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Signals for Majorana neutrinos in a $gamma gamma$ collider

a r X i v :h e p -p h /0211355v 1 22 N o v 2002Signals for Majorana neutrinos in a γγcollider

J.Peressutti and O.A.Sampayo

Departamento de F′?sica,Universidad Nacional de Mar del Plata

Funes 3350,(7600)Mar del Plata,Argentina

Abstract

We study the possibilities to detect Majorana neutrinos in γγcolliders for di?erent center of mass energies.We study the W ±W ±l ?j l ?k (l j ≡e,μ,τ)?nal states which are,due to leptonic number violation,a clear signature for intermediate Majorana neutrino contribution.Such a signal (?nal dileptons of the same sign)is not possible if the heavy neutrinos are Dirac particles.We present our results for the total cross-section as a function of the neutrino mass and the center of mass energies.

Typeset using REVT E X

I.INTRODUCTION

Massive neutrinos can come in two di?erent types:as Dirac or Majorana particles. Dirac fermions have distinct particles and antiparticle degrees of freedom while Majorana

fermions make no such distinction and have half as many degrees of freedom[1].In this conditions fermions with conserved charges(color,electric charged,lepton number,...)must

be of Dirac type,while fermions without conserved charges may be of either type.New

neutrinos could have large masses and be of either type.If there are heavy neutrinos(N), then the present and future experiments o?er the possibility of establishing their nature.

The production of Majorana neutrinos via e+e?,e?γ,γγand hadronic collision have been

extensively investigated in the past[2,3,4,5,6,7,8,9].In this work we study the possibility of theγγlinear collider to produce clear signatures for Majorana neutrinos.The photon linear

collider[10]may be the best alternative to the electron positron colliders.In this paper we discuss the possible detection of Majorana neutrinos in the reactionsγγ→W±W±l?j l?k

(l j≡e,μ,τ)where the real gamma beam are obtained by Comptom backscattering of laser photons o?the linear electron beam.In this process most of the photons are produced at the high energy regions.For the cross section calculation we have used the helicity formalism

[11,12],considering the complete set of Feynman diagrams show in Fig.1.The phase space

integration was done taking account that the intermediate neutrinos can be either on shell

or o?shell.In this point the present work di?er of previous calculation[9]where the √

restriction M N>

s the new heavy neutrino is more likely to be?rst discovered via

single production in e+e?→νN.However theγγcollider have some facilities that make it suitable to search Majorana neutrinos and study their interactions.In particular aγγcollider o?er the possibility to control the helicity of the colliding photons controlling the helicity of the Laser https://www.sodocs.net/doc/054439535.html,ing these polarized high energy photon beams we have the possibility to study in detail the interactions of Majorana neutrinos and reject possible backgrounds.Due the large CM energies of these colliders we have considered that the mass of the?nal lepton vanishes.

For the couplings of the Majorana neutrinos we follow Ref[6]starting with rather general

lagrangian densities for the interaction of N with W and light leptons l j(e,μ,τ):

L NW l=?3 j=1gB(j)L2ˉl jγμP L NW?μ+h.c.(1)

The heavy Majorana neutrino couples to the three?avors lepton with couplings proportional to B(j)L,where j labels the family.This(B(j)L)2constant are,in notation of[13],the sin square of the mixing angle between light and heavy neutrinos((Sνe L)2,(SνμL)2,(SντL)2).The constant g is the standard SU(2)L gauge coupling.

This B(j)L parameters will a?ect the?nal results via the combinations

H i=|B(i)L|2and H=3 j=1|B(j)L|2(2)

The?nal leptons can be either of e?,μ?orτ?because this is allowed by the interaction lagrangian(eq.1).All these possible?nal states are a clear signal for intermediary Majorana neutrino and then we sum the cross section over the?avors of the?nal lepton.This sum depend of H,H1,H2and H3in the numerator of the total cross section.In the other hand this cross-section also depends on H through the total widthΓN→all in the Majorana neutrino propagator.This last dependence is relevant when the Majorana neutrino is on-shell.We use the Breit-Wigner propagator for the Majorana neutrino N for di?erent values of the mass M N.The total widthΓN→all of N was determined at tree level considering the dominant decay modes N→W±l?j:

g2H

ΓN→all=

2 factor is included to avoid double counting of the two W and another1

s and M N.The H dependence is complicate due to the Majorana

neutrino propagator.We have founded that the most important contribution to|ˉM|2

√coming from the couplings is proportional to H2.However in the M W

s?M W region(Reg.II),where the Majorana neutrino is o?-shell,the total cross-section is approximately proportional to H2.The behaviour in Reg.I is easy to realize if we

make the so-called peaking approximation,in which the Breit-Wigner shape of the Majorana neutrino propagator is replaced by a delta function.In this region the H2dependence in the numerator is canceled by the H factor in the total width.Considering only the relevant factors in the cross section,we have

σ= jσj~···H21

(q2?M2N)2+M2NΓ2N···→

π

s(the center of mass energie of theγγsubprocess)and M N.The numerical Monte Carlo integration was done using the FORTRAN subroutine RAMBO[16].The Fig.2show the M N dependence of the unpolarized cross-section σat?xed

s=500GeV. Moreover,partial results were also checked using the CalcHep program[17].In Fig.3we show the

dτ σγγ→W±W±l?l?(τs)(8)

The di?erential luminosity dLγγ/dτis de?ned as usual in terms of photons structure functions of electrons(f(x))beam:

dLγγ

x max dx

x

)(9)

whereτ= s/s.

and x is the fraction of the parent electron’s energies carried by the photons.The maximum possible value for x is

x max=ξ

m e

;(11)

where E0andω0are the incident electron and laser light energies.To avoid unwanted e+e?pair production from the collitions between the incident and back-scattered photons, we should no choose too largeω0.This fact constraint the maximum value forξto be ξ=2(1+

x a

dx b f(x a)f(x b) σ(x a x b s)(12)

where x min

a

=τmin/x max.

To illustrate the possible impact of this process in the discovery of Majorana neutrinos we show in Fig4the number of events as a function of

s for M N=300GeV.The horizontal line represent the maximum possible value for H.

Summarizing,we calculate the cross-section for the processγγ→W±W±l?j l?k where l1,l2and l3are light leptons(e,μ,τ)respectively.We show the total unpolarized cross-section for the subprocessγγfor di?erent values of

s considering the real gamma beam is obtained by the Comptom backscattering of laser photons o?the linear electron beam.

Acknowledgements

We thank CONICET(Argentina)and Universidad Nacional de Mar del Plata(Ar-gentina)for their?nancial supports.

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Figure Captions

Figure1:Feynman graph contributing to the amplitude of theγγ→W+W+l?l?process.

Figure2:Unpolarized cross-section( σ)for theγγ-subprocess as a function of the Majorana

neutrino masses(M N)for di?erent center of mass energies(

s=500GeV,a plot ofσ(γγ→l?NW±)Br(N→l?W±)(Dot-Dash).

Figure3:Unpolarized cross section( σ)for theγγ-subprocess as a function of the center √

of mass energies(

s for M N=300GeV.

Figure5:Contour Plot for the number of events(1000,500,100,30,1)as a function of √

100200300400500

10-8

10-7

10-6

10-510-4

10-3

10-2

10-1

^^^^s=200 GeV

s=300 GeV

s=500 GeV

σ [p b ]m N [GeV]

300350400450500

10-610-5

10-4

10-310-2^^

M

N =500 GeV

M N =300 GeV M N =200 GeV σ [

p

b

]

s [GeV]

2004006008001000

100

101

102

103

Fig.4

M N =300 GeV N u m b e r o f E v e n t s s [GeV]

200300400500600700800900100010-5

10-410-3

10-2

10-1100

H

M N = 300 GeV 130

100

500

1000s [GeV]

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