• composite models
• chiral gauge theories
• dark matter

The nature of dark matter, whose existence has been inferred indirectly from a large variety of astrophysical and cosmological observations, is arguably one of the greatest mysteries in fundamental
physics today. So far, many alternatives have been suggested as a possible solution, ranging from modified theories of gravity to beyond the Standard Model physics or primordial black holes, but unfortunately none of them has received any compelling empirical justification. Amongst them, particle dark matter seems particularly well motivated from a theoretical point of view, since it could also help to shed some light on the open issues in the Standard Model, such as the strong CP problem, grand unification or supersymmetry.
An intriguing proposal is that dark matter may be realized as a composite state of a strongly interacting dynamics, coming from a non abelian gauge theory which confines in the infrared. This idea is particularly appealing, since it can account for many of the properties of dark matter in a conceptually economical way, mimicking some already well-known mechanisms in particle physics. For example, adopting an effective field theory point of view, we see that neglecting the non-renormalizable interactions at low energies can enforce some accidental symmetries in our description, which may naturally give rise to the stability of the lightest particle in each multiplet. This is exactly what happens in the Standard Model for baryon number, forbidding proton decay. Since all of these theories do not aim to address electroweak symmetry breaking and related issues, an important fact to keep in mind is that the dark condensation must not break the Standard Model gauge group, and this is what distinguishes them, for example, from Technicolor or Composite Higgs. Up to now, most of the work has focused on Vector-like Confinement 1 scenarios, which were first considered in the context of LHC Phenomenology [1] and later applied to dark matter model building. Their structure provides significant simplifications with respect to the general case, since anomaly cancellation constraints are trivially satisfied and the real representation 2 enables one to conjecture the existence of a global symmetry breaking pattern in the dark sector [2] which preserves the electroweak group. In [3], all possible models consistent with a SU (5) unification of SM gauge forces have been classified, showing 1
A model is called Vector-like if, for any set of fields transforming under a certain represention of the gauge group, a corresponding set of fields transforming under the conjugate representation is also present (or alternatively, the model can be constructed out of Dirac fermions only) 2 at least in the absence of Yukawa couplings 1 that many of them are compatible with current bounds and may exhibit characteristic detection signatures. It is then relevant to ask if the same framework can be successfully applied to chiral models, and whether new phenomenological features can be obtained this way. By chiral we mean that the new fermions transform in a complex representation of the gauge group, with the immediate effect that mass terms are forbidden by gauge invariance. This hypothesis appears to possess some elegant features, and to emerge naturally in the context of physics beyond the Standard Model:
• Since mass terms for the dark fermions are not allowed, there is no need for any new, artificial scale. The only relevant one is generated dynamically through dimensional transmutation, and it is what determines the spectrum of the composite states.
• Chiral theories play an important role in our understanding of particle physics, with the Standard Model itself being the most obvious example.
• If the Standard Model interactions unify in a single gauge group at high energies, the resulting theory must be chiral. The prototypical GUT is the famous SU(5) [4], where each generation of SM matter fields is embedded into a ̄5 and a 10. While it is certainly possible to add vector-like fermions transforming in fragments of chiral GUT representations, one must then introduce an additional mechanism to explain why the other members of the multiplets have acquired a much higher mass. This is analogous to the doublet-triplet splitting problem of Grand Unified Theories (See [5] for a review).
For these reasons, chiral models are often thought to be more fundamental; an instructive example can be found in the vector-like QED-QCD system, which finds the explanation of its structure and mass scales in a chiral UV completion, the SM. Chiral models 3 have been considered in [6, 7], where the possibility of a dark, non-anomalous U(1) spontaneously broken by a Higgs mechanism is examined, and also in the context of the mirror world scenario [8]. In addition, some algorithmic methods to construct chiral, anomaly-free extensions of the Standard Model have been devised in [9, 10].
An interesting example was recently considered in [11, 12], where the authors introduced a composite chiral model with four dark fermions charged under the gauge group SU(N ) DC ⊗ U (1) D 4 . The theory confines in the infrared, breaking U (1) D spontaneously (thus giving the dark photon a mass) and forming dark pions and dark baryons, which are bound states exactly analogous to those of QCD.
Due to the existence of a global, accidental U (1) V symmetry in the renormalizable lagrangian, the two dark pions are stable and provide a viable dark matter candidate. Interactions with the Standard Model are solely achieved by means of a mixing between the dark and the standard photon [13], which is expected to happen on quite general grounds. The purpose of the thesis is to search for possible extensions of this framework, and examine their phenomenological implications. A possible generalization involves the assignement of charges under the SM gauge groups, adding new portals between the dark sector and SM; this could potentially be very relevant for collider experiments, and also for 3 4
But not necessarily composite D and DC stand for dark and dark colour respectively 2direct detection. In fact, there are no previous examples of a composite chiral model where the dark constituents are not singlets with respect to the SM.
More specifically, we identify a new scenario in which the dark fermions also transform as representations of SU(2) L , resulting in a non trivial dark sector characterized by a rich and distinctive phenomenology. Since the model exhibits an approximate SU(4) L ⊗ SU(4) R ⊗ U(1) B symmetry (spontaneously broken to SU(4) V ⊗ U(1) B ), the low energy spectrum of the theory contains 15 Pseudo Nambu-Goldstone bosons (NGBs), one of which is eaten by the dark photon due to the spontaneous breaking of U(1) D induced by condensation in the dark sector. In addition to the U (1) V symmetry described above, which is still present, we point out the existence of a discrete symmetry analogous to charge conjugation, C D , with important implications for processes involving a dark photon.
The model satisifies all the necessary requirements to provide viable dark matter candidates:
• The cancellation of gauge anomalies is still guaranteed
• Landau poles below the GUT scale are avoided for a reasonable range in the choices of the dark charge e D and the number of dark colours N DC
• The symmetry breaking pattern is under control, preserving the weak gauge group SU(2) L
• A calculation of the pion effective potential shows that the explicit breaking induced by the gauge interactions is sufficient for each of them to obtain a mass, which can be calculated under the assumption of QCD-like sum rules.
We write down an appropriate chiral lagrangian for the dark pions containing all the interactions between themselves and with the gauge bosons, thus making the model very predictive. An inspection of these interactions enables one to conclude that only the lightest states with U(1) V charge different from zero are stable and electromagnetically neutral, and to analyze all the decay channels in detail.
Since the dark matter candidates are singlets of the electroweak group, interactions with the SM are very suppressed and there are no relevant prospects for direct detection. However, the situation changes dramatically at the collider, where SU(2)-charged NGBs 5 can be efficiently produced through Drell-Yan processes and then decay partially to SM particles. Many of the experimental signatures 6 are similar to those of supersymmetry, and pre-existing searches are used to derive stringent bounds on the mass of the electroweak triplets after calculating their production cross section at LHC. As regards Cosmology and Astrophysics, we derive constraints assuming the correct relic abundance is obtained through a standard thermal freeze-out proceeding via the annihilation channel DM DM → γ D γ D (1) and examine the possible bounds coming from indirect detection.
The main result consists in a characterization of the viable parameter space for this class of models, 5 6 Triplets in particular
There are, however, some important differences even at the qualitative level 3obtained through a combination of theoretical constraints, cosmological observations and collider data.
In particular, we find that only a closed triangle region 7 in the m s − e D plane is allowed, where m s is the dark matter candidate mass (proportional to the dark color condensation scale Λ DC ) and e D the dark charge. This makes the model very predictive, and fully testable in future collider experiments.
However, our analysis also leaves a certain number of open questions and future directions to explore. A first possibility is to investigate whether a refinement of our collider bounds may give sensibly different constraints on the model, excluding some or all of the cases. This could be achieved with a more accurate (NLO) computation of the triplet production cross section, and by calculating the precise shape of the kinematic distributions (e.g. in missing energy) to compare with experiment.
On the other hand, a more long-term goal is to provide a systematic classification of chiral models, along the lines of what has already been carried out in the case of real representations [3].
References
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7
Only assuming our NGB dark matter candidate does not overclose the universe (i.e. allowing for other particles, such as baryons, to give subdominant contributions to Ω DM ). If, on the other hand, we require the NGBs to reproduce the whole relic density the allowed region becomes a finite curve.
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