Diagnosing the nature of the 126 GeV Higgs signal

Transcription

1 Diagnosing the nature of the 6 GeV Higgs signal Jack Gunion U.C. Davis CERN, BSM lunch/forum, January 4, 3 Higgs couplings Collaborators: Belanger, Beranger, Ellwanger, Kraml. Higgs Couplings at the End of G. Belanger, B. Dumont, U. Ellwanger, J. F. Gunion and S. Kraml. arxiv:.544 [hep-ph] NMSSM Collaborators: G. Belanger, U. Ellwanger, Y. Jiang, S. Kraml, J. Schwarz. Higgs Bosons at 98 and 5 GeV at LEP and the LHC G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang, S. Kraml and J. H. Schwarz. arxiv:.976 [hep-ph]. Two Higgs Bosons at the Tevatron and the LHC? G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang and S. Kraml. arxiv:8.495 [hep-ph] 3. Diagnosing Degenerate Higgs Bosons at 5 GeV J. F. Gunion, Y. Jiang and S. Kraml. arxiv:8.87 [hep-ph] 4. Could two NMSSM Higgs bosons be present near 5 GeV? J. F. Gunion, Y. Jiang and S. Kraml. arxiv:7.545 [hep-ph] 5. The Constrained NMSSM and Higgs near 5 GeV J. F. Gunion, Y. Jiang and S. Kraml. arxiv:.98 [hep-ph] Phys. Lett. B 7, 454 ()

2 HDM Collaborators: Alexandra Drozd, Bohdan Grzadkowski, Yun Jiang. Two-Higgs-Doublet Models and Enhanced Rates for a 5 GeV Higgs A. Drozd, B. Grzadkowski, J. F. Gunion and Y. Jiang. arxiv:.358 [hep-ph] J. Gunion, CERN, BSM lunch/forum, January 4, 3

3 Higgs-like LHC Excesses at 5 6 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), Rh (X) = Y R h Y, () where Y = gg, V V, V h or tth. The notation µ R is sometimes employed. Experimental results are now available for many channels, where the experimental channel is usually a mixture of the theoretical channels. µ k = T i k µ i () where the T i k give the amount of contribution to the experimental channel k coming from the theoretically defined channel i and µ i is the prediction for a given theoretical channel. The observed µ k values and T i k values are summarized in the following tables. J. Gunion, CERN, BSM lunch/forum, January 4, 3

4 Channel Signal strength µ m H (GeV) Production mode ggf VBF VH tth H γγ (4.8 fb at 7 TeV + 3. fb at 8 TeV) [?] µ(ggf + tth, γγ).85 ± % µ(vbf + VH, γγ). ± % 4% H ZZ (4.6 fb at 7 TeV + 3. fb at 8 TeV) [?,?] Inclusive % 7% 5% % H W W (3. fb at 8 TeV) [?,?] eνµν % 3% % H b b (4.7 fb at 7 TeV + 3. fb at 8 TeV) [?,?] VH tag.39 ±. 5.5 % H τ τ (4.6 fb at 7 TeV + 3. fb at 8 TeV) [?] µ(ggf, τ τ ).4 ±.57 5 % µ(vbf + VH, τ τ ).6 ±. 5 6% 4% Table : ATLAS results as employed in this analysis. The correlations included in the fits are ρ =.37 for the γγ and ρ =.5 for the τ τ channels. J. Gunion, CERN, BSM lunch/forum, January 4, 3 3

5 Channel Signal strength µ m H (GeV) Production mode ggf VBF VH tth H γγ (5. fb at 7 TeV fb at 8 TeV) [?,?,?] µ(ggf + tth, γγ).95 ± % µ(vbf + VH, γγ) 3.77 ± % 4% H ZZ (5. fb at 7 TeV +. fb at 8 TeV) [?,?] Inclusive % 7% 5% % H W W (up to 4.9 fb at 7 TeV +. fb at 8 TeV) [?,?,?] / jet % 3% VBF tag % 83% VH tag % H b b (up to 5. fb at 7 TeV +. fb at 8 TeV) [?,?,?] VH tag % tth tag % H τ τ (up to 5. fb at 7 TeV +. fb at 8 TeV) [?,?,?] / jet % 6% 7% % VBF tag % 8% VH tag % Table : CMS results as employed in this analysis. The correlation included for the γγ channel is ρ =.54. J. Gunion, CERN, BSM lunch/forum, January 4, 3 4

6 Channel Signal strength µ m H (GeV) Production mode ggf VBF VH tth H γγ [?] Combined % 5% 7% H W W [?] Combined % 5% 7% H b b [?] VH tag % Table 3: Tevatron results for up to fb at s =.96 TeV, as employed in this analysis. Note: general enhancement of γγ final states in both ggf (not CMS) and especially VBF. 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?. If they do survive, how far beyond the standard model must we go to describe them? J. Gunion, CERN, BSM lunch/forum, January 4, 3 5

7 Higgs coupling fits Suppose the signal derives from just one Higgs boson we assume +. The structure we will test is ( L = g [C V m W W µ W µ + m ) Z Z µ Z µ cos θ W m t m b m τ C U tt C D bb CD τ τ m W m W m W ] H. (3) In general, the C I can take on negative as well as positive values; there is one overall sign ambiguity which we fix by taking C V >. We will be fitting the data given earlier. In addition to the tree-level couplings given above, the H has couplings to gg and γγ that are first induced at one loop and J. Gunion, CERN, BSM lunch/forum, January 4, 3 6

8 are completely computable in terms of C U, C D and C V if only loops containing SM particles are present. We define C g and C γ to be the ratio of these couplings so computed to the SM (i.e. C U = C D = C V = ) values. However, in some of our fits we will also allow for additional loop contributions C g and C γ from new particles; in this case C g = C g + C g and C γ = C γ + C γ. The largest set of independent parameters in our fits is thus C U, C D, C V, C g, C γ. (4) J. Gunion, CERN, BSM lunch/forum, January 4, 3 7

9 Fit I: C U = C D = C V =, C g and C γ free..5 Cg C γ Figure : Two parameter fit of C γ and C g, assuming C U = C D = C V = (Fit I). The red, orange and yellow ellipses show the 68%, 95% and 99.7% CL regions, respectively. The white star marks the best-fit point C γ =.46, C g =.86. It has χ =.3 vs. SM χ =.. i.e. SM is σ worse. J. Gunion, CERN, BSM lunch/forum, January 4, 3 8

10 Fit II: varying C U, C D and C V ( C γ = C g = ).5.5 CD CV CV.5.5 C U C U C D Cg CV Cg C U.5.5 C γ.5.5 C γ Figure : Two-dimensional χ distributions for the three parameter fit, Fit II, of C U, C D, C V with C γ = C γ and C g = C g as computed in terms of C U, C D, C V. Details on the minima in different sectors of the (C U, C D ) plane can be found in Table 5. Note strong preference for negative C U = (γγ t-loop adds to W loop). Negative C U is hard in most models. But, χ =.6 is much better than for SM. J. Gunion, CERN, BSM lunch/forum, January 4, 3 9

11 Fit II: varying C U, C D and C V ( C γ = C g = ) requiring C U, C D > (and C V > by convention) CD CV Cg C U.5.5 C U C γ.5 CD CV.6.4 Cg C U.5.5 C U.5.5 C γ Figure 3: Two-dimensional χ distributions for the three parameter fit, Fit II, as in Fig. but with C U >, C D >, C V >. The upper row of plots allows for C V >, while in the lower row of plots C V is imposed. The best fit point has χ = 8.66, a value that is not much lower than that for the SM. J. Gunion, CERN, BSM lunch/forum, January 4, 3

12 Fit III: varying C U, C D, C V, C γ and C g.5.5 CD Cg.5 Cγ C U.5 C U.5 C U CV Cγ Cg C γ C g 3 C γ Figure 4: Two-dimensional distributions for the five parameter fit of C U, C D, C V, C γ and C g (Fit III). Details regarding the best fit point are given in Table 4. Note from top middle plot how C g can be traded for C U. J. Gunion, CERN, BSM lunch/forum, January 4, 3

13 Fit I II III, st min. III, nd min. C U ±.3.6 ±.3 C D C V C γ C g C γ C g χ min χ min /d.o.f Table 4: Summary of results for Fits I III. For Fit II, the tabulated results are from the best fit, cf. column of Table 5. J. Gunion, CERN, BSM lunch/forum, January 4, 3

14 Sector C U <, C D > C U, C D < C U, C D > C U C D C V C γ C g χ min χ min /d.o.f Table 5: Results for Fit II in different sectors of the (C U, C D ) plane. J. Gunion, CERN, BSM lunch/forum, January 4, 3 3

15 C U C D I II III I II III C V I II III C γ C g I II III I II III C γ C g I II III I II III Figure 5: Graphical representation of the best fit values for C U, C D, C V, C γ and C g of Table 4. The labels refer to the fits discussed in the text. The dashed lines indicate the SM value for the given quantity. was fixed to its SM value. The s indicate cases where the parameter in question If the γγ mode excesses persist, it would appear necessary to have C γ.4 by some means or other (C U negative with C γ small, or C U normal with C γ.4.) Note that C g and C V for all fits. J. Gunion, CERN, BSM lunch/forum, January 4, 3 4

16 Impact on Two-Higgs-Doublet Models Only α and β needed to describe a single Higgs. So good fit is not exactly guaranteed. β π/.5 β π/ α α Figure 6: HDM fits for the h in the Type I (left) and Type II (right) models. Note: β π/ = α π is SM limit. Fit is far from SM limit and requires small tan β, the latter being problematical for perturbativity of top-quark coupling. If we require tan β >, must move to long valley which is near SM-like limit and has much higher χ. J. Gunion, CERN, BSM lunch/forum, January 4, 3 5

17 Fit THDM-I THDM-II THDM-I, tan β > THDM-II, tan β > α [rad] β [rad] [π/4, π/] cos α tan β [, + ] [, + ] C U C D C V C γ C g χ min Table 6: Summary of fit results for the h in HDMs of Type I and Type II. Summary of Fitting Results Best χ s are achieved pretty far from SM limit and would have to involve exotic parameters. One cure: light charged Higgs, but then other constraints become a problem. Second cure: degenerate Higgs bosons. J. Gunion, CERN, BSM lunch/forum, January 4, 3 6

18 Enhanced Higgs signals in the NMSSM NMSSM=MSSM+Ŝ. The extra complex S component of Ŝ the NMSSM has h, h, h, a, a. 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 (5) 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 5 GeV? Answer: Yes, so long as it is not a highly unified model. For our studies, we employed universal m, except for NUHM (m H u, J. Gunion, CERN, BSM lunch/forum, January 4, 3 7

19 m H d, m 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. 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:.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 h to have similar masses (for singlet-doublet 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:.98 [hep-ph]) J. Gunion, CERN, BSM lunch/forum, January 4, 3 8

20 The enhanced SM-like Higgs can be either h or h. R h i gg (X) (Ch i gg ) BR(h i X) BR(h SM X), Rh i VBF (X) (Ch i V V ) BR(h i X) BR(h SM X), (6) 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. Some illustrative R gg results from (J. F. Gunion, Y. Jiang and S. Kraml. arxiv:7.545): J. Gunion, CERN, BSM lunch/forum, January 4, 3 9

21 µ eff 3 Figure Legend LEP/Teva B-physics Ωh > δa µ ( ) XENON R h /h (γγ).36 [.5, ].94 (,.].94 > (,.] > R h (γγ) <m h < m h [GeV] Figure 7: The plot shows R gg (γγ) for the cases of 3 < m h < 8 GeV and 3 < m h < 8 GeV. Note: red triangle (orange square) is for WMAP window with R gg (γγ) >. (R gg (γγ) = [,.]). J. Gunion, CERN, BSM lunch/forum, January 4, 3

22 R h (γγ) <m h < Figure 8: Observe the clear general increase in maximum R gg (γγ) with increasing λ. Green points have good δa µ, m h > TeV BUT R gg (γγ). λ R h (γγ) 3<m h < m~ t [GeV] Figure 9: The lightest stop has mass 3 7 GeV for red-triangle points. J. Gunion, CERN, BSM lunch/forum, January 4, 3

23 If we ignore δa µ, then R gg (γγ) >. (even > ) is possible while satisfying all other constraints provided h and h are close in mass, especially in the case where m h [3, 8] GeV window. This raises the issue of scenarios in which both m h and m h are in the [3, 8] GeV window where the experiments see the Higgs signal. Supporting reasons: If h and h 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 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 J. Gunion, CERN, BSM lunch/forum, January 4, 3

24 γγ channel and other channels, such as bb or 4l, than in non-degenerate situation. In particular, the h and h will generally have different gg and V V production rates and branching ratios. The general coupling analysis suggests that suppressing the V V coupling and the bb coupling through mixing does not provide a wonderful fit if only one of the h or h is identified as the 6 GeV resonance. J. Gunion, CERN, BSM lunch/forum, January 4, 3 3

25 Degenerate NMSSM Higgs Scenarios: (arxiv:7.545, JFG, Jiang, Kraml) For the numerical analysis, we use NMSSMTools version 3.., 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 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 σ as encoded in NMSSMTools-3.., plus updates. 3. Dark Matter: Ωh <.36, thus allowing for scenarios in which the relic density arises at least in part from some other source. J. Gunion, CERN, BSM lunch/forum, January 4, 3 4

26 However, we single out points with.94 Ωh.36, which is the WMAP window defined in NMSSMTools XENON : spin-independent LSP proton scattering cross section bounds implied by the neutralino-mass-dependent XENON bound. (For points with Ωh <.94, we rescale these bounds by a factor of./ωh.) ( 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 Rgg h as m Y h (X) Rh Y (X)m h + R h Y (X)m h R h Y (X) + Rh Y (X) R h Y (X) = Rh Y (X) + Rh Y (X). (7) The extent to which it is appropriate to combine the rates from the h and h depends upon the degree of degeneracy and the J. Gunion, CERN, BSM lunch/forum, January 4, 3 5

27 experimental resolution. Very roughly, one should probably think of σ res.5 GeV or larger. The widths of the h and h are very much smaller than this resolution. We perform scans covering the following parameter ranges: m 3; m / 3; tan β 4; 6 A 6;. λ.7;.5 κ.5; A λ ; A κ ; µ eff 5. (8) We only display points which pass the basic constraints, satisfy B-physics constraints, have Ωh <.36, obey the XENON limit on the LSP scattering cross-section off protons and have both h and h in the desired mass range: 3 GeV < m h, m h < 8 GeV. In Fig., points are color coded according to m h m h. Circular points have Ωh <.94, while diamond points have.94 Ωh.36 (i.e. lie within the WMAP window). J. Gunion, CERN, BSM lunch/forum, January 4, 3 6

28 Many of the displayed points have R h gg (γγ) + Rh (γγ) >. 3<m h,m h <8 gg.5 m h -m h > 3. GeV. GeV < m h -m h 3. GeV.5 GeV < m h -m h. GeV. GeV < m h -m h.5 GeV.5 GeV < m h -m h. GeV m h -m h.5 GeV.5 R h gg (γγ) R h gg (γγ) Figure : Correlation of gg (h, h ) γγ signal strengths when both h and h lie in the 3 8 GeV mass range. The circular points have Ωh <.94, while diamond points have.94 Ωh.36. Points are color coded according to m h m h. Probably green and cyan points can be resolved in mass. J. Gunion, CERN, BSM lunch/forum, January 4, 3 7

29 A few such points have Ωh in the WMAP window. These points are such that either R h gg (γγ) > or Rh gg (γγ) >, with the R h gg (γγ) or Rh gg (γγ), respectively, being small. However, the majority of the points with R h gg (γγ)+rh gg (γγ) > have Ωh <.94 and the γγ signal is often shared between the h and the h. Now combine the h and h signals as described above. Recall: circular (diamond) points have Ωh <.94 (.94 Ωh.36). Color code:. red for m h m h GeV;. blue for GeV < m h m h GeV; 3. green for GeV < m h m h 3 GeV. For current statistics and σ res >.5 GeV we estimate that the h and h signals will not be seen separately for m h m h GeV. J. Gunion, CERN, BSM lunch/forum, January 4, 3 8

30 In Fig., we show results for Rgg h (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 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, CERN, BSM lunch/forum, January 4, 3 9

31 R h gg (γγ) R h gg (bb) <m h,m h < m h [GeV] <m h,m h < m h [GeV] R h gg (VV) R h VBF (bb) 3<m h,m h < m h [GeV] <m h,m h < m h [GeV] Figure : 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, CERN, BSM lunch/forum, January 4, 3 3

32 3<m h,m h <8 3<m h,m h < R h gg (γγ).5 R h gg (γγ) R h gg (VV) R h VBF (bb) Figure : 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. :. Left-hand plot shows the strong correlation between Rgg h (γγ) and Rgg h (V V ). J. Gunion, CERN, BSM lunch/forum, January 4, 3 3

33 Note that if Rgg h (γγ).5, as suggested by current experimental results, then in this model Rgg h (V V )... The right-hand plot shows the (anti) correlation between Rgg h (γγ) and Rh V V h (bb) = Rh VBF (bb). In general, the larger Rgg h (γγ) is, the smaller the value of RV h 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. 3. It is often the case that one of the h or h dominates Rgg h (γγ) while the other dominates Rh V V h (bb). This is typical of the diamond WMAP-window points. However, a significant number of the circular Ωh <.94 points are such that either the γγ or the bb signal receives J. Gunion, CERN, BSM lunch/forum, January 4, 3 3

34 substantial contributions from both the h and the h. We did not find points where the γγ and bb final states both receive substantial contributions from both the h and h. 3<m h,m h <8 3<m h,m h < m h (VV) [GeV] R h gg (γγ) m h (γγ) [GeV] (C h bb ) Figure 3: 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 ). Here, C h b b R h ] [ gg (γγ)ch b b + R h gg (γγ)ch / R h b b gg (γγ) + Rh gg ]. (γγ) J. Gunion, CERN, BSM lunch/forum, January 4, 3 33

35 Comments on Fig. 3. 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 GeV and are most often much closer, see the left plot of Fig. 3.. The right plot of Fig. 3 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. J. Gunion, CERN, BSM lunch/forum, January 4, 3 34

36 Separate Mass Peaks for ZZ vs. γγ h should have m h 3 GeV and ZZ rate not too much smaller than SM-like rate, but suppressed γγ rate. h should have m h 6 GeV and enhanced γγ and somewhat suppressed ZZ rate. J. Gunion, CERN, BSM lunch/forum, January 4, 3 35

37 The kind of extreme apparently seen by ATLAS is hard to arrange in the NMSSM. This is because the mechanism for getting enhanced γγ (suppression of bb partial width through mixing) automatically also enhances ZZ. Recall the correlation plot given earlier To assess a bit more quantitatively, we compute m h (V V ) vs. m h (γγ) using previous formula involving weighting by R h,h gg (ZZ) and R h,h gg (γγ) and accepting points with GeV m h,, m h 8 GeV. Or, selecting points with GeV < m h 5 GeV < m h < 7 GeV. < 4 GeV and J. Gunion, CERN, BSM lunch/forum, January 4, 3 36

38 <m h,m h <8 <m h <4,5<m h < (VV) [GeV] m gg h 5 4 m h VV m gg h (γγ) [GeV] Figure 4: m h obtained in ZZ vs. γγ final state when scanning and requiring: GeV m h, m h 8 GeV (Left) or GeV < m h < 4 GeV, 5 GeV < m h < 7 GeV (Right). Dashed lines show m h (ZZ) = m h (γγ) (,.5,,.5). Hard to get a mass shift of more than GeV. m h γγ J. Gunion, CERN, BSM lunch/forum, January 4, 3 37

39 R h (γγ) gg R h (VV) gg <m h <4,5<m h < R h gg (γγ) <m h <4,5<m h < R h gg (γγ) R h (γγ) gg R h (VV) gg <m h <4,5<m h < R h gg (VV) <m h <4,5<m h < Figure 5: Too much correlation between V V and γγ channels for the h and h separately. J. Gunion, CERN, BSM lunch/forum, January 4, 3 38 R h gg (VV)

40 Diagnosing the presence of degenerate Higgses (J. F. Gunion, Y. Jiang and S. Kraml. arxiv:8.87) Given that enhanced Rgg h is very natural if there are degenerate Higgs mass eigenstates, how do we detect degeneracy if closely degenerate? 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). (9) Let us now look in more detail at a given RY h (X). It takes the form R h Y (X) = (C h i Y ) (C h i X ) () where C h i X i=, C h i Γ for X = γγ, W W, ZZ,... is the ratio of the h ix J. Gunion, CERN, BSM lunch/forum, January 4, 3 39

41 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 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. (), 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 J. Gunion, CERN, BSM lunch/forum, January 4, 3 4

42 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. 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. 6, 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 J. Gunion, CERN, BSM lunch/forum, January 4, 3 4

43 require (as apparently preferred by LHC data) Rgg h (γγ) >, see the solid (vs. open) symbols of Fig. 6. This is further elucidated in Fig. 7 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 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 dominates the gg γγ rate, see the top right plot of Fig. 7. In comparison, double ratio II) is most useful for scenarios with Rgg h (γγ), as illustrated by the bottom left plot of Fig. 7. J. Gunion, CERN, BSM lunch/forum, January 4, 3 4

44 Thus, as illustrated by the bottom right plot of Fig. 7, 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, CERN, BSM lunch/forum, January 4, 3 43

45 3<m h,m h <8 3<m h,m h < R h VBF (γγ)/rh gg (γγ)..8.6 R h gg (bb)/rh gg (γγ) R h VBF (bb)/rh gg (bb).5.5 R h VBF (bb)/rh VBF (γγ) Figure 6: 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 GeV < m h m h 3 GeV, blue for GeV < m h m h GeV, and red for m h m h GeV. Large diamond points have Ωh in the WMAP window of [.94,.36], while circular points have Ωh <.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, CERN, BSM lunch/forum, January 4, 3 44

46 3<m h,m h <8 3<m h,m h <8 [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (bb)/rh gg (bb)] R h gg (γγ) [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (bb)/rh gg (bb)] max [R h gg (γγ),rh gg (γγ)]/rh gg (γγ) [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (VV)/Rh gg (VV)] <m h,m h < R h gg (γγ) [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (bb)/rh gg (bb)] <m h,m h < [R h VBF (γγ)/rh gg (γγ)]/[rh VBF (VV)/Rh gg (VV)] Figure 7: 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 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, CERN, BSM lunch/forum, January 4, 3 45

47 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--) 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 5 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, CERN, BSM lunch/forum, January 4, 3 46

48 The pure HDM Two-Higgs-Doublet Models and Enhanced Rates for a 5 GeV Higgs A. Drozd, B. Grzadkowski, J. F. Gunion and Y. Jiang. arxiv:.358 [hep-ph] see also, Mass-degenerate Higgs bosons at 5 GeV in the Two-Higgs-Doublet Model P. M. Ferreira, H. E. Haber, R. Santos and J. P. Silva. arxiv:.33 [hep-ph] There are some differences. NMSSM-like degeneracy can be explored in this context also, but no time to discuss. J. Gunion, CERN, BSM lunch/forum, January 4, 3 47

49 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. J. Gunion, CERN, BSM lunch/forum, January 4, 3 48

50 Certainly, I will continue watching and waiting J. Gunion, CERN, BSM lunch/forum, January 4, 3 49