Jul 3, 2015 - e+WâZÎ½e at the Compact Linear Collider (CLIC) are examined to probe the anomalous quartic. WWZÎ³ gauge couplings. For âs = 0.5,1.5 ...

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arXiv:1406.2496v3 [hep-ph] 3 Jul 2015

Cumhuriyet University, 58140, Sivas, Turkey A. Senol† Department of Physics, Abant Izzet Baysal University, 14280, Bolu, Turkey

Abstract In this paper, the potentials of two different processes e+ e− → W − W + γ and e+ e− → e+ γ ∗ e− → e+ W − Zνe at the Compact Linear Collider (CLIC) are examined to probe the anomalous quartic √ W W Zγ gauge couplings. For s = 0.5, 1.5 and 3 TeV energies at the CLIC, 95% confidence level limits on the anomalous coupling parameters defining the dimension-six operators are found via the effective Lagrangian approach in a model independent way. The best limits on the anomalous

fb−1

k0W Λ2

kcW Λ2

k2m Λ2

an and Λ 2 which can be achieved with the integrated luminosity of Lint = 590 √ at the CLIC with s = 3 TeV are [−8.80; 8.73] × 10−8 GeV−2 , [−1.53; 1.51] × 10−7 GeV−2 ,

couplings

,

,

[−3.75; 3.74] × 10−7 GeV−2 and [−9.13; 9.09] × 10−7 GeV−2 , respectively.

∗

[email protected]

†

senol˙[email protected]

1

I.

INTRODUCTION

The Standard Model (SM) of particle physics has been demonstrated to be quite successful until now through very important experimental tests, particularly by the recent discovery of a new particle in the mass region around 125 GeV which is consistent with the SM Higgs boson [1, 2]. However, the SM does not fully answer some of the most fundamental questions such as the origin of mass, the large hierarchy between electroweak and Planck scale, the strong CP problem, and matter/antimatter asymmetry. To clarify these questions, new physics beyond the SM is needed. A simple way to discover new physics beyond SM is to probe anomalous gauge boson self-interactions. In the electroweak sector of SM, gauge boson self-interactions are completely determined by SUL (2) × UY (1) gauge invariance. Hence, the high precision measurements of gauge boson self-interactions are extremely important in the understanding of the gauge structure of the SM. Any deviation from the expected values of these couplings would imply the existence of new physics beyond the SM. Investigation of the new physics through effective Lagrangian method is a well known approach. The origin of this method is based on the assumption that at high energies above the SM, there is a grander theory which reduces to the SM at lower energies. Therefore, SM is supposed to be an effective low energy theory in which heavy fields have been integrated out. Since this fundamental method is independent of the details of the model, it is occasionally called model independent analysis. In this paper, we examine the anomalous quartic W W Zγ gauge boson couplings by analyzing two different processes e+ e− → W − W + γ and e+ e− → e+ γ ∗ e− → e+ W − Zνe at the CLIC. Genuine quartic couplings consisting of effective operators, have different origins than anomalous trilinear gauge boson couplings. Hence, we assume that genuine quartic gauge couplings can be independently analyzed from the effects arosen from any trilinear gauge couplings. In the literature, to examine genuine quartic W W Zγ couplings, there are usually two different dimension-six effective quartic Lagrangians that keep custodial SU(2)c symmetry and local U(1)QED symmetry. The first one, CP-violating effective Lagrangian is given as the following [3]

Ln =

iπα (i) an ǫijk Wµα Wν(j) W (k)α F µν 2 4Λ

(1)

where α is the electroweak coupling constant, W (i) is the SU(2)c weak isospin triplet, Fµν , 2

which equals to ∂µ Aν − ∂ν Aµ , is the tensor for electromagnetic field strength, an represents the strength of anomalous coupling and Λ represents the energy scale of possible new physics. The anomalous vertex generated from the above effective Lagrangian is given in the Appendix. Additionally we perform the notation of Ref. [4] in the writing of CP-conserving effective operators. There are fourteen effective photonic operators associated with the anomalous quartic gauge couplings (as shown in Eq. (5) of Ref. [4]). They are determined by fourteen w,b,m w,m b independent couplings k0,c , k1,2,3 and k1,2 that parameterise the strength of the anomalous

quartic gauge couplings. These effective photonic operators can be described in terms of independent Lorentz structures. Among them, the lowest order effective W W γγ and ZZγγ interactions are expressed by four Lorentz invariant structures

−e2 g 2 Fµν F µν W +α Wα− , 2

(2)

−e2 g 2 Fµν F µα (W +ν Wα− + W −ν Wα+ ), 4

(3)

Zγ0 =

−e2 g 2 Fµν F µν Z α Zα , 4cos2 θW

(4)

Zγc =

−e2 g 2 Fµν F µα Z ν Zα . 4cos2 θW

(5)

Wγ0 =

Wγc =

In addition, the lowest order effective ZZZγ operators are parameterized as

ZZ0 =

−e2 g 2 Fµν Z µν Z α Zα , 2cos2 θW

(6)

ZZc =

−e2 g 2 Fµν Z µα Z ν Zα . 2cos2 θW

(7)

There are only five basic Lorentz structures also related to anomalous quartic W W Zγ vertex as follows: 3

WZ0 = −e2 g 2Fµν Z µν W +α Wα− ,

e2 g 2 Fµν Z µα (W +ν Wα− + W −ν Wα+ ) 2

(9)

egz g 2 µν + − F (Wµν Wα− Z α + Wµν Wα+ Z α ) 2

(10)

egz g 2 µν + − F (Wµα W −α Zν + Wµα W +α Zν ) 2

(11)

egz g 2 µν + − F (Wµα Wν− Z α + Wµα Wν+ Z α ) 2

(12)

WZc = −

WZ1 = −

WZ2 = −

(8)

WZ3 = −

with g = e/sin θW , gz = e/sin θW cos θW and Vµν = ∂µ Vν − ∂ν Vµ where V = W ± , Z. The vertex functions for the anomalous quartic W W Zγ couplings generated from Eqs. (8)-(12) are given in Appendix. As a result, these fourteen effective operators can be written more simply as the following: kcγ γ k1γ γ k0γ γ γ γ (Z + W0 ) + 2 (Zc + Wc ) + 2 Z0 L= Λ2 0 Λ Λ γ Z Z X kW k23 k k i + 2 Zγc + 02 ZZ0 + c2 ZZc + WZi , 2 Λ Λ Λ Λ i (13) where kjγ = kjw + kjb + kjm

(j = 0, c, 1)

γ k23 = k2w + k2b + k2m + k3w + k3m

k0Z =

sin θW b cos2 θW − sin2 θW cos θW w (k0 + k1w ) − (k0 + k1b ) + ( )(k0m + k1m ), sin θW cos θW 2cos θW sin θW 4

(14)

(15)

(16)

kcZ =

cos θW w sin θW b cos2 θW − sin2 θW (kc + k2w + k3w ) − (kc + k2b ) + ( )(kcm + k2m + k3m ),(17) sin θW cos θW 2cos θW sin θW

k0W =

cos θW w sin θW b cos2 θW − sin2 θW m k0 − k0 + ( )k0 , sin θW cos θW 2cos θW sin θW

(18)

kcW =

cos θW w sin θW b cos2 θW − sin2 θW m kc − kc + ( )kc , sin θW cos θW 2cos θW sin θW

(19)

1 kjW = kjw + kjm 2

(j = 1, 2, 3).

(20)

In this work, we are only interested in the kiW (i = 0, c, 1, 2, 3) parameters given in Eqs. (18)-(20) related to the anomalous W W Zγ couplings. These kiW parameters are correlated with couplings defining anomalous W W γγ, ZZγγ and ZZZγ interactions [4]. Hence, we need to separate the anomalous W W Zγ couplings from the other anomalous quartic couplings. This can be achieved by imposing additional restrictions on kij parameters [6]. Thus, we set all kij parameters to zero except k2m and k3m in the anomalous W W Zγ couplings. Additionally, we require k2m = −k3m . Therefore, the effective interactions can be obtained below Lef f = In the literature, the

k2m Λ2

k2m (W Z − W3Z ). 2Λ2 2

(21)

couplings describing the anomalous quartic W W Zγ vertex are

examined by Refs. [4–6]. However, the

k0W Λ2

and

kcW Λ2

couplings obtained with the aid of Eqs.

(18)-(19) provide the current experimental limits related to the anomalous quartic W W Zγ couplings. In this paper, we analyze the limits on the CP-conserving parameters the CP-violating parameter

an Λ2

k0W Λ2

,

kcW Λ2

and

which are the current experimental limits on the anomalous

quartic W W Zγ gauge couplings, and compare our limits with the phenomenological studies on

k2m . Λ2

Anomalous quartic W W Zγ couplings at linear colliders and their eγ and γγ modes have been examined through the processes e+ e− → W + W − Z, W + W − γ, W + W − (γ) → 4f γ [7– 11], eγ → W + W − e, νe W − Z [3, 12] and γγ → W + W − Z [13, 14]. These couplings appear as 5

W + W − e and νe W − Z final state productions of eγ collision at linear colliders. νe ZW − production is more sensitive to anomalous quartic W W Zγ couplings with respect to eW − W + production [3]. This production isolates the anomalous W W Zγ couplings from W W γγ couplings. These couplings have also been investigated at the Large Hadron Collider (LHC) via the processes pp → W (→ jj)γZ(→ ℓ+ ℓ− ) [4] and pp → W (→ ℓνℓ )γZ(→ ℓ+ ℓ− ) [6]. Although anomalous quartic W W Zγ couplings have been examined in many studies by analyzing either CP-violating or CP-conserving effective Lagrangians in the literature, these couplings have been investigated using two effective Lagrangians only by Ref. [6]. On the other hand, the limits on

an Λ2

parameter of the anomalous quartic W W Zγ couplings

are constrained at the LEP by analysing the process e+ e− → W + W − γ [15–17]. This reaction is sensitive to both the anomalous W W γγ and W W Zγ couplings. The latest results obtained by L3, OPAL and DELPHI collaborations are given by −0.14 GeV−2 < an Λ2

an Λ2 −2

< 0.14 GeV

< 0.13 GeV−2 , −0.16 GeV−2 <

an Λ2

< 0.15 GeV−2 , and −0.18 GeV−2 <

at 95% confidence level (C. L.), respectively. However, the recent most

restrictive experimental limits on

k0W Λ2

and

kcW Λ2

parameters of the anomalous quartic W W Zγ

couplings are determined through the process qq ′ → W (→ ℓν)Z(→ jj)γ by CMS col-

laboration at the LHC [18]. These are −1.2 × 10−5 GeV−2 < −1.8 × 10−5 GeV−2 <

kcW Λ2

< 1.7 × 10−5 GeV−2 at 95% C. L..

k0W Λ2

< 1 × 10−5 GeV−2 and

The LHC which is the current most powerful particle collider, is able to carry out proton√ proton collisions at s = 14 TeV. It may generate large massive particles and allow us to reveal new physics effects beyond the SM. However, the analysis of the LHC data is quite difficult due to backgrounds from strong interactions. The linear e− e+ colliders generally provide clean environment with reference to hadron colliders and they can be used to determine new physics effects with high precision measurements. The Compact Linear Collider (CLIC) is one of the most popular linear colliders, planned to realize e− -e+ collisions in three energy stages of 0.5, 1.5, and 3 TeV [19]. The CLIC’s first energy stage will provide an opportunity for the achievement of high precision measurements of various observables of the SM gauge bosons, top quark and Higgs boson. The second energy stage will allow the detection of theories that lie beyond the SM. Moreover, Higgs boson properties such as the Higgs self-coupling and rare Higgs decay modes will be investigated in this stage [20]. √ CLIC’s operation at s = 3 TeV reaches a higher effective center-of-mass energy than the LHC for elementary particle collisions [21]. This enables the determination of new parti6

cles and the testing of various models such as supersymmetry, extra dimensions, and so forth beyond the LHC’s capability. Besides, the linear colliders have eγ and γγ modes to probe the new physics beyond the SM. High energy real photons in the eγ and γγ processes can be produced by converting the original e− or e+ beam into a photon beam through the Compton back-scattering technique [22, 23]. In addition, eγ ∗ , γγ ∗ and γ ∗ γ ∗ collisions coming from quasireal photons at the linear colliders also are examined. eγ ∗ collision is the interaction of an incoming lepton beam and a quasireal γ ∗ photon associated with the other beam particle; γγ ∗ collision is the interaction of a real photon and a quasireal photon; and γ ∗ γ ∗ collision is the interaction between quasireal photons. The Weizsacker-Williams approach, known as the Equivalent Photon Approximation (EPA), can be applied to the photons in these processes [24–28]. In the framework of EPA, the virtuality of the quasireal γ ∗ photons is very low and they are assumed to be almost real. In EPA, these photons carry a small transverse momentum. Hence, they deviate at very small angles from the incoming lepton beam path. Moreover, eγ ∗ and γ ∗ γ ∗ processes are more realistic than eγ and γγ processes since they naturally occur spontaneously from the e− e+ process itself. In the literature, photon-induced reactions through the EPA have been extensively studied at the LEP, Tevatron, and LHC [29–57].

II.

CROSS SECTIONS AND NUMERICAL ANALYSIS

In this work, we obtain limits on the CP-conserving parameters violating parameter

an Λ2

k0W Λ2

,

kcW Λ2

and the CP-

which are the current experimental limits on the anomalous quartic

W W Zγ gauge couplings, and also compare our limits with phenomenological studies on

k2m Λ2

derived in Refs. [3, 4, 6]. In order to examine our numerical calculations, we have used the W W Zγ vertex in CompHEP [58]. The general form of the total cross sections for two processes e+ e− → W − W + γ and e+ e− → e+ γ ∗ e− → e+ W − Zνe including CP-conserving

anomalous quartic couplings kiW (i = 0, c) can be written as σtot = σSM +

X kW i

i

Λ

σi + 2 int

X kiW kjW i,j

Λ4

ij σano

(22)

where σSM is the SM cross section, σint is the interference terms between SM and the anomalous contribution, and σano is the pure anomalous contribution. The contributions of the interference terms to total cross section for both processes are negligibly small comparing 7

to pure anomalous terms. But in this study, the small contributions of the interference terms are taken into account in the numerical calculations. Moreover, the general expression of the cross section including CP-violating anomalous quartic coupling is derived by replacing kiW = kjW with an in Eq. (23). But this anomalous coupling (an ) does not interfere with the SM amplitude in all processes [5]. Therefore the total cross section depends only on the quadratic function of anomalous coupling an . The total cross sections of the process kW

km

W

e+ e− → W − W + γ are presented in Figs. 1-4 as functions of anomalous Λ02 , kΛc2 , Λ22 and √ an couplings with s = 0.5, 1.5 and 3 TeV. In Figs. 1-4, we consider that only one of the 2 Λ anomalous quartic gauge coupling parameters is non-zero at any given time, while the other couplings are fixed at zero. We can see from Figs. 1-3 that the value of the anomalous cross section including on

k0W Λ2

k0W Λ2

is larger than the value of

k2m Λ2

and

kcW Λ2

couplings. Hence, the limits

coupling are expected to be more sensitive according to the limits on

k2m Λ2

and

kcW Λ2

couplings. Similarly, the total cross sections of the process e+ e− → e+ γ ∗ e− → e+ W − Zνe are presented in Figs. 5-8 as functions of anomalous √ s = 0.5, 1.5 and 3 TeV.

k0W Λ2

,

kcW Λ2

,

k2m Λ2

and

an Λ2

couplings with

The pT distribution of the final state photon in e+ e− → W − W + γ process with the √ W km kW anomalous W W Zγ couplings Λ02 , kΛc2 , Λ22 and Λan2 , together with SM backgrounds at s=0.5, 1.5 and 3 TeV are given in Figs. 9-11, respectively. From these figures, the final state photon in the e+ e− → W − W + γ process is radiated from massless fermion-photon, W W γ and W W Zγ vertices. The massless fermion-photon vertex causes infrared singularities in the cross section. Therefore, the strong peak arises at the low pT region of the photons. Above pT of 20 GeV we see an obvious splitting and enhancement of the signal from SM background. The effects of infrared singularities which diminish the contribution of anomalous couplings to SM cross section become dominant for the high pT region, as shown in Fig. 9-11. It is km

clear from Fig. 9 that the distributions are more sensitive to Λ22 than to Λan2 . On the other √ hand, at s = 1.5 and 3 TeV, it shows exactly the opposite behavior. In addition, the momentum dependence of

k0W Λ2

for all center of mass energies is bigger than

kcW Λ2

. Especially,

k0W Λ2

between four different anomalous couplings is highest at the momentum dependence of √ s = 3 TeV. Consequently, we impose a pT > 20 GeV cut to reduce the SM background without affecting the signal cross sections due to anomalous quartic couplings. In the course of statistical analysis, the limits of anomalous

k0W Λ2

,

kcW Λ2

,

k2m Λ2

and

an Λ2

couplings

at 95% C.L. are obtained by using χ2 test since the number of SM background events of the 8

examined processes is greater than 10. The χ2 function is defined as follows

2

χ =

σSM − σN P σSM δstat

2

(23)

where σN P is the total cross section in the existence of anomalous gauge couplings, δstat =

√1 N

is the statistical error in which N is the number of events. The number of expected events of the process e+ e− → W − W + γ, N is obtained by N = Lint ×σSM ×BR(W → ℓνℓ )×BR(W →

q q¯′ ) where Lint is the integrated luminosity, σSM is the SM cross section and ℓ = e− or µ− .

Similarly, the number of expected events of the process e+ e− → e+ γ ∗ e− → e+ W − Zνe is calculated as N = Lint × σSM × BR(W → ℓνℓ ) × BR(Z → q q¯). In addition, we impose the acceptance cuts on the pseudorapidity |η γ | < 2.5 and the transverse momentum pTγ > 20

GeV for photons in the process e+ e− → W − W + γ. After applying these cuts, the SM √ background cross sections for the process e+ e− → W − W + γ are 1.65 × 10−1 pb at s = 0.5 √ √ TeV, 6.00 × 10−2 pb at s = 1.5 TeV, and 2.63 × 10−2 pb at s = 3 TeV. They are √ √ 3.58 × 10−3 pb at s = 0.5 TeV, 5.92 × 10−2 pb at s = 1.5 TeV, and 1.61 × 10−1 pb at √ s = 3 TeV for the process e+ e− → e+ γ ∗ e− → e+ W − Ze− . The one-dimensional limits on anomalous couplings

k0W Λ2

,

kcW Λ2

,

k2m Λ2

and

an Λ2

at 95% C.L.

sensitivity at various integrated luminosities and center-of-mass energies are given in Tables I-VI. As can be seen in Tables I and II, the limits on

k0W Λ2

,

kcW Λ2

are approximately several

orders of magnitude more restrictive than those obtained from the LHC [18] while the best limits obtained on

an Λ2

for the process e+ e− → W − W + γ is five orders of magnitude more

restrictive than those obtained from the LEP [15]. In addition, as shown in Table III, we improve sensitivity to

k2m Λ2

coupling with respect to limits derived by Ref. [6], in which

the best limits on this coupling in the literature are obtained. An important advantage of the examined e+ e− → e+ γ ∗ e− → e+ W − Zνe process is that it isolates the anomalous W W Zγ couplings, and therefore it enables us to examine W W Zγ couplings independently from W W γγ couplings. In Table IV, the limits on the anomalous couplings

k0W Λ2

and

kcW Λ2

are obtained as [−3.24; 3.24] × 10−7 and [−4.71; 4.70] × 10−7 which can almost improve the sensitivities up to 37 times for

k0W Λ2

and

kcW Λ2

with respect to LHC’s results. We show in

Table V that the best limits on the anomalous coupling

an Λ2

through the process e+ e− →

e+ γ ∗ e− → e+ W − Zνe are calculated as [−1.17; 1.17] × 10−6 GeV−2 which are more stringent than LEP’s results by almost five orders of magnitude. The best limits on 9

k2m Λ2

via the

process e+ e− → e+ γ ∗ e− → e+ W − Zνe are 10 times than the process e+ e− → W − W + γ which improves the current experimental limits by a factor of 1.1. In addition, we compare our limits with phenomenological studies on the anomalous couplings on

k2m Λ2

k2m Λ2

and

an . Λ2

Our limits

obtained from eγ ∗ collision are 11 times more restrictive than the best limits obtained

with the integrated luminosity of 200 fb−1 corresponding to W ± Zγ production at the 14 TeV LHC [6]. These limits are almost of the same order with our result obtained through the √ process e+ e− → e+ γ ∗ e− → e+ W − Zνe at the CLIC with Lint = 100 fb−1 and s = 1.5 TeV. However, Ref. [14] has considered incoming beam polarizations as well as the final state polarizations of the gauge bosons in the cross-section calculations to improve the bounds on an Λ2

coupling. We can see that the limits expected to be obtained for the future √ γγ colliders with Lint = 500 fb−1 and s = 1.5 TeV are 5 times worse than our best limits √ when comparing to the unpolarized case. At the CLIC with s = 3 TeV for Lint = 590 anomalous

fb−1 , we can set more stringent limit by two orders of magnitude comparing to the limits on

an Λ2

in Ref.[6]. k0W kcW Λ2 Λ2

plane for the e+ e− → W − W + γ process in √ Figs. 12-14 for various integrated luminosity at s = 0.5 , 1 and 3 TeV, respectively. We show 95% C.L. contours in the

Similarly, the same contours for the process e+ e− → e+ γ ∗ e− → e+ W − Zνe are depicted in Figs. 15-17. As we can see from Fig. 14, the best limits on anomalous couplings kcW Λ2

are [−1.90; 1.92] × 10−7 GeV−2 and [−3.34; 3.29] × 10−7 GeV−2 , respectively at

TeV for Lint = 590 fb−1 . According to Fig. 17, the attainable limits on

k0W Λ2

and

k0W Λ2

√

and

s=3

kcW Λ2

are

[−3.86; 3.85] × 10−7 GeV−2 and [−5.62; 5.60] × 10−7 GeV−2 , respectively. III.

CONCLUSIONS

The CLIC is an proposed collider with energies on the TeV scale and extremely high luminosity. Particularly, operating with its high energy and luminosity is extremely important in order to investigate geniue anomalous W W Zγ quartic gauge couplings that are described by dimension-six effective Lagrangians. Since energy dependences of the anomalous couplings are very high, the anomalous cross sections containing these couplings would have a higher momentum dependence than the SM cross section. We can easily understand that the contribution to the cross section of anomalous quartic couplings rapidly increases when the center-of-mass energy increases. Moreover, the geniue anomalous couplings can obtain 10

higher sensitivity via analyzed reactions in the linear colliders due to very clean experimental conditions and being free from strong interactions with respect to LHC. Thus in this paper, we have examined CP-violating and CP-conserving Lagrangians for the anomalous W W Zγ couplings in the processes e+ e− → W − W + γ and e+ e− → e+ γ ∗ e− → e+ W − Zνe at the CLIC. Appendix: The anomalous vertex functions for W W Zγ

The anomalous vertex for W + (pα1 )W − (pβ2 )Z(k2ν )γ(k1µ ) with the help of effective Lagrangian Eq. (1) is generated as follows

πα an [gαν [gβµ k1 .(k2 − p1 ) − k1β .(k2 − p1 )µ ] 4cos θW Λ2 −gβν [gαµ k1 .(k2 − p2 ) − k1α .(k2 − p2 )µ ]

i

+gαβ [gνµ k1 .(p1 − p2 ) − k1ν .(p1 − p2 )µ ] −k2α (gβµ k1ν − gνµ k1β ) + k2β (gαµ k1ν − gνµ k1α ) −p2ν (gαµ k1β − gβµ k1α ) + p1ν (gβµ k1α − gαµ k1β ) +p1β (gνµ k1α − gαµ k1ν ) + p2α (gνµ k1β − gβµ k1ν )]. (A.1) In addition, the vertex functions for W + (pα1 )W − (pβ2 )Z(k2ν )γ(k1µ ) produced from the effective Lagrangians Eqs. (8)-(12) are expressed below

2ie2 g 2gαβ [gµν (k1 .k2 ) − k1ν k2µ ],

e2 g 2 [(gµα gνβ + gνα gµβ )(k1 .k2 ) + gµν (k2β k1α + k1β k2α ) 2 −k2µ k1α gνβ − k2β k1ν gµα − k2α k1ν gµβ − k2µ k1β gνα ].

(A.2)

i

iegz g 2 ((gµα k1 .p1 − p1µ k1α )gνβ + (gµβ k1 .p2 − p2µ k1β )gνα )

11

(A.3)

(A.4)

egz g 2 ((k1 .p1 + k1 .p2 )gµν gαβ − (k1α p1β + k1β p2α )gµν 2 −(p1µ + p2µ )k1ν gαβ + (p1β gµα + p2α gµβ )k1ν )

i

egz g 2 (k1 .p1 gµβ gνα + k1 .p2 gµα gνβ + (p1ν − p2ν )k1β gµα 2 −(p1ν − p2ν )k1α gµβ − p1µ k1β gνα − p2µ k1α gνβ ).

(A.5)

i

(A.6)

Acknowledgments

This work partially supported by the Abant Izzet Baysal University Scientific Research Projects under the Project no: 2015.03.02.867.

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12

[17] G. Abbiendi et al., OPAL Collaboration, Phys. Lett. B580, 17 (2004). [18] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. D 90, 032008 (2014). [19] D. Dannheim et al., CLIC e+ e− Linear Collider Studies, arXiv:1305.5766. [20] D. Dannheim et al., CLIC e+ e− Linear Collider Studies, arXiv:1208.1402. [21] L. Linssen, A. Miyamoto, M. Stanitzki and H. Weerts, CERN-2012-003 ; ANL-HEP-TR-12-01 ; DESY-12-008 ; KEK-Report-2011-7. [22] I. F. Ginzburg, G. L. Kotkin, V. G. Serbo and V. I. Telnov, Nucl. Instr. and Meth. 205, 47 (1983). [23] I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo and V. I. Telnov, Nucl. Instr. and Meth. 219, 5 (1984). [24] S. J. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. D 4, 1532 (1971). [25] H. Terazawa, Rev. Mod. Phys. 45, 615 (1973). [26] V.M. Budnev, I.F. Ginzburg, G.V. Meledin and V.G. Serbo, Phys. Rept. 15, 181 (1974). [27] K. Piotrzkowski, Phys. Rev. D 63, 071502 (2001). [28] G. Baur et al., Phys. Rep. 364, 359 (2002). [29] J. Abdallah et al., DELPHI Collaboration, Eur. Phys. J. C 35, 159 (2004). [30] A. Abulencia et al., CDF Collaboration, Phys. Rev. Lett. 98, 112001 (2007). [31] T. Aaltonen et al., CDF Collaboration, Phys. Rev. Lett. 102, 222002 (2009). [32] T. Aaltonen et al., CDF Collaboration, Phys. Rev. Lett. 102, 242001 (2009). [33] V. M. Abazov et al. [D0 Collaboration], Phys. Rev. D 88 012005 (2013). [34] M. Tasevsky [ATLAS Collaboration], AIP Conf. Proc. 1350, 164 (2011). [35] S. Chatrchyan et al., CMS Collaboration, JHEP 1201, 052 (2012). [36] S. Chatrchyan et al:, CMS Collaboration, JHEP 1211, 080 (2012). [37] S. Atag and A. Billur, JHEP 11, 060 (2010). ˙ ˙ S [38] S. Atag, S. C. Inan and I. ¸ ahin, Phys. Rev. D 80, 075009 (2009). ˙ S¸ahin and S. C. Inan, ˙ [39] I. JHEP 09, 069 (2009). ˙ [40] S. C. Inan, Phys. Rev. D 81, 115002 (2010). ˙ S¸ahin and M. K¨ [41] I. oksal, JHEP 11, 100 (2011). ˙ [42] M. K¨ oksal and S. C. Inan, Advances in High Energy Physics, Volume 2014, Article ID 935840, 11 Pages (2014). ˙ [43] M. K¨ oksal and S. C. Inan, Advances in High Energy Physics Volume 2014, Article ID 315826,

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Pukhov

et

al.,

Report

No.

INP

arXiv:hep-ph/0412191.

14

MSU

98-41/542;

arXiv:hep-ph/9908288;

k0W L2 100.0

kcW L2

ΣHpbL

50.0

k2m L2

10.0 5.0

1.0 0.5

-0.010

0.000

-0.005

0.005

0.010

[email protected] D

FIG. 1: The total cross sections as function of anomalous √ e+ e− → W − W + γ at the CLIC with s = 0.5 TeV.

k0W Λ2

,

kcW Λ2

and

k2m Λ2

couplings for the

k0W L2

1000

kcW L2 k2m L2

ΣHpbL

100

10

1

0.1 -0.0010

-0.0005

0.0000

0.0005

[email protected] D -2

FIG. 2: The same as Fig. 1 but for

15

√

s = 1.5 TeV.

0.0010

ΣHpbL

104

100

k0W L2

1

kcW L2 k2m L2 -0.0010

-0.0005

0.0000

0.0005

0.0010

[email protected] D -2

FIG. 3: The same as Fig. 1 but for

√

s = 3 TeV.

ΣHpbL

104

s = 3 TeV

100

s = 1.5 TeV s = 0.5 TeV

1

-0.010

0.000

-0.005

0.005

0.010

an L2 @GeV-2 D FIG. 4: The total cross sections as function of anomalous √ W − W + γ at the CLIC with s = 0.5, 1.5 and 3 TeV.

16

an Λ2

coupling for the process e+ e− →

5.00

k0W L2 k2m L2 kcW L2

1.00

ΣHpbL

0.50

0.10 0.05

0.01

-0.004

0.000

-0.002

0.002

0.004

[email protected] D -2

kW

W

FIG. 5: The total cross sections as function of anomalous Λ02 , kΛc2 and √ e+ e− → e+ γ ∗ e− → e+ W − Zνe at the CLIC with s = 0.5 TeV.

k2m Λ2

couplings for the process

k0W L2 2.0

k2m L2 kcW L2

ΣHpbL

1.0 0.5

0.2 0.1

-0.0001

-0.00005

0.0000

0.00005

[email protected] D -2

FIG. 6: The same as Fig. 5 but for

17

√

s = 1.5 TeV.

0.0001

k0W L2 100.0

k2m L2

ΣHpbL

50.0

kcW L2

10.0 5.0

1.0 0.5

-0.0001

0.0000

-0.00005

0.00005

0.0001

[email protected] D -2

FIG. 7: The same as Fig. 5 but for

√

s = 3 TeV.

ΣHpbL

104

s = 3 TeV

100

s = 1.5 TeV s = 0.5 TeV

1

0.01 -0.010

0.000

-0.005

0.005

0.010

an L2 @Gev-2 D an + − → FIG. 8: The total cross sections as function of anomalous Λ 2 coupling for the process e e √ e+ γ ∗ e− → e+ W − Zνe at the CLIC with s = 0.5, 1.5 and 3 TeV.

18

10

an/Λ2=10-2 GeV-2

k0W/Λ2=10-3 GeV-2 kcW/Λ2=10-3 GeV-2 k2m/Λ2=10-2 GeV-2 SM

dσ/dpTγ(pb/GeV)

1

0.1

0.01

0.001

0.0001 0

10

20

30

40

50 60 γ p (GeV)

70

80

90

100

T

FIG. 9: The pT distribution of the final state photon in e+ e− → W − W + γ process with the W /Λ2 , k m /Λ2 and a /Λ2 at √s = 0.5 TeV. anomalous W W Zγ couplings k0,c n 2

1

an/Λ2=10-3 GeV-2 k0W/Λ2=10-4 GeV-2 kcW/Λ2=10-4 GeV-2 k2m/Λ2=10-3 GeV-2 SM

dσ/dpTγ(pb/GeV)

0.1

0.01

0.001

0.0001 0

10

20

30

40

50

pTγ(GeV)

FIG. 10: The same as Fig. 9 but for

19

60

√

70

80

s = 1.5 TeV.

90

100

dσ/dpTγ(pb/GeV)

0.1

an/Λ2=10-4 GeV-2

k0W/Λ2=10-5 GeV-2 kcW/Λ2=10-5 GeV-2 k2m/Λ2=10-4 GeV-2 SM

0.01

0.001

0.0001 0

10

20

30

40

50

pTγ(GeV)

FIG. 11: The same as Fig. 9 but for

kW

TABLE I: 95% C.L. sensitivity bounds of the Λ02 and √ W − W + γ at the CLIC with s = 0.5, 1.5 and 3 TeV.

kcW Λ2

60

70

80

90

100

√ s = 3 TeV.

couplings through the process e+ e− →

√ s (TeV)

Lint (fb−1 )

0.5

10

[−1.01; 0.99] × 10−4

[−1.83; 1.82] × 10−4

0.5

50

[−6.79; 6.50] × 10−5

[−1.22; 1.21] × 10−4

0.5

100

[−5.73; 5.50] × 10−5

[−1.03; 1.02] × 10−4

0.5

230

[−4.67; 4.44] × 10−5

[−8.39; 8.32] × 10−5

1.5

10

[−2.44; 2.43] × 10−6

[−4.24; 4.23] × 10−6

1.5

50

[−1.63; 1.61] × 10−6

[−2.83; 2.82] × 10−6

1.5

100

[−1.38; 1.36] × 10−6

[−2.38; 2.37] × 10−6

1.5

320

[−1.03; 1.01] × 10−6

[−1.78; 1.77] × 10−6

3

10

[−2.43; 2.42] × 10−7

[−4.23; 4.21] × 10−7

3

100

[−1.37; 1.35] × 10−7

[−2.81; 2.79] × 10−7

3

300

[−1.04; 1.03] × 10−7

[−1.81; 1.79] × 10−7

3

590

[−8.80; 8.73] × 10−8

[−1.53; 1.51] × 10−7

k0W Λ2

20

(GeV−2 )

kcW Λ2

(GeV−2 )

3

Lint = 10 fb-1 Lint = 50 fb-1 Lint = 100 fb-1

2

kcW L2 Hx10-4 GeV-2 L

Lint = 230 fb-1 1

0

-1

-2

-3 -3

-2

0

-1

1

2

3

k0W L2 Hx10-4 GeV-2 L FIG. 12: 95% C.L. contours for anomalous √ at the CLIC with s = 0.5 TeV.

k0W Λ2

and

21

kcW Λ2

couplings for the process e+ e− → W − W + γ

1.0

Lint = 10 fb-1 Lint = 50 fb-1 Lint = 100 fb-1 Lint = 320 fb-1

kcW L2 Hx10-5 GeV-2 L

0.5

0.0

-0.5

-1.0 -1.0

0.0

-0.5

0.5

k0W L2 Hx10-5 GeV-2 L FIG. 13: The same as Fig. 12 but for

22

√

s = 1.5 TeV.

1.0

1.0

Lint = 10 fb-1 Lint = 100 fb-1 Lint = 300 fb-1 Lint = 590 fb-1

kcW L2 Hx10-6 GeV-2 L

0.5

0.0

-0.5

-1.0 -1.0

0.0

-0.5

0.5

k0W L2 Hx10-6 GeV-2 L FIG. 14: The same as Fig. 12 but for

23

√

s = 3 TeV.

1.0

2

Lint = 10 fb-1 Lint = 50 fb-1 Lint = 100 fb-1 Lint = 230 fb-1

kcW L2 Hx10-4 GeV-2 L

1

0

-1

-2 -2

0

-1

1

2

k0W L2 Hx10-4 GeV-2 L kW

FIG. 15: 95% C.L. contours for anomalous Λ02 and √ e+ W − Zνe at the CLIC with s = 0.5 TeV.

24

kcW Λ2

couplings for the process e+ e− → e+ γ ∗ e− →

1.5

Lint = 10 fb-1 Lint = 50 fb-1 Lint = 100 fb-1

1.0

kcW L2 Hx10-5 GeV-2 L

Lint = 320 fb-1 0.5

0.0

-0.5

-1.0

-1.5 -1.5

-1.0

0.0

-0.5

0.5

1.0

k0W L2 Hx10-5 GeV-2 L FIG. 16: The same as Fig. 15 but for

25

√

s = 1.5 TeV.

1.5

2

Lint = 10 fb-1 Lint = 100 fb-1 Lint = 300 fb-1 Lint = 590 fb-1

kcW L2 Hx10-6 GeV-2 L

1

0

-1

-2 -2

0

-1

1

k0W L2 Hx10-6 GeV-2 L FIG. 17: The same as Fig. 15 but for

26

√

s = 3 TeV.

2

TABLE II: 95% C.L. sensitivity bounds of the √ at the CLIC with s = 0.5, 1.5 and 3 TeV.

an Λ2

couplings through the process e+ e− → W − W + γ

√ s (TeV)

Lint (fb−1 )

0.5

10

[−8.47; 8.45] × 10−4

0.5

50

[−5.67; 5.65] × 10−4

0.5

100

[−4.77; 4.75] × 10−4

0.5

230

[−3.88; 3.85] × 10−4

1.5

10

[−2.59; 2.57] × 10−5

1.5

50

[−1.85; 1.83] × 10−5

1.5

100

[−1.63; 1.61] × 10−5

1.5

320

[−1.35; 1.33] × 10−5

3

10

[−2.46; 2.46] × 10−6

3

100

[−1.38; 1.38] × 10−6

3

300

[−1.05; 1.05] × 10−6

3

590

[−9.13; 9.09] × 10−7

27

an Λ2

(GeV−2 )

TABLE III: 95% C.L. sensitivity bounds of the √ at the CLIC with s = 0.5, 1.5 and 3 TeV.

k2m Λ2

couplings through the process e+ e− → W − W + γ

√ s (TeV)

Lint (fb−1 )

k2m (GeV−2 ) Λ2

0.5

10

[−6.87; 6.68] × 10−4

0.5

50

[−4.62; 4.43] × 10−4

0.5

100

[−3.90; 3.72] × 10−4

0.5

230

[−3.19; 3.00] × 10−4

1.5

10

[−5.17; 5.15] × 10−5

1.5

50

[−3.46; 3.44] × 10−5

1.5

100

[−2.91; 2.89] × 10−5

1.5

320

[−2.18; 2.16] × 10−5

3

10

[−1.05; 1.03] × 10−5

3

100

[−5.92; 5.79] × 10−6

3

300

[−4.51; 4.38] × 10−6

3

590

[−3.82; 3.69] × 10−6

28

kW

W

TABLE IV: 95% C.L. sensitivity bounds of the Λ02 and kΛc2 couplings through the processes e+ e− → √ e+ γ ∗ e− → e+ W − Zνe at the CLIC with s = 0.5, 1.5 and 3 TeV. √ s (TeV)

Lint (fb−1 )

0.5

10

[−1.03; 1.01] × 10−4

[−1.53; 1.48] × 10−4

0.5

50

[−6.97; 6.69] × 10−5

[−1.04; 0.98] × 10−4

0.5

100

[−5.88; 5.60] × 10−5

[−8.75; 8.22] × 10−5

0.5

230

[−4.80; 4.52] × 10−5

[−7.16; 6.62] × 10−5

1.5

10

[−5.76; 5.75] × 10−6

[−8.37; 8.35] × 10−6

1.5

50

[−3.86; 3.85] × 10−6

[−5.60; 5.58] × 10−6

1.5

100

[−3.24; 3.23] × 10−6

[−4.71; 4.69] × 10−6

1.5

320

[−2.43; 2.42] × 10−6

[−3.53; 3.50] × 10−6

3

10

[−8.98; 8.97] × 10−7

[−1.31; 1.30] × 10−6

3

100

[−5.05; 5.04] × 10−7

[−7.34; 7.33] × 10−7

3

300

[−3.84; 3.83] × 10−7

[−5.58; 5.57] × 10−7

3

590

[−3.24; 3.24] × 10−7

[−4.71; 4.70] × 10−7

k0W Λ2

29

(GeV−2 )

kcW Λ2

(GeV−2 )

an + − → TABLE V: 95% C.L. sensitivity bounds of the Λ 2 couplings through the processes e e √ e+ γ ∗ e− → e+ W − Zνe at the CLIC with s = 0.5, 1.5 and 3 TeV.

√ s (TeV)

Lint (fb−1 )

0.5

10

[−4.08; 3.96] × 10−4

0.5

50

[−2.75; 2.63] × 10−4

0.5

100

[−2.33; 2.20] × 10−4

0.5

230

[−1.90; 1.78] × 10−4

1.5

10

[−2.19; 2.17] × 10−5

1.5

50

[−1.47; 1.45] × 10−5

1.5

100

[−1.23; 1.22] × 10−5

1.5

320

[−9.26; 9.07] × 10−6

3

10

[−3.16; 3.16] × 10−6

3

100

[−1.78; 1.77] × 10−6

3

300

[−1.35; 1.35] × 10−6

3

590

[−1.17; 1.17] × 10−6

30

an Λ2

(GeV−2 )

km

TABLE VI: 95% C.L. sensitivity bounds of the Λ22 couplings through the processes e+ e− → √ e+ γ ∗ e− → e+ W − Zνe at the CLIC with s = 0.5, 1.5 and 3 TeV. √ s (TeV)

Lint (fb−1 )

k2m (GeV−2 ) Λ2

0.5

10

[−1.48; 1.41] × 10−4

0.5

50

[−9.98; 9.36] × 10−5

0.5

100

[−8.45; 7.42] × 10−5

0.5

230

[−6.92; 6.29] × 10−5

1.5

10

[−7.38; 7.37] × 10−6

1.5

50

[−4.94; 4.92] × 10−6

1.5

100

[−4.15; 4.14] × 10−6

1.5

320

[−3.11; 3.09] × 10−6

3

10

[−1.04; 1.04] × 10−6

3

100

[−5.85; 5.84] × 10−7

3

300

[−4.44; 4.43] × 10−7

3

590

[−3.75; 3.74] × 10−7

31