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Phenomenology of non-universal gaugino masses in supersymmetric grand unified theories

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HIP-2005-05/TH hep-ph/0502100Phenomenology of non-universal gaugino masses in supersymmetric grand uni?ed theories Katri Huitu,1,2,?Jari Laamanen,1,2,?Pran N.Pandita,3,?and Sourov Roy 2,§1High Energy Physics Division,Department of Physical Sciences,P.O.Box 64,FIN-00014University of Helsinki,Finland 2Helsinki Institute of Physics,P.O.Box 64,FIN-00014University of Helsinki,Finland 3Department of Physics,North-Eastern Hill University,Shillong 793022,India (Received February 2,2008)Abstract Grand uni?ed theories can lead to non-universal boundary conditions for the gaugino masses at the uni?cation scale.We consider the implications of such non-universal boundary conditions for the composition of the lightest neutralino as well as for the upper bound on its mass in the simplest supersymmetric grand uni?ed theory based on the SU (5)gauge group.We derive sum rules for neutralino and chargino masses in di?erent representations of SU (5)which lead to di?erent non-universal boundary conditions for the gaugino masses at the uni?cation scale.We also consider the phenomenological implications of the non-universal gaugino masses arising from a grand uni?ed theory in the context of Large Hadron Collider.In particular we investigate the detection of heavy neutral Higgs bosons H 0,A 0from H 0,A 0→?χ02?χ02→4l ,and study the possibilities of detecting the neutral Higgs bosons in cascade decays,including the decays ?χ02→h 0(H 0,A 0)?χ01→b ˉb ?χ01.

PACS numbers:12.60.Jv,11.30.Er,14.80.Ly

I.INTRODUCTION

Supersymmetry is at present an attractive framework in which the Higgs sector of the Standard Model(SM),so crucial for its consistency,is technically natural.It is widely expected that some of the supersymmetric partners of the SM particles will be produced at the CERN Large Hadron Collider(LHC)which is going to start operation in a few years time. In the experimental search for supersymmetry(SUSY)the lightest supersymmetric particle will play a crucial role since the heavier supersymmetric particles will decay into it.In SUSY models with R-parity conservation,the lightest supersymmetric particle is absolutely stable.The lightest supersymmetric particle is constrained to be a weakly interacting neutral particle[1].

In most of the supersymmetric models the lightest neutralino(?χ01),which is typically an admixture of gauginos and higgsinos,is the lightest supersymmetric particle(LSP).Such an LSP is a good candidate for a particle dark matter[2].From the point of view of experimental discovery of supersymmetry at a collider like the LHC,the LSP is the?nal product of the cascade decay of a SUSY particle.In this work we will assume that the LSP is the lightest neutralino,and that it escapes the collider experiments undetected. The cascade chain will typically also contain other neutralinos(?χ0j,j=2,3,4)as well as charginos(?χ±i,i=1,2).The charginos are an admixture of charged gauginos and charged higgsinos.The composition and mass of the neutralinos and charginos will play a key role in the search for supersymmetric particles.These properties determine also the time-scale of their decays.The mass patterns of the neutralinos in models with di?erent particle content, or with speci?c SUSY breaking patterns were considered in some detail in[3,4].

Although most of the phenomenological studies involving neutralinos and charginos have been performed with universal gaugino masses at the grand uni?cation scale,there is no compelling theoretical reason for such a choice.Gaugino masses follow from higher dimen-sional interaction terms which involve gauginos and auxiliary parts of chiral super?elds in a given supersymmetric model.Assuming an SU(5)grand uni?ed theory(GUT)model, the auxiliary part of a chiral super?eld in these higher dimensional terms can be in the representation1,24,75,or200,or some combination of these,of the underlying SU(5) gauge group.If the auxiliary?eld of one of the SU(5)nonsinglet chiral super?elds obtains a vacuum expectation value(VEV),then the gaugino masses are not universal at the grand

uni?cation scale.Moreover,nonuniversal soft supersymmetry breaking masses,like gaugino masses,are a necessary feature in some of the supersymmetric models,e.g.in anomaly mediated supersymmetry breaking models the gaugino masses are not uni?ed[5].

As indicated above,the phenomenology of supersymmetric models depends crucially on the composition of neutralinos and charginos.Thus,it is important to investigate the changes in the experimental signals for supersymmetry with the changes in the composition of neutralinos and charginos that may arise because of the changes in the underlying bound-ary conditions at the grand uni?cation scale,or when the underlying supersymmetric model is changed.The implications of nonuniversal gaugino masses has been considered in a num-ber of works,e.g.in a study of constraints arising from experimental measurements[6,7,8], and in the context of supersymmetric dark matter[9,10].In[8],the decays of the second lightest neutralino were studied in the context of nonuniversal gaugino masses.

In this paper we shall study the implications of the nonuniversal gaugino masses for the phenomenology of neutral Higgs bosons.It has been known for quite some time that the cascade decays of the SUSY particles may be a major source of the Higgs bosons[11,12,13]: the copiously produced strongly interacting particles can cascade decay to the Higgs bosons. In addition to the obvious interest in producing the Higgs bosons,it has been realized that this method of producing the Higgs bosons does not depend on the value of tanβ.Thus,this method of producing Higgs bosons may help to cover a larger parameter space as compared to the more conventional methods of studying the Higgs sector of supersymmetric models, including also the heavier Higgs bosons.The gauginos also play an important role in the decays of Higgs bosons when they are kinematically allowed to decay to the second lightest neutralino pair,which in turn may decay to the lightest neutralinos and two leptons[14]. Such a signal seems to be relatively easy to discover at the LHC[15,16].We note here that Higgs boson production via cascade decays and detection via Higgs decay to neutralinos has been studied in CMS detector simulations at LHC[15,16,17]in the case of minimal supersymmetric standard model(MSSM)with universal gaugino masses.Here we study the Higgs production and decay when gaugino masses are nonuniversal.

The plan of the paper is as follows.In Section II we consider in detail the nonuniver-sality of gaugino masses as it arises in SU(5)supersymmetric grand uni?ed theory.In this Section we consider analytically the implications of such a nonuniversality for neutralino and chargino masses.We derive sum rules involving the neutralino and chargino squared

masses when the supersymmetry breaking gaugino masses are nonuniversal.In Section III we consider the phenomenology of Higgs bosons when the gaugino masses are nonuniversal. In this Section we consider Higgs decays to heavier neutralinos which then cascade into the lightest neutralino and leptons.In Section IV we calculate the production of squark and gluino pairs in a particular scenario where the gluinos are heavier than squarks,and then study the cascade decays of the squarks into Higgs bosons.We conclude our paper with a summary in Section V.

II.NONUNIVERSAL GAUGINO MASSES IN SUPERSYMMETRIC SU(5)

The masses and the compositions of neutralinos and charginos are determined by the soft supersymmetry breaking gaugino masses M1,M2,and M3,corresponding to U(1),SU(2), and SU(3)gauge groups,respectively,the supersymmetric Higgs mixing parameterμ,and the ratio of the vacuum expectation values of the two neutral Higgs bosons H01and H02, H02 / H01 =tanβ.In the simplest supersymmetric models with universal gaugino masses,

M1,M2,and M3are taken to be equal at the grand uni?ed scale.However,in supersymmetric theories with an underlying grand uni?ed gauge group,the gaugino masses need not be equal at the GUT scale.In this Section we consider the nonuniversality of gaugino masses as it arises in the simplest of the supersymmetric grand uni?ed theories,namely supersymmetric SU(5)grand uni?ed theory,and its implications.

In grand uni?ed supersymmetric models,including SU(5)grand uni?ed models,non-universal gaugino masses are generated by a non-singlet chiral super?eldΦn that appears linearly in the gauge kinetic function f(Φ)(the chiral super?eldsΦare classi?ed into a set of gauge singlet super?eldsΦs,and gauge nonsinglet super?eldsΦn,respectively under the grand uni?ed group),which is an analytic function of the chiral super?eldsΦin the theory [18].If the auxiliary part FΦof a chiral super?eldΦin f(Φ)gets a VEV,then gaugino masses arise from the coupling of f(Φ)with the?eld strength super?eld W a.The Lagrangian for the coupling of gauge kinetic function to the gauge?eld strength is written as

L g.k.= d2θf ab(Φ)W a W b+h.c.,(1) where a and b are gauge group indices,and repeated indices are summed over.The gauge

kinetic function f ab(Φ)is

f ab(Φ)=f0(Φs)δab+ n f n(Φs)Φn ab

λaλb+h.c.,(3)

M P

whereλa,b are gaugino?elds.Note that we denote byλ1,λ2andλ3the U(1),SU(2) and SU(3)gauginos,respectively.Since the gauginos belong to the adjoint representation of SU(5),Φand FΦcan belong to any of the following representations appearing in the symmetric product of the two24dimensional representations of SU(5):

(24?24)Symm=1⊕24⊕75⊕200.(4) In the minimal,and the simplest,caseΦand FΦare assumed to be in the singlet repre-sentation of SU(5),which implies equal gaugino masses at the GUT scale.However,as is clear from the decomposition(4),Φcan belong to any of the non-singlet representations 24,75,and200of SU(5),in which case these gaugino masses are unequal but related to one another via the representation invariants[19].In Table I we show the ratios of resulting gaugino masses at tree-level as they arise when FΦbelongs to various representations of SU(5).For de?niteness,we shall study the case of each representation separately,although an arbitrary combination of these is obviously also allowed.

These results are consistent with the uni?cation of gauge couplings

αG3=αG2=αG1=αG(≈1/25),(5) at the grand uni?cation scale,where we have neglected the contribution of nonuniversality to the gauge couplings.Such contributions have little e?ect on the phenomenological aspects that we are interested in this paper.Because of the renormalization group(RG)evolution we have at any scale(at the one-loop level)[20]

M i(t)

.(6)

αi(GUT)

TABLE I:Ratios of the gaugino masses at the GUT scale in the normalization M3(GUT)=1, and at the electroweak scale in the normalization M3(EW)=1at the1-loop level.

FΦM G1M G2M G3M EW

1M EW

2

M EW

3

11110.140.291

24-0.5-1.51-0.07-0.431

75-531-0.720.871

2001021 1.440.581 Thus,at any scale we have

M1=5

cos2θW M1(GUT)sin2θW

M2(GUT)α3(GUT) .

(7)

For the24dimensional representation of SU(5),we then have

M1

2 5cos2θW

1M3=?3sin2θW 1

M3

=?5 5cos2θW 1M3=3 αα3 ,(9) and for the200dimensional representation of SU(5)we have

M1

α3 ,M2sin2θW

1

M 2 [GeV], rep. 1t a n β

0 200 400 600 800 1000

5 10 15 20 25 30 35 40 45

50M 2 [GeV], rep. 24t a n β 0 200 400 600 800 1000 0 5 10 15 20 25 30 35 40 45

50M 2 [GeV], rep. 75t a n β

0 200 400 600 800 1000

5 10 15 20 25 30 35 40 45

50h ~2h ~1w ~b ~M 2 [GeV], rep. 200t a n β

0 200 400 600 800 1000 0 5 10 15 20 25 30 35 40 45

50FIG.1:Main component of the lightest neutralino in di?erent representations of SU (5)that arise in the product (4)for a common universal scalar mass m 0=1TeV given at the GUT scale.The value of M 2is calculated and plotted at the electroweak scale.

breaking scalar mass m 0(GUT )=1TeV.The values of μused in the computations were determined by requiring the radiative electroweak symmetry breaking at the relevant scale.The universal trilinear coupling A 0was set to zero at the GUT scale and the sign of the Higgs mixing parameter μwas set to +1,but the choice of the sign is not crucial to the composition of the lightest neutralino.The scan was done using the program SOFTSUSY

[21]that uses two loop RG β-functions for the relevant parameters.

For the case of the singlet representation,the dominant component is always the bino,as expected.This is also true for the 24dimensional representation of SU (5).For the singlet case the experimental mass limit of the lighter chargino (m ?χ±1

>103GeV if m ?ν>200GeV,m ?χ±1

>45GeV if m ?ν<200GeV [22])restricts the lower end of the M 2range.In the 24dimensional representation the lower end of the M 2range is restricted by the lightest

neutralino mass limit m ?χ0

1

>36GeV [22].

2004006008001000

200400

600

800

24

1

20075a)(M 21?M 22)2+M 4Z ?2(M 21?M 22)M 2Z cos 2θW

.

(11)

In Fig.2we plot this upper bound for the lightest neutralino mass for the four di?erent representations of SU (5)that we have considered in this paper.From Fig.2(a)we see that the large coe?cients in the Table I result in large di?erences in the upper bound on

-30-25

-20

-15

-10-5 0 5

10 200 400 600 800 1000 1200 1400 1600

M 2s u m × 10-5 [G e V 2]m g ~ [GeV]

singlet 2475200FIG.3:The sum rule 2 m 2?χ±

i ? m 2?χ0i

as a function of the gluino mass.the mass of the lightest neutralino for the four di?erent representations in (4).Similarly,as discussed in [4],an upper bound can be obtained for the second lightest neutralino.This upper bound for ?χ02is shown in Fig.2(b).The gaugino masses here are calculated in the next-to-leading order (see e.g.[4]).

In order to study analytically the implications of the nonuniversal gaugino masses on the neutralino and chargino mass spectrum,we consider the trace of the neutralino and chargino mass squared matrices.From the trace of these matrices,we can calculate the average mass squared di?erence of the charginos and neutralinos.This mass squared di?erence depends only on the physical masses,and not on the Higgs(ino)mass parameter μor the ratio of VEV’s,tan β[20].For the four di?erent representations of SU (5)which arise in (4),we ?nd at the tree-level the sum rules

M 2sum =2(M 2?χ±1+M 2?χ±2

)?(M 2?χ01+M 2?χ02+M 2?χ03+M 2?χ04)=(α22?α21)

M 2?g 4α22?1

α23

+4m 2W ?2m 2Z ,for 24,(13)=(9α22?25α21)

M 2?g α23+4m 2W ?2m 2Z ,for 200.(15)

From these sum rules we see that at the tree-level the average mass squared di?erence between charginos and neutralinos is positive for the representations1,24and75,whereas for the representation200it is negative.In this respect the representation200resembles the anomaly mediated supersymmetry breaking scenario,where it was found that the average mass squared di?erence is negative[23].In Fig.3,we have plotted the above sum rules for the di?erent SU(5)representations that arise in(4).For the numerical evaluation of the masses,we have used the program SOFTSUSY[21],including radiative corrections to the neutralino and chargino masses.

III.HIGGS DETECTION USING H0,A0→?χ02?χ02→4l

It is often assumed,when considering the detection of the Higgs bosons in supersymmetric models,that supersymmetric partners are too heavy so that Higgs bosons cannot decay into supersymmetric particles.However,it may well be that for the heavy Higgs bosons H0,A0, and H±the decays to supersymmetric particles are important or even dominant[15,16].On the other hand,the decay branching ratios of neutralinos and charginos have been analyzed in[24].In the case of large tanβ,when the couplings to the heavy fermions are enhanced, the decays to the third generation particles have been discussed in[25].For large values of tanβ,the decays to the third generation particles for the nonuniversal gaugino masses were discussed in[8].Here we are interested in Higgs decay to?χ02,which in turn decays to electrons and muons in the case of non-universal gaugino masses.

A.Decay of?χ02to leptons

Of the supersymmetric particles,the light neutralinos?χ01,2,the light chargino?χ±1,and the lightest sleptons are usually among the lightest particles in the spectrum.Higgs decays to sleptons are suppressed because of the small coupling,which is proportional to the cor-responding lepton mass.The decay to the lightest neutralino LSP is among the invisible decays,which may be extremely di?cult to detect at the LHC.In the minimal SUGRA model,the second lightest neutralino and the lighter of the charginos have similar mass.In [15],the decay of the heavy neutral Higgs boson to a pair of the second lightest neutralinos was studied.It was found that in the case when the branching ratio of?χ02to two leptons

1

0.9

0.8

0.7

0.60.50.4

0.3

0.2

0.1

0 5 10 15 20 25 30B .R .(χ20 --> χ10 l l )tan β175μ = -500 GeV M 2 = 150 GeV m = 250 GeV

l = e + μ

(including the staus)are assumed to have soft SUSY breaking masses of250GeV and the value ofμ=-500GeV.In this analysis M2is a free parameter,and its value at the electroweak scale is taken to be150GeV.The squark masses are all taken equal to1TeV. We have also taken a large value of the trilinear scalar coupling A t=1TeV in order to have experimentally acceptable mass for the lightest Higgs boson.All the soft scalar masses, the value of A t and the value ofμare taken at the electroweak scale.The pseudoscalar Higgs mass m A is a free parameter and its value is taken to be340GeV.The value of M1 is determined from the ratio of the gaugino mass parameters in the singlet representation of SU(5)in(4).Due to the mentioned choice of M2,?χ02is predominantly a wino,and?χ01 is a bino-dominated state.The decay of?χ02into?χ01and a Z0is kinematically disallowed. The branching ratio of the three-body decay is shown in Fig.4as a function of tanβfor the singlet case as well as for the representation75.We have calculated the branching ratio using the program SDECAY[27].In this?gure the initial value of tanβis4.5,since for a lower value of tanβthe light Higgs mass m h is less than114.4GeV,which is the LEP lower limit[28].We see from the?gure that for higher values of tanβthis branching ratio decreases since the branching ratio?χ02→?χ01τ+τ?increases with tanβdue to a larger

Yukawa coupling.

For the representation75,?χ02is wino-dominated and?χ01is bino-dominated as in the singlet case.However,the mass di?erence between the?χ02and the?χ01is much smaller compared to the singlet case.As we see from Fig.4,in the low tanβregion the branching ratio for these two di?erent representations are very close though the branching ratio for the75 representation is slightly larger.This is due to the fact that BR(?χ02→?χ01qˉq)is slightly larger in the singlet case as compared to the case of75dimensional representation.The leptonic branching ratio is then almost equally distributed among the available channels.However, for large tanβthe branching ratio in the?χ01τ+τ?channel is larger for the75case than for the singlet case.For large tanβthis makes the branching ratio in the?χ01l+l?channel smaller for the case of75dimensional representation.We also note that in the case of75 dimensional representation the partial decay width of?χ02→?χ01νˉνis larger than the partial decay width of?χ02→?χ01l+l?in the large tanβregion.On the other hand,in the singlet case the partial decay width of?χ02→?χ01νˉνis always smaller than that of?χ02→?χ01l+l?.

For the set of parameters that we have discussed and in the case of the representation 200,the spectrum is such that all the left and right handed sleptons are lighter than?χ02and

1

0.9

0.80.7

0.6

0.50.4

0.3

0.2

0.1

0 5

10

15 20 25 30

B

.

R .

(

χ

20

-

-

>

χ

10

l

l

)

tan β

200

μ = -500 GeV M 2 = 150 GeV

m = 250 GeV l = e + μ

representation.

??χ±1and ?χ01are almost exclusively winos,and they are nearly degenerate in mass.

??χ02is predominantly a bino for |μ|>M 1.Consider the decay ?χ02→?χ01l +l ?for the 200dimensional representation.We again choose

the scalar masses in such a way that m ?l R ,m ?τ1

is highly suppressed due to the very small bino component in ?χ01,?l R will decay eventually in this mode with a one hundred percent branching ratio.Of course,one should be careful to consider the possibility of a displaced vertex in the decay of ?l R .The BR(?χ02→?χ01

l +l ?)calculated in this manner depends very strongly on μ(increases with increasing μ)since as μincreases ?χ02becomes more and more bino like,and thus the partial decay widths of

?χ02→?χ±1W ?and ?χ02→?χ01h are suppressed and the partial decay width of ?χ02→?l R l is

enhanced.This makes the branching ratio into ?l R l mode larger for large values of μ.This is shown in Fig.6.The branching ratio in the channel ?χ02→?χ01Z is always very small for all

values of tan β.We note that in the case of the 200dimensional representation we use the constraint m ?χ±

1

>88GeV applicable for nearly mass degenerate lighter chargino and the lightest neutralino

[29].

Let us now discuss the BR(?χ02→?χ01l +l ?)for this set of parameters for the representa-

tions 1and 75.We do not compare the case for the representation 24here since for the parameter choice of this ?gure the 24dimensional representation always produces a lightest neutralino with mass below the current experimental limit [22].For this set of parameters the representations 1and 75give similar kind of spectrum so that no two-body decays of ?χ02are allowed.In Fig.7we show the branching ratio for these two representations as a function of tan βand for a value of μ=500GeV.2.The case of 24

In this subsection we will consider the case of 24dimensional representation where |M 1|≈

0.166|M 2|.We look for a set of parameters such that the mass of the lightest neutralino is not below the current experimental lower limit as was the case in the previous sub-sections.For

the present study we again consider the mass spectrum m ?χ01

0.9

0.8

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0.60.50.4

0.3

0.2

0.1

0 10 15 20 25 30B .R .(χ20 --> χ10 l l )tan β500 GeV 300 GeV μ = 250 GeV M 2 = 120 GeV m = 300 GeV m = 150 GeV

l = e + μ

0.9

0.8

0.7

0.60.50.4

0.3

0.2

0.10 10 15

20 25 30B .R .(χ20 --> χ10 l l )tan β175

μ = 500 GeV M 2 = 120 GeV m = 300 GeV m = 150 GeV

l = e + μ2[Z i 3(Z j 2?Z j 1tan θW )+Z j 3(Z i 2?Z i 1tan θW )]?i ,S ′′ij =1

0.9

0.8

0.7

0.60.50.4

0.3

0.2

0.1

0 10 15 20 25 30B .R .(χ20 --> χ10 l l )tan β24μ = -200 GeV M 2 = 750 GeV m = 300 GeV m = 150 GeV

l = e + μ

0.0001 0.001 0.01

0.11000

900

800700600500400300200100B .R .(H 0 --> χ02 χ02)m A (GeV)

tan β = 6.5m = 300 GeV μ = 500 GeV M 2 = 120 GeV m = 150 GeV 751200

3020

15

12

10

9

8

7

100 200 300 400 500

600 700 800

t a n βm A (GeV)1510Representation 1

FIG.11:Contours of σ(pp ?→H 0,A 0?→?χ02?χ

02?→4l +X )in fb,where l =e ±or μ±and X represents invisible ?nal state particles.This is the case for the singlet representation.Other

MSSM parameters are the same as in Fig.9.√s =14TeV for two di?erent representation,the singlet and 75.We

show the contours of constant cross section in the (m A ,tan β)plane for a representative set of MSSM parameters at the electroweak scale.As in Fig.9,we have taken μ=500GeV,M 2=120GeV,all left slepton masses to be 300GeV and all the right slepton masses to be 150GeV.All squark masses are taken to be 1TeV.The top mass is m t =178GeV and the bottom mass m b is 4.25GeV.The production cross section gg →H 0/A 0has been calculated in the next-to-leading order using the package HIGLU [33],which is based on the calculations in Ref.[34].For the gluon distribution function we have used the distribution given in [35].We note that for low values of tan βthis channel dominates the production cross section.We have also considered the inclusive associated production q ˉq ,gg →b ˉbH 0/A 0at the leading order [36](which is essentially the leading order subprocess b ˉb →H 0/A 0).The factorization and the renormalization scale are chosen to be μF =μR =(m H/A +2m b )/2.The process gg →b ˉbH 0/A 0as well as the process gg →H 0/A 0is enhanced for larger values

3020

15

12

10

987

100 200 300 400 500 600 700 800

t

a n

βm A (GeV)

1

5

7

Representation 75

FIG.12:Contours of σ(pp ?→H 0,A 0?→?χ02?χ02?→4l +X )in fb,where l =e ±or μ±and X represents invisible ?nal state particles.This is the case for the representation 75.Other MSSM parameters are the same as in Fig.9.√

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