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Reduced Fine-Tuning in Supersymmetry with R-parity violation Linda M Carpenter, David E Kaplan, Eun-Jung Rhee Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (Dated: February 2, 2008) Both electroweak precision measurementsand simple supersymmetricextensionsof thestandard modelpreferamassoftheHiggsbosonlessthantheexperimentallowerlimitof114GeV.Weshow thatsupersymmetricmodelswithRparityviolationandbaryonnumberviolationhaveasignificant rangeof parameter space in which theHiggs dominantlydecaysto six jets. These decaysaremuch moreweaklyconstrainedbycurrentLEPanalysesandwouldallowforaHiggsmassnearthatofthe Z. In general, lighter scalar quark and other superpartner masses are allowed and the fine-tuning typicallyrequiredtogeneratethemeasured scaleofelectroweak symmetrybreakingisameliorated. TheHiggs would potentially bediscovered at hadron colliders via theappearance of new displaced vertices. The lightest neutralino could bediscovered by a scan of vertex-lesseventsLEP I data. 7 0 0 TheStandardModelofparticlephysicsisarguablythe top quark mass) through corrections to the Higgs quar- 2 crowning achievement of the last half-century’s work to- tic interaction. On the other hand, the Z boson mass n wards the understanding of the laws of nature at short andthescaleofelectroweaksymmetrybreakinggetscor- a distances. However, two somewhat nagging features re- rections proportional to superpartner masses. To satisfy J main. The first is that while statistical fits of standard the current bound on the physical mass, large scalar top 25 mbeosdtefiltpavraalumeetfeorrstthoepHreicgigssionscamlaerasmuraesmseonfts85p+ro39duGceeVa mΛ,asssaeys o(mf to˜r≃der1tTheeVP)laanreckresqcuailree,dc.onFtorribautliaorngsetcouttohffe −28 [1], LEP II places a lower bound of 114.4 GeV at 95% (squared)Z masswillbe roughlyoforderthe superpart- 3 CL [2]. While these constraints taken together do not ner masses, say δm2 m2. A cancelation would be v Z ∼ t˜ 4 constitute a discrepancy, a Higgs mass measured below required among contributions with a tuning of the order 0 the current LEP bound would have improved the fit to onepartin(mt˜/mZ)2. Thus,1TeVscalartopswouldre- 2 precision data. In addition, it has been argued that the quire 1%tuning. Abeautifuldiscussionofthistension 7 electroweakobservablesmostsensitivetotheHiggsmass in the∼MSSM is contained in [5]. 0 are themselves not in good agreement and imply a dis- 6 crepancy with the LEP II bound [3]. The secondfeature OnepossibleresolutiontotheparadoxisthattheHiggs 0 / isthatthescaleofelectroweaksymmetrybreakingisvery is in fact light but missed by experiments. The quoted h sensitive to quantum corrections. If the standard model lower bound on the Higgs mass comes from analyses as- p is valid to some very high energy scale M 1 TeV, sumingaHiggswithstandardmodelpropertiessuchasa - ≫ p the parameters of the ultraviolet theory would require standardmodelcrosssectionforZ-Higgsproductionand e an unnatural tuning of order one part in (M/1TeV)2 to standardmodelbranchingratiosintobottomquarksand h maintain the hierarchy. While this fact alone does not tau leptons. If the branching ratio to standard model : v guaranteenew physicsbeyondaHiggsbosonatthe elec- final states are uniformly suppressed by, for example, a i troweak scale, it is strongly suggestive of physics at the factor of five – and the new decay modes are not picked X weak scale which stabilizes scalarmasses with respect to up by any LEP searches – the 95% CL lower limit on r a radiative corrections. the Higgs mass reduces to roughly 93-95 GeV (see Fig- Awell-knownsolutiontothenaturalnessproblemisto ure 2 of [2]). Our model exploits this weakness. Other imposesupersymmetryonthestandardmodelandsoftly attempts to modify Higgs decays for the purpose of nat- break it at a scale of M 1 TeV (for a review, see [4]). uralness have been made in the context of the next-to- ∼ Radiative corrections to scalar masses in these theories minimal supersymmetric standard model [6], and in a are proportionalto the scale of supersymmetry breaking general analysis of the MSSM with an additional singlet andthereforenaturallystabilizethemassoftheHiggsat superfield [? ]. aroundthe weakscale. Remarkably,theminimalversion of these theories predict the unification of couplings at a In this letter, we show that in the MSSM with R par- renormalization scale near the Planck scale. A discrete ity violation and non-unified gaugino masses, there is a symmetry, R parity, is introduced to forbid dimension- significantamountofparameterspaceinwhichtheHiggs four baryon and lepton number violating operators and dominantlydecaystoapairofunstableneutralinos,each avoid proton decay as we discuss below. ofwhichsubsequentlydecaystothreequarkjets. Thepa- While the MSSM (Minimal Supersymmetric Standard rameter space allows, as we detail below, Higgs masses Model) contains over a hundred new parameters, it has around the Z mass even with a standard model produc- become tightly constrained. A robust constraint on the tion cross section; this is our main result. MSSM is the bound on the Higgs mass. The physical mass gets contributions which depend only logarithmi- R parity is a symmetry under which all superpartners cally on superpartner masses (for example, the scalar areodd. Itforbidsthefollowingrenormalizableoperators 2 in the superpotential: the loss of the extra b quarks in the final state cuts the efficiency in half, we estimate that our soft jets with 2 W µ L H¯ +λ L L Ec+λ′ L Q Dc b’s in the final state wouldbe pickedup by the 2b search ⊃ i i ijk i j k ijk i j k + λ′i′jkUicDjcDkc, (1) bweitthruaenoefffithceieflnacvyoorlfe∼ss1se/a7r×ch1[/120]∼,w7h%ic.hTishsiismwiloaurldtoatlhsoe 2bsearchwiththeb-taggingrequirementremoved. While where L, Ec, H¯, Q, Uc, and Dc are lepton doublet, lep- we feel this estimate is conservative,it is very roughand tonsinglet,up-typeHiggs,quarkdoublet,up-type quark a full analysis is warranted. singlet, and down-type quark singlet superfields respec- What are the constraints on the mass of the lightest tively, and the ijk are flavor indices. These interac- neutralino? The neutralino shouldbe lightenoughto al- tions violate lepton number (the first line) and baryon < low for our Higgs decay ( 50 GeV), while the lightest number (the second). Their existence would predict un- charginomustsatisfyitscu∼rrentlowerbound( 103GeV acceptable levels of proton decay unless at least some ∼ in most of parameter space, even for R-parity violating of these couplings are extremely small. However, pro- decays[13]). ThisconstrainstheMSSMparameterssuch ton stability could be provided by a symmetry that allows only the lepton-number or baryon-number violat- that M1 < M2,µ, and the lightest neutralino is mostly bino – although it must have enough of a higgsino com- ing terms [7]. In this paper, we focus on the latter. ′′ ponentto allowthe Higgswidthto bedominatedbythis Bounds on the individual λ couplings are only strin- decay, and thus the µ parameter shouldn’t be too much gent from neutron–anti-neutron oscillations and double nucleondecay,requiringλ′′ <10−7 andλ′′ <10−4 for larger than 100 GeV as we see below (see also [14]). 112 113 200GeVscalarquarkandglui∼nomasses. Theo∼therseven The remainingquestion then is how could sucha light coupling are less constrained. The tightest bounds are neutralinowithstrongenoughcouplingstodominatethe on products of two different couplings which range from Higgs width not being detected indirectly by its effect λ′′ λ′′ <10−2 10−4andcomedominantlyfromlim- on the Z width or directly in searches at LEP II. There itisjkoni′jr′akr′e hadron−ic decays of B mesons. For a broad are two reasons: the first is that the width of the Z in review of R parity violation in supersymmetry, see [8]. the standard model ( 2.5 GeV) is three orders of mag- ∼ nitude bigger than the standard model width of a 100 Do LEP searches put a bound on a Higgs that de- GeV Higgs. The second is that in the range of small to cays to 6 quarks (via two neutralinos)? No analysis has moderatebino-higgsinomixing,theHiggsdecayrateinto been performed looking for this exclusive final state. A neutralinos is roughly proportional to the mixing angle decay-mode-independent search for a Higgs boson was squared while the same rate for the Z goes like the mix- performed by the OPAL experiment (by looking for the ing angle to the fourthpower. The decay width ofthe Z associated Z in leptonic channels [9]) and puts a lower into the lightest neutralino at tree level is bound of 82 GeV when the production cross section is equal to that of the standard model. In addition, the search for a Higgs decaying to two jets of any flavor [10] 2m 2 m 2 could be sensitive to our Higgs to six jets when the lat- Γχ0 =Γν ∆2 1 χ 1 χ (2) ter canbe forcedinto a two-jettopology(there may also × s −(cid:18) mZ (cid:19) −(cid:18)mZ(cid:19) ! be sensitivity from h 2b when each neutralino decay contains a b quark). A→n analysis of this type was done where ∆, defined in the appendix, is roughly the bino- by DELPHI [11] in the searchfor a cascade decay of the higgsino mixing angle squared, and Γν is the standard Higgs to four b quarks via two pseudo scalars, a [12]. model Z width into one species of neutrino. We require They modified the search for e+e− hZ (b¯b)Z to be this contribution to the total and hadronic widths to sensitive to the cascade h aa →b¯bb¯b b→y forcing the be less than 0.1% – roughly 1σ as determined by the latter into two jets and est→imatin→g the efficiency of the electroweak fit [1]. This requirement sets a bound of < h 2b search to pick up h 4b. Comparing Tables ∆ 1/10foraverylightneutralino,andweakerforheav- 27→and 29 in [11], one can see→that DELPHI rules out a ier∼neutrinos as phase space gets reduced. We find that 100 GeV Higgs decaying exclusively to b¯b with roughly in most of our parameter space – where the decay to a quarter of the standard model cross section, while it neutralinos dominates the Higgs width and the chargino requires 80% of the cross section to rule out the same bound is satisfied – we satisfy this constraint. mass Higgs decaying to 4b’s (about three times the sig- Searches for neutralinos which decay via baryon num- nal events). In our case, the Higgs decaysto six jets and ber violation have been preformed by Aleph, DELPHI thus the jets will be softer and more numerous and thus and L3 [13]. None of the three searches were able to put harder to reconstruct into two jets. To see the effect of a bound on the neutralino mass via a direct search, but softerjets,thesametablesshowthatfora65GeVHiggs only through a search for a chargino and the theoreti- decaying to 4b’s vs. 2b’s requires 7-8 times more signal cal assumption M1 = (5/3)tan2θWM2 M2/2 relat- ∼ events – and this is even with pseudo scalars as light as ing the two masses through the assumption of gaugino 12 GeV. In addition, part of the DELPHI analysis takes mass unification. The L3 experiment does present cross- advantage of the additional b quarks in the final state, section bounds for neutralino masses between 30 GeV whereas our final state will have at most 2b’s. Assuming and roughly 100 GeV of around 0.1 pb. The neutralino 3 10 different branching ratios of the Higgs to neutralinos for 7 M2 , M1, and the Higgs mass fixed at 250, 50, and 100 GeVrespectively. Eachpointalsosatisfiestheconstraint 5 on the contribution to the hadronic Z width. We also Β an requiremχ0 >12GeVtoallowforsignificantphasespace t 3 forthedecay. Weseethatalargebranchingratiorequires relatively low values of tanβ and µ. In Figure 2 we scan 2 over M1, M2, µ, and tanβ and plot points which satisfy thecharginomassandZ widthbounds. Forthesepoints, 120 140 160 180 200 220 240 the branching ratio is less than 25% to normal standard Μ@GeVD modeldecays,thusloweringtheHiggsmassboundinthis partofparameterspacetoroughly95-100GeVaccording FIG. 1: A random scan of the parameters µ and tanβ with to Figure 2 of [2]. M2 = 250 GeV, M1 = 50 GeV and mhiggs = 100 GeV. The The scans are done in the decoupling limit (i.e., the borders between the alternating black and gray points rep- resent Higgs branching ratios to neutralinos of (from left to pseudo-scalarmass is fixed at 1 TeV), where the heavier right)90%,85%,80%,75%,and70%respectively. Thewhite CP-evenHiggs boson is much more massive and thus all space to theleft is excluded by thechargino mass bound. couplings of this lightest Higgs are standard model like. Awayfromthislimit,thedecaywidthtostandardmodel 200 channelsincreaseswhile theoverallproductioncrosssec- DV 180 tiongoesdown. ModeratemixingwiththeheavierHiggs e does not significantly change the qualitative features of G @ 160 these plots. ± Χ Thedecaylengthofthe neutralinocanbe longenough of 140 to leave a displaced vertex. The average decay length of s as 120 the lightest neutralino is [15] M 10 20 30 40 50 384π2cos2θw m4q˜ L (βγ) (4) Massof Χ0 @GeVD ≃ α U21 2λ′′2 m5χ | | 3µm 10−2 2 mq˜ 4 30GeV 5 pχ FIG.2: Thelightest chargino massversuslightest neutralino , mass in a scan of µ (from 120 to 250 GeV), tanβ (2 to 5), ∼ |U21|2 (cid:18) λ′′ (cid:19) (cid:16)100GeV(cid:17) (cid:18) mχ (cid:19) mχ M1 (10-100GeV),andM2 (150-400GeV).Forallpoints,the branchingratio to neutralinos is at least 75%. where |U21| is an element of the mixing matrix in the appendix and p is the neutralino’s momentum. Final- χ stateparticlemasses,YukawacouplingsandQCDcorrec- cross section through an s-channel Z at LEP II is tions have all been neglected. For very small couplings, lightneutralinos,orheavyscalarquarks,thedecaylength 4m2 m2 couldbe quite long andmight have been seenas anoma- σ→χ0χ0 =σ→νν¯×∆2r1− sχ 1− sχ!, (3) louseventsatLEPiftheydecayinthetrackingchamber, and perhaps by searches for stable squarks and gluinos where σ→νν¯, the neutrino pair-production cross section, [16] if they decay in or near the hadronic calorimeter. If is 1 pb at center of mass energy √s = 200 GeV. To their decay length is longer than about a meter, the in- ∼ satisfy the L3 bound, we require ∆ < 1/3. This bound visible Higgs search would pick up these events and rule is satisfied in our entire parameter space. However, if out masses up to 114 GeV [17]. scalar leptons are relatively light, a t-channel diagram Whatdoesbaryonnumberviolationdoforsusyparam- candominatethecrosssectionandoverwhelmthebound. eter space? In general, bounds on superpartner masses Requiring the cross section to satisfy the L3 constraint are weaker than in the case of the R-parity conserv- places a lower bound of 300 GeV on scalar electron ing MSSM due to a lack of missing energy in the sig- ∼ masses (in the case degenerate scalars). This becomes nal. The current bounds of 200 - 300 GeV on squarks our strongest constraint on a superpartner mass in the and gluinos from Tevatron searches came from analy- baryon-numberviolatingMSSM.Thelightestneutralino, ses which required significant missing transverse energy due to the weakness of their couplings and the nature of cuts [18]. With baryon-number and R-parity violating theirdecays,hasnosignificantcolliderboundwithinour interactions, the bounds on all superpartners are below parameter space. 100 GeV, except for the chargino, whose bound remains The points in parameter space which predict a large roughly the same (102.5 GeV) [19]. The bounds on the Higgstoneutralinosbranchingratioandsatisfythelower lightest neutralino quoted in the particle data book are bound on the chargino mass satisfy M2 >3M1 [14], and due to chargino searchesand the requirementof gaugino the effect on the branching ratio becomes unimportant massunification. ThedirectsearchatLEPforadecaying above M2 > 250 GeV. In Figure 1 we show a plot of lightest neutralino is unable to put bounds on its mass. 4 Ofcourseanotherimpactofthismodelistheallowance ging at LHCb would be well suited for this search, and of a lighter Higgs mass thus reducing the need for large the statistics high enough - roughly 30% of the Higgs radiative corrections to the quartic potential from the bosons produced via gluon fusion are expected to fall in stop loop. For the same value of tanβ = 3, the allowed the detector’s acceptance range [26]. In addition, half lighter Higgs mass (say around 96 GeV) requires an en- of these decays wouldbe baryonviolating (assuming the hancement of the quartic of only half as much as in the lightestneutralinoisaMajoranaparticle)andthiscould MSSM with R-parity conservation. If instead we com- potentially be a striking signal. Finally, the small but pare allowed MSSM Higgs masses at large tanβ to our non-zerocoupling oflong-livedneutralinosto the Z may model’s allowed Higgs masses at tanβ = 3 (since we re- allow them to be discovered by studying the beam gas quire lowvalues for ourdecayto dominate),we still typ- (“vertex-less”)events in LEP I data [27]. ically require a lower quartic enhancement by roughly Appendix: The neutralino mass matrix 10 30%. This translates into lower stop masses needed and−less tuning. However, while R parity violation and mχ1 0 0 0 non-unified gaugino masses help to relieve much of the U 0 mχ2 0 0 UT = (5) persistent fine tuning in the MSSM, they clearly do not  0 0 mχ3 0  eliminate it [20]. Among the strongest constraints are  0 0 0 mχ4  the chargino mass bound and the restrictions on contri-  M2 0 mZcwcβ mZcwsβ bbuoutinodnsretqoubir→esosγne. Itnobadedinitiaonn,oanv-goeidnienrgictphaertHoigfgpsamraamss-  m c0 c mMs1 c −mZ0swcβ −mZsµwsβ  Z w β Z w β eter space in which the Higgs decays to neutralinos. m c s −m s s µ −0 R parity violation can allow for other non-standard  − Z w β Z w β −  Higgs decays which evade LEP searches. For example, isdiagonalizedfromthe gaugebasistothe massbasisby one linear combination of scalar bottom squarks can be the orthogonalmatrixU. The eigenvaluesarein ascend- perhaps as light as 7.5 GeV [21] due to suppressed cou- ing order in magnitude, and thus m is the mass of the χ1 plings to the Z. With baryon number violation, and lightest neutralino. In the gauge basis, the mass matrix sbottom masses below half the Higgs mass, this would above multiplies the vector W˜,B˜,H˜,H˜¯ corresponding allow the Higgs to decay to four light jets, and the de- to the wino, bino anddown-{and up-type}higgsinos. The cay would dominate standard Higgs decays at moderate bino-higgsino mixing can be characterized by a parame- to large tanβ [22]. On the other hand, lepton number ter ∆ (used in the text) defined as violation through, for example, the superpotential oper- ator λ′i33LiQ3D3c could produce a dominant Higgs decay ∆= U13 2 U14 2 (6) of h 4b+E to which the standard 2b and 4b searches | | −| | → 6 should have significantly reduced sensitivity. These and other lepton-number violating decays are being explored Acknowledgments [23]. Iftheabovescenarioiscorrect,searchingfortheHiggs We thank P. Maksimovic, M. Swartz and N. Weiner at hadron colliders could pose great difficulty. However, forusefulconversations,Y.Gaofor collaborationinearly if the neutralinos decay at a displaced vertex with a de- stagesofthiswork,andR.Sundrumforreadingthedraft. cay length greater than about 50 microns, these events This work is supported in part by NSF grants PHY- could potentially be picked up by a dedicated search at 0244990 and PHY-0401513, by DOE grant DE-FG02- the Tevatron, LHC, or LHCb [24, 25]. The vertex tag- 03ER41271,and by the Alfred P. Sloan Foundation. [1] The LEP Electroweak Working Group, [arXiv:hep-ph/0406039]. http://lepewwg.web.cern.ch/LEPEWWG/. [9] G. Abbiendi et al. [OPAL Collaboration], Eur. Phys. J. [2] [ALEPH Collaboration], arXiv:hep-ex/0602042. C 27, 311 (2003) [arXiv:hep-ex/0206022]. [3] See, for example, M. S. Chanowitz, Phys. Rev. D 66, [10] [LEP Higgs Working Group for Higgs boson searches], 073002 (2002) [arXiv:hep-ph/0207123];P.Gambino,Int. arXiv:hep-ex/0107034. J.Mod.Phys.A19,808(2004) [arXiv:hep-ph/0311257]. [11] J. Abdallah et al. 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