Measuring a Light Neutralino Mass at the ILC: Testing the MSSM Neutralino Cold Dark Matter Model

0.19 MB·English

by  John A. Conley

BONN-TH-2010-12
BONN-HE-2010-01
Measuring a Light Neutralino Mass at the ILC: Testing the MSSM Neutralino Cold
Dark Matter Model
J. A. Conley
∗
Physikalisches Institut and Bethe Center for Theoretical Physics,
Universita¨t Bonn, Nußallee 12, 53115 Bonn, Germany
H. K. Dreiner
†
Physikalisches Institut and Bethe Center for Theoretical Physics,
Universita¨t Bonn, Nußallee 12, 53115 Bonn, Germany and
SCIPP, University of California, Santa Cruz, CA 95064
P. Wienemann
‡
Physikalisches Institut, Universita¨t Bonn, Nußallee 12, 53115 Bonn, Germany
TheLEPexperimentsgivealowerboundontheneutralinomassofabout46GeVwhich,however,
relies on a supersymmetric grand unification relation. Droppingthis assumption, theexperimental
lowerboundon theneutralinomassvanishescompletely. Recentanalyses suggest, however,that in
1 theminimalsupersymmetricstandardmodel(MSSM),alightneutralinodarkmattercandidatehas
1 a lower bound on its mass of about 7 GeV. In light of this, we investigate the mass sensitivity at
0 the ILC for very light neutralinos. We study slepton pair production, followed by the decay of the
2 sleptons to a lepton and the lightest neutralino. We find that the mass measurement accuracy for
n a few-GeV neutralino is around 2 GeV, or even less if the relevant slepton is sufficiently light. We
a thusconclude that theILC can help verify or falsify theMSSMneutralino cold dark matter model
J even for very light neutralinos.

4

] I. INTRODUCTION Within the MSSM the spin–1/2 superpartners of the
h hypercharge B boson, the neutral SU(2) W boson and
p
the two CP–even neutral Higgs bosons mix after elec-
-
p The supersymmetric StandardModel (SSM) [1,2] is a troweak symmetry breaking. The resulting four mass
e well motivated extension of the Standard Model of par- eigenstates are the neutralinos and are denoted χ0i, i =
h ticle physicswhichsolvesthe hierarchyproblembetween 1,...,4. ThemassesareorderedMχ0<...<Mχ0. Ifpro-
[ 1 4
the weak scale and the Planck scale [3, 4]. In order to duced at colliders, the lightest neutralino behaves like a

2 guarantee a stable proton, usually a discrete symmetry heavy stable neutrino and escapes detection. The spin–
v beyond the SM gauge symmetries is imposed which pro- 1/2 superpartners of the charged SU(2) W boson and of
5 hibitsthe baryon–andlepton–numberviolatingtermsin the chargedHiggsbosonalsomix after electroweaksym-
3
the superpotential: R–parity [5], proton hexality [6], or metry breaking. The resulting mass eigenstates are the
0
1 a Z4 R–symmetry [7]. This is then called the minimal charginos and denoted χ±i=1,2, with ordered masses. See
. supersymmetric Standard Model (MSSM). The discrete Appendix A for details.
2 symmetry furthermore guarantees that the lightest su- The current Particle Data Group (PDG) mass bound
1
persymmetric particle (LSP) is stable and thus a dark from LEP on the lightest neutralino is [22–25]
0
1 matter candidate [8–11]. If it is to constitute the en-
M > 46 GeV. (1)
v: tire dark matter in the universe it must be electrically χ01
and color neutral [8]. Here we focus on the lightest neu-
i This bound is obtained by searching for charginos and
X tralino χ0 as the LSP. In order to avoid overclosure of
1 thussetting aboundonthe SU(2)gauginomassM and
2
r the universe, the neutralino must be either very light
the Higgs mixing parameter µ. Using the supersymmet-
a
M < (1eV) (Cowsik–McLelland bound) [12, 13] or
χ01 O ric grand unified theory (SUSY GUT) relation between
heavy M > (10GeV) (Lee–Weinberg bound) [14].
χ01 O M2 and the U(1)Y gaugino mass term M1
We shall make this latter lower bound more precise [15–
21]. In this paper we are interested in how a neutralino 5
M = tan2θ M , (2)
mass close to the Lee–Weinberg bound could be mea- 1 3 w 2
suredatthe ILC. This is potentially a stringenttestof a
the chargino search can be translated into a bound on
MSSM light dark matter model.
M . The neutralino mass matrix is computed for all al-
1
lowed values of the supersymmetric parameters, taking
into account Eq. (2), as well as the lower bound on the
ratio of the Higgs vacuum expectation values, tanβ &2,
∗[email protected]
†[email protected] from the LEP Higgs search [25]. Then one obtains as
‡[email protected] thelowestpossibleneutralinomasstheboundinEq.(1).
2
If, however, the assumption Eq. (2) is dropped, there is evidencefornon-minimalsupersymmetricmodelsand/or
no lower laboratory or astrophysical bound on the neu- non-standard cosmologies.
tralino mass [13, 26–32]. Even a massless neutralino is Thepaperisorganizedasfollows. InsectionII,wepro-
allowed. This is now included in the PDG as a comment vide an overview of some of the methods that have been
[33]. There is however a cosmological bound which we suggestedto measure the lightest neutralino mass at the
now discuss. ILC. We then focus, in Section III, on the neutralino
Relaxing the SUSY GUT assumption in Eq. (2), it mass measurement that can be done using slepton pair
is possible to derive the Lee–Weinberg lower limit on production, and make a first estimate of the accuracy of
the mass of the neutralino LSP, Mmin, in the MSSM this method for a very light neutralino. In Section IV,
χ0
with real parameters. It was first det1ermined for large wedescribeasimulationofsleptonpairproductionatthe
pseudoscalar Higgs masses [15, 16], obtaining Mmin = ILC,anduseittomakeabetterdeterminationoftheac-
χ0
1 curacy attainable for the neutralino mass measurement.
(15GeV). It was subsequently realized however [17,
O We summarize and conclude in Section V.
18], that a region of parameter space exists with a low
pseudoscalar Higgs mass and high tanβ, in which the
neutralinolowermasslimitreachesMmin 6 GeV. This
χ01 ≈ II. NEUTRALINO MASS MEASUREMENTS
is due to an enhancement in the neutralino annihila-
tioncrosssectionfromannihilationtob-quarksviaHiggs
bosons,whichkeepsthepredictedrelicdensitybelowthe Several methods have been suggested in the literature
observedlimits. ThiswasconfirmedinRef.[34]. Thereit tomeasurethemassofthelightestneutralinoattheILC
was furthermorenoted that this areaof parameterspace [64–68]. Throughout,theauthorshavefocusedonaneu-
wouldbe testable atthe Tevatron,for example,with the tralinoheavierthantheLEPboundinEq.(1). Forexam-
HiggssearchresultsinwhichtheHiggsisproducedinas- ple,thewidelystudiedSPS1apoint(withoutaslope)[69]
sociation with a b-quark, as well as via the Bs µ+µ− has Mχ0 =97.1 GeV. The most straightforwardmethod
→ 1
limit. See also the more recent work in Ref. [35–38]. In involvesconsideringsleptonpairproduction,followedby
a very recent paper [39], the authors argue that these the decay of each slepton to the lightest neutralino and
constraints have a relatively minor impact on the light a charged lepton
neutralino parameter space of the MSSM [83], and that
the lower bound is e+e− → ℓ˜−ℓ˜+ →ℓ−ℓ++2χ01, ℓ=e, µ. (4)
Mmin 7 8 GeV. (3) Herethe (s)leptons arerestrictedto the firsttwogenera-
χ01 ≈ − tions. Themeasurementviathethirdgeneration(s)tauis
Recently there has also been an increased interest in diluted by the additional decay to the neutrino(s). Mea-
lightdarkmattercandidateswithamassoforder5GeV suring the energies of the final state leptons, one can ex-
due to the DAMA/LIBRA [40] and CoGeNT [41] direct tract information on the neutralino and slepton masses.
search results. Ref. [42] suggests that the required scat- The typicalrelativeprecisionachievedis in the per mille
tering cross sections in the detectors cannot be obtained range [64, 66–68]. We go beyond this work and discuss
within the MSSM, though in Ref. [39] it is claimed that this method in detail for a very light neutralino.
the current constraints do in fact allow sufficiently high A secondmethod in the literature is basedonthe pair
crosssectionsfortheseexperimentalhintstobeexplained production of the second lightest neutralinos. This is
by an MSSM neutralino. In the NMSSM, it is similarly followed by the decay of each neutralino via a (virtual)
claimed in Ref. [43, 44] that high cross sections cannot slepton to a charged lepton pair and the lightest neu-
be obtained, though Refs. [45, 46] identify regions of pa- tralino,
rameter space in this model in which the presence of a
light singlet Higgs can lead to large enough cross sec- e+e− → χ02χ02 →(χ01ℓ+1ℓ−1)(χ01ℓ+2ℓ−2). (5)
tions. The authors of Refs. [47] arguethat solutions also
exist for an extended NMSSM. The experimental results where each χ02 decays independently and thus ℓ1 need
in Refs. [40, 41] have lead to a flourish of alternative not equal ℓ2. In fact, the case ℓ1 = ℓ2 reduces the com-
6
schemes,e.g.[48–58]. Wenote,however,thatthesemod- binatorialuncertainty. In Refs. [70, 71] the authors then
els are severelyconstrainedby the CDMS-II [59, 60] and propose to measure the di-lepton invariantmass and the
XENON10 [61] and XENON100 data [62, 63]. di-lepton energy and to use these to measure the two
Given these considerations it is thus of great interest lightest neutralino masses.
how well the neutralino mass can be determined in the Of necessity these methods also always involve other
low-mass region. It is the goal of this paper to test the supersymmetric particles and their masses. For exam-
sensitivityofthemassmeasurementattheILC.Thereis ple,thefirstmethodreliesontheproductionofsleptons.
the possibility that a neutralino mass will be measured Thesecondmethodreliesontheproductionofthesecond
which is too small to be reconciled with the observed lightestneutralino andthen its decay to an intermediate
relic abundance, if the realMSSM and standard cosmol- slepton. Thus both of these methods can be improved
ogyareassumed. Suchameasurementwouldbe striking by measuring the corresponding supersymmetric masses
3
directly. Forexamplethesleptonmasscanbewelldeter- expectthe accuracyofthe neutralinomassmeasurement
mined by an energy scan over the slepton mass thresh- todeteriorateforsufficientlysmallneutralinomasses. We
old [70]. Similarly a scan over the production threshold set out to quantify this below.
energy of the process given in Eq. (5) gives a tight con- Limited statistics and detector and beam effects in-
straint on the mass Mχ0 [70]. troduce uncertainty into the endpoint determination.
2
Nonetheless, for typical slepton and heavy neutralino
masses,the endpointsandthe massescanbe determined
III. SLEPTON PAIR PRODUCTION AND THE to sub-GeV accuracy [67]. For very light neutralinos,
NEUTRALINO MASS however,evensmallerrorsintheendpointmeasurements
canleadtoalargefractionalerrorintheneutralinomass
Inthissection,westudythemeasurementofthelight- determination.
est neutralino mass using slepton pair production at the Beforestudyingthisissuewithasimulation,wecanes-
ILC, as shown in Eq. (4). The slepton decay to a lepton timate the mass determination accuracy for a light neu-
and the lightest neutralino is a two-body decay. There- tralinobycombiningthequotedaccuracyfromanexper-
fore in the slepton rest-frame the lepton energy is com- imental study by Martyn [67] with a simple error analy-
pletely fixed by the slepton and neutralino mass. Ig- sis. Assuming that E and E are independent random
+
noring initial and final state radiation (ISR and FSR), variables, then from Eq. (10)−we can derive
beamstrahlung,and detector effects for the moment, the
slelepptotonn’selnaebr-gfryamisethenenergjuystEthies bfuelalymdeenteerrmgyi.neTdhbuys tthhee δMχ01 = δMℓ˜Mχ01 Mℓ˜2 . (11)
angle θ0, with which the slepℓton emits the lepton in the δE± δE± Mℓ˜ − Mχ01√s
slepton rest-frame. The angle is measured with respect
Forlightneutralinos,the firstterminEq.(11)isnegligi-
to the slepton lab momentum direction. We then have
ble. The second term dominates and is identical for E
for the lepton energy +
and E , so we can write
−
E = √s 1 Mχ201 (1+βcosθ ). (6) M2
ℓ 4 − Mℓ˜2 ! 0 δMχ01 ≃ Mχ0ℓ˜√s δE+2 +δE−2 . (12)
1 q
Here β = 1 4m2/s is the slepton velocity in the lab
− ℓ˜ In the simulation we describe below, we consider SUSY
frame, √sq/2 is the beam energy, and Mℓ˜ denotes the scenarios with Me˜R = 100 and 200 GeV and varying
sleptonmass. TheeventdistributionofEℓisflatbetween Mχ0, a center-of-mass energy √s = 500 GeV and an
1
its maximum E+, when cosθ0 = 1, and its minimum integrated luminosity =250 fb−1. For illustration, we
E , when cosθ0 = 1. The equations for E+ and E hereassumetheseexpeLrimentalparametersaswellasa2
ca−nbeinvertedtofin−dthesleptonandneutralinomasse−s GeVneutralinomassand100GeVselectronmass. Thus
squared in terms of these endpoints, the factor in front of the square root in Eq. (12) is 10.
InRef.[67],theerrorontheendpointdeterminationsis
E E
Mℓ˜2 =s(E+++E− )2 , (7) ngiavreinowasitδhEM+ ==0.1913GGeeVV,aMndδ=E1−4=3G0e.0V2,Ge=V2fo0r0afbsce1-,
− χ01 ℓ˜ L −
and and √s = 400 GeV. In this scenario, because the neu-
tralinoisheavythetwotermsinEq.(11)arecomparable,
E +E
Mχ201 =Mℓ˜2 1− +√s/2− . (8) soobtwaiencδaMnnot us1e00EMq.e(V1,2)w.hUicshinaggrEeeqs. e(1x1a)ctilnystweiatdh,twhee
(cid:18) (cid:19) χ01 ≃
quoted result of the detailed study in Ref. [67].
Wehavelistedthesquaredformulæforlateruse. Taking
Totranslatetheseinto anestimate forδE inoursce-
the positive square root we then obtain for the masses
nario,weneedtotakeintoaccountseveralm±odifications.
E E (i)Theendpointlocationshavechangedsignificantlybe-
+
Mℓ˜=√sE +E− , (9) cause the slepton and neutralino masses are different.
p+ − Therefore also the experimental energy resolution at the
and endpointlocationsisdifferent. (ii)Thenumberofevents
for slepton pair production is different in our scenario
E++E due to the different masses, center-of-mass energy, and
Mχ01 =Mℓ˜s1− √s/2− . (10) luminosity, so that the statistical error on the endpoint
determination is different. Determining the effect of (i)
Thesensitivityofthe neutralinomassmeasurementthus requires choosing a parametrizationof the detector’s en-
dependsontheaccuracywithwhichE canbemeasured. ergyresolution,whichwe discuss inthe next sectionand
Looking at Eq. (6), it is clear tha±t E only have a provide in Eqs. (14) and (15). Taking these two factors
weakdependenceonMχ01 forMχ01 ≪Mℓ˜. T±huswewould into account, we can estimate the ratio of our endpoint
4
energy uncertainty to Martyn’s in Ref. [67] spectrum computed by GUINEA PIG [77]. The energy
difference √s √s is lost in the form of beamstrahlung
− ′
δEδMEa±urstyn ≃ δEδeExpe(xEp(E==EMEa±urst)yn) ×sNNeMevuvesaenrntttyssn , (13) pspheTocthtorenursme.sAualrsteiansgrmelseoupoltttohtnehdeenoseuhrtagriaepsbeaidtrg.eessuibnstehqeuelenptltyonsmeneaerrgedy
± ±
accordingtotheexpectedmomentumandenergyresolu-
wherewehaveestimatedthattheuncertaintyintheend-
tion. Thissmoothesouttheedgesevenfurther. Forelec-
point determination drops with the square root of the
trons, the minimum of track momentum resolution and
number of observed events. Plugging the relevant num-
the energy resolution of the electromagnetic calorimeter
bers into the above expression for E , which dominates
+ (ECAL) for the considered electron energy is employed.
δEus
theerror,infactyields δEMa+rtyn ≃1.3,sincetheincreased In the case of muons, the momentum resolution of the
+
number of events in our scenario is partially canceled by trackingsystem is always used. For these quantities, the
thereduceddetectorresolutionatthehighervalueofE . following parametrizations are used:
+
Referringagainto Eq.(12),we canthenestimate that
1
nδMeuχtr01a≃lin1o.4mGasesVoffo2r oGuerVs,cetnhaermio.asIsncoatnhebrewdoertdesr,mfionreda ∆pT = 1·10−4 GeV−1 (tracker), (14)
∆E 0.166
to about70%accuracy. This suggeststhata usefulmass
= 0.011 (ECAL). (15)
measurementcanbeperformedforverylightneutralinos, E E/GeV ⊕
and in particular in the range M 5 GeV that is
χ01 ∼ Any polar angle deppendence of the tracker resolution is
particularly interesting for dark matter phenomenology,
neglected. Instead a rather conservative average reso-
sub-GeV accuracy should be possible.
lution is applied (compare e.g. Ref. [78]). We checked
On the other hand, if we carry out the same estimate
that the results do not depend strongly on the assumed
fora2GeVneutralinoandinsteada100GeVe˜ ,wefind
R
trackerresolutionsince for the consideredSUSY masses,
that the factor in front of the square root in Eq. (12) is
the χ0 mass measurementis dominated by the calorime-
now 40, and the cross section for selectron pair produc- 1
ter resolution. The above parametrization of the ECAL
tion is also lower so that the statistical uncertainty is
resolution which we employ is the one obtained with a
larger. In this case we find δM 15 GeV, suggesting
χ01 ≃ detector prototypein testbeam measurements[79]. The
thatinthis caseatbestanupper limitonthe neutralino
effects of a limited detector acceptance, signal selection
mass can be set.
cuts and inefficiencies in the electron and muon recon-
While this simple estimate gives a qualitative illustra-
struction are approximately accounted for by applying
tionofthedifficultyofmeasuringalightneutralinomass,
anoverallefficiencyof50%. Thisroughlycorrespondsto
we would would like to check it with a more thorough
thevaluesobtainedinRef.[67]usingamoredetailedsim-
analysis and more precisely quantify the accuracy possi-
ulation. Thismoredetailedstudyalsoshowedthatback-
ble for a light neutralino mass measurement at the ILC.
ground rates are rather small [70]. Therefore, outside of
We do this in the next section.
thisoverallefficiency,weneglectbackgroundscompletely
in our study.
The edge positions of the lepton spectrum obtained in
IV. SIMULATION OF NEUTRALINO MASS
the described way are finally fitted using an unbinned
MEASUREMENT FROM SLEPTON PAIR
likelihood fit. The fitted shapes are
PRODUCTION
Thanks to the simple kinematics of slepton pair pro- f (E)= 12 erf E√−2σEˆ1−− +1 : E <Eˆ− (16)
dχu0cmtioanss, miteaissuproemssiebnlteattothesetiImLaCtefrtohme aprreactihsieornsifmorplae −  12herf(cid:16)E√−2σEˆ2−−(cid:17)+1i : E ≥Eˆ−
1 h (cid:16) (cid:17) i
Monte Carlo simulation. We describe this in the follow- for E and 
ing. −
ufcoesrniFntaigrresb-ttoe,hfate-mhmeparpnsoousglmeraanrbmieserargtSoyiPof√hnpersonofaodn(uP[dc7ee2l−du],,msPlwieenph+oti)csoihnt=ypim(La+ipri8lsse0fmc%oare,lnca−utgs6lai0vtt%heende) f+(E)= 1221eerrffcc(cid:16)(cid:16)EE√√−−22σσEEˆˆ12++++(cid:17)(cid:17) :: EE <≥EEˆˆ++ (17)
cross section formulae from Refs. [73–76]. This choice of for E+. If onechooses σ1± = σ2±, Eqs (16) and (17) are
signs for the beam polarization maximizes the produc- the results of a convolution of an upward and a down-
tion cross-section. For each event, two lepton energies ward step function with a Gaussian. Between the nom-
are thrown according to a flat probability density dis- inal edge positions E and E the shape of the lepton
+
tribution between E and E . In order to take effects energyspectrum is infl−uenced by beamstrahlung anden-
+
caused by beamstrah−lung into account, E and E are ergy/momentumresolution,whereasoutsidethenominal
+
evaluatedforeacheventusingthereducedc−entre-of-mass edge positions, the shape is only determined by the en-
energy √s′ which is thrown according to the luminosity ergy/momentum resolution. For this reason σ1± and σ2±
5
be achieved for M =100 GeV.
V)V) e˜R
GeGe 33..55 e+ e- fi e~+ e~- s = 500 GeV We find that below about 2 (4) GeV for a 100
sion (sion ( 33 R R L = 250 fb-1 (p2o0s0si)bGleeaVndsewleecctaronno,nalymseatssanmuepaspuerrebmoeunntdisonnothleonngeuer-
precipreci 22..55 tralino mass. For example, for mχ01 = 1 GeV, the 95 %
0011 CL upper limits are 2.5 GeV (7.6 GeV) for a selectron
mm~~cc 22 me~ = 200 GeV mass of 100 GeV (200 GeV).
R
11..55 We note that the precision of the mass measurement
that we obtain in this simulation is roughly a factor of
11
twobetterthantheroughestimateoftheprecisionmade
00..55 me~ = 100 GeV in Section III. This is due to the simplistic scaling as-
R
sumptions made there, namely that the endpoint energy
00
00 1100 2200 3300 4400 5500 determinationaccuraciesscale like 1/√N as the number
mmc~c~00 ((GGeeVV)) of events changes, and linearly with the detector reso-
11
lution as the endpoint energy changes. Using dedicated
FIG. 1: Estimated precision of the χ0 mass measurement simulationswefindsomedeviationfromthissimplescal-
1
from e˜Re˜R production as function of the χ01 mass for e˜R ing which is due in a large part to the effect of beam-
masses of 100 GeV and 200 GeV. The yellow bands repre- strahlung. This more realistic scaling can account for
sent the estimated uncertainty of 30% related to the sim- the discrepancybetweenour estimate andsimulationre-
plifications of the Monte Carlo simulation used. The as- sults.
sumed centre-of-mass energy is √s = 500 GeV, the inte- Combining the results from µ˜ µ˜ production with
grated luminosity = 250 fb−1 and the beam polarization those from e˜ e˜ production doesRnoRt lead to a sizable
L R R
(Pe−,Pe+)=(+80%,−60%). improvement of the obtained precision. The reason is
the significantly higher cross-section for e˜ e˜ produc-
R R
tion due to the additional t-channel contribution, which
are treated as separate parameters in the fit. The fitted
is especially important for low neutralino masses, lead-
values of the parameters Eˆ and Eˆ do not in general
+ ing to a factor of 2 to 3 weaker constraints from µ˜ µ˜
coincide with the values of−E and E . The reason is R R
+ production.
that the asymmetric shape of−the beamstrahlung energy
spectrum leads to a certain offset. To correct for this
bias, a Monte Carlo based calibration procedure is used.
V. SUMMARY AND CONCLUSION
The uncertainty on the edge positions, and thus the
masses, is determined by creating toy Monte Carlo
Alightneutralinointheseveral-GeVmassrangeiscur-
datasets. For each toy data set, the fitted and corrected
rently of special phenomenologicalinterest. Recent dark
values of E and E can be converted into the squared
neutralino m+ass usin−g Eq. (8). The distribution of m2 matter direct detection experiments hint at the possible
χ0 existence of such a light particle. On the other hand,
1
from the ensemble toy data sets is approximately Gaus-
recent phenomenological analyses claim that an MSSM
sian, and we use the width of this distribution to deter-
lightneutralinodarkmattercandidatehasalowerbound
mine the uncertaintyonthe mass measurement. For low
on its mass around 7 GeV.
neutralino masses, the distribution can have support in
If a light neutralino exists, it would therefore be ex-
the unphysical region where m2 < 0. To account for
χ0 tremely important to obtain an accurate determination
1
this, we used the Feldman-Cousins method [80] to have of its mass. Techniques for measuring neutralino masses
asmoothtransitionbetweenamassmeasurement,which at the ILC have been developed and shown to have ex-
is possible for heavier neutralinos, and an upper bound, traordinary precision for the more conventional 50–100
which is necessary for very light neutralinos. GeV range. These techniques, however, have not been
Using the described procedure, we agree within studied for much lighter neutralinos.
roughly 30% with the results in Refs. [66, 67, 70], which In this paper, we have studied one of these
were obtained for Mχ0 =71.9, 96, and 135 GeV, respec- techniques—measuring the lepton energy spectrum in
1
tively. Therefore we assign a systematic uncertainty of slepton pair production events—and determined its use-
30% to our results due to the simplifications of our sim- fulness for the measurement of very light neutralino
ulation. masses. Weshowedwithasimulationthatthistechnique
Our estimate of the precision of the χ0 mass mea- continues to have useful accuracy for a neutralino with
1
surement from e˜ e˜ production at the ILC is shown a mass as low as a few GeV. For example, we showed
R R
in Fig. 1 as a function of the χ0 mass. The assumed that it is possible to measure the mass of even a 2 GeV
1
luminosity is 250 fb 1 at a centre-of-mass energy of neutralino to sub-GeV accuracy if the mass of the right-
−
√s=500GeVwithabeampolarizationof( e−, e+)= handed selectron is 100 GeV. For a 200 GeV selectron,
(+80%, 60%). Evenforχ0 massesassmallPas2PGeV,a the precision is about 2.7 GeV for a 4 GeV neutralino.
precision−ontheχ0 massm1easurementof 0.6 GeV can Forevenlighterneutralinos,weshowedthatthismethod
1 ≈
6
cangive an 95 % CL upper bound of 2.5 (7.6)GeV for a Higgs mix after electroweak symmetry breaking. The
100 (200) GeV selectron. 4 4 mixing matrix is given in the bino, wino, Higgsino
×
SuchmassmeasurementsattheILCwillthusbeindis- basis by [82]
pensable in testing the MSSM thermal cold dark matter
picture if a very light neutralino exists. M1 0 −MZswcβ MZswsβ
0 M M c cosβ M c s
 M s c M c2 c Z 0w − Zµw β .
− Z w β Z w β −
Appendix A: Chargino and Neutralino Mixing  MZswsβ −MZcwsβ −µ 0 
 (A2)
Herewesummarizethemixingoftheelectroweakgaug- HereM1denotesthesupersymmetrybreakingbinomass.
inosandHiggsinos,whichweuseinthepaper. Thespin- Furthermore sw ≡ sinθw, cw ≡ cosθw and θW is the
1/2superpartnersoftheW± gaugebosonsandthescalar electroweakmixingangle. MZ denotestheZ bosonmass.
chargedHiggsfield, H mix afterelectroweaksymmetry
±
breaking. The resulting mixing matrix in the wino, Hig-
gsino basis is given by [81] Acknowledgments
M √2M sinβ HD would like to thank Stefano Profumo for discus-
2 W . (A1)
√2M cosβ µ sionsontherecentdarkmattersearchdata. PWisgrate-
W
(cid:18) (cid:19)
fultoAnthonyHartinandKarstenBu¨ßerforhelpfuldis-
Here M is the SU(2) soft breaking gaugino mass. µ is cussionsonbreamstrahlungandforprovidingaGUINEA
2
thesupersymmetricHiggsmixingparameter,tanβ isthe PIG beamstrahlung spectrum. HD and JC were sup-
ratio of the vacuum expectation values of the two Higgs portedby BMBF“VerbundprojektHEP-Theorie”under
doublets and M is the mass of the W boson. the contract 0509PDE. The work of HD was also sup-
W
Similarly the spin-1/2 superpartners of the W0 and ported by the Helmholtz Alliance “Physicsat the Teras-
B gauge bosons as well as of the two CP-even neutral cale.”
[1] H.P. Nilles, Phys.Rept. 110 (1984) 1. Lees, arXiv:hep-ph/0212227.
[2] S.P. Martin, arXiv:hep-ph/9709356. [17] A.Bottino,N.FornengoandS.Scopel,Phys.Rev.D67
[3] E. Gildener and S. Weinberg, Phys. Rev. D 13 (1976) (2003) 063519 [arXiv:hep-ph/0212379].
3333; E. Gildener, Phys.Rev. D 14 (1976) 1667. [18] A.Bottino,F.Donato,N.FornengoandS.Scopel,Phys.
[4] M. J. G. Veltman,Acta Phys.Polon. B 12 (1981) 437. Rev. D 68 (2003) 043506 [arXiv:hep-ph/0304080].
[5] G. R.Farrar and P. Fayet,Phys. Lett.B 76 (1978) 575. [19] A.Bottino,F.Donato,N.FornengoandS.Scopel,Phys.
[6] H.K.Dreiner,C.LuhnandM.Thormeier,Phys.Rev.D Rev. D 69 (2004) 037302 [arXiv:hep-ph/0307303].
73(2006)075007[arXiv:hep-ph/0512163];H.K.Dreiner, [20] A.Bottino,F.Donato,N.FornengoandS.Scopel,Phys.
C. Luhn, H. Murayama and M. Thormeier, Nucl. Phys. Rev. D 70 (2004) 015005 [arXiv:hep-ph/0401186].
B 795 (2008) 172 [arXiv:0708.0989 [hep-ph]]. [21] A.Bottino,F.Donato,N.FornengoandS.Scopel,Phys.
[7] H. M. Lee, S. Raby, M. Ratz, G. G. Ross, Rev. D 77 (2008) 015002 [arXiv:0710.0553 [hep-ph]].
R. Schieren, K. Schmidt-Hoberg and P. K. S. Vau- [22] J. Abdallah et al. [DELPHI Collaboration], Eur. Phys.
drevange,arXiv:1009.0905 [hep-ph]. J. C 31 (2003) 421 [arXiv:hep-ex/0311019].
[8] J.R.Ellis, J. S.Hagelin, D.V.Nanopoulos, K. A.Olive [23] A. Heister et al. [ALEPH Collaboration], Phys. Lett. B
and M. Srednicki, Nucl.Phys. B 238 (1984) 453. 583 (2004) 247.
[9] H.PagelsandJ.R.Primack,Phys.Rev.Lett.48(1982) [24] G. Abbiendi et al. [OPAL Collaboration], Eur. Phys. J.
223. C 35 (2004) 1 [arXiv:hep-ex/0401026].
[10] G. Jungman, M. Kamionkowski and K. Griest, Phys. [25] C.Amsleretal.[ParticleDataGroup],Phys.Lett.B667
Rept.267 (1996) 195 [arXiv:hep-ph/9506380]. (2008) 1.
[11] M.Drees,M.M.Nojiri,D.P.RoyandY.Yamada,Phys. [26] A. Dedes, H. K. Dreiner and P. Richardson, Phys. Rev.
Rev.D56(1997)276[Erratum-ibid.D64(2001)039901] D 65 (2001) 015001 [arXiv:hep-ph/0106199].
[arXiv:hep-ph/9701219]. [27] I. Gogoladze, J. D. Lykken, C. Macesanu and S. Nandi,
[12] R.CowsikandJ.McClelland,Phys.Rev.Lett.29(1972) Phys.Rev.D 68(2003) 073004 [arXiv:hep-ph/0211391].
669. [28] H. K. Dreiner, C. Hanhart, U. Langenfeld and
[13] H. K. Dreiner, S. Heinemeyer, O. Kittel, U. Langenfeld, D. R. Phillips, Phys. Rev. D 68 (2003) 055004
A.M.WeberandG.Weiglein,Eur.Phys.J.C62(2009) [arXiv:hep-ph/0304289].
547 [arXiv:0901.3485 [hep-ph]]. [29] H.K.Dreiner,O.KittelandU.Langenfeld,Eur.Phys.J.
[14] B. W. Lee and S. Weinberg, Phys. Rev. Lett. 39 (1977) C 54(2008) 277 [arXiv:hep-ph/0703009]; H.K.Dreiner,
165. O. Kittel and U. Langenfeld, Phys. Rev. D 74 (2006)
[15] D. Hooper and T. Plehn, Phys. Lett. B 562 (2003) 18 115010 [arXiv:hep-ph/0610020].
[arXiv:hep-ph/0212226]. [30] M. Kachelriess, JHEP 0002 (2000) 010
[16] G. Belanger, F. Boudjema, A. Pukhov and S. Rosier- [arXiv:hep-ph/0001160].
7
[31] H. K. Dreiner, S. Grab, D. Koschade, M. Kramer, [arXiv:1005.5131 [hep-ph]].
B. O’Leary and U. Langenfeld, Phys. Rev. D 80 (2009) [59] Z. Ahmed et al. [The CDMS-II Collaboration], Science
035018 [arXiv:0905.2051 [hep-ph]]. 327 (2010) 1619 [arXiv:0912.3592 [astro-ph.CO]].
[32] D. Choudhury, H. K. Dreiner, P. Richardson [60] Z.Ahmedet al.[CDMSCollaboration], Phys.Rev.Lett.
and S. Sarkar, Phys. Rev. D 61 (2000) 095009 102 (2009) 011301 [arXiv:0802.3530 [astro-ph]].
[arXiv:hep-ph/9911365]. [61] J.Angleetal.[XENONCollaboration], Phys.Rev.Lett.
[33] K. Nakamura et al. (Particle Data Group), J. Phys. G 100 (2008) 021303 [arXiv:0706.0039 [astro-ph]].
37, 075021 (2010) [62] E. Aprile et al. [XENON100 Collaboration],
[34] G. Belanger, F. Boudjema, A. Cottrant, A. Pukhov arXiv:1005.0380 [astro-ph.CO].
and S. Rosier-Lees, JHEP 0403 (2004) 012 [63] L. Baudis, talk at the 18th international con-
[arXiv:hep-ph/0310037]. ference on Supersymmetry and the Unification of
[35] A. Bottino, N. Fornengo, G. Polesello and S. Scopel, Fundamental Interactions, Bonn, Germany, 2010.
Phys. Rev. D 77 (2008) 115026 [arXiv:0801.3334 [hep- http://susy10.uni-bonn.de/program.php
ph]]. [64] G.Moortgat-Pick,J.Phys.Conf.Ser.110(2008)072027
[36] V. Niro, A. Bottino, N. Fornengo and S. Scopel, Phys. [arXiv:0801.2414 [hep-ph]].
Rev. D 80 (2009) 095019 [arXiv:0909.2348 [hep-ph]]; [65] J. Brau et al. [ILC Collaboration], arXiv:0712.1950
S.Scopel, AIPConf. Proc. 1115 (2009) 111. [physics.acc-ph].
[37] A. Badin, G. K. Yeghiyan and A. A. Petrov, [66] H. U.Martyn, arXiv:hep-ph/0408226.
arXiv:0909.5219 [Unknown]. [67] H. U.Martyn, arXiv:hep-ph/0406123.
[38] D. Feldman, Z. Liu and P. Nath, arXiv:1003.0437 [Un- [68] A. Freitas, H. U. Martyn, U. Nauenberg and P. M. Zer-
known]. was, arXiv:hep-ph/0409129.
[39] N.Fornengo, S.Scopel, A.Bottino, [69] B. C. Allanach et al., in Proc. of the APS/DPF/DPB
[arXiv:1011.4743 [hep-ph]]. Summer Study on the Future of Particle Physics (Snow-
[40] R. Bernabei et al., Eur. Phys. J. C 67 (2010) 39 mass 2001) ed. N. Graf, Eur. Phys. J. C 25 (2002) 113
[arXiv:1002.1028 [astro-ph.GA]]. [arXiv:hep-ph/0202233].
[41] C. E. Aalseth et al. [CoGeNT collaboration], [70] J. A. Aguilar-Saavedra et al. [ECFA/DESY LC Physics
arXiv:1002.4703 [astro-ph.CO]. Working Group], arXiv:hep-ph/0106315.
[42] E. Kuflik, A. Pierce and K. M. Zurek, Phys. Rev. D 81 [71] G. Aarons et al. [ILC Collaboration], arXiv:0709.1893
(2010) 111701 [arXiv:1003.0682 [hep-ph]]. [hep-ph].
[43] D.Das and U.Ellwanger, arXiv:1007.1151 [hep-ph]. [72] W. Porod, Comput. Phys. Commun. 153 (2003) 275
[44] J. F. Gunion, A. V. Belikov, D. Hooper, [arXiv:hep-ph/0301101].
[arXiv:1009.2555 [hep-ph]]. [73] A.Bartl,H.FraasandW.Majerotto,Z.Phys.C34,411
[45] P.Draper, T. Liu, C. E. M. Wagneret al., (1987).
[arXiv:1009.3963 [hep-ph]]. [74] A. Bartl, H. Eberl, S. Kraml, W. Majerotto,
[46] D. A. Vasquez, G. Belanger, C. Boehm, A. Pukhov and W. Porod and A. Sopczak, Z. Phys. C 76, 549 (1997)
J. Silk, arXiv:1009.4380 [hep-ph]. [arXiv:hep-ph/9701336].
[47] A.V.Belikov,J.F.Gunion,D.HooperandT.M.P.Tait, [75] C. Blochinger, H. Fraas, G. A. Moortgat-Pick
arXiv:1009.0549 [hep-ph]. and W. Porod, Eur. Phys. J. C 24, 297 (2002)
[48] Y. G. Kim, S. Shin, JHEP 0905 (2009) 036. [arXiv:hep-ph/0201282].
[arXiv:0901.2609 [hep-ph]]. [76] S. Kraml, arXiv:hep-ph/9903257.
[49] A. L. Fitzpatrick, D. Hooper and K. M. Zurek, [77] D.Schulte,Beam-beam simulationswithGUINEA-PIG,
arXiv:1003.0014 [Unknown]. CERN-CLIC-NOTE-387.
[50] S. Andreas, C. Arina, T. Hambye, F. S. Ling and [78] ILD Concept Group, The International Large De-
M. H. G. Tytgat, Phys. Rev. D 82 (2010) 043522 tector, Letter of Intent, March 2009, available at
[arXiv:1003.2595 [hep-ph]]. http://www.ilcild.org/documents/ild-letter-of-intent
[51] M. T. Frandsen and S. Sarkar, Phys. Rev. Lett. 105 [79] C. Adloff et al. [CALICE Collaboration], J. Phys. Conf.
(2010) 011301 [arXiv:1003.4505 [hep-ph]]. Ser. 160 (2009) 012065 [arXiv:0811.2354 [physics.ins-
[52] D. S. M. Alves, S. R. Behbahani, P. Schuster and det]].
J. G. Wacker, JHEP 1006 (2010) 113 [arXiv:1003.4729 [80] G.J.FeldmanandR.D.Cousins,Phys.Rev.D57,3873
[hep-ph]]. (1998) [arXiv:physics/9711021].
[53] D.Feldman,Z.Liu,P.Nathand G.Peim, Phys.Rev.D [81] A.Bartl,H.FraasandW.Majerotto,Z.Phys.C30,441
81 (2010) 095017 [arXiv:1004.0649 [hep-ph]]. (1986).
[54] R. Essig, J. Kaplan, P. Schuster and N. Toro, [82] A.Bartl,H.FraasandW.Majerotto,Nucl.Phys.B278
arXiv:1004.0691 [hep-ph]. (1986) 1.
[55] S. Chang, J. Liu, A. Pierce, N. Weiner and I. Yavin, [83] Note, howeverthat in an earlier work [46], thisregion of
JCAP 1008 (2010) 018 [arXiv:1004.0697 [hep-ph]]. parameter space isalso examined,and thereit is argued
[56] P.W.Graham,R.Harnik,S.RajendranandP.Saraswat, that theTevatron Higgs searches, themost recent Bs
arXiv:1004.0937 [hep-ph]. µ+µ− limit,anddarkmatterdirectdetectionnullresul→ts
[57] R.Kappl, M. Ratz, M. W. Winkler, together rule out neutralinos lighter than 28 GeV in the
[arXiv:1010.0553 [hep-ph]]. MSSM.
[58] K.J. Bae, H.D. Kim, S.Shin,