Full one-loop corrections to neutralino pair production in e

We present the full one-loop radiative corrections to pair production of neutralinos in e+e- collisions within the Minimal Supersymmetric Standard Model. Particular attention is paid to the definition of weak and QED corrections. The non-universal QED corr

HEPHY-PUB785/04

arXiv:hep-ph/0402134v2 13 Feb 2004

Fullone-loopcorrectionstoneutralinopair

productionine+e annihilation

¨W.Oller,H.Eberl,W.Majerotto

¨Institutf¨urHochenergiephysikderOsterreichischenAkademiederWissenschaften,

A–1050Vienna,Austria

Abstract

Wepresentthefullone-loopradiativecorrectionstopairproductionofneu-tralinosine+e collisionswithintheMinimalSupersymmetricStandardModel.Particularattentionispaidtothede nitionofweakandQEDcorrections.Thenon-universalQEDcorrectionsareextractedbysubtractingtheinitialstateradia- 0tion.Wegivenumericalresultsfortwodi erentSUSYscenariosfore+e →χ 021χ

0+ 0 2.TheweakandQEDcorrectionsareuptoseveralpercentorandee→χ 2χ

evenhigherandneedtobetakenintoaccountatfuturelinearcolliderexperiments.

We present the full one-loop radiative corrections to pair production of neutralinos in e+e- collisions within the Minimal Supersymmetric Standard Model. Particular attention is paid to the definition of weak and QED corrections. The non-universal QED corr

1Introduction

IntheMinimalSupersymmetricStandardModel(MSSM)[1],onehastwocharginosχ ±andχ ±

whicharethefermionmasseigenstatesofthesupersymmetricpartnersofthe

1

W±and2,thechargedHiggsstatesH1±

,2.Likewise,therearefourneutralinosχ 01-χ 04,whicharethefermionmasseigenstatesofthesupersymmetricpartnersofthephoton,theZ0

boson,andtheneutralHiggsbosonsH10

,2.TheirmassmatrixdependsontheparametersM,M′,µ,andtanβ,whereMandM′aretheSU(2)andU(1)gaugemassparameter,andtanβ=v2

We present the full one-loop radiative corrections to pair production of neutralinos in e+e- collisions within the Minimal Supersymmetric Standard Model. Particular attention is paid to the definition of weak and QED corrections. The non-universal QED corr

2Tree-level

IntheMSSMtheneutralinosectorisspeci edbythegauginomassparametersMandM′,thehiggsinomassparameterµandtheHiggsmixingangletanβ,allappearingintheneutralinomassmatrix(inthebino,W3-ino,H1,2-inobasis)

Y=

M′0 mZsinθWcosβmZsinθWsinβ0MmZcosθWcosβ mZcosθWsinβ

mZsinθWcosβmZcosθWcosβ0 µmZsinθWsinβ mZcosθWsinβ µ0

.(1)(2)

WiththeunitarymatrixN,whichdiagonalizesthemassmatrixY

0)=NYN,0,mχ0,mχ,mdiag(mχ χ 04321

0=( iλ ′, iλ 3,ψ 1,ψ 2)totheneutralinowecanrotatefromthegaugeeigenstatesψjH1H2j

0.masseigenstatebasisχ 0=Nijψ

i

j

Attree-levelandneglectingtheelectronmassinallYukawacouplingstheproduction

process

e+e →χ 0 0iχj

(i,j=1,2,3,4)

containscontributionsfromtheFeynmandiagramsshowninFig.

1:Thedirects–channel

duetotheZ0exchangeandthecrossedt–andu–channelduetothee L,Rexchanges.

Figure1:Tree–Level

FromtheinteractionLagrangian

LZ0e¯e= Lee χ 0i

g

µLR0¯χ0Zµχ 0iγ[OijPL+OijPR] j,

′′

′′

2cosθW

=gfiLe¯PRχ 0 L+gfiRe¯PLχ 0 R+h.c.,ieie

(4)(5)

We present the full one-loop radiative corrections to pair production of neutralinos in e+e- collisions within the Minimal Supersymmetric Standard Model. Particular attention is paid to the definition of weak and QED corrections. The non-universal QED corr

weobtainthecouplings

CL,R=I3L,R+sin2θW,

2

2

I3L=

1

2tanθWNi 1.

(8)

1

Ni3Nj 3+

3One-loopcorrections

Theradiativecorrectionstotheneutralinopairproductionincludethefollowinggeneric

structureofone-loopFeynmandiagrams:ThevirtualvertexcorrectionsFig.2,thecor-rectionstothee L,RandZ0propagatorsFig.3,andtheboxgraphcontributionsFig.4.ThenotationF,V,andSstandforallpossiblefermion,vectorandscalarparticlesintheMSSM,respectively.UdenotestheFPghosts.Diagramswithloopsontheexternalfermionlinesareincludedinthede nitionofthecountertermsaswavefunctioncorrec-tions.Inthiswork,thecompletesetofFeynmangraphsiscalculatedwithhelpofthepackagesFeynArtsandFormCalc[12].Weimplementedourrenormalizationprocedureintothesepackages.ForapropertreatmentoftheappearingUVdivergencies,countertermsareintroducedintheon-shellrenormalizationscheme.Topreservesupersymme-try,theusedregularizationschemeisdimensionalreduction(

LPL+δZij2

2

1

1

2

δZL

1+

1

δZZZ)Zµ+

f

δZL0201+1

We present the full one-loop radiative corrections to pair production of neutralinos in e+e- collisions within the Minimal Supersymmetric Standard Model. Particular attention is paid to the definition of weak and QED corrections. The non-universal QED corr

Figure2:GenericVertexCorrections

S/V

Figure3:GenericPropagatorCorrections

δZZZ=

˙ZZ(m2), ΠZ

δZZγ=

2 ΠZγ(0)

We present the full one-loop radiative corrections to pair production of neutralinos in e+e- collisions within the Minimal Supersymmetric Standard Model. Particular attention is paid to the definition of weak and QED corrections. The non-universal QED corr

+crossedgraphs

+crossedgraphs

Figure4:GenericBoxCorrections

δZ

L

=

1R22˙L2˙ ΠL(m2) m(Π(m)+Π(m))+ffff

LδZijδZR

==

cij

˙SL(m20)+Π˙SR(m20)),(Π mχ 0iiiiχ χ i

i

i

2mχ 0i

2SR2

(ΠSLii(mχ 0) Πii(mχ 0))

i

i

(15)

+

SR2

Π(m)mχ 0ijχ 0jj

22

mχΠL(mχ)ij 0 0jj

+

R2

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