We present a three-site Pati-Salam gauge model able to explain the Standard Model flavor hierarchies while, at the same time, accommodating the recent experimental hints of lepton-flavor non-universality in B decays. The model is consistent with low-and high-energy bounds, and predicts a rich spectrum of new states at the TeV scale that could be probed in the near future by the high-pT experiments at the LHC.

We present a thorough investigation of the vector leptoquark hypothesis for a combined explanation of the B-physics anomalies. We analyze this hypothesis from a twofold perspective, taking into account recent results from B-physics observables and high-p T searches. First, using a simplified model, we determine the general conditions for a successful lowenergy fit in presence of right-handed leptoquark couplings (neglected in previous analyses). Second, we show how these conditions, in particular a sizable 2-3 family mixing, can be achieved in a motivated ultraviolet completion. Our analysis reinforces the phenomenological success of the vector leptoquark hypothesis in addressing the anomalies, and its compatibility with motivated extensions of the Standard Model based on the idea of flavor non-universal gauge interactions. The implications of right-handed leptoquark couplings for a series of key low-energy observables, namely B s → τ τ and τ → µ lepton flavor violating processes, both in τ and in B decays, are discussed in detail. The role of the ultraviolet completion in precisely estimating other low-energy observables, most notably ∆F = 2 amplitudes, is also addressed. also [32,37]).We provide a detailed implementation of the U 1 leptoquark in a renormalizable model based on the (flavor non-universal) gauge group SU (4) 3 × SU (3) 1+2 × SU (2) L × U (1) , which in turn can be embedded in PS 3 [31]. In this context, we complement the simplified-model analysis by including oneloop contributions to low-energy observables (most notably ∆F = 2 amplitudes and dipole operators) which can be reliably computed only within a UV-complete framework.The paper is organized as follows. In Section 2 we present the simplified-model analysis: we introduce the Lagrangian describing the U 1 couplings to SM fermions, and analyze its low-energy limit. We discuss all the observables insensitive to the UV completion (Section 2.2), which are later used to fit low-energy data (Section 2.3). We finally comment on the high-p T constraints (Section 2.4).The UV-complete model is presented and discussed in Section 3: on the model-building side we pay particular attention to the flavor structure of the model (Section 3.2); on the phenomenological side we present complete expressions for the UV-dependent (loop-induced) observables, which were omitted in the low-energy fit (Section 3.3). The results are summarized in Section 4.

We propose a mechanism that allows for sizeable flavour violation in quark-lepton currents, while suppressing flavour changing neutral currents in quark-quark and lepton-lepton sectors. The mechanism is applied to the recently proposed "4321" renormalizable model, which can accommodate the current experimental anomalies in B-meson decays, both in charged and neutral currents, while remaining consistent with all other indirect flavour and electroweak precision measurements and direct searches at high-p T . To support this claim, we present an exhaustive phenomenological survey of this fully calculable UV complete model and highlight the rich complementarity between indirect and direct searches. A.7 Vector-fermion interactions in the mass basis 47 A.8 Tri-linear gauge boson vertices 49 A.9 Renormalisation group equations 51 A.10 SU (4) generators 524. there are very severe constraints from flavour observables in pure leptonic channels, most notably in processes violating lepton universality and lepton flavour.Since the first point clearly contrasts with the remaining ones, finding a coherent NP framework to explain all these facts remains a non-trivial challenge. However, the points above are also suggesting in a (qualitative) way their own solutions. Indeed a viable NP scenario should:1. contain a leptoquark with large flavour violating couplings in order to trigger the anomalous semileptonic decays in charged currents; *

We study the generic features of minimal gauge extensions of the Standard Model in view of recent hints of lepton-flavor non-universality in semi-leptonic $b \to s \ell^+ \ell^-$ and $b \to c \ell \nu$ decays. We classify the possible models according to the symmetry-breaking pattern and the source of flavor non-universality. We find that in viable models the $\mathrm{SU(2)}_L$ factor is embedded non-trivially in the extended gauge group, and that gauge couplings should be universal, hinting to the presence of new degrees of freedom sourcing non-universality. Finally, we provide an explicit model that can explain the $B$-decay anomalies in a coherent way and confront it with the relevant phenomenological constraints.Comment: 8 pages, 2 figures; discussion improved, a figure and references added; conclusions unchange

The three-site Pati-Salam gauge model provides a consistent description for the hints of lepton-flavor non-universality observed in B decays, connecting the present pattern of "anomalies" to the origin of the Standard Model Yukawa couplings. We present here a detailed analysis of the model predictions for a series of low-energy observables, mainly in B and τ physics. The model is in good agreement with present data and predicts a well-defined pattern of non-standard effects in lowenergy observables that could allow us to test it in the near future. Particularly interesting are the predictions of large τ → µ Lepton Flavor Violating processes, such as τ → µγ, τ → 3µ, B → Kτ µ, and B s → τ µ. Also µ → 3e, µ → eγ, and K L → µe decays could be not far from the present exclusion bounds, although this conclusion is more model dependent.

We present a systematic procedure to obtain the one-loop low-energy effective Lagrangian resulting from integrating out the heavy fields of a given ultraviolet theory. We show that the matching coefficients are determined entirely by the hard region of the functional determinant involving the heavy fields. This represents an important simplification with respect the conventional matching approach, where the full and effective theory contributions have to be computed separately and a cancellation of the infrared divergent parts has to take place. We illustrate the method with a descriptive toy model and with an extension of the Standard Model with a heavy real scalar triplet. A comparison with other schemes that have been put forward recently is also provided.

Motivated by the recent LHCb announcement of a 3.1σ violation of lepton- flavor universality in the ratio RK = Γ(B → Kμ+μ−)/Γ(B → Ke+e−), we present an updated, comprehensive analysis of the flavor anomalies seen in both neutral-current (b → sℓ+ℓ−) and charged-current (b → $$ c\tau \overline{\nu} $$ cτ ν ¯ ) decays of B mesons. Our study starts from a model-independent effective field-theory approach and then considers both a simplified model and a UV-complete extension of the Standard Model featuring a vector leptoquark U1 as the main mediator of the anomalies. We show that the new LHCb data corroborate the emerging pattern of a new, predominantly left-handed, semileptonic current-current interaction with a flavor structure respecting a (minimally) broken U(2)5 flavor symmetry. New aspects of our analysis include a combined analysis of the semileptonic operators involving tau leptons, including in particular the important constraint from Bs-$$ {\overline{B}}_s $$ B ¯ s mixing, a systematic study of the effects of right-handed leptoquark couplings and of deviations from minimal flavor-symmetry breaking, a detailed analysis of various rare B-decay modes which would provide smoking-gun signatures of this non-standard framework (LFV decays, di-tau modes, and B → K(*)$$ \nu \overline{\nu} $$ ν ν ¯ ), and finally an updated analysis of collider bounds on the leptoquark mass and couplings.

We define a new class of Z models with neutral flavor-changing interactions at tree level in the down-quark sector. They are related in an exact way to elements of the quark mixing matrix due to an underlying flavored U(1) gauge symmetry, rendering these models particularly predictive. The same symmetry implies lepton-flavor non-universal couplings, fully determined by the gauge structure of the model. Our models allow to address presently observed deviations from the SM and specific correlations among the new physics contributions to the Wilson coefficients C ( ) 9,10 can be tested in b → s + − transitions. We furthermore predict lepton-universality violations in Z decays, testable at the LHC.