We discuss the neutralino dark matter within classes of extended
supersymmetric models, referred to as the USSM, containing one additional SM
singlet Higgs plus an extra Z', together with their superpartners the singlino
and bino'.Comment: 4 pages, 3 figs. Talk given at LCWS08, Chicago, IL, USA,
  11/16-20/200

Kalinowski, J.

King, S. F.

Roberts, J. P.

English

arXiv

We discuss the neutralino dark matter within classes of extended supersymmetric models, referred to as the USSM, containing one additional SM singlet Higgs plus an extra Z', together with their superpartners the singlino and bino'

King, S.F.

Roberts, J.P.

CERN Document Server

arXiv:0812.2384v1  [hep-ph]  12 Dec 2008D ark M atter in the U SSMJ.K alinowski,1S.F.K ing2and J.P.Roberts31-PhysicsD epartm ent,University ofW arsaw,00-681 W arsaw,Polandand Theory D ivision,CERN,CH-1211 G eneva 23,Switzerland2-SchoolofPhysicsand Astronom y,University ofSoutham pton,Southam pton,SO 17 1BJ,U.K .3-CenterforCosm ology and Particle Physics,New York University,New York,NY 10003,USAW ediscusstheneutralino dark m atterwithin classesofextended supersym m etricm od-els,referred to astheUSSM ,containing oneadditionalSM singletHiggsplusan extraZ0,togetherwith theirsuperpartnersthe singlino and bino’.1 IntroductionM odels with additionalU (1) gauge group provide an elegant solution to the  problemofthe m inim alsupersym m etric standard m odel(M SSM ).The Higgs/Higgsino m ass termH^ 1H^ 2 ofthe M SSM isreplaced by S^H^ 1H^ 2 (with a dim ensionlesscoupling ),where theadditionalsuper eldS^ isasingletundertheStandard M odel(SM ).Thevacuum expectationvaluehSithen notonly dynam ically generatesa SUSY Higgs/Higgsino m assneartheweakscale as required but also results in an increased Higgs boson m ass upper bound whichin turn gives a welcom e reduction in electroweak  ne tuning. M oreover,by gauging theAbelian U (1)X sym m etry arising from the S^H^ 1H^ 2 term the troublesom eaxion isavoidedvia theHiggsm echanism resulting in a m assiveZ 0gaugeboson [1].Theessentialadditionalelem ents ofsuch a scenario then consist oftwo extra super elds relative to those oftheM SSM ,nam ely the singletsuper eldS^ and the U (1)X gauge super eld B0. The USSM isthen de ned as a m odelwith the M SSM super elds plus these two additionalsuper eldsat the TeV scale. Since it does not include other super elds necessary for cancelation oftheferm ionicU (1)X gaugeanom alies,ithasto beconsidered asa truncation ofa com pletem odel.Forexam ple,identifying theAbelian gaugegroup asasubgroup ofE 6 with com plete27dim ensionalrepresentationsofm atterdown totheTeV scalesolvestheanom alyproblem ,whilerequiring furthertheright-handed neutrinosto besingletsunderU (1)X (fora see-sawm echanism )de nesthe theory uniquely asthe E6SSM [2].FortheUSSM weadoptthechargeassignm entundertheextra U (1)X asin theE6SSMand study thephysicsand cosm ologyin thissim pli ed settingtolearn aboutcrucialfeatureswhich willbe relevantto any com plete m odelinvolving an additionalU (1)X gauge groupand a singlet. Thistalk,which updatesthe prelim inary resultspresented previously [3],isbased on the recentcom prehensive analysisofneutralino dark m atterin the USSM in [4],wherefulldetails(and an extensivelistofreferences)can be found.2 T he U SSM m odelCom pared to the M SSM the particle spectrum isextended by a new CP-even HiggsbosonS,a gaugeboson Z 0 and two neutral{inos:a singlino ~S and a bino’ ~B 0.O thersectorsarenotenlarged butthe sferm ion scalarpotentialreceivesadditionalD-term s.LCW S/ILC 2008W ith two additionaldegreesoffreedom the neutralino sectorcannotbe solved analyt-ically any m ore. However,since the originalM SSM and the new degrees offreedom arecoupled weakly,an approxim ateanalyticalsolution can befound following a two-step diago-nalization procedure[5].First-the4 4 M SSM and thenew 2 2 singlino-bino’sectorsareseparately diagonalised;second -a block{diagonalization provides approxim ate solutions.500 1000 1500 2000 2500 3000M¢1 @GeVD25050075010001250150017502000mΧi0  @GeVDFigure1:Neutralino m assspectrum .SinceU (1)X forbidsthesinglino m assterm(in contrastto the NM SSM ) the m inisee-saw structureofthesinglino-bino’m assm a-trix im plies a singlino{dom inated lightestneutralino in the lim it oflarge bino’m ass.Figure 1 shows the neutralino m ass spec-trum as a function ofthe soft bino’m assparam eterM 01in a G UT-scaleunifying sce-nario M 01= M 1 = M 2=2, where M 1;M 2are the U (1);SU (2) m ass param eters re-spectively;tan = 5,otherparam etersarechosen so that the e ective  = 600 G eV,the heavy M Z 2 = 950 G eV,and the pseu-doscalarHiggsm A = 500 G eV.3 R esultsThe presence ofnew singlino and bino’states greatly m odi es the phenom enology oftheneutralino sectorboth atcollidersand in cosm ology-related processes. Itisinform ative toconsiderthe generalform ofthe interactionsthatarise from the singlino and bino’com po-nentsofthelightestneutralino beforepresenting ournum ericalresults.Theinteractionsofthebino’com ponent,which isalwayssubdom inantduetothesee-sawstructureoftheneutralino m assm atrix,closely m irrorthoseofthebino com ponent,exceptforthe di erentcoupling constantand chargesunderthe new U (1)X . O n the otherhand,theS^ H^ u H^ d term in thesuperpotentialgivesriseto a new typeofneutralino coupling:thelightest neutralino with signi cant singlino and higgsino com ponents willcouple stronglyto Higgsbosonswith a signi cantHu orH d com ponent,usually the lighterHiggsbosons,H 1;2 and A in thespectrum .M oreover,theabsenceofthesingletcubicterm ~S3,in contrastto the NM SSM ,im plies that the singlino-dom inated LSP needs an adm ixture ofM SSMhiggsinosto annihilate through s-channelHiggsbosons.Since the singlino com ponentdoesnot interact with the SU (2) or U (1)Y gauginos or with ferm ions, a signi cant singlinocom ponent in the lightest neutralino willsuppress couplings to W or Z1 bosons and toferm ions.3.1 R elic densityThedi erencesbetween theM SSM relicdensity calculation and theUSSM calculation arisethrough the extension ofthe particle spectrum and through the new interactionsthatareintroduced. W e have im plem ented allnew interactionsinto the micrOMEGAs[6]code whichtakesfullaccountofallannihilation and coannihilation processesand calculatestheire ectwheneverthey arerelevant.LCW S/ILC 20080 5 10 15 20M′1(TeV)10−310−210−1100101102ΩCDMh2Figure2:Therelicdensity acrossvarying M 01Figure 2 shows the relic density as afunction ofM 01. Ignoring initially the res-onance e ects,a generaltrend in the relicdensity from a largevalueatlow M 01,downto a lowervalue ataround M 01= 0:75 TeVand then back tolargervaluesathigh M 01iseasily understood asthisfollowsthe evolu-tion oftheLSP from bino through higgsinoto singlino,seeFigure1.Beyond this generalbehavior there areinteresting resonancestructuresastheLSPm ass  rst increases with the M 01increasereachingam axim um of 560G eV atM 01800 G eV and then fallsdown crossingallpossibles-channelresonancestwice.Starting fromM 01= 0 we  rstarriveata little dip in the relic density around M 01= 250 G eV due to thes-channelH 2=A resonance,and a little wiggle around M01= 500 G eV due to Z2=H 3 astheLSP hasnotyetdeveloped an appreciablesinglino com ponent.The rstappreciabledip intherelicdensity occursaround M 01= 0:8TeV whereC D M h2 dropsto 0:02.HeretheLSPhasa strong higgsino com ponentwhich enhancesthe annihilation via the s-channelZ2=H 3resonancesconsiderably.IncreasingM 01further,theLSP m assincreases,goingo -resonance(hence localm axim um in the relic density),untilit reachesits m axim um of  590 G eVatM 01 800 G eV.From now on the LSP m assdecreasesand itsnature becom essinglino-dom inated. Around M 01= 1:5 TeV itonce again hitsthe Z2=H 3 resonance. However,thistim e the LSP ispredom inantly singlino. Although pure singlino neutralinosdo notcoupleto thesingletHiggs,sotheH 3 resonanceissubdom inant,they couplestrongly to theZ0andannihilate very e ciently. Asa result,the relic density dropsto  2 10  3. The kink atM 01= 2:5TeV developsastheLSP m assdropsbelow threshold forproduction ofH 1A in the nalstate.Increasing M 01furtherwe nd a pseudoscalarHiggsresonanceatM 01= 3:5 TeV,thetop threshold atM 01= 5 TeV,thelightHiggsthreshold atM 01= 11 TeV,thelightHiggsresonanceatM 01= 14 TeV and the Z resonanceatM 01= 19 TeV.3.2 D irect detectionCom pared to the M SSM ,the spin-dependentelastic scattering receivesan additionalcon-tribution dueto a heavy Z2 gaugeboson,whilethespin-independentonegetscontributionsfrom additionalHiggsaswellasfrom interactionsgenerated by the g01~B 0(~H iH i+ ~SS)and ~H i(~SH j + ~H jS) couplings. In Figure 3 the spin-independent as wellas spin-dependentelastic crosssection ofthe lightestneutralino on the proton is shown as a function ofM 01(restricted to 0{3 TeV,asbeyond thisrangecrosssectionsfallm onotonically).Referring toFig.1,itiseasy tounderstand theM 01behaviorofthecrosssection.ForM 01below 800G eV,theLSP ism ostly a m ixtureoftheM SSM states.Itstartsasa bino and asM 01approaches500 G eV,itreceivesan appreciableadm ixtureofboth higgsinos.Asa resultboth SD andSI  rstriseand then fall.Thefallisduetothedim inishing binocom ponent,which reducesthe Higgscontribution to SI,and increasesthe cancelation in c34 = jN 13j2   jN 14j2,thatcontrolsthe Z contribution to SD . AtM01 800 G eV the discontinuitiesre ectcrossingoftwo lighteststatessince the m ixing with singlino forcesthe second-lighteststate to be-com e the lightest.AtthispointSI dropsby a factor3.Asthe singlino com ponentoftheLCW S/ILC 20080 1000 2000 3000M ′1(GeV)00.010.020.030.040.050.060.070.080.090.10.11 σSI (ab)M ′1= M1 = M2/2µ = 600 GeV, tanβ = 50 1000 2000 3000M ′1(GeV)01020304050M ′1= M1 = M2/2 GeVµ = 600 GeV, tanβ = 5σSD (ab)Figure 3: The elastic spin-independent(left)and spin-dependent(right)LSP-proton crosssection asa function ofM 01LSP increaseswith M 01the ~H i~SH j term becom esresponsibleforthelittleriseofthecrosssection.O n the otherhand,SD jum psby a factor6 atthe discontinuity since the m ixingwith singlino upsetsthe cancelation in c34. W ith furtherincrease ofM01the LSP becom esalm osta puresinglino which explainsa steady fallofboth crosssections.4 Sum m aryTheUSSM ,despiteitsm odestadditionalparticlecontentcom paredtotheM SSM orNM SSM ,leadstoasurprisinglyrich and interestingdarkm atterphenom enologywhich distinguishesitfrom thesem odels.Therearem any caseswheresuccessfulrelicabundancesm ay bereached,eitherthrough aproperbalanceofthesinglino/higgsinom ixture,orthrough abalanceofthesinglino m assagainstthe m assofa boson thatm ediatesannihilation in the s-channel.Thedi erencein theHiggsspectrum and thesinglinointeractionsresultsin signi cantdi erencesin the directdetection predictionsaswell.A cknow ledgm entsW ork partially supported by the Polish M NiSW G rant No 1 P03B 108 30,the EC Pro-gram m es M TK D{CT{2005{029466 and M RTN-CT-2006-035505,as wellas STFC RollingG rant PPA/G /S/2003/00096,EU Network M RTN-CT-2004-503369,EU ILIAS RII3-CT-2004-506222,NSF CAREER grantPHY-0449818and DO E O JIgrant# DE-FG 02-06ER41417.R eferences[1] P.Fayet,Phys.Lett.B 69 (1977) 489.[2] S.F.K ing,S.M orettiand R .N evzorov,Phys.R ev.D 73 (2006) 035009.[3] D .Jarecka, J.K alinowski, S. F.K ing and J.P. R oberts, Proc. of LCW S07 and ILC07, H am burg,G erm any,2007,pp SU S15 [arX iv:0709.1862 [hep-ph]];J.Phys.Conf.Ser.110,072019 (2008).[4] J.K alinowski,S.F.K ing and J.P.R oberts,arX iv:0811.2204 [hep-ph].[5] S.Y .Choi,H .E.H aber,J.K alinowskiand P.M .Zerwas,N ucl.Phys.B 778 (2007) 85.[6] G .Belanger,F.Boudjem a,A .Pukhov and A .Sem enov,Com put.Phys.Com m un.176,367 (2007).LCW S/ILC 2008

Dark Matter in the USSM

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