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Web End = Eur. Phys. J. C (2015) 75:512DOI 10.1140/epjc/s10052-015-3746-5

Regular Article - Experimental Physics

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Web End = A precise characterisation of the top quark electro-weak vertices at the ILC

M. S. Amjad1,3, S. Bilokin1, M. Boronat2, P. Doublet2,5, T. Frisson1,4, I. Garca Garca2, M. Perell2,R. Pschl1,a, F. Richard1, E. Ros2, J. Roun1, P. Ruiz Femenia2,6, M. Vos2

1 Laboratoire de lAcclrateur Linaire (LAL), Centre Scientique dOrsay, BP 34, Btiment 200, 91898 Orsay Cedex, France

2 IFIC, Universitat de Valencia CSIC, c/Catedrtico Jos Beltrn, 2, 46980 Paterna, Spain

3 Present address: COMSATS Institute of Information Technology, Islamabad, Pakistan

4 Present address: CERN, 1211 Geneva 23, Switzerland

5 Present address: IUT dOrsay, Universit Paris-Sud, Orsay Cedex, France

6 Present address: Technische Universitt Mnchen, 85748 Garching, Germany

Received: 25 May 2015 / Accepted: 19 October 2015 The Author(s) 2015. This article is published with open access at Springerlink.com

Abstract Top quark production in the process e+e t t

at a future linear electron positron collider with polarised beams is a powerful tool to determine indirectly the scale of new physics. The presented study, based on a detailed simulation of the ILD detector concept, assumes a centre-of-mass energy of s = 500 GeV and a luminosity of L = 500 fb1

equally shared between the incoming beam polarisations of

Pe , Pe+ = 0.8, 0.3. Events are selected in which the

top pair decays semi-leptonically and the cross sections and the forwardbackward asymmetries are determined. Based on these results, the vector, axial vector and tensorial C P conserving couplings are extracted separately for the photon and the Z0 component. With the expected precision, a large number of models in which the top quark acts as a messenger to new physics can be distinguished with many standard deviations. This will dramatically improve expectations from e.g. the LHC for electro-weak couplings of the top quark.

1 Introduction

The main goal of current and future machines at the energy frontier is to understand the nature of electro-weak symmetry breaking. This symmetry breaking can be generated by the existence of a new strong sector, inspired by QCD, that may manifest itself at energies of around 1TeV. In all realisations of the new strong sector, as for example RandallSundrum models [1] or compositeness models [2], the strength of the coupling to this new sector of the Standard Model elds are

a e-mail: mailto:[email protected]

Web End [email protected]

supposed to increase with their mass. For this and other reasons, the heavy top quark or t quark with a mass of approximately mt = 173 GeV [3] is expected to be a window to

any new physics at the TeV energy scale. New physics can modify the electro-weak t t X vertex described in the Stan

dard Model by Vector and Axial vector couplings V and A to the vector bosons X = , Z0. At the International Linear

Collider, ILC [4], that will collide electron and positrons at a centre-of-mass energy of 500 GeV, t quark electro-weak couplings can be measured at the % level.

In contrast to the situation at hadron colliders, the leading-order pair production process e+e t t goes directly

through the t t Z0 and t t vertices. There is no concurrent

QCD production of t quark pairs, which increases greatly the potential for a clean measurement. A parametrisation of the t t X vertex valid to all orders of perturbation theory may

be written as 1:

tt X(k2, q, q) = ie (F X1V (k2) + 5F X1A(k2))

2mt (q + q)(i F X2V (k2) + 5F X2A(k2)) , (1)

with e being the electrical charge of the electron, k2 =

(q + q)2 being the squared four-momentum of the exchanged

boson and q and q being the four-vectors of the t and t quark, respectively. Further, are the Dirac matrices leading to vector currents of fermions and 5 is the Dirac matrix allowing to introduce an axial-vector current into the theory. Finally, =

i2 ( ) allows for describing the

1 A dependence on an additional term (q + q) F3 can be neglected

in the limit of a vanishing electron mass [5].

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512 Page 2 of 11 Eur. Phys. J. C (2015) 75:512

scattering of a particle with spin 1/2 and a given magnetic moment.

Within the Standard Model the F1 have the following values at tree level:

F,SM1V =

3, F,SM1A = 0, F Z,SM1V

W +

14swcw , (2)

while all the F2 are zero. In Eq. 2 sw and cw are the sine and the cosine of the Weinberg angle W . The scale dependence of the form factors is a consequence of higher order corrections. The corrections of the vector currents lead to the anomalous electro-magnetic and weak-magnetic moments represented by F X2V that correct the gyromagnetic ratio gt of the t quark.

Typical values for these corrections are in the range O(103

102) [6]. Corrections to the axial-vector current result in the Form Factors F X2A that are related to the dipole moment dXt =

(e/2mt)F X2A(0) that in turn violates the combined Charge and Parity symmetry C P. Otherwise said, all couplings but

F X2A(k2) conserve C P.

The Form Factors F Z1V,A are related to couplings of t quarks with left and right-handed helicity to the Z0:

gZL = F Z1V F Z1A, gZR = F Z1V + F Z1A (3)

Trivially, the same equations apply correspondingly to the photon couplings gL

In this paper the precision of C P conserving form factors and couplings as introduced above will be derived by means of a full simulation study of the reaction e+e

t t at a centre-of-mass energy of s = 500 GeV with

80% polarised electron beams and 30% polarised positron beams using experimentally well dened observables. Special emphasis will be put on the selection efciency and the polar angle of the nal state t quarks. Both experimental quantities are suited to monitor carefully experimental systematics that may occur in the extraction of form factors and couplings.

The results presented in the following are based on the studies described in detail in Refs. [7,8].

2 Top quark production at the ILC

The tree level diagram for pair production of t quarks at the ILC is presented in Fig. 1a.

The decay of the top quarks proceeds predominantly through t Wb. The subsequent decays of the W bosons

to a charged lepton and a neutrino or a quark-anti-quark pair lead to a six-fermion nal state. The study presented in this article focuses on the lepton+jets nal state lb bq q rep-

/Z0

1 4swcw

1 83s2w , F Z,SM1A =

(a) (b)

Fig. 1 Diagrams that contribute to the e+e lb bq q production:

a tree level t t pair production, b single t quark production

resenting a branching fraction of about 43.4% on all t t pair

decays.

Several other Standard Model processes give rise to the same nal state. The most important source is single t quark production through the process e+e W W Wt b

lb bq q. One of the diagrams contributing to this pro

cess is presented in Fig. 1b. Another relevant source is the Z0W+W production. Due to the coupling of initial state electrons or positrons to W bosons both sources contribute nearly exclusively in a conguration with left-handed polarised electron beams and right-handed polarised positron beams.

In that case single t quark and Z0W+W boson production can yield a total production rate of up to 10% of that of the pair production diagram of Fig. 1a. Experimentally, Z0W+W production can be distinguished rather efciently from t t pair production, but a clean separation of nal states

with a single t quark seems impossible. A realistic experimental strategy must therefore consider the W+bW b inclu

sively [9].

2.1 Observables and form factors

In case of polarised beams Ref. [10] suggests to express the form factors introduced in Sect. 1 in terms of the helicity of the incoming electrons,

F Li j = Fi j +

12 + s2w swcw

ss m2Z

F Zi j

F Zi j , (4)

with i = 1, 2 and j = V, A and mZ being the mass of

the Z0 boson. The tree level cross section for t t quark pair

production for an electron beam polarisation I = L, R reads

I = 2ANc[(1 + 0.5 2)(F I1V )2 + (F I 1A)2 + 3F I1V F I2V

+(1 + 0.5 2)(F I2V )2], (5)

F Ri j = Fi j +

s2w swcw

s m2Z

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Eur. Phys. J. C (2015) 75:512 Page 3 of 11 512

Table 1 Unpolarised cross-sections and cross-sections at tree level for 100% beam polarisation for signal and background processes

Channel unpol. (fb) ,+ (fb) +, (fb)

t t 572 1564 724 + 456 969 854

q=u,d,s,c q q 2208 6032 2793b b 372 1212 276 Z0 11,185 25,500 19,126

W+W 6603 26,000 150 Z0 Z0 422 1106 582

Z0W+W 40 151 8.7

Z0 Z0 Z0 1.1 3.2 1.22

Single t for e+e

et b [11]

3.1 10.0 1.7

where A = 423s with the running electromagnetic coupling

(s) and Nc is the number of quark colours. Furthermore and are the Lorentz factor and the velocity of the t quark, respectively. The term F I 1A = F I1A describes the reduced

sensitivity to axial vector couplings near the t t production

threshold. The cross sections at the Born level of the signal process e+e t t and the main Standard Model back

ground processes at a centre-of-mass energy of 500 GeV are summarised in Table 1.

The forwardbackward asymmetry AtFB can be expressed as

(AtFB)I = ANc

3F I 1A(F I1V + F I2V )

I . (6)

The - sign applies in case of an initial left-handed polarised electron beam, i.e. I = L, and the + applies correspond

ingly in case of an initial right-handed polarised electron beam, i.e. I = R. In the Standard Model the forward

backward asymmetry takes the values (AtFB)L = 0.37 and

(AtFB)R = 0.45 at tree level.

Neglecting CP violating form factors, the fraction of right-handed t quarks is given by the following expression:

(FR)I = 0.5

3(AtFB)I (7)

The - sign applies in case of an initial left-handed polarised electron beam, i.e. I = L, and the + applies correspond

ingly in case of an initial right-handed polarised electron beam, i.e. I = R. The values expected in the Standard Model

at tree level are (FR)L = 0.25 and (FR)R = 0.80.

With the introduced observables the six C P conserving form factors dened for the Z0 and the photon can in principle be extracted simultaneously. However, close to the t t thresh

old the observables depend always on the sum F1V + F2V .

Therefore, a full disentangling of the form factors will be imprecise for energies below about 1 TeV. Hence, in the

present study either the precision on the Form Factors F X1V,A, or equivalently on the Couplings gXL,R, are determined simultaneously, while the two F2V are kept at their Standard Model values or vice versa. Due to these considerations the study will only make use of the cross section and AtFB since these are either the most precise observable in case of the cross section or the one that is most sensitive to axial couplings in case of AtFB. It is however reminded that in [7] the fraction of right-handed t quarks is determined to a precision of about 2%.

2.2 Theory uncertainties

The extraction of form factors requires precise predictions of the inclusive top quark pair production rate and of several differential distributions. In this section the state-of-the-art calculations and estimate theoretical uncertainties are briey reviewed.

As discussed at the beginning of this section, the optimal experimental strategy should consider e+e W+bW b

inclusively, without attempting to distinguish single top and top quark pair production. However, today, sufciently precise calculations are not available for the full process e+e W+bW b. Therefore the discussion in this paper

is based on the current state of the art calculations for e+e t t, assuming that in the next decade theorists

will rise to the challenge of extending the calculations to e+e W+bW b.

The QCD corrections to e+e t tproduction are known

up to N3L O for the inclusive cross section [12], and to N N L O for the forward backward asymmetry AtFB [13]. The perturbative series shows good convergence.

In the kinematic region at around s = 500 GeV as rel

evant for this study the N3L O correction to the total cross-section is below 1 %. An estimate of the size of the next order obtained from the conventional variation of the renormalisation scale by a factor two and one half yields 0.3 %. It can therefore be concluded that the uncertainty of todays state-of-the-art calculations is at the per mil level.

In a similar manner the QCD corrections to the prediction of differential distributions and quantities such as the forwardbackward asymmetry can be estimated. The size of the N3L O correction to AtFB is estimated using the scale variation to be smaller than 1%, see also the discussion in e.g. [13].

Electro-weak (EW) corrections to the same process have also been calculated. A full one-loop calculation is presented in [14]. The correction to the total cross section is found to be approximately 5%. The electro-weak correction to the forwardbackward asymmetry is large, approximately 10% [14,15]. Recent studies [16] show that the corrections are notably different for different beam polari-

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sations. They change for example the shape of the angular distribution in case of Pe , Pe+ = 1, +1 beam polarisa

tion while they only inuence the normalisation in case of

Pe , Pe+ = +1, 1.

The above discussion refers to corrections to the process e+e t t. Further corrections of order t/mt 1% are

expected to appear if the decay of the top quarks is included in the calculation.

It can be concluded that the state-of-the-art calculations of QCD corrections offer the precision required for this study. Uncertainties are under relatively good control, with uncertainties to the cross section of the order of a few per mil and order 1% on the forwardbackward asymmetry. Electro-weak (one-loop) corrections are large. Further work is needed to estimate the size of the two-loop correction and, ultimately, to calculate this contribution. Currently these aspects are discussed with theory groups.

3 Analysis of simulated events

The study has been carried out on a fully polarised sample albeit realistic values for the ILC are Pe , Pe+ =

0.8, 0.3. The cross section and therefore its uncertainty

scales with the polarisation in a well dened way according

to [17]

Pe,Pe+ =

14[(1 Pe Pe+ )(,+ + +,)

+(Pe Pe+ )(+, ,+)]. (8) The observable AtFB varies only very mildly with the beam polarisation. The realistic beam polarisation will be correctly taken into account in the uncertainty of the results.

Signal and background events corresponding to a luminosity of 250 fb1 at s = 500 GeV for each of the two

polarisation congurations are generated with version 1.95 of the WHIZARD event generator [18,19] that provides lowest order calculations of the 2 6 fermions subprocess

and simulates multiple photon radiation from the initial state electron and positron in leading-logarithmic approximation. WHIZARD is interfaced to the PYTHIA Monte Carlo programme [20] for QCD and QED showering. The generated events were subject to a full simulation of the ILD Detector [4] and subsequent event reconstruction using the version ILD_o1_v05 of the ILD software.

The decay of the t quarks proceeds predominantly through t Wb. The subsequent decays of the W bosons to a

charged lepton and a neutrino or a quark-anti-quark pair lead to a six-fermion nal state. The study presented in this article focuses on the semi-leptonic nal state lb bq q. Several

other Standard Model processes give rise to the same nal state. The most important source is single t quark production. Another relevant source is the Z0W+W production.

Experimentally, Z0W+W production can be distinguished rather efciently from t quark pair production. The separation between single t quark production and t t pair production is

much more involved. Note however, that according to Table 1 single t quark production is strongly suppressed in case of

Pe , Pe+ = +1, 1.

The entire selection procedure including lepton and b jet identication, top quark reconstruction and suppression multi-peripheral hadrons background is explained in

detail in [7,8,21]. The total selection efciency of about 56% for semi-leptonic t t events includes events with a lepton in

the nal state. Background processes can be very efciently removed down to a negligible level. A powerful tool is the b likeness or b-tag value that suppresses about 97% of the dominant W+W background. Additional selection criteria comprise cuts on the t quark and W boson masses and of the invariant mass of the total hadronic nal state.

With the determined efciencies a statistical uncertainty of the cross section e+e t tof 0.47% in case Pe , Pe+ =

0.8, +0.3 and 0.63% in case Pe , Pe+ = +0.8, 0.3 can

be derived.

3.1 Forwardbackward asymmetry AtFB

The forwardbackward asymmetry AtFB has the well known denition

AtFB =

N(costop > 0) N(costop < 0) N(costop > 0) + N(costop < 0)

, (9)

where N is the number of events in the two detector hemispheres w.r.t. the polar angle top of the t quark calculated from the decay products in the hadronic decay branch. The direction measurement depends on the correct association of the b quarks to the jets of the hadronic W boson decays. The analysis is carried out separately for a left-handed polarised electron beam and for a right-handed polarised beam. In case of a right-handed electron beam the direction of the t quark can be precisely reconstructed. In case of a left-handed electron beam the nal state features two hard jets from the b quarks and soft jets from the hadronically decaying W boson. This conguration leads to migrations in the polar angle distribution of the t quark as visible in the left part of Fig 2. This implication motivates to restrict the determination of AtFB in case of Pe , Pe+ = 1, +1 to cleanly

reconstructed events. For this a test variable 2 is dened that compares the measured values of the Lorentz factor of the top, the momentum of the b quark in the rest frame of the top and the angle cosbW between the b quark and the W boson. The reconstructed polar angle distribution of the t quark is compared with the generated one for different cuts on 2. For a value of 2 < 15 an excellent agreement between the generated and reconstructed polar angle distributions is obtained, see the right part of Fig. 2. The

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Eur. Phys. J. C (2015) 75:512 Page 5 of 11 512

5000

eReconstructed Generator - Whizard

5000

Reconstructed with cut on

SM Background Generator - Whizard

4000

3000

2000

1000

-1 -0.5 0 0.5 1

cos(

)

top

cos(

)

top

Fig. 2 Left Reconstructed forwardbackward asymmetry compared with the prediction by the event generator WHIZARD [18] for two congurations of the beam polarisations. Right The same but after the application of a on 2 < 15 for the beam polarisations Pe , Pe+ = 1, +1

as explained in the text. Note, that in both gures no correction is applied for the beam polarisations Pe , Pe+ = +1, 1. The gure on the right

hand side shows also the residual Standard Model background

Table 2 Statistical precisions expected for the cross sections and AtFB for different beam polarisations

Pe , Pe+ (/)stat. (%) ( AtFB/AtFB)stat. (%)

0.8, +0.3 0.47 1.8

+0.8, 0.3 0.63 1.3

tight selection however reduces the efciency in case of left-handed initial electron beams from 55 to 28%. With this the forward backward asymmetry can be determined to a statistical precision of better than 2%. The precise results corrected to the beam polarisations Pe , Pe+ = 0.8, 0.3

are given in Table 2 together with those for the cross section, see previous section. A more straightforward, albeit experimentally more challenging, way to control the migrations is to measure the charge of the b quarks that are issue of the t quark decay. References [22,23] describe the determination of the b quark charge using secondary tracks. The same value of AtFB is obtained at a comparable selection efciency [8].

This means that AtFB can be determined with two independent methods.

Hard gluon radiation may alter the polar angle distribution of the nal state t quarks. The WHIZARD version 1.95 used for the study generates hard gluons only via the interface to PYTHIA that generates the parton shower. Therefore results presented before have been checked with a study on parton level using the most recent version 2.2.2 of WHIZARD that correctly accounts for hard gluon radiation. No signicant difference has been observed.

4 Discussion of systematic uncertainties

In the previous sections measurements of either cross sections or asymmetries have been presented. This section

makes an attempt to identify and quantify systematic uncertainties, which may inuence the precision measurements.

Luminosity The luminosity is a critical parameter for

cross section measurements only. The luminosity can be controlled to 0.1% [24].

Polarisation The polarisation is a critical parameter for

all analyses. It enters directly the cross section measurements. The studies presented in [25] using W pair production lead to an uncertainty of 0.1% for the polarisation of the electron beam and to an uncertainty of 0.35% for the polarisation of the positron beam. This translates into an uncertainty of 0.25% on the cross section for

Pe , Pe+ = 0.8, +0.3 and 0.18% on the cross sec

tion for Pe , Pe+ = +0.8, 0.3. The uncertainty on the

polarisation can be neglected with respect to the statistical uncertainty for AtFB.

Beamstrahlung and beam energy spread The mutual

inuence of the electromagnetic elds of the colliding bunches provokes radiation of photons known as Beam-strahlung. This Beamstrahlung modulates the luminosity spectrum, i.e.moves particles from the nominal energy to smaller energies. At the ILC for a centre-of-mass energy of 500 GeV about 60% of the particles are expected to have 99% or more of the nominal energy [4]. The beam energy spread, i.e.the RMS of this main luminosity peak is 124MeV for the electron beam and 70MeV for the positron beam [4]. Both effects play a role at the t tthresh

old [26] and can be neglected at energies well above this threshold.

Experimental uncertainties in top quark reconstruction

As discussed in Sect. 3.1 migrations have to be taken into account for the measurement of AtFB, in particular for the polarisations Pe , Pe+ = 0.8, +0.3. These

migrations are reduced by stringent requirements on the event selection using a 2 analysis. This in turn leads

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Table 3 Standard deviations and resulting relative precisions of form factors and couplings derived from the statistical precisions on the observables cross section and AtFB as listed in Table 2

Quantity F1V F Z1V F Z1A F2V F Z2V gL gR gZL gZR

SM value at tree level 2/3 0.230 0.595 0 0 2/3 2/3 0.824 0.364

Standard deviation 0.002 0.003 0.007 0.001 0.002 0.005 0.005 0.008 0.009

Relative precision (%) 0.3 0.9 1.2 0.8 0.8 1.0 2.5

to a penalty in the efciency. The success of the method depends in addition on a very sharp measurement of the variables used for the 2 analysis. It is expected that these ambiguities can be (partially) eliminated by an event-by-event determination of the charge of the b quark from the t decay. As has been shown in Sect. 3, the effect will be very much suppressed in case of Pe , Pe+ = +0.8, 0.3

beam polarisation.

Other experimental effects There is a number of other

experimental effects such as acceptance, uncertainties of the b tagging or the inuence of passive detector material. The LEP1 experiments quote a systematic uncertainty on Rb of 0.2% a value which may serve as a guide line for values to be expected at the ILC, which on the other hand will benet from far superior detector resolution and b tagging capabilities.

Theory The uncertainties of todays state-of-the-art cal

culations are discussed in Sect. 2.2. The uncertainties in the QCD corrections to the total cross section and AFB are of the same order as the experimental uncertainties. Two-loop electro-weak calculations are required for a reliable estimation of the uncertainties due to electro-weak corrections. It is however intuitively clear that the latter will benet from the insight of the different impact for different beam polarisations, see Sect. 2.2 and [16].

Single-top production Single top production at the LC in

association with a W boson and bottom quark (through W W production) leads to the same nal state as t quark pair production. Being largely suppressed in case of

Pe , Pe+ = +0.8, 0.3 beam polarisation, it forms a

sizeable contribution to the six-fermion nal state in case of Pe , Pe+ = 0.8, +0.3 beam polarisation. It must

therefore be taken into account in a realistic experimental strategy. This is left for a future study.

Beyond Standard Model physics Possible BSM effects

may affect the various components of the background, in particular the t t induced background. This will there

fore require a careful iterative procedure with tuning of event generators. This procedure seems feasible without a signicant loss of accuracy.

As a summary it can be concluded that the total systematic uncertainties will not exceed the statistical uncertainties.

This, however, requires an excellent control of a number of experimental and theoretical quantities.

5 Precision of form factors and electro-weak couplings

The measured cross sections and AtFB lead for two polarisation congurations to a set of four observables. By means of

Eqs. 5 and 6 the uncertainties on these observables are used to build up a system of linear equations to determine the variances of up to four variables2. The variances are equivalent to the square of the standard deviations of the variables under study. These variables can be the form factors or alternatively directly the couplings. More explicitly, in this paper the following quantities will be determined separately:

1. The standard deviations of the Form Factors F1V , F Z1V , F Z1A assuming no variation of the Form Factors F X2j;2. The standard deviations of the Form Factors F2V , F Z2V assuming no variation of the Form Factors F X1j ;

3. The standard deviations of the Couplings gL , gR, gZL, gZR.

Note, that the Form Factor F Z1A is xed to be 0 in order to respect QED gauge invariance. On the other hand all four

Couplings gXIare allowed to vary freely. The resulting standard deviations are listed in Table 3.

The complete covariance matrices are given in Appendix 7. From there it can be told that e.g. gZL and gZR are strongly correlated while F Z1V and F Z1A are nearly uncorrelated.

The expected high precision at a linear e+e collider allows for a profound discussion of effects by new physics.

The ndings can be confronted with predictions in the framework of RandallSundrum models and/or compositeness models such as [2,28,29,3134,36] or Little Higgs models as e.g. [30]. All these models entail deviations from the Standard Model values of the t quark couplings to the Z0 boson that will be measurable at the ILC as illustrated in Fig. 3. Therefore, the couplings of the t quark to the Z0 boson will discussed in a broader context in the following.

2 For the Linear Algebra the software package Eigen [27] version3.2.2 has been used.

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Eur. Phys. J. C (2015) 75:512 Page 7 of 11 512

Fig. 3 Predictions of several models that incorporate RandallSundrum (RS) models and/or compositeness or Little Higgs models on the deviations of the left- and right-handed couplings of the t quark to the Z0 boson. The ellipse in the frame in the upper right corner indicates the precision that can be expected for the ILC running at a centre-of-mass energy of s = 500 GeV after having

accumulated L = 500 fb1 of

integrated luminosity shared equally between the beam polarisations

Pe , Pe+ = 0.8, 0.3. The

original version of this gure can be found in [35]

Uncertainty

5.1 Discussion of couplings to the Z0 Boson: comparison with perspectives for LHC and avour physics

Electro-weak couplings can be measured at the LHC in associated tt and tt Z0 production. A comprehensive compila

tion on the statistical precisions on the form factors that can be expected at the end of the HL-LHC is given in [37,38] for an update on tt Z0 form factors. The values published there

are compared with the results in the present study in Fig. 4.

All but one form factor will be measured at about a factor 10 better at the ILC for the scenario discussed in this paper than it will be possible at the LHC. This exception is F Z1A where [38] quotes a possible statistical precision of F Z1A 0.031. It should however be pointed out that the

considerable precision expected for F Z1A benets strongly from LEP/SLC bounds on the oblique parameters that e.g.

render it unlikely that F Z1A ips sign due to New Physics. The study presented by [38] is an analysis at leading order

QCD. The analysis carried out in [39] suggests that higher-order effects in the theory may allow for an improvement of the LHC precision by up to 40%. Note at this point that the interference between the and the Z0 in case of e+e t t will allow for measuring ips of the signs of the

form factors that will be unnoticed in associated tt Z0 at the

LHC.

While the prospects for the LHC discussed so far are based on analyses differential in given jet observables of the nal state, LHC experiments observe the process pp tt Z0 [40

43]. The interpretation of the results is however still limited by the small statistics available for the analyses.

At the LHC electro-weak couplings are measured also in single t quark production. In the effective eld theory

ILC,

=500 GeV, L=500 fb

-1

LHC,

=14 TeV, L=3000 fb

Phys.Rev.D71 (2005) 054013

-1

Phys.Rev.D73 (2006) 034016

F 1V

F 2V

Fig. 4 Graphical comparison of statistical precisions on C P conserving form factors expected at the LHC, taken from [37,38], and at the ILC. The LHC results assume an integrated luminosity of L = 3000 fb1

at s = 14 TeV. The results for the ILC assume an integrated lumi

nosity of L = 500 fb1 at s = 500 GeV and a beam polarisation Pe = 0.8, Pe+ = 0.3

approach, assuming SU(2)L U(1)Y gauge symmetry for

the operators, the relation

gtbWL

0.35gZL gZL

(10)

can be established. Here gtbWL is the charged current coupling of the decay t Wb. The CMS Collaboration [44] reports

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512 Page 8 of 11 Eur. Phys. J. C (2015) 75:512

a precision for the t-b transition probability Vtb of about 4%. In the Standard Model Vtb is identical to gtbWL . Hence, by means of Eq. 10 the precision of the coupling of left-handed t quarks to the Z boson can be derived to be of the order of 11%. Noting that (pp tt Z) (gZL)2 + (gZR)2

this allows in principle also for deriving (gZR)2, albeit with a poor precision given that (gZL)2 (gZR)2. Loop corrections

in heavy avour physics as e.g. in the processes b s ,

B + or K +, respectively, may also lead to

competitive determinations of gZL [45]. However, again gZR can only be constrained rather poorly.

It follows that the ILC will allow for measurements superior to those that can be expected from existing experiments. This is particularly true for the determination of gZR.

5.2 Coupling measurements and form factors at different centre-of-mass energies

Given the fact that at the ILC in its current layout centreof-mass energies of up to 1 TeV can be reached and that the alternative project for a linear collider, CLIC [46], may even reach higher energies, it is instructive to discuss the results presented in this paper with this possibility in mind. The selection and reconstruction of the decay topology of boosted t quarks is very different from that of t quarks with moderate velocity. Therefore, the study must be extrapolated to high centre-of-mass energy with some care. Still, the following observations can be made:

Neglecting varying detector systematics and theory

uncertainties with varying centre-of-mass energy, and assuming the linear collider luminosity vs. centre-of-mass energy curve, the sensitivity to the form factors considered in this paper is greatest at approximately s =

400700 GeV. At lower centre-of-mass energy, as e.g.

studied in [47], the small velocity of the t quarks reduces the potential of the AtFB measurement compromising thus the measurement of the axial vector couplings to the

Z0 boson and by virtue of Eq. 3 the disentangling of left- and right-handed couplings. On the other hand running at centre-of-mass energies close to the t t threshold

offers sensitivity to virtual Higgs exchange [4850]. In case the Higgs has a CP odd component this may give rise to recognisable CP violating effects in the threshold region [51]. However, in the transition region between the t t threshold and the continuum region starting at around

380 GeV the current QCD uncertainties are at least 10%.

This is due to uncertainties on higher QCD order corrections and on the correct matching procedure between the non-relativistic calculations at the t t threshold and the

relativistic continuum calculations [52].

If an effect is seen at s = 500 GeV it will be crucial

to know how it evolves with energy with a decent lever arm. If, for instance, the effect is due to mixing of the Z0 boson with a new Z boson it will remain unchanged.

If, however, a Z boson leads to a propagator term, the corresponding effect will grow like s/M2Z . In the case of RandallSundrum models both effects are present and therefore measurements at two energies are needed to extract MZ , see e.g. [35] for a deeper discussion.

The impact of high-scale new physics on the observables

can increase strongly with centre-of-mass energy. Operators corresponding to the top quark dipole moments and four-fermion contact interactions induce larger anomalous form factors at higher energy. For other anomalous couplings, however, the impact is nearly independent of the centre-of-mass energy as is the case for F Z1V and F Z1A.

A full simulation study at different centre-of-mass energies is left for a future publication.

6 Summary and outlook

This article presents a comprehensive analysis fully simulated events of t t quark production at the International Lin

ear Collider using the semi-leptonic decay channel. Results are given for a centre-of-mass energy of s = 500 GeV and

an integrated luminosity of L = 500 fb1 shared equally

between the beam polarisations Pe , Pe+ = 0.8, 0.3.

Semi-leptonic events, including those with leptons in the nal state can be selected with an efciency of about 55%. The cross section of the semi-leptonic channel of t t quark

production can therefore be measured to a statistical precision of about 0.5%. The second observable is the forward backward asymmetry AtFB. It was shown that in particular for predominantly left-handed polarisation of the initial electron beam the V A structure leads to migrations, which dis

tort the theoretical expected AtFB. These migrations can be remedied by tightening the selection criteria of the events or alternatively by measuring the charge of the b quark produced in the decay of the t quark. Taking into account this correction the forwardbackward asymmetry can be determined to a statistical precision of better than 2% for both beam polarisations.

The observables together with the unique feature of the ILC to provide polarised beams allow for a largely unbiased disentangling of the individual couplings of the t quark to the Z0 boson and the photon. These couplings can be measured with high precision at the ILC and, when referring to the results in [37,38], considerably better than it will be possible at the LHC even with an integrated luminosity of

123

Eur. Phys. J. C (2015) 75:512 Page 9 of 11 512

L = 3000 fb1. The improving analyses of the LHC experi

ments will however be observed with great interest.

Beam polarisation is a critical asset for the high precision measurements of the electroweak t quark couplings. Experimental and theoretical effects manifest themselves differently for different beam polarisations. It seems to be that the conguration Pe , Pe+ = +0.8, 0.3 is more benign in

both, experimental aspects due to the suppression of migrations in the polar angle spectrum of the nal state t quark and theoretical aspects due to the somewhat simpler structure of higher order electroweak corrections. It is intuitively clear that the described facts would greatly support the discovery of effects due to new physics.

The precision as obtained in the present study for the ILC would allow for the verication of a great number of models for physics beyond the Standard Model. Examples for these models are extra dimensions and compositeness. The results obtained here constitute therefore a perfect basis for discussions with theoretical groups. Note at this point that running scenarios for the ILC have been proposed that would yield between 8 and 10 times more integrated luminosity [53] than it is assumed for the present study. Moreover it can be expected that the event reconstruction will be improved by e.g.the measurement of the b quark charge. It is therefore not statistics that will limit the nal accuracy but most likely theory and experimental systematics.

Hence, the study of systematic errors, only partially addressed in this study, will become very important. Already from the achieved precision it is mandatory that systematics are controlled to the 1% level or better in particular for the measurement of the cross section. This issue is addressed in ongoing studies.

The study presented in [16] based on generated events suggests that by exploiting the polarisation of the nal state t quarks a simultaneous extraction of all ten form factors, see Eq. 1, to a precision below the percent level is feasible. A detailed comparison between the advantages and drawbacks of the method applied there and the method presented in this paper is left for a future study.

Acknowledgments This work was supported within the Quarks and Leptons programme of the CNRS/IN2P3, France, and by the Spanish Grant Agreement Detector developments and physics studies for future colliders, FPA2012-39055-C02-01. The results benet from the enlightening discussions in the framework of the French-Japanese FJPPL/TYL virtual laboratory on top physics, particularly through comments by Emi Kou, Keisuke Fujii and Franois LeDiberder. We would like to thank Fabian Bach and Maximilan Stahlhofen for the profound discussion on QCD uncertainties in the t t threshold region.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http://creativecomm http://creativecommons.org/licenses/by/4.0/

Web End =ons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative

Commons license, and indicate if changes were made. Funded by SCOAP3.

7 Covariance matrices

For completeness the underlying covariance matrices of the results presented in Sect. 5 are given in this appendix.

The covariance matrix resulting from the system of lin

ear equations built for the Form Factors F1V , F Z1V , F Z1A reads:

var(F1V ) cov(F1V , F Z1V ) cov(F1V , F Z1A) var(F Z1V ) cov(F Z1V , F Z1A)

var(F Z1A)

0.260 0.043 0.506

0.791 0.118 5.460

105. (11)

The covariance matrix resulting from the system of linear

equations built for the Form Factors F2V , F Z2V reads:

var(F2V ) cov(F2V , F Z2V )

var(F Z2V )

0.160 0.046

0.473

105. (12)

The covariance matrix resulting from the system of linear

equations built for the Couplings gL, gR, gZL, gZR reads:

var(gL) cov(gL, gR) cov(gL, gZL) cov(gL, gZR) var(gR) cov(gR, gZL) cov(gR, gZR)

var(gZL) cov(gZL, gZR) var(gZR)

2.801 2.357 0.339 1.234

2.949 0.780 2.247

5.988 4.691

7.306

105.

(13)

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(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

Top quark production in the process ...... at a future linear electron positron collider with polarised beams is a powerful tool to determine indirectly the scale of new physics. The presented study, based on a detailed simulation of the ILD detector concept, assumes a centre-of-mass energy of ...... GeV and a luminosity of ...... equally shared between the incoming beam polarisations of ....... Events are selected in which the top pair decays semi-leptonically and the cross sections and the forward-backward asymmetries are determined. Based on these results, the vector, axial vector and tensorial CP conserving couplings are extracted separately for the photon and the ...... component. With the expected precision, a large number of models in which the top quark acts as a messenger to new physics can be distinguished with many standard deviations. This will dramatically improve expectations from e.g. the LHC for electro-weak couplings of the top quark.

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Title

A precise characterisation of the top quark electro-weak vertices at the ILC

Author

Amjad, M S; Bilokin, S; Boronat, M; Doublet, P; Frisson, T; García, I García; Perelló, M; Pöschl, R; Richard, F; Ros, E; Rouëné, J; Femenia, P Ruiz; Vos, M

Pages

1-11

Publication year

2015

Publication date

Oct 2015

Publisher

Springer Nature B.V.

ISSN

14346044

e-ISSN

14346052

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1140/epjc/s10052-015-3746-5

ProQuest document ID

1732879138

SIF and Springer-Verlag Berlin Heidelberg 2015

A precise characterisation of the top quark electro-weak vertices at the ILC

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