The presence of fields at an intermediate scale between the Electroweak and
the Grand Unification scale modifies the evolution of the gauge couplings and
consequently the running of other parameters of the Minimal Supersymmetric
Standard Model, such as gauginos and scalar masses. The net effect is a
modification of the low energy spectrum which affects both the collider
phenomenology and the dark matter relic density.Comment: 6 pages, 12 figures, contribution to Moriond EW 2012 proceeding

Biggio, C.

English

arXiv

The presence of fields at an intermediate scale between the Electroweak and the Grand Unification scale modifies the evolution of the gauge couplings and consequently the running of other parameters of the Minimal Supersymmetric Standard Model, such as gauginos and scalar masses. The net effect is a modification of the low energy spectrum which affects both the collider phenomenology and the dark matter relic density

BIGGIO, CARLA

Archivio istituzionale della ricerca - Università di Genova

PHENOMENOLOGY OF SUSY WITH INTERMEDIATE SCALE PHYSICSC. BIGGIOInstitut de F́ısica d’Altes EnergiesUniversitat Autònoma de Barcelona, 08193 Bellaterra, SpainThe presence of fields at an intermediate scale between the Electroweak and the Grand Uni-fication scale modifies the evolution of the gauge couplings and consequently the runningof other parameters of the Minimal Supersymmetric Standard Model, such as gauginos andscalar masses. The net effect is a modification of the low energy spectrum which affects boththe collider phenomenology and the dark matter relic density.1 IntroductionThe presence of new physics at a scale intermediate between the electroweak (EW) and thegrand unified theory (GUT) scale is common to many supersymmetric (SUSY) models. Forexample, in order to give mass to the neutrinos, the minimal supersymmetric standard model(MSSM) must be extended. The simplest extension consists in the addition of 2 or 3 chiralsuperfields which are singlets under the standard model (SM) gauge group (type I seesaw 1), butother extensions are possible, such as the addition of a pair of 15 + 15 SU(5) representations(type II) 2 or 1 (or 2 or 3) 24 (type III) 3,4. Except for the singlet case, the presence of newchiral superfields (and, in general, of new fields) at an intermediate scale, affects the running ofthe MSSM parameters, with a consequent distorsion of the low energy SUSY spectrum. Otherexamples are models where the breaking of the GUT symmetry to the SM one is realized throughintermediate steps or flavour models with messengers. In the present work we restrict to consideronly chiral superfields at the intermediate scale: as we will see, their main effect is to increasethe value of the unified gauge coupling. The presence of gauge fields would drive the resultin the opposite direction. However, as long as the net effect is the enhancement of the unifiedcoupling, the results shown here will be qualitatively valid also in the presence of vector fields.In the following we will describe the main effects on the running of the MSSM parameters aswell as some phenomenological consequences. We redirect the readers to Ref. 5 for an extendedanalysis.2 MSSM running with intermediate scaleIn order to maintain gauge coupling unification, we assume that only chiral superfields in com-plete vector-like representations of SU(5) are present at the intermediate scale MI . Even if theunification is preserved, the running of gauge couplings is deflected, above the scale MI , by thepresence of the new fields, as can be observed in the left panel of Fig. 1. The net effect is anarXiv:1206.0134v1  [hep-ph]  1 Jun 2012 0 10 20 30 40 50 60102104106108101010121014101610181/αiµ (GeV)MGUTMI0.115101520252 4 6 8 10 12 14 1605101520Log10HMILDb1ΑUFigure 1: Left: modification of the gauge couplings running in the presence of matter at the intermediate scaleMI = 1013 GeV with ∆b = 5 (corresponding, for instance, to a copy of 24); the dashed lines correspond to theMSSM running. Right: contours on the plane MI -∆b of the inverse of the unified gauge coupling 1/αU .increment of the unified gauge coupling, as can be seen by solving 1 loop RGEs:1αU=1αi(MZ)− bSMi2πlnMSMZ− b0i2πlnMGUTMS− ∆b2πlnMGUTMI≡ 1α0U− ∆b2πlnMGUTMI, (1)where α0U is the unified coupling in the MSSM without intermediate scale (α0U ' 1/25), bSMi =(41/10,−19/6,−7) and b0i = (33/5, 1,−3) are respectively the SM and MSSM β-function coeffi-cients for αi (i = 1, 2, 3), ∆b is the universal contribution of the additional fields at MI , given bythe sum of the Dynkin indexes of the SU(5) representations, and MS is the typical low-energySUSY scale. From Eq. (1), we see that, since ∆b ≥ 0 for chiral superfields, the unified couplingαU is in general larger than the MSSM one.The increment of αU is the principal effect of the presence of the intermediate scale and theone which drives all the others. Moreover, by requiring the perturbativity of αU up to the GUTscale, a large portion of the parameter space can already be excluded, as it is shown in the rightpanel of Fig. 1, where the white area corresponds to a Landau pole below MGUT . Notice thatwe are considering 1 loop RGEs. We have checked5 that the consequence of two loops running isto strengthen the effect especially close to the Landau pole, while it is almost irrelevant for low∆b and/or large MI . The perturbativity bounds are then slightly stronger than the ones shownhere and the allowed region is consequently smaller (also for the other plots in the following).Let us now move to consider the effect of the intermediate scale on the other MSSM pa-rameters. Since the RGEs of gaugino masses Mi are strictly related to the ones of the gaugecouplings, the increase of αi above MI will determine a faster running of each Mi. However,since we are assuming gaugino mass unification, the MSSM low energy ratio of gaugino masseswill be maintained and the same MSSM low energy spectrum could be obtained by a simplerescaling of the unified gaugino mass M1/2, which would become larger. Then, if only gauginoswere there, no interesting observable effect would be produced.On the other hand, if we consider scalar masses, we observe a different situation: the incre-ment of gauge couplings and gaugino masses above MI will determine an increase of the lowenergy scalar masses with respect to the MSSM case, for the same low energy gaugino massspectra. This is because, to obtain the same low energy gaugino masses, a higher value for M1/2is needed which, together with the larger values of αi above MI , enhances the gauge part ofthe running of scalar masses in the upper part of the RG flow, generating larger values for lowenergy masses. In a nutshell, the net effect of the intermediate scale is to increase the ratioof scalar over gaugino masses. This is shown in Fig. 2, where the ratio of the first generationsleft-handed squark over the gluino mass is plotted.0.911.32.32 4 6 8 10 12 14 1605101520Log10HMILDbmQ M311.11.523.72 4 6 8 10 12 14 1605101520Log10HMILDbmQ M31.31.52362 4 6 8 10 12 14 1605101520Log10HMILDbmQ M3Figure 2: Ratio of the 1st or 2nd generation LH squarks over the gluino mass M3 for mQ̃/M3 = 0, 1, 2 at MGUT.This has interesting phenomenological consequences, both for what concerns SUSY searchesat the LHC and for the dark matter (DM) phenomenology.3 LHC ObservablesBy looking at the ratio of the first generation left-handed squark over gluino masses in Fig. 2,we already see a potential consequence of the presence of intermediate scale for SUSY collidersearches: the configuration M3 ≈ mQ̃, that gives the highest sensitivity at the LHC, could benever reached, since the tendency is to have heavier squarks. However, if this will be the case,no definite conclusion will be extract, since a similar behaviour could be obtained simply byincreasing the value of the high energy scalar mass (see the right panels of Fig. 2). On the otherhand, if the case M3 ≈ mQ̃ will be observed, this would give an upper bound on αU and stronglyconstrain the intermediate scale parameters.In order to obtain clear information on the intermediate scale physics, observables as muchindipendent as possible of the high energy parameters are necessary. If we assume gaugino massunification and consider one loop RGEs, the gaugino and first generations sfermion masses canbe written as:Mi(MS) = Ai(MS ,∆b,MI)M1/2 (2)m2f̃(MS) = m2f̃(MGUT) +Bf̃ (MS ,∆b,MI)M21/2 , (3)where the coefficients Ai and Bf̃ are functions of ∆b, MI and MS . It is then clear that in thecombination∆ff′i ≡m2f̃−m2f̃ ′M2i(4)the explicit dependence on the GUT-scale parameters drops, if m2f̃ ′(MGUT) = m2f̃(MGUT) ≡ m20as in CMSSM-like scenarios or, more in general, in the case of GUT-symmetric initial conditions(a well-motivated assumption in our setup, as we are requiring unification).As in Ref. 6, where it has been suggested to use these invariants to discriminate amongdifferent SUSY seesaw models, we consider the SU(5)-inspired combinations:∆QU1 ≡m2Q̃−m2ŨM21, ∆QE1 ≡m2Q̃−m2ẼM21, ∆DL1 ≡m2D̃−m2L̃M21. (5)Contours for these quantities on the (MI ,∆b) plane are shown in Fig. 3 (taking MS = 1 TeV).As we can see, the invariants rapidly grow for increasing αU . If the SUSY spectrum will be22.55202 4 6 8 10 12 14 1605101520Log10HMILDbD1QU212230501102 4 6 8 10 12 14 1605101520Log10HMILDbD1QE1718202540702 4 6 8 10 12 14 1605101520Log10HMILDbD1DLFigure 3: Contours for the mass invariants ∆QU1 , ∆QE1 , ∆DL1 for MS = 1TeV.2012 4 6 8 10 12 14 1605101520Log10HMILDbFigure 4: Left panel: an example of cascade decay. Right panel: maximum number of edges.measured at the LHC with enough precision, from these invariants it should be possibile totest if the spectrum is MSSM-like or not, and, in the latter case, even to distinguish betweenthe presence of intermediate scale physics or non-universal boundary conditions, if correlationamong these invariants are verified.aA possible way to measure sparticle masses at the LHC is through cascade decays like theone depicted in Fig. 4. The intermediate particles are real ifmQ̃ > mχ̃02> m˜̀L,R> mχ̃01. (6)In this case the invariant mass distributions of the outgoing SM particles (jets and isolatedleptons) exihibit sharp kinematic end-points. By measuring the position of these endpoints indifferent invariant mass distributions, the masses of the involved sparticles can be measured 7.The presence of intermediate scale physics moves the position of the edges and, if independentmeasurements of sparticle masses and edges were available, then important information on theintermediate scale could be extracted.Moreover, notice that, depending on the spectrum, zero, one or two sharp edges can bepresent. Indeed, this depends if the above condition is satisfied by both m˜̀Land m˜̀Ror byone of them (typically m˜̀R) or none. Since the effect of the intermediate scale is precisely thatof enhancing the ratio of scalar over gaugino masses, the above inequality will be more hardlysatisfied in the presence of intermediate scale physics. In the right panel of Fig. 4 the maximumaIn Ref. 5 also another set of invariants is considered, namely ratios of differences of scalar masses. These havethe advantage of being less dependent on the scale MS . Analogous plots can be obtained.Figure 5: Left: region on the (MI ,∆b) plane where the correct relic density for χ̃01 is obtained via τ̃ coannihilation(blue points corresponds to tanβ = 10, red to tanβ = 30). Right: the same for the A-funnel region.number of edges on the plane (MI ,∆b) is depicted. It is then clear that the observation of two orone edge in the mass invariant distributions would rule out a large portion of parameter space.4 Neutralino Dark MatterThe modification of the SUSY spectrum described in the previous sections can destabilise theregions of the parameter space where precise relations among the parameters are required inorder to fulfill the WMAP bound on DM relic abundance. Indeed the lightest neutralino χ01 isoverproduced in the early universe and the measured DM relic density is not obtained unless theneutralino (co)annihilation cross section is enhanced by particular conditions. Such conditionsdefine few regions in the parameter space where the WMAP bound is satisfied: (i) the τ̃ coanni-hilation region, where the correct relic density is achieved thanks to an efficient τ̃ -χ̃01 coannihi-lation, which requires mτ̃1 ≈ mχ̃01 ; (ii) the “focus-point” region, where the Higgsino-componentof χ̃01 is sizable, i.e. µ ≈ M1; (iii) the A-funnel region, where the neutralino annihilation is en-hanced by a resonant s-channel CP-odd Higgs exchange, if mA ' 2×mχ̃01 . Notice that typicallythe neutralino is B̃-like, which means mχ01≈ M1. Then it is clear that, since the intermediatescale tends to increase the ratio of scalar over gaugino masses, the high-energy parameter spaceregions where the above conditions are satisfied will be distorted and could eventually disappear.We first consider the τ̃ coannihilation region. In the constrained MSSM it usually corre-sponds to a thin strip on the border of an area excluded because it gives a τ̃ lightest SUSYparticle. It has already been noticed in specific models 8,9,3,4,10 that the introduction of newphysics at intermediate scale distorts this region. If the effect is large enough the τ̃ will neverbe ligher than χ01 and the coannihilation region will disappear. In the left panel of Fig. 5 theblue points represent the area on the (MI ,∆b) plane where the coannihilation is possible fortanβ = 10, while the red ones correspond to tanβ = 30 (grey dots correspond to the regionallowed by the perturbativity bounds).b Even if the allowed area can be enlarged for even highertanβ, for αU ≥ 0.1 the coannihilation region will anyway disappear.A similar fate will follow the A-funnel region, as it is shown in the right panel of Fig. 5 fortanβ = 45. Indeed in this case the mass of the CP-odd scalar Higgs is given by m2A ≈ m2Hd−m2Huand, since the ratios |m2Hu,d |/M1 grow with αU , mA/M1 gets increased too. Again, for largeenough αU , the correct neutralino relic density cannot be obtained with such a mechanism.The situation with the focus point region is a bit different. Even if the intermediate scaletends generically to increase the ratio µ/M1 rendering the neutralino more and more B̃-like,it is always possible to find configurations with µ ≈ M1, such that the Higgsino component ofbThe results of this section have been obtained performing numerical two loops computations.χ̃01 is sufficiently large to give a sizeable annihilation cross-section. The focus point region istherefore the only DM branch which is not destabilised by the intermediate scale, if CMSSM-likeboundary conditions are assumed.5 ConclusionsIn this talk we have discussed the main consequences of the presence of chiral superfields ata scale intermediate between the EW and the GUT scale. The main effect is the incrementof the unified gauge coupling, which causes the increment of the ratio of scalar over gauginomasses. This has interesting phenomenological consequences that we have discussed here. Inparticular it destabilises the regions of the parameter space where the correct DM relic densitycan be achieved; only the focus-point region is practically unaffected. The presence of such newphysics can be tested indirectly at the LHC by looking at the (number of) edges in cascadedecays and/or by building mass invariants, once the sparticle spectrum is measured. Thereforewe have shown that precious information, i.e. mainly constraints, on intermediate scale physicscan be obtained by considering the appropriate low energy observables.AcknowledgmentsI thank the organisers of this conference for the pleasant and exciting atmosphere.References1. P. Minkowski, Phys. Lett. B 67 421 (1977); M. Gell-Mann, P. Ramond and R. Slansky, inSupergravity, edited by P. van Nieuwenhuizen and D. Freedman, (North-Holland, 1979),p. 315; T. Yanagida, in Proceedings of the Workshop on the Unified Theory and the BaryonNumber in the Universe, edited by O. Sawada and A. 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Phenomenology of SUSY with intermediate scale physics

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