Higgs Physics in SMEFT
Finally, we compare the accuracy of the determination of the Higgs couplings with flat theoretical uncertainties with a Gaussian nuisance parameter. In the linear sigma model we construct a SU(2)L ⇥ U(1)Y -symmetric Higgs Lagrangian based on the doublet and order it according to the inverse powers of the cuto↵ scale.
For example, calculating the standard deviation of a flat data set lies well below the box size. In itself, it is not clear which of the two e↵ects will dominate in a given fit.
OR TAN T
A standard approach is defined by e↵ective field theory [53], where we categorize a Lagrangian with appropriate symmetries in terms of the expansion parameter. Before presenting the result of the LHC analysis, we must define our basis of dimension 6 operators.
Second, it is not clear at what Gaussian significance we should identify the edges of the box-shaped distribution. This means that if we compare the range of one standard deviation for the RFit scheme with one standard deviation of the Gaussian, the error in the flat distribution appears smaller.
Interplay HVV and TGV
All these couplings are correlated!!
HEFT
Independent!!
DecorrelaUons & New Signals
Investigates decorrelation signals: due to the nature of the chiral expansion vs.
What is HEFT?
The HEFT Lagrangian
Higgs analysis similar to SMEFT: 10 parameters to SMEFT's 9 The fit to Higgs is very close to that of SMEFT.
DecorrelaUons
We show in Figure 3 the current status of the boundaries on the two relevant coefficient planes, after considering all Higgs measurements included in the presented global Higgs analysis (based on [49]), together with the most recent combination of TGV searches. presented in the previous subsection (based on [59]). Secondly, the combination of the significant LHC run I diboson production analysis described in [59] also has a huge impact on the results. This combination of improvements leads to a significant improvement in the sensitivity of the combined results shown in Figure 3, despite the greater dimensionality of the parameter space considered in the current study with respect to the global analysis in [33].
SM vs. BSM
Therefore, any deviation from (0, 0) in the left panel would indicate BSM physics, regardless of the nature of the EWSB realization. On the other hand, if this were accompanied by a deviation in the right panel, this would be indicative of a non-linear process. nature of the Higgs boson. The observed constraints of ⌃B, ⌃W , B and W, shown in Figure 3, represent a significant improvement over the previous bounds shown in Figure 2 of [33]. The reason for such a significant improvement depends on two important points. First, the more complete set of run I LHC Higgs event rate measurements and the addition of relevant kinematic distributions sensitive to the anomalous SM Lorentz structures generated by a5 and a3, introduced in [49], increases the strength of the derived results.
SMEFT
The black dots signal the point (0, 0), while the stars signal the actual point of the best fit obtained in the analysis. 33], given the variables shown in Figure 3, while in the left panel the point (0, 0) corresponds to the SM, in the right it also corresponds to the possible BSM signals generated in the linear approach.
New Signals
Signals expected in the chiral basis, but not in the linear one (d=8)
The black histogram corresponds to the sum of all background sources with the exception of SM electroweak pp. In the first approach, we performed a simple event count analysis assuming that the number of observed events corresponds to the SM prediction (g5Z = 0) and we look for the values of g5Z which are within the 68% and 95% CL allowable regions. Once again, the observed pZT spectrum was assumed to match the SM expectations, and we searched for values of g5Z that lie within 68% and 95%.
WZ producUon
W ± Z process, while the red histogram corresponds to the sum of all SM backgrounds, and the dotted distribution corresponds to the summation of the anomalous signal for g5Z = 0.2 (g5Z = 0.1). We present in the first row of Table 7 the expected LHC limits for the combination of the existing 7 TeV and 8 TeV data sets, where we find an integrated brightness of 4.64 fb 1 for the 7 TeV run and 19.6 fb 1 for the 8 TeV considered. An. Finally, the last row of Table 7 shows the expected accuracy at g5Z when the 14 TeV run with an integrated brightness of 300 fb 1 is included in the combination.
Conclusions
A very powerful probe of the Higgs portal DM in the mass region mS < mh/2 is provided by searches for an invisible decay width of the Higgs boson at the LHC. Mono-Higgs searches [81–84] have recently been proposed as a probe of DM interactions with the SM, particularly in the context of Higgs portal scenarios. A sample of the Feynman diagrams contributing to mono-h in this case is shown in Figure 6.
Mono-h searchesDD+ID+ invisible h
For the standard Higgs portal, mono-h processes are gg-initiated and the amplitude receives contributions from Feynman diagrams scaled as ⇠ S and ⇠ 2S, as shown in Figure 6 (within the frame), the latter having a significant improves the cross ratio. section when S ⇠ 1. However, we note that for S = 1 satisfying the direct detection limit of LUX requires mS > 127 GeV (see Figure 3), and for that mass range the mono-h cross section is suppressed due to the intermediate o ↵-shell Higgs state and the steep drop of the gluon PDF at high p. Overall, the cross section for mono-h in the standard scalar DM Higgs portal is predicted to be very small.
Thanks
The low-mass endpoint for the solid-black and dotted-purple lines, given by mS = 127 GeV, corresponds to the mass limit for the standard Higgs portal scenario for S = 1 (see Figure 3). The presence of non-linear Higgs-DM interactions can significantly change the previous picture, as the suppression factors for the standard scenario can be overcome by the emergence of new production channels - e.g. If the Higgs is found to deviate from a pure double, then many other consequences: for example, the DM Higgs scalar portal.
Backup
Non-linear Scalar DM Portal
Standard case Chiral case
No other portals
New Portals
Dark Matter relic density
Assuming that the single scalar particle S is a thermal relic, its abundance ⌦ S today is determined by the average thermal annihilation cross section in SM particles in the early Universe (v)ann = (SS ! XX) v. Assuming that the single scalar particle S is a thermal relic, its abundance ⌦ S today is determined by the average thermal annihilation cross section in SM particles in the early Universe (v)ann = (SS ! XX) v. For negative values of c1, positive interference with linear amplitude (see Feynman's rules in Appendix A) increases the total annihilation cross section everywhere, and some of the excluded points in the standard Higgs portal scenario become viable.
DM Relic Density
It shows the drastic increase that results in the parameter space for DM masses greater than tens of GeV compared to the allowed range for the standard portal above the black curve. In the presence of A1, the DM can directly interact with the SM gauge bosons via the SSZZ and SSW+W nodes. 4a1 (b1) parametrizes nodes SSV V h (SSV V hh), with V = Z, W±, whose tree-level contribution to the DM annihilation cross section is strongly suppressed due to phase space considerations; the variation of a2 can be reabsorbed in the normalization of c2; finally b2 enters SS.
SSW W SSZZ
The middle green region corresponds to the standard Higgs portal case b = 1, while the light/dark green regions (superimposed) correspond to b = 0.5 and b = 2, respectively. 65 GeV, where DM annihilates dominantly to b¯b, while they strongly influence the DM destruction process in two caliber bosons, which becomes important as mS grows, as shown in Figure 2 (left). On the other hand, if c1 > 0 the interference is destructive and false cancellations can occur in regions of the parameter space that are allowed for standard Higgs portals but are now excluded.
ConstrucUve Int
Noting that hvi2 = 6/xF, where xF is given by the freezing temperature as xF = mS/TF ' 20, the relic density is given by. Finally, a comment on the scope of the analysis is in order: while the couplings studied do not depend on the actual value of ⇤DM, our results below should only be taken as indicative for values of mS above 1 TeV, since the hard scale of ⇤DM cannot possibly be much larger and still affects the present and predicted experimental sensitivity. The influence of the operator A2 shown in Figure 2 (right) can be understood in a similar way: the coefficient c2 enters the couplings SShh and SSh, with the double effect of increasing SS.
DestrucUve Int
Invisible Higgs decay width
SS is open for mS < mh/2 and contributes to inv as the invisible Higgs width. For Figure 4a the limit coincides with that derived for the standard Higgs portal also shown in Figure 3 (see e.g. [71]), while Figure 4b illustrates the e↵ect of c2 6= 0: even for small values of above this coefficient, the limit becomes very strict, practically excluding the entire region mS < mh/2. Impact of nonlinear contributions on the parameter space of Higgs portals, combining information from DM relic densities, direct detection experiments, and searches for the invisible.
Direct Detec. + Invisible h Decay
For the last two cases, the red and orange dotted lines show the ¯qq-initiated contribution from A4 and A5. The low mass endpoint for the solid black and dashed purple lines, given by mS = 127 GeV, corresponds to the mass limit for the standard Higgs portal scenario for S = 1 (see Figure 3). However, we note that for S = 1 satisfying the direct detection limit of LUX requires mS > 127 GeV (see Figure 3), and for that range of masses the mono-h cross section is suppressed due to the intermediate o↵-shell Higgs state and the steep fall of the gluon PDF at high p.
Mono-h Searches
While the effect of the A2 operator on this observatory cannot be effectively separated from that of the standard Higgs portal (as you can see by comparing the black and blue curves in Fig. 12 (left)), the RW Z relation is a very strong non-linear discriminator for cases A1 and A4 (also trivial for A5, for which there is no mono-W± process and RW Z ⌘ 1), corresponding to the green and red curves in Fig. 12 (left) ). By applying this technique to a more thorough analysis that would account for all relevant uncertainties, it would be possible to quantify the confidence level for excluding the standard portal. Therefore, the RW Z ratio may be an effective probe of the nature of the DM to SM portal.
Mono-Z & Mono-W Searches
Surprisingly, the influence of any nonlinear operator on this ratio is determined only by its gauge and Lorentz structure, regardless of the value of the ci coefficient. Moreover, remembering that the operator A3 enters the mono-Z process with the corresponding coefficient in the combination (c1 + 2c3) (see Appendix A), while it does not enter the mono-W ± process, the green curve in Figure 12 (Left) will be rescaled by (c1 + 2c3)2/c21 in the presence of A3. Note that the nonlinear scenario cannot be excluded from this type of study, since each point in the space (mS, RW Z) corresponds to a whole set of combinations of coefficients c1 5.
Results of the fit
1, where we show (in the left panel) the production cross section as a function of MW h, for both the full model and the EFT. While, as expected, the EFT description is valid in all cases close to the production threshold, above a certain point MW hmax the EFT is no longer a good approximation of the UV theory. As an illustration of our discussion of setting limits on the EFT parameters and estimating the associated theoretical errors, consider the following example of an idealized measurement.
Validity of SMEFT
The corresponding EFT predictions are shown in the linear approximation (solid red), and when quadratic terms in D = 6 parameters are included in the calculation of the cross section (solid purple). The limits come from reinterpreting the hypothetical experimental constraints with Mcut = 3 TeV, as described in the text. In this case, it is the quadratic approximation that provides a good e↵ective description of the UV theory.
HEFT basis
HEFT (bosonic) basis
The h funcUons
ConnecUon with the Linear Basis
The results of a global analysis of the Higgs data, including all kinematic distributions described in [49] (except the o↵-shell m4` distribution) for the set of nonlinear operators described here (corresponding to the parameters in Eq. For each of the 95% CL ranges, we profiled on the other 9 not shown coefficients that are included in the global analysis In summary, in this appendix we have presented the results of SFitter Run I Higgs analysis [1] in terms of nonlinear effective operators.
What if the Higgs is a
Generic Composite
