We introduce a set of clockwork models of flavor that can naturally explain the large hierarchies of the Standard Model quark masses and mixing angles. Since the clockwork only contains chains of new vector-like fermions without any other dynamical fields, the flavor constraints allow for relatively light new physics scale. For two benchmarks with gear masses just above 1 TeV, allowed by flavor constraints, we discuss the collider searches and the possible ways of reconstructing gear spectra at the LHC. We also examine the similarities and differences with the other common solutions to the SM flavor puzzle, i.e., with the Froggatt-Nielsen models, where we identify a new {\it clockworked } version, and with the Randall-Sundrum models.
Clockwork models can explain the flavor hierarchies in the Standard Model quark and lepton spectrum. We construct supersymmetric versions of such flavor clockwork models. The zero modes of the clockwork are identified with the fermions and sfermions of the Minimal Supersymmetric Standard Model. In addition to generating a hierarchical fermion spectrum, the clockwork also predicts a specific flavor structure for the soft SUSY breaking sfermion masses. We find sizeable flavor mixing among first and second generation squarks. Constraints from Kaon oscillations require the masses of either squarks…
Maybe the biggest puzzle in grand unified theories (GUTs) is the apparent large splitting of the doublet and triplet Higgs masses. We suggest a novel mechanism to solve this puzzle, which relies on the clockwork mechanism to generate large hierarchies from order-one numbers. The tension between gauge coupling unification and proton lifetime from minimal SU(5) GUTs is also removed in this scenario, and the theory remains perturbative until the Planck scale.
We study the capability of generating correct flavor neutrino mass matrix in a scalar clockwork model. First, we assume that the flavor structure is controlled by the Yukawa couplings as same as the standard model. In this case, the correct flavor neutrino mass matrix could be obtained by appropriate Yukawa couplings $Y_{\ell^\prime\ell}$ where $\ell^\prime, \ell = e, μ, τ$. Next, we assume that the Yukawa couplings are extremely democratic $|Y_{\ell^\prime\ell} |=1$. In this case, the model parameters of the scalar clockwork sector, such as the site number of a clockwork gear in a clockwork c…
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.
We investigate the generation of small neutrino masses in a clockwork framework which includes Dirac mass terms as well as Majorana mass terms for the new fermions. We derive analytic formulas for the masses of the new particles and for their Yukawa couplings to the lepton doublets, in the scenario where the clockwork parameters are universal. When the Majorana masses all vanish, the zero mode of the clockwork sector forms a Dirac pair with the active neutrino, with a mass which is in agreement with oscillations experiments for a sufficiently large number of clockwork gears. On the other hand,…
The clockwork mechanism, which can naturally explain the origin of small numbers, is implemented in $SO(10)$ grand unified theories to address the origin of hierarchies in fermion masses and mixings. We show that a minimal Yukawa sector involving a $10_H$ and $\overline{126}_H$ of Higgs bosons, extended with two clockwork chains consisting of $16+\overline{16}$ vector-like fermions, can explain the hierarchical patterns with all the Yukawa couplings being of order one. Emergence of a realistic mass spectrum does not require any symmetry that distinguishes the three generations. We develop cloc…
We present realistic models of flavor in SU(5) and SO(10) grand unified theories (GUTs). The models are renormalizable and do not require any exotic representations in order to accommodate the necessary GUT breaking effects in the Yukawa couplings. They are based on a simple clockwork Lagrangian whose structure is enforced with just two (one) vectorlike U(1) symmetries in the case of SU(5) and SO(10) respectively. The inter-generational hierarchies arise spontaneously from products of matrices with order one random entries.
Clockwork (CW) mechanism can explain the smallness of neutrino masses without introducing unnaturally small input parameters. In this paper we study the simplest CW neutrino model, the "uniform" clockwork, as well as a broader class of "generalized" clockwork models. We derive constraints on such models from lepton-flavor violating processes, as well as precision electroweak fits. These constraints allow excited CW neutrino states with masses of order 100 GeV -- 1 TeV, within reach of the LHC and proposed lepton colliders, as long as the input neutrino Yukawa coupling is of order $10^{-1}-10^{…
The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This review article is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.
We present an economical model where an $S^{}_1$ leptoquark and an anomaly-free $U(1)^{}_X$ gauge symmetry with $X = B^{}_3-2L^{}_μ/3-L^{}_τ/3$ are introduced, to account for the muon anomalous magnetic moment $a^{}_μ\equiv (g^{}_μ-2)$ and flavor puzzles including $R^{}_{K^{(\ast)_{}}}$ and $R^{}_{D^{(\ast)_{}}}$ anomalies together with quark and lepton flavor mixing. The $Z^\prime_{}$ gauge boson associated with the $U(1)^{}_X$ symmetry is responsible for the $R^{}_{K^{(\ast)_{}}}$ anomaly. Meanwhile, the specific flavor mixing patterns of quarks and leptons can be generated after the spontan…
Supersymmetry, local horizontal unification, and a solution to the flavor puzzle
具有局域水平对称性的超对称规范模型会产生由超对称破缺D项引起的大的变味中性流效应。我们展示了U（1）规范对称性的存在如何解决这个问题。然后我们构造了一个以SU（2）_H × U（1）_H为局域水平对称的现实规范模型，并提出U（1）_H因子可以等同于弦紧化引起的反常U（1）。这个模型解释了夸克质量和混合角之间的层次结构，自然地容纳太阳和大气中微子数据，并同时提供了一个解决超对称味问题。如果在当前一轮实验中没有观察到稀有衰变μ--> e γ，则可以排除该模型。
Flavor-specific scalar bosons exist in various Standard Model extensions and couple to a single generation of fermions via a global flavor symmetry breaking mechanism. Given this strategy, we propose a MeV flavor-specific scalar model in dimension-$5$ operator series, which explains the muon g-2 anomaly and proton radius puzzle by coupling with the muon and down-quark at the same time. The framework is consistent with the null result of high-intensity searches. Specifically, the supernova constraints for muon couplings become weakened by including the contribution of down-quark interaction. Th…
We explain the many reasons for the interest in flavor physics. We describe flavor physics and the related CP violation within the Standard Model, and explain how the B-factories proved that the Kobayashi-Maskawa mechanism dominates the CP violation that is observed in meson decays. We explain the implications of flavor physics for new physics, with emphasis on the "new physics flavor puzzle", and present the idea of minimal flavor violation as a possible solution. We explain why the values flavor parameters of the Standard Model are puzzling, present the Froggatt-Nielsen mechanism as a possib…
We propose a minimal extension of the standard model which includes only one additional complex scalar field, flavon, with flavor-dependent global U(1) symmetry. It not only explains the hierarchical flavor structure in the quark and lepton sector (including neutrino sector), but also solves the strong CP problem by identifying the CP-odd component of the flavon as the QCD axion, which we call flaxion. Furthermore, the flaxion model solves the cosmological puzzles in the standard model, i.e., origin of dark matter, baryon asymmetry of the universe, and inflation. We show that the radial compon…
We propose a low-scale renormalizable trinification theory that successfully explains the flavor hierarchies and neutrino puzzle in the Standard Model (SM), as well as provides a dark matter candidate and also contains the necessary means for efficient leptogenesis. The proposed theory is based on the trinification $\SU{3}{C}\times \SU{3}{L}\times \SU{3}{R}$ gauge symmetry, which is supplemented with an additional flavor symmetry $\U{X}\times Z_{2}^{(1)} \times Z_{2}^{(2)}$. In the proposed model the top quark and the exotic fermions acquire tree-level masses, whereas the lighter SM charged fe…
It has been known that when a charged fermion scatters off a monopole, the fermion in the $s$-wave component must flip its chirality, i.e., fermion number violation must happen. This fact has led to a puzzle; if there are two or more flavors of massless fermions, any superposition of the fermion states cannot be the final state of the $s$-wave scattering as it is forbidden by conservation of the electric and flavor charges. The unitary evolution of the state vector, on the other hand, requires some interpretation of the final states. We solve the puzzle by finding new particle excitations in t…
We propose that three recent anomalies in $B$ meson decays, $R_{D^{(*)}}$, $R_K$, and $P_5'$, might be explained by a single vector leptoquark weak triplet state. The constraints on the parameter space are obtained by considering $t \to b τ^+ ν$ data, lepton flavor universality tests in the kaon sector, bounds on $B \to K^{(*)} \bar νν$, bound on the lepton flavor violating decay $B \to K μτ$, and measurements of $b \to c μ^- \barν$ decays. The presence of such vector leptoquark could be exposed in precise measurements of $t \to b τν$ and $B \to K^{(*)} \bar νν$ decays. The model also predicts…
Heavy-flavored hadrons are unique probes to study the properties of hot and dense QCD medium produced in ultra-relativistic heavy-ion collisions at RHIC and the LHC. Transverse spherocity is one of the event-topology variables used to separate jetty and isotropic events from the pool of event samples. This study aims to understand the production dynamics of heavy-flavors through the transverse momentum spectra, double differential yield and mean transverse momentum of J/$ψ$, $\rm D^{0}$ and $Λ_{c}^{+}$ as a function of charged-particle multiplicity and transverse spherocity. Further to investi…
We revisit the puzzle of $|V_{us}|$ values obtained from the conventional implementation of hadronic-$τ$-decay-based flavor-breaking finite-energy sum rules lying $>3 σ$ below the expectations of three-family unitarity. Significant unphysical dependences of $|V_{us}|$ on the choice of weight, w, and upper limit, $s_0$, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, $D>4$, OPE contributions is identified as the main source of these problems. A combination of continuum and lattice results is shown to…
A combination of continuum and lattice methods is used to investigate systematic issues in the finite-energy-sum-rule determination of $V_{us}$ based on flavor-breaking combinations of hadronic $τ$ decay data. Results for $V_{us}$ obtained using assumptions for $D>4$ OPE contributions employed in previous conventional implementations of this approach are shown to display significant unphysical dependences on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest the necessity of a new implementation of …
One of the exciting results in flavor physics in recent times is the $R_D$/$R_{D^*}$ puzzle. The measurements of these flavor ratios performed by the B-factory experiments, BaBar and Belle, and the LHCb experiment are about $4σ$ away from the Standard Model expectation. These measurements indicate that the mechanism of $b\rightarrow cτ\barν$ decay is not identical to that of $b\rightarrow c(μ/e)\barν$. This charge lepton universality violation is particularly intriguing because these decays occur at tree level in the Standard Model. In particular, we expect a moderately large new physics contr…
The strong CP problem is one of many puzzles in the theoretical description of elementary particle physics that still lacks an explanation. While top-down solutions to that problem usually comprise new symmetries or fields or both, we want to present a rather bottom-up perspective. The main problem seems to be how to achieve small CP violation in the strong interactions despite large CP violation in weak interactions. Observation of CP violation is exclusively through the Higgs--Yukawa interactions. In this paper, we show that with minimal assumptions on the structure of mass (Yukawa) matrices…
The standard model does not provide an explanation of the observed alignment of quark flavors i.e. why are the up and down quarks approximately aligned in their weak interactions according to their masses? We suggest a resolution of this puzzle using a combination of left-right and Peccei-Quinn (PQ) symmetry. The quark mixings in this model vanish at the tree level and arise out of one loop radiative corrections which explains their smallness. The lepton mixings on the other hand appear at the tree level and are therefore larger. We show that all fermion masses and mixings can be fitted with a…
Puzzles in charmed baryon semileptonic decays with $SU(3)_F$ flavor symmetry and lattice inputs
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院）；Institute of Theoretical Physics, UCAS（理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of $V_{us}$ using inclusive hadronic $τ$ decay data. Results for $V_{us}$ employing assumptions for $D>4$ OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, $w$, and choice of upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just $\vert V_{us}\vert$, but also $D>4$ effective condensates,…
For all the success of the Standard Model (SM), it is on the verge of being surpassed. In this regard we argue, by showing a minimal flavor-structured model based on the non-Abelian discrete $SL_2(F_3)$ symmetry, that $U(1)$ mixed-gravitational anomaly cancellation could be of central importance in constraining the fermion contents of a new chiral gauge theory. Such anomaly-free condition together with the SM flavor structure demands a condition $k_1\,X_1/2=k_2\,X_2$ with $X_i$ being a charge of $U(1)_{X_i}$ and $k_i$ being an integer, both of which are flavor dependent. We show that axionic d…
We study the ratio of $R=2 Γ(Ξ_c^0 \to Ξ^- e^+ ν_e )/3Γ(Λ_c^+ \to Λe^+ ν_e )$, which is found to be $R= 1 (0.8)$ from the exact (broken) $SU(3)$ flavor symmetry, in sharp contrast to the average value of $R_{av}=0.59\pm 0.10 $ from the ALICE collaboration and lattice QCD results. We propose to use the mixing of $Ξ_c-Ξ_c'$ to resolve the puzzle. With the model-independent mass relations, we find that the mixing angle is $|θ_c| = 0.137(5)π$, which suppresses $Ξ_c\to Ξe^+ ν_e$ about $20\%$ model-independently, resulting in $R\approx 0.6$ with the $SU(3)$ flavor breaking effect. We explicitly demo…
