Multiple Higgs models and the 25 GeV state: NMSSM and 2HDM perspectives Jack Gunion U.C. Davis University of Pittsburgh, December 4, 22 NMSSM Collaborators: G. Belanger, U. Ellwanger, Y. Jiang, S. Kraml, J. Schwarz. Higgs Bosons at 98 and 25 GeV at LEP and the LHC G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang, S. Kraml and J. H. Schwarz. arxiv:2.976 [hep-ph] 2. Two Higgs Bosons at the Tevatron and the LHC? G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang and S. Kraml. arxiv:28.4952 [hep-ph] 3. Diagnosing Degenerate Higgs Bosons at 25 GeV J. F. Gunion, Y. Jiang and S. Kraml. arxiv:28.87 [hep-ph] 4. Could two NMSSM Higgs bosons be present near 25 GeV? J. F. Gunion, Y. Jiang and S. Kraml. arxiv:27.545 [hep-ph] 5. The Constrained NMSSM and Higgs near 25 GeV J. F. Gunion, Y. Jiang and S. Kraml. arxiv:2.982 [hep-ph] Phys. Lett. B 7, 454 (22) 2HDM Collaborators: Alexandra Drozd, Bohdan Grzadkowski, Yun Jiang. Two-Higgs-Doublet Models and Enhanced Rates for a 25 GeV Higgs A. Drozd, B. Grzadkowski, J. F. Gunion and Y. Jiang. arxiv:2.358 [hep-ph]
Higgs-like LHC Excesses at 25 GeV Experimental Higgs-like excesses: define R h Y (X) = σ(pp Y h)br(h X) σ(pp Y h SM )BR(h SM X), where Y = gg or V V. Rh (X) = Y R h Y, () Table : Summary of status for 25 26 GeV Higgs as of HCP R(X), X = γγ 4l lνlν bb τ + τ ATLAS.8 ±.5.4 ±.6.5 ±.6. ±.9 ±.9 ±. (22).7 ±.7.4 ±.8 ±.7 (2+22) CMS.56 ±.43.8 +.35.28.74 ±.25.3 +.7.6.72 ±.52 In addition, we have, combining 2 and 22 data and the various dijet categories, R ATLAS V V (γγ) = 2.9 ±.5 R CMS V V (γγ) =.64 ±.89 (2) J. Gunion, University of Pittsburgh, December 4, 22
and also there is the D+CDF=Tevatron measurements of V h production with h bb giving at 25 GeV (higher if M H 36 GeV is assumed) R Tev V h (bb).56 +.72.73. (3) Note: R(ZZ, W W ) > for ATLAS, whereas R(ZZ, W W ) < for CMS. The big questions:. if the deviations from a single SM Higgs survive what is the model? 2. If they do survive, how far beyond the standard model must we go to describe them? Here, I focus on a a number of amusing possibilities in the NMSSM and summarize some recent pure 2HDM results. J. Gunion, University of Pittsburgh, December 4, 22 2
Enhanced Higgs signals in the NMSSM NMSSM=MSSM+Ŝ. The extra complex S component of Ŝ the NMSSM has h, h 2, h 2, a, a 2. The new NMSSM parameters of the superpotential (λ and κ) and scalar potential (A λ and A κ ) appear as: W λŝĥuĥd + κ 3 Ŝ3, V soft λa λ SH u H d + κ 3 A κs 3 (4) S = is generated by SUSY breakng and solves µ problem: µ eff = λ S. First question: Can the NMSSM give a Higgs mass as large as 25 GeV? Answer: Yes, so long as it is not a highly unified model. For our studies, we employed universal m, except for NUHM (m 2 H u, m 2 H d, m 2 S free), universal A t = A b = A τ = A but allow A λ and A κ to vary freely. Of course, λ > and κ are scanned demanding perturbativity up to the GUT scale. J. Gunion, University of Pittsburgh, December 4, 22 3
Can this model achieve rates in γγ and 4l that are >SM? Answer: it depends on whether or not we insist on getting good a µ. The possible mechanism (arxiv:2.3548, Ellwanger) is to reduce the bb width of the mainly SM-like Higgs by giving it some singlet component. The gg and γγ couplings are less affected. Typically, this requires m h and m h2 to have similar masses (for singletdoublet mixing) and large λ (to enhance Higgs mass). Large λ (by which we mean λ >.) is only possible while retaining perturbativity up to m P l if tan β is modest in size. In the semi-unified model we employ, enhanced rates and/or large λ cannot be made consistent with decent δa µ. (J. F. Gunion, Y. Jiang and S. Kraml.arXiv:2.982 [hep-ph]) The enhanced SM-like Higgs can be either h or h 2. R h i gg (X) (Ch i gg )2 BR(h i X) BR(h SM X), Rh i VBF (X) (Ch i V V )2 BR(h i X) BR(h SM X), (5) where h i is the i th NMSSM scalar Higgs, and h SM is the SM Higgs boson. C h i Y = g Y h i /g Y hsm and R V h for V V h i (V = W, Z) with h i X is equal to R h i VBF (X) in doublets + singlets models. J. Gunion, University of Pittsburgh, December 4, 22 4
7 A λ 5 4 A κ 2 µ eff 3 Some illustrative R gg results from (J. F. Gunion, Y. Jiang and S. Kraml. arxiv:27.545): Figure Legend LEP/Teva B-physics Ωh 2 > δa µ ( ) XENON R h /h 2 (γγ).36 [.5, ].94 (,.2].94 >.2.94-.36 (,.2].94-.36 >.2.94.36 4.27-49. R h 2 (γγ) 2.4 2.2 2.8.6.4.2.8.6.4 23<m h2 <28 4 6 8 2 4 m h [GeV] Figure : The plot shows R gg (γγ) for the cases of 23 < m h < 28 GeV and 23 < m h2 < 28 GeV. Note: red triangle (orange square) is for WMAP window with R gg (γγ) >.2 (R gg (γγ) = [,.2]). J. Gunion, University of Pittsburgh, December 4, 22 5
R h 2 (γγ) 2.4 2.2 2.8.6.4.2.8.6 23<m h2 <28.4..2.3.4.5.6.7 Figure 2: Observe the clear general increase in maximum R gg (γγ) with increasing λ. Green points have good δa µ, m h2 > TeV BUT R gg (γγ). λ R h 2 (γγ) 23<m h2 <28 2.4 2.2 2.8.6.4.2.8.6.4 5 5 2 25 3 35 4 45 m~ t [GeV] Figure 3: The lightest stop has mass 3 7 GeV for red-triangle points. J. Gunion, University of Pittsburgh, December 4, 22 6
If we ignore δa µ, then R gg (γγ) >.2 (even > 2) is possible while satisfying all other constraints provided h and h 2 are close in mass, especially in the case where m h2 [23, 28] GeV window. This raises the issue of scenarios in which both m h and m h2 are in the [23, 28] GeV window where the experiments see the Higgs signal. If h and h 2 are sufficiently degenerate, the experimentalists might not have resolved the two distinct peaks, even in the γγ channel. The rates for the h and h 2 could then add together to give an enhanced γγ, for example, signal. The apparent width or shape of the γγ mass distribution could be altered. There is more room for an apparent mismatch between the γγ channel and other channels, such as bb or 4l, than in non-degenerate situation. In particular, the h and h 2 will generally have different gg and V V production rates and branching ratios. J. Gunion, University of Pittsburgh, December 4, 22 7
Degenerate NMSSM Higgs Scenarios: (arxiv:27.545, JFG, Jiang, Kraml) For the numerical analysis, we use NMSSMTools version 3.2., which has improved convergence of RGEs in the case of large Yukawa couplings. The precise constraints imposed are the following.. Basic constraints: proper RGE solution, no Landau pole, neutralino LSP, Higgs and SUSY mass limits as implemented in NMSSMTools-3.2.. 2. B physics: BR(B s X s γ), M s, M d, BR(B s µ + µ ) (old upper limit), BR(B + τ + ν τ ) and BR(B X s µ + µ ) at 2σ as encoded in NMSSMTools-3.2., plus updates. 3. Dark Matter: Ωh 2 <.36, thus allowing for scenarios in which the relic density arises at least in part from some other source. However, we single out points with.94 Ωh 2.36, which is the WMAP window defined in NMSSMTools-3.2.. J. Gunion, University of Pittsburgh, December 4, 22 8
4. 2 XENON : spin-independent LSP proton scattering cross section bounds implied by the neutralino-mass-dependent XENON bound. (For points with Ωh 2 <.94, we rescale these bounds by a factor of./ωh 2.) (22 XENON has little additional impact.) 5. δa µ ignored: impossible to satisfy for scenarios we study here. Compute the effective Higgs mass in given production and final decay channels Y and X, respectively, and R h gg as m Y h (X) Rh Y (X)m h + R h 2 Y (X)m h 2 R h Y (X) + Rh 2 Y (X) R h Y (X) = Rh Y (X) + Rh 2 Y (X). (6) The extent to which it is appropriate to combine the rates from the h and h 2 depends upon the degree of degeneracy and the experimental resolution. Very roughly, one should probably think of σ res.5 GeV or larger. The widths of the h and h 2 are very much smaller than this resolution. We perform scans covering the following parameter ranges: m 3; m /2 3; tan β 4; J. Gunion, University of Pittsburgh, December 4, 22 9
6 A 6;. λ.7;.5 κ.5; A λ ; A κ ; µ eff 5. (7) We only display points which pass the basic constraints, satisfy B-physics constraints, have Ωh 2 <.36, obey the 2 XENON limit on the LSP scattering cross-section off protons and have both h and h 2 in the desired mass range: 23 GeV < m h, m h2 < 28 GeV. In Fig. 4, points are color coded according to m h2 m h. Circular points have Ωh 2 <.94, while diamond points have.94 Ωh 2.36 (i.e. lie within the WMAP window). Many of the displayed points are such that R h gg (γγ) + Rh 2 gg (γγ) >. A few such points have Ωh 2 in the WMAP window. These points are such that either R h gg (γγ) > 2 or Rh 2 gg (γγ) > 2, with the (γγ) for the other Higgs being small. R h gg However, the majority of the points with R h gg (γγ) + Rh 2 gg (γγ) > have Ωh 2 <.94 and the γγ signal is often shared between the h and the h 2. J. Gunion, University of Pittsburgh, December 4, 22
23<m h,m h2 <28 2.5 2 m h2 -m h > 3. GeV 2. GeV < m h2 -m h 3. GeV.5 GeV < m h2 -m h 2. GeV. GeV < m h2 -m h.5 GeV.5 GeV < m h2 -m h. GeV m h2 -m h.5 GeV.5 R h 2 gg (γγ).5.5.5 2 2.5 R h gg (γγ) Figure 4: Correlation of gg (h, h 2 ) γγ signal strengths when both h and h 2 lie in the 23 28 GeV mass range. The circular points have Ωh 2 <.94, while diamond points have.94 Ωh 2.36. Points are color coded according to m h2 m h. Probably green and cyan points can be resolved in mass. Now combine the h and h 2 signals as described above. Recall: circular (diamond) points have Ωh 2 <.94 (.94 Ωh 2.36). Color code: J. Gunion, University of Pittsburgh, December 4, 22
. red for m h2 m h GeV; 2. blue for GeV < m h2 m h 2 GeV; 3. green for 2 GeV < m h2 m h 3 GeV. For current statistics and σ res >.5 GeV we estimate that the h and h 2 signals will not be seen separately for m h2 m h 2 GeV. In Fig. 5, we show results for R h gg (X) for X = γγ, V V, b b. Enhanced γγ and V V rates from gluon fusion are very common. The bottom-right plot shows that enhancement in the V h with h bb rate is also natural, though not as large as the best fit value suggested by the new Tevatron analysis. Diamond points (i.e. those in the WMAP window) are rare, but typically show enhanced rates. J. Gunion, University of Pittsburgh, December 4, 22 2
R h gg (γγ) R h gg (bb) 3 2.5 2.5.5 23<m h,m h2 <28 23 24 25 26 27 28 m h [GeV].4.2.8.6.4.2 23<m h,m h2 <28 23 24 25 26 27 28 m h [GeV] R h gg (VV) R h VBF (bb) 23<m h,m h2 <28 2.8.6.4.2.8.6.4.2 23 24 25 26 27 28 m h [GeV].2.8.6.4.2 23<m h,m h2 <28 23 24 25 26 27 28 m h [GeV] Figure 5: R h gg (X) for X = γγ, V V, bb, and Rh VBF (bb) versus m h. For application to the Tevatron, note that R h VBF (bb) = Rh V V h (bb). J. Gunion, University of Pittsburgh, December 4, 22 3
23<m h,m h2 <28 23<m h,m h2 <28 3 3 2.5 2.5 2 2 R h gg (γγ).5 R h gg (γγ).5.5.5.2.4.6.8.2.4.6.8 2 R h gg (VV).2.4.6.8.2 R h VBF (bb) Figure 6: Left: correlation between the gluon fusion induced γγ and V V rates relative to the SM. Right: correlation between the gluon fusion induced γγ rate and the V V fusion induced bb rates relative to the SM; the relative rate for V V h with h bb (relevant for the Tevatron) is equal to the latter. Comments on Fig. 6:. Left-hand plot shows the strong correlation between Rgg h (γγ) and (V V ). R h gg J. Gunion, University of Pittsburgh, December 4, 22 4
Note that if Rgg h (γγ).5, as suggested by current experimental results, then in this model Rgg h (V V ).2. 2. The right-hand plot shows the (anti) correlation between Rgg h (γγ) and RV h V h (bb) = Rh VBF (bb). In general, the larger Rgg h (γγ) is, the smaller the value of Rh V V h (bb). However, this latter plot shows that there are parameter choices for which both the γγ rate at the LHC and the V V h( bb) rate at the Tevatron (and LHC) can be enhanced relative to the SM as a result of there being contributions to these rates from both the h and h 2. 3. It is often the case that one of the h or h 2 dominates Rgg h (γγ) while the other dominates RV h V h (bb). This is typical of the diamond WMAP-window points. However, a significant number of the circular Ωh 2 <.94 points are such that either the γγ or the bb signal receives substantial contributions from both the h and the h 2. We did not find points where the γγ and bb final states both receive substantial contributions from both the h and h 2. J. Gunion, University of Pittsburgh, December 4, 22 5
23<m h,m h2 <28 23<m h,m h2 <28 28 3 27 2.5 m h (VV) [GeV] 26 25 24 R h gg (γγ) 2.5.5 23 23 24 25 26 27 28 m h (γγ) [GeV].2.4.6.8.2.4 (C h bb )2 Figure 7: Left: effective Higgs masses obtained from different channels: m gg h (γγ) versus m gg h (V V ). Right: γγ signal strength Rh gg (γγ) versus effective coupling to b b quarks [ (C h b b )2. Here, C h 2 b b R h 2 2 ] [ gg (γγ)ch b b + R h 2 gg (γγ)ch 2 / R h b b gg (γγ) + Rh 2 gg ]. (γγ) Comments on Fig. 7. The m h values for the gluon fusion induced γγ and V V cases are also strongly correlated in fact, they differ by no more than a fraction of a J. Gunion, University of Pittsburgh, December 4, 22 6
GeV and are most often much closer, see the left plot of Fig. 7. 2. The right plot of Fig. 7 illustrates the mechanism behind enhanced rates, namely that large net γγ branching ratio is achieved by reducing the average total width by reducing the average bb coupling strength. The dependence of R h gg (γγ) on λ, κ, tan β and µ eff is illustrated in Fig. 8. We observe that the largest Rgg h (γγ) values arise at large λ, moderate κ, small tan β < 5 (but note that Rgg h (γγ) >.5 is possible even for tan β = 5) and small µ eff < 5 GeV. Such low values of µ eff are very favorable in point of view of fine-tuning, in particular if stops are also light. J. Gunion, University of Pittsburgh, December 4, 22 7
3 2.5 23<m h,m h2 <28 3 2.5 23<m h,m h2 <28 2 2 R h gg (γγ).5 R h gg (γγ).5.5.5..2.3.4.5.6.7 λ.5..5.2.25.3.35.4.45.5.55 κ 23<m h,m h2 <28 23<m h,m h2 <28 3 3 2.5 2.5 R h gg (γγ) 2.5.5 2 4 6 8 2 4 6 tan β R h gg (γγ) 2.5.5 2 4 6 8 2 22 24 26 28 µ eff [GeV] Figure 8: Dependence of R h gg (γγ) on λ, κ, tan β and µ eff. J. Gunion, University of Pittsburgh, December 4, 22 8
Fig. 9 shows that the stop mixing is typically large in these cases, (A t µ eff cot β)/m SUSY.5 2. Moreover, the few points which we found in the WMAP window always have m t < 7 GeV. 23<m h,m h2 <28; R h gg (γγ)>.3 23<m h,m h2 <28; R h gg (γγ)>.3 A t -µcotβ 35 3 25 2 5 5-5 5 5 2 25 3 35 4 (m~ t m~ t ) /2 2 m τ ~ [GeV] 3 25 2 5 5 5 5 2 25 3 35 m~ t [GeV] Figure 9: Left: Stop mixing parameter vs. M SUSY m t m t 2. Right: m τ vs. m t.. Points plotted have R h gg (γγ) >.3. Implications of the enhanced γγ rate scenarios for other observables are also quite interesting. J. Gunion, University of Pittsburgh, December 4, 22 9
First, let us observe from Fig. that these scenarios have squark and gluino masses that are above about.25 TeV ranging up to as high as 6 TeV (where our scanning more or less ended). The WMAP-window points with large Rgg h (γγ) are located at low masses of m g.3 TeV and m q.6 TeV. 23<m h,m h2 <28 m q ~ [GeV] 6 55 5 45 4 35 3 25 2 5 2 3 4 5 6 7 m~ g [GeV] Figure : Average light-flavor squark mass, m q, versus gluino mass, m g, for the points plotted in the previous figures. J. Gunion, University of Pittsburgh, December 4, 22 2
The value of Rgg h (γγ) as a function of the masses of the other Higgs bosons is illustrated in Fig.. 23<m h,m h2 <28 23<m h,m h2 <28 3 3 2.5 2.5 2 2 R h gg (γγ).5 R h gg (γγ).5.5.5 2 3 4 5 6 7 8 m a [GeV] 5 5 2 25 3 m H ± [GeV] Figure : R h gg (γγ) versus the masses of m a and m H ± (note that m H ± m a2 m h3 ). Comments on Fig. :. We see that values above of R h (γγ) >.7 are associated with masses J. Gunion, University of Pittsburgh, December 4, 22 2
for the a 2, h 3 and H ± of order < 5 GeV and for the a of order < 5 GeV. (Note that m a2 m h3 m H ±) Althought these states have moderate masses, their detectability requires further study. 2. One interesting point is that m a 25 GeV is common for points with Rgg h (γγ) > points. We have checked that R a gg (γγ) is quite small for such points typically <.. In Fig. 2, we display Ωh 2 and the spin-independent cross section for LSP scattering on protons, σ SI, for the points plotted in previous figures. Comments on Fig. 2:. Very limited range of LSP masses consistent with the WMAP window, roughly m χ [6, 8] GeV. 2. Corresponding σ SI values range from few 9 pb to as low as few pb. J. Gunion, University of Pittsburgh, December 4, 22 22
23<m h,m h2 <28 23<m h,m h2 <28 Ωh 2.... 6 8 2 4 6 8 2 22 24 26 28 LSP mass [GeV] 23<m h,m h2 <28 σ SI [pb] e-8 e-9 e- e- e-2 e-3 e-4 e-5 e-6 e-7 6 8 2 4 6 8 2 22 24 26 28 LSP mass [GeV] 23<m h,m h2 <28.. Ωh 2. Ωh 2.....3.4.5.6.7.8.9 LSP higgsino component...2.3.4.5.6 LSP singlino component Figure 2: Top row: Ωh 2 and spin-independent cross section on protons versus LSP mass for the points plotted in previous figures. Bottom row: Ωh 2 versus LSP higgsino (left) and singlino (right) components. J. Gunion, University of Pittsburgh, December 4, 22 23
3. Owing to the small µ eff, the LSP is dominantly higgsino, which is also the reason for Ωh 2 typically being too low. The points with Ωh 2 within the WMAP window are mixed higgsino singlino, with a singlino component of the order of 2%, see the bottomrow plots of Fig. 2. It is interesting to note a few points regarding the parameters associated with the points plotted in previous figures.. For the WMAP-window diamond points,λ [.58,.65], κ [.28,.35], and tan β [2.5, 3.5]. 2. Points with Rgg h (γγ) >.3 have λ [.33,.67], κ [.22,.36], and tan β [2, 4]. Can t find scenarios of this degenerate/enhanced type such that δa µ consistent with that needed to explain the current discrepancy. is In particular, the very largest value of δa µ achieved is of order.8 and, further, the WMAP-window points with large Rgg h (γγ, V V ) have δa µ < 6. J. Gunion, University of Pittsburgh, December 4, 22 24
Diagnosing the presence of degenerate Higgses (J. F. Gunion, Y. Jiang and S. Kraml. arxiv:28.87) Given that enhanced Rgg h is very natural if there are degenerate Higgs mass eigenstates, how do we detect degeneracy? Must look at correlations among different R h s. In the context of any doublets plus singlets model not all the R h i s are independent; a complete independent set of R h s can be taken to be: R h gg (V V ), Rh gg (bb), Rh gg (γγ), Rh V BF (V V ), Rh V BF (bb), Rh V BF (γγ). (8) Let us now look in more detail at a given R h Y (X). It takes the form R h Y (X) = i=,2 (C h i Y )2 (C h i X )2 C h i Γ (9) where C h i X for X = γγ, W W, ZZ,... is the ratio of the h ix to h SM X coupling and C h i Γ is the ratio of the total width of the h i to the SM Higgs J. Gunion, University of Pittsburgh, December 4, 22 25
total width. The diagnostic tools that can reveal the existence of a second, quasi-degenerate (but non-interfering in the small width approximation) Higgs state are the double ratios: I): RV h BF (γγ)/rh gg (γγ) h R V h BF (bb)/rh gg (bb), II): RV BF (γγ)/rh gg (γγ) h R V h BF (V V )/Rh gg (V V ), III): RV BF (V V )/Rh gg (V V ) R V h BF (bb)/rh gg (bb), () each of which should be unity if only a single Higgs boson is present but, due to the non-factorizing nature of the sum in Eq. (9), are generally expected to deviate from if two (or more) Higgs bosons are contributing to the net h signals. In a doublets+singlets model all other double ratios that are equal to unity for single Higgs exchange are not independent of the above three. Of course, the above three double ratios are not all independent. Which will be most useful depends upon the precision with which the R h s for different initial/final states can be measured. E.g measurements of R h for the bb final state may continue to be somewhat imprecise and it is then double ratio II) that might prove most discriminating. J. Gunion, University of Pittsburgh, December 4, 22 26
Or, it could be that one of the double ratios deviates from unity by a much larger amount than the others, in which case it might be most discriminating even if the R h s involved are not measured with great precision. In Fig. 3, we plot the numerator versus the denominator of the double ratios I) and II), [III) being very like I) due to the correlation between the Rgg h (γγ) and Rh gg (V V ) values discussed earlier]. We observe that any one of these double ratios will often, but not always, deviate from unity (the diagonal dashed line in the figure). The probability of such deviation increases dramatically if we require (as apparently preferred by LHC data) Rgg h (γγ) >, see the solid (vs. open) symbols of Fig. 3. This is further elucidated in Fig. 4 where we display the double ratios I) and II) as functions of Rgg h (γγ) (left plots). For the NMSSM, it seems that the double ratio I) provides the greatest discrimination between degenerate vs. non-degenerate scenarios with values J. Gunion, University of Pittsburgh, December 4, 22 27
very substantially different from unity (the dashed line) for the majority of the degenerate NMSSM scenarios explored in the earlier section of this talk that have enhanced γγ rates. Note in particular that I), being sensitive to the bb final state, singles out degenerate Higgs scenarios even when one or the other of h or h 2 dominates the gg γγ rate, see the top right plot of Fig. 4. In comparison, double ratio II) is most useful for scenarios with R h gg (γγ), as illustrated by the bottom left plot of Fig. 4. Thus, as illustrated by the bottom right plot of Fig. 4, the greatest discriminating power is clearly obtained by measuring both double ratios. In fact, a close examination reveals that there are no points for which both double ratios are exactly! Of course, experimental errors may lead to a region containing a certain number of points in which both double ratios are merely consistent with within the errors. J. Gunion, University of Pittsburgh, December 4, 22 28
23<m h,m h2 <28 23<m h,m h2 <28.8.6 2.4 R h VBF (γγ)/rh gg (γγ).2.8.6 R h gg (bb)/rh gg (γγ).5.4.5.2.2.4.6.8.2.4.6.8 R h VBF (bb)/rh gg (bb).5.5 2 R h VBF (bb)/rh VBF (γγ) Figure 3: Comparisons of pairs of event rate ratios that should be equal if only a single Higgs boson is present. The color code is green for points with 2 GeV < m h2 m h 3 GeV, blue for GeV < m h2 m h 2 GeV, and red for m h2 m h GeV. Large diamond points have Ωh 2 in the WMAP window of [.94,.36], while circular points have Ωh 2 <.94. Solid points are those with R h gg (γγ) > and open symbols have R h gg (γγ). Current experimental values for the ratios from CMS data along with their σ error bars are also shown. J. Gunion, University of Pittsburgh, December 4, 22 29
23<m h,m h2 <28 23<m h,m h2 <28 [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (bb)/rh gg (bb)].2..9.8.7.6.5.4.5.5 2 2.5 3 R h gg (γγ) [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (bb)/rh gg (bb)].2..9.8.7.6.5.4.4.5.6.7.8.9 max [R h gg (γγ),rh 2 gg (γγ)]/rh gg (γγ) [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (VV)/Rh gg (VV)].2..9.8.7.6.5 23<m h,m h2 <28.4.5.5 2 2.5 3 R h gg (γγ) [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (bb)/rh gg (bb)].2..9.8.7.6.5 23<m h,m h2 <28.4.4.5.6.7.8.9..2 [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (VV)/Rh gg (VV)] Figure 4: Double ratios I) and II) of Eq. () as functions of R h gg (γγ) (on the left). [ ] On the right we show (top) double ratio I) vs. max R h gg (γγ), Rh 2 gg (γγ) /R h gg (γγ) and (bottom) double ratio I) vs. double ratio II) for the points displayed in Fig. 6. Colors and symbols are the same as in Fig. 6. J. Gunion, University of Pittsburgh, December 4, 22 3
What does current LHC data say about these various double ratios? The central values and σ error bars for the numerator and denominator of double ratios I) and II) obtained from CMS data (CMS-PAS-HIG-2-2) are also shown in Fig. 6. Obviously, current statistics are inadequate to discriminate whether or not the double ratios deviate from unity. About times increased statistics will be needed. This will not be achieved until the s = 4 TeV run with fb of accumulated luminosity. Nonetheless, it is clear that the double-ratio diagnostic tools will ultimately prove viable and perhaps crucial for determining if the 25 GeV Higgs signal is really only due to a single Higgs-like resonance or if two resonances are contributing. Degeneracy has significant probability in model contexts if enhanced γγ rates are indeed confirmed at higher statistics. J. Gunion, University of Pittsburgh, December 4, 22 3
Higgs at 25 GeV for LHC and 36 GeV for the Tevatron (and LHC?): (G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang and S. Kraml. arxiv:28.4952) Need to rexamine in light of HCP data. However, some salient points that appear to remain relevant are the following:. There is a clear signal for an H at 25 GeV. 2. CMS may have an H 2 at 36 GeV in the γγ final state. ATLAS so far does not see a corresponding γγ peak. 3. If RV BF (τ τ ) at CMS and ATAS remains somewhat suppressed while R V H (bb) measured at the Tevatron remains enhanced over a broad M bb mass range and above what can come from the H, then an H 2 with M H2 35 36 GeV could provide the source of the extra bb events. This possibility is one of the main advantages of this 25+36 idea. J. Gunion, University of Pittsburgh, December 4, 22 32
4. Of course, the H 2 should not appear in the ZZ final state with much strength, since neither CMS nor ATLAS sees a 4l mass peak near 36 GeV. (CMS appears to have something at 44 GeV, but ATLAS has only fluctuations in the relevant mass region.) The NMSSM is flexibile enough to easily give a relevant scenario, but the precise model proposed in our original paper will need some adjustment. And, of course, ATLAS would eventually need to see some signal in the γγ final state at 35 GeV. J. Gunion, University of Pittsburgh, December 4, 22 33
Higgses at 98 GeV for LEP and 25 GeV for LHC: ( G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang, S. Kraml and J. H. Schwarz. arxiv:2.976) We demonstrate that the two lightest CP-even Higgs bosons, h and h 2, of the NMSSM could have properties such that the h fits the LEP excess at 98 GeV while the h 2 is reasonably consistent with the Higgs-like LHC signals at 25 GeV, including in particular the larger-than-sm signal in the γγ channel. To describe the LEP and LHC data the h must be largely singlet and the h 2 primarily doublet (mainly H u for the scenarios we consider). An h 2 with m h2 25 GeV and enhanced γγ rate is obtained, as in previous cases, at large λ and moderate tan β. In order to display the ability of the NMSSM to simultaneously explain the LEP and LHC Higgs-like signals, we (once again) turn to NMSSM scenarios with semi-unified GUT scale soft-susy-breaking. J. Gunion, University of Pittsburgh, December 4, 22 34
All the accepted points correspond to scenarios that obey all experimental constraints (mass limits and flavor constraints as implemented in NMSSMTools, Ωh 2 <.36 and 2 XENON constraints on the spin-independent scattering cross section) except that the SUSY contribution to the anomalous magnetic moment of the muon, δa µ, is too small to explain the discrepancy between the observed value of a µ and the SM prediction. Fig. 5, the crucial plot, shows R h V BF (bb) (which = Rh Z Zh (bb) as for LEP) versus R h 2 gg (γγ) when m h [96, ] GeV and m h2 [23, 28] GeV are imposed in addition to the above mentioned experimental constraints. (In this and all subsequent plots, points with Ωh 2 <.94 are represented by blue circles and points with Ωh 2 [.94,.36] (the WMAP window ) are represented by orange diamonds.) Note that R h V BF (bb) values are required to be smaller than.3 by virtue of the fact that the LEP constraint on the e + e Zbb channel with M bb 98 GeV is included in the NMSSMTools program. Here the Higgs mass windows are designed to allow for theoretical errors in the computation of the Higgs masses. J. Gunion, University of Pittsburgh, December 4, 22 35
Those points with R h V BF (bb) between about. and.25 would provide the best fit to the LEP excess..3.25.2 R h VBF (bb).5..5.2.4.6.8.2.4.6.8 2 R h 2 gg (γγ) Figure 5: Signal strengths (relative to SM) R h V BF (bb) versus Rh 2 gg (γγ) for m h [96, ] GeV and m h2 [23, 28] GeV. In this and all subsequent plots, points with Ωh 2 <.94 are represented by blue circles and points with Ωh 2 [.94,.36] (the WMAP window ) are represented by orange diamonds. J. Gunion, University of Pittsburgh, December 4, 22 36
In all the remaining plots we will impose the additional requirements: R h 2 gg (γγ) > (for LHC enhancement) and. Rh V BF (bb).25 (for LEP fit). In the following, we will refer to these NMSSM scenarios as the 98 + 25 GeV Higgs scenarios or LEP-LHC scenarios. Fig. 6 gives the essential results. The upper plots show that the h 2 can easily have an enhanced γγ signal for both gg and VBF production whereas the γγ signal arising from the h for both production mechanisms is quite small and unlikely to be observable. Note the two different R h 2 gg (γγ) regions with orange diamonds (for which (γγ). and the other These same 2 regions emerge in many later figures. Ωh 2 lies in the WMAP window), one with R h 2 gg with R h 2 gg (γγ).6. The first region corresponds to m χ > 93 GeV and m t >.8 TeV while the second region corresponds to m χ 77 GeV and m t between 97 GeV and TeV. If R h 2 gg (γγ) ends up converging to a large value, then masses for all strongly interacting SUSY particles would be close to current limits. J. Gunion, University of Pittsburgh, December 4, 22 37
.6.7.5.6.4.5 R h gg (γγ).3 R h VBF (γγ).4.3.2.2...2.4.6.8.2.4.6.8 2 R h 2 gg (γγ).2.4.6.8.2.4.6 R h 2 VBF (γγ).25.25.2.2 R h gg (bb).5. R h VBF (bb).5..5.5..2.3.4.5.6.7.8.9 R h 2 gg (bb)..2.3.4.5.6.7.8.9 R h 2 VBF (bb) Figure 6: For h = h and h = h 2, we plot (top) R h gg (γγ) and Rh V BF (γγ) and (bottom) R h gg (bb) and Rh V BF (bb) we show only points satisfying all the basic constraints as well as m h [96, ] GeV, m h2 [23, 28] GeV, R h 2 and R h V BF (bb) [.,.25], i.e. the 98 + 25 GeV Higgs scenarios. gg (γγ) > J. Gunion, University of Pittsburgh, December 4, 22 38
The bottom row of the figure focuses on the bb final state. We observe the reduced R h 2 gg (bb) and Rh 2 V BF (bb) values associated with reduced bb width (relative to the SM) needed for enhanced R h 2 gg (γγ) and Rh 2 V BF (γγ). The R h gg (bb) and Rh V BF (bb) values the h could not have been seen at the Tevatron nor (yet) at the LHC. Sensitivity to R h gg (bb) (Rh V BF (bb)) values from.5 to.2 (. to.25) will be needed at the LHC. This compares to expected sensitivities after the s = 8 TeV run in these channels to R values of at best.8. 2 Statistically, a factor of 4 to improvement requires integrated luminosity of order 6 to times the current L = fb. Such large L values will only be achieved after the LHC is upgraded to 4 TeV. Finally, note that for WMAP-window points the largest R h V BF (bb) values occur for the light-m χ point group described above for which supersymmetric particle masses are as small as possible. 2 Here, we have used Fig. 2 of cmshiggs extrapolated to a Higgs mass near 98 GeV and assumed L = 2 fb each for ATLAS and CMS. J. Gunion, University of Pittsburgh, December 4, 22 39
Other NMSSM particles, properties and parameters, including χ and χ± compositions 2 8 6 4 m a2 [GeV] 2 8 6 4 2 2 3 4 5 6 7 m a [GeV] Figure 7: Scatter plot of m a2 versus m a for the 98+25 GeV scenario; note that m a2 m h3 m H ±. Note that in this figure there is a dense region, located at (m a, m a2 ) (3, 33) GeV, of strongly overlapping orange diamond points. These are the points associated with the low-m χ WMAP-window region of parameter space. Corresponding dense regions appear in other figures. We note without a plot that the good Ωh 2 points all have, m lr m νl, m τ and m ντ larger than.5 TeV. J. Gunion, University of Pittsburgh, December 4, 22 4
26 5 24 45 22 4 m ± [GeV] χ 2 8 6 m t ~ 2 [GeV] 35 3 25 4 2 2 5 6 8 2 4 6 8 2 22 m χ [GeV] 5 5 2 25 3 35 4 m~ t [GeV] 6 -.8 55 - m q ~ [GeV] 5 45 4 35 3 25 (A t -µcotβ)/(m t ~ m t ~ 2 ) /2 -.2 -.4 -.6 -.8-2 2-2.2 5-2.4 2 3 4 5 6 5 5 2 25 3 35 4 m~ g [GeV] m~ t [GeV] Figure 8: Plots showing m χ, m χ ± (A t µ cot β)/ m t m t 2., m t, m t 2, m q, m g, and the mixing parameter J. Gunion, University of Pittsburgh, December 4, 22 4
Input parameters Note that the low-m χ WMAP-window scenarios have not only low m t but also low µ eff, implying not much fine-tuning. m /2 [GeV] 3 25 2 5 5 5 5 2 25 3 m [GeV] A κ [GeV] 8 6 4 2-2 -4-6 -8 - -8-6 -4-2 2 4 6 8 A λ [GeV].5 24.45 22.4 2 κ.35.3.25 µ eff [GeV] 8 6.2 4.5 2..5.2.25.3.35.4.45.5.55.6.65 λ 2 4 6 8 2 4 tanβ Figure 9: GUT scale and SUSY scale parameters leading to the LEP LHC scenarios. J. Gunion, University of Pittsburgh, December 4, 22 42
Dark Matter Issues - -7-8 -9 XENON(2) XENON(22) Ωh 2-2 -3 σ SI [pb] - - -2-4 -3-4 -5 6 8 2 4 6 8 2 22 m χ [GeV] -5 6 8 2 4 6 8 2 22 m χ [GeV].4 -.2. Ωh 2-2 -3 Ωh 2.8.6-4.4.2-5..2.3.4.5.6.7.8.9 LSP higgsino component sum N 2 3 +N2 2 4 6 8 2 4 4 tan β Figure 2: Dark matter properties for the LEP LHC scenarios. J. Gunion, University of Pittsburgh, December 4, 22 43
Dark matter (DM) properties for the surviving NMSSM parameter points are summarized in Fig. 2. Referring to the figure, we see a mixture of blue circle points (those with Ωh 2 <.94) and orange diamond points (those with.94 Ωh 2.36, i.e. in the WMAP window). The main mechanism at work to make Ωh 2 too small for many points is rapid χ χ annihilation to W + W due to a substantial higgsino component of the χ (see third plot of Fig. 2). Indeed, the relic density of a higgsino LSP is typically of order Ωh 2 3 2. To avoid this, need χ χ W + W below threshold as for the light χ point group (the strongly overlapping points with m χ < m W ) As the higgsino component declines Ωh 2 increases it is the points for which the LSP is dominantly singlino that have large enough Ωh 2 to fall in the WMAP window. This kind of point appears in the large-m χ point group. J. Gunion, University of Pittsburgh, December 4, 22 44
LSP higgsino component sum N 2 3 +N2 4.9.8.7.6.5.4.3.2 χ + -H~+ u mixing2.98.96.94.92.9. 6 8 2 4 6 8 2 22 [GeV] m χ.88 2 4 6 8 2 22 24 26 m χ ± [GeV] Figure 2: Neutralino and chargino compositions for the LEP LHC scenarios. Also plotted in Fig. 2 is the spin-independent direct detection cross section, σ SI, as a function of m χ. Experiments will reach sensitivities that will probe some of the predicted σ SI values relatively soon, especially the m χ > 93 GeV points that are in the WMAP window. However, it is also noteworthy that the m χ points can have very small σ SI. 75 GeV WMAP-window J. Gunion, University of Pittsburgh, December 4, 22 45
Direct Higgs production and decay at the LHC We have already noted in the discussion of Fig. 6 that gg and VBF production of the h with h bb provide event rates that might eventually be observable at the LHC once much higher integrated luminosity is attained. Other possibilities include production and decay of the a, a 2, and h 3. Since the a is dominantly singlet in nature, its production rates at the LHC are rather small. Since the a 2 and h 3 are dominantly doublet they provide better discovery prospects. Decay branching ratios and LHC cross sections in the gg fusion mode for a 2 and h 3 are shown in Fig. 22. J. Gunion, University of Pittsburgh, December 4, 22 46
.7 tt.6 bb BR(a 2 X).5.4.3.2. σ(gg a 2 )BR(a 2 X) [pb] - -2-3 Zh a h 2 χ χ χ χ 3 χ 2 χ 2 χ 2 χ 3 χ ± χ± 2 3 4 5 6 7 8 9 m a2 [GeV] -4 25 3 35 4 45 5 55 m a2 [GeV].6 tt BR(h 3 X).5.4.3.2. σ(gg h 3 )BR(h 3 X) [pb] - -2-3 bb h h 2 Za χ χ χ χ 3 χ 2 χ 3 χ ± χ± Figure 22: 2 3 4 5 6 7 8 9 m h3 [GeV] -4 25 3 35 4 45 5 55 m h3 [GeV] Decay branching ratios and LHC cross sections in the gg fusion mode (at s = 8 TeV) for a2 and h 3 J. Gunion, University of Pittsburgh, December 4, 22 47
If m a2 > 2m t, the tt final state has σ(gg a 2 )BR(a 2 tt) >. pb for m a2 < 55 GeV, implying > 2 events for L = 2 fb. A study is needed to determine if this would be observable in the presence of the tt continuum background. No doubt, efficient b tagging and reconstruction of the tt invariant mass in, say, the single lepton final state would be needed. For m a2 < 2m t, the X = a h 2 final state with both a and h 2 decaying to bb might be visible above backgrounds. However, a dedicated study of this particular decay mode is still lacking. Similar remarks apply in the case of the h 3 where the possibly visible final states are tt for m h3 > 2m t and h h 2 for m h3 < 2m t. For both the a 2 and h 3, σbr(x) is substantial for X = χ χ, but to isolate this invisible final state would require an additional photon or jet tag which would reduce the cross section from the level shown. Well, the story goes, with complicated decays of neutralinos and charginos to the various lighter Higgs bosons. J. Gunion, University of Pittsburgh, December 4, 22 48
No time to go into it all here. We do think this scenario is an intriguing one and hope experimentalists will educate themselves about some of its peculiarities. It is possible, but far from guaranteed (in the low-m χ region), that σ SI is large enough to be detectable soon. J. Gunion, University of Pittsburgh, December 4, 22 49
The pure 2HDM Two-Higgs-Doublet Models and Enhanced Rates for a 25 GeV Higgs A. Drozd, B. Grzadkowski, J. F. Gunion and Y. Jiang. arxiv:2.358 [hep-ph] see also, Mass-degenerate Higgs bosons at 25 GeV in the Two-Higgs-Doublet Model P. M. Ferreira, H. E. Haber, R. Santos and J. P. Silva. arxiv:2.33 [hep-ph] There are some differences. We employ the 2HDMC code. 3 It implements:. Precision electroweak constraints (denoted STU) 2. Limits coming from requiring vacuum stability, unitarity and coupling-constant perturbativity (denoted jointly as SUP). The SUP constraints are particularly crucial in limiting the level of enhancement of the gg h γγ channel, our main focus. For all our scans, we have supplemented the 2HDMC code by including the B/LEP constraints.. For the LEP data we adopt upper limits on σ(e + e Z h/h) and σ(e + e A h/h) from Abbiendi:22qp and Abbiendi:24gn, respectively. 3 We have modified the subroutine in 2HDMC that calculates the Higgs boson decays to γγ and also the part of the code relevant for QCD corrections to the q q final state. J. Gunion, University of Pittsburgh, December 4, 22 5
2. Regarding B physics, the constraints imposed are those from BR(B s X s γ), R b, M B s, ɛ K, BR(B + τ + ν τ ) and BR(B + Dτ + ν τ ). The most important implications of these results are to place a lower bound on m H ± as a function of tan β as shown in Fig. 5 of Branco:2iw in the case of the Type II model and to place a lower bound on tan β as a function of m H ± as shown in Fig. 8 of Branco:2iw. We scan and find results illustrated by the following plot. 2HDM (typei) m h =25 GeV 2HDM (typeii) m h =25 GeV R h gg max (γγ) no constraints B/LEP okay STU okay B/LEP+STU okay SUP okay B/LEP+SUP okay all okay R h gg max (γγ) no constraints B/LEP okay STU okay B/LEP+STU okay SUP okay B/LEP+SUP okay all okay.. 5 5 2 tanβ. 5 5 2 The top two plots show the maximum R h gg (γγ) values in the Type I (left) and Type II (right) models for m h = 25 GeV as a function of tan β after imposing various constraints see figure legend. Disappearance of a point after imposing a given constraint set means that the point did not satisfy that set of constraints. tanβ J. Gunion, University of Pittsburgh, December 4, 22 5
For boxes and circles, if a given point satisfies subsequent constraints then the resulting color is chosen according to the color ordering shown in the legend. Corresponding R h gg (ZZ) and Rh gg (bb) are shown in Fig. 23. 2HDM (typei) m h =25 GeV 2HDM (typeii) m h =25 GeV R h gg max (ZZ) no constraints B/LEP okay STU okay B/LEP+STU okay SUP okay B/LEP+SUP okay all okay R h gg max (ZZ). no constraints B/LEP okay STU okay B/LEP+STU okay SUP okay B/LEP+SUP okay all okay. 2 4 6 8 2 4 6 8 2 tanβ. 2 4 6 8 2 4 6 8 2 tanβ 2HDM (typei) m h =25 GeV 2HDM (typeii) m h =25 GeV R h gg max (bb) no constraints B/LEP okay STU okay B/LEP+STU okay SUP okay B/LEP+SUP okay all okay R h gg max (bb) no constraints B/LEP okay STU okay B/LEP+STU okay SUP okay B/LEP+SUP okay all okay. 2 4 6 8 2 4 6 8 2 tanβ 2 4 6 8 2 4 6 8 2 tanβ Figure 23: ZZ and bb final states for parameters with maximum R h gg (γγ). J. Gunion, University of Pittsburgh, December 4, 22 52
Summary of results: Type II model:. For only h at 25 GeV, the parameters that give R h gg (γγ) >.3 are characterized by R h gg (ZZ) > Rh gg (γγ), a result that is inconsistent with experimental results in the gg h ZZ 4l channel. Thus, if R h gg (γγ) >.3 and Rh gg (ZZ) <.3 both persist experimentally, the Type II model cannot describe the data if only the h resides at 25 GeV. 2. Similar statements apply to the case of the heavier H having a mass of 25 GeV. 3. For approximately degenerate h and A Higgs bosons at 25 GeV there exist theoretically consistent parameter choices for Type II models for which R h+a gg (γγ) >.3 while R h+a gg (ZZ) <.3, but in these cases R h+a gg (b b) > 3.75, a value far above that observed. Thus, the Type II 2HDMs cannot yield R h+a gg (γγ) >.3 without conflicting with other observables. In short, the Type II model is unable to give a significantly enhanced gg h γγ signal while maintaining consistency with other channels. Type I model:. The maximal R h gg (γγ) is of order of.3, as found if tan β = 4 or 2. 2. In these cases, R h gg (ZZ) and Rh gg (b b) are of order as fairly consistent with current data. 3. For these scenarios, the charged Higgs is light, m H ± = 9 GeV. 4. Despite this small mass, there is no conflict with LHC data due to the fact that J. Gunion, University of Pittsburgh, December 4, 22 53
BR(t H + b) / tan 2 β is small enough to be below current limits. Thus, Type I models could provide a consistent picture if the LHC results converge to only a modest enhancement for R h gg (γγ) <.3. But, if R h gg (γγ) is definitively measured to have a value much above.3 while the ZZ and b b channels show little enhancement then there is no consistent 2HDM description. Perhaps the pure 2HDM is too limiting and one must go beyond the 2HDM to include new physics such as supersymmetry. J. Gunion, University of Pittsburgh, December 4, 22 54
Conclusions It seems likely that the Higgs responsible for EWSB has emerged. Perhaps, other Higgs-like objects are emerging. Survival of enhanced signals for one or more Higgs boson would be one of the most exciting outcomes of the current LHC run and would guarantee years of theoretical and experimental exploration of BSM models with elementary scalars. >SM signals would appear to guarantee the importance of a linear collider or LEP3 or muon collider in order to understand fully the responsible BSM physics. In any case, the current situation illusrates the fact that we must never assume we have uncovered all the Higgs. Certainly, I will continue watching and waiting J. Gunion, University of Pittsburgh, December 4, 22 55
J. Gunion, University of Pittsburgh, December 4, 22 56