Search

We propose an extension of the three-Higgs-doublet model (3HDM), where the Standard Model (SM) particle content is enlarged by the inclusion of two inert $SU_{2L}$ scalar doublets, three inert and two active electrically neutral gauge singlet scalars, charged vector like fermions and Majorana neutrinos. These additional particles are introduced to generate the SM fermion mass hierarchy from a sequential loop suppression mechanism. In our model the top and exotic fermion masses appear at tree level, whereas the remaining fermions get their masses radiatively. Specifically, bottom, charm, tau and muon masses appear at 1-loop; the masses for the light up, down and strange quarks as well as for the electron at 2-loop and masses for the light active neutrinos at 3-loop. Our model successfully accounts for SM fermion masses and mixings and accommodates the observed Dark Matter relic density, the electron and muon anomalous magnetic moments, as well the constraints arising from charged Lepton Flavor Violating (LFV) processes. The proposed model predicts charged LFV decays within the reach of forthcoming experiments., Comment: Matches published version in JHEP

We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant $g_A$ in the neutron $\beta$-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function $g_1$, we determine the contribution from the $\gamma W$-box diagram to a precision better than $10^{-4}$. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron $\beta$-decay are almost identical, i.e. the ratio $\lambda=g_A/g_V$ is almost unrenormalized. With this result, we predict the bare axial coupling constant to be {$\mathring{g}_A=-1.2754(13)_\mathrm{exp}(2)_\mathrm{RC}$} based on the PDG average $\lambda=-1.2756(13)$, Comment: Revised manuscript

Precision studies of the Higgs boson at future $e^+e^-$ colliders can help to shed light on fundamental questions related to electroweak symmetry breaking, baryogenesis, the hierarchy problem, and dark matter. The main production process, $e^+e^- \to HZ$, will need to be controlled with sub-percent precision, which requires the inclusion of next-to-next-to-leading order (NNLO) electroweak corrections. The most challenging class of diagrams are planar and non-planar double-box topologies with multiple massive propagators in the loops. This article proposes a technique for computing these diagrams numerically, by transforming one of the sub-loops through the use of Feynman parameters and a dispersion relation, while standard one-loop formulae can be used for the other sub-loop. This approach can be extended to deal with tensor integrals. The resulting numerical integrals can be evaluated in minutes on a single CPU core, to achieve about 0.1% relative precision., 16 pages, 4 figures and 1 table

Measurements of electroweak precision observables at future electron-positron colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard Model expectations of these observables are needed, including corrections at the three- and four-loop level. In this article, results are presented for the calculation of a subset of three-loop mixed electroweak-QCD corrections, stemming from diagrams with a gluon exchange and two closed fermion loops. The numerical impact of these corrections is illustrated for a number of applications: the prediction of the W-boson mass from the Fermi constant, the effective weak mixing angle, and the partial and total widths of the Z boson. Two alternative renormalization schemes for the top-quark mass are considered, on-shell and $\overline{\mbox{MS}}$., Comment: 15 pages, 5 figures

We investigate the impact of extra leptons on observed tensions in the muon $g-2$ and the first-row CKM unitarity. By introducing a new SU(2)$_L$ doublet lepton and a SU(2)$_L$ triplet lepton, we find that both of the tensions can be explained simultaneously under constraints from electroweak precision observables and Higgs-boson decays. Our model could be tested by measurements of $h\to\mu\mu$ at future collider experiments., Comment: 25 pages, 4 figures; version published in JHEP

Due to a recent more precise evaluation of $V_{ud}$ and $V_{us}$, the unitarity condition of the first row in the Cabibbo-Kobayashi-Maskawa (CKM) matrix: $|V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2 = 0.99798 \pm 0.00038$ now stands at a deviation more than $4\sigma$ from unity. Furthermore, a mild excess in the overall Higgs signal strength appears at about $2\sigma$ above the standard model (SM) prediction, as well as the long-lasting discrepancy in the forward-backward asymmetry ${\cal A}_{\rm FB}^b$ in $Z\to b\bar b$ at LEP. Motivated from the above three anomalies we investigate an extension of the SM with vector-like quarks (VLQs) associated with the down-quark sector, with the goal of alleviating the tension among these datasets. We perform global fits of the model under the constraints coming from the unitarity condition of the first row of the CKM matrix, the $Z$-pole observables ${\cal A}_{\rm FB}^b$, $R_b$ and $\Gamma_{\rm had}$, Electro-Weak precision observables $\Delta S$ and $\Delta T$, $B$-meson observables $B_d^0$-$\overline{B}_d^0$ mixing, $B^+ \to \pi^+ \ell^+ \ell^-$ and $B^0 \to \mu^+ \mu^-$, and direct searches for VLQs at the Large Hadron Collider (LHC). Our results suggest that adding VLQs to the SM provides better agreement than the SM., Comment: 30 pages, 3 figures, version published in JHEP

We provide a general method to effectively compute differential and cumulative event-shape distributions to $\mathcal{O}(\alpha_s)$ precision for massive quarks produced primarily at an $e^+e^-$ collider. In particular, we show that at this order, due to the screening of collinear singularities by the quark mass, for all event shapes linearly sensitive to soft dynamics, there appear only two distributions at threshold: a Dirac delta function and a plus distribution. Furthermore, we show that the coefficient of the latter is universal for any infra-red and collinear safe event shape, and provide an analytic expression for it. Likewise, we compute a general formula for the coefficient of the Dirac delta function, which depends only on the event-shape measurement function in the soft limit. Finally, we present an efficient algorithm to compute the differential and cumulative distributions, which does not rely on Monte Carlo methods, therefore achieving a priory arbitrary precision even in the extreme dijet region. We implement this algorithm in a numeric code and show that it agrees with analytic results on the distribution for 2-jettiness, heavy jet mass and a massive generalization of C-parameter., Comment: 37 pages + appendices, 21 figures; v2: journal version

We report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3$\times$3 Yukawa matrices $Y$ valid when $Y Y^\dagger \rightarrow U^\dagger \,Y Y^\dagger \, U$ under global $U(3)_{Q_L}$ flavour symmetry transformations $U$. The results apply to the Standard Model Effective Field Theory (SMEFT) and its `geometric' realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the $\sqrt{2 \langle H^\dagger H \rangle} / \Lambda$ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism's utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond., Comment: Matches published version

Properly separating and subtracting renormalons in the framework of the operator product expansion (OPE) is a way to realize high precision computation of QCD effects in high energy physics. We propose a new method (FTRS method), which enables to subtract multiple renormalons simultaneously from a general observable. It utilizes a property of Fourier transform, and the leading Wilson coefficient is written in a one-parameter integral form whose integrand has suppressed (or vanishing) renormalons. The renormalon subtraction scheme coincides with the usual principal-value prescription at large orders. We perform test analyses and subtract the ${\cal O}(\Lambda_{\rm QCD}^4)$ renormalon from the Adler function, the ${\cal O}(\Lambda_{\rm QCD}^2)$ renormalon from the $B\to X_ul\bar{\nu}$ decay width, and the ${\cal O}(\Lambda_{\rm QCD})$ and ${\cal O}(\Lambda_{\rm QCD}^2)$ renormalons from the $B,\,D$ meson masses. The analyses show good consistency with theoretical expectations, such as improved convergence and scale dependence. In particular we obtain $\bar{\Lambda}_{\rm FTRS}=0.495\pm0.053~\text{GeV}$ and$ (\mu_\pi^2)_{\rm FTRS}=-0.12\pm 0.23~\text{GeV}^2$ for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail., Comment: 67 pages, 14 figures, More discussions, figures and references added in revision

The determination of $|V_{ub}|$ in inclusive semileptonic $B \to X_u \ell \nu$ decays will be among the pivotal tasks of Belle II. In this paper we study the potential and limitations of machine learning approaches that attempt to reduce theory uncertainties by extending the experimentally accessible fiducial region of the $B\to X_u \ell\nu$ signal into regions where the $B\to X_c \ell\nu$ background is dominant. We find that a deep neural network trained on low-level single particle features offers modest improvement in separating signal from background, compared to BDT set-ups using physicist-engineered high-level features. We further illustrate that while the signal acceptance of such a deep neural network deteriorates in kinematic regions where the signal is small, such as at high hadronic invariant mass, neural networks which exclude kinematic features are flatter in kinematics but less inclusive in the sampling of exclusive hadronic final states at fixed kinematics. The trade-off between these two set-ups is somewhat Monte Carlo dependent, and we study this issue using the multipurpose event generator Sherpa in addition to the widely used $B$-physics tool EvtGen., Comment: 20 pages, 11 figures; v2: Final version published in JHEP

We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa $ \beta $-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the $ \beta $-functions, we compare the general form to the specific $ \beta $-functions of known theories to constrain the unknown coefficients. The Weyl consistency conditions provide additional constraints, completing the determination., Comment: 27 pages, 519 tensor structures and coefficients

We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $\overline{\rm MS}$ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy., 17 pages

We point out that hints of deviations from unitarity in the first row of the CKM matrix may be explained by the presence of a single vector-like top. We study how the stringent experimental constraints arising from CP Violation in the kaon sector and from meson mixing such as $D^0$-$\overline{D}^0$, $K^0$-$\overline{K}^0$ and $B^0_{d,s}$-$\overline{B}^0_{d,s}$ can be satisfied in the proposed framework. In order for the deviations from unitarity to be of the required size while keeping the theory perturbative, the new top quark should have a mass $m_T \lesssim 7$ TeV which could be probed in upcoming experiments at the energy frontier., 24 pages, 4 figures, 2 tables; comments and references added

The K → μ+μ− decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, ℬ(KS → μ+μ−)ℓ=0 can be experimentally determined without the need to separate the ℓ = 0 and ℓ = 1 final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination $$ \mid {V}_{ts}{V}_{td}\sin \left(\beta +{\beta}_s\right)\mid \approx \mid {A}^2{\lambda}^5\overline{\eta}\mid $$ ∣ V ts V td sin β + β s ∣ ≈ ∣ A 2 λ 5 η ¯ ∣ with hadronic uncertainties below 1%.

Solutions of the Strong CP Problem based on the spontaneous breaking of CP must feature a non-generic structure and simultaneously explain a coincidence between a priori unrelated CP-even and CP-odd mass scales. We show that these properties can emerge from gauge invariance and a CP-conserving, but otherwise generic, physics at the Planck scale. In our scenarios no fundamental scalar is introduced beyond the Standard Model Higgs doublet, and CP is broken at naturally small scales by a confining non-abelian dynamics. This approach is remarkably predictive: robustness against uncontrollable UV corrections to the QCD topological angle requires one or more families of vector-like quarks below a few $10$'s of TeV, hence potentially accessible at colliders. Because CP violation is communicated to the SM at these super-soft scales, our solution of the Strong CP Problem is not spoiled by the presence of heavy new states motivated by other puzzles in physics beyond the Standard Model. In addition, these models generically predict a dark sector that may lead to interesting cosmological signatures., Comment: 19 pages. v2: matches the published version

The vanishing of the Higgs quartic coupling of the Standard Model at high energies may be explained by spontaneous breaking of Higgs Parity. Taking Higgs Parity to originate from the Left-Right symmetry of the $SO(10)$ gauge group, leads to a new scheme for precision gauge coupling unification that is consistent with proton decay. We compute the relevant running of couplings and threshold corrections to allow a precise correlation among Standard Model parameters. The scheme has a built-in solution for obtaining a realistic value for $m_b/m_\tau$, which further improves the precision from gauge coupling unification, allowing the QCD coupling constant to be predicted to the level of 1 % or, alternatively, the top quark mass to 0.2 %. Future measurements of these parameters may significantly constrain the detailed structure of the theory. We also study an $SO(10)$ embedding of quark and lepton masses, showing how large neutrino mixing is compatible with small quark mixing, and predict a normal neutrino mass hierarchy. The strong CP problem may be explained by combining Higgs Parity with space-time parity., Comment: 39 pages, 9 figures

We consider a minimal left-right model with a Peccei-Quinn symmetry, where generalised charge conjugation plays the role of the left-right symmetry. We show how the spontaneous breaking of the Peccei-Quinn symmetry by a scalar singlet can provide us with solutions not only to the strong CP and dark matter problems but can also help to generate naturally suppressed off-diagonal CKM elements and small neutrino masses via the inverse seesaw mechanism. For this, we make use of an economical scalar sector composed of a bi-doublet, two doublets and a singlet only. As a result of the new gauge bosons and neutrinos, the neutrinoless double beta decay, as well as lepton flavour violating processes, receives new contributions which can, in principle, become relevant due to the low-scale nature of the inverse seesaw mechanism. The model can easily accommodate all the current data on fermion masses and mixing even if the left-right scale is only high enough to evade the current experimental constraints., Comment: 25 pages. Version accepted for publication in JHEP

We propose a 3+1 Higgs Doublet Model based on the $\Delta(27)$ family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings. The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields. The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved $Z_2^{\left( 1\right)}$ discrete symmetry, which also leads to stable scalar and fermionic dark matter candidates. The leptonic sector features the predictive cobimaximal mixing pattern, consistent with the experimental data from neutrino oscillations. For the scenario of normal neutrino mass hierarchy, the model predicts an effective Majorana neutrino mass parameter in the range $3$~meV$\lesssim m_{\beta\beta}\lesssim$ $18$ meV, which is within the declared range of sensitivity of modern experiments. The model predicts Flavour Changing Neutral Currents which constrain the model, for instance Kaon mixing and $\mu \to e$ nuclear conversion processes, the latter which are found to be within the reach of the forthcoming experiments., Comment: 21 pages, 7 figures, version published in JHEP

Recent measurements of the Higgs-muon coupling are directly probing muon mass generation for the first time. We classify minimal models with a one-loop radiative mass mechanism and show that benchmark models are consistent with current experimental results. We find that these models are best probed by measurements of $(g-2)_\mu$, even when taking into account the precision of Higgs measurements expected at future colliders. The current $(g-2)_\mu$ anomaly, if confirmed, could therefore be a first hint that the muon mass has a radiative origin., Comment: 14 pages, 5 figures; v2: references added, updated experimental g-2 measurement, matches published version

Triple heavy vector boson production, $p p \to VVV$ $(V = W, Z)$, has recently been observed for the first time. We propose that precision measurements of this process provide an excellent probe of the first generation light quark Yukawa couplings. Modified quark interactions with the off-shell Higgs in this process lead to a rapid growth of the partonic cross sections with energy, which manifests in an enhanced $p_T$ distribution of the final state leptons and quarks. We quantify this effect and estimate the present and future 2$\sigma$ sensitivity to the up, down, and strange Yukawas. In particular, we find that HL-LHC can reach $\mathcal{O}(400)$ sensitivity to the down Yukawa relative to the Standard Model value, improving the current sensitivity in this process by a factor of $10$, and which can be further improved to $\mathcal{O}(30)$ at FCC-hh. This is competitive with and complementary to constraints from global fits and other on-shell probes of the first generation Yukawas. The triboson sensitivity at HL-LHC corresponds to probing dimension-6 SMEFT operators suppressed by an $\mathcal{O}(1)$ TeV scale, similarly to other LHC Higgs probes., Comment: 22 pages, 6 figures

We propose a theory of quark and lepton mass and mixing with non-universal $Z'$ couplings based on a 5d Standard Model with quarks and leptons transforming as triplets under a new gauged $SO(3)$ isospin. In the 4d effective theory, the $SO(3)$ isospin is broken to $U(1)'$, through a $S^1/(\mathbb{Z}_2\times \mathbb{Z}'_2)$ orbifold, then subsequently dynamically broken, resulting in a massive $Z'$. Quarks and leptons in the 5d bulk appear as massless modes, with zero Yukawa couplings to the Higgs on the brane, and zero couplings to $Z'$, at leading order, due to the $U(1)'$ symmetry. However, after the $U(1)'$ breaking, both Yukawa couplings and non-universal $Z'$ couplings are generated by heavy Kaluza-Klein exchanges. Hierarchical quark and lepton masses result from a hierarchy of 5d Dirac fermion masses. Neutrino mass and mixing arises from a novel type Ib seesaw mechanism, mediated by Kaluza-Klein Dirac neutrinos. The non-universal $Z'$ couplings may contribute to semi-leptonic $B$ decay ratios which violate $\mu - e$ universality. In this model such couplings are related to the corresponding quark and lepton effective Yukawa couplings., Comment: 25 pages, 5 figures. v3: matches published version

The Nelson-Barr (NB) mechanism to solve the strong CP problem assumes CP conservation, arranges vanishing $\bar{\theta}$ at tree-level and requires vector-like quarks (VLQs) to transmit the CP breaking to the SM. We analyze the flavor constraints coming from the presence of one such down type VLQ of NB type by performing a global fit on the relevant flavor observables. A comparison is made to the case of one generic VLQ. We find that the allowed parameter space for the VLQ Yukawa couplings and the mixing to the SM are confined to a region much smaller than in the generic case, making the NB case falsifiable in principle., Comment: Appendices added

We combine $SU(5)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the representation assignments of the matter fields under $A_4$, we find that there are seven types of $SU(5)$ models with $A_4$ modular symmetry. We present 53 benchmark models with the fewest free parameters. The parameter space of each model is scanned to optimize the agreement between predictions and experimental data, and predictions for the masses and mixing parameters of quarks and leptons are given at the best fitting points. The best fit predictions for the leptonic CP violating Dirac phase, the lightest neutrino mass and the neutrinoless double beta decay parameter when displayed graphically are observed to cover a wide range of possible values, but are clustered around particular regions, allowing future neutrino experiments to discriminate between the different types of models., Comment: 57 pages, 4 figures

A non-supersymmetric renormalizable $SO(10)$ model is investigated for its viability in explaining the observed fermion masses and mixing parameters along with the baryon asymmetry produced via thermal leptogenesis. The Yukawa sector of the model consists of complex $10_H$ and $\overline{126}_H$ scalars with a Peccei-Quinn like symmetry and it leads to strong correlations among the Yukawa couplings of all the standard model fermions including the couplings and masses of the right-handed (RH) neutrinos. The latter implies the necessity to include the second lightest RH neutrino and flavor effects for the precision computation of leptogenesis. We use the most general density matrix equations to calculate the temperature evolution of flavoured leptonic asymmetry. A simplified analytical solution of these equations, applicable to the RH neutrino spectrum predicted in the model, is also obtained which allows one to fit the observed baryon to photon ratio along with the other fermion mass observables in a numerically efficient way. The analytical and numerical solutions are found to be in agreement within a factor of ${\cal O}(1)$. We find that the successful leptogenesis in this model does not prefer any particular value for leptonic Dirac and Majorana CP phases and the entire range of values of these observables is found to be consistent. The model specifically predicts (a) the lightest neutrino mass $m_{\nu_1}$ between 2-8 meV, (b) the effective mass of neutrinoless double beta decay $m_{\beta \beta}$ between 4-10 meV, and (c) a particular correlation between the Dirac and one of the Majorana CP phases., Comment: 26 pages, 4 captioned figures, 2 tables; a reference and a few explanatory sentences are added;Published version

In this paper, a model inspired by Grand Unification principles featuring three generations of vector-like fermions, new Higgs doublets and a rich neutrino sector at the low scale is presented. Using the state-of-the-art Deep Learning techniques we perform the first phenomenological analysis of this model focusing on the study of new charged vector-like leptons (VLLs) and their possible signatures at CERN's Large Hadron Collider (LHC). In our numerical analysis we consider signal events for vector-boson fusion and VLL pair production topologies, both involving a final state containing a pair of charged leptons of different flavor and two sterile neutrinos that provide a missing energy. We also consider the case of VLL single production where, in addition to a pair of sterile neutrinos, the final state contains only one charged lepton. All calculated observables are provided as data sets for Deep Learning analysis, where a neural network is constructed, based on results obtained via an evolutive algorithm, whose objective is to maximise either the accuracy metric or the Asimov significance for different masses of the VLL. Taking into account the effect of the three analysed topologies, we have found that the combined significance for the observation of new VLLs at the high-luminosity LHC can range from $5.7\sigma$, for a mass of $1.25~\mathrm{TeV}$, all the way up to $28\sigma$ if the VLL mass is $200~\mathrm{GeV}$. We have also shown that by the end of the LHC Run-III a $200~\mathrm{GeV}$ VLL can be excluded with a confidence of $8.8$ standard deviations. The results obtained show that our model can be probed well before the end of the LHC operations and, in particular, providing important phenomenological information to constrain the energy scale at which new gauge symmetries emergent from the considered Grand Unification picture can be manifest., Comment: 60 pages, 31 figures, 15 tables

Parity solutions to the strong CP problem are a compelling alternative to approaches based on Peccei-Quinn symmetry, particularly given the expected violation of global symmetries in a theory of quantum gravity. The most natural of these solutions break parity at a low scale, giving rise to a host of experimentally accessible signals. We assess the status of the simplest parity-based solution in light of LHC data and flavor constraints, highlighting the prospects for near-future tests at colliders, tabletop experiments, and gravitational wave observatories. The origin of parity breaking and associated gravitational effects play crucial roles, providing new avenues for discovery through EDMs and gravity waves. These experimental opportunities underline the promise of generalized parity, rather than Peccei-Quinn symmetry, as a robust and testable solution to the strong CP problem.

We analyze the stability of the Higgs sector of a three-site model with flavor-non-universal gauge interactions, whose spectrum of non-Standard-Model states spans three orders of magnitude. This model is inspired by deconstructing a five-dimensional theory where the generation index is in one-to-one relation to the position in the fifth dimension. It provides a good description of masses and mixing of the SM fermions in terms of scale hierarchies. We demonstrate that, within this construction, the mass term of the SM-like Higgs does not receive large corrections proportional to the highest mass scales. The model suffers only of the unavoidable "little hierarchy problem" between the electroweak scale and the lightest NP states, which are expected to be at the TeV scale., 17 pages, 1 figure, 2 tables

Precision measurements in allowed nuclear beta decays and neutron decay are reviewed and analyzed both within the Standard Model and looking for new physics. The analysis incorporates the most recent experimental and theoretical developments. The results are interpreted in terms of Wilson coefficients describing the effective interactions between leptons and nucleons (or quarks) that are responsible for beta decay. New global fits are performed incorporating a comprehensive list of precision measurements in neutron decay, superallowed $0^+\rightarrow 0^+$ transitions, and other nuclear decays that include, for the first time, data from mirror beta transitions. The results confirm the $V$-$A$ character of the interaction and translate into updated values for $V_{ud}$ and $g_A$ at the $10^{-4}$ level. We also place new stringent limits on exotic couplings involving left-handed and right-handed neutrinos, which benefit significantly from the inclusion of mirror decays in the analysis., 35 pages; v2: analysis updated, comments and references added; v3: compared to the JHEP version, typos in Eqs. 2.1, A3, A4 corrected, Eq. 4.4 updated, comment on aCORN update added in footnote 12

We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $\Gamma$, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space $G/K$, where $G$ is a Lie group and $K$ is a compact subgroup of $G$, modded out by $\Gamma$. For a general choice of $G$, $K$, $\Gamma$ and a generic matter content, we explicitly construct a minimal K\"ahler potential and a general superpotential, for both rigid and local $N=1$ supersymmetric theories. We also specialize our construction to the case $G=Sp(2g,R)$, $K=U(g)$ and $\Gamma=Sp(2g,Z)$, whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing $g=2$, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2., Comment: 60 pages, 1 figure

The Nelson-Barr mechanism to solve the strong CP problem requires vector-like quarks (VLQs) to transmit the spontaneous CP breaking to the SM. We study the scenario where only these VLQs are within reach at the TeV scale while the spontaneous CP breaking sector is inaccessible. We investigate how these VLQs of Nelson-Barr type differ from generic VLQs and find from parameter counting that one less parameter is needed. In particular, for one VLQ of Nelson-Barr type, there is only one CP odd quantity that is responsible for all CP violation. In this case, we solve the technical problem of parametrizing only the new physics parameters while keeping the SM parameters as independent inputs. For one down-type VLQ, the model is largely flavor safe because the VLQ couplings to the SM up quarks and the $W$ are hierarchically smaller for lighter quarks., Slightly updates; references and appendix added. Comply with published version

The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries $\Gamma_N$ and for a given element $\gamma \in \Gamma_N$, we present an algorithm for finding stabilisers (specific values for moduli fields $\tau_\gamma$ which remain unchanged under the action associated to $\gamma$). We then employ this algorithm to find all stabilisers for each element of finite modular groups for $N=2$ to $5$, namely, $\Gamma_2\simeq S_3$, $\Gamma_3\simeq A_4$, $\Gamma_4\simeq S_4$ and $\Gamma_5\simeq A_5$. These stabilisers then leave preserved a specific cyclic subgroup of $\Gamma_N$. This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry., Comment: 18 pages, 5 figures, 4 tables, accepted for publication in JHEP

We study the determination of the top-quark mass using leptonic observables in t-channel single top-quark production at the LHC. We demonstrate sensitivity of transverse momentum of the charged lepton on the input top-quark mass. We present predictions at next-to-next-to-leading order (NNLO) in QCD with narrow width approximation and structure function approach. Further corrections due to parton shower and hadronization, non-resonant and non-factorized contributions are discussed. To reduce impact of SM backgrounds we propose to use the charge weighted distribution for the measurement, i.e., differences between distributions of charged lepton with positive and negative charges. By modeling both signal and background processes, we found the projections for (HL-)LHC to be promising, with a total theoretical uncertainty on the extracted top-quark mass of about 1 $\sim$ 2 GeV., 29 pages, 8 figures; version to appear on JHEP

Future electron-position colliders, such as CEPC and FCC-ee, have the capability to dramatically improve the experimental precision for W and Z-boson masses and couplings. This would enable indirect probes of physics beyond the Standard Model at multi-TeV scales. For this purpose, one must complement the experimental measurements with equally precise calculations for the theoretical predictions of these quantities within the Standard Model, including three-loop electroweak corrections. This article reports on the calculation of a subset of these corrections, stemming from diagrams with three closed fermion loops to the following quantities: the prediction of the W-boson mass from the Fermi constant, the effective weak mixing angle, and partial and total widths of the Z boson. The numerical size of these corrections is relatively modest, but non-negligible compared to the precision targets of future colliders. In passing, an error is identified in previous results for the two-loop corrections to the Z width, with a small yet non-zero numerical impact., Comment: 15 pages, 3 figures

We point out that testing the equality of the Cabibbo angle as extracted from $\Gamma(K\rightarrow \pi l\nu)$, the ratio $\Gamma(K\rightarrow l\nu)/\Gamma(\pi\rightarrow l\nu)$ and nuclear $\beta$ decays is not identical to a test of first row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The reason is that a CKM unitarity test involves only two parameters, while the degrees of freedom for the assessment of the goodness-of-fit of the universality of the Cabibbo angle entailed by the Standard Model (SM) is equal to the number of measurements minus one. Beyond the SM all different processes could in principle give different Cabibbo angles. Consequently, the difference between the two tests becomes relevant starting from three observables giving results for the Cabibbo angle that are in tension with each other. With current data, depending on the treatment of the nuclear $\beta$ decays, we find that New Physics is favored over the SM at $5.1\,\sigma$ or $3.6\,\sigma$ while CKM unitarity is rejected at $4.8\sigma$ or $3.0\sigma$, respectively. We argue that the best method to test the SM is to test the equality of the Cabibbo angle, because CKM unitarity is only one aspect of the SM., Comment: 15 pages, 1 figure. Matches published version

We propose a model that explains the fermion mass hierarchy by the Froggatt-Nielsen mechanism with a discrete $Z_N^F$ symmetry. As a concrete model, we study a supersymmetric model with a single flavon coupled to the minimal supersymmetric Standard Model. Flavon develops a TeV scale vacuum expectation value for realizing flavor hierarchy, an appropriate $\mu$-term and the electroweak scale, hence the model has a low cutoff scale. We demonstrate how the flavon is successfully stabilized together with the Higgs bosons in the model. The discrete flavor symmetry $Z_N^F$ controls not only the Standard Model fermion masses, but also the Higgs potential and a mass of the Higgsino which is a good candidate for dark matter. The hierarchy in the Higgs-flavon sector is determined in order to make the model anomaly-free and realize a stable electroweak vacuum. We show that this model can explain the fermion mass hierarchy, realistic Higgs-flavon potential and thermally produced dark matter at the same time. We discuss flavor violating processes induced by the light flavon which would be detected in future experiments., Comment: 47 pages, 6 figures and 4 tables; v2: version published in JHEP

We propose a simple clockwork model of flavor which successfully generates the Standard Model flavor hierarchies from random order-one couplings. With very few parameters we achieve distributions of models in excellent agreement with observation. We explain in some detail the interpretation of our mechanism as random localization of zero modes in theory space. The scale of the vectorlike fermions is mostly constrained by lepton flavor violation with secondary constraints arising from rare meson decays., 27 pages + appendices

The simultaneous study of top-down and bottom-up approaches to modular flavor symmetry leads necessarily to the concept of eclectic flavor groups. These are nontrivial products of modular and traditional flavor symmetries that exhibit the phenomenon of local flavor enhancement in moduli space. We develop methods to determine the eclectic flavor groups that can be consistently associated with a given traditional flavor symmetry. Applying these methods to a large family of prominent traditional flavor symmetries, we try to identify potential candidates for realistic eclectic flavor groups and show that they are relatively rare. Model building with finite modular flavor symmetries thus appears to be much more restrictive than previously thought., 23 pages, 2 tables; v2: interpretation of outer automorphisms clarified

We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C. The set of master integrals under consideration was found with self-energy diagrams containing two closed fermion loops in mind. Two techniques are employed in deriving the expressions for the finite pieces that are then numerically integrated: (a) Sub-loop dispersion relations in the case of topologies containing sub-bubbles, and (b) a modification of the procedure suggested by Ghinculov for integrals with only sub-loop triangles., 26 pages, 3 figures, 5 tables. Code available at http://www.pitt.edu/~afreitas/

The vanishing of the Higgs quartic coupling at a high energy scale may be explained by Intermediate Scale Supersymmetry, where supersymmetry breaks at $(10^9$-$10^{12})$ GeV. The possible range of supersymmetry breaking scales can be narrowed down by precise measurements of the top quark mass and the strong coupling constant. On the other hand, nuclear recoil experiments can probe Higgsino or sneutrino dark matter up to a mass of $10^{12}$ GeV. We derive the correlation between the dark matter mass and precision measurements of standard model parameters, including supersymmetric threshold corrections. The dark matter mass is bounded from above as a function of the top quark mass and the strong coupling constant. The top quark mass and the strong coupling constant are bounded from above and below respectively for a given dark matter mass. We also discuss how the observed dark matter abundance can be explained by freeze-out or freeze-in during a matter-dominated era after inflation, with the inflaton condensate being dissipated by thermal effects., Comment: 22 pages, 9 figures

We investigate top quark pair production near the threshold where the pair invariant mass $M_{t\bar{t}}$ approaches $2m_t$, which provides sensitive observables to extract the top quark mass $m_t$. Using the effective field theory methods, we derive a factorization and resummation formula for kinematic distributions in the threshold limit up to the next-to-leading power, which resums higher order Coulomb corrections to all orders in the strong coupling constant. Our formula is similar to those in the literature but differs in several important aspects. We apply our formula to the $M_{t\bar{t}}$ distribution, as well as to the double differential cross section with respect to $M_{t\bar{t}}$ and the rapidity of the $t\bar{t}$ pair. We find that the resummation effects significantly increase the cross sections near the threshold, and lead to predictions better compatible with experimental data than the fixed-order ones. We demonstrate that incorporating resummation effects in the top quark mass determination can shift the extracted value of $m_t$ by as large as 1.4 GeV. The shift is much larger than the estimated uncertainties in previous experimental studies, and leads to a value of the top quark pole mass more consistent with the current world average., Comment: 44 pages, 14 figures; comments are welcome; v2: journal version

Precision measurements of the Higgs couplings are, for the first time, directly probing the mechanism of fermion mass generation. The purpose of this work is to determine to what extent these measurements can distinguish between the tree-level mechanism of the Standard Model and the theoretically motivated alternative of radiative mass generation. Focusing on the third-family, we classify the minimal one-loop models and find that they fall into two general classes. By exploring several benchmark models in detail, we demonstrate that a radiative origin for the tau-lepton and bottom-quark masses is consistent with current observations. While future colliders will not be able to rule out a radiative origin, they can probe interesting regions of parameter space., Comment: 39 pages, 15 figures; v2: references updated, published version

A $Z_2$ symmetry that extends the weak interaction, $SU(2)_L \rightarrow SU(2)_L \times SU(2)'$, and the Higgs sector, $H(2) \rightarrow H(2,1) + H'(1,2)$, yields a Standard Model quartic coupling that vanishes at scale $v' = ~\gg~$. Near $v'$, theories either have a "prime" sector, or possess "Left-Right" (LR) symmetry with $SU(2)' = SU(2)_R$. If the $Z_2$ symmetry incorporates spacetime parity, these theories can solve the strong CP problem. The LR theories have all quark and lepton masses arising from operators of dimension 5 or more, requiring Froggatt-Nielsen structures. Two-loop contributions to $\bar{\theta}$ are estimated and typically lead to a neutron electric dipole moment of order $10^{-27}$e cm that can be observed in future experiments. Minimal models, with gauge group $SU(3) \times SU(2)_L \times SU(2)_L \times U(1)_{B-L}$, have precise gauge coupling unification for $v' = 10^{10\pm1}$ GeV, successfully correlating gauge unification with the observed Higgs mass of $125$ GeV. With $SU(3) \times U(1)_{B-L}$ embedded in $SU(4)$, the central value of the unification scale is reduced from $10^{16-17}$ GeV to below $10^{16}$ GeV, improving the likelihood of proton decay discovery. Unified theories based on $SO(10) \times CP$ are constructed that have $H+H'$ in a ${\bf 16}$ or ${\bf 144}$ and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings., Comment: 36 pages, 5 figures

We present a mechanism that addresses the electroweak, the strong CP, and the flavor hierarchies of the Standard Model (including neutrino masses) in a unified way. The naturalness of the electroweak scale is solved together with the strong CP problem by the Nelson-Barr relaxion: the relaxion field is identified with the pseudo-Nambu-Goldstone boson of an abelian symmetry with no QCD anomaly. The Nelson-Barr sector generates the "rolling" potential and the relaxion vacuum expectation value at the stopping point is mapped to the Cabibbo-Kobayashi-Maskawa phase. An abelian symmetry accounts for the Standard Model's mass hierarchies and flavor textures through the Froggatt-Nielsen mechanism. We show how the "backreaction" potential of the relaxion can be induced by a sterile neutrino sector, without any extra state with electroweak quantum numbers. The same construction successfully explains neutrino masses and mixings. The only light field in our construction is the relaxion, which we call the hierarchion because it is essentially linked to our construct that accounts for all the Standard Model hierarchies. Given its interplay with flavor symmetries, the hierarchion can be probed in flavor-violating decays of the Standard Model fermions, motivating a further experimental effort in looking for new physics in rare decays of leptons and mesons., 33 pages, 2 figures

We propose a simple $U(2)$ model of flavor compatible with an $SU(5)$ GUT structure. All hierarchies in fermion masses and mixings arise from powers of two small parameters that control the $U(2)$ breaking. In contrast to previous $U(2)$ models this setup can be realized without supersymmetry and provides an excellent fit to all SM flavor observables including neutrinos. We also consider a variant of this model based on a $D_6 \times U(1)_F$ flavor symmetry, which closely resembles the $U(2)$ structure, but allows for Majorana neutrino masses from the Weinberg operator. Remarkably, in this case one naturally obtains large mixing in the lepton sector from small mixing in the quark sector. The model also offers a natural option for addressing the Strong CP Problem and Dark Matter by identifying the Goldstone boson of the $U(1)_F$ factor as the QCD axion., 30 pages, 1 figure, minor modifications, matches published version

We propose an extension of the 3-3-1 model with an additional symmetry group $Z_{2}\times Z_{4} \times U(1)_{L_g}$ and an extended scalar sector. To our best knowledge this is the first example of a renormalizable 3-3-1 model, which allows explanation of the SM fermion mass hierarchy by a sequential loop suppression: tree-level top and exotic fermion masses, 1-loop bottom, charm, tau and muon masses; 2-loop masses for the light up, down, strange quarks as well as for the electron. The light active neutrino masses are generated from a combination of linear and inverse seesaw mechanisms at two loop level. The model also has viable fermionic and scalar dark matter candidates., Comment: 35 pages, 4 figures. Version accepted for publication in JHEP

We show that a universal texture zero in the (1,1) position of all fermionic mass matrices, including heavy right-handed Majorana neutrinos driving a type-I see-saw mechanism, can lead to a viable spectrum of mass, mixing and CP violation for both quarks and leptons, including (but not limited to) three important postdictions: the Cabibbo angle, the charged lepton masses, and the leptonic `reactor' angle. We model this texture zero with a non-Abelian discrete family symmetry that can easily be embedded in a grand unified framework, and discuss the details of the phenomenology after electroweak and family symmetry breaking. We provide an explicit numerical fit to the available data and obtain excellent agreement with the 18 observables in the charged fermion and neutrino sectors with just 9 free parameters. We further show that the vacua of our new scalar familon fields are readily aligned along desired directions in family space, and also demonstrate discrete gauge anomaly freedom at the relevant scale of our effective theory., 17 pages, 2 figures. Version accepted for publication in JHEP

We propose a new framework to generate the Standard Model (SM) quark flavor hierarchies in the context of two Higgs doublet models (2HDM). The `flavorful' 2HDM couples the SM-like Higgs doublet exclusively to the third quark generation, while the first two generations couple exclusively to an additional source of electroweak symmetry breaking, potentially generating striking collider signatures. We synthesize the flavorful 2HDM with the `flavor-locking' mechanism, that dynamically generates large quark mass hierarchies through a flavor-blind portal to distinct flavon and hierarchon sectors: Dynamical alignment of the flavons allows a unique hierarchon to control the respective quark masses. We further develop the theoretical construction of this mechanism, and show that in the context of a flavorful 2HDM-type setup, it can automatically achieve realistic flavor structures: The CKM matrix is automatically hierarchical with $|V_{cb}|$ and $|V_{ub}|$ generically of the observed size. Exotic contributions to meson oscillation observables may also be generated, that may accommodate current data mildly better than the SM itself., Comment: 34 pages, 2 tables, 2 figures

The quark and lepton mass patterns upset their naive unification. In this paper, a new approach to solve this problem is proposed. Model-independently, we find that a successful unification can be achieved. A mechanism is identified by which the large top quark mass renders its third-generation leptonic partner very light. This state is thus identified with the electron. We then provide a generic dynamical implementation of this mechanism, using tree-level exchanges of vector leptons to relate the quark and lepton flavor structures. In a supersymmetric context, this same mechanism splits the squark masses, and third generation squarks end up much lighter than the others. Finally, the implementation of this mechanism in SU(5) GUT permits to avoid introducing any flavor structure beyond the two minimal Yukawa couplings, ensuring the absence of unknown mixing matrices and their potentially large impact on FCNC., Comment: 31 pages, 5 figures

We embed Two Higgs Doublet Models (2HDMs) in the Froggatt Nielsen (FN) framework. We find that the approximate FN symmetry predicts i) approximate Natural Flavor Conservation (NFC) of Types II or IV in the Yukawa sector, and ii) approximate Peccei-Quinn (PQ) symmetry in the scalar sector. We discuss the phenomenological consequences of these features.

In the standard model (SM), the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the only origin of flavor violations (FVs). On the other hand, in general, there are a lot of sources of the FVs in a physics beyond the SM, through the diagonalizing matrices which make Yukawa matrices diagonal. Although most of the diagonalizing matrices are unknown ones, grand unified theories (GUTs) can fix these matrices. In particular, if we consider a GUT model based on the $SO(10)$ group, these diagonalizing matrices are strongly related to each other because of the matter unification. However, this unification causes the problem on the realization of measured SM fermion masses and mixing angles. Up to now, many people showed that supersymmetric (SUSY) threshold corrections can solve this problem, especially unfavorable fermion mass relations. In this paper, we show that how these SUSY threshold corrections affect unknown diagonalizing matrices. Since these contributions are also related to the FVs induced by SUSY particles, we can estimate the maximal effect to the diagonalizing matrices. We found that the $(1, 3)$ and $(3, 1)$ elements of diagonalizing matrices for quarks can be as large as the corresponding mixing angle of the CKM matrix. Moreover, we found that the higher SUSY scale can predict the larger mixing angles, although strong cancellation between the Higgs mass parameters is needed to realize the electroweak symmetry breaking., 22 pages, 5 figures