Subgroup 1: LHC Higgs Off-shell Interpretations Models/EFTs

The main task of our subgroup is to discuss and make recommendations on which models/AnomCoupls/EFTs should be investigated with what priority in the context of off-shell H -> VV analyses. The following list of topics and questions should help start the discussion:

- What types of BSM benchmark models should be analysed? Light degrees of freedom up to what scale? In particular to uncover limitations of EFT fits. Are common models sufficient (MSSM, 2HDM, SM+scalar)? What toy models (composite inspired, ...)? Mostly theory activity until experimental evidence for New Physics?

- Interplay with other channels due to shared couplings, e.g. top production Can coefficients of operators with less sensitivity really be set to zero? HOW TO DISENTANGLE? Independent subsets? Proper treatment? Best use of limited number of degrees of freedom in fits. How to expand?

- Should operators that go beyond Higgs from EW doublets be studied? e.g. arXiv:1403.4951

- Should the Higgs width be treated as model output or independent parameter, perhaps constrained by on-peak signal strength?

- NLO effects in EFT studies QCD: studies/tools available. Is BSM@NLO required? Justification?

- specific BSM extended with higher-dim. operators, e.g. arXiv:2003.10449 Is it worthwhile? Which models? Are technical issues understood?

- EFT fits compatibility: Tools to convert results and for validation What is essential? Available? Concrete examples? Thoughts on EFT basis choice? Need off-shell and on-shell compatibility due to complementarity.

- Are a_i coefficients used by CMS equivalent to SMEFT@LO? Clarification: Is the CMS model a specialisation of the SMEFT@LO in the Higgs basis? Are the HVV couplings in the Warsaw and Higgs basis related by a block-diagonal transformation?

- Should we also consider associated Higgs production, e.g. VBF -> H -> VV or VH? Less model dependent, but less data. But much higher signal at high M_4l than ggF. See e.g. Figs. 17 & 18 of arXiv:2002.09888. In certain EFT scenarios, VH becomes equally dominant as VBF. ggF production with 2-jets is included implicitly as one of the main backgrounds for these processes.

- How does the off-shell signal strength fit in?

- It is subleading in gg -> H -> VV, but should New Physics in the Higgs self-energy be modelled via an oblique parameter? see arXiv:1903.07725

Let's carefully consider and compare theoretical assumptions/choices made. We should also explore to what degree compatibility/translatability between ATLAS and CMS results is feasible.

We propose to discuss and agree recommendations regarding specific tools and how to use them in the experimental analyses in subgroup 2 (simulation), with input from the above discussions.

Could you please share your initial thoughts by writing to this email list? Can the experimentalists please point to info about the models they've employed so far, so that the theorists can form an opinion? As second step, we envisage a discussion via Vidyo.

Please recall, our goal is to produce a first write-up with recommendations/guidance as input to the experimental analyses by ~July.

If you can think of someone else who should join or would like to be involved, please encourage them to sign up directly or to contact the conveners.

- Concerning EFTs, I think we should focus on the SMEFT. Going beyond the doublet Higgs assumption would be interesting, but in my view it has lower priority.

- Taking gg -> ZZ as starting point (but including both the Higgs-mediated and continuum components), I try to summarize the EFT effects that have been considered/studied so far. I refer to eqs (II.2.20), (II.218) and (II.2.11) of the YR4, https://arxiv.org/abs/1610.07922 , namely the independent couplings in the Higgs basis. There are corrections to the hgg coupling { c_gg, \tilde{c}_gg }, corrections to htt { (\delta y_u)_33, (\phi_u)_33 }, corrections to hZZ { \delta c_z, c_zz, c_z\Box, \tilde{c}_zz }, corrections to ttZ { (\delta g_L^Zu)_33 , (\delta g_R^Zu)_33 }, and the dipole operators { ctG, ctW, ctZ } as defined in Eleni's slides https://indico.cern.ch/event/860442/ . Some of these are already strongly constrained elsewhere: in particular the gluon dipole ctG, from ttbar as Eleni showed, but also I believe that within SMEFT the Z-t_L-t_L coupling is constrained to ~ 5% after we combine LEP bounds on Z-b_L-b_L and LHC bounds on W-t_L-b_L (to be checked). We could also imagine to restrict to CP-even effects to start, if limiting the number of parameters is crucial. Am I missing other effects? The way I see it, the goal here would be to discuss and converge to a "minimal" list of couplings/operators that deserve priority at this stage.

- Concerning the relation to the parametrization used by CMS (see Andrei's talk https://indico.cern.ch/event/860442/ for reference), we have the one-to-one correspondence a2 <-> c_zz and a3 <-> \tilde{c}_zz . The correspondence \Lambda1 <-> c_z\Box is less immediate to me -- it is clear that they give the same hZZ amplitude with on-shell Z's, but I did not check the general statement.

- About the width, I certainly agree that this is a central aspect of the discussion. E.g. we can easily imagine theoretical scenarios where, in addition to the above EFT effects from heavy new physics, we also have some light state(s) X that the Higgs decays to. One question is how to describe such a setup in a theoretically consistent way: is an extra constant contribution to the Higgs width sufficient? Personally I need to think about this more. Further comments are of course encouraged.

Your list of questions contains very relevant issues for which we don’t have yet clear answers (and therefore if we can make any good progress, a publication will certainly be warranted).

Let me try to inject some thoughts (not necessarily very deep and for sure not complete). A more thorough discussion is definitively needed. It might actually be interesting and productive to start this discussion before the next vidyo meeting. But maybe a more appropriate format would be a dedicated twiki page, rather than a long email thread.

> - What types of BSM benchmark models should be analysed? Light degrees of freedom up to what scale? In particular to uncover limitations of EFT fits. Are common models sufficient (MSSM, 2HDM, SM+scalar)? What toy models (composite inspired, ...)? Mostly theory activity until experimental evidence for New Physics?

It will be important to have toy models that could at least cover the 2 extreme situations: - no exotic/undetected width but large/visible effects in off-shell measurements; - some sizeable exotic/undetected width but no deviation in off-shell measurements. Then we should see to which limit the common models are the closest.

> - Interplay with other channels due to shared couplings, e.g. top production
> Can coefficients of operators with less sensitivity really be set to zero?
> HOW TO DISENTANGLE? Independent subsets? Proper treatment? Best use of limited number of degrees of freedom in fits. How to expand?

Given the list of previous models, we can check compare the width and off-shell constraints to other constraints from EW or top measurements for instance. I would start the discussion with the explicit models. Then we can move to EFT.

> - Should operators that go beyond Higgs from EW doublets be studied? e.g. arXiv:1403.4951

On the EFT side, I would focus first on SMEFT, i.e. with a Higgs as part of an SU(2) doublet. Other cases, with the Higgs as an SU(2) singlet for instance, are a bit marginal and not so well motivated any longer.

> - Should the Higgs width be treated as model output or independent parameter, perhaps constrained by on-peak signal strength?

Here, we have to be a bit careful, at least in our EFT treatment: modifying the width, requires light degrees of freedom, which should a priori be included in the EFT Lagrangian. In some cases, it is possible to rely on SMEFT and still consider the width as a free parameter. But this comes with some extra assumptions that we’ll need to spell out clearly (in particular to avoid messing up with EW precision constraints).

> - NLO effects in EFT studies
> QCD: studies/tools available. Is BSM@NLO required? Justification?

When available, we should include NLO effects. BSM@NLO in general, for instance dim-8 operators, are probably beyond the scope of what we can do for the moment. There is a way to estimate the neglected BSM higher order effects and to test the validity of the EFT expansion. Still, at an existence proof, we might want to consider a very specific case where one dim-8 operator will play an important role.

> - specific BSM extended with higher-dim. operators, e.g. arXiv:2003.10449
> Is it worthwhile? Which models? Are technical issues understood?

That’s is related to the question of the width as a free parameter in an EFT approach. An EFT with an extra field, like a singlet, might help us approach the problem of a consistent framework SMEFT+free width.

> - EFT fits compatibility: Tools to convert results and for validation
> What is essential? Available? Concrete examples? Thoughts on EFT basis choice? Need off-shell and on-shell compatibility due to complementarity.

At LO, all the tools should exist. At NLO, we’ll have to check.

> - Are a_i coefficients used by CMS equivalent to SMEFT@LO?

The equivalence might depend on extra assumptions, in particular, concerning the flavour structure. That should be a relatively easy point to clarify.

> - Should we also consider associated Higgs production, e.g. VBF -> H -> VV or VH?
> Less model dependent, but less data. But much higher signal at high M_4l than ggF. See e.g. Figs. 17 & 18 of arXiv:2002.09888. In certain EFT scenarios, VH becomes equally dominant as VBF. ggF production with 2-jets is included implicitly as one of the main backgrounds for these processes.

I think these different production modes should be considered and compared to each others.

> - How does the off-shell signal strength fit in?
>
> - It is subleading in gg -> H -> VV, but should New Physics in the Higgs self-energy be modelled via an oblique parameter? see arXiv:1903.07725

The Higgs self-energy is one among many parameters to consider. The class of models where the Higgs self-energy is the only relevant deformation of the SM is rather thin. So I wouldn’t limit to this study.

> Please recall, our goal is to produce a first write-up with recommendations/guidance as input to the experimental analyses by ~July.

Given the current situation the world is experiencing, a deadline in July might sound very ambitious. There are many very interesting questions to think about. And hopefully, we’ll collect many good answers.

0. Overall strategy

We can provide interesting examples and general recommendations, but not exact prescriptions. Therefore, it is better to be more inclusive in recommendations, rather than restrictive, especially if the options differ simply by setting certain parameter to zero or not. The ultimate choice of experimental measurements will depend on practical limitations, such as amount of data, the number of possible free parameters in the fit, etc. Full EFT analysis of Higgs data is extremely difficult experimentally even without consideration of non-Higgs operators. Therefore, we should try to limit consideration of non-Higgs couplings (such as appearing in backgrounds) whenever it is possible to have better constraints on those non-Higgs couplings from non-Higgs data.

In the following, the focus is mostly on the practical considerations in application to experimental analyses.

1. Including width as a free parameter or express through couplings

It is better to cover both options with the detectable part of the width expressed through couplings to known states and leaving the option for undetected Higgs decays to be either unconstrained or constrain them to zero. This should accommodate both options.

We should also be clear when we discuss a grand combination of all on-shell and off-shell Higgs data from LHC, or focus on analysis of a given channel, such as H->4f. Expressing the detectable part through couplings is possible only in the grand combination of LHC data. Therefore, analysis of a given channel is inevitably parameterized with the width as a free parameter (unless we simply measure off-shell only cross section).

2. Choice of EFT basis of the Higgs operators

Two bases have been discussed: Warsaw and Higgs bases. The two appear to be equivalent. The Hff couplings match one-to-one. The HVV and Hgg couplings match between the two bases following Eq.(14) in https://arxiv.org/pdf/1508.05895.pdf for CP-even operators and following Eq.(A1) in https://arxiv.org/pdf/2002.09888.pdf for CP-odd operators. There are 6 CP-even and 4 CP-odd HVV operators (after EFT relationship is enforced) and their constraints can be reported in either, or better in both, bases. These 10 operators split into 2 Hgg and 8 HVV.

Taking the dominant gg->H->4f process as the baseline, the number of independent operators to be constrained is reduced significantly because H->HZgamma* and Hgamma*gamma* states do not contribute to the off-shell production. This reduces the number of HVV operators to be tested experimentally in the off-shell region from 8 to 4. This practical consideration suggests the Higgs basis to be convenient to perform and report the experimental results, especially the covariance matrix. The results can be rotated from 4 to 8 operators using Rosetta or other tools. Including the EW processes (VBF+VH), the same logic appears in decay, while some contribution of the remaining 4 operators appears in production. Nonetheless, the statistical significance of this contribution is still very limited until HL-LHC.

This brings us to targeting primarily 4 HVV, 2 Hgg, 2 Htt (appearing in gluon fusion loop) operators in off-shell. Other HVV and Hff operators may also contribute, but are less important, as discussed above. Therefore, let us count them as 8+ Higgs operators.

3. Choice of non-Higgs EFT operators

Following from (2), in off-shell Higgs production, the focus should be on 8+ Higgs operators. Even this set may be too much for experiments to handle in a single fit with available data (we should remember that we barely have ~2 sigma signal at this point), but practical considerations can be left to experiments. Other non-Higgs operators will appear in background contributions interfering with the Higgs processes. In gg->4f production, this may include ttV. In VBS and VVV production, there are TGC and QGC. Enlarging the number of degrees of freedom further in experimental Higgs analyses to include variations of non-Higgs couplings will make experimental analysis enormously more difficult, though not impossible. Therefore, we should try to limit those whenever possible, hopefully setting tighter constraints from non-Higgs data or/and showing limited sensitivity from available Higgs data. Otherwise, a very limited set of non-Higgs operators could be considered.

4. Non-EFT treatment of off-shell data

We do not have to limit ourselves to EFT considerations only. While EFT provides a self-consistent and convenient framework for both theoretical and experimental work, non-EFT treatment allows more general exploration of data and could be pursued in parallel.