PDF Measurement of the top quark mass and couplings at Linear Colliders

Nuclear Physics B Proceedings Supplement 00 (2014) 1–4

Nuclear Physics B Proceedings Supplement

Measurement of the top quark mass and couplings at Linear Colliders

Ignacio Garc´ıa

On behalf of the ILC Physics and Detector Study and CLICdp

IFIC (UVEG / CSIC) Valencia, Spain

Abstract

Future precision studies of the Standard Model require excellent knowledge of the top quark mass, to an accuracy of 100 MeV or better. This mass can be measured in a way that is free of any ambiguities from soft QCD by locating the threshold position for e + e − annihilation to top quark pairs, or, more precisely, the mass of the unstable 1S resonance.

This contribution reports the current status of this program, with results from full-simulation studies of the top quark threshold scan in the detectors proposed for ILC and CLIC. Precision studies of the pair production process, including its full dependence on beam polarisation, has the potential to extract the form factors for the top quark couplings with precision that exceeds the prospects at the LHC by an order of magnitude.

Keywords: top quark, mass, couplings, ILC, CLIC, linear collider

1. Introduction

Future high-luminosity, high-energy e + e − colliders will offer a great opportunity for precision tests of the Standard Model. Thanks to the precise control of the initial state, the calculable electroweak production and the continued progress in detector RD, an e + e − collider owns a potential beyond that of hadron colliders [1].

Therefore the physics case for such a machine has focussed on studying the exact relation of the Higgs bo- son to the electro-weak symmetry breaking mechanism.

However, a linear e + e − collider with a center-of-mass energy tuneable between 200 GeV and 3 TeV o ff ers a much wider range of opportunities.

Two technological proposals exist to realize a lin- ear e + e − collider. The International Linear Collider (ILC [2]) is based on superconducting RF cavities. With the accelerating gradient achieved to date, such a ma- chine naturally covers an energy range from 200 GeV to 500 GeV, with a posible upgrade to 1 TeV. The ILC also o ff ers the option of running with polarised beams.

The beam polarisation expected for (e − , e + ) is ( ± 80%,

± 30%) respectively at 500 GeV.

The Compact Linear Collider (CLIC [3]) pursues a more ambitious two-beam acceleration scheme, that raises the gradient to 100 MV/m and brings multi-TeV operation within reach. The center-of-mass energy of the default design is 3 TeV but it could start working at 500 GeV and afterwards 1.5 TeV during the first years of running.

There are two detector concepts developed for lepton colliders, ILD [4] and SiD [5]. These detectors are opti- mised for the Particle Flow Algorithm (PFLOW), which consists in measuring the different particles in the event with the most suitable sub-detectors, i.e. while charged particles are measured by the tracking system, photons and neutral hadrons are measured by the electromag- netic and hadronic calorimeters respectively.

The focus of these proceedings is on two measure-

ments where the unique properties of the LC can greatly

enhance the knowledge of the top quark. The potential

of LC experiments to measure the top quark mass and

the prospects of a linear collider experiment to precisely

characterise the t tZ/γ ¯ ∗ vertices.

/ Nuclear Physics B Proceedings Supplement 00 (2014) 1–4 2

2. Top quark mass measurement

ICHEP Valencia 2-9 July 2014 [email protected]

Motivation

5

0 50 100 150 200

0 50 100 150 200

Higgs massMhin GeV TopmassMtinGeV

Instability

Non-perturbativity

Stability Meta-stability

Instability

10⁷

10⁹

10¹⁰

10¹²

115 120 125 130 135

165 170 175 180

Higgs massMhin GeV PoletopmassMtinGeV

1,2,3s Instability

Stability Meta-stability

Figure 5: Regions of absolute stability, meta-stability and instability of the SM vacuum in the M

t

– M

_h

plane (upper left) and in the –y

t

plane, in terms of parameter renormalized at the Planck scale (upper right). Bottom: Zoom in the region of the preferred experimental range of M

h

and M

t

(the gray areas denote the allowed region at 1, 2, and 3 ). The three boundary lines correspond to ↵

_s

(M

_Z

) = 0.1184 ± 0.0007, and the grading of the colors indicates the size of the theoretical error. The dotted contour-lines show the instability scale ⇤ in GeV assuming ↵

s

(M

Z

) = 0.1184.

determined at hadron colliders su↵ers from O(⇤

QCD

) non-perturbative uncertainties [41]. A possibility to overcome this problem and, at the same time, to improve the experimental error on M

t

, would be a direct determination of the MS top-quark running mass from ex- periments, for instance from the t t ¯ cross-section at a future e

⁺

e collider operating above the t t ¯ threshold. In this respect, such a collider could become crucial for establishing the structure of the vacuum and the ultimate fate of our universe.

As far as the RG equations are concerned, the error of ± 0.2 GeV is a conservative estimate, based on the parametric size of the missing terms. The smallness of this error, compared to the uncertainty due to threshold corrections, can be understood by the smallness of all the couplings at high scales: four-loop terms in the RG equations do not compete with finite tree-loop corrections close to the electroweak scale, where the strong and the top-quark Yukawa coupling are large.

The LHC will be able to measure the Higgs mass with an accuracy of about 100–200 MeV, which is far better than the theoretical error with which we are able to determine the condition of absolute stability.

18

• A small change in M

h

and M

t

can drastically modify the conclusions regarding vacuum stability!

• M

t

must be characterised well

• Learn about BSM physics from the deviations observed on Higgs and top EW couplings.

• LHC cannot achieve enough accuracy in the measurement of the coupling deviations -> ILC accuracies are needed to access to fully significant deviations arXiv:1403.2893

arXiv:1205.6497 Top quark mass

Top quark electroweak couplings Figure 1: Region of full stability, meta-stability and instability of the SM vacuum in the M

_t

− M

_h

plane in terms of parameter renormalised at the Planck scale. This figure is taken from the Reference [6].

Because of its large mass the top quark plays a special role in the Standard Model and many of its extensions.

In Figure 1 the regions of the (M t ,M h ) space are shown.

A small change in the masses can drastically modify the conclusions regarding the stability of the vacuum. So a precise determination of the top mass is a crucial to test the consistency of the Standard Model.

Recently became known a historical result [7], a com- bination of measurements of the mass of the top quark, m top , performed by the CDF and D0 experiments at the Tevatron collider and the ATLAS and CMS experiments at the Large Hadron Collider (LHC).

[GeV]

mtop

170 172 174 176 178 180

1 16

LHC September 2013 173.29 ± 0.95 (0.23 ± 0.26 ± 0.88)

Tevatron March 2013 (Run I+II) 173.20 ± 0.87 (0.51 ± 0.36 ± 0.61)

World comb. 2014 173.34 ± 0.76 (0.27 ± 0.24 ± 0.67)

LHC 173.28 ± 0.94 (0.22 ± 0.26 ± 0.88)

Tevatron 173.58 ± 0.94 (0.44 ± 0.36 ± 0.74)

CMS 173.58 ± 1.03 (0.29 ± 0.28 ± 0.95)

ATLAS 172.65 ± 1.44 (0.31 ± 0.41 ± 1.34)

D0 174.85 ± 1.48 (0.78 ± 0.48 ± 1.16)

CDF 173.19 ± 1.00 (0.52 ± 0.44 ± 0.73)

+jets miss

ET 173.93 ± 1.85 (1.26 ± 1.05 ± 0.86)

all jets 173.17 ± 1.20 (0.65 ± 0.30 ± 0.96)

di-lepton 172.74 ± 1.15 (0.43 ± 0.06 ± 1.07)

l+jets 173.29 ± 0.80 (0.23 ± 0.24 ± 0.72)

- 8.7 fb-1 = 3.5 fb-1 indiv. comb. - March 2014, Lint Tevatron+LHC mtop

ATLAS + CDF + CMS + D0 Preliminary

) syst.

iJES stat.

total (

Individual Combinations

PreviousComb.

Figure 2: Comparison of the world

mtop

combination result with the individual

mtop

determinations pert¯

t

decay channel, experiment, and collider. Results are compared with the Tevatron and LHC combined

mtop

values from Refs. [6, 7]. The grey vertical band reflect the total uncertainty on the combined

mtop

value.

Tevatron and LHC colliders (m

^TEV

,

m^LHC

). Figure 2 reports the comparison of the world

mtop

combination with the individual

mtop

determinations per

t¯t

decay channel, experiment, and collider. In addition

mtop

combination results from Refs. [6, 7] are also reported (see Appendix B, Figure 4 for the correlated

mtop

determinations).

The full uncertainty breakdown of the individual CDF, D0, ATLAS, CMS, Tevatron and LHC combinations is reported in Appendix C. The individual combination for

m^TEV

and

m^LHC

present some di↵erences with respect to the results documented in Refs. [6, 7]. For

m^TEV

, these mainly originate from the reduced set of input measurements used in the combination with respect to Ref. [6], and to a lesser extent from the use of a finer MC modelling uncertainty splitting (four separate categories: MC, Rad, CR, PDF, rather than a single one including all of them), and the change in the JES uncertainty categories for the CDF measurements. The slight di↵erences in the uncertainty breakdown of the separate combination of

m^LHC

with respect to Ref. [7]

are mainly attributed to the changes of the uncertainty categorisation and correlation assumption underlying the stdJES and

b-tagging categories.

7 E ↵ ects of using alternative correlation models and uncertainty treatments

The categorisation and the correlation assumptions summarised in Tables 3 and 4 reflect the present understand- ing and the limitations due to the di↵erent choices made by the experiments when evaluating the individual uncertainty sources. In this preliminary result, the e↵ects of the approximations are evaluated by perform- ing stability cross checks, in which the input assumptions are changed with respect to the values reported in Section 5. The results of these cross checks are described in the following, and summarised in Figure 3.

17

Figure 2: Comparison of the world m

top

combination result with the individual m

top

determinations per t t ¯ decay channel, experiment, and collider. Figure is taken from the Reference [7].

The resulting combined measurement of m top is 173 . 34 ± 0 . 27 (stat) ± 0 . 71 (syst) GeV.

The mass measurements mentioned so far are ex- tracted from a comparison of a Monte Carlo template to the mass distribution of the colour neutral system formed by the top quark decay products. The result is interpreted as the top quark pole mass. The uncertainty

inherent in this interpretation limits the precision that can be achieved with this procedure [7, 8].

At e + e − colliders two techniques to determine the mass of the top quark could be considered. The first one is the direct reconstruction of the top from its prod- uct decays necessarily above the t t ¯ production thresh- old. This technique is experimentally well-defined but suffers from the ambiguity in the interpretation. On the other hand, top mass can be measured in a scan of the beam energy through the top pair production threshold.

This procedure has a high degree of precision using a theoretically well-defined top mass.

The idea that a scan of the center-of-mass energy at an e + e − collider could yield a potentially high precision strategy for the determination of the top quark mass [9]

was known well before the top quark was discovered.

12

[GeV]

s

345 350 355

cross section [pb]

0 0.2 0.4 0.6

0.8 tt threshold - 1S mass 174.0 GeV TOPPIK NNLO + ILC350 LS + ISR

/point simulated data: 10 fb-1

200 MeV

± top mass

ILC CLIC detector

Fig. 7Background-subtracted simulated cross section measurements with the ILC luminosity spectrum for 10 fb¹per data point, together with the cross section for the generator mass of 174 GeV as well as for a shift in mass of±200 MeV.

1S top mass andascombined 2D fit

mtstat. error 27 MeV

m_ttheory syst. (1%/3%) 5 MeV / 9 MeV

asstat. error 0.0008

astheory syst. (1%/3%) 0.0007 / 0.0022 Table 4Summary of the 2D simultaneous top mass andasdetermina- tion with a threshold scan at ILC for 10 points with a total integrated luminosity of 100 fb¹. Event selection and background rejection from CLIC_ILD is used.

section rises faster due to the sharper main luminosity peak at the ILC. This faster rise of the cross section is expected to lead to somewhat reduced statistical uncertainties on the top mass for a given integrated luminosity due to increased dif- ferences between different mass hypotheses in the threshold region.

For the generation of data points with the ILC luminosity spectrum, the signal selection efficiencies and the residual background contribution are determined with the CLIC_ILD detector concept. While there are some differences between this detector concept and the ones developed for the ILC, it is not expected that this will have a sizeable impact on the efficiencies in the present study.

Figure7and Table4summarize the results of the com- bined extraction of the 1S top mass and the strong coupling constant at ILC. As expected, the statistical uncertainties are reduced compared to a threshold scan at CLIC, with a 20%

reduction of the uncertainty of the mass and a 10% reduc- tion of the uncertainty ofas. The theory systematics as well as other systematic uncertainties studied here are unchanged compared to those at CLIC. Thus, the difference in statisti- cal precision provided by the two different collider concepts

top mass [GeV]

173.95 174 174.05

sα

0.116 0.118 0.12

σ 1

2 σ

[174.01 GeV; 0.1180]

ILC CLIC detector

Fig. 8Expected statistical errors from a simultaneous fit of the top mass and the strong coupling constant using the ILC luminosity spec- trum, showing the correlation of the two variables and the achieved precision.

does not result in a significant difference of the overall pre- cision of the top mass measurement in a threshold scan.

7 Conclusions

A lineare⁺e collider based on CLIC technology provides the capabilities for a precise measurement of the mass of the top quark both at and above threshold. We have stud- ied the expected precision obtainable in top pair production events with a scan around the threshold and with the direct reconstruction of the invariant mass of the top decay prod- ucts at an energy of 500 GeV, each assuming a total inte- grated luminosity of 100 fb¹. The studies have been per- formed with realistic GEANT4-based detector simulations including physics and machine-related backgrounds using full particle flow event reconstruction.

Above threshold, the mass of the top quark, here de- fined as the invariant mass of the decay products, can be measured with a statistical precision of 80 MeV combining fully-hadronic and semi-leptonic top pair decays. System- atic uncertainties originating from the jet energy scale can be controlled to a similar level using the direct reconstruction of theWbosons in the top pair decays andZdecays tob¯bfrom other sources. Since the measurement of the invariant mass is interpreted in the context of the top mass definition pro- vided by the event generator PYTHIA, there are additional, potentially sizeable theoretical uncertainties when translat- ing the result into theoretically well-defined mass schemes, which are not included in the quoted uncertainty.

In a threshold scan, the top mass can be determined in a theoretically well defined way, here using the 1S mass, with 12

[GeV]

s

345 350 355

cross section [pb]

0 0.2 0.4 0.6

0.8 tt threshold - 1S mass 174.0 GeV TOPPIK NNLO + ILC350 LS + ISR

/point simulated data: 10 fb-1

200 MeV

± top mass

ILC CLIC detector

Fig. 7Background-subtracted simulated cross section measurements with the ILC luminosity spectrum for 10 fb¹per data point, together with the cross section for the generator mass of 174 GeV as well as for a shift in mass of±200 MeV.

1S top mass andascombined 2D fit

mtstat. error 27 MeV

mttheory syst. (1%/3%) 5 MeV / 9 MeV

asstat. error 0.0008

astheory syst. (1%/3%) 0.0007 / 0.0022 Table 4Summary of the 2D simultaneous top mass andasdetermina- tion with a threshold scan at ILC for 10 points with a total integrated luminosity of 100 fb¹. Event selection and background rejection from CLIC_ILD is used.

section rises faster due to the sharper main luminosity peak at the ILC. This faster rise of the cross section is expected to lead to somewhat reduced statistical uncertainties on the top mass for a given integrated luminosity due to increased dif- ferences between different mass hypotheses in the threshold region.

For the generation of data points with the ILC luminosity spectrum, the signal selection efficiencies and the residual background contribution are determined with the CLIC_ILD detector concept. While there are some differences between this detector concept and the ones developed for the ILC, it is not expected that this will have a sizeable impact on the efficiencies in the present study.

Figure7and Table4summarize the results of the com- bined extraction of the 1S top mass and the strong coupling constant at ILC. As expected, the statistical uncertainties are reduced compared to a threshold scan at CLIC, with a 20%

reduction of the uncertainty of the mass and a 10% reduc- tion of the uncertainty ofas. The theory systematics as well as other systematic uncertainties studied here are unchanged compared to those at CLIC. Thus, the difference in statisti- cal precision provided by the two different collider concepts

top mass [GeV]

173.95 174 174.05

sα

0.116 0.118 0.12

σ 1

2 σ

[174.01 GeV; 0.1180]

ILC CLIC detector

Fig. 8Expected statistical errors from a simultaneous fit of the top mass and the strong coupling constant using the ILC luminosity spec- trum, showing the correlation of the two variables and the achieved precision.

does not result in a significant difference of the overall pre- cision of the top mass measurement in a threshold scan.

7 Conclusions

A lineare⁺e collider based on CLIC technology provides the capabilities for a precise measurement of the mass of the top quark both at and above threshold. We have stud- ied the expected precision obtainable in top pair production events with a scan around the threshold and with the direct reconstruction of the invariant mass of the top decay prod- ucts at an energy of 500 GeV, each assuming a total inte- grated luminosity of 100 fb¹. The studies have been per- formed with realistic GEANT4-based detector simulations including physics and machine-related backgrounds using full particle flow event reconstruction.

Above threshold, the mass of the top quark, here de- fined as the invariant mass of the decay products, can be measured with a statistical precision of 80 MeV combining fully-hadronic and semi-leptonic top pair decays. System- atic uncertainties originating from the jet energy scale can be controlled to a similar level using the direct reconstruction of theWbosons in the top pair decays andZdecays tob¯bfrom other sources. Since the measurement of the invariant mass is interpreted in the context of the top mass definition pro- vided by the event generator PYTHIA, there are additional, potentially sizeable theoretical uncertainties when translat- ing the result into theoretically well-defined mass schemes, which are not included in the quoted uncertainty.

In a threshold scan, the top mass can be determined in a theoretically well defined way, here using the 1S mass, with 10

[GeV]

s

345 350 355

cross section [pb]

0 0.2 0.4 0.6

0.8 tt threshold - 1S mass 174.0 GeV TOPPIK NNLO + CLIC350 LS + ISR

/point simulated data: 10 fb-1

200 MeV

± top mass

CLIC

Fig. 5Background-subtracted simulated cross section measurements for 10 fb¹per data point, together with the cross section for the gen- erator mass of 174 GeV as well as for a shift in mass of±200 MeV.

6.2 Generation of data points

The signal and background efficiencies are determined using fully simulated events as outlined in Section3. The kine- matic fit and the likelihood-based background rejection are used to eliminate the majority of the non-t¯tbackground.

Overall, a signal selection efficiency of 70.2%, including the branching fractions of the considered fully-hadronic and semi-leptonic top pair decays, is achieved. As for the 500 GeV case, the dominant background channels are rejected at the 99.8% level, resulting in an effective cross section for the remaining background of 73 fb.

Simulated data points are generated by taking the ISR and luminosity-spectrum corrected top pair cross section at the desired energy to calculate the nominal number of events expected. The simulated number of signal events is deter- mined on a random basis following a Gaussian distribution with the mean set to the nominal number of events and the standard deviation given by the square root of that number.

With the same method, background events are added, us- ing a constant cross section of 73 fb as discussed above.

It is assumed that the nominal background contribution is well known both from theory and from measurements below threshold, so that the nominal number of background events can be subtracted from the signal, leaving just the statistical variations on top of the signal data with its own statistical uncertainty.

Figure5shows the ten simulated data points for CLIC with an integrated luminosity of 10 fb¹at each point. To illustrate the sensitivity of the data to the top quark mass, the threshold behavior for a shift in mass of±200 MeV is also shown in the figure.

top mass [GeV]

173.95 174.00 174.05

sα

0.116 0.118 0.120

1 σ 2 σ

[174.00 GeV; 0.1179]

CLIC

Fig. 6Expected statistical errors from a simultaneous fit of the top mass and the strong coupling constant, showing the correlation of the two variables and the achieved precision.

6.3 Measurement of the top mass andas

The 1S mass of the top quark and the strong coupling con- stant are extracted simultaneously with a two-dimensional template fit. During the fitting procedure, the simulated data points are compared with calculated cross sections (“tem- plates”) for a grid of different mass and strong coupling val- ues, generated with step sizes of 50 MeV and 0.0007 for mtandas, respectively. The fit results are then given by the minimum of a two-dimensional parabolic fit to thec²dis- tribution of the different templates in themt,asplane. The expected statistical uncertainty of these parameters from a threshold scan is taken from the standard deviation of the measured mass in 5000 trials with different simulated data points. The results are illustrated in Figure6, which shows the clear correlation between the two parameters, and also demonstrates that the fit itself does not introduce a bias on the results.

At this stage of the analysis, the systematic error due to theory uncertainties is included, taken as an overall nor- malization uncertainty of the calculated cross section. Here, two levels are considered: A normalization uncertainty of 3%, assumed as a reasonably conservative estimate of cur- rent theory uncertainties [40], and an uncertainty of 1% op- timistically assumed to be achievable with additional theo- retical work in time for experiments at linear colliders.

The full results, including the theory uncertainty, are giv- en in Table3.

6.3.1 Alternative scenarios

In addition to the two dimensional fit with 10 data points, other running and analysis scenarios are considered. When 10

[GeV]

s

345 350 355

cross section [pb]

0 0.2 0.4 0.6

0.8 tt threshold - 1S mass 174.0 GeV TOPPIK NNLO + CLIC350 LS + ISR

/point simulated data: 10 fb-1

200 MeV

± top mass

CLIC

Fig. 5Background-subtracted simulated cross section measurements for 10 fb¹per data point, together with the cross section for the gen- erator mass of 174 GeV as well as for a shift in mass of±200 MeV.

6.2 Generation of data points

The signal and background efficiencies are determined using fully simulated events as outlined in Section3. The kine- matic fit and the likelihood-based background rejection are used to eliminate the majority of the non-t¯tbackground.

Overall, a signal selection efficiency of 70.2%, including the branching fractions of the considered fully-hadronic and semi-leptonic top pair decays, is achieved. As for the 500 GeV case, the dominant background channels are rejected at the 99.8% level, resulting in an effective cross section for the remaining background of 73 fb.

Simulated data points are generated by taking the ISR and luminosity-spectrum corrected top pair cross section at the desired energy to calculate the nominal number of events expected. The simulated number of signal events is deter- mined on a random basis following a Gaussian distribution with the mean set to the nominal number of events and the standard deviation given by the square root of that number.

With the same method, background events are added, us- ing a constant cross section of 73 fb as discussed above.

It is assumed that the nominal background contribution is well known both from theory and from measurements below threshold, so that the nominal number of background events can be subtracted from the signal, leaving just the statistical variations on top of the signal data with its own statistical uncertainty.

Figure5shows the ten simulated data points for CLIC with an integrated luminosity of 10 fb¹at each point. To illustrate the sensitivity of the data to the top quark mass, the threshold behavior for a shift in mass of±200 MeV is also shown in the figure.

top mass [GeV]

173.95 174.00 174.05

sα

0.116 0.118 0.120

1 σ σ 2

[174.00 GeV; 0.1179]

CLIC

Fig. 6Expected statistical errors from a simultaneous fit of the top mass and the strong coupling constant, showing the correlation of the two variables and the achieved precision.

6.3 Measurement of the top mass andas

The 1S mass of the top quark and the strong coupling con- stant are extracted simultaneously with a two-dimensional template fit. During the fitting procedure, the simulated data points are compared with calculated cross sections (“tem- plates”) for a grid of different mass and strong coupling val- ues, generated with step sizes of 50 MeV and 0.0007 for mtandas, respectively. The fit results are then given by the minimum of a two-dimensional parabolic fit to thec²dis- tribution of the different templates in themt,asplane. The expected statistical uncertainty of these parameters from a threshold scan is taken from the standard deviation of the measured mass in 5000 trials with different simulated data points. The results are illustrated in Figure6, which shows the clear correlation between the two parameters, and also demonstrates that the fit itself does not introduce a bias on the results.

At this stage of the analysis, the systematic error due to theory uncertainties is included, taken as an overall nor- malization uncertainty of the calculated cross section. Here, two levels are considered: A normalization uncertainty of 3%, assumed as a reasonably conservative estimate of cur- rent theory uncertainties [40], and an uncertainty of 1% op- timistically assumed to be achievable with additional theo- retical work in time for experiments at linear colliders.

The full results, including the theory uncertainty, are giv- en in Table3.

6.3.1 Alternative scenarios

In addition to the two dimensional fit with 10 data points, other running and analysis scenarios are considered. When

Figure 3: The production cross section versus center-of-mass energy (leftmost panels) at ILC (top) and CLIC (bottom) and the constraint in the (α

_s

, m

t

) plane. Resulting from a fit to a 10 point scan with 10 fb

⁻¹

per point (rightmost panels). Figures are taken from the full simulation study of Reference [10].

A recent study [10] has reviewed the prospect for this measurement. The authors use detailed studies of the accelerator to estimate the effect of beam energy spread for ILC and CLIC operation at √

s ∼ 350 GeV.

GEANT4 is used for simulating the detector effects in full detail. The dependence of the production cross sec- tion on the center-of-mass energy is shown in the left- most panels of (in the upper panel for ILC and in the bottom panel for CLIC) Figure 3. With 100 fb −1 divided over ten √

s values from 344 GeV to 353 GeV the fit

submits the constraint in the ( α s , m t ) plane shown in the

rightmost panels. A statistical precision of the top quark

mass in the 1S scheme [11] of 30 MeV is obtained at

/ Nuclear Physics B Proceedings Supplement 00 (2014) 1–4 3

CLIC in a combined fit together with the strong cou- pling constant, which is determined with a precision of 0.0009. With the ILC luminosity spectrum the uncer- tainties on m t and α s are reduced by 20% and 10%, re- spectively.

The theory uncertainty, incorporated as an overall normalisation uncertainty of the cross section, is sub- stantially smaller than the statistical error on the mass, and comparable to or larger than the statistical error on the strong coupling. Additional systematic uncertainties from the beam energy, from the luminosity spectrum and from the background subtraction are comparable or smaller than the statistical uncertainty on the mass, re- sulting in a total uncertainty of the top mass below 100 MeV in a theoretically well-defined mass scheme. Un- certainties from the conversion to the MS mass scheme are currently of the order of 100 MeV.

3. The t t Z ¯ and t ¯ tγ couplings

The study of the top quark electroweak couplings has excellent sensitivity to beyond Standard Model physics [12]. The top quark was discovered in 1995 by DØ and CDF so it was not studied by the previous gen- eration of e + e − colliders. The efforts of the Tevatron and LHC experiments determine many aspects of top quark production and its decay, but have limited potential to constrain the t tZ ¯ and t t ¯ γ vertices. A precise character- isation of these vertices at a lepton collider may prove to be a very sensitive probe of physics Beyond the Stan- dard Model.

Following the notation of Reference [13] the top quark couplings to photon and Z boson can be written as follows:

Γ t¯ µ tX (k 2 , q , q) ¯ = ie

γ µ ( ˜ F X 1V (k 2 ) + γ 5 F ˜ 1A X (k 2 )) + (q − q) ¯ µ

2m t ( ˜ F 2V X (k 2 ) + γ 5 F ˜ X 2A (k 2 )) (1) where X = γ, Z and the ˜ F satisfy ˜ F V 1V = − (F V 1V + F V 2V ), F ˜ V 2V = F V 2V , ˜ F V 1A = − F V 1A and ˜ F V 2A = − iF V 2A . Only three form factors are non-zero in the SM at tree level (F γ 1V , F Z 1V and F Z 1A ). Further form factors describe the (weak) electric dipole moment (F γ 2A and F Z 2A ) and mag- netic (F 2V γ and F Z 2V ) dipole moment of the top quark.

Hadron colliders can probe some of these form fac- tors through the study of associated production of top quark pairs with photons or Z bosons, specifically the first direct constraints on the t tZ ¯ couplings at the LHC []Rontsch:2014cca . The process p p ¯ → t t ¯ γ was observed at the Tevatron [15]. The LHC potential is es- timated in the 2005 Snowmass report [13], assuming an

1V

Fγ

~

1V

FZ

~

1A

FZ

~

2V

Fγ

~

2V

FZ

~

Uncertainty

10-3

10-2

10-1

1

ILC (preliminary)

LHC (hep-ph/0601112)

Figure 4: The prospects for measurements of the form factors dis- cussed in the text, from Reference [14]. The LHC potential is based on the report of the 2005 Snowmass top/QCD working group [13].

integrated luminosity of 300 fb −1 at a center-of-mass en- ergy of 14 TeV.

Several studies [13, 14, 16] have established that at a future Linear Collider operated at √

s = 500 GeV the top quark couplings to the photon and, particularly, the Z boson can be characterised much more precisely. The polarisation of the e + e − beams allow to disentangle the photon and Z boson vertices. Recently, the authors of Reference [17] have revisited the LC potential using ef- fective operators. A study of the fully hadronic final state using a detailed simulation show that measurement of the jet charge allows for efficient tagging of top and anti-top quarks [18]. The measurement of the charge asymmetry in t t ¯ production allows to constrain the t tZ ¯ vertex to the 5 − 10% level.

In Reference [14] the lepton+jets final state is evalu- ated in full detector simulation. Multiple form factors are allowed to deviate from their SM values in con- trast to earlier studies of the LC potential . The result- ing prospects for the measurement of the form factors F 1V γ , F 1A γ , F 1V Z and F 1A Z on 500 fb − 1 of 500 GeV data are compared to the LHC potential from Reference [13]

in Figure 4. Despite the increasing realism of these re- cent studies, the precision of the extracted form factors is similar, and in some cases even better than in older work, primarily due to a di ff erent choice of observables.

In LC with polarised beams we can thus measure the top

quark couplings t¯ tγ and t¯ tZ with accuracies one or two

/ Nuclear Physics B Proceedings Supplement 00 (2014) 1–4 4

orders of magnitude better than LHC.

4. Summary & discussion

Future linear e + e − colliders o ff er an excellent oppor- tunity for precision measurements of top quark prop- erties because of a large integrated luminosity (order ab − 1 ) and a center-of-mass energy that goes from the electroweak scale to several TeV.

A 100 fb −1 scan of the center-of-mass energy of the collider around the t¯ t production threshold allows for a precise extraction of the top quark mass in a the- oretically well-defined mass scheme. A recent study based on a realistic simulation of the luminosity spec- trum and a detailed model of the detector response es- timates a total uncertainty on the MS mass of approxi- mately 100 MeV.

Measurement of di ff erential cross section of t t ¯ pair production in the continuum ( √

s = 500 GeV) can be used to constrain anomalous contributions to the t t ¯ γ/ Z vertices. The use of polarised beams allows to disentan- gle the contributions related to the photon and Z boson.

The characterisation of the form factors can thus reach a precision superior to predicted for the LHC by an order of magnitude.

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