We complete the analysis of the effective field theory at the electroweak scale for minimal models of fundamental partial compositeness. Specifically, we consider fermions in the complex and real representation of the gauge group underlying the composite Higgs dynamics, since the pseudo real representation was investigated earlier. The minimal models feature the cosets SU(4)xSU(4)/SU(4)_D and SU(5)/SO(5) respectively for the complex and real representations. We determine the vacuum alignment, the electroweak precision constraints, additional collider constraints. We finally discuss the main differences among the different models of minimal partial compositeness.
Several measurements of B-meson decay observables show deviations from Standard Model (SM) predictions, some of them hinting at violation of lepton flavour universality (LFU). I discusses how the anomalies in rare B decays can be explained by partial compositeness. Partial compositeness is a key ingredient of models with a composite Higgs boson and generically leads to violation of LFU. After presenting a simple model with partial compositeness that is able to explain the anomalies in rare B decays, the flavour phenomenology of a minimal UV completion of a composite Higgs model with partial co…
We revisit the impact of top partial compositeness on electroweak precision observables in the misaligned vacuum basis. We identify a new source for $S$ in the singlet mixing case, and for $S$-$T$ in the bi-doublet mixing, stemming from misalignment in the gauge couplings of the top partners. Hence, a positive shift in $T$ can be obtained in both cases, as preferred by the recent CDF measurement of the $W$ mass. These results, obtained for the minimal fundamental coset SU(4)/Sp(4), apply to any composite Higgs model with top partial compositeness.
Providing an Ultra-Violet completion valid up to the Planck scale is of paramount importance to validate the composite Higgs paradigm, at par with supersymmetry. We propose the first complete and feasible framework, based on partial unification of a confining hypercolor gauge group, where couplings of the standard model fermions are mediated by both gauge and scalar bosons. We demonstrate our approach by providing an explicit model based on a Techni-Pati-Salam unification, $SU(8)_{\rm PS}\times SU(2)_L\times SU(2)_R$, able to generate masses for all fermion generations, including neutrinos, vi…
Building upon the fundamental partial compositeness framework we provide consistent and complete composite extensions of the standard model. These are used to determine the effective operators emerging at the electroweak scale in terms of the standard model fields upon consistently integrating out the heavy composite dynamics. We exhibit the first effective field theories matching these complete composite theories of flavour and analyse their physical consequences for the third generation quarks. Relations with other approaches, ranging from effective analyses for partial compositeness to extr…
Partial compositeness is a key ingredient of models where the electroweak symmetry is broken by a composite Higgs state. Recently, a UV completion of partial compositeness was proposed, featuring a new strongly coupled gauge interaction as well as new fundamental fermions and scalars. We work out the full flavor structure of the minimal realization of this idea and investigate in detail the consequences for flavor physics. While CP violation in kaon mixing represents a significant constraint on the model, we find many viable parameter points passing all precision tests. We also demonstrate tha…
In theories of Partial Compositeness the top quark is a mixture of a composite and an elementary state, and as a consequence its interactions with gauge bosons are expected to deviate from those of a point-like object. At sufficiently large energies, such deviations cannot be parametrized by the leading effective field theory operators and form factors (i.e. energy dependent interactions) must be introduced. In this work, we argue that such effects might appear at relatively low energies with interesting phenomenological consequences. In analogy to the proton electromagnetic interactions, we d…
UV Completions of Partial Compositeness: The Case for a SU(4) Gauge Group
我们提出了一个部分复合性模型，该模型是由只有费米子物质的SU（4）规范理论的IR极限引起的。这个群体是少数几个可能的选择中最有前途的一个，允许一个对称破缺模式，结合保管对称和一个顶级伙伴候选人，同时保持渐近自由。这是有利的，因为它不会在SM规范耦合中产生瘦夸克或朗道极。最小UV理论由反对称表象中的五个超费米子和基本和反基本表象中的三个超费米子组成。IR理论以陪集SU（5）/SO（5）为中心，在SO（5）的基础中有顶级伙伴，产生一个电荷为5/3的复合费米子，三个电荷为2/3的复合费米子和一个电荷为-1/3的复合费米子。电弱对称性破缺通过顶夸克驱动的真空失准发生。顶夸克的质量是通过部分复合机制产生的，而其余的费米子则通过与希格斯玻色子的标准二次耦合获得质量。我们计算了复合费米子的顶夸克和底夸克质量矩阵和电弱流。该模型不会引起SM Z \to b \bar b衰减宽度的不可接受的大偏差。
We continue our investigation of gauge theories in which the Higgs boson arises as a pseudo-Nambu-Goldstone boson (pNGB) and top-partners arise as bound states of three hyperfermions. All models have additional pNGBs in their spectrum that should be accessible at LHC. We analyze the patterns of symmetry breaking and present all relevant couplings of the pNGBs with the gauge fields. We discuss how vacuum misalignment and a mass for the pNGBs is generated by a loop-induced potential. Finally, we paint a very broad, qualitative, picture of the kind of experimental signatures these models give ris…
Composite Higgs Models are often constructed including fermionic top partners with a mass around the TeV scale, with the top partners playing the role of stabilizing the Higgs potential and enforcing partial compositeness for the top quark. A class of models of this kind can be formulated in terms of fermionic strongly coupled gauge theories. A common feature they all share is the presence of specific additional scalar resonances, namely two neutral singlets and a colored octet, described by a simple effective Lagrangian. We study the phenomenology of these scalars, both in a model independent…
The top quark can be naturally singled out from other fermions in the Standard Model due to its large mass, of the order of the electroweak scale. We follow this reasoning in models of pseudo Nambu Goldstone Boson composite Higgs, which may derive from an underlying confining dynamics. We consider a new class of flavour models, where the top quark obtains its mass via partial compositeness, while the lighter fermions acquire their masses by a deformation of the dynamics generated at a high flavour scale. One interesting feature of such scenario is that it can avoid all the flavour constraints …
We consider a class of models in which the neutrinos acquire Majorana masses through mixing with singlet neutrinos that emerge as composite states of a strongly coupled hidden sector. In this framework, the light neutrinos are partially composite particles that obtain their masses through the inverse seesaw mechanism. We focus on the scenario in which the strong dynamics is approximately conformal in the ultraviolet, and the compositeness scale lies at or below the weak scale. The small parameters in the Lagrangian necessary to realize the observed neutrino masses can naturally arise as a cons…
Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an SU(4) gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the…
We consider the scenario of composite Higgs with partial compositeness to address the muon g-2 anomaly. We show that this anomaly is resolved by one-loop correction due to composite muon partners with mass scale of order TeVs and large Yukawa coupling to composite Higgs, which is different from interpretations of vectorlike lepton models. We present parameter space by imposing indirect constraints from precise measurements on Higgs, Z and oblique electroweak parameters. We analyze direct constraints in light of both Drell-Yan and Higgs-associated productions of the composite muon partners at h…
Anatomy of flavour-changing Z couplings in models with partial compositeness
在部分复合夸克的模型中，夸克与Z玻色子的耦合一般会受到非普适修正，这不仅受到电弱精密检验的约束，而且会导致树水平上的味道变化中性电流。我们在三种情况下的双场点模型中研究了这些变味耦合对稀有K和B衰变的影响：一种是具有两种不同费米子表示选择的无政府强扇区，这两种情况都导致了Z->bb耦合的监护保护，另一种是在U（2）^3变味对称下的强扇区不变量。在完整的数值分析中，考虑了Delta（F）=2过程的所有相关约束。在所有情况下，在罕见的K和B衰变中，如K->pi nu anti-nu，B（s）->mu+mu-和B->K*mu+mu-的可见效应是可能的，可以在不久的将来通过实验进行详细检查。可观测量之间的特征相关性允许区分不同的情况。为了对无政府模型的大参数空间进行采样，提出了一种新的方法，该方法允许比传统方法更大的统计量。
Partial top quark compositeness is a crucial aspect of theories with strong electroweak symmetry breaking. Together with the heavy top partners that lift the top quark mass to its observed value, these theories predict correlated modifications of the top quark's electroweak couplings. Associated measurements therefore provide direct constraints on the ultraviolet structure of the underlying hypercolour dynamics. In this paper we employ a minimal version of top compositeness to discuss how measurements related to the top's electroweak gauge interactions can inform the potential composite nature…
We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these "chimera baryons" has a straightforward interpretation in terms of a non-relativistic quark model based on SU(4). Our results are particularly relevant to composite Higgs models in which the top quark is partially composite.
Composite Higgs models, together with partial compositeness, predict the existence of new scalars and vector-like quarks (partners) at and above the TeV scale. Generically, the presence of these additional scalars opens up new decay topologies for the partners. In this paper we show how to systematically construct the general low energy Lagrangian to capture this feature. We emphasize the specific pattern in the top-partner spectrum arising in this class of models. We then present a concrete realization in the context of the SU(5)/SO(5) coset. We show that the top-partners in this model can ha…
We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Under certain assumptions on the dynamics of the scalars, successful models exist because gauge quantum numbers of Standard Model fermions admit a minimal enough 'square root'. Furthermore, right-handed SM fermions have an SU(2)$_R$-like structure, yielding a custodially-protected composite Higgs. Baryon a…
In this talk, I will present the status of lepton flavor physics in composite Higgs models with partial compositeness in the light of recent data in the lepton sector. I will consider anarchic flavor setups, scenarios with flavor symmetries, and minimal incarnations of the see-saw mechanism that naturally predict non-negligible lepton compositeness. The focus will be on lepton flavor violating processes, dipole moments, and on probes of lepton flavor universality, all providing stringent tests of partial compositeness. The expected size of effects in the different approaches to lepton flavor a…
Composite Higgs models with anarchic partial compositeness require a scale of new physics ${\cal O}(10-100)$ TeV, with the bounds being dominated by the dipole moments and $ε_K$. The presence of anarchic bilinear interactions can change this picture. We show a solution to the SM flavor puzzle where the electron and the Right-handed quarks of the first generation have negligible linear interactions, and the bilinear interactions account for most of their masses, whereas the other chiral fermions follow a similar pattern to anarchic partial compositeness. We compute the bounds from flavor and CP…
Multi-boson splashes at future colliders from electroweak compositeness
Sorbonne Université & CNRS（索邦大学与法国国家科学研究中心）；Southern Denmark Univ.（南丹麦大学）；Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I（里昂第一大学、法国国家科学研究中心/法国国家粒子物理研究所、IP2I）；University of Johannesburg（约翰内斯堡大学）；Indian Institute of Technology Delhi（德里印度理工学院）；University of Graz（格拉茨大学）
We discuss in detail the constraints on partial compositeness coming from flavour and CP violation in the leptonic sector. In a first part we present a formulation of partial compositeness in terms of a flavour symmetry group and a set of spurions, whose background values specify the symmetry breaking pattern. In such a framework we construct the complete set of dimension-six operators describing lepton flavour violation and CP violation. By exploiting the existing bounds, we derive limits on the compositeness scale in different scenarios, characterised by increasing restrictions on the spurio…
We review numerical results for models with gauge group Sp(2N), discussing the glueball spectrum in the large-N limit, the quenched meson spectrum of Sp(4) with Dirac fermions in the fundamental and in the antisymmetric representation and the Sp(4) gauge model with two dynamical Dirac flavours. We also present preliminary results for the meson spectrum in the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac flavours. The main motivation of our programme is to test whether this latter model is viable as a realisation of Higgs compositeness via the pseudo Nambu Goldstone mec…
Composite Higgs models can be extended to the Planck scale by means of the partially unified partial compositeness (PUPC) framework. We present in detail the Techni-Pati-Salam model, based on a renormalizable gauge theory $SU(8)_{PS}\times SU(2)_L\times SU(2)_R$. We demonstrate that masses and mixings for all generations of standard model fermions can be obtained via partial compositeness at low energy, with four-fermion operators mediated by either heavy gauge bosons or scalars. The strong dynamics is predicted to be that of a confining $Sp(4)_{\rm HC}$ gauge group, with hyper-fermions in the…
We consider the renormalizable $SO(5)/SO(4)$ $σ$-model, in which the Higgs particle has a pseudo-Nambu-Goldstone boson character, and explore what the minimal field extension required to implement the Peccei-Quinn symmetry (PQ) is, within the partial compositeness scenario. It turns out that the minimal model does not require the enlargement of the exotic fermionic sector, but only the addition of a singlet scalar: it is sufficient that the exotic fermions involved in partial compositeness and the singlet scalar become charged under Peccei-Quinn transformations. We explore the phenomenological…
Structure of the $a_{0}(980)$ and $f_{0}(980)$ resonances is investigated with the $a_{0}(980)$-$f_{0}(980)$ mixing intensity from the viewpoint of compositeness, which corresponds to the amount of two-body states composing resonances as well as bound states. For this purpose we first formulate the $a_{0}(980)$-$f_{0}(980)$ mixing intensity as the ratio of two partial decay widths of a parent particle, in the same manner as the recent analysis in BES experiments. Calculating the $a_{0}(980)$-$f_{0}(980)$ mixing intensity with the existing Flatte parameters from experiments, we find that many c…
We study the weight or compositeness of the $ππ$-$K\bar{K}$ and $πη$-$K\bar{K}$ in the composition of the $f_0(980)$ and $a_0(980)$ resonances, respectively. Either we use the saturation of the total width and compositeness, or we use a Flatté parameterization taking also into account the spectral function of a near-threshold resonance. We make connections and compare between these two methods. We take input values for the pole mass and width from several determinations in the literature. In addition, we take as third input either the total compositeness or the decay-width branching ratio to t…
We present a non-perturbative lattice study of SU(4) gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation: a theory closely related to a minimal partial-compositeness model for physics beyond the Standard Model, that was proposed by G. Ferretti. We discuss the phase structure of the lattice theory and report results for various observables of interest, including the masses of states obtained from different combinations of valence fermions and the spectrum of the Dirac operator. Finally, we comment on the extension of …
We show that QCD instantons can generate large effects at small length scales in the ultraviolet in standard composite Higgs models that utilise partial compositeness. This has important implications for possible solutions of the strong CP problem in these models. First we show that in the simplest known UV completions of composite Higgs models, if an axion is also present, it can have a mass much larger than the usual QCD axion. Even more remarkable is the case where there are no axions, but the strong CP problem can be solved by generating the up quark mass entirely from the contribution of …
A natural composite Higgs demands the presence of light resonances at the TeV scale, that in general are in conflict with bounds from flavor and CP violation. We propose a composite model with a Froggatt-Nielsen mechanism, that offers new possibilities for the origin of flavor. We analyse the interplay of partial compositeness and the horizontal U(1) symmetry in achieving the quark masses and mixing angles. We study the contributions to $ΔF=2$ 4-fermion operators, as well as to $ΔF=1$ and neutron dipole operators. We find scenarios in which the contribution to Left-Right and Right-handed opera…
In recent times, one of the strongest hints of Physics Beyond the Standard Model (BSM) has been the anomaly in the ratios $R_D$ and $R_{D^\ast}$ measured in the charged current decays of $B$-mesons. In this work, we perform a comprehensive analysis of these decay modes, first in a model independent way and subsequently, in the context of composite Higgs models. We discuss in depth as to how linearly realised $\rm SU(2)_L \times U(1)_Y$ symmetry imposes severe constraint on the various scenarios because of correlations with other $ΔF =1$ processes and $Z\,τ\,τ$ and $Z\,ν\,ν$ couplings. In the c…
We present a novel paradigm that allows to define a composite theory at the electroweak scale that is well defined all the way up to any energy by means of safety in the UV. The theory flows from a complete UV fixed point to an IR fixed point for the strong dynamics (which gives the desired walking) before generating a mass gap at the TeV scale. We discuss two models featuring a composite Higgs, Dark Matter and partial compositeness for all SM fermions. The UV theories can also be embedded in a Pati-Salam partial unification, thus removing the instability generated by the $\mbox{U}(1)$ running…
We look for possible (partial) compositeness properties of the bottom quark according to the Composite Standard Model (CSM) concept in the same way this was previously done for Higgs boson and top quark. After looking at the direct form factor effects appearing in $e^+e^-\to b\bar b$ we analyze the more complex features of the $e^+e^-, gg, γγ\to b\bar b H, b\bar b Z, t\bar b W^-$ processes. We emphasize typical differences appearing between CSM concerving and CSM violating cases. We also mention the possible appearence of an effective bottom mass.
The Silence of the Dipoles: Accidental Symmetries in Lepton Flavor
Scuola Normale Superiore（高等师范学校）；INFN（意大利国家核物理研究所）；PSI Center for Neutron and Muon Sciences（PSI中子与缪子科学中心）；DAMTP, University of Cambridge（剑桥大学数学物理系）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术学院）
Gauge theories describe the interactions of the fundamental building blocks of nature with great success. The Standard Model achieves a partial unification of the electromagnetic and weak interactions, and it also acomodates the strong interactions. The known quarks and leptons appear in the fundamental representations (or singlets) of the SU(3)_cxSU(2)_L x U(1)_Y gauge symmetry. However, larger representations (EW triplets, color sextes, etc.) could also occur in principle. Bounds on such exotic states based on electroweak precision tests, unitarity, perturbativity and collider searches, indi…
We consider the $Sp(4)$ gauge theory coupled to $N_f=2$ fundamental and $n_f=3$ antisymmetric flavours of Dirac fermions in four dimensions. This theory serves as the microscopic origin for composite Higgs models with $SU(4)/Sp(4)$ coset, supplemented by partial top compositeness. We study numerically its lattice realisation, and couple the fundamental plaquette action to Wilson-Dirac fermions in mixed representations, by adopting a (rational) hybrid Monte Carlo method, to perform non-trivial tests of the properties of the resulting lattice theory. We find evidence of a surface (with boundarie…
