from the HL–LHC and ILC, all Higgs coupling scale factors are probed to at least a precision of 1.5%. The Higgs-weak gauge boson couplings can even be probed at the per-mille level. At this level the estimated accuracies are dominated by the assumed theory uncertainties. We find that our estimates for the later ILC stages have a slight tendency to be more conservative than those of e.g. Refs. [379,380], since we include larger theoretical uncertainties for the ILC production cross sections as well as their correlations.
values of an additional Higgs branching fraction, BR(H→NP), are also compatible with zero.
Uncertainties on the fitted scale factors range from around 10% in the most constrained case, i.e. a fit of only one universal scaling parameter, up to 40% for the top Yukawa scale factor,κu, in the seven-dimensional fit discussed in Section 5.2.6. Comparing these results with the latest official scale factor determination performed by CMS for the Moriond 2013 conference, we find significant improvements in all scale factor precisions. This illustrates the power of a common interpretation of ATLAS and CMS (and Tevatron) measurements, as well as the importance of the recent measurements in the ATLASH →τ+τ− and CMSt¯tH-tagged searches.
The corresponding weakest observed limit from the fits on the invisible Higgs decay is BR(H → inv.) < 17 [39]% at the 68% [95%] C.L., also taking into account direct searches for BR(H → inv.) at the LHC. We furthermore find for the total signal strength to known SM final states a lower limit of κ2 ×(1−BR(H → NP)) >81% at the 95% C.L., employing the benchmark fit with one universal Higgs coupling scale factor κ. This limit is independ-ent of any further assumption. Moreover, under the assumption that κW,Z ≤ 1 holds, we find from the most general fit to the present data, which has seven free parameters, the limit BR(H →NP)<40% at the 95% C.L., where the final state(s) of such Higgs decay(s) may be undetectable to current LHC experiments.
Beyond the current measurements from the LHC and the Tevatron, we have explored the capabilities of future Higgs coupling determinations using projections of the signal rate meas-urements for the LHC with 300 fb−1 (LHC 300) and 3000 fb−1 (HL–LHC) at 14 TeV, as well as for various scenarios of an International Linear Collider (ILC). At the LHC 300 we find estimated precisions for the determination of the Higgs coupling scale factors within∼5−18%
under the assumption BR(H → NP) ≡BR(H → inv.). Possible improvements of theoretical uncertainties on the cross sections and branching ratios turn out to have only a marginal effect on those estimated precisions. This changes at the HL–LHC, where the achievable precision of the Higgs-gluon coupling scale factor is significantly limited by the theoretical uncertainty. The precision estimates of the remaining scale factors, however, are hardly affected by varying as-sumptions on the theoretical uncertainties. Overall, assuming BR(H →NP)≡BR(H →inv.), we find scale factor precisions of ∼3−10% at the HL–LHC. If we make the model assumption κV ≤ 1 instead of the assumption that additional non-standard Higgs decays result only in invisible final states, then most of the estimated scale factor precisions marginally improve.
Concerning the prospects at the ILC, we have compared the ILC capabilities of determining Higgs couplings with those of the HL–LHC first for a model-dependent approach, i.e. using the same assumptions as for the HL–LHC analyses, namely assuming either BR(H →NP)≡ BR(H → inv.) or κV ≤ 1 as a means to constrain the total width. We find that already ILC measurements at 250 GeV for ‘baseline’ assumptions on the integrated luminosity provide significant improvements compared to the most optimistic scenario for the HL–LHC along with complementary measurements that are of similar or slightly worse accuracy compared with the projections for the HL–LHC. Starting from a CM energy of √
s = 500 GeV for the corresponding ‘baseline’ luminosity the ILC in fact has the potential to considerably improve upon all measurements of the HL–LHC, apart from the coupling of the Higgs to photons. At
√s= 500 GeV, the W W fusion channel can be measured significantly better than at 250 GeV, which leads to a significantly higher statistics for all considered quantities and in particular to a further improvement in the determination of the total width. The further improvements from ILC running at 1 TeV and from exploiting the ultimate ILC luminosity (LumiUp) turn out to be rather moderate for the considered case of a model-dependent 8-parameter fit, which is related to our fairly conservative estimates of the future theoretical uncertainties.
The impact of the ILC on improving the determination of the Higgs couplings becomes apparent most strikingly for the model-independent analyses. Without employing additional theoretical assumptions the scale factors at the LHC are essentially unconstrained from above.
However, taking into account a single measurement of the ILC — the decay-mode independent recoil analysis of the total Higgs production rate at 250 GeV — in conjunction with the HL–LHC measurements already allows to perform a significantly less model-dependent and more precise fit than with the HL–LHC alone. In particular, with this ILC measurement the assumptions on the additional Higgs decay modes and on κV can be dropped.
From prospective measurements at the ILC up to √
s = 1 TeV with the ‘baseline’ assump-tions for the integrated luminosity together with those from the HL–LHC, we find precision estimates forall fitted Higgs coupling scale factors of better than 2.5%. For some scale factors a precision better than 1% is achieved. These estimates are obtained with the least amount of model assumptions and 8 free fit parameters. With the ultimate ILC luminosity (LumiUp) this precision would further increase significantly, reaching a level of better than 1.5% for all scale factors.
The Higgs coupling scale factor benchmark scenarios considered in this study typically have more freedom to adjust the predicted signal rates to the measurements than realistic models.
Realistic model generally feature specific correlations among the predicted rates which depend non-trivially on the model parameters. Moreover, limits from the electroweak precision data and other sectors, such as dark matter, collider searches, etc., may further restrict the allowed parameter space and thus the room for Higgs coupling deviations. The fact that the exploration of the Higgs couplings with those rather general parametrizations does not improve the fit quality with respect to the SM is a clear indication of the good agreement of the data with the SM predictions. On the basis of this analysis one would not expect a significant improvement in the description of the data from a realistic model of physics beyond the SM. Thus, the full set of the present public measurements from ATLAS, CMS, CDF and DØ in the Higgs sector does not show any indications for physics beyond the SM.
Despite the lack of a concrete hint for any deviation from the SM in the current measurements, there still is ample room for future discoveries of deviations from the SM predictions for the Higgs couplings. In fact, the current uncertainties are still rather large and thus still allow for sizable deviations from the SM at the level of∼ O(10−40%) at the 1σ level, even when making additional theory assumptions, namely BR(H →NP)≡BR(H→inv.) orκV ≤1. Comparing those accuracies with the typical deviations expected in realistic models of physics beyond the SM, a large improvement in the experimental precision will be needed in order to sensitively probe the parameter space of the most popular extensions of the SM. The measurements at an ILC-like machine, in conjunction with the HL–LHC, will be crucial in this context for model-independent determinations of absolute Higgs couplings with precisions at the percent level or better, offering great prospects for identifying the underlying mechanism of electroweak symmetry breaking.
Implications of the Higgs Boson Discovery for Supersymmetry
One of the prime goals of the LHC is to explore the origin of electroweak symmetry breaking.
The Higgs boson discovery at the LHC marks a milestone in this important scientific quest.
As we discussed in Chapter 5, the Higgs signal strengths measured at the LHC experiments are currently in very good agreement with the predictions for the SM Higgs boson. Still, the question arises whether the MSSM (or another model beyond the SM) can give a prediction for the production cross sections and decay widths of the observed Higgs state that yields a better description of the data than the one provided by the SM. The main aim of the work presented in this chapter is to investigate whether, and if so by how much, the MSSM can improve the theoretical description of the current experimental data, and potentially which parts of the parameter space of the MSSM are favored by the current experimental data from the various Higgs search channels.
It was shown that in particular the interpretation of the new state as the lightCP-even Higgs boson of the MSSM is a viable possibility (called the “light Higgs case” in the following). The implications and phenomenology of this scenario have been studied in a series of papers [270, 272, 309, 385]. On the other hand, it was also pointed out that the heavy CP-even Higgs boson can have a mass around 125.7 GeV [270, 272] (called the “heavy Higgs case”) while maintaining a SM-like behavior. All five MSSM Higgs bosons in this scenario would be rather light, and it would in particular imply the existence of another light Higgs boson with a mass below ∼ 125 GeV and suppressed couplings to W and Z bosons. A detailed discussion of the phenomenology of this scenario can also be found in Ref. [273].
In this chapter we study the implications of the Higgs boson mass and signal strength meas-urements for the MSSM parameter space, considering both interpretations of the discovered Higgs state in terms of the light and the heavy CP-even Higgs boson. In Section 6.1we study three of the two-dimensional MSSM benchmark planes suggested for interpretation of SUSY Higgs search results at the LHC [246]. In Section 6.2, we go beyond this rather restricted pic-ture of the MSSM by performing a global fit of the seven-dimensional phenomenological MSSM (pMSSM), taking into account also low energy observables. For this study, we present both the published results from November 2012 as well as updated preliminary results.
6.1 MSSM Higgs benchmark scenarios
In this section we investigate the viability of three MSSM Higgs benchmark scenarios [246,255, 266–268], namely the mmaxh ,mmod+h and low-MH, in the light of current experimental results from Higgs searches. These scenarios were introduced in Section 2.4.3. They are defined in terms of two free parameters, which are chosen to be tanβ and either the CP-odd Higgs boson mass, MA, or the Higgsino mass parameter, µ. The purpose of these benchmark scenarios is to provide a useful framework for the experimental collaborations to present the results from MSSM Higgs searches in a comparable and, if possible, representative way1, see Section 3.1.
Recently, new MSSM benchmark planes have been proposed in Ref. [246] (see Section2.4.3) to account for the observed Higgs state with a mass around 125.7 GeV and the improved exclusion limits from direct LHC searches for SUSY particles. However, so far the LHC experiments have presented their results only for the old version of themmaxh scenario [278–280].
The purpose of the following study is twofold: Firstly, by studying the impact of updated constraints from Higgs searches and the mass and signal rate measurements of the discovered Higgs state, we find the parameter regions within these planes that are most compatible with the experimental data. This complements the discussion presented in Ref. [246]. Although such a study gives a first glimpse on the possible MSSM interpretations of the Higgs boson discovery, it should be kept in mind that these two-dimensional fits are rather restricted and do not represent the full pMSSM parameter space. Hence, a more complete study of the (higher-dimensional) pMSSM will be presented in the next section. Secondly, this study serves as a demonstration of the usefulness of the computer codesHiggsBounds-4and HiggsSignals. These benchmark models provide a comprehensive but non-trivial example to illustrate some important features of these codes.
For each parameter point in these two-dimensional planes we calculated the model predic-tions withFeynHiggs-2.9.4[155–157] and evaluated the totalχ2, comprised of the LEP Higgs exclusionχ2 value [90,257], χ2LEP,HB, obtained from HiggsBounds-4, cf. Section 4.1.4, as well as the totalχ2 fromHiggsSignals-1.2.0using the peak-centeredχ2 method and the experi-mental data presented in Section4.2.3. The 95% C.L. exclusion limits from LHC and Tevatron are applied using2 HiggsBounds-4.0.0. The theoretical mass uncertainty of the lightest Higgs boson is set to 2 GeV when treated as a Gaussian uncertainty (i.e. in the LEP exclusion χ2 fromHiggsBoundsand inHiggsSignals), and to 3 GeV in the evaluation of 95% C.L.excluded regions with HiggsBounds, cf. Section 4.1.3.
The results for the updated mmaxh scenario are shown in Fig.6.1 in the (MA, tanβ) plane.
Besides the colors indicating the ∆χ2 =χ2−χ2best−fit distribution relative to the best fit point (shown as a green star) we also show the parameter regions that are excluded at 95% C.L. by LHC searches for a light charged Higgs boson (dark-green, coarsely striped) [260], neutral Higgs boson(s) in the τ τ final state (orange, checkered) [386] and the combination of SM search channels (red, striped) [339], as obtained using HiggsBounds3. As an indication for the parameter regions that are 95% C.L. excluded by neutral Higgs searches at LEP [90, 257] we include a corresponding contour (black, dashed) for the valueχ2LEP,HB = 4.0. Conversely, the
1 As discussed in Section3.1, a complementary and more usable format to present the null-results from Higgs searches are the model-independent cross section limits for the relevant signal channel(s).
2 Note, that the latest ATLAS limit from charged Higgs boson searches [261], shown in Fig.3.3, is not contained in thisHiggsBoundsversion. However, we do comment on its implications in the following discussion.
3 The exclusion regions imposed from these constraints were also shown in Fig.4.7, albeit, for lower values of the theoretical mass uncertainty for the lightCP-even Higgs boson.
100 200 300 400 500 600 700 800 900 1000 MA / GeV
5 10 15 20 25
tanβ
0 5 10 15 20 25 30
∆χ2
h excl.
h/H/A → ττ excl.
H+ excl.
h LEP excl.
68.3% C.L.
95.5% C.L.
HiggsSignals-1.2.0 (updated) mhmax scenario (MSSM)
Figure 6.1: Distribution of ∆χ2 in the (updated) mmaxh benchmark scenario of the MSSM [246]. The result fromHiggsSignals and the LEP exclusion χ2 ofHiggsBounds are added. The patterned areas indicate parameter regions excluded at 95% C.L.from the following LHC Higgs searches: CMSh/H/A→ τ τ [386] (orange, checkered), ATLAS t → H+b → τ+ντb [260] (green, coarsely striped), CMS SM Higgs combination [339] (red, striped). The 95% C.L.LEP excluded region [90, 257], corresponding to χ2LEP,HB = 4.0, is below the black dashed line. The best fit point, (MA,tanβ) = (872 GeV,5.0) with χ2/ndf = 84.9/83, is indicated by a green star. The 68% and 95% C.L. preferred regions (based on the 2D ∆χ2 probability with respect to the best fit point) are shown as solid and dashed gray lines, respectively.
parameter regions favored by the fit are shown as 68% and 95% C.L. regions (based on the two-dimensional ∆χ2 compatibility with the best fit point) by the solid and dashed gray lines, respectively.
As can be seen in the figure, the best fit regions are obtained in a strip at relatively small values of tanβ ≈ 4.5−7, where in this scenario mh ∼ 125.7 GeV is found. At larger tanβ values the light Higgs mass in this benchmark scenario, which was designed to maximize mh for a given tanβ in the region of large MA, turns out to be higher than the measured mass of the observed signal, resulting in a corresponding χ2 penalty. At very low tanβ values the light Higgs mass is found to be below the preferred mass region, again resulting in aχ2 penalty.
Here, the χ2 obtained from HiggsSignals steeply rises for mh .122 GeV, because the mass-sensitive observables from the H →γγ and H →ZZ(∗)→4`searches cannot be explained by the light Higgs boson anymore, cf. Section 4.2.4. Values ofMA>300 GeV are preferred in this scenario, and thus the light Higgs boson has mainly SM-like couplings. Consequently, the χ2 contribution from the rate measurements is similar to the one for a SM Higgs boson. In this regime, the Higgs mass dependence of the total χ2 from HiggsSignals is comparable to the results shown in Fig.4.12(d). We find the best fit point at (MA,tanβ) = (872 GeV,5.0) with a totalχ2 value over the number of degrees of freedom (ndf)4 of χ2/ndf = 84.9/83.
4 The ndf is calculated here as the sum of 80 Higgs signal strength and four Higgs mass measurements (from
100 200 300 400 500 600 700 800 900 1000 MA / GeV
5 10 15 20 25 30 35 40
tanβ
0 5 10 15 20
∆χ2
h excl.
h/H/A → ττ excl.
H+ excl.
h LEP excl.
68.3% C.L.
95.5% C.L.
HiggsSignals-1.2.0 mhmod+ scenario (MSSM)
Figure 6.2: ∆χ2 distribution (HiggsSignalsandHiggsBounds LEP exclusionχ2 added) in themmod+h benchmark scenario of the MSSM [246]. The excluded regions and contour lines have the same meaning as in Fig.6.1. The best fit point (indicated by a green star) is found at (MA,tanβ) = (988 GeV,9.0)
withχ2/ndf = 85.2/83 .
The second scenario that we discuss here is the mmod+h scenario, i.e. a modification of the mmaxh scenario with a lower value ofXt, leading tomh ∼125.7 GeV over nearly the whole (MA, tanβ) plane [246]. The result is shown in Fig. 6.2 (with the same colors and meaning of the contours as for themmaxh scenario, Fig.6.1). The 95% C.L. excluded regions fromHiggsBounds have already been discussed in Chapter 4, cf. Figs. 4.2 and 4.3. The best fit point is found at (MA,tanβ) = (988 GeV,9.0) with χ2 = 85.2/83. Only slightly larger χ2 values are found over the rest of the plane, except for rather low values MA .300 GeV and tanβ .6.0, where mh is found to be below the preferred mass region. Similar as for the mmaxh scenario the lightest Higgs boson is mostly SM-like in the preferred region, and theχ2 from the signal rates is close to the one found in themmaxh scenario and in the SM.
Finally, we performed a fit in the low-MH benchmark scenario of the MSSM. This scenario is based on the assumption that the Higgs boson observed at∼125.7 GeV is the heavy CP-even Higgs boson of the MSSM. In this case the lightCP-even Higgs has a mass below the LEP limit for a SM Higgs boson of 114.4 GeV [90], but is effectively decoupled from the SM gauge bosons.
The other states of the Higgs spectrum are also rather light, with masses around∼ 130 GeV, thus this scenario is also very sensitive to searches for additional Higgs bosons. SinceMAmust be relatively small in this case the (µ, tanβ) plane is scanned [246], where only tanβ .10 is considered. The CP-odd Higgs boson mass is fixed to MA = 110 GeV. Our results are shown in Fig. 6.3. The 95% C.L. excluded regions are obtained from the same Higgs searches as in Fig. 6.1, except for the red patterned region, which results from applying the limit from the CMS SM Higgs searchH →ZZ(∗)→4`[316] to the SM-like, heavy CP-even Higgs boson.
HiggsSignals) plus one LEP exclusion observable (fromHiggsBounds) minus two free fit parameters.
500 1000 1500 2000 2500 3000 3500 µ / GeV
1 2 3 4 5 6 7 8 9 10
tanβ
0 5 10 15 20 25 30
∆χ2
h/A → ττ excl.
H excl.
H+ excl.
h LEP excl.
68.3% C.L.
95.5% C.L.
HiggsSignals-1.2.0 low-MH scenario (MSSM)
Figure 6.3: ∆χ2distribution (HiggsSignalsandHiggsBoundsLEP exclusionχ2added) in the low-MH
benchmark scenario of the MSSM [246]. The excluded regions and contour lines have the same meaning as in Fig. 6.1, except the red, finely striped region, which gives the 95% C.L. exclusion from the CMS Higgs search H →ZZ(∗)→4` [316], applied to the SM-like heavyCP even Higgs boson. The best fit point (indicated by a green star) is found at (µ,tanβ) = (2810 GeV,6.2) withχ2/ndf = 91.6/83.
Two distinct best fit regions are found [246]: The parameter space with µ∼(1.7−2.2) TeV and tanβ ∼ 3−6 predicts a heavy CP-even Higgs boson with a well compatible mass value mH ≈125.7 GeV and SM-like couplings. However, large parts of this region (with tanβ .4.9) favored by the rate and mass measurements are severely constrained by charged Higgs searches5. The second region favored by the fit is located at large values of µ ∼ (2.3−2.9) TeV and tanβ ∼6−8. Here, the masses of theCP-even Higgs bosons are generally lower. For instance, at the best fit point at (µ, tanβ)∼(2810 GeV,6.2), we havemh≈83.1 GeV andmH ≈123.1 GeV.
For slightly larger (lower) values of µ (tanβ) we find a steep edge in the HiggsSignals χ2 distribution, because mH becomes too low to allow for an assignment of the heavy CP-even Higgs boson to all mass-sensitive peak observables, cf. the results shown in Fig. 4.12(d) in Section 4.2.4. The constraints from LEP Higgs searches for this scenario have already been shown in Fig. 4.9. Due to the low mass of the light CP-even Higgs boson in this region, the LEP channel e+e− → hA[257] is kinematically accessible and contributes a non-negligible χ2 which increases withµ. The parameter space between the two preferred regions suffers a rather large χ2 penalty, since in particular the predicted rates for the H →ZZ∗, W W∗ channels are above the rates measured at the LHC, as can also be seen from the 95% C.L. exclusion by HiggsBoundsin this region.
At the best fit point we find a χ2/ndf = 91.6/83. Compared with the light CP-even Higgs interpretation of the observed signal, as discussed in the mmaxh and mmod+h scenarios, the fit
5 The excluded region shown in Fig.6.3is obtained from an old limit from the ATLAS charged Higgs search [260], based on an integrated luminosity of 4.6 fb−1 collected at √
s = 7 TeV. We discuss the implications of the updated ATLAS limit [261] below.
0.001 0.01 0.1 1
128 129 130 131 132 133 134
BR( t → H+ b ) × BR( H+ →τντ )
MH+ [GeV]
99.7% C.L. region 95.5% C.L. region 68.3% C.L. region
ATLAS H+ limit (7 TeV, 4.6 fb-1) ATLAS H+ limit (8 TeV, 19.5 fb-1) low-MH scenario (MSSM)
Figure 6.4: Branching ratio for the charged Higgs boson signature in top quark decays, BR(t→H+b→ (τ ντ)b), as a function of the charged Higgs mass,MH+, as predicted for the favored (1σ, 2σ and 3σ) regions of the low-MH benchmark scenario. The 95% C.L. upper limits from the old and new ATLAS charged Higgs search analysis [260,261] are overlaid as black and red lines, respectively.
quality is only slightly worse. However, the recently published update of the ATLAS search for light charged Higgs bosons in top quark decays [261], which is based on the full integrated luminosity from the 8 TeV run, leads to an exclusion (at 95% C.L.) of the entire benchmark scenario. This is illustrated in Fig.6.4, where we show the prediction of BR(t→H+b→(τ ντ)b) as a function of the charged Higgs mass, MH+, for the low-MH parameter regions favored by the previous fit. The upper (lower) branch corresponds to the left (right) best fit region in Fig. 6.3. The old [260] and new upper limit [261] from the ATLAS charged Higgs search are included in Fig.6.4as black and red lines, respectively.