Anomalous couplings at LEP2

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D. Fayolle

To cite this version:

ANOMALOUSCOUPLINGS AT LEP2

D.Fayolle a

Laboratoire dePhysiqueCorpusculaire

UniversiteBlaisePascalIN2P3/CNRS

24avenuedesLandais,63177AubiereCedex,France

Abstract. Initssecondphase,LEP hasallowedto studyfourfermionprocesses

neverobservedbefore. Resultsare presentedon the charged triplegaugeboson

couplings(TGC)fromtheW-pair,SingleWandSingle production. The

anoma-lousquartic gauge couplings (QGC)areconstrained usingproduction of WW ,

  and Z nalstates. Finally,limitson theneutral anomalousgauge

cou-plings(NGC)using theZ and ZZproduction processesarealsoreported. All

resultsareconsistentwiththeStandardModelexpectations.

1 Introduction

TheLargeElectron-Positron(LEP)colliderhasbeenrunningabovetheW-pair

production thresholdsince 1996until theLEP stoppedin 2000, at

centre-of-mass energies between 161 GeVand 208 GeV.This has allowed each of the

four experimentsALEPH, DELPHI,L3and OPALto collectnearly700pb

1

ofdata.

The non-abelian structure ofthe Standard Model (SM) leadsto three and

four charged gaugeboson verticesof which the couplingsare speciedin the

bosonicpartofthelagrangian. Theself-interactionsofthesebosonscorrespond

tothevertices WW,ZWW andfourquarticWWXX

0

,whereXX

0

iseither

WW, ,ZZ or Z . EventhoughtheSMisexperimentallyso reliable,there

are still sometheoretical problems if one looks at higher energies. One way

to cope with this is to consider the SM as an eective theory and assume

that NewPhysics (NP) exists at an higherenergy scale, inducingdeviations

of physicalobservablevaluesfrom theSMpredictions. Theanomalous gauge

bosoncouplingsarethusintroducedin theupper-dimensionallagrangian.

The study of the charged TGCs is presented in the next section, and the

constraints on QGCs are reported in section 3. The NGCs are described in

section4. Conclusionsaregiveninsection5.

2 Charged TGCs

2.1 W

+

W channel

Oneof themostimportant SMprocess at LEP2 energiesisthe W

+

W

pro-ductionbecauseitallowstomeasuretheW massandthechargedtriplegauge

bosoncouplings.

In addition to the t-channel -exchange, W-pair production in e +

e

anni-hilationinvolvesthe triple gaugeboson verticesWW andWWZ which are

presentintheSMduetoitsnon-abeliannature. ThemostgeneralLorentz

in-variantlagrangianwhichdescribesthetriplegaugebosoninteractioninvolving

Wbosonshasfourteenindependentterms,sevendescribingeachWWV vertex,

withV =Z ; . Assumingelectromagneticgaugeinvariance,C,PandCP

con-servation,atotalofvecouplingsremain,whichare
g

Z 1 ,
 , ,
 Z and  Z [1] b

. Atthe treelevelin theSM, g

Z 1 = = Z =1,while = Z =0. RequiringSU(2) L U(1) Y

leadstothree independentcouplings

c ,
g Z 1 ,


and,relatedthrough


Z =
g Z 1
 tan 2  W and Z = .

AnomalousTGCsaectboththetotalcross-sectionandtheproduction

an-gular distributions. Moreover,the relativecontributions of each helicitysate

would be modied, which in turn aect the angular distributions of the W

decayproducts.

Allthefourcollaborationsusetheeventrateinformationinthethreedecay

channels(hadronic,semileptonicandfullyleptonic)tomeasurethevaluesofthe

TGCs, together with theeventshape. Dierentmethods are used toanalyse

WW events in order to extract the TGCs

d

: multidimensional phase-space

t or optimal observables[2]. Then the distributions arecompared withthe

expectations relativeto dierent valuesof the parameters, as obtained from

fullysimulatedWW Monte Carloevents. A newmethodconsistsin theSpin

Density Matrix (SDM) of which the elements (see gure 1) are observables

directlyrelatedtothepolarisationoftheW [3]. Thecomparison oftheSDM

elementswith thetheoretical predictions allows amodel independent test of

theTGCs.

There is no LEP combination since last summer because the experiments

arewaitingforanewWW generatorincludinghigherordercorrections. With

respect tothe oldgenerators,O() Monte CarlospredictalowerWW

cross-section (2.5%) and a sizeablechange in the slope of the cos

W

distributions

(2%). Only ALEPH has preliminary results [4], listed in table 1, including

thesehigherordercorrections.

coupling
g Z 1
  tresult 0:015 +0:035 0:032 0:020 +0:078 0:072 0:001 +0:034 0:031

Table1: ALEPHchargedcurrentTGCresultsincludingO()corrections.

b

denotesthedierenceofthesecouplingswithrespecttotheSMvalue.

c

Thecommonsetusedincludesg Z

5

whichisC-andP-violating.

Figure1: TheSDMelementsfortheW +

W production.

2.2 Other channels

The Single W, that is We nal state, also gives information on the WW

vertex. Thesignatureisoneelectronlost inthebeampipeandmissing

trans-versemomentum coming from theneutrino. The We channel hasthe same

sensitivityto


thantheWW channeland isalsosensitiveto.

TheSingle ,thatis ,concernstheWW vertexonly. Thesignatureis

ahighenergyphotonisolatedinthedetector. Thesensitivitytothecouplings

isabouttentimeslowerthantheWW sensitivity.

3 Quartic gaugecouplings

Four quartic gauge boson vertices are predicted in the SM with xed

cou-plings, W + W W + W ,W + W Z 0 Z 0 , W + W Z 0 andW + W ,but their

contributionstoprocessesstudiedat LEP2arenegligible. Ontheotherhand,

anomalouscontributionstoeectiveQGCsarisingfromphysicsbeyondtheSM

couldleadtomeasurableeects.

The formalism of anomalous QGCs involvingat least onephoton leads to

the\genuine"QGCoperatorsofdimension6afterneglectingoperatorsleading

to triplegaugecouplings. Threeanomalous QGCs, a

0 , a c anda n are

vertices[5], whereasa n

isCP-violatingandcontributesto theWWZ vertex

only[6].

Figure2:ThethreeanomalousverticesWWZ ,WW andZZ .

Limitsona

i =

2

(i=0;c;n),withtheenergyscalewherethisnewphysicsis

supposedtoappear,areobtainedbycomparingthecross-section(seegure3)

and kinematic distributions (see gure 4) of the WW ,   and Z nal

stateswiththeSMpredictions. Theresultsarelistedintable 2[7] e

.

The WW channel is analysed in the semileptonic and hadronic channels

wherethestandardWW selectionisappliedinadditiontothesearchofahigh

energyandisolatedphoton. Acutonlowpolar anglesforthephotonreduces

theinitial stateradiationsandasharpmasswindowforthedijet reducesthe

nalstateradiations. TheW radiationsarenegligible.

The second charged anomalous QGC comes from the   channel where

twoacoplanarphotonsareexpected. Acutonmissingmassisused toreduce

theZ background.

TheanalysisconcerningtheneutralprocessleadingtotheZ channel

f is

basedonthesearchof highenergyandisolatedphotonsinhadronicevents.

parameter[GeV 2 ] vertex 95%CL a W 0 = 2 WW + [-0.018,0.018] a W c = 2 WW + [-0.033,0.047] a n = 2 WW [-0.17,0.15]

Table2:95%CLcombinedLEPQGCresults.

e

There is no combination of neutral and charged QGCs because under more general

theoreticalhypothesis,eectsinneutralQGCsmaybedierentfromchargedQGCs(a Z i 6= a W i ). f

Figure3: Z cross-sectionwith

anoma-louscontributionsfroma 0

andac.

Figure4:Energydistributionofthe

pho-tonfortheWW channel.

4 NeutralTGCs

TheSMdoesnotpredictanydirectcouplingbetweentheneutralgaugebosons

themselves, but there are twopossibleanomalous verticesin the neutral

sec-tor [8]. Each vertexis parametrizedbythemostgeneralLorentz andU(1)

em

invariant lagrangianplusBosesymmetry and requiringonly oneo-shell

bo-son g

. TheseZZZ,ZZ andZ verticesareallforbiddenattreelevelinthe

SMandhaveunobservablysmallvaluesthroughloops.

Z nalstatesaresensitivetopossible

contributionsfromanomalousZ and

Z Z vertices which are parametrized

by height couplings: h V 1 , h V 2 (CP-violating)andh V 3 ,h V 4 (CP-conserving) with V = Z  ; 

. Z events are

in-vestigatedin qq and decay

prod-ucts where a hard visible photon and

twojetsorlargemissingenergyand

mo-mentum fortheneutrinosare searched

for. The h

V

i

couplings are tted from

theeventrate(seegure5),theangular

andenergydistributionsofthephoton.

Theresultsareshownintable3[7]and

gure6.

Figure 5: Variation of the Z

cross-sectionwithrespectto(h 3 ;h 4 ). g

DELPHIisalsolookingato-shellcouplings[9],cancelingtheconditionoftwooutgoing

on-shellbosons.Thisleadsto44newcouplingsthatarerelatedtothef V

andh V

Similarly to Z , Z-pairs can be used to constrain couplingsrelated to the

anomalousZZ andZZZvertices. Therearefourcouplings: f

V 4 (CP-violating) and f V 5 (CP-conserving) with V = Z  ; 

. The ve visible decay channels

are investigated: Z ! qqqq, Z ! qq, Z ! qql + l , Z ! l + l  and Z ! l + l l +

l with anexpected branching ratioof 49%, 28%, 14%,4% and

1%respectively. TheZ-paireventrate,aswellasangulardistributions(mainly

cos Z

) areused to constrain thevalues ofthe f

V

i

couplings. Theresultsare

summarizedin table3[7]andgure6.

h i 95%CL h Z i 95%CL f V i 95%CL h 1 [-0.056,0.055] h Z 1 [-0.128,0.126] f 4 [-0.17,0.19] h 2 [-0.045,0.025] h Z 2 [-0.078,0.071] f Z 4 [-0.31,0.28] h 3 [-0.049,0.008] h Z 3 [-0.197,0.074] f 5 [-0.36,0.40] h 4 [-0.002,0.034] h Z 4 [-0.049,0.124] f Z 5 [-0.36,0.39]

Table3: 95%CLcombinedLEPneutralcurrentTGCresults.

SM

LEP

Preliminary

68% CL

95% CL

h

₁

γ

h

2

γ

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

SM

LEP

Preliminary

68% CL

95% CL

h

₁

Z

h

2

Z

-0.7

-0.35

0

0.35

0.7

-0.7

-0.35

0

0.35

0.7

SM

LEP

Preliminary

68% CL

95% CL

f

₄

γ

f

4

Z

-0.5

-0.25

0

0.25

0.5

-0.5

-0.25

0

0.25

0.5

SM

LEP

Preliminary

68% CL

95% CL

h

3

γ

h

4

γ

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

SM

LEP

Preliminary

68% CL

95% CL

h

Z

3

h

4

Z

-0.7

-0.35

0

0.35

0.7

-0.7

-0.35

0

0.35

0.7

SM

LEP

Preliminary

68% CL

95% CL

f

5

γ

f

5

Z

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

Figure6:2DtcontoursforcombinedLEPneutralcurrentTGC.

5 Conclusions

Values and limits for anomalous triple and quartic gaugecouplings in e

+ e

collisions atcentre ofmassenergiesupto208GeVhavebeenpresented. The

priortotheLEP2startup. ThefullpotentialoftheLEP2dataisnotyetfully

exploited everywhere and future improvements of the combined LEP results

canbeexpected.

Acknowledgments

I would liketo thankmy ALEPHcolleaguesfor interestingdiscussions about

the physicsof W and Z bosons. Moreover, thewarmhospitality of the10th

LomonosovConferencehasbeenwellappreciated.

References

[1] PhysicsatLEP2,ed. byG.Altarelli,T.SjostrandandF.Zwirner,CERN

96-01Vol. 1,525.

[2] M.Diehl etal.,Z.Phys. C62,397(1994).

[3] G.Gounariset al,Int.J.Mod.Phys. A19,3285(1993).

[4] TheALEPHCollaboration,ALEPH2001-060,CONF 040.

[5] G.Belangeret al,Eur.Phys.J.C13,283(2000).

[6] O.J.P.Ebolietal, Nucl.Phys. B411,381(1994).

[7] TheLEPCollaborationALEPH,DELPHI,L3,OPAL,andtheLEPGC

Working Group, \Combined

Pre-liminary Results on Electroweak Gauge Coupling Measurements by the

LEP Experiments", LEPEWWG/TGC/2001-03,and referencestherein,

http://lepww.web.cern.ch/lepww/tgc/bp01/gc main.ps.gz

[8] K.Hagiwaraetal,Nucl.Phys. B282,253(1987).