Analysis of the anomalous electromagnetic moments of the tau lepton in γ p collisions at the LHC

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Analysis

of

the

anomalous

electromagnetic

moments

of

the

tau

lepton

in

γ

p collisions

at

the

LHC

M. Köksal

a

,

S.C. ˙Inan

b

,

A.A. Billur

b

,

∗

,

Y. Özgüven

b

,

M.K. Bahar

c a_{DepartmentofOpticalEngineering,CumhuriyetUniversity,58140,Sivas,Turkey}

b_{DepartmentofPhysics,CumhuriyetUniversity,58140,Sivas,Turkey}

c_{DepartmentofEnergySystemsEngineering,KaramanogluMehmetbeyUniversity,70100,Karaman,Turkey}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received8November2017 Receivedinrevisedform9July2018 Accepted10July2018

Availableonline11July2018 Editor:A.Ringwald

Inthisstudy,weinvestigatethepotentialoftheprocesspp→p

γ

∗p→p

τ

ν

¯τqX attheLHCtoexamine

theanomalouselectromagneticmomentsofthetaulepton.Weobtain95% confidencelevelboundson theanomalouscouplingparameterswithvariousvaluesoftheintegratedluminosityandcenter-of-mass energy. The improvedbounds have been obtainedon the anomalous coupling parameters ofelectric andmagneticmomentsofthetauleptonaτ and|dτ|comparedtothecurrentexperimentalsensitivity

bounds. The

γ

p modeofphotonreactions atthe LHChaveshownthat ithas greatpotential forthe electromagneticdipolemomentsstudiesofthetaulepton.

©2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Theresultsobtainedintheexperimentalstudiesofthe anoma-lousmagneticmomentsofleptonscontainboththeestimated val-uesandthenewphysicscontributions,whichcannotbepredicted bytheStandardModel(SM).Thetauleptonismoreadvantageous than other leptons in determination ofnew physics effects since thetau lepton has a larger mass.In many newphysics theories, newcontributionsarising fromthe anomalous magneticmoment fora leptonwithmassm areproportional to m2.Forthisreason, sincethemass ofthetauleptonis muchheavierthanother lep-tons,providinganomalous magneticmomentofthe tauleptonto bemoresensitive toelectroweakandnewphysics loop contribu-tions.Additionally,thetauleptonhasamuchshorterlifetimethan otherleptons,soitisextremelydifficulttomeasurethemagnetic momentof thetau lepton by usingspin precession experiments. Insteadofspinprecessionexperiments,highenergyaccelerator ex-periments have been done which include pair production oftau leptons. However, in these experimental studies, aτ can not be measureddirectly,since

τ

τ γ

¯

containsoff-shellphotonortau lep-tons(photon virtuality Q2

₌

₁₀5_–107 _GeV2_{). The most sensitive}

*

Correspondingauthor.

E-mailaddresses:[email protected](M. Köksal),

[email protected](S.C. ˙Inan),[email protected](A.A. Billur), [email protected](Y. Özgüven),[email protected](M.K. Bahar).

experimental boundshavebeenobtainedforaτ throughthe pro-cesse+e−

→

e+e−

τ

+

τ

−atthe95% ConfidenceLevel(C.L.)inLEP isonlyofO

(10

−2

)

[1–3];

L3:

−

0

.

052

<

aτ

<

0

.

058

,

OPAL:

−

0

.

068

<

aτ

<

0

.

065

,

DELPHI:

−

0

.

052

<

aτ

<

0

.

013

.

Giventheseconditions,itcanbesaidthattheuseofaccelerator ismoresuitabletoexaminetheanomalous magneticmomentsof thetaulepton.

TheSM theoretical predictionoftheanomalous magnetic mo-mentofthetaulepton canbefoundby summingofall following additives[4–7]:

aQED_τ

=

117324

×

10−8

,

(1)

aEW_τ

=

47

×

10−8

,

(2)

aHAD_τ

=

350

.

1

×

10−8

.

(3)

Hence, theSM value is obtainedasaSM_τ

=

0.00117721. Since this valueisfarfromtheexperimental sensitivitybounds,whichisan orderofmagnitudebelowleading QEDcalculations,moreprecise experimentalmeasurementsshouldbemade.

AnotherinteractionbetweenthetauleptonandphotonisCP vi-olatinginteractionwhichisinducedbytheelectricdipolemoment

|

dτ

|

.The SM doesnothave sufficientinformationaboutoriginof https://doi.org/10.1016/j.physletb.2018.07.018

0370-2693/©2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Fig. 1. Feynman diagrams of the subprocessγ∗q→τν¯τqX . thisinteraction [8].SinceCPviolating dipolemomenthighly

sup-pressedintheSM(induceswiththreelooplevel[9]),any measure-mentatcollidersoftheelectricdipole momentofthetaulepton giveshintsaboutthenewphysicsbeyondtheSM.TheCPviolation maycomefromnewphysicstheoriesinleptonsectorsuchas lep-toquark[10,11],SUSY[12],left-rightsymmetric[13,14] andHiggs models[15–18].

The value of the electric dipole moment of the taulepton in theSMisobtainedas

|

dτ

|

≤

10−34ecm [19].Inaddition,themost restrictive experimentalsensitivityboundsfor

|

dτ

|

havebeen ob-tainedasfollows[20],

−

2

.

2

<

Re

(

dτ

) <

4

.

5

× (

10−17e cm

),

−

2

.

5

<

Im

(

d_τ

) <

0

.

8

× (

10−17e cm

).

These results have been measured through the process e+e−

→

γ

→

τ

+

τ

− by BELLE collaboration [20]. Since the value of Q2 inthisprocessisvery large(100 GeV2_{),the obtainedboundsare}

givenintwoparts,asrealandvirtual.

Feynman diagramsof theprocess pp

→

p

γ

∗p

→

p

τ

ν

¯

τ qX are shown in Fig. 1 and it is clear that the anomalous electromag-netic moments contribution of the tau lepton comes from only the diagram (b). The photon in

τ τ γ

¯

∗ vertex in this diagram is Weizsacker-Williamsphoton.Thesephotonshaveaverysmall vir-tuality( Qmax2

=

2 GeV2),asdetailsareexplainedbelow.

Themostgeneralanomalousvertexfunctiondescribing

τ

τ γ

¯

in-teractionfortwoon-shelltauandaphotonwithphotonmomenta q andmass of the tau lepton mτ can be givenin the following form[21,22],



ν

=

F1

(

q2

)

γ

ν

+

i 2mτ F2

(

q2

)

σ

νμqμ

+

1 2mτ F3

(

q2

)

σ

νμqμ

γ

5

,

(4) where

σ

νμ

₌

i 2

(

γ

ν

γ

μ

−

γ

μ

γ

ν

)

and F1,2,3



q2



are the electric charge,themagneticdipoleandelectricdipoleformfactorsofthe

tau lepton, respectively. As known, electromagnetic form factors are givenas F1

=

1, F2

=

F3

=

0 in theSM.Usually, formfactors

are not physicalquantities dueto the fact that they can contain infrared divergences [23,24]. However, when taking into account thelimitingcaseof Q2

→

0,theformfactorsbecomemeasurable andcalleddipolemoments.Thesearedescribedthroughthestatic propertiesofthefermions[25],

F1

(

0

)

=

1

,

F2

(

0

)

=

aτ

,

F3

(

0

)

=

2mτdτ

e

.

(5)

The kinematical situation (all particles on-shell) relevant to the static dipole moments (5) can not be realized for thetau lepton atacolliderexperimentasthementionedabove.Tostudythe sig-nature ofthedipolecouplings andto computesensitivitybounds oneadoptsinamodelindependentwaybymeansoftheeffective Lagrangianmethod.Inthisstudy,wewillusedimension-six oper-atorsspecifiedinRef. [26] forthe electromagneticmomentsofthe taulepton. Onlytwo oftheseoperators usedinRef. [26] directly contributetotheelectromagneticdipolmomentsofthetaulepton attreelevel:

Q_LW33

= ( ¯



τ

σ

μν

τ

R

)

σ

I

ϕ

WμνI

,

(6)

Q_LB33

= ( ¯



τ

σ

μν

τ

R

)

ϕ

Bμν

,

(7)

where

ϕ

and



τ aretheHiggsandtheleft-handedSU

(2)

doublets,

σ

I _{are thePauli matricesand W}I

μν and Bμν are the gauge field strength tensors. Thus, the effective Lagrangian is parameterized asfollows, Leff

=

1

2

[

C 33 LWQLW33

+

C33LBQLB33

+

h

.

c

.

].

(8)

After the electroweak symmetry breaking, contributions to the anomalousmagneticandelectricdipolemomentsofthetaulepton aregivenby

κ

=

2mτ e

√

2

υ

2 Re

[

cos

θ

WC 33 LB

−

sin

θ

WC33LW

],

(9)

˜

κ

=

2mτ e

√

2

υ

2 Im

[

cos

θ

WC 33 LB

−

sin

θ

WCLW33

],

(10)

where

υ

=

246 GeV and sin

θ

W is the weak mixing angle. The

CPevenparameter

κ

andCPodd parameter

κ

˜

are relatedtothe anomalousdipole momentsofthetauleptonviathefollowing re-lations:

κ

=

a_τ

,

κ

˜

=

2mτ

e dτ

.

(11)

Proton–proton collisions at the LHC reach very high luminos-ityandcenter-of-massenergy.Ontheother hand,thesecollisions have not very clean environment due to the remnants of both protonbeamsafterthecollision.Theresultingjetsfromthese rem-nantsgeneratecertainuncertaintiesandmakeitdifficulttorealize thesignalswhichmayoriginatefromthenewphysicsbeyondthe SM.Ontheotherhand,photonemittingprotonsinphoton-induced processes, that is to say

γ

∗

γ

∗ and

γ

∗p, survive intact without decomposeintopartons.Forthisreason,thecleanestchannel be-tween

γ

∗

γ

∗,

γ

∗p and pp processesis

γ

∗

γ

∗.In

γ

∗p process,only one of the incomingprotons decomposes into partons butother protonsurvivesintact.Asaresult,sincephoton-inducedprocesses havebetterknowninitialconditionsandmuchsimplerfinalstates, theycancompensatetheadvantagesofpp process.

γ

∗

γ

∗ process is generally electromagneticin nature andthis process haslessbackgrounds withrespectto

γ

∗p process. How-ever,

γ

∗p process can reach much higher energy and effective luminositycomparedto

γ

∗

γ

∗ process.Thissituationmaybe im-portantfornewphysicsbecauseofthehighenergydependenceof thecross section including anomalous couplings. Thus,

γ

∗p pro-cessis expectedto haveahighsensitivityto theanomalous cou-plingssinceithasahigherenergyreachthan

γ

∗

γ

∗process.

Photons emitted from one of the proton beams in

γ

∗

γ

∗ and

γ

∗p processes can be identified in the framework of the Weizsacker-WilliamsApproximation(WWA) [27–29].Virtuality of thealmost-realphotonsintheWWAisverylow( Q_max2

=

2 GeV2). Since protons emit almost-real photons, they do not decompose intopartons.IntheWWA,almost-realphotonshaveasmall trans-verse momentum. For this reason, almost-real photons emitting intactprotonsdeviateslightlyfromtheprotonbeampath.Photons emittedwithverysmallanglesescapewithoutbeingidentifiedby thecentraldetectors.Hence,inadditiontoATLASandCMScentral detectors,forward detectorequipment is needed to detect intact protons.Theseequipmentscandetectintactscatteredprotonswith averylargepseudorapidity. Theyareplannedtobeplaced220 to 440 metersaway fromthecentraldetectorsinordertodetect in-tactprotonsintheinterval

ξ

min

< ξ < ξ

max.Thisintervalisknown

asthe acceptanceof the forward detectors[30,31]. The new de-tectorscan detectintactscatteredprotonswith9.5

<

η

<

13 ina continuousrangeof

ξ

where

ξ

istheprotonmomentumfraction lossdescribedby

ξ

= (|

p

|

− |

p

|)/|

p

|

;



p and



parethemomentum ofincomingproton andthe momentum ofintactproton, respec-tively.Thus,theenergyofthephotonsthatareinteractingcanbe determined.The relationbetweenthetransverse momentum and pseudorapidityofintactprotonisasfollows,

pT

=



E2p

(

1

− ξ)

2

−

m2p

cosh

η

(12)

where mp is the mass of proton and Ep is the energy of

proton. Photon-induced processes were investigated experimen-tally through the processes pp

¯

→

p

γ

∗

γ

∗

¯

p

→

pe+e−p,

¯

pp

¯

→

Table 1

Numerical computations of the total cross sections versus κ and κ˜ at √s=

14,33 TeV. Mode σ2 σ1 σ0 σ2 √ s=14 TeV 7.00277 −0.03345 0.312531 7.00277 √ s=33 TeV 28.5649 −0.123529 0.574318 28.5649 p

γ

∗

γ

∗p

¯

→

p

μ

+

μ

−p,

¯

pp

¯

→

p

γ

∗p

¯

→

pW W

¯

p and pp

¯

→

p

γ

p

¯

→

p J

/ψ(ψ(2S))

p by

¯

the CDF and D0 collaborations at the Fermi-labTevatron[32–36].Afterthesestudies,theLHCasa

γ

∗

γ

∗ and

γ

∗p collidershasbegunto examinethenewphysicsbeyondand within the SM. Hence, the processes pp

→

p

γ

∗

γ

∗p

→

pe+e−p, pp

→

p

γ

∗

γ

∗p

→

p

μ

+

μ

−p, and pp

→

p

γ

∗

γ

∗p

→

pW+W−p have been observed at the LHC by the CMS and ATLAS collabo-ration [37–41]. However, newphysics researches beyondthe SM through

γ

∗

γ

∗ and

γ

∗p processes attheLHChavebeenanalyzed intheliterature[42–72].Therearealsoalotofphenomenological studiesabouttheanomalousmagneticmomentsofthetaulepton [73–80].

Our main motivation in thisstudy is to determine the sensi-tivityboundsontheelectromagneticmomentsofthetauleptonat theLHCthroughtheprocesspp

→

p

γ

∗p

→

p

τ

ν

¯

τ qX .Weconsider that thisprocess ismuchmoreimportantinthemeasurement of electromagnetic moment of the tau lepton since photon-induced processeshave betterknown initialconditions andhaveclean fi-nalstates.

2. Crosssectionsandsensitivityanalysis

Inthiswork, we haveinvestigatedanomalous electromagnetic dipole momentsofthetaulepton viatheprocess pp

→

p

γ

∗p

→

p

τ

ν

¯

τ qX . In calculations, we have takeninto account subprocess

γ

∗q

→

τ

ν

¯

τ qX (q

,

q

=

u

,

u

¯

,

d

,

d

¯

,

s

,

s

¯

,

c

,

¯

c). The b quark’s distribu-tionisnotincludedinthecalculationsbecauseit’scontributionis too small.The anomalous electromagnetic moments contribution ofthe taulepton comesfrom onediagram (diagram b),which is showninFig.1.Here, wehaveusedthefollowingkinematiccuts onfinalstateparticles,

pντ_T¯

>

10 GeV

,

pτ_T

,

pq_T

>

20 GeV

,

|

η

τ

,

η

q

| <

2

.

5

.

(13)

Allcalculationshaveperformedusingthetreelevelevent genera-torCalcHEP [81] byaddingthe newvertexfunctions. Inaddition, we haveused CTEQ6L1[82] forthepartondistribution functions and the WWA embedded in CalcHEP for the photon spectra. In thenumericalcalculations,wehavetakentheinputparametersas Mp

=

0.938 GeV, MW

=

80.38 GeV, Mτ

=

1.777 GeV.The cross

sectionsasapolynomialinpowersof

κ

and

κ

˜

forthetwomodes

√

s

=

14,33 TeVcanbegivenby

σ

T ot

(

κ

,

κ

˜

)

=

σ

2

κ

2

+

σ

2

κ

˜

2

+

σ

1

κ

+

σ

0 (14)

where

σ

i

₍

_σ

i

₎

_i

₌

_{1,2 istheanomalous contribution,while}

_σ

0 is

thecontributionoftheSM.Thisprovidesmorepreciseand conve-nientinformationforeachprocess.TheBSMcrosssectionmustbe proportionalto

κ

2

_{+ ˜}

_κ

2_{.Forthisreason,the}

_κ

2_and

_κ

˜

2_dependence

oftheBSMcrosssection cannot be distinguished.Hence the co-efficients

σ

2and

σ

2 shouldbethesame[83].Numerical

computa-tionsofthetotalcrosssectionsversus

κ

and

κ

˜

at

√

s

=

14,33 TeV aregiveninTable1.

Insensitivityanalysis,wetakeintoaccount

χ

2 _method,

χ

2

=



σ

SM

−

σ

(

κ

,

κ

˜

)

σ

SM

δ



2

,

(15)

where

σ

(

κ

,

κ

˜

)

is the total cross section which includes the SM andnewphysics,

δ

=



(δ

st

)

2

+ (δ

sys

)

2;

δ

st

=

√_N1

SM isthestatistical

errorand

δ

sys isthesystematicerror.Inthiswork,wehaveused

cumulativedistributionfunctionfor

χ

2_{whichhasbeendefinedfor}

usewith a methodof least-squares.We have takeninto account Table39.2in[84] valuesforcoverageprobabilityinthelargedata samplelimitforoneandtwofreeparameters.

Systematicerrorsarealsotakenintoaccountinthiswork.One of the reasons for these errors comes from the identification of thetauleptonintheexperiments.Asknown,therearemany de-cay channelsofthe taulepton.The taulepton decayshavemore than oneparticle inthe final state. Forthisreason, thisis called taujets.Thesedecaychannels, calledone prongandthreeprong, are divided into two accordingto the number of charged parti-clesinthe final state.These finalstates includeQCDor hadronic backgrounds.Thedeterminationofthesesituationsismuchmore difficult than in the leptonic final states. In other words, it is difficult to identify the tau lepton. Due to these difficulties and complicatedbackground,the tauidentificationefficiencies are al-ways determined for specific process, luminosity, and kinematic parameters. However, the hadronic decay of the tau jetscan be distinguishedfromotherhadronicdecaysduetotheir different fi-nalstatetopology.TauidentificationshavebeenstudiedattheLHC [85–87] andInternationalLinearDetector(ILD)[88].Asmentioned above, these calculationsare madefor specific processes. Hence, the general values of the kinematic parameters of the detectors havebeentakensothatthetauleptoncanbeidentified.

Other reasons for these errors are the experimental errors. However, a systematicerror forthe processes studied in this ar-ticle has not yet been studied in the LHC. But, the processes pp

→

pp

μ

+

μ

− forthe

√

s

=

13 TeVhave beenexamined atthe LHC [41]. Inthisarticle, systematicerrorhas beenfound around 3%. In addition, a systematic error in a phenomenological study was takenas2% via theprocess pp

→

p

γ

∗

γ

∗p

→

pp

τ

+

τ

− [89]. Thesystematicuncertaintythatarisesonthesignalis4.8% inthis

article by summing quadratically all uncorrelated contributions. Experiments in which DELPHI collaboration have performed on anomalous magneticandelectricdipole moments ofthe tau lep-tonhavealsobeenbasedonsystematicerrorsthroughtheprocess e+e−

→

e+e−

τ

+

τ

− [3]. The systematicerrors obtainedin these experimentsforcenter-of-massenergiesbetween183 and208 GeV energies aregivenintheTable2.IntheLEP experimentwiththe L3detector,thetotalsystematicerrorwasobtained7% and 9% at center-of-massenergies161 GeV



√

s



209 GeV throughthe pro-cesse+e−

→

e+e−

τ

+

τ

−.

Finally, such error can result from theoretical uncertainties. TheseerrorscomefromQED,electroweakandhadronicloop con-tributions are extremelysmall(δtheoretical

=

5.10−8) [90–93,22]. In

the light of these discussions, three different systematic error values have been taken into account in our calculations (δsys

=

3%,5%,7%). The limits obtained by this work are given in Ta-bles3–4withthesesystematicerrors.

3. Conclusions

The photon induced reactions atthe LHC provideus new op-portunities to investigate highenergyand highluminosity

γ

∗

γ

∗ and

γ

∗p interactions at higherenergy than that at any existing collider.Theseinteractionsyieldfewer backgroundsthan pp deep inelastic scattering. With this clean environment, any discrepant signalwiththeprospectoftheSMwouldbeaconclusive cluefor newphysicsbeyondtheSM.

In this paper, we have searched the tau lepton anomalous dipole moments in a model independent way through the pro-cess pp

→

p

γ

∗p

→

p

τ

ν

¯

τ qX (where q

,

q

=

u

,

d

,

s

,

c

,

u

¯

,

d

¯

,

s

¯

,

¯

c) at Table 2

SystematicerrorsgivenbytheDELPHIcollaboration[3].

1997 1998 1999 2000 Trigger efficiency 7.0 2.7 3.6 4.5 Selection efficiency 5.1 3.2 3.0 3.0 Background 1.7 0.9 0.9 0.9 Luminosity 0.6 0.6 0.6 0.6 Total 8.9 4.3 4.7 5.4 Table 3

95%C.L.sensitivityboundsoftheaτ couplingsforvariouscenter-of-massenergiesandintegratedLHCluminosities.Theboundsareshowedwithnosystematicerror(0%)

andwithsystematicerrorsof3%,5%,7%.

√ s (TeV) Luminosity (fb−1_{) 0% 3% 5% 7%} 10 (−0.0372, 0.0420) (−0.0529, 0.0577) (−0.0658, 0.0706) (−0.0771, 0.0819) 50 (−0.0242, 0.0290) (−0.0498, 0.0546) (−0.0642, 0.0690) (−0.0762, 0.0809) 14 100 (−0.0200, 0.0248) (−0.0493, 0.0541) (−0.0640, 0.0688) (−0.0760, 0.0808) 200 (−0.0165, 0.0212) (−0.0491, 0.0539) (−0.0639, 0.0687) (−0.0760, 0.0807) 100 (−0.0108, 0.0152) (−0.0325, 0.0368) (−0.0424, 0.0467) (−0.0505, 0.0548) 500 (−0.0067, 0.0110) (−0.0323, 0.0366) (−0.0423, 0.0466) (−0.0504, 0.0547) 33 1000 (−0.0054, 0.0097) (−0.0323, 0.0366) (−0.0423, 0.0466) (−0.0504, 0.0547) 3000 (−0.0037, 0.0081) (−0.0323, 0.0366) (−0.0423, 0.0466) (−0.0504, 0.0547) Table 4

SameastheTable3butforthe|dτ|.

√ s TeV Luminosity (fb−1_{) 0% 3% 5% 7%} 10 2.16×10−16 _3.01×10−16 _3.70×10−16 _4.32×10−16 50 1.44×10−16 _2.83×10−16 _3.61×10−16 _4.26×10−16 14 100 1.22×10−16 _2.81×10−16 _3.60×10−16 _4.25×10−16 200 1.02×10−16 _2.79×10−16 _3.59×10−16 _4.25×10−16 100 7.12×10−17 _1.96×10−16 _2.45×10−16 _2.90×10−16 500 4.76×10−17 _1.90×10−16 _2.45×10−16 _2.90×10−16 33 1000 4.00×10−17 ₁ .90×10−16 ₂ .45×10−16 ₂ .90×10−16 3000 3.04×10−17 ₁ .90×10−16 ₂ .45×10−16 ₂ .90×10−16

Fig. 2. Thetotalcrosssectionsoftheprocesspp→pγ∗p→pτν¯τqX asafunction

ofκfortwodifferentcenter-of-massenergiesof√s=14,33 TeV.

Fig. 3. Thetotalcrosssectionsoftheprocesspp→pγ∗p→pτν¯τqX asafunction

ofκ˜fortwodifferentcenter-of-massenergiesof√s=14,33 TeV.

Fig. 4. Contour limits at the 95% C.L. in theκ− ˜κplane for√s=14 TeV.

Fig. 5. Contour limits at the 95% C.L. in theκ− ˜κplane for√s=33 TeV.

the LHC. As can be seen from Fig. 2 and Fig. 3, the total cross sections ofthe examined processes increase when the center-of-massenergy increases.Theanomalousmagneticdipolemomentis asymmetric,andelectricdipolemomentissymmetricinthecross sections. This situation can be seen from Eq. (14). In Figs. 4–5, weshow contourdiagramsfortheanomalous

κ

and

κ

˜

couplings. It isunderstood fromTables 3–4 that we improveboundsvalues withthe increasing energyand luminosity values.An interesting pointcanbe analyzedfromthesetablesthat theboundswith in-creasing systematicerror valuesare almost unchanged according totheluminosityvaluesandforthecenter-of-massenergyvalues. The reasonof thissituation isthestatisticalerrorwhichismuch smallerthanthesystematicerrorforthesesystematicerrorvalues. However, our bounds onthe anomalous magneticdipole mo-mentsarebetterthanthecurrentexperimentalboundsfor system-aticuncertaintyis0% andinthesameorderofmagnitudefor 7%. Therewithal,ourbestresultsareclosetootherstudiesinthe liter-ature[50,51].Fortheanomalouselectricdipolemoment,thebest bounds are the same order of magnitudewith the experimental bounds.

Acknowledgements

This work has been supported by the Scientific and Techno-logicalResearchCouncilofTurkey(TUBITAK)intheframework of ProjectNo.115F136.

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