In the hidden valley scenario [1
], a sector of SM-singlet particles, interacting amongst themselves, is appended to the SM. These are then coupled to the SM through irrelevant operators at the TeV scale, or through marginal operators with weak couplings. An important additional feature of a hidden valley, distinct from a general hidden sector, is that a mass gap (or a symmetry) forbids one or more of the valley particles from decaying entirely to hidden-sector particles; instead, these particles decay to SM particles. Interactions between the SM and hidden valley may also allow the 125 GeV Higgs to decay to valley particles, which in turn decay to SM particles.
The phenomenology of Higgs decays to hidden valleys can sometimes be captured by "simplified" models, including others on this website, but much more complex patterns of decays may easily arise. This is especially true if hidden valleys have strong and perhaps confining interactions. For instance, if hidden-valley confinement generates hidden "hadrons", then, just as QCD has a variety of hadrons that decay to non-hadronic final states, often with long lifetimes, and with masses that are spread widely around 1 GeV, the hidden valley may have multiple particles of comparable masses that decay to SM particles, sometimes with very long lifetimes.
More generally, common features that arise in hidden valleys, generally as a result of self-interactions of one sort or another, include
- Multiple types of neutral particles with narrow widths, decaying to the SM particles via very weak interactions.
- Because their decays are mediated by very weak interactions, their lifetimes may be long, though they are sensitive to unknown parameters; decays may occur promptly, at a displaced vertex, or far outside the detector, giving a MET signal.
- As they interact so weakly with the SM, they are rarely produced directly; instead, they are dominantly produced in the decays of heavy particles, including the Higgs, neutralinos, etc.
- When created in the decays of heavy particles, the new particles, if sufficiently light, may commonly be highly boosted.
- Because of their self-interactions, the new particles are often produced in clusters, just as QCD hadrons (and their parent gluons) are produced in the showering and hadronization that forms QCD jets.
Hidden valleys arise in several theoretical contexts. Dark matter may well be from a hidden sector; for instance, the "WIMP miracle" can apply to particles that are not WIMPs at all [4
]. Many of the models that have attempted to explain recent hints of indirect and direct dark matter detection have involved hidden valleys, the most famous being [5
]. Supersymmetry breaking models typically have a hidden sector, within which some particles (often just a single spin-one or spin-zero particle) occasionally survives to low energy. And model building that attempts to generate the SM from string theory generally leads to additional non-SM gauge groups under which no SM particles are charged. Hidden valleys have also appeared in certain attempts to address the hierarchy problem (cf. Twin Higgs [7
], in which the top quark and W
loops that correct the Higgs mass are cancelled by particles in a hidden valley).
Entry to the hidden valley may occur through a wide variety of "portals"; any neutral particle, or particle/anti-particle pair, may couple to operators made from valley fields, and consequently may itself decay to such particles, and may mediate transitions between SM and valley fields. The Z
boson can be a portal; rare Z
decays, and rare Z
-mediated processes, can be used to put significant bounds on certain types of hidden valleys. However, explicit calculation shows these bounds are not sufficient to rule out the possibility [1
] that the Higgs itself has decays to a hidden valley that could be discovered in current or future LHC data. This is because of the Higgs' narrow width, which makes it far more sensitive to very small couplings than is the Z
, which is nearly 3 orders of magnitude wider.
Aside from direct limits from Z
decays, rare B
and other meson decays, and direct production limits, constraints on hidden valleys can arise from precision tests of the SM, but these are generally rather weak. Cosmological constraints are sometimes important, but very large classes of models evade them easily [1
New Higgs decays commonly arise in hidden valley models. We first give a few examples of phenomena that can arise in hidden valleys that, though very different in their origin from theories we have already discussed, give signals that we have already discussed. We then give some examples of phenomena that we have not discussed that can arise in these models.
SM + Scalar, 2DHM + Scalar
Consider a confining hidden valley, with its own gauge group G
and quarks Qi
, and a Higgs-like scalar S
that gives mass to the Qi
via a S QiQi
coupling, but does not break G
. We imagine that S
mixes with one of the SM Higgs doublets; for example, this model could be an extension of the NMSSM. If the gauge group confines and breaks chiral symmetry, with PNGBs Kv
, then a S Kv Kv
coupling and the mixing of S
and the Higgs allows the decay h
→ Kv Kv
. The Kv
may then decay to SM fermions, with the heaviest fermions available typically most common; this can occur for instance via mixing with a heavy Z
′ or with a SM pseudoscalar Higgs. An example (not at all unique) is given in the model of [1
], which shows decays may be prompt for mKv
above about 20 GeV.
SM + 2 Fermions (and similar)
The same signal that arises in a simplified model with fermions may arise in hidden valleys, for much the same reasons. But it may arise even when there are no fermions at all. Consider the same model just mentioned, but with two flavors of PNGBs (as with pions and kaons in the SM), Kv
. It may be that the Kv
are stable or very long-lived, and produce only MET
, while K
cannot decay to two or more Kv
. This could be due to kinematic constraints (like Kaons in QCD if mK
were less than 2 mπ
), or symmetries. In that case K
may decay via a small coupling to a scalar field S
that mixes with h
, or via a spin-one vector V
that mixes with Z
. This opens up the possibility of K
→ Kv h*
→ Kv Z*
, which would produce a non-resonant pair of SM fermions, or resonant decays such as K
→ Kv S
→ Kv V
In other hidden valleys, it can happen that there are two states, the heavier of which can only decay to the lighter via a loop of heavy particles, which allows for a radiative (i.e. photon emission) decay. If the lighter state is stable or decays invisibly, then the signal of two photons + MET
Generally these signals can arise whenever we have two states, the lighter of which is invisible and the heavier of which can only decay to the lighter via emission of an on- or off-shell particle that decays to SM fermions or gauge bosons.
SM + Vector
There are several ways for spin-one particles to arise naturally in a hidden valley, and for these to mix with the photon and/or Z
to allow them to decay to SM fermions. There could be a broken U
(1) symmetry, giving what is often called a "dark photon". Mixing with the hypercharge boson is through renormalizable kinetic mixing. There could be a broken non-abelian gauge symmetry; in this case, there could be several spin-one particles, with the heavier ones decaying to the lighter ones via a cascade. Such a scenario only permits mixing with hypercharge through a dimension-five version of kinetic mixing. Finally, the spin-one particles could be stable bound states ρv
, like a ρ meson in a theory with no chiral symmetry breaking and no pions. (An example with a stable vector and a stable pseudovector was given in [1
Decays of the Higgs to such particles can be induced using any of the mechanisms mentioned above or in the simplified model discussion. For instance, decay of a Higgs to two ρv
(or, if there are two vectors ρ1
, the decay h
) can occur along the same lines as the decay h
→ Kv Kv
A particularly well-known example of this type of hidden valley is [8
], in which an elementary "dark photon" of low mass preferentially creates light leptons with very few photons or neutral pions. Since it is lightweight, it tends to be produced with a high boost, giving the now-famous phenomenon of a "lepton-jet". A simple lepton-jet contains two nearby leptons, isolated from other particles but not from one another. (More complex lepton jets will be addressed below.)
In this paper, we have limited ourselves to relatively simple final states to which the Higgs might decay. However, the complex final states that are common in hidden valleys are very important to keep in mind, as they can pose considerable (though interesting) experimental challenges. For instance, even limited complexity can lead to 8 or more visible partons, from four hidden valley scalars, pseudoscalars, or vectors (possibly plus MET) in a Higgs decay. The kinematics are then dependent on the hidden sector's mass spectrum and internal dynamics, giving rise to a wide array of signals.
This direction of research lies beyond our scope and should be returned to in the future. However, a couple of relatively simple experimental cases deserve note. First, any of the final states mentioned above may be accompanied by valley particles that are long-lived on detector time-scales and therefore invisible. This motivates searches for similar final states accompanied by MET, which we address in h→γ+MET
, h→ Isolated leptons+MET
, h→ Collimated leptons+MET
, and h→ 2τ+MET
Second, many models produce "complex" lepton-jets, in which multiple "dark-photons" (or dark non-abelian bosons or ρ mesons) are created near one another, clustered either by the kinematics of a cascade decay or by the physics of hidden-valley showering and hadronization. Some efforts have been made to find such objects [9
]. Another interesting possibility would give several such dark photons created with low momentum along with MET, leading to many unclustered very soft leptons. An attempt to search for such final states was made by CDF [10
]. Unfortunately, in models where the vector bosons can decay also to pions, the leptons are fewer and hadrons often take their place, making the challenges much greater. One important signature, which is useful for particles of mass up to several GeV, is a di-pion resonance with the same mass as a di-lepton resonance. In models where the light particles are pseudo-scalars, and often produce taus and rarely muons, it is not clear whether a good search strategy exists, unless rates are sufficient for a di-muon resonance search.
Another issue that commonly arises in hidden valleys is long-lived neutral particles [1
]. Valley particles, by definition, are neutral under all SM gauge groups. The case of hadrons in QCD offers a useful analogy: most are highly unstable, but a few are stable, and others are metastable, for a diversity of reasons (exact and approximate symmetries, weak forces, kinematic constraints, etc.) Generally it is quite common, given a rich spectrum of particles with a variety of lifetimes, that one or more will decay typically with a displaced vertex. An example of a natural theory where such particles may arise in Higgs decays [2
] is the Twin Higgs [7
]. This issue takes us beyond our current purposes, but has already received some amount of experimental study, as in [11
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