# Project A - Higgs Precision Physics

**S. Dittmaier, G. Herten, H. Ita, K. Jakobs, A. Knue, M. Schumacher, C. Weiser **

So far investigations of the Higgs boson have mostly focused on the measurement of total event rates, cross sections and branching ratios assuming the coupling structure as predicted in the Standard Model (SM). No significant deviations from the predictions in the SM have been observed. A tightening of this fundamental tests of the SM and improved constraints on models with modified and extended Higgs sectors require a larger precision on both the experimental and theoretical side. In addition the measurements shall be extended to cross-sections in well-defined phase space regions ("Simplified Template Cross Sections"', STXS) and to differential measurements.

Further on searches for CP violation (CPV) and lepton flavour violation (LFV) will be performed. On the experimental and theoretical side new and more complex analysis methods and field-theoretical techniques have to be developed, respectively, in order to reach the envisaged precision.

The interpretation of the data will be performed in two complementary ways: model independent in the context of effective field theories (EFT) and model dependent in specific extensions of the SM, which are interesting from a theoretical end phenomenological point of view . We will follow both paths and will profit from a combination of predictions in theory, experimental data and a common interpretation. In theory and experiment we will focus on the "Standard Model EFT" (SMEFT), which utilizes a complex set of 59 operators of mass-dimension six in the SM fields and the Higgs field in a linear representation.

**A1 Analysis of couplings strength and structures from total and differential cross section measurements**

The foreseen measurement shall answer the question, whether the observed Higgs particle shows a deviation from the predictions of the SM for couplings strength and structure .in the different production mechanisms and decay modes. Further on hints may be derived, which extensions of the SM can be concluded and which are favoured in the light of the new measurements. The observation of the bosonic decay modes into a pair of electroweak gauge bosons was already obtained with the Run-1 data set. Only recently observation of the fermionic decay modes into a pair of tau-leptons and b-quarks was achieved. The couplings strengths assuming the SM coupling structure could be determined with a precision of 10 to 25%. First measurements of differential cross sections and their interpretation in the framework of EFTs have been performed in the decay modes H--> 2 photons and H-->ZZ--> 4 leptons. Measurement of similar and further differential cross sections in the decay modes H-->WW, tau tau, bb as well of simplified template cross sections (STXS) will be the focus of the research plan. The results will be interpreted in the context of the SMEFT and in specific models with extended Higgs sectors

The top quark due to its large mass posses the larges Yukawa coupling to the Higgs boson in the SM. Many extensions of the SM predict modified couplings in particular for the top quark. The top-quark Yukawa coupling can be determined directly from a measurement of the cross section for Higgs-boson production in association with a pair of top quark (ttH). Recently this production process has been observed by a combination of various Higgs boson decay modes. The decay H-->bb has the largest decay branching ratio, but faces several experimental challenges. The Yukawa coupling strength an structuere will be measured exploiting the ttH, H-->bb topology.

__Thesis topics:__

- Measurement of total and differential cross section in the decay modes H-->WW, H-->tau tau and H--> bb and interpretation in SM and in EFT (several thesis)
- Measurement of the strength and structure of the top-Quark Yukawa coupling in pp-->Htt with H-->bb

**A2 Search for non.resonant Higgs-pair production, CP violation and Lepton Flavour Violation in the Higgs sector**

The determination of the trilnear Higgs-boson self-coupling allows (at least in parts) to reconstruct the Higgs potential and to finally provide evidence, that the electroweak is broken spontaneously. Therefore its determination is a central goal of the research programme at current and future colliders. It requires as a first step the evidence for and cross section measurement of non-resonant di-Higgs boson production (pp→HH), i.e. without contributions from new particles coupling to the observed Higgs boson. The current analysis of Run-1 and Run-2 data allow to exclude production-cross section, which are enhanced by an order of magnitude with respect to the SM prediction.One of the most sensitive decay mode combination is given by HH→bb τ τ. An optimized measurement in this topology will be performed and be interpreted in the SM and SMEFT with modified top-quark Yukawa coupling and trilinear Higgs-boson self coupling.

New sources of CP violation (CPV) beyonds those contained in the SM are needed in order to explain the observed baryon asymmetry in the universe. Such new sources of CPV naturally show up in models with extended Higgs sectors.

The production of Higgs-bosons in vector boson fusion (VBF) and in the associated production with a weak gauge boson (VH) provide the largest sensitivity to search for CPV in the coupling of the Higgs boson to electroweak gauge bosons.

The first direct search for CPV in the Higgs sector was performed in our group by investigation VBF production in the H→ττ decay mode and utilizing the method of the Optimal Observable. No signs for CPV were observed and the most stringent limits on CPV in the Higgs sector from Run-1 data were derived.

Lepton flavour violating (LFV) decay of the Higgs boson appear in my extended models, e.g. with two Higgs doubletsor which are based on the Froggatt Nilsen mechanism. The analysis of the Run-1 data collected allowed to exclude branching ratios above approximately 1% for the decay modes H→τ e and H→ τ mu. The search in the final state consisting of one electron, one muon and two neutrinos posses the highest sensitivity. The "so-called symmetry method" allows a completely data-driven estimation of the dominant backgrounds and hence is expected to provide the best sensitivity in particular for newly collected larger data sets.

__Thesis topics: __

Search for non-resonant Higgs-boson pair production in the decay mode combination HH→bb τ $tau;

Test of CP invariance in Higgs-boson production using the decay mode H→ τ τ

Search for lepton-flavour violating Higgs boson decays H→ τ μ (τ e)

**A3 NNLO corrections to Higgs-boson production in the Standard model**

Theory predictions for Higgs-boson production processes are required for measuring the boson's coupling and properties. Furthermore, precise prediction are important backgrounds to the measurement of electroweak interactions in vector-boson scattering. However, obtaining precision predictions in the Standard Model (SM) is very challenging due to the required loop order and the complicated coupling structure of the electroweak interactions. In addition, the number of physical scales in the problem leads to challenging mathematics. We will tackle these challenges by applying modern field-theory methods combined with already available tools and results of our groups.

Here we focus on theory predictions for the pp → HZ/HH and the pp → H + 2-jet processes. These types of processes depend on an a relatively large number of scales. Initially we consider the computation of two-loop scattering amplitudes and leave the computation of NNLO cross-section predictions to follow-up projects.

In recent years the theory groups in Freiburg have already obtained important results in this field of research. The group of Stefan Dittmaier has contributed many important results in loop computations in QCD and the electroweak interactions. These include theory predictions in the SM and its extensions including two-loop computations to the gluon-fusion production processes gg→ HH/ZH in the heavy top-mass limit. The group of Harald Ita has developed conceptual and numerical methods for the computation of scattering amplitudes. These new approaches are based on the unitarity method and are particularly suitable for dealing with multi-scale processes.

The planned research reaches from extending existing matrix-element generators up to developing new numerical and analytical methods in field theory. The methods will include symbolic and numerical programming as well as work in algebraic geometry and advanced Feynman-integral calculus.

__Thesis topics: __

Mixed QCD-EW-corrections to Higgs-boson decay and production

QCD-corrections to Higgs-boson production in association with jets

Top-quark mass effects in gluon-fusion processes of Higgs production

**A4 Precision prediction in extensions of the Standard model**

Even though LHC data of Run 2 pose strong constraints on non-standard realizations of the Higgs sector, there is still room for SM extensions with a decoupling limit, such as models with additional Higgs singlets, doublets, or triplets, or more complicated variants. As long as no direct evidence for new particles emerges, precision in theory and experiment is the key in the procedure to favour or disfavour specific models. Even if the considered SM extensions do not demand to unify the fundamental forces or to solve the big open questions of particle physics directly, they still carry salient, generic features of more comprehensive theories and thus serve as "simplified models", and their analysis might give future directions. In the theory preparation for future analyses this means that several approximations made in the past, such as trivial rescalings of SM predictions by Higgs coupling modifiers, will not be good enough. Instead full amplitude calculations in specific SM extensions or in SM Effective Field Theory (SMEFT) are required that include quantum corrections of the strong and electroweak interactions.

In SM extensions, the calculation of electroweak corrections involves the problem of finding appropriate parametrizations of the new-physics sector, including its renormalization. In this context, it is important to realize that model parameters can significantly differ in different "renormalization schemes" for one and the same physics scenario, in particular in the "alignment region" where Higgs couplings to known particles look SM like. The quest for generally valid renormalization procedures and schemes, in which predictions are perturbatively stable and theoretically consistent, was a very active field of research in previous years. SM extensions with a weakly interacting Dark Matter candidate are particularly interesting, e.g., in view of possible Higgs-boson decays into invisible particles. In the RTG we theoretically investigate models of this kind (singlet, doublet, triplet extensions, etc.) with precision and carry out predictions for the direct search of new Higgs bosons and for precision analyses of Higgs-boson couplings to identify traces of non-standard physics. In addition to investigations within specific models, we pursue more model-independent analyses in SMEFT as well.

Some of the projects aim at the further development of the Monte Carlo programs Prophecy4f and HAWK, which provide precision calculations for specific Higgs-boson production and decay processes including quantum corrections. Prophecy4f deals with the four-body Higgs decays H→WW/ZZ→4fermions, and HAWK calculates Higgs production cross sections via weak-boson fusion and Higgs-strahlung off W/Z bosons.

__Theses topics:__

Renormalization of and precision calculations in models with Higgs triplets

SMEFT calculations with quantum corrections