusion contours predict that nodistinction can be made with SM if f L2 [0.025, 0] andf R2 [0.20, 0.20]. Another study, by Batra and Tait, showsthe sensitivity of the anomalous couplings are of the orderof 3 % with 100 fb1 data [69]. Errors in the measurementat ILC can, however, drastically be reduced by improvingthe top/antitop reconstruction tools like b-tagging efficiency,the vertex charge determination, and the top identification,though ILC is better suited to explore the sensitivity of thedimension six operators associated with flavor conservingand flavor changing neutral currents [7076].

Our analysis shows that we can probe the Wtb vertex atthe LHeC to a very high accuracy and can obtain much morestringent upper limits on the anomalous couplings, in com-parison to existing limits from the LHC, electroweak physics,and B meson decays. The arXiv version of this study hasbeen discussed in the High Energy Particle Physics Work-shop 2015 [38], LHeC Workshop 2015 [77] and in the DIS2015 wokshop [78]. We hope that our report will be usefulin studying the physics potential of the LHeC project.

Acknowledgments SD, AG, and MK would like to acknowledge thepartial support from DST, India, under grant SR/S2/HEP-12/2006. AGwould like to acknowledge the CSIR (ES) award for the partial financialsupport.

OpenAccess This article is distributed under the terms of the CreativeCommons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided you give appropriate creditto the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made.Funded by SCOAP3.

References

1. G.L. Kane, G.A. Ladinsky, C.P. Yuan, Phys. Rev. D 45, 124 (1992)2. J.A. Aguilar-Saavedra, Nucl. Phys. B 812, 181 (2009)3. J.A. Aguilar-Saavedra, Nucl. Phys. B 821, 215 (2009)

4. H.S. Do, S. Groote, J.G. Korner, M.C. Mauser, Phys. Rev. D 67,091501 (2003)

5. F. Larios, M.A. Perez, C.P. Yuan, Phys. Lett. B 457, 334 (1999)6. G. Burdman, M.C. Gonzalez-Garcia, S.F. Novaes, Phys. Rev. D 61,

114016 (2000)7. E. Barberio et al. [Heavy Flavor Averaging Group (HFAG) Collab-

oration], arXiv:0704.3575 [hep-ex]8. B. Grzadkowski, M. Misiak, Phys. Rev. D 78, 077501 (2008).

(Erratum-ibid. D 84, 059903 (2011))9. J. Drobnak, S. Fajfer, J.F. Kamenik, Nucl. Phys. B 855, 82 (2012)

10. V.M. Abazov et al. [D0 Collaboration], Phys. Rev. Lett. 100,062004 (2008)

11. V.M. Abazov et al. [D0 Collaboration], Phys. Rev. Lett. 103,092001 (2009)

12. CDF/PUB/TOP/PUBLIC/1079313. S. Chatrchyan et al. [CMS Collaboration], JHEP 1212, 035 (2012)14. G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 717, 330 (2012)15. V.M. Abazov et al. [D0 Collaboration], Phys. Lett. B 713, 165

(2012)16. B. Sahin, A.A. Billur, Phys. Rev. D 86, 074026 (2012)17. C. Zhang, N. Greiner, S. Willenbrock, Phys. Rev. D 86, 014024

(2012)18. N. Greiner, S. Willenbrock, C. Zhang, Phys. Lett. B 704, 218 (2011)19. J. Drobnak, S. Fajfer, J.F. Kamenik, Phys. Rev. D82, 114008 (2010)20. J.A. Aguilar-Saavedra, J. Carvalho, N.F. Castro, F. Veloso, A.

Onofre, Eur. Phys. J. C 50, 519 (2007)21. ATLAS-CONF-2011-03722. ATLAS-CONF-2013-03323. CMS PAS TOP-12-02524. J.A. Aguilar-Saavedra, N.F. Castro, A. Onofre, Phys. Rev. D 83,

117301 (2011)25. F. Bach, T. Ohl, Phys. Rev. D 86, 114026 (2012)26. K. Cieckiewicz, K. Kolodziej, Acta Phys. Polon. B 34, 5497 (2003)27. B. Grzadkowski, Z. Hioki, Phys. Lett. B 557, 55 (2003)28. S.D. Rindani, Pramana 54, 791 (2000)29. K. Kolodziej, Phys. Lett. B 584, 89 (2004)30. S. Atag, O. Cakir, B. Dilec, Phys. Lett. B 522, 76 (2001)31. J.L. Abelleira Fernandez et al. [LHeC Study Group Collaboration],

J. Phys. G 39, 075001 (2012)32. J.L. Abelleira Fernandez, C. Adolphsen, P. Adzic, A.N. Akay,

H. Aksakal, J.L. Albacete, B. Allanach, S. Alekhin et al.,arXiv:1211.4831 [hep-ex]

33. O. Bruening, M. Klein, Mod. Phys. Lett. A 28(16), 1330011 (2013)34. A. Senol, Nucl. Phys. B 873, 293 (2013)35. S.S. Biswal, R.M. Godbole, B. Mellado, S. Raychaudhuri, Phys.

Rev. Lett. 109, 261801 (2012)36. T. Han, B. Mellado, Phys. Rev. D 82, 016009 (2010)37. J.L. Abelleira Fernandez et al. [LHeC Study Group Collaboration],

arXiv:1211.5102 [hep-ex]38. M. Kumar, J. Phys. Conf. Ser. 645(1), 012005 (2015). doi:10.1088/

1742-6596/645/1/01200539. A. Andreazza, M. Anselmino, P. Azzi, W. Baldini, R. Barbieri, F.

Bedeschi, E. Bertuzzo, C. Biino et al., Frascati Phys. Ser. 60, 1(2015)

40. S. Forte, A. Nisati, G. Passarino, R. Tenchini, C.M.C. Calame,M. Chiesa, M. Cobal, G. Corcella et al., arXiv:1505.01279 [hep-ph]

41. I.A. Sarmiento-Alvarado, A.O. Bouzas, F. Larios, J. Phys. G 42(8),085001 (2015)

42. K. Agashe et al. [Top Quark Working Group Collaboration],arXiv:1311.2028 [hep-ph]

43. A.O. Bouzas, F. Larios, Phys. Rev. D 88(9), 094007 (2013)44. S. Dutta, A. Goyal, M. Kumar, Phys. Rev. D 87, 094016 (2013)45. I.T. Cakir, A. Senol, A.T. Tasci, arXiv:1301.2617 [hep-ph]46. I.T. Cakir, O. Cakir, S. Sultansoy, Phys. Lett. B 685, 170 (2010)

123

http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://arxiv.org/abs/0704.3575http://arxiv.org/abs/1211.4831http://arxiv.org/abs/1211.5102http://dx.doi.org/10.1088/1742-6596/645/1/012005http://dx.doi.org/10.1088/1742-6596/645/1/012005http://arxiv.org/abs/1505.01279http://arxiv.org/abs/1311.2028http://arxiv.org/abs/1301.2617


47. J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, JHEP1106, 128 (2011)

48. A. Alloul, J. DHondt, K. De Causmaecker, B. Fuks, M.R. deTraubenberg, Eur. Phys. J. C 73, 2325 (2013)

49. S. Chatrchyan et al. [CMS Collaboration], JHEP 1310, 167 (2013)50. CMS Collaboration [CMS Collaboration], CMS-PAS-TOP-14-01751. J.A. Aguilar-Saavedra, J. Carvalho, N.F. Castro, A. Onofre, F.

Veloso, Eur. Phys. J. C 53, 689 (2008)52. S. Dutta, K. Hagiwara, Y. Matsumoto, Phys. Rev. D 78, 115016

(2008)53. J.F. Gunion, J. Pliszka, Phys. Lett. B 444, 136 (1998)54. J.F. Gunion, B. Grzadkowski, X.G. He, Phys. Rev. Lett. 77, 5172

(1996)55. J.F. Gunion, B. Grzadkowski, X.G. He, Phys. Lett. B 444, 136

(1998)56. O. Nachtmann, F. Nagel, Eur. Phys. J. C 40, 497 (2005)57. M. Diehl, O. Nachtmann, F. Nagel, Eur. Phys. J. C 27, 375 (2003)58. M. Diehl, O. Nachtmann, Eur. Phys. J. C 1, 177 (1998)59. G.K. Fanourakis, D. Fassouliotis, S.E. Tzamarias, Nucl. Instrum.

Meth. A 414, 399 (1998)60. P. Achard et al., L3 Collaboration, Phys. Lett. B 597, 119 (2004)61. P. Achard et al., L3 Collaboration, Phys. Lett. B 586, 151 (2004)62. A. Heister et al., ALEPH Collaboration, Eur. Phys. J. C 21, 423

(2001)63. A. Heister et al., ALEPH Collaboration, Eur. Phys. J. C 19, 1 (2001)64. P. Abreu et al., DELPHI Collaboration, Phys. Lett. B 423, 194

(1998)

65. J.A. Aguilar-Saavedra, R.V. Herrero-Hahn, Phys. Lett. B 718, 983(2013)

66. E. Devetak, arXiv:0810.4831 [hep-ex]67. R. Frey, In: Morioka-Appi 1995, Physics and experiments with

linear colliders, pp. 144178. arXiv:hep-ph/960620168. E. Boos, M. Dubinin, M. Sachwitz, H.J. Schreiber, Eur. Phys. J. C

16, 269 (2000)69. P. Batra, T.M.P. Tait, Phys. Rev. D 74, 054021 (2006)70. H. Baer et al., The International Linear Collider Technical Design

Report: Physics, vol. 2. arXiv:1306.6352 [hep-ph]71. M.S. Amjad et al., arXiv:1505.06020 [hep-ex]72. R. Rauntsch, M. Schulze, JHEP 1508, 044 (2015)73. M.S. Amjad et al., arXiv:1307.810274. J.A. Aguilar-Saavedra, M.C.N. Fiolhais, A. Onofre, JHEP 1207,

180 (2012)75. M.C.N. Fiolhais, J. Phys. Conf. Ser. 447, 012032 (2013)76. S. Groote, J.G. Korner, B. Melic, S. Prelovsek, arXiv:1209.0547

[hep-ph]77. LHeC Workshop 2015 at CERN om 24 June 2015 and at

Chavannes-de-Bogis on 2526 June 201578. DIS 2015XXIII. International Workshop on Deep-Inelastic Scat-

tering and Related Subjects, 27 April1 May, at Dallas (Texas,USA, 2015)

123

http://arxiv.org/abs/0810.4831http://arxiv.org/abs/hep-ph/9606201http://arxiv.org/abs/1306.6352http://arxiv.org/abs/1505.06020http://arxiv.org/abs/1307.8102http://arxiv.org/abs/1209.0547

Measuring anomalous Wtb couplings at e-p colliderAbstract 1 Introduction2 Single antitop-quark production2.1 Sensitivity in the hadronic mode2.2 Sensitivity in the leptonic mode

3 Estimators and 2 analysis3.1 Angular asymmetries from histograms3.2 Exclusion contours from bin analysis3.3 Errors and correlations3.3.1 Luminosity error

4 Observations and discussion4.1 Observations4.2 Comparison and analysis

AcknowledgmentsReferences

Measuring anomalous Wtbcouplings at e p collider. Phys. J. C (2015) 75:577 DOI...

Documents

Transcript of Measuring anomalous Wtbcouplings at e p collider. Phys. J. C (2015) 75:577 DOI...