Table Of ContentDFTT 3/2008, KIAS–P08014
Light neutralinos at LHC in cosmologically–inspired scenarios: new benchmarks in
the search for supersymmetry
A. Bottino,1 N. Fornengo,1 G. Polesello,2 and S. Scopel3
1Dipartimento di Fisica Teorica, Universit`a di Torino
Istituto Nazionale di Fisica Nucleare, Sezione di Torino
via P. Giuria 1, I–10125 Torino, Italy
2Istituto Nazionale di Fisica Nucleare, Sezione di Pavia
via Bassi 6, 27100 Pavia Italy
3Korea Institute for Advanced Study
8
Seoul 130-722, Korea
0
(Dated: February 2, 2008)
0
2
n
a
J
Westudyhowthepropertiesofthefourneutralinostates, χi (i= 1,2, 3,4), can beinvestigated
2 attheLargeHadronCollider(LHC),inthecasewhenthelightestone,χ1,hasamassmχ <50GeV
2 and is stable. This situation arises naturally in supersymmetric models where gaugino m∼asses are
not unified at a Grand Unified (GUT) scale and R-parity is conserved. The main features of these
]
h neutralinostatesareestablishedbyanalyticalandnumericalanalyses,andtwoscenariosaresingled
p out on the basis of the cosmological properties required for the relic neutralinos. Signals expected
-
p atLHCarediscussed throughthemain chainprocessesstarted byasquark,producedintheinitial
e proton-proton scattering. We motivate the selection of some convenient benchmarks, in the light
h of the spectroscopical properties (mass spectrum and transitions) of the four neutralino states.
[ Branching ratios and the expected total number of events are derived in the various benchmarks,
1 and their relevance for experimental determination of neutralino properties is finally discussed.
v
4 PACSnumbers: 95.35.+d,11.30.Pb,12.60.Jv,95.30.Cq
3
3
3 I. INTRODUCTION
.
1
0 Light neutralinos, i.e. neutralinos with a mass m < 50 GeV, arise naturally in supersymmetric models where
8 χ
gaugino masses are not unified at a Grand Unified (G∼UT) scale. When R-parity conservation is assumed, these
0
: neutralinos offer a very rich phenomenology under various cosmologicaland astrophysicalaspects [1, 2].
v
Inthe presentpaper westudy howthese lightneutralinoscanbe investigatedatthe LargeHadronCollider(LHC),
i
X
which will soon start being operated at CERN [3, 4].
r To this purpose we first delineate what are the main properties of the four neutralino states, χ (i = 1, 2, 3, 4),
a i
in the case when the lightest one, χ (or χ in short), has a mass m < 50 GeV. This neutralino is stable, in case
1 χ
it occurs to be the Lightest Supersymmetric Particle and R-parity is ∼conserved. In particular, special asymptotic
schemes for the four neutralino states are analysed: two hierarchical schemes (with so-called normal and inverted
hierarchy, respectively) and an almost degenerate one.
Once the properties of all the neutralino states are established by analytical and numerical analyses, two main
scenarios are singled out on the basis of the cosmologicalproperties required for the relic neutralinos.
Then,weanalysethesignalsexpectedatLHC,intermsofthe mainchainprocesseswhichareinitiatedbyasquark
andleadfinallytoχ throughanintermediateproductionofχ (i=2,3,4). We evaluatethebranchingratiosforthe
1 i
various processes and discuss their features in terms of the spectroscopic properties (mass spectrum and transitions)
of the four neutralino states. Various benchmarks of special physical interest are considered.
ThetotalnumberofeventsexpectedfortheseprocessesatLHCisestimatedforatypicalrepresentativevalueofthe
integratedluminosity and their relevance for experimental determination of neutralino properties is finally discussed.
The scheme of our paper is the following. The features of the employed supersymmetric model are presented in
Sect. II,wherealsothemainstructuralpropertiesofthefourneutralinostatesaredescribed. InSect. IIIwedelineate
2
the scenarios imposed by cosmology on light relic neutralinos. In Sect. IV we derive branching ratios and the total
number of events expected at LHC. Finally, conclusions are drawn in Sect. V.
II. THE SUPERSYMMETRIC MODEL
The supersymmetric scheme we employ in the present paper is the one described in Ref. [1]: an
effective MSSM scheme (effMSSM) at the electroweak scale, with the following independent parameters:
M ,M ,M ,µ,tanβ,m ,m ,m and A. Notations are as follows: M , M and M are the U(1), SU(2) and SU(3)
1 2 3 A q˜ ˜l 1 2 3
gaugino masses (these parameters are taken here to be positive), µ is the Higgs mixing mass parameter, tanβ the
ratio of the two Higgs v.e.v.’s, m the mass of the CP-odd neutral Higgs boson, m is a squark soft–mass com-
A q˜
mon to all squarks, m is a slepton soft–mass common to all sleptons, and A is a common dimensionless trilinear
˜l
parameter for the third family, A = A Am and A Am (the trilinear parameters for the other families
˜b t˜ ≡ q˜ τ˜ ≡ ˜l
being set equal to zero). In our model, no gaugino mass unification at a Grand Unified (GUT) scale is assumed.
The following experimental constraints are imposed: accelerators data on supersymmetric and Higgs boson searches
(CERN e+e− collider LEP2 [5] and Collider Detectors D0 and CDF at Fermilab [6]); measurements of the b s+γ
→
decay process [7]: 2.89 B(b s+γ) 104 4.21 is employed here (this interval is larger by 25% with respect
≤ → · ≤
to the experimental determination [7] in order to take into account theoretical uncertainties in the supersymmetric
(SUSY) contributions [8] to the branching ratio of the process (for the Standard Model calculation, we employ the
recent NNLO results from Ref. [9])); the upper bound on the branching ratio BR(B0 µ− +µ+) [10]: we take
BR(B0 µ−+µ+)<1.2 10−7; measurements of the muon anomalous magnetic momse→nt a (g 2)/2: for the
s → · µ ≡ µ−
deviation ∆a of the experimental world average from the theoretical evaluation within the Standard Model we use
µ
here the range 98 ∆a 1011 565, derived from the latest experimental [11] and theoretical [12] data.
µ
− ≤ · ≤
A. Composition of the neutralino states
The linear superpositions of bino B˜, wino W˜(3) and of the two Higgsino states H˜◦, H˜◦ which define the four
1 2
neutralino states are written in the following way:
χ a(i)B˜+a(i)W˜(3)+a(i)H˜◦+a(i)H˜◦ (i=1,2,3,4). (1)
i ≡ 1 2 3 1 4 2
These states diagonalize the mass matrix
M 0 m s c m s s
1 Z θ β Z θ β
−
0 M m c c m c s
2 Z θ β − Z θ β , (2)
m s c m c c 0 µ
− Z θ β Z θ β −
m s s m c s µ 0
Z θ β Z θ β
− −
where s sinβ, c cosβ, and s sinθ, c cosθ, θ being the Weinberg angle. The mass eigenvalues (with
β β θ θ
≡ ≡ ≡ ≡
signs) will be denoted by m . The smallest mass eigenvalue m will also be denoted by m .
i 1 χ
| |
From the set of equations
(i) (i) (i)
(M m )a m s c a +m s s a =0
1− i 1 − Z θ β 3 Z θ β 4
(M m )a(i)+m c c a(i) m c s a(i) =0
2− i 2 Z θ β 3 − Z θ β 4
m s c a(i)+m c c a(i) m a(i) µa(i) =0
− Z θ β 1 Z θ β 2 − i 3 − 4
(i) (i) (i) (i)
m s s a m c s a µa m a =0, (3)
Z θ β 1 − Z θ β 2 − 3 − i 4
that follow from the diagonalization of the mass matrix of Eq. (2), one obtains the ratios
a(i) M m
2 = 1− icotθ
a(i) −M2 mi
1 −
3
a(i) m (m c +µs )(s2M +c2M m )
3 = Z i β β θ 2 θ 1− i
a(1i) sθ(M2−mi)(µ2−m2i)
a(i) m c +µs
3 = i β β, (4)
a(i) −µcβ +misβ
4
which, together with the normalization conditions, provide the compositions of the four neutralino states [13].
The LEP lower limit on the chargino mass (mχ± > 100 GeV) sets a lower bound on both |µ| and M2: |µ|,M2 >
100 GeV. Since, on the contrary, M is unbound, the∼lowest value for m occurs when ∼
1 χ
m M << µ,M . (5)
χ 1 2
≃ | |
Thus, χ χ is mainly a Bino, whose mixings with the other interaction eigenstates are readily derived from Eqs.
1
≡
(4) to be
a(1) ξ a(1) m a(1) µs
2 1 cot , 3 s s Z, 3 β , (6)
a(1) ≃ M2 θ a(1) ≃ θ β µ a(1) ≃−M1sβ +µcβ
1 1 4
where ξ m M . Notice that, in deriving Eq. (5), we have also taken into account that in the present paper we
1 1 1
≡ −
will only consider tanβ 10.
≥
From Eqs. (4) one also obtains approximate expressions for the compositions of the eigenstates which correspond
to the asymptotic mass eigenvalues: m µ and m M . That is:
i i 2
∼± ∼
a) for the neutralino states χ with m µ,
i i
≃±
a(i) µ a(i) 2ξ s ( µ M ) a(i) ξ
2 ± cot , 1 2 θ ± − 2 , 3 1+ 2, (7)
a(i) ≃ M2 µ θ a(i) ≃ MZsβ(sθ2M2 µ) a(i) ≃∓ µ
1 ∓ 3 ∓ 4
where ξ µ m .
2 i
≡± −
b) for the neutralino state χ with m M ,
i i 2
≃
a(i) ξ a(i) ξ s (M2 µ2) a(i) µs +M c
1 3 tan , 1 3 θ 2 − , 3 β 2 β, (8)
a(2i) ≃ M2 θ a(3i) ≃ MZ(M2cβ +µsβ)c2θM2 a4(i) ≃−M2sβ +µcβ
where ξ M m .
3 2 i
≡ −
For illustrative purposes, in Figs.1–2 we show the results of the numerical diagonalizationof the matrix of Eq. (2)
versusM , forthe representativepointdefinedby the followingvaluesofthe other supersymmetricparameterswhich
2
enter in the mass matrix of Eq. (2): M = 25 GeV, µ = 300 GeV, tanβ = 10. Fig. 1 displays the behaviour of the
1
mass eigenvalues m , Fig. 2 the compositions of the states χ .
i i
| |
The approximate analytic expressions in Eqs. (6-8) and the numerical results in Fig. 2 display quantitatively the
followingproperties: (i)χ ismainlyaB-inowhosemixingwithH˜◦ issizableatsmallµ,(ii)χ hasamass m µ
with a large H˜◦ H˜◦ mix1ing, independently of M , (iii) χ and χ1 interchange their main st3ructures dep|end3|in≃g|on|
the value of th1e −ratio2 µ/M : χ is dominantly a W2 -ino (w2ith a si4zable subdominance of H˜◦) for M << µ and a
maximalH˜◦ H˜◦ adm|ix|tur2e for2M >> µ, whereas χ is a maximal H˜◦ H˜◦ admixture fo1r M <<2 µ an|d|a very
1 − 2 2 | | 4 1 − 2 2 | |
pure W-ino for M >> µ. Also their properties relevant to the case M µ are transparent from Eqs. (6-8) and
2 2
| | ∼ | |
Fig. 2.
Depending on the relative values of the parameters M and µ, it is useful, for the discussion to be developed later,
2
to define the following neutralino spectroscopic schemes (notice that we always assume (M <<M , µ): (i) normal
1 2
| |
hierarchical scheme (M < µ), (ii) degenerate scheme (M µ), (iii) inverted hierarchical scheme (M > µ).
2 2 2
| | ∼ | | | |
These schemes are depicted in Fig. 3.
4
FIG. 1: Neutralino masses as functions of M2 for M1 =25 GeV, µ=300 GeV and tanβ=10. .
FIG. 2: Compositions of the neutralino states χi as functions of M2 for M1 = 25 GeV, µ = 300 GeV and tanβ =10. Up–
left panel: χ1, up–right panel: χ2, bottom–left panel: χ3, bottom–right panel: χ4. Solid lines denote ai1 , dotted lines ai2,
| | | |
short–dashed lines ai3 , long–dashed lines ai4 . .
| | | |
5
FIG. 3: Asymptoticspectroscopic schemes for the χi (i=1,2,3,4) neutralino states .
B. Cosmological properties
As discussed in Ref. [1], under the assumption that R-parityis conserved,the lower bound on the neutralino mass
m is provided by the upper bound on the relic abundance for cold dark matter (CDM), Ω h2.
χ CDM
We recall that the neutralino relic abundance is given by
x 3.3 10−38 cm2
Ω h2 = f · , (9)
χ g⋆(xf)1/2 <σannv >
g
where <σ v > x σ v , σ v being the integral from the present temperature up to the freeze-out
ann f ann int ann int
≡ h i h i
temperaturgeTf ofthethermallyaveragedproductoftheannihilationcross-sectiontimestherelativevelocityofapair
of neutralinos,x is defined as x mχ andg (x ) denotes the relativistic degrees offreedom ofthe thermodynamic
f f ≡ Tf ⋆ f
bath at x . For σ v we use here the standard expansion in S and P waves: σ v a˜+˜b(2x )−1.
f ann ann f
h i h i≃
A host of cosmoglogical observations imply that the cold dark matter content hgas to stay in the range 0.092
≤
Ω h2 0.124 [14]. Thus the supersymmetric configurations have to satisfy the cosmological constraint Ω h2
CDM χ
≤ ≤
(Ω h2) =0.124.
CDM max
III. SCENARIOS FOR LIGHT NEUTRALINOS
In Ref. [1] it is shown that the cosmologicalcondition Ω h2 (Ω h2) =0.124 provides a lower limit m >
χ CDM max χ
≤
∼
7 GeV. Such a situation occurs when M 10 GeV and σ v a˜ receives a sizable contribution by the exchange
1 ann
∼ h i≃
ofthe AHiggsbosoninthe s channel. This, inturn, happengs when the two followingconditionsare met: a)m is as
A
small as its experimental lower bound, m =90 GeV, b) the B-ino component of the χ configuration is maximally
A 1
mixed with the H˜◦ component (i. e. a(31) 0.4). From the second expression in Eq. (6) one sees that condition (b)
1 a(1) ≃
1
is satisfied when µ is small (µ 100-200GeV). Moreover,it turns out that tanβ must be large (tanβ 30 - 45) in
| |∼ ∼
orderforthe annihilationcrosssectionthroughthe exchangeofthe A Higgsbosonto be sizable. Finally, the trilinear
coupling is mildly constrained to stay in the interval 1<A<+1.
−
In the following we will characterize such a set of sup∼ersym∼metric parameters as Scenario . More specifically,
A
this scenario is identified by the following sector of the supersymmetric parameter space: M 10 GeV, µ (100 -
1
∼ | |∼
200)GeV, m 90 GeV, tanβ 30 - 45,-1 <A<+1; the other supersymmetric parameters are not a priori fixed.
A
∼ ∼
From Eqs. (6) it turns out that, in this scen∼ario∼, the following hierarchy holds for the coefficients a(1) of χ
i 1
a(1) > a(1) >> a(1) , a(1) . (10)
| 1 | | 3 | | 2 | | 4 |
It is proved in Ref. [1] that at small mχ, when m > (200 - 300) GeV, the cosmological constraint Ω h2
A χ
≤
(Ω h2) is satisfied because of stau-exchangecontrib∼utions (in the t, u channels)to <σ v >, providedthat:
CDM max ann
g
6
scenario M1 [GeV] |µ| [GeV] tanβ mA [GeV] m˜l [GeV]
10 100–200 30–45 90 –
A ∼ ∼
25 >500 <20 >200 100–200
B ∼
∼ ∼ ∼
TABLE I: Scenarios for light neutralinos as described in Section III. In scenario A the slepton soft mass m˜l is unconstrained:
in our analysis a few representative values for m˜l are considered within its natural range 115 GeV ≤m˜l ≤ 1 TeV. Moreover,
in scenario : -1 <A<+1, in scenario : -2 <A<+2.
A B
∼ ∼ ∼ ∼
(i) m is sufficiently light, m 90 GeV (notice that the current experimental limit is m 87 GeV) and (ii) χ is
τ˜ τ˜ τ˜ 1
∼ ∼
a very pure B-ino (i.e. (1 a(1)) = O(10−3). In such a situation, the lower limit on the neutralino mass is mχ> (15
− 1
- 18) Gev [15]. ∼
Let us first discuss the implications of the prerequisite (i). The experimental lower bounds on the sneutrino mass
and on the charged slepton masses of the first two families imply a lower bound on the soft slepton mass: m > 115
˜l
GeV.Inordertomakethe requestm 90GeV compatiblewithm >115GeV,itis necessarythatthe off-dia∼gonal
τ˜ ∼ ˜l
terms of the sleptonic mass matrix in the eigenstate basis, which are∼proportional to µtanβ, are large. Numerically,
one finds µ tanβ 5000 GeV.
| | ∼
On the other side, the condition (ii) requires that a(1)/a(1) < 10−1, i. e., according to the second expression of
3
Eq. (6), a(31) s s mZ <10−1. Combining this last expressio∼n with the condition µ tanβ 5000 GeV, one finds
a(1) ≃ θ β µ | | ∼
1 ∼
that µ and tanβ are bounded by: µ > 500 GeV, tanβ < 10. These bounds are somewhat weaker for values of the
| | | |
neutralino mass larger than 15–18 G∼eV. ∼
∼
The previous arguments lead us to introduce a new scenario, denoted as Scenario , identified by the following
B
sector of the supersymmetric parameter space: M 25 GeV, µ > 500 GeV, tanβ < 20; m > (100 - 200) GeV,
1 ∼ | | ˜l
2.5<A<+2.5; the other supersymmetric parameters are not a pr∼iori fixed. ∼ ∼
−
Fro∼m Eq∼s. (6) it turns out that, in this scenario, the following hierarchy holds for the coefficients a(1) of χ
i 1
(1) (1) (1) (1)
a >> a , a , a . (11)
| 1 | | 3 | | 2 | | 4 |
The features of scenarios and are summarized in Table I.
A B
IV. SIGNALS AT LHC
If kinematically accessible, squarks and gluinos are expected to be copiously produced in the pp scattering process
at the LHC. In the present paper we limit our discussion to the case in which the gluino is heavier than the squark;
for definiteness, we set the SU(3) gaugino mass at the representative value M = 2 TeV and the squark soft-mass at
3
the value m = 1TeV. Notice that these twoparametersareirrelevantin the specificationofthe scenariospreviously
q˜
defined.
Many experimental studies are available showing that the production of 1 TeV squarks can be easily discoveredat
the LHC through inclusive analysesbased on the request of a high multiplicity of hard jets ant Emiss, see e.g [3] and
T
[4].
In order to check the supersymmetric model described in the previous sections, the SUSY parameters need to be
measured. For this purpose, we employ here a strategy which has been developed for the measurement of the masses
ofthe SUSYparticlesbasedonthe identificationofexclusivedecaychainsconsistinginsequencesoftwo-bodydecays
[3, 16, 17, 18] . The most promising decay chains considered in the literature are:
q˜ qχ qf˜f qf¯fχ (sequential chain), (12)
i 1
→ → →
and
q˜ qχ q(Z,h,H,A)χ qf¯fχ (branched chain), (13)
i 1 1
→ → →
7
wheref standsforafermion,andtheneutralinosubscripticantakethevalues2,3or4. Fromtheexperimentalpoint
ofview,giventhelargemultiplicityofQCDjetspresentinppevents,theonlyinterestingdecayswhichcanbeusedfor
the identification of exclusive chains are the ones involving light charged leptons (e and µ), the hadronic decays of τ
(τ-jets) andthe fragmentationofb quarks(b-jets), whichcanbe experimentally separatedfromthe background. The
sequentialchainwithtwoe orµinthe finalstate is particularlyuseful, as the wholechainconsistsofthree successive
2-body decayswhich canbe measuredverywell, andprovides enoughconstraints to allow a model-independent mass
determination. Thesequentialchainwithtwoτ-jetsallowsamuchlesscleanmeasurement,asneutrinosareproduced
in the decay of the τ which make the event kinematic less clear, and a much higher jet background is present. It
is however important to detect this chain as well, because by comparing its rate with the rate for the e, µ chain,
informationcanbe extractedonthe τ˜ mixing [19]. Finally, the branchedchainprovidesless constraintsonthe SUSY
masses,astheinvariantmassofthetwofinal-statefermionsjustshowsapeakatthevalueoftheresonanceappearing
inthedecay. Inthiscasetheexperimentallyinterestingdecaysaretheonesinbpairs,especiallyfortheHiggsbosons,
and in e and µ for the Z.
Thesetwodecaychainshaveincommonthefirststepconsistinginthesquarkdecayq˜ qχ . Twotypesofcouplings
i
→
occurinthisprocess: (a)gaugecouplings,universalinthequarkflavor,and(b)Yukawacouplings,hierarchicalinthe
quark mass. Gauge (Yukawa) couplings are proportional to the gaugino (Higgsino) components in χ , respectively.
i
The actual number of the qχ states produced in a pp collision depends on the product of the cross section for the
i
production process σ(pp q˜q˜,q˜q˜∗,g˜g˜,q˜g˜) times the branching ratio BR(q˜ qχ ). In this product the contribution
i
→ →
of the heavy quarks is strongly suppressed, because of their scarcity in the proton composition. Moreover, since the
relative importance of the Yukawa couplings as compared to the gauge couplings depends on the ratio m /m (m
q Z q
and m being the quark mass and the Z-boson mass, respectively) the production of χ is more sizable when gauge
Z i
couplingsareeffective,i. e. whenχ haslargegauginocomponents. Toaccountforthesepropertiesitisconvenientto
i
defineaneffectivebranchingratioBR(q˜ qχ ),i. e. anaverageofthebranchingrationsBR(q˜ qχ )’soverthelight
i i
→ →
quarks [20], including both q˜ and q˜ . To be conservative, we will use as an effective branching ratio BR(q˜ qχ )
R L i
→
the average over the four lightest quarks. From now on we will simply denote this average as BR(q˜ qχ ).
i
→
We turn now to a discussion of the decay process for χ , which takes different routes in sequential and branched
i
chains, respectively. In the sequential case, since we have taken m = 1 TeV, the decay can only proceed through
q˜
a slepton: χ ˜ll ¯llχ with a branching ratio BR(χ ˜ll ¯llχ ) = BR(χ ˜ll) BR(˜l lχ ). The size of
i 1 i 1 i 1
BR(χ ˜ll) d→epend→s sensitively on the χ composition. If→χ is→dominantly a gau→gino, becaus→e of the universality
i i i
of the g→augino couplings, the branching ratios BR(χ ˜ll) for the three lepton flavours are about the same ; if χ
i i
→
is dominantly a Higgsino, χ decays predominantly into a τ˜τ pair. In the branched chain χ decays either through
i i
the Z-boson or through a Higgs boson. The first case, i. e. χ Z +χ , involves only the Higgsino components
i 1
of the two neutralino states; the Z boson subsequently decays int→o all (kinematically possible) f¯f pairs according to
the Standard Model branching fractions. The second case, i. e. χ (h,A,H)+χ , in order to have a sizable BR,
i 1
→
requires that one neutralino state is dominantly a gaugino, the other dominantly a Higgsino. Since in our scenarios
χ is dominantly a B-ino state, χ (h,A,H)+χ is of interest when χ is dominated by the Higgsino components.
1 i 1 i
→
BecauseofthehierarchicalcharacteroftheYukawacoupling,thesubsequentdecaysoftheHiggsbosonsaredominated
by the production of a b – ¯b pair. We note that in the case of a pronounced hierarchical (inverted) scheme (see Fig.
3) the direct χ (h,H,A,Z)χ decay is suppressed because both χ and χ are dominantly gauginos. This entails
4 1 4 1
→
that the “long” chains χ (h,H,A,Z)χ (h,H,A,Z)χ can give a sizable contribution. Indeed, for both the
4 2,3 1
sequential and branched d→ecays, longer multi→-step decay chains, of the type e.g. χ Xχ XX′χ , are in
4 2,3 1
→ →
principle very interesting as they provide additional kinematic constraints. In practice, the superposition of many
decayswiththe samefinalstatemaybe extremelydifficulttodisentangleexperimentally,andwillthusaddconfusion
rather than information. For this study we will therefore limit ourselves to studying the branching ration for direct
decays.
In the following sections, for the sequential decays we will consider the two cases f =e,τ. We will first analyze e,
for which the two chirality states e˜ and e˜ will be considered separately. The decay χ ee˜is largely dominated
R L i
→
by the gaugino components in χ ; thus, if the χ decays into both e˜ and e˜ are kinematically allowed, the ratio
i i R L
of the two branching ratios scales approximately as BR(χ ee˜ )/BR(χ ee˜ ) 1/4(1+cot a(i)/a(i))2, where
i → L i → R ≃ θ 2 1
a(i)/a(i) can be approximated by Eqs. (7,8). This implies that χ decays dominantly to e˜ when it is a pure wino
2 1 i L
(a(i)/a(i) 1), while either of the two selectron final states e˜ may be important for other compositions. For the
2 1 ≫ L,R
τ case we will consider both the mixed (eigenmass) states τ˜ and τ˜ . The presence of both states in the decay can
1 2
be hard to disentangle, and thus make the mass and rate measurements more difficult. For the branched decays we
8
FIG.4: Qualitativeschemesforbenchmarksinsequentialdecaychains: –seq1, –seq2, –seq. Foreachbenchmark,extremes
A A B
values for M2 are considered: M2 µ and M2 > µ for scenario ; M2 < µ, M2 µ and M2 > µ for scenario . .
∼| | | | A | | ∼| | | | B
benchmark M1 [GeV] µ [GeV] tanβ mA [GeV] m˜l [GeV]
–seq1 10 110 35 90 150,300,500,700
A
–seq2 10 150 35 90 120
A
–brc 10 110 35 90 150
A
–seq 25 -500 10 1000 120
B
–brc1 25 -500 10 200 120
B
–brc2 25 -500 10 1000 120
B
TABLE II: Benchmarks for light neutralinos, singled out within the two scenarios and of Table I. All results will be
A B
presentedasfunctionsofM2,M2 beingvariedintherange100GeV M2 1000 GeV.Theothersupersymmetricparameters
≤ ≤
are set at therepresentative values: M3 = 2 TeV, mq˜= 1 TeV, A = 0.
consider the decay into b pairs for the Higgs bosons and the decays into b and e pairs for the Z. In most of the
consideredmodels the Z andthe SUSY Higgsesare almostdegenerate,and, giventhe experimentalresolutionon the
b¯b peak, cannot be separated. It is therefore very useful to have also the decay into leptons, which will allow the
experiments to determine the presence of SUSY Higgses in the decay chains.
Based on this discussion, we report our numerical results for all the decay branching ratios relevant for the decay
chains of Eqs. (12- 13) in a number of benchmarks within the scenarios and , previously defined (see Table II).
A B
In these benchmarks,all values of the supersymmetric parameters,except M , are fixed. The branching ratios,given
2
as functions of M , have been calculated by using the ISASUSY code[21],
2
A. Sequential chain benchmarks
In scenario the parameter µ is required to be µ (100-200)GeV, while slepton masses are unconstrained. On
A | | ∼
the other hand the sequential chain is sensitive to the hierarchy between µ and m , since, when m > µ, the decay
| | ˜l ˜l | |
of the χ states is not allowed by kinematics, and the process (12) can proceed only through χ . On the contrary,
2,3 4
when m < µ, the three states χ (i=2,3,4) take part in the chain (12).
˜l | | i
We then fix the following benchmarks for scenario :
A
seq1: µ=110GeV m =150,300,500,700GeV (14)
A− ˜l
seq2: µ=150GeV m =120GeV, (15)
A− ˜l
where,inbothcases,M =10GeV,tanβ=35,m =90GeVandA=0. Thesetwobenchmarksaredepictedqualitatively
1 A
in Fig.4 and summarized in Table II.
For the benchmark –seq1 the branching ratios for the sequential decay chain are shown in Figs.5,6 where, as
A
already mentioned, only the decay of χ is kinematically allowed. Each panel of the figure corresponds to a different
4
value of m among those of Eq.(14): m =150, 300,500,700 GeV. The notations for the various curves are explained
˜l ˜l
in the figure caption.
The main features of Figs.5 and 6 are readily understood. The Branching Ratio (BR) for q˜ qχ is 15%, since
4
→ ∼ ±
the χ is dominantly wino, and therefore the q has no BR into it, and the q˜ decays 60% into a chargino χ and
4 R L 2
30% into χ , according to the left-handed couplings of the wino. In the regime M >> m , the χ decays with 40%
4 2 ˜l 4
BR into W, Z and Higgses because of its non-zero Higgsino component, 60% BR into the left-handed sleptons. So
9
FIG.5: Branchingratiosforthesequentialprocessq˜ e¯eχ1 inbenchmark –seq1asfunctionsofM2. Eachpanelcorresponds
→ A
to a different value of m˜l. The dashed lines show the branching ratio for the process q˜→ qχ4; the thin–dotted lines denote
the branching ratio for the process χ4 ee˜L ee¯χ1; the thick–dotted line in the top–left panel denotes the branching ratio
→ →
for theprocess χ4 ee˜R ee¯χ1 (thecorresponding curvescannot be seen in theother panels because they are too low); the
→ →
thick solid lines denotethe branchingratio for the whole sequential decay chain q˜ qχ4 qee˜ qee¯χ1.
→ → →
for e˜ the BR is 10%. For each of the two τ˜ states, which are in this case rather similar in composition and mass,
L
∼
the BR is 5% for each state. For instance, for m = 150 GeV: m = 133 GeV, m = 176 GeV and for m = 300
∼ ˜l τ˜1 τ˜2 ˜l
GeV: m = 192 GeV, m = 314 GeV.
τ˜1 τ˜2
The different quadrants of Figs. 5 and 6 show by how muchthe branchingratios are suppressedfor growingvalues
of m , due to the reduction ofthe availablephase space for the decay χ l˜l. On the other hand, a growingvalue of
m d˜loesnot affectBR(˜l lχ ), whichis verycloseto 1 in allcases. No4te→thatinthis benchmarkwheneverM > µ
˜l → 1 2 | |
one has m M , thus a measurement of m would typically give direct access to the value of M . ∼
χ4 ∼ 2 χ4 2
Thephenomenologyofthesequentialdecaybecomesricherinthe benchmark –seq2,whichis showninFigs.7and
A
8. In fact in this case the process (12) can proceed through the production and decay of any of the χ states. The
i
corresponding separate contributions to the decay branching ratios for i=2,3,4 are shown in each of the first three
panels of Figs.7 and 8 while the last panel shows the combined total branching ratios.
Thebranchingratiosfortheprocessq˜ qχ ,showninthebottom-leftpanelofFigs.7–8,areobviouslyverysimilar
4
→
theonesalreadydisplayedinFigs.5–6,andpreviouslycommented. Ascomparedtothese,thebranchingratiosforthe
processes q˜ qχ (i=2,3) are somewhat suppressed, due to the prevalent Higgsino compositions of χ ,χ . For the
i 2 3
→
same reason,the BR of χ and χ into e , is at most a couple of percent. The contrary happens for the branching
2 3 L,R
ratios BR(χ τ˜τχ ). In this case χ ,χ decay into τ˜τ with larger BRs than χ , because the dominance of the
i 1 2 3 4
→
Higgsinocomponentsinχ ,χ favorstheirdecaysintothirdgenerationleptons. Noticethatinthecaseofχ ,onlythe
2 3 2
lighterstaucontributes,sinceτ˜ isheavierthanχ ;inthecaseofχ ,theτ˜ contributionisverystronglysuppressedas
2 2 3 2
10
FIG.6: Branchingratiosforthesequentialprocessq˜ τ¯τχ1inbenchmark –seq1asfunctionsofM2. Eachpanelcorresponds
→ A
toadifferentvalueofm˜l. Thedashedlinesshowthebranchingratiofortheprocessq˜→qχ4;thethin–dottedlinesdenotethe
branchingratiofortheprocessχ4 ττ˜1 ττ¯χ1;thethick–dottedlinesdenotethebranchingratiofortheprocessχ4 ττ˜2
→ → → →
ττ¯χ1; thethin–solid lines denote thebranchingratio for thewhole sequentialdecay chain q˜ qχ4 qττ˜1 qττ¯χ1; thesolid
→ → →
lines with intermediate thickness denote the branching ratio for the whole sequential decay chain q˜ qχ4 qττ˜2 qττ¯χ1;
→ → →
thethickest solid lines denote thetotal branchingratio for the whole sequential decay chain q˜ qχ4 qττ˜ qττ¯χ1.
→ → →
comparedto the τ˜ contributionagainfor phase–spacereasons. All in all, in the full process q˜ qχ qτ˜ qττ¯χ ,
1 i 1
→ → →
the most relevant contribution turns out to be provided by χ .
2
Thescenario ischaracterizedbyaheavypseudoscalarHiggsmass(m >200GeV)andbyaverylightstau,which
A
B
is required in order to keep the neutralino relic abundance below the obse∼rvational limit. Moreover, as explained in
SectionIIB, µ mustbe large. We define inthis casethe following benchmark,correspondingto the lightest possible
| |
mass of the neutralino χ :
1
seq : M =25GeV µ= 500GeV tanβ =10
1
B− −
m =87GeV (m =120GeV) A=0. (16)
τ˜ ˜l
ThisbenchmarkisdepictedqualitativelyinFig.4andsummarizedinTableII. Thebranchingratiosforthisbenchmark
areshowninFigs. 9–10. InthiscasethepossiblehierarchybetweenM and µ isricherthaninthepreviousbenchmark
2
| |
-seq1, since now also M << µ can occur. In particular, this implies that the compositions of χ and χ flip the
2 2 4
A | |
one into the other in going from M < µ to M > µ (an example of this behaviour can be seen in Fig.2, although
2 2
| | | |
for a slightly different set of supersymmetric parameters). Here, for M < 500 GeV, χ is mainly a gaugino,whereas
2 2
χ is dominantly a Higgsino; the other way around, for M > 500 GeV. While χ and χ exchange their roles as M
4 2 2 4 2
runs over its range,χ is steadily a Higgsino, independently of M . On the basis of these properties one understands
3 2
