Present status of radiative and rare kaon decays
I review recent developments in rare and radiative kaon decays from the theory side, with emphasis on those modes that are actively analyzed by the experimental collaborations.
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arXiv subjects
Oscar Cata
Publications and source records attributed to Oscar Cata.
Constraining flavour patterns of scalar leptoquarks in the effective field theory
We investigate the viability of extending the Standard Model with $S_1$ and $S_3$ scalar leptoquarks when the flavour structure is parametrized in terms of Froggatt-Nielsen charges. In contrast to a similar analysis with a vector leptoquark, we find essentially two solutions for the charges that fit the experimental constraints, which are dominated by the current tensions in $B$ decays. These two scenarios differ in their estimate of the anomalous magnetic moment of the muon, $(g-2)$, but they both predict sizeable contributions to $τ\toμγ$, $\bar B_s\toτ^\pmμ^\mp$ and $B^+\to K^+τ^+μ^-$ decays, whose branching ratios are close to the current experimental limits.
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On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$
Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the MV constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.
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Gauge anomalies in the Standard-Model Effective Field Theory
If the Standard Model is understood as the first term of an effective field theory, the anomaly-cancellation conditions have to be worked out and fulfilled order by order in the effective field-theory expansion. We bring attention to this issue and study in detail a subset of the anomalies of the effective field theories at the electroweak scale. The end result is a set of sum rules for the operator coefficients. These conditions, which are necessary for the internal consistency of the theory, lead to a number of phenomenological consequences when implemented in analyses of experimental data. In particular, they not only decrease the number of free parameters in different physical processes but have the potential to relate processes with different flavor content. Conversely, a violation of these conditions would necessarily imply the existence of undetected non-decoupling new physics associated with the electroweak energy scale.
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Chiral effective theories with a light scalar at one loop
There are indications that some theories with spontaneous symmetry breaking also feature a light scalar in their spectrum, with a mass comparable to the one of the Goldstone modes. In this paper, we perform the one-loop renormalization of a theory of Goldstone modes invariant under a chiral $SU(n)\times SU(n)$ symmetry group coupled to a generic scalar singlet. We employ the background field method, together with the heat kernel expansion, to get an expression for the effective action at one loop and single out the anomalous dimensions, which can be read off from the second Seeley-DeWitt coefficient. As a relevant application, we use our master formula to renormalize chiral-scale perturbation theory, an alternative to $SU(3)$ chiral perturbation theory where the $f_0(500)$ meson is interpreted as a dilaton. Based on our results, we briefly discuss strategies to test and discern both effective field theories using lattice simulations.
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Linking lepton number violation with $B$ anomalies
Hints of violation of lepton flavor universality in semileptonic $B$ decays have prompted a renewed interest in leptoquarks at the low TeV scale. Among the different scenarios suggested, some happen to violate also lepton number, yet not much attention has been paid to the expected size of the associated lepton number violating processes. In this note we examine this issue. We find that there is a single leptoquark scenario compatible with the current size of the anomalies which also violates lepton number. In this scenario (Majorana) neutrino masses are radiatively generated. With the leptoquark parameters extracted from fitting the flavor anomalies, one actually gets the right order of magnitude for neutrino masses. We examine the associated effective field theories both at the electroweak scale and at the hadronic scale and estimate the size of the most relevant lepton number violating processes.
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Closing in on the radiative weak chiral couplings
We point out that, given the current experimental status of radiative kaon decays, a subclass of the ${\cal O} (p^4)$ counterterms of the weak chiral lagrangian can be determined in closed form. This involves in a decisive way the decay $K^\pm \to π^\pm π^0 l^+ l^-$, currently being measured at CERN by the NA48/2 and NA62 collaborations. We show that consistency with other radiative kaon decay measurements leads to a rather clean prediction for the ${\cal{O}}(p^4)$ weak couplings entering this decay mode. This results in a characteristic pattern for the interference Dalitz plot, susceptible to be tested already with the limited statistics available at NA48/2. We also provide the first analysis of $K_S\to π^+π^-γ^*$, which will be measured by LHCb and will help reduce (together with the related $K_L$ decay) the experimental uncertainty on the radiative weak chiral couplings. A precise experimental determination of the ${\cal{O}}(p^4)$ weak couplings is important in order to assess the validity of the existing theoretical models in a conclusive way. We briefly comment on the current theoretical situation and discuss the merits of the different theoretical approaches.
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Chiral methods at the electroweak scale
I review the main features of the effective field theory (EFT) behind scenarios of dynamical electroweak symmetry breaking, placing particular emphasis on the systematics and the parallels that can be drawn with Chiral Perturbation Theory. The notion of chiral dimensions will be introduced and shown to be the right tool to describe nonlinear expansions. I will also discuss why such an EFT is of interest in phenomenological studies at the LHC. The most important aspect is that the EFT is engineered to recover the Standard Model in a particular limit, and therefore provides a general framework to test the Higgs hypothesis. Additionally, I will argue that the $κ$ formalism used currently by experimental collaborations to study Higgs couplings at the LHC can actually be embedded into this EFT. This not only gives the $κ$ parametrization a solid QFT foundation but also shows the way to improve it systematically, and in particular how to upgrade analyses on Higgs processes from the level of rates to the level of distributions.
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Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO
We consider the Standard Model, including a light scalar boson $h$, as an effective theory at the weak scale $v=246\,{\rm GeV}$ of some unknown dynamics of electroweak symmetry breaking. This dynamics may be strong, with $h$ emerging as a pseudo-Goldstone boson. The symmetry breaking scale $Λ$ is taken to be at $4πv$ or above. We review the leading-order Lagrangian within this framework, which is nonrenormalizable in general. A chiral Lagrangian can then be constructed based on a loop expansion. A systematic power counting is derived and used to identify the classes of counterterms that appear at one loop order. With this result the complete Lagrangian is constructed at next-to-leading order, ${\cal O}(v^2/Λ^2)$. This Lagrangian is the most general effective description of the Standard Model containing a light scalar boson, in general with strong dynamics of electroweak symmetry breaking. Scenarios such as the SILH ansatz or the dimension-6 Lagrangian of a linearly realized Higgs sector can be recovered as special cases.
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A Systematic Approach to the SILH Lagrangian
We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small $ξ=v^2/f^2$. Here $v$ is the electroweak scale and $f$ is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in $ξ$, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in $ξ$ has to be performed. We point out that terms of order $ξ^2$, which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order $ξ/16π^2$ that are retained, as long as $ξ> 1/16π^2$. Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset $SO(5)/SO(4)$ is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on $SU(2)_L\otimes SU(2)_R/SU(2)_V$.
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Dark Matter Stability without New Symmetries
The stability of dark matter is normally achieved by imposing extra symmetries beyond those of the Standard Model of Particle Physics. In this paper we present a framework where the dark matter stability emerges as a consequence of the Standard Model symmetries. The dark matter particle is an antisymmetric tensor field (analogous to the one used for spin-1 mesons in QCD), singlet under the Standard Model gauge group. The Lagrangian possesses an accidental $Z_2$ symmetry which makes the dark matter stable on cosmological time scales. Interactions with the Standard Model fields proceed through the Higgs portal, which allows the observed dark matter abundance to be generated via thermal freeze-out. We also discuss the prospects for observing this dark matter particle in direct detection experiments.
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Lurking pseudovectors below the TeV scale
If electroweak symmetry breaking is driven by a new strongly-coupled dynamical sector, one expects their bound states to appear at the TeV scale or slightly below. However, electroweak precision data imposes severe constraints on most of the existing models, putting them under strain. Conventional models require the new composite states to come in pairs of rather heavy, close to degenerate spin-1 resonances. In this paper I argue that spin-1 states can actually be lighter without clashing with experimental bounds. As an example, I consider a composite model with a light pseudovector resonance that couples to the Standard Model gauge boson, fermion and scalar fields. I show how such a resonance leaves basically no imprint on the NLO corrections to the Standard Model. This happens not through parameter tuning, but rather as a consequence of generic properties of realistic UV completions. This pseudovector is mostly unconstrained by existing data and could be as light as 600 GeV. In the last part of the paper I briefly discuss its most characteristic signatures for direct detection at colliders.
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On the Power Counting in Effective Field Theories
We discuss the systematics of power counting in general effective field theories, focussing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic $U(1)$ symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.
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Nonstandard Higgs Couplings from Angular Distributions in $h\to Z \ell^+\ell^-$
We compute the fully differential rate for the Higgs-boson decay $h\to Z\ell^+\ell^-$, with $Z\to\ell^{'+}\ell^{'-}$. For these processes we assume the most general matrix elements within an effective Lagrangian framework. The electroweak chiral Lagrangian we employ assumes minimal particle content and Standard Model gauge symmetries, but is otherwise completely general. We discuss how information on new physics in the decay form factors may be obtained that is inaccessible in the dilepton-mass spectrum integrated over angular variables. The form factors are related to the coefficients of the effective Lagrangian, which are used to estimate the potential size of new-physics effects.
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Recent developments in nonleptonic kaon decays
I review the current status of nonleptonic kaon decays, placing special emphasis on the recent theoretical progress. In particular, I concentrate on 3 points: (i) the improved determination of ε_K, including both perturbative and nonperturbative contributions; (ii) the efforts to tame (K -> 2π) transitions in lattice QCD; and (iii) the use of holographic methods to solve the vector meson dominance puzzle in (K -> 3π).
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EWSB from strongly-coupled dynamics: an EFT approach and implications for WW production
If the dynamics behind EWSB are of strongly-coupled nature, the Standard Model ceases to be renormalizable and should be instead understood as an effective field theory (EFT). Here I will discuss the systematics behind this effective field theory description. My focus will be on deriving a consistent power-counting formula and building the basis of NLO operators. As an application, I will consider WW production both at linear and hadron colliders.
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Searches for strong dynamics signals in gauge boson pair production
I briefly review the construction of the effective field theory of a nonlinearly realized electroweak symmetry breaking and apply it to the study of gauge boson pair production. I will consider WW, ZZ and γZ production at linear colliders as reference illustrative examples. I will show that in all cases a consistent effective field theory treatment allows to encode the dominant new physics effects entirely as gauge-fermion vertex corrections. From naive dimensional analysis one expects these corrections to be at the per mille level. However, they grow with energy, such that at TeV colliders (LHC and futures linear collider facilities) these new physics effects can easily amount to 20% corrections to the production cross sections.
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Standard Model prediction and new physics tests for D0 -> h+h-l+l- (h=π,K; l=e,μ)
Motivated by the recent evidence for direct CP-violation in D0 -> h+h- decays, we provide an exhaustive study of both Cabibbo-favored and Cabibbo-suppressed (singly and doubly) D0 -> h1+h2-l+l- decays. In particular, we study the Dalitz plot for the long-distance contributions in the (m_{ll}^2,m_{hh}^2) parameter space. We find that near-resonant effects, i.e., D0 -> V(h1+h2-)l+l- with V=ρ,K*,ϕ, are sizeable and even dominant (over Bremsstrahlung) for the μ+μ- decay modes, bringing the branching ratios close to the LHCb reach. We also provide a detailed study of the angular asymmetries for such decays and identify signatures for new physics detection. In particular, new physics signals can be neatly isolated in asymmetries involving the semileptonic operator Q_{10}, where for typical new physics scenarios the effects can be as sizeable as O(1%) for the doubly Cabibbo-suppressed modes.
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