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Lightest Higgs boson masses in the R-parity violating supersymmetry Marek Gó´zd´z∗ Department of Informatics, Maria Curie-Skl odowska University, pl. Marii Curie–Sk lodowskiej 5, 20-031 Lublin, Poland The first results on the searches of the Higgs boson appeared this Summer from the LHC and Tevatrongroups,andhasbeenrecentlybackedupbytheATLASandCMSexperimentstakingdata atCERN’sLHC.Eventhoughtheexcitementthatthisparticlehasbeendetectedisstillpremature, the new data constrain the mass of the lightest Higgs boson mh0 to a very narrow 120–140 GeV region with a possible peak at approximately 125 GeV. Inthiscommunication weshortly presenttheHiggssector inaminimal supergravitymodelwith broken R-parity. Imposing the constraint on mh0 we show that there is a relatively large set of 2 free parameters of the model, for which that constraint is fulfilled. We indetify also points which 1 result in the lightest Higgs boson mass being approximately 125 GeV. Also the dependenceon the 0 magnitudeof theR–parity admixture to themodel is discussed. 2 n PACSnumbers: 11.30.Pb,12.60.Jv,14.60.Pq a Keywords: Higgsbosonmass,neutrinomass,supersymmetry,R-parity J 4 I. INTRODUCTION tested against the newly reported findings [3]. Follow- ] ing this line of research, in this communication we dis- h cuss an R-parity violating minimal supergravity (RpV The Standard Model and most of its supersymmetric p mSUGRA) model and constrain it by the liberal condi- - extensions suffer from being a theory of massless parti- p cles. Therefore a mechanism that would provide masses tionforthe lightestHiggsbosonmass120 GeV≤mh0 ≤ e is required. Among several possibilities the Higgs mech- 140 GeV. Also the specific case of mh0 ≈ 125 GeV is h considered. [ anism plays a major role. It assumes the existence of an additionalscalarfield,theHiggsfield,whichhasnon-zero 1 vacuum expectation value (vev). The correct implemen- v tation of this mechanism leads in the Standard Model II. THE MODEL 5 not only to massive gauge bosons (with the photon cor- 7 8 rectlyremainingmassless),butalsotomassivefermions, The R-parity is a multiplicative quantum number de- 0 and a proper electroweak symmetry breaking from the fined as R = (−1)2s+3(b−ℓ) and implies stability of the . weak gauge groups SU(2) ×U(1) to the electromag- lightestsupersymmetricparticle. Inthispaper,following 1 L Y 0 netism U(1)q. These features make this mechanism an Ref.[4],weadopttheso-calledgeneralizedbaryonparity 2 extremely convenient and elegant solution. The experi- in the form of a discrete Z3 symmetry B3 =R3L3 which 1 mentalsmokinggunconfirmingthis theorywouldbe the ensures the stability of the proton and lack of unwanted : discovery of the Higgs boson. dimension-5 operators. In short, R is equal to +1 for v i Earlierthisyearthe TevatroncollaborationsCDFand ordinaryparticles,andR=−1forsupersymmetricpart- X D0 reportedan excessof eventsin the Higgs to two pho- ners, and this R is usually assumed to be conserved in r tonschannel(H →γγ)observedinthemassregion120– interactions. This assumption, however, is based mainly a 140Gev[1]. Thesignificanceofthesedatawerereported on our will to exclude lepton and baryonnumber violat- on the level of 2.5σ. Only recently the newly announced ing processes, which has not been observed in the low- LHC–7 results [2] fromthe ATLAS and CMS Collabora- energy regime. Notice, that the generation lepton num- tions confirmed an excess of events in the same channel bersℓe,ℓµ,andℓτ,alsoconservedinthestandardmodel, within115–130GeVrange,withamaximumat125GeV, are broken in the neutrino oscillations. There is in fact at the statistical significance of ≈2σ. Even though 2.5σ no underlying principle which forbids breaking of ℓ or b. cannot be named a discovery, an effect independently Thebaryonnumberviolationishighlyconstrainedbythe obtainedwithin verysimilar massrangesbyfour project protondecay,buttheleptonnumberviolationmayoccur workingontwobiggestacceleratorsintheworldmaygive at high energies. In general supersymmetric models one hope that some new particle has been observed. often discusses the possibility of having the R-parity vi- Even though the experimental results are at first in- olating terms, properly suppressed, in the theory. These terpretedwithinthestandardmodel,itssupersymmetric are the so-called R–parity violating models. and other exotic extensions of various kinds can also be We performthe calculationswithin the frameworkde- scribedindetailinRef.[4]. Thismodeltakesintoaccount fulldependenceofthemassmatricesandrenormalization groupequationsontheR–parityviolatingcouplings. We ∗Electronicaddress: [email protected] define it below by quoting the expressions for the super- 2 potential and soft supersymmetry breaking Lagrangian. mayexceed100. Thislowerssignificantlytheirpredictive Next, we discuss the free parameters of the model, and power. Therefore it is a custom approachto impose cer- the Higgs sector. tain boundary conditions, which allow in turn to derive The interactions are defined by the superpotential, other unknown parameters. One may either start with which consists of the R–parityconserving(RpC) and vi- certain known values at low energies and evaluate the olating part valuesofotherparametersathigherenergies,orassume, alongtheGrandUnifiedTheories(GUT)lineofthinking, W =WRpC+WRpV, (1) commonvaluesattheunificationscaleandevaluatethem down. Inbothcasestherenormalizationgroupequations where (RGE)areused. Wefollowthetop-downapproachbyas- suming the following: W = ǫ (Y ) LaHbE¯ +(Y ) QaxHbD¯ RpC ab E ij i d j D ij i d jx h • we introduceacommonmassm for allthe scalars 0 + (Y ) QaxHbU¯ −µHaHb , (2) at the GUT scale m ≈1.2×1016 GeV, U ij i u jx d u GUT i 1 • we introduce a similar common mass m for all WRpV = ǫab(cid:20)2(ΛEk)ijLaiLbjE¯k+(ΛDk)ijLaiQxjbD¯kx(cid:21). the fermions at the GUT scale, 1/2 (3) • wesetallthetrilinearsoftsupersymmetrybreaking couplings A to be proportional to the respective Here Y’s are the 3×3 trilinear Yukawa-like couplings, µ Yukawa couplings with a common factor A , A = the bilinear Higgs coupling, and (Λ) and (κi) are the A Y at m . 0 i R-parity violating trilinear and bilinear terms. L and 0 i GUT Q denote the SU(2) left-handed doublets, while E¯, U¯ The only couplings which we allow to evolve freely, are and D¯ are the right-handed lepton, up-quark and down- theRpVΛ’s,whicharesettoacommonvalueΛ atm 0 Z quark SU(2) singlets, respectively. H and H mean and are being modified by the RGE running only. The d u two Higgs doublets. We have introduced color indices reason for this is, that we want to keep them non-zero, x,y,z =1,2,3,generationindicesi,j,k =1,2,3=e,µ,τ but on the other hand their influence at the low scale and the SU(2) gauge indices a,b=1,2. must be small. In the first part of this presentation we The supersymmetry is not observed in the regime of will fix Λ = 10−4, which assures only small admixture 0 energies accessible to our experiments, therefore it must of the RpV interactions. Later, we discuss the impact be broken at some point. A convenient method to take of Λ on the results for certain set of input parameters. 0 thisfactintoaccountistointroduceexplicitterms,which (For a discussion of the Λ’s impact on the RGE running breaksupersymmetryinasoftway,ie.,theydonotsuffer see, eg., Ref. [5]). from ultraviolet divergencies. We add them in the form Therearetworemainingfreeparametersinthemodel, of a scalar Lagrangian[4], onedescribingtheratioofthevacuumexpectationvalues of the two Higgs doublets tanβ = v /v , the other be- u d −L = m2 h†h +m2 h†h +l†(m2)l (4) ing the sign of the Higgs self-coupling constant, sgn(µ), Hd d d Hu u u L + l †(m2 )h +h†(m2 )l which gives altogether only six free parameters. In this i LiHd d d HdLi i calculationswehavekeptµpositive,andfixedΛ ,sothe 0 + q†(m2)q+e(m2)e†+d(m2 )d†+u(m2)u† resultantparameterspacetoanalyzeisfourdimensional. Q E D U + 1 M B˜†B˜+M W˜ †W˜i+M g˜†g˜α+h.c. Itisalsoacommonpracticetorestrictthecalculations 1 2 i 3 α to the third family of quarks and leptons only, which is 2 (cid:16) (cid:17) + [(A ) l h e +(A ) q h d +(A ) q h u supposed to give the dominant contributions. Since this E ij i d j D ij i d j U ij i u j issue is difficult to keep under control, we keep depen- −Bh h +h.c.] d u dence on all three families. Also, unlike the Authors of + [(AEk)ijliljek+(ADk)ijliqjdk+(AUi)jkuidjdk Ref.[4],wekeepthe fulldependenceonalltheRpVcou- −D l h +h.c.], plings. i i u where the lowercaseletter denotes the scalarpartofthe respective superfield. M are the gauginomasses, and A B. The Higgs sector i (B, D )arethesoftsupersymmetrybreakingequivalents i of the trilinear (bilinear) couplings fromthe superpoten- The procedure of finding the minimum for the scalar tial. potential is quite involving. The equations one has to solve in this model are given in Ref. [4], however, the numerical procedure used by us differs slightly from the A. Free parameters one presented in the cited paper. The goal is to find the values of µ, κ , B, and D , as i i Oneoftheweaknessesofthesupersymmetricmodelsis well as the five vacuum expectation values v of u,d,1,2,3 their enormous number of free parameters, which easily the two Higgs bosons and three sneutrinos. The initial 3 values for the vev’s are v =vsinβ, v =vcosβ, v =0, valuesfor the κ andD , providingstartingpointfor the u d i i i where v2 =(246 GeV)2. We start by setting next iteration. The second iteration repeats the same steps as the first one, with the exception that now all µ, µ=κi =B =Di =0 (5) κi, B, and Di contribute to the RGE running. Getting back to the (new) q scale, we solve for µ, B, and v andevaluatinggi,YU,D,E,andΛD,E tothemGUT scale. using the loop-correcmtiendequations i ThereweimposetheGUTunificationconditionsandrun everything down back to the m scale. In this first iter- Z ationthe bestminimizationscalefor the scalarpotential |µ|2 = 1 m2 +m2 vi +κ∗µvi tan2β−1(cid:26)(cid:20) Hd LiHdv i v (cid:21) d d q = [(m2) ]1/2[(m2) ]1/2 (6) 1 v min U 33 Q 33 − m2 +|κ |2− (g2+g2)v2−D i tan2β q (cid:20) Hu i 2 2 i i v (cid:21) (cid:27) u is calculated. At this scale initial values of µ and B are M2 found, according to the relations − Z, (9) 2 |µ|2 = m2Hd −m2Hutan2β − MZ2, (7) B = sin22β (m2Hd −m2Hu +2|µ|2+|κi|2) tan2β−1 2 h v v B = sin2β(m2 −m2 +2|µ|2). (8) +(m2LiHd +κ∗iµ)vdi −Di vuii, (10) 2 Hd Hu Next,aRGErunisperformedfromq to m ,butthis and the so-called tadpole equations for the sneutrino min Z time the non-zero values of µ and B generate non-zero vev’s, which explicitely read v [(m2) +|κ |2+D′]+v [(m2) +κ κ∗]+v [(m2) +κ κ∗]=−[m2 +µ∗κ ]v +D v , 1 L 11 1 2 L 21 1 2 3 L 31 1 3 HdL1 1 d 1 u v [(m2) +κ κ∗]+v [(m2) +|κ |2+D′]+v [(m2) +κ κ∗]=−[m2 +µ∗κ ]v +D v , (11) 1 L 12 2 1 2 L 22 2 3 L 32 2 3 HdL2 2 d 2 u v [(m2) +κ κ∗]+v [(m2) +κ κ∗]+v [(m2) +|κ |2+D′]=−[m2 +µ∗κ ]v +D v , 1 L 13 3 1 2 L 23 3 2 3 L 33 3 HdL3 3 d 3 u where D′ =M2cos2β +(g2+g2)sin2β(v2−v2 −v2). This set of three equations can be easily solved and we get Z 2 2 2 u d detW i v = , i=1,2,3, (12) i detW where (m2) +|κ |2+D′ (m2) +κ κ∗ (m2) +κ κ∗ L 11 1 L 21 1 2 L 31 1 3 W =(m2L)12+κ2κ∗1 (m2L)22+|κ2|2+D′ (m2L)32+κ2κ∗3 , (13) (m2) +κ κ∗ (m2) +κ κ∗ (m2) +|κ |2+D′  L 13 3 1 L 23 3 2 L 33 3  and W can be obtained from W by replacing the i-th column with i −[m2 +µ∗κ ]v +D v HdL1 1 d 1 u −[m2HdL2 +µ∗κ2]vd+D2vu . (14) −[m2 +µ∗κ ]v +D v  HdL3 3 d 3 u  Theequations(9)–(11)aresolvedsubsequentlyuntilcon- III. CONSTRAINING THE MASS SPECTRUM vergence and self-consistency of the results is obtained. After this procedure we add also the dominant radiative Not allinitial parametersresultin an acceptable mass corrections [6], and get back to the m scale to obtain Z spectrum. One may impose several different constraints the mass spectrum of the model. to test the model. The problem, however, is in the fact thattheavailableexperimentaldataareinmostcasesnot confirmedinotherexperiments,nottomentionthatthey For the details of the mass matrices which need to be are very model dependent. Therefore caution is needed diagonalized see Ref. [4]. before such constraints will be imposed. 4 1000 1000 900 900 800 800 700 700 V] V] e 600 e 600 G G [2 [2 1/ 500 1/ 500 m m 400 400 300 300 200 200 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 700 800 900 1000 m [GeV] m [GeV] 0 0 FIG. 1: Solutions for tanβ = 5. For each point there is an FIG. 3: Like Fig. 1 but for tanβ=15. 200 GeV < A < 1000 GeV such that the mass of lightest Higgs boson is in theregion 120–140 GeV. 1000 1000 900 900 800 800 700 700 V] V] Ge 600 Ge 600 m [1/2 500 m [1/2 500 400 400 300 300 200 200 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 700 800 900 1000 m0 [GeV] m0 [GeV] FIG. 2: Like Fig. 1 but for tanβ =10. FIG. 4: Like Fig. 1 but for tanβ=20. A. The (120–140) GeV Higgs boson 1000 First, we are going to check whether the recently sug- 900 gested 120 GeV < mh0 < 140 GeV may be obtained within the described model. The only additional con- 800 straints that we have used are the mass limits for differ- 700 entparticles,aspublishedbytheParticleDataGroupin V] 2m0χ˜1030.>Th1e0y0 GreeaVd,[7m]:χ˜04mχ>˜01 >11646GGeVeV, ,mmχ˜±1χ˜02 >> 6924 GGeeVV,, m [Ge1/2 560000 mχ˜±2 > 94 GeV, me˜ > 107 GeV, mµ˜ > 94 GeV, mτ˜ > 400 82 GeV, m >379 GeV, m >308 GeV. q˜ g˜ We have performed a scan over the whole parameter 300 spacegivenbythefollowingranges: 200 GeV≤m0,1/2 ≤ 200 1000 GeVwithstepof20GeV,5≤tanβ ≤40withstep 200 300 400 500 600 700 800 900 1000 5,200 GeV≤A0 ≤1000 GeVwithstep100. Duringthis m0 [GeV] scanwehavekeptµ>0andafixedΛ =10−4. Foreach 0 point the mass spectrum was calculated and confronted FIG. 5: Like Fig. 1 but for tanβ=25. with the imposed constraints. The results are presented in Figs. 1–8. There is a sep- 5 1000 arate diagram in the m0−m1/2 plane for each tanβ = 5,10,...,40. Everypointonthese diagramssays,thatfor 900 certain values of m , m , and tanβ there is an A be- 0 1/2 0 800 tween 200 GeV and 1000 GeV for which mh0 is between 120GeVand140GeV.ThereforeFigs.1–8representthe 700 ranges of free parameters, for which the model is com- V] Ge 600 patible with the newest experimental suggestions within [2 error margins. 1/ 500 m One sees that for small values of tanβ ≤ 10 the pa- 400 rameter range is quite constrained. For higher values of 300 tanβ the common fermion mass m is preferred to be 1/2 below roughly 600 GeV. A characteristic feature of the 200 200 300 400 500 600 700 800 900 1000 model is presented in Fig. 8, ie., that it breaks down for tanβ ≈40. This is because for suchhigh values the bot- m [GeV] 0 tom and tau Yukawa couplings tend to obtain unaccept- ably highvalues during the RGE running. Similarly, too FIG. 6: Like Fig. 1 but for tanβ =30. small values of tanβ ≤2 make the top Yukawa coupling explode. 1000 B. The 125 GeV Higgs boson 900 800 If we assume, according to the newest data, the lightest Higgs boson mass to be centered around 125 GeV, 700 the allowed parameter space shrinks drastically. First, V] Ge 600 let us allow for a 5 GeV spread in the lightest Higgs [2 boson mass. On Fig. 9 the points corresponding to 1/ 500 m mh0 = (125±2.5) GeV are presented. As a reference, 400 we give the whole list in Tab. I. If we narrowour field of 300 interest to the, say, (125−126) GeV regiononly, we end up with the parameter space listed in Tab. II. It is ap- 200 200 300 400 500 600 700 800 900 1000 parent, that higher values of A0 and tanβ are favoured. Also, quite often if one of the m’s takes smaller value, it m [GeV] 0 is compensated by a high value of the other. Itisworthtocommentatthispointatthe recentcon- FIG. 7: Like Fig. 1 but for tanβ =35. straint on supersymmetry formulated by the LHC col- laborations CMS and ATLAS [8, 9]. It excludes the existence of supersymmetric particles with masses below roughly1 Tev. However,this conclusionhas been drawn 1000 forthesimplestsupersymmetricmodelsinwhich,among others, the R-parity is conserved, and as such do not 900 directly apply to the model discussed here. 800 700 eV] 600 C. The Λ0 dependence G [2 1/ 500 m All the calculations have been presented so far for 400 a fixed Λ = 10−4 parameter. This is just the value 0 300 forwhichthe RpVeffects startto appear,however,their contributionisverysmall. ForΛ =10−5 andbelow,the 200 0 200 300 400 500 600 700 800 900 1000 model essentially becomes R–parity conserving. On the otherhand,valuesofΛ oftheorderof10−2−10−1 have m [GeV] 0 0 averybigimpactontheresults,oftenthrowingthemass spectrum out of the allowed ranges. There is therefore FIG. 8: Like Fig. 1 but for tanβ = 40. For such high value arathermodestregionoftheΛ parametersinwhichthe 0 themodel breaksdown and the results are not reliable. modelisstillphysicallyacceptable,andatthesametime the RpV contributions are not marginal. 6 1000 tan(β)=15 tan(β)=20 tan(β)=25 900 A=500-1000 A=500-1000 A=400-1000 800 V] e 700 G 600 [1/2 500 m 400 300 1000 900 800 V] Ge 700 tan(β)=30 tan(β)=35 600 [2 A=500-1000 A=300-1000 1/ 500 m 400 tan(β)=40 300 A=200-1000 200 200 600 200 600 200 600 1000 m [GeV] m [GeV] m [GeV] 0 0 0 FIG. 9: Parameter space of the mSUGRAmodel constrained by thecondition mh0 =(125±2.5) GeV. 175 126 150 125 V] 100 V] e e m [G0h 75 ppooiinntt ((0035)) m [G0h 125 point (09) 50 point (11) point (12) point (14) 25 point (15) point (06) point (16) point (07) point (18) point (08) 0 124 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1e-07 1e-06 1e-05 0.0001 0.001 0.01 Λ Λ 0 0 300 300 point (01) point (02) 275 point (17) 275 point (04) point (10) 250 point (13) 250 point (19) 225 V] 200 V] 225 e e m [G0h 115705 m [G0h 127050 125 150 100 75 125 50 100 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 Λ Λ 0 0 FIG. 10: The Λ0 dependenceof thelightest Higgs boson mass for candidate points listed in Tab. II. 7 TABLE I: List of free parameters of the model for which TABLEII:ListoffreeparametersofthemSUGRAmodelfor mh0 = (125.5 ±2.5) GeV (cf. Fig. 9). Here, µ > 0 and whichmh0 =(125.5±0.5) GeV. Here,µ>0andΛ0 =10−5. Λ0 =10−5. point no. A0 m0 m1/2 tanβ mh0 A0 m0 m1/2 tanβ mh0 A0 m0 m1/2 tanβ mh0 (01) 200 700 780 40 125.2 200 720 540 40 123.7 700 260 300 15 125.8 (02) 500 360 960 40 125.3 200 700 780 40 125.2 700 400 300 20 126.1 (03) 500 400 300 25 125.4 200 680 940 40 123.0 700 560 340 25 127.0 (04) 500 540 920 40 125.6 300 520 200 35 127.4 700 300 1000 30 124.3 (05) 500 560 340 30 125.6 300 220 620 40 123.2 700 540 880 30 123.4 (06) 500 600 480 40 125.2 300 200 640 40 124.9 700 720 640 30 125.3 (07) 500 620 480 40 125.1 400 460 200 30 126.8 700 760 520 30 123.4 (08) 500 680 480 40 125.8 400 460 220 30 126.0 700 240 900 35 124.2 (09) 600 340 300 20 125.5 400 460 240 30 126.4 700 300 880 35 126.7 (10) 700 240 980 40 125.7 400 460 260 30 127.3 700 300 840 40 126.9 (11) 700 260 300 15 125.8 400 680 240 35 124.7 700 320 840 40 123.2 (12) 700 720 640 30 125.3 400 680 260 35 123.1 700 340 860 40 127.0 (13) 800 300 960 40 125.6 400 680 300 35 124.3 700 360 860 40 124.7 (14) 900 220 520 35 125.7 400 680 320 35 126.9 700 380 860 40 124.0 (15) 900 320 380 15 125.8 400 280 800 40 126.1 700 420 880 40 126.5 (16) 900 460 520 20 125.8 400 260 820 40 126.9 700 200 980 40 124.5 (17) 900 920 820 30 125.6 500 300 220 20 126.9 700 240 980 40 125.7 (18) 1000 340 460 15 125.3 500 400 240 25 123.0 800 280 340 15 123.1 (19) 1000 740 660 25 125.2 500 400 260 25 122.7 800 440 380 20 123.4 500 400 280 25 122.8 800 620 460 25 124.7 500 400 300 25 125.4 800 580 580 25 126.8 LetusnowcheckwhatistheΛ0dependenceofthemh0 500 560 320 30 122.8 800 220 1000 30 122.8 massfor the 19 candidate points listed in Tab.II. We do 500 560 340 30 125.6 800 240 1000 30 124.5 not expect all of them to behave in the same way un- derthe changeoftheΛ parameter,especiallythatsome 500 200 780 35 126.7 800 300 980 30 124.3 0 of them are found in the tanβ = 40 region, which is 500 580 480 40 125.0 800 780 820 30 126.4 in parts numerically unstable. The results are presented 500 600 480 40 125.2 800 880 540 30 126.8 in Fig. 10, where we have grouped the points according 500 620 480 40 125.1 800 200 560 35 122.6 to their functional dependence on Λ . On the lower left 0 500 680 480 40 125.8 800 220 980 35 124.5 hand side pannel two point are presented which seem to 500 540 920 40 125.6 800 300 960 35 126.9 be found by accident only, and they yield the wanted 500 400 940 40 126.2 800 340 940 35 126.8 lightest Higgs boson mass just for the Λ = 10−4 value. 0 500 360 960 40 125.3 800 200 940 40 124.2 Onthelowerrighthandsideandtheupperlefthandside 500 280 1000 40 127.2 800 280 960 40 123.2 pannelswepresentthecategoryofpoints,whichconverge 600 220 260 15 123.1 800 300 960 40 125.6 to the correct mh0 value for decresing Λ0. These points would be the sought solutions in the R–parity conserv- 600 340 260 20 123.4 800 440 1000 40 126.7 ing model, and also in the RpV case presented here for 600 340 280 20 123.6 900 320 380 15 125.8 fine-tuned values of Λ . We see that deviations from 0 600 340 300 20 125.5 900 500 400 20 125.0 the mh0 ≈ 125 GeV may be substantial for Λ0 greater 600 480 300 25 124.9 900 460 520 20 125.8 thanfew×10−4,withgeneraltendencytoincrease(lower 600 480 320 25 126.1 900 680 560 25 123.9 right hand side pannel) or decrease/oscillate (upper left 600 460 400 25 126.3 900 660 620 25 126.7 hand side pannel). The last, upper right hand side pan- 600 640 500 30 126.0 900 920 820 30 125.6 nel shows three points which very weakly depend on the changing of Λ . The solutions obtained form them are 600 200 840 35 123.6 900 980 640 30 127.3 0 stable, regardles in the RpC and RpV regime. These 600 220 840 35 127.3 900 220 520 35 125.7 points, surprisingly, also have tanβ =40. 600 260 820 35 124.5 900 220 540 35 124.4 600 300 800 35 127.3 900 220 560 35 123.3 600 820 920 35 123.3 1000 340 460 15 125.3 IV. CONCLUSIONS 600 240 740 40 124.6 1000 760 600 25 124.9 1000 740 660 25 125.2 It was interesting to check, that for the typical minimal supergravity model with broken R-parity there is 8 a quite wide parameter space, for which the mass of the mSUGRA model which result in a physically acceptable lightest Higgs boson is compatible with the recent Teva- massspectrumandareatthesametimecompatiblewith tronobservations. However,ifonerefinestheconstraints the newest Higgs boson searches. There are many more using the LHC–7 results, the parameter space shrinks points, like the one numbered (1) and (17), which would drastically to a set of points roughly given in Tab. II. alsogivethedesiredmassspectrum,butforwhichaspe- In this communication we have used a very modest set cific fine–tuning of the parametes is necessary. of constraints on the low-energy spectrum, keeping only themostobviousones. 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