The spontaneous breaking of U(1)B−L around the scale of grand unification can simultaneously account for hybrid inflation, leptogenesis, and neutralino dark matter, thus resolving three major puzzles ...of particle physics and cosmology in a single predictive framework. The B−L phase transition also results in a network of cosmic strings. If strong and electroweak interactions are unified in an SO(10) gauge group, containing U(1)B−L as a subgroup, these strings are metastable. In this case, they produce a stochastic background of gravitational waves that evades current pulsar timing bounds, but features a flat spectrum with amplitude h2ΩGW∼10−8 at interferometer frequencies. Ongoing and future LIGO observations will hence probe the scale of B−L breaking.
Using the effective Lagrangian approach, we clarify general issues about Nambu-Goldstone bosons without Lorentz invariance. We show how to count their number and study their dispersion relations. ...Their number is less than the number of broken generators when some of them form canonically conjugate pairs. The pairing occurs when the generators have a nonzero expectation value of their commutator. For non-semi-simple algebras, central extensions are possible. The underlying geometry of the coset space in general is partially symplectic.
A
bstract
Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where
S
-matrix kinematics and symmetry considerations are encoded ...in the operator spectrum of the EFT. In this paper we use the
S
-matrix to derive the structure of the EFT operator basis, providing complementary descriptions in (i) position space utilizing the conformal algebra and cohomology and (ii) momentum space via an algebraic formulation in terms of a ring of momenta with kinematics implemented as an ideal. These frameworks systematically handle redundancies associated with equations of motion (on-shell) and integration by parts (momentum conservation).
We introduce a partition function, termed the Hilbert series, to enumerate the operator basis — correspondingly, the
S
-matrix — and derive a matrix integral expression to compute the Hilbert series. The expression is general, easily applied in any spacetime dimension, with arbitrary field content and (linearly realized) symmetries.
In addition to counting, we discuss construction of the basis. Simple algorithms follow from the algebraic formulation in momentum space. We explicitly compute the basis for operators involving up to
n
= 5 scalar fields. This construction universally applies to fields with spin, since the operator basis for scalars encodes the momentum dependence of
n
-point amplitudes.
We discuss in detail the operator basis for non-linearly realized symmetries. In the presence of massless particles, there is freedom to impose additional structure on the
S
- matrix in the form of soft limits. The most na¨ıve implementation for massless scalars leads to the operator basis for pions, which we confirm using the standard CCWZ formulation for non-linear realizations.
Although primarily discussed in the language of EFT, some of our results — conceptual and quantitative — may be of broader use in studying conformal field theories as well as the AdS/CFT correspondence.
A
bstract
We present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision ...observables. With this procedure, one can interpret precision measurements as constraints on a given UV model. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. This covariant derivative expansion method dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV models. A few general aspects of RG running effects and choosing operator bases are discussed. Finally, we provide mapping results between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. Many results and tools which should prove useful to those wishing to use the SM EFT are detailed in several appendices.
A
bstract
In a companion paper 1, we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can ...be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)
A
bstract
We present a very minimal model for baryogenesis by a dark first-order phase transition. It employs a new dark SU(2)
D
gauge group with two doublet Higgs bosons, two lepton doublets, and ...two singlets. The singlets act as a neutrino portal that transfer the generated asymmetry to the Standard Model. The model predicts ∆
N
eff
= 0
.
09–0.13 detectable by future experiments as well as possible signals from exotic decays of the Higgs and
Z
bosons and stochastic gravitational waves.
A
bstract
We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting ...from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.
We introduce a model for matter genesis in which both the baryonic and dark matter asymmetries originate from a first-order phase transition in a dark sector with an $SU(3)$ × $SU(2)$ × $U(1)$ gauge ...group and minimal matter content. In the simplest scenario, we predict that dark matter is a dark antineutron with mass of either $m_\bar{n}$ = 1.36 GeV or $m_\bar{n}$ = 1.63 GeV. Alternatively, dark matter may be comprised of equal numbers of dark antiprotons and pions. In either scenario, this model is highly discoverable through both dark matter direct detection and dark photon search experiments. The strong dark matter self-interactions may ameliorate small-scale structure problems, while the strongly first-order phase transition may be confirmed at future gravitational wave observatories.
The dark matter density distribution in small-scale astrophysical objects may indicate that dark matter is self-interacting, while observations from clusters of galaxies suggest that the ...corresponding cross section depends on the velocity. Using a model-independent approach, we show that resonant self-interacting dark matter can naturally explain such a behavior. In contrast to what is often assumed, this does not require a light mediator. We present explicit realizations of this mechanism and discuss the corresponding astrophysical constraints.
Dark matter could be a thermal relic comprised of strongly interacting massive particles (SIMPs), where 3 → 2 interactions set the relic abundance. Such interactions generically arise in theories of ...chiral symmetry breaking via the Wess-Zumino-Witten term. In this work, we show that an axionlike particle can successfully maintain kinetic equilibrium between the dark matter and the visible sector, allowing the requisite entropy transfer that is crucial for SIMPs to be a cold dark matter candidate. Constraints on this scenario arise from beam dump and collider experiments, from the cosmic microwave background, and from supernovae. We find a viable parameter space when the axionlike particle is close in mass to the SIMP dark matter, with strong-scale masses of order a few hundred MeV. Many planned experiments are set to probe the parameter space in the near future.
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