# Higgs Bosons Near 125 GeV in the NMSSM with Constraints at the GUT Scale

Authors: Ulrich Ellwanger; Cyril Hugonie
Journal: Advances in High Energy Physics
 (2012)

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## Abstract

We study the NMSSM with universal Susy breaking terms (besides the Higgs
sector) at the GUT scale. Within this constrained parameter space, it is not difficult
to find a Higgs boson with a mass of about 125 GeV and an enhanced cross-section in
the diphoton channel. An additional lighter Higgs boson with reduced couplings and a
mass≲ 123 GeV is potentially observable at the LHC. The NMSSM-specific Yukawa
couplings λ and κ are relatively large and tan β is small, such that λ, κ, and the top
Yukawa coupling are of 𝒪(1) at the GUT scale. The lightest stop can be as light
as 105 GeV, and the fine-tuning is modest. WMAP constraints can be satisfied by
a dominantly Higgsino-like LSP with substantial bino, wino, and singlino admixtures
and a mass of ~60–90 GeV, which would potentially be detectable by XENON100.


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## Body

## 1. Introduction

Recently, the ATLAS [1–3] and CMS [4–6] collaborations have presented evidence for a Higgs boson with a mass near 126 GeV (ATLAS) and 125 GeV (CMS in [6]). Interestingly, the best fit to the signal strength σγγ≡σprod(H)×BR(H→γγ) in the γγ search channel is about one standard deviation larger than expected in the Standard Model (SM), σobsγγ/σSMγγ~2 for ATLAS [1, 2], and σobsγγ/σSMγγ~1.6 for CMS [6].Since then, several publications have studied the impact of a Higgs boson in the 125 GeV range on the parameter space of supersymmetric (Susy) extensions of the SM [7–38]. Whereas a Higgs boson in the 125 GeV range is possible within the parameter space of the Minimal Susy SM (MSSM) [7–13, 15, 17–21, 25, 29–37], large radiative corrections involving heavy stops are required, which aggravate the “little fine-tuning problem” of the MSSM. In addition, it would be difficult to explain a large enhancement of the diphoton signal strength in the MSSM [15, 34, 37].Within the Next-to-Minimal Supersymmetric SM (NMSSM [39, 40]), a Higgs boson in the 125 GeV range is much more natural [7, 16, 21, 26, 27, 34]. Additional tree-level contributions and large singlet-doublet mixings in the CP-even Higgs sector can push up the mass of the mostly SM-like Higgs boson and, simultaneously, reduce its coupling to b-quarks which results in a substantial enhancement of its branching fraction into two photons [7, 16, 26, 34]. Studies of the parameter space of the general NMSSM—including the dark matter relic density and dark matter nucleon cross section—were performed in [34, 38].An important question is whether these interesting features of the NMSSM survive universality constraints on the soft Susy breaking parameters at the GUT scale. Since this approach imposes severe restrictions on the sparticle masses and couplings, it allows to study whether these would be consistent with present constraints from direct and indirect sparticle searches, the dark matter relic density and dark matter direct detection experiments. Moreover, it allows to make predictions for future searches, both in the sparticle and the Higgs sector.The (fully constrained) CNMSSM [41, 42] was analysed in [11] with the result that once a relic density in agreement with WMAP [43] is imposed, the Higgs boson mass can barely be above 123 GeV. We find that one should allow for deviations from full universality in the Higgs sector, both for the NMSSM-specific soft Susy breaking terms and the MSSM-like Higgs soft masses like in the MSSM studies in [8, 11, 17, 20]. In analogy to the NUHM version of the MSSM, we will refer to such a model as NUH-NMSSM for nonuniversal Higgs NMSSM. A first study of the NUH-NMSSM was made in [23] which was confined, however, to the more MSSM-like region of the parameter space of the NMSSM involving small values of the NMSSM-specific coupling λ and hence small NMSSM-specific effects in the CP-even Higgs sector.In the present paper we study the NUH-NMSSM for large values of the NMSSM-specific couplingλ (and low tanβ), where the singlet-doublet mixing in the CP-even Higgs sector is large, and we find that the interesting features of the Higgs sector of the NMSSM observed in [7, 16, 21, 26, 27, 34] can remain present, including constraints from searches for squarks and gluinos from ATLAS and CMS [44–46], constraints on the dark matter relic density from WMAP [43] and on the dark matter nucleon cross section from XENON100 [47].Our results in the Higgs sector originate essentially from the strong mixing between all three CP-even Higgs states in the NMSSM: first, a Higgs boson with a mass in the 125 GeV range can have an enhanced diphoton signal strength up toσobsγγ/σSMγγ~2.8. Second, a lighter less SM-like Higgs boson H1 exists, with small couplings to electroweak gauge bosons if MH1≲114 GeV (complying with LEP constraints [48]), but a possibly detectable production cross section at the LHC if MH1≳114 GeV. In fact, a strongly enhanced diphoton signal strength ≳2 of the Higgs boson H2 with its mass in the 125 GeV range is possible only if MH1≳90 GeV. The heaviest CP-even Higgs boson H3, like the heaviest MSSM-like CP-odd and charged Higgs bosons, has masses in the 250–650 GeV range, while the lightest mostly singlet-like CP-odd Higgs state has a mass in the 160–400 GeV range. These comply with constraints both from B-physics and direct Susy Higgs searches also for lower masses due to the low values of tanβ considered here and the large singlet component of the lightest CP-odd state.In the sparticle sector we require masses for the gluino and the first generation squarks to comply with constraints from present direct searches [44–46], but we also study the effect of a reduced sensitivity due to the more complicated decay cascades in the NMSSM [49]. The lightest stop t~1 can be as light as ~105 GeV (still satisfying constraints from ATLAS [50] and the Tevatron [51], the latter due to its dominant decay into a chargino and a b-quark), and the required fine-tuning among the parameters at the GUT scale remains modest. In the neutralino sector, the mixings among the five states (bino, wino, two Higgsinos, and the singlino) are large. The LSP, with a dominant Higgsino component and a mass of 60–90 GeV, has a relic density complying with the WMAP constraints [43] and a direct detection cross-section possibly within the reach of XENON100 [47]. However, the supersymmetric contribution to the anomalous magnetic moment of the muon is somewhat smaller than desired to account for the deviation of the measurement [52] from the SM.In the next section we present the analysed parameter space of the NMSSM with boundary conditions at the GUT scale and the imposed phenomenological constraints; our results are given in Section3 and conclusions in Section 4.


## 2. The NMSSM with Constraints at the GUT Scale

The NMSSM differs from the MSSM due to the presence of the gauge singlet superfieldS. In the simplest Z3 invariant realisation of the NMSSM, the Higgs mass term μHuHd in the superpotential WMSSM of the MSSM is replaced by the coupling λ of S to Hu and Hd and a self-coupling κS3. Hence, in this simplest version the superpotential WNMSSM is scale invariant and given by
(2.1)WNMSSM=λS^H^u·H^d+κ3S^3+⋯,
where hatted letters denote superfields, and the ellipsis denote the MSSM-like Yukawa couplings of H^u and H^d to the quark and lepton superfields. Once the real scalar component of S^ develops a vev s, the first term in WNMSSM generates an effective μ-term,
(2.2)μeff=λs.The soft Susy breaking terms consist of mass terms for the Higgs bosonsHu, Hd, S, squarks q~i≡(u~iL,d~iL), u~iRc, d~iRc, and sleptons ℓ~i≡(ν~iL,e~iL) and e~iRc (where i=1,…,3 is a generation index):
(2.3)-ℒ0=mHu2|Hu|2+mHd2|Hd|2+mS2|S|2+mq~i2|q~i|2+mu~i2|u~iRc|2+md~i2|d~iRc|2+mℓ~i2|ℓ~i|2+me~i2|e~iRc|2,
trilinear interactions involving the third generation squarks, sleptons, and the Higgs fields (neglecting the Yukawa couplings of the two first generations):
(2.4)-ℒ3=({13}htAtQ·Huu~3Rc+hbAbHd·Qd~3Rc+hτAτHd·Le~3Rc+λAλHu·HdS+13κAκS3)+h.c.,
and mass terms for the gauginos B~ (bino), W~a (winos), and G~a (gluinos):
(2.5)-ℒ1/2=12[M1B~B~+M2∑a=13‍W~aW~a+M3∑a=18‍G~aG~a]+h.c.Expressions for the mass matrices of the physical CP-even and CP-odd Higgs states—afterHu, Hd, and S have assumed vevs vu, vd, and s and including the dominant radiative corrections—can be found in [40] and will not be repeated here. The couplings of the CP-even Higgs states depend on their decompositions into the weak eigenstates Hd, Hu, and S, which are denoted by
(2.6)H1=S1,dHd+S1,uHu+S1,sS,H2=S2,dHd+S2,uHu+S2,sS,H3=S3,dHd+S3,uHu+S3,sS.Then the reduced tree-level couplings (relative to a SM-like Higgs boson) ofHi to b quarks, τ leptons, t quarks, and electroweak gauge bosons V are
(2.7)gHibbgHSMbb=gHiττgHSMττ=Si,dcosβ,gHittgHSMtt=Si,usinβ,g-i≡gHiVVgHSMVV=cosβSi,d+sinβSi,u.Mixings between the SU(2)-doublet and singlet sectors are always proportional toλ.As compared to two independent parameters in the Higgs sector of the MSSM at tree level (often chosen astanβ and MA), the Higgs sector of the NMSSM is described by the six parameters,
(2.8)λ,κ,Aλ,Aκ,tanβ≡vu/vd,μeff.Then the soft Susy breaking mass terms for the Higgs bosonsmHu2, mHd2, and mS2 are determined implicitly by MZ, tanβ, and μeff.In constrained versions of the NMSSM (as in the constrained MSSM) one assumes that the soft Susy breaking terms involving gauginos, squarks, or sleptons are identical at the GUT scale:(2.9)M1=M2=M3≡M1/2,mq~i2=mu~i2=md~i2=mℓ~i2=me~i2≡m02,At=Ab=Aτ≡A0.In the NUH-NMSSM considered here one allows the Higgs sector to play a special role: the Higgs soft mass termsmHu2, mHd2, and mS2 are allowed to differ from m02 (and determined implicitly as noted above), and the trilinear couplings Aλ, Aκ can differ from A0. Hence, the complete parameter space is characterized by
(2.10)λ,κ,tanβ,μeff,Aλ,Aκ,A0,M1/2,m0,
where the latter five parameters are taken at the GUT scale.Subsequently we are interested in regions of the parameter space implying large doublet-singlet mixing in the Higgs sector, that is, large values ofλ (and κ) and low values of tanβ, which lead naturally to a SM-like Higgs boson H2 in the 125 GeV range [7, 16, 21, 26, 27, 34]. Requiring 124GeV<MH2<127GeV and σobsγγ(H2)/σSMγγ>1, we find
(2.11)0.41<λ<0.69,0.21<κ<0.46,1.7<tanβ<6,
with many points for tanβ≲2.5. It is intriguing that with these choices at the weak scale, one obtains λ~κ~ht~𝒪(1) for the running couplings at the GUT scale; hence, all 3 Yukawa couplings are close to (but still below) a Landau singularity.We assumeμeff>0. Aκ≲0 at the weak scale is required for positive CP-odd Higgs masses squared. We found that, as a consequence, the coupled RG equations imply essentially A0,Aλ,Aκ<0 at the GUT scale. Constraints on the soft Susy breaking parameters depend strongly on the sparticle decay cascades. Using the absence of signal at the LHC in the jets and missing transverse momentum search channels, bounds in the m0, M1/2 plane have been derived in the CMSSM with tanβ=10 [44–46]. In the NUH-NMSSM, however, we find lighter stops (due to the lower values of tanβ implying a larger value of the top Yukawa coupling, which affects the RGE running of the soft Susy breaking stop masses) and a modified neutralino sector which reduces the sensitivity in these search channels [49].Hence, to start with, we impose only constraints from sparticle searches at LEP [53] and the Tevatron [54, 55], and from stop searches at the Tevatron [51] and the LHC [50]. These imply
(2.12)m0≳140GeV,M1/2≳270GeV,mq~≳580GeV,Mg~≳640GeV.In addition we require that the fine-tuningΔ defined in (3.4) satisfies Δ<120, which implies upper bounds which will be discussed below. However, it is possible that the stronger CMSSM-like constraints in the m0,M1/2 plane [46] also apply to the NUH-NMSSM considered here. These stronger constraints further reduce the allowed points in the parameter space approximately to
(2.13)mq~≳1250GeV,Mg~≳850GeV,
but we implemented the constraints from [46] in the m0, M1/2 plane exactly. These constraints are used for the points shown in the Figures 1–3 below, but the difference between the constraints (2.12) and (2.13) has practically no impact on our results in the Higgs sector. Remarkably, regardless of the constraints in the m0, M1/2 plane, the lightest stop mass can be as low as ~105 GeV.Reduced signal cross sectionsR2 for H2 with a mass in the 124–127 GeV range, as a function of MH1 for a representative sample of viable points in parameter space. (a) R2γγ(gg) (diphoton channel, H2 production via gluon fusion), (b) R2γγ (VBF) (diphoton channel, H2 production via VBF), (c) R2VV (ZZ, WW channels, H2 production via gluon fusion), and (d) R2ττ (VBF) (ττ channel, H2 production via VBF).
(a)
(b)
(c)
(d)(a)R2VV(gg) as function of R2γγ(gg). (b) R2bb¯ (VH) (associate production W/Z+H2 with H2→bb¯) as a function of R2γγ(gg).
(a)
(b)Reduced signal cross sectionsR1 as a function of MH1. (a) R1γγ(gg) (diphoton channel, H1 production via gluon fusion), (b) R1γγ (VBF) (diphoton channel, H1 production via VBF), (c) R1VV(gg) (ZZ and WW channels, H1 production via gluon fusion), and (d) R1ττ (VBF) (ττ channel, H1 production via VBF).
(a)
(b)
(c)
(d)Together with these bounds onm0, M1/2, the above constraints on the Higgs sector and the LEP bound on the chargino mass lead to
(2.14)105<μeff<205GeVforweakconstraints(2.12),105<μeff<160GeVforstrongconstraints(2.13).Appropriate combinations of the bino/wino/higgsino/singlino components ofχ10 are required in order to satisfy the WMAP and XENON100 bounds. This leads to constraints on μeff—relevant for the higgsino components—as function of Mg~, which is proportional to the bino/wino mass terms.We have scanned the parameter space of the NUH-NMSSM given in (2.10) using a Markov Chain Monte Carlo (MCMC) technique, which yields a very large number of points (~106) satisfying all the phenomenological constraints described below. To do so, we have modified the code NMSPEC [56] inside NMSSMTools [57, 58] in order to allow for κ and μeff to be used as input parameters at the weak scale and to compute the Higgs soft masses mHu2, mHd2 at the GUT scale; a corresponding version 3.2.0 will be made public soon. In NMSPEC, the two-loop renormalization group equations (RGEs) between the weak and GUT scales are integrated numerically for all parameters. In the presence of boundary conditions both at the weak and the GUT scales as it is the case here, these can be satisfied only through an iterative process. This iterative process is not guaranteed to converge, notably for large Yukawa couplings as in (2.11). In fact, the RGE integration algorithm within the latest public version 3.1.0 of NMSSMTools had to be modified in version 3.2.0 to achieve convergence for large Yukawa couplings.In the Higgs sector we have used two-loop radiative corrections from [59], and for the top quark pole mass we use mtop=172.9 GeV. Our results in the next section use the reduced Higgs production rates (normalized with respect to the SM production rates) in various channels. For gluon-gluon fusion we use the reduced Higgs-gluon coupling as computed in NMSSMTools, which takes care of all colored (s)particles in the loop. For the low values of tanβ considered here, the top quark loop dominates by far and leads essentially to gHitt/gHSMtt as given in (2.7). Since a single particle loop dominates, radiative corrections not considered in NMSSMTools tend to cancel in the ratio to the SM. Likewise, Higgs production rates via associate production with W/Z (≡V) or vector boson fusion (VBF) are simply proportional to the SM rates rescaled by g-i2 defined in (2.7). The Higgs branching fractions are computed in NMSSMTools to the same accuracy both for the NMSSM and a SM-like Higgs boson, such that radiative corrections not considered in NMSSMTools tend again to cancel in the ratio to the SM.Next we turn to the imposed phenomenological constraints. In the Higgs sector we impose constraints from LEP [48], which still allow for a Higgs mass below 114 GeV if its coupling to the Z boson is reduced. Constraints on Higgs bosons from the LHC are those implemented in version 3.1.0 of NMSSMTools, which are based on public ATLAS and CMS results available at the end of 2011, including constraints from CMS on heavy MSSM-like Higgs bosons decaying to tau pairs [60]. In version 3.2.0, however, we have updated the important γγ search channel with the results from ATLAS [2] and CMS [5]. In order to fit the evidence of both experiments in the γγ channel, we impose 124GeV<MH<127GeV, which is satisfied exclusively by H2 for larger values of λ, and we require a good visibility of H2 in the γγ channel, that is, σobsγγ(H2)/σSMγγ>1 in both the gluon fusion and VBF production modes.Also the constraints fromB-physics are those implemented in version 3.1.0 of NMSSMTools. In spite of charged (resp., CP-odd) Higgs masses as low as ~250 (resp., 160) GeV, these are easily satisfied for low values of tanβ or a large singlet component for the lightest CP-odd state (i.e., the couplings of these Higgs bosons to b-quarks are hardly enhanced with respect to the SM Higgs).The dark matter relic density and direct detection cross section of the LSPχ10 (the lightest neutralino) are computed with the help of MicrOmegas [61–63] implemented in NMSSMTools. The default constraints 0.094<Ωh2<0.136 are slightly weaker than the most recent ones from WMAP [43], but this has no impact on the viable regions in parameter space (only on the number of points retained). We also apply the bounds from XENON100 [47] on the spin-independent χ10-nucleon cross section (roughly σsi(p)≲10-8 pb for Mχ10~60– 90 GeV).Since we hardly find light sleptons of the second generation (and again due to the low values oftanβ), the Susy contribution Δaμ to the anomalous magnetic moment of the muon is below Δaμ≲7·10-10, violating the constraint implemented in NMSSMTools. However, it still improves the discrepancy between the SM and the measured value [52] and can reduce the discrepancy to two standard deviations depending on the employed SM value.


## 3. Results

Some remarks on our results have already been made above. Notably we have no difficulties to find points in the parameter space satisfying the above constraints, including the dark matter relic density and the direct detection cross section,124GeV<MH2<127 GeV and R2γγ>1, where we define
(3.1)R2γγ≡σobsγγ(H2)σSMγγ.The mechanism behind this enhancement has been discussed earlier in [7, 16, 64]: the BR(H2→γγ) is strongly enhanced due to a reduced total width (dominated by Γ(H2→bb-)) for a small reduced coupling gH2bb/gHSMbb in (2.7), that is, a small value of the mixing angle S2,d, in spite of a milder reduction of the partial width Γ(H2→γγ). This occurs for large singlet-doublet mixing (which also leads to an increase of MH2) and requires that the third eigenstate H3 is not decoupled, that is, not too heavy. The enhancement of the BR(H2→γγ) also overcompensates a milder reduction of the production cross section of H2 due to singlet-doublet mixing.The reduction of the total width leads also to a potential increase of the reduced signal rate in theZZ/WW channels (via gluon fusion),
(3.2)R2VV(gg)≡σobsZZ(gg→H2)σSMZZ(gg→H)=σobsWW(gg→H2)σSMWW(gg→H),
in spite of the reduction of the partial widths Γ(H2→ZZ/WW) due to singlet-doublet mixing. A fourth interesting reduced signal cross section is the ττ channel via VBF:
(3.3)R2ττ(VBF)≡σobsττ(WW→H2)σSMττ(WW→H),
which tends to be reduced, however, for a small mixing angle S2,d.Singlet-doublet mixing angles are typically large, if the eigenstates are close in mass. Hence, we should expect thatR2γγ is the larger, the closer MH1 is to MH2, that is, the heavier is H1. Subsequently we consider separately R2γγ(gg) (where H2 is produced via gluon fusion) and R2γγ(VBF) (where H2 is produced via VBF). In Figure 1 we show R2γγ(gg), R2γγ(VBF), R2VV(gg), and R2ττ(VBF) as a function of MH1 for a representative sample of ~2000 points in the scanned parameter space of the semiconstrained NMSSM described above. All points satisfy the WMAP bound on the dark matter relic density, the XENON100 bound on σsi(p), and the stronger lower bound on M1/2 given in (2.13). Relaxing this bound to the one given in (2.12) does not lead to additional regions in Figure 1.We see that, as expected, the ratiosR2γγ(gg), R2γγ(VBF), and R2VV(gg) can increase with MH1, and R2γγ(gg) can become as large as 2.8 for MH1≳115 GeV. The inverse conclusion does not hold: MH1≳115 GeV does not imply R2γγ>2. R2ττ(VBF) is below ~1, and the very small values of R2ττ(VBF) correspond to the highest values of R2γγ(gg). The jump in R2ττ(VBF) near MH1~60 GeV is caused by a combination of LEP, B-physics, and WMAP constraints as well as the condition R2γγ>1. For MH2 in the range 124–127 GeV, none of these reduced signal rates show a significant dependency on MH2; corresponding plots would only transcribe the LHC constraints on each rate as a function MH2, but they would not provide additional informations and are hence omitted.In Figure1(c) we see that R2VV(gg) may be below 1. In fact, the “best fit” to R2WW(gg) by ATLAS [1] and by CMS [4] is below 1, whereas the “best fit” to R2ZZ(gg) is below 1 by CMS [4], but above 1 by ATLAS [1]. We recall that we have R2WW(gg)≡R2ZZ(gg)≡R2VV(gg). Hence, it may be interesting to see to which extend R2VV(gg) and R2γγ(gg) (~R2γγ(VBF)) are correlated. This correlation is shown in Figure 2(a), and we see that R2VV(gg)<1 is possible for R2γγ(gg) up to ~1.5.Recently, excesses compatible with a Higgs boson in the 125 GeV range have also been observed at the Tevatron [65]. Here, the dominant excess originates from associated VH production with H→bb-. The corresponding reduced signal rate for the candidate H2, R2bb-(VH) (which is equal to R2ττ(VBF)) cannot be very small given the observations at the Tevatron. In Figure 2(b) we show R2bb-(VH) against R2γγ(gg). We see that R2bb-(VH)≳0.7 is possible only for R2γγ(gg)≲2, but R2γγ(gg)≳1.6 still allows for R2bb-(VH)≳0.9.Obviously the reduced signal rates ofH1 are also very important. For instance, H1 could be compatible with the excess of events observed by CMS for MH~119.5 GeV in the ZZ channel [4]. On the other hand, for MH~95–100 GeV the upper bounds from LEP on its reduced coupling to the Z boson are particularly weak, and a mostly (but not completely) singlet-like H1 could explain the mild excess of events observed there [48, 66, 67]. The corresponding reduced signal cross-sections as a function of MH1 are shown in Figure 3. As explained in [16], the reduced signal cross-section in the bb- channel at LEP coincides with Rττ(VBF).We see that the reduced signal cross-sections are mostly small forMH1≲110 GeV where the singlet component of H1 is large, but R1ττ(VBF) can be as large as ~0.25 for MH1~95–100 GeV which is interesting given the mild excess of events observed at LEP. On the other hand, for MH1≳110 GeV, R1γγ(gg), R1γγ(VBF) and R1VV(gg) can become as large as ~0.5 and R1ττ(VBF) as large as ~0.9, hence, H1 is potentially detectable.The Higgs sector of the NMSSM contains a third CP-even stateH3, two CP-odd states A1 and A2, and, as in the MSSM, a charged Higgs boson H±. We find that the lightest CP-odd state A1 is mostly singlet-like with a mass in the range 160–400 GeV, and hardly visible at the LHC due to its small production cross-sections. The states H3, A2, and H± all have similar masses in the 250–650 GeV range and would also be difficult to see at the LHC due to the small value of tanβ in the region of the parameter space of interest (2.11).The masses of the sparticles are essentially determined byM1/2, m0, A0, and μeff. In Figure 4 we show the mass mq~ of the lightest first generation squark (dR for our choice of parameters) as well as the mass mt~1 of the lightest (mostly right-handed) stop as a function of the gluino mass Mg~. Here it makes a difference whether we impose the weaker bounds (2.12) or the stronger bounds (2.13): points in red satisfy only the weaker bounds while points in green satisfy both constraints. For Mg~≳640 GeV, a stop mass as small as 105 GeV is not excluded by present searches at the LHC [50], but could become observable in the near future.m
t
~
1 (a) and mq~ (b) as a function of Mg~. Points in red (darker points) satisfy the weaker bounds (2.12), but not the stronger bounds (2.13), while points in green (brighter) satisfy both constraints.
(a)
(b)It is known that the stop mass has an impact on the fine-tuning with respect to the fundamental parameters of Susy extensions of the SM, due to its impact on the running soft Susy breaking Higgs mass terms. In addition, both are affected by the gluino mass. We have estimated the quantitative amount of fine-tuning with respect to the parameters at the GUT scale following the procedure outlined in [68]. There, a fine-tuning measure
(3.4)Δ=Max{ΔiGUT},ΔiGUT=|∂ln(MZ)∂ln(piGUT)|,
was used, where piGUT are all parameters at the GUT scale (Yukawa couplings and soft Susy breaking terms). Note that sometimes ln(MZ2) instead of ln(MZ) is used in the definition of Δ, leading to an obvious factor of 2. We find that Δ, shown as a function of mt~1 and Mg~ in Figure 5, is dominated as usual by piGUT=M1/2.Fine-tuning as a function ofmt~1 (a) and Mg~ (b). The color code is as in Figure 4.
(a)
(b)We see that the fine-tuning1/Δ can be as low as 𝒪(5%) (with the definition in (3.4)) in the range of smaller stop and gluino masses allowed by the weaker lower bounds (2.12), and still as low as 𝒪(2.5%) in the range of stop and gluino masses allowed by the stronger bounds (2.13). Both values are an order of magnitude better than in the MSSM [69].Turning to the neutralino sector we observe, as in the CP-even Higgs sector, large mixing angles involving all 5 neutralinos of the NMSSM. The lightest eigenstateχ10 (the LSP) is mostly higgsino-like, but with sizeable bino, wino, and singlino components and a mass in the 60–90 GeV range. The lower bound on Mχ10 follows from the conditions that invisible decays H2→χ10χ10 do not spoil the condition σobsγγ(H2)/σSMγγ>1, together with the lower LEP bound on chargino masses. Its direct detection cross-section is reduced with respect to pure higgsino-like neutralinos, and can well comply with the constraints from XENON100. In Figure 6 we show the spin-independent neutralino-proton scattering cross-section σsi(p) as a function of Mχ10. We see that the stronger bounds (2.13) imply 60GeV≲Mχ10≲85 GeV, similar to the range within the general NMSSM obtained in [34]. In particular, the plateau observed in Figure 6 for 80≲Mχ10≲90 GeV and σsi(p)~10-7 pb, corresponding to small values of m0,M1/2 and a mostly bino-like χ10, is excluded by both the XENON100 and the strong LHC Susy constraints. The spin-independent neutralino-proton scattering cross-section σsi(p) can vary over a wide range both above and below the XENON100 limit [47] (which remains to be confirmed by other experiments), but plenty of points would satisfy this constraint and become observable in the future.Figure 6
The spin-independent neutralino-proton scattering cross sectionσsi(p) as a function of Mχ10. The blue line indicates the bound from XENON100 [47], and we have added points violating this bound (but respecting all the others). The color code is as in Figure 4.It may be interesting to know some of the properties of the Higgs and sparticle sectors beyond the ones shown in the scatter plots above; to this end we show two benchmark points in Table1. The point (1) has MH1~100 GeV, the point (2) MH1~120 GeV, and they differ in the values for M1/2 and m0. The branching fractions of t~1 are similar for both points: BR(t~1→χ1±+b)~0.7, BR(t~1→χ10+t)~0.2, BR(t~1→χ20+t)~0.1.Table 1
Properties of two benchmark points corresponding to different values ofMH1. All dimensionful parameters are given in GeV. The components of χ10, as well as the components of Hi, are defined such that their squares sum up to 1. The Susy contributions Δaμ to the muon anomalous magnetic moment are those given by NMSSMTools without any theoretical errors.
Point
(
1
)
(
2
)
Param. atMGUT:
M1/2
600
525
m0
600
960
A0
-
1550
-
1140
Aλ
-
625
-
575
Aκ
-
275
-
360
mHu
1670
1880
mHd
445
757
mS
885
1380
λ
0.96
1.48
κ
0.73
1.08
ht
0.83
0.97
Param. atMSusy:
λ
0.545
0.6
κ
0.253
0.321
tanβ
2.40
2.29
μeff
120
122
Sparticle masses:
mg~
1390
1250
mq~
1320
1400
mt~1
359
463
mb~1
1001
1060
mτ~1
528
900
Mχ1±
108
108
Mχ10
77
78
Components ofχ10:
B~
0.20
0.25
W~
-
0.16
-
0.20
H~d
0.48
0.52
H~u
-
0.70
-
0.70
S~
0.46
0.37
Ωh2
0.10
0.10
σsi(p)[10-8 pb]
1.00
0.13
Δaμ[10-10]
0.93
0.52
MH1
100
120
Components ofH1:
Hd
0.39
0.50
Hu
0.34
0.74
S
0.86
0.45
R1γγ(gg)
0.01
0.32
R1γγ(VBF)
0.03
0.40
R1VV(gg)
0.03
0.34
R1ττ(VBF)
0.23
0.88
MH2
124
125
Components ofH2:
Hd
0.26
0.04
Hu
0.85
-
0.54
S
-
0.45
0.84
R2γγ(gg)
1.54
1.77
R2γγ(VBF)
1.42
0.98
R2VV(gg)
1.22
1.01
R2ττ(VBF)
0.63
0.03
MH3
329
305
Components ofH3:
Hd
0.88
0.86
Hu
-
0.40
-
0.40
S
-
0.25
-
0.30
R3γγ(gg)
0.21
0.29
R3γγ(VBF)
0.0006
0.0007
R3VV(gg)
0.001
0.002
R3ττ(VBF)
0.04
0.03


## 4. Conclusions

It has already been noted in [7, 16, 21, 26, 27, 34] that the NMSSM can naturally accomodate Higgs bosons in the 124–127 GeV mass range. In addition, the NMSSM can explain excesses in the γγ channel, as well as potential excesses at different values of the Higgs mass (due to the extended Higgs sector). In the present paper we have shown that these features persist in the constrained NMSSM with nonuniversal Higgs sector, designated here as NUH-NMSSM. The dominant deviation from full universality of all soft Susy breaking terms at the GUT scale originates from the need to have mHu>m0.The following properties of the Higgs sector are peculiar:(i)
the signal rate in theγγ channel can be 2.8 as large as the one of a SM-like Higgs boson, provided the mass of the lighter CP-even state H1 is in the 115–123 GeV range;(ii)
requiring a visible signal rate in thebb- channel of 0.9 times the SM value allows for a signal rate in the γγ channel about 1.6 as large as the one of a SM-like Higgs boson;(iii)
the lighter CP-even stateH1 could explain a mild excess of events around 95–100 GeV observed at LEP, or a second visible Higgs boson below ~123 GeV.In the sparticle sector, the assumption of universality at the GUT scale leads to the following features:(i)
the mass of the lightest stop can be as small as 105 GeV, complying with present constraints forMg~≳640 GeV;(ii)
the fine-tuning with respect to parameters at the GUT scale remains modest, an order of magnitude below the one required in the MSSM;(iii)
the eigenstates in the neutralino sector are strongly mixed, and the lightest neutralino can have a relic density in agreement with WMAP constraints. Its direct detection cross-section can be above or below present XENON100 bounds; most of the points below these bounds should be observable in the near future.Given the large values of the NMSSM-specific couplingλ, all scenarios presented here differ strongly from the MSSM (also by the low value of tanβ). The fact that all 3 Yukawa couplings λ, κ, and ht are of 𝒪(1) at the GUT scale may hint at some strong dynamics present at that scale. It is possible that the deviation from full universality of soft Susy breaking terms at the GUT scale remains confined to mHu>m0; such possibilities require further studies.Of course, first of all the present evidence for a Higgs boson in the 124–127 GeV mass range should be confirmed by more data; then possible evidence for non-SM properties of the Higgs sector like an enhanced cross-section in the diphoton channel will show whether the scenarios presented here are realistic.



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*Source: 625389-2012-09-13.xml*