In the contest of supersymmetric extensions of the Standard Model, we
consider a spectrum in which the lightest Higgs boson has mass between 200 and
300 GeV and the first two generations of squarks have masses above 20 TeV,
considering the Higgs boson mass and the Supersymmetric Flavour Problem as
related naturalness problems. After the analysis of some models in which the
previous spectrum can be naturally realised, we consider the phenomenological
consequences for the LHC and for Dark Matter.Comment: 8 pages, 5 figures, proceedings of the LC10 worksho

Bertuzzo, Enrico

English

arXiv

In the context of supersymmetric extensions of the Standard Model, we consider a spectrum in which the lightest Higgs boson has mass between 200 and 300 GeV and the first two generations of squarks have masses above 20TeV, considering the Higgs boson mass and the Supersymmetric Flavour Problem as related naturalness problems. After the analysis of some models in which the previous spectrum can be naturally realized, we consider the phenomenological consequences for the LHC and for Dark Matter

Bertuzzo, E.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2011-11010-1Colloquia: LC10IL NUOVO CIMENTO Vol. 34 C, N. 5 Suppl. 1 Settembre-Ottobre 2011On the MSSM with hierarchical squark massesand a heavier Higgs boson(∗)E. BertuzzoScuola Normale Superiore and INFN - Piazza dei Cavalieri 7, 56126 Pisa, Italy(ricevuto il 20 Luglio 2011; pubblicato online il 19 Ottobre 2011)Summary. — In the context of supersymmetric extensions of the Standard Model,we consider a spectrum in which the lightest Higgs boson has mass between 200and 300GeV and the first two generations of squarks have masses above 20TeV,considering the Higgs boson mass and the Supersymmetric Flavour Problem as re-lated naturalness problems. After the analysis of some models in which the previousspectrum can be naturally realized, we consider the phenomenological consequencesfor the LHC and for Dark Matter.PACS 11.30.Pb – Supersymmetry.PACS 12.60.Jv – Supersymmetric models.1. – Introduction and statement of the problemSupersymmetry is surely one of the best motivated extensions of the Standard Model(SM). However, it is well known that the Minimal Supersymmetric Standard Model(MSSM) suffers for at least two phenomenological problems: on the one hand, the MSSMpredicts mh ≤ mZ | cos 2β| as upper bound for the lightest Higgs boson mass at treelevel, in potential conflict with the LEP II lower bound mh ≥ 114GeV [2]. On the otherhand, the MSSM general flavour structure predicts signals potentially in conflict with thepresent good agreement between the SM prediction and the data. As is well known, thefirst problem is a naturalness problem: the sensitivity of the Fermi scale on the averagestop mass makes unnatural to raise the mass of the lightest Higgs boson much above thetree level upper bound [3, 4]. At the same time, the flavour problem can be solved (orat least ameliorated) allowing the masses of the first two generations of squarks to beheavy enough to suppress unwanted signals [5]. Up to which value they can be pushedcan be a naturalness problem as well, so that we argue in favour of a view in which thetwo issues, the “Higgs problem” and the “Flavour problem” may be related naturalnessproblems.(∗) Review of [1].c© Societa` Italiana di Fisica 1516 E. BERTUZZO100100010 000H, H+, Ahf~1,2f~3g~χGeVFig. 1. – A representative of the spectrum we are considering, with mh = 200–300GeV andmq˜1,2 ≥ 20TeV.To be more precise, the more stringent bounds on the masses of the squarks of thefirst two generations come from the ΔS = 2 transitions, both real and especially imagi-nary [6]; demanding only for heavy squark masses, one ends up with masses of the orderof hundreds of TeV, while demanding also for degeneracy and alignment between thefirst two generations of order of the Cabibbo angle, the lower bounds are relaxed: i.e.assuming δLL  δRR,LR (where, according to the standard notation, δ  |m21−m22|(m21+m22)/2andLL, RR and LR refers to left and right sector, respectively) and δLL  λ  0.22 we have(for details, see [1])(1) ΔC = 2 ⇒ mq˜1,2 ≥ 3TeV,Im(ΔS) = 2, sinϕCP  0.3 ⇒ mq˜1,2 ≥ 12TeV.Let us now formulate in equations our starting point: the two naturalness bounds (where1/Δ is the amount of fine-tuning and mt˜ is the average stop mass) [3](2)m2t˜m2h∂m2h∂m2t˜< Δ,m2q˜1,2m2h∂m2h∂m2q˜1,2< Δmust be considered together. It is clear from eq. (2) that increasing the Higgs bosonmass goes in the direction of relaxing any naturalness bound, so that it is conceivable tohave squarks of the first two generations with masses high enough to solve the flavourproblem without introducing too much fine-tuning. In summary, we seek for models inwhich the spectrum of fig. 1 can be realized in a natural manner.Extensions of the MSSM that allow for a significant increase of the Higgs boson masshave been studied in the literature; a representative set is the following:– Extra U(1) factor [7]. The MSSM gauge group is extended to include an additionalU(1)X factor with coupling gx and charge ±1/2 of the two standard Higgs doublet.The extra gauge factor is broken by two extra scalars, φ and φc, at a scale signifi-cantly higher than v. The tree level upper bound on the mass of the lightest scalarbecomes(3) m2h ≤⎛⎜⎝m2Z + g2xv22(1 + M2X2M2φ)⎞⎟⎠ cos2 2βON THE MSSM WITH HIERARCHICAL SQUARK MASSES AND A HEAVIER HIGGS BOSON 1710 102 103 104 105 106 107 1080100200300400Λ (TeV)mhmax(GeV)Fig. 2. – Upper bounds on mh as a function of the scale Λ where some couplings become semi-perturbative in the three different cases: extra U(1) (dot-dashed), λSUSY (solid) and SU(2)(dashed).where MX and Mφ are the masses of the gauge boson and the soft breaking massof φ and φc taken approximately degenerate.– Extra SU(2) factor [7, 8]. The extended gage group is now SU(3)c × SU(2)I ×SU(2)II×U(1)Y where the two SU(2) gauge groups are broken down to the diagonalsubgroup by a chiral bidoublet Σ at a scale much higher than the electroweak scale.The upper bound on the mass of the Higgs boson is now(4) m2h ≤ m2Zg′2 + ηg2g′2 + g2, η =1 + g2IM2Σg2M2X1 + M2ΣM2X,where gI is the gauge coupling associated to SU(2)I , MΣ the soft breaking mass ofthe Σ scalar and MX the mass of the quasi-degenerate heavy gauge triplet vectors.– λSUSY [9, 10]. This is the NMSSM [11] with a largish coupling λ between thesinglet and the two Higgs doublets. The upper bound in this case is(5) m2h ≤ m2Z(cos2 2β +2λ2g2 + g′2sin2 2β).Figure 2 shows the maximal value of mh in the three different cases (tanβ  1 in theextra-gauge cases and low tanβ for λSUSY) as a function of the scale at which therelevant coupling becomes semi-perturbative.2. – Constraints from naturalness and from colour conservationWe can now discuss what happens to the naturalness bounds of eqs. (2) once we raisethe Higgs boson mass. First of all, the bound on the stop mass is relaxed, but now its18 E. BERTUZZO15101520304060 100 100010203040501510152030 40 501002 4 6 8 10 1223456789Log10 (M/TeV)mˆ(TeV)mˆ(TeV)M (TeV)Fig. 3. – Naturalness upper bounds on the common mass of the squarks of the first two gener-ations as a function of the scale M at which the renormalization group flow begins. Left panel:MSSM (mh = 120GeV, tanβ  1), right panel: λSUSY (mh = 200GeV, tanβ  1).value is no longer relevant for the “Higgs boson problem”, since the mass of the lightestHiggs boson is above the LEP bound already at tree level. Concerning the bound on themass of the squarks of the first two generations, fig. 3 shows the comparison between theMSSM (mh = 115GeV, tanβ  1) and λSUSY (mh = 250GeV, tanβ  1), assuming acommon mass m1 = m2 = mˆ at the scale M at which the RGE flow begins (for details,see [1]). We do not show the analogous plot for the two gauge extensions since the boundsare much stronger than the MSSM case.A complementary issue we have to care about is colour conservation, since the largevalues of the masses of the squarks of the first two generations can drive to negative valuesthe squared mass of the third one [12]. To properly analyse the problem, we proceed asfollows: first of all we take a value of mQ˜3 at M that gives at most a 10% fine-tuningon the Fermi scale; we then demand the running due to the squarks of the first twogeneration not to drive mQ˜3 to negative values. The upper bounds on mˆ are shown infig. 4 for different values of the gluino mass, in the MSSM (left panel) and λSUSY (rightpanel), for mh = mZ and mh = 250GeV, respectively. As can be seen, they are similaror weaker than the corresponding bounds obtained from naturalness considerations.3. – PhenomenologyWe now focus on the main phenomenological features of λSUSY: sparticle productionand decays at the LHC, Higgs boson phenomenology and Dark Matter Direct Detection.– It is well known that, at least in the first stage of the LHC run, the relativelymore interesting signals will probably come from gluino pair production (at leastfor gluino masses not too large). An effective way to parametrize the signal isto consider the semi-inclusive branching ratios into tt¯χ (Btt), tb¯χ (Btb) and intobb¯χ (Bbb) where χ stands for the LSP plus W and/or Z bosons. To an excellentON THE MSSM WITH HIERARCHICAL SQUARK MASSES AND A HEAVIER HIGGS BOSON 192 4 6 8 10 122468101214Log10 (M/TeV)mˆ(TeV)mˆ(TeV)60 100 10001020304050M (TeV)Fig. 4. – Upper bounds on the common mass mˆ coming from colour conservation for differentvalues of the gluino mass: 2TeV (solid), 1TeV (dashed) and 0.5TeV (dot-dashed). Left panel:MSSM (mh = mZ), right panel: λSUSY (mh = 250GeV).approximation,(6) Btt + 2Btb + Bbb  1in most of the relevant parameter space [1], so that the final state of gluino pairproduction is pp → g˜g˜ → qqq¯q¯ + χχ with q either a top or a bottom quark.A particularly interesting signal comes from same-sign dilepton production, witha branching ratio given by BR(±±) = 2B2 (Btb + Btt)2 where B = 21% is thebranching ratio of the W boson into leptons. In a relevant portion of the parameterspace, BR(±±) = (2–4)%, unless the two sbottoms become the lightest squarksand/or mg˜ ≤ mLSP + mt.– As a consequence of the large Higgs boson mass, the most striking feature of λSUSYis the discovery of the Golden Mode h→ ZZ with two real Z bosons. However, itmust be stressed that such a signal depends on the chosen superpotential: indeed, ina non scale-invariant case [13], the decoupling of the singlet allows to simply have aheavier Higgs boson with standard couplings to fermions and gauge bosons, so thatthe Golden decay mode is typical. On the other hand, choosing a scale-invariantsuperpotential [14,15], in a relevant region of the parameter space the decay of thelightest Higgs boson into a pair of pseudoscalars is the dominant decay channel, sothat the discovery potential relies essentially on the ability of analyse signaturescoming from this decay. Also intermediate situations are conceivable [16] in which,depending on the region of parameter space, both behaviours can be present.– In λSUSY the LSP can acquire a singlino component, in contrast to what happensin the MSSM. Let us consider the case in which this component is negligible due toa decoupled singlino, so that the LSP is as usual an higgsinos/gauginos admixture20 E. BERTUZZOFig. 5. – (Colour on-line) Isolines of DM abundance (solid) and of LSP masses (dashed) fora decoupled Wino. Dark blue regions: CDMS exclusion, light blue: Xenon100 2010 exclusionprojection. Left: MSSM, mh = 120GeV, tanβ = 7. Right: λSUSY, mh = 200GeV, tanβ = 2.that must satisfy the “Well-Temperament” [17] in order to reproduce correctlythe Dark Matter (DM) relic abundance. To be more precise, let us focus on thewell-tempered bino/higgsino with a decoupled wino. The situation is shown infig. 5 for the MSSM (mh = 120GeV, tanβ = 7) and λSUSY (mh = 200GeV,tanβ = 2). The solid lines represent the DM abundance while the dashed lines arethe LSP mass. The red region corresponds to a DM abundance compatible withthe experiments, the dark blue region is the CDMS exclusion while the light blueregion is the 2010 exclusion projection for Xenon100. As can be seen, in the MSSMcase there is a precise correlation between μ and M1, manifestation of the Well-Temperament. This is not the case for λSUSY, in which the Well-Temperament iscompletely disrupted around the region corresponding to a resonant Higgs bosonexchange in the s-channel. Moreover, the exclusion coming from the direct searchesare much weaker in the λSUSY case, since the spin-independent cross section of aDM particle on a nucleon falls off as 1/m4h.4. – ConclusionsWe considered the possibility of regarding the “Higgs boson problem” and the “Su-persymmetric Flavour Problem” as related naturalness problems, giving attention tomodels in which the Higgs boson mass is increased already at tree level. Among the con-sidered possibilities, we found that in λSUSY [13] an Higgs boson mass of 250–300GeVallows to raise the masses of the squarks of the first two generations up to 20TeV with-out introducing too much fine-tuning, softening in this way the supersymmetric flavourproblem. Among the main phenomenological consequences, it is interesting to stressthe possibility of detecting the golden decay mode h → ZZ in association to typicalsupersymmetric signals due to multi-top final states. Regarding the DM, and focusingon a bino/higgsino LSP, the effect of an increased Higgs boson mass is twofold: on theone hand, the “Well-Temperament” pointed out in [17] is completely disrupted; on theON THE MSSM WITH HIERARCHICAL SQUARK MASSES AND A HEAVIER HIGGS BOSON 21other hand, only a small portion of parameter space is constrained by direct detectionexperiments, since the cross section falls off as 1/m4h.∗ ∗ ∗This work is supported in part by the European Programme “Unification in the LHCEra”, contract PITN-GA-2009-237920 (UNILHC).REFERENCES[1] Barbieri R., Bertuzzo E., Farina M., Lodone P. and Pappadopulo D., JHEP, 1008(2010) 024 [arXiv:1004.2256].[2] Barate R. et al. (LEP Working Group for Higgs boson searches and ALEPHand DELPHI and L3 and OPAL Collaborations), Phys. Lett. B, 565 (2003) 61 [hep-ex/0306033].[3] Barbieri R. and Giudice G. F., Nucl. Phys. B, 306 (1988) 63.[4] Dimopoulos S. and Giudice G. F., Phys. Lett. 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On the MSSM with hierarchical squark masses and a heavier Higgs boson

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