DOCSLIB.ORG

Composite Higgs Models

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Composite Higgs Models University of S~aoPaulo Physics Institute Composite Higgs models Juan Pablo Hoyos Daza Dissertation submitted to the Physics Institute of the University of S~aoPaulo in partial fulfillment of the requirements for the degree of Master of Science. arXiv:1908.10204v1 [hep-ph] 25 Aug 2019 S~aoPaulo 2018 Acknowledgments I would like to thank the working people of Brazil, to share me his progress and wealth. I would also like to extend my gratitude to: • My family for all the collaboration provided; • The USP and IFUSP for hospitality, the amazing research environment and re- sources necessary for my academic education; • My research advisor, Dr. Enrico Bertuzzo for his great disposition and patience; • The brothers Gina Ordo~nezand Gustavo Ordo~nezfor their valuable collaboration; • The CNPq for a Master Scholarship. ii Abstract One of the solutions to the hierarchy problem of the Standard Model is the composite Higgs scenario, where the Higgs emerges as a composite pseudo-Nambu-Goldstone boson. In this work we present and study the basic characteristics of the composite Higgs sce- nario, based on the SO (5) =SO (4) and SO (6) =SO (5) cosets. We construct their effective Lagrangians through the Callan-Coleman-Wess-Zumino construction. The first coset does not differ much from the Standard Model and the second contains a singlet scalar in addi- tion to the Higgs doublet. In these models we study the gauge sector, the fermion sector and we estimate the composite Higgs potential. Keywords: Composite Higgs; Higgs boson; Callan-Coleman-Wess-Zumino construction; Standard Model. iii Notation In this work we will use the natural units ~ = c = 1 where ~ = h=2π with h the Planck constant and c the velocity of light. Greek indices µ and ν run over the four spacetime coordinate, usually taken as 0, 1, 2, 3. The Einstein's summation convention is used, i.e. indices that are repeated are summed over. L Lagrangian density, frequently called Lagrangian. "αβγ Levi -Civita symbol. The transpose of a matrix A is AT . The complex conjugate of a matrix A is A∗. The Hermitian adjoint of a matrix A is Ay = A∗T . a b abc (AAd)c = if is the adjoint representation. 1 is the identity matrix, or sometimes called a unit matrix. Dirac conjugation is expressed by = yγ0. +h:c is the addition of the Hermitian adjoint or complex conjugate. The Pauli matrix are given by 0 1 0 −i 1 0 σ = ; σ = ; σ = : 1 1 0 2 i 0 3 0 −1 iv Contents Notation iv 1 Introduction1 1.1 Hierarchy problem . .1 2 Composite Higgs models5 2.1 Vacuum misalignment . .6 2.2 The CCWZ construction . .8 3 The minimal composite Higgs model SO(5)/SO(4) 13 3.1 Group generators and dµ symbol . 13 3.2 Gauge Lagrangian . 15 3.3 Fermions in the model . 18 4 The Non-Minimal Composite Higgs Model SO(6)/SO(5) 25 4.1 From NBG's to Higgs doublet . 25 4.2 Kinetic and Gauge Lagrangians . 28 4.3 Embedding Fermions . 31 5 Estimation of the composite Higgs potential 37 5.1 Case MCHM5 .................................. 37 5.2 Case NMCHM6 ................................. 41 6 Conclusions 46 A The Standard Model 47 A.1 Electroweak Symmetry Breaking in the Standard Model . 50 A.2 Custodial symmetry . 52 v CONTENTS vi B The Goldstone matrix 54 B.1 Explicit computation of the Goldstone matrix . 54 B.2 Inverse and derived of the Goldstone matrix . 57 C Useful Taylor series. 58 Bibliography 61 Chapter 1 Introduction Experimental tests such as the discovery of the weak neutral interaction, the production of the W and Z bosons, the recent discovery of a Higgs-like boson [1,2], among another data sets [3], confirm the extraordinary success of the Standard Model (SM) to explain the interactions of the fundamental particles. However some drawbacks observed experimentally (neutrino masses, baryon asymmetry in the universe, dark matter), and other of theoretical type (strong Charge-Parity viola- tion, electric charge quantization and the hierarchy or \naturalness" problem) require an extension of the theory. We will focus on the Hierarchy problem 1, since in this thesis we will study a scenario which addresses this problem. 1.1 Hierarchy problem The problem stems out when we assume that the SM is an Effective Field Theory (EFT), where the Lagrangian of the SM is generated at a smaller scale than that of the funda- mental theory. If there is just the SM, then there is no naturalness problem, but as there is no description of gravity in the SM and we expect gravity to kick in at a certain energy 19 (around the Planck scale MP ≈ 10 GeV), we can consider the SM as an EFT. Almost everything we see in Nature is described by d = 4 operators of the SM Lagrangian (see AppendixA). In the SM however there is one operator of dimension d = 2, the Higgs mass term. The coefficients in front of operators of dimension d are proportional to d−4 2 1=ΛSM (Λ is the cut-off scale [4]). This means that the Higgs mass is enhanced by ΛSM , 1The first references to the problem are in [5] and [6,7]. 1 CHAPTER 1. INTRODUCTION 2 so we can write the Higgs mass term as 2 y kΛSM H H; (1.1) where k is a numerical coefficient. Currently we know that the coefficient in front of HyH 2 2 2 2 in the SM is µ = mH =2 = (89 GeV) , but if we take the SM cutoff as reference at 16 ΛSM ∼ MGUT ∼ 10 GeV then −28 k ∼ 10 n 1: (1.2) This enormous hierarchy is basically the Naturalness problem. This problem is sometimes presented also as a problem of quadratic divergences, due to the fact that if we use the cut- off regularization, the radiative corrections to the Higgs mass are quadratically divergent, a feature not present when applying the dimensional regularization method. This does not mean that the problem disappears (physics does not depend on the regularization method), rather that it is a problem of quadratic divergences in the sense that if we calculate the Renormalization Group Equation (RGE) for the running scalar mass3 we obtain dm2 3λ2 µ = − M 2 + ::: (1.3) dµ π2 It is apparent that a quadratic sensitivity to a heavy mass scale exists even in dimensional regularization. For comparison, for a running fermion mass we have dm µ f / m ; (1.4) dµ f that is to say, there is no dependence on the details of the high energy theory at low energy. On the other hand, effects analogous to Eq. (1.3) are obtained from the interactions with vectors and scalar particles, so that the running scalar mass receives contributions from the mass of all kinds of particle it couples to. In the Standard Model the problem is present because we have an elementary scalar in the theory (the Higgs boson). With λ and M constants we can write down a solution to (1.3), given by 2 2 2 3λ 2 Λ m (Λ) − m (ΛEW ) = − 2 M log : (1.5) π ΛEW 2This cutoff of reference is not necessarily the cutoff of the new physics. 3 1 µ m2 2 = We obtain this result from Lagrangian L = 2 @µφ∂ φ − 2 φ + λφ + i@ − M , with M m, but it is totally valid in the SM if this is considered as EFT. CHAPTER 1. INTRODUCTION 3 Let us see the consequences arising from the term M 2. In order to do that we must change a little bit the details pertaining to the high energy limit: M ! M +δM. Then we obtain 2 2 2 2 3λ 2 Λ 6λ Λ m (ΛEW ) !m (Λ) + 2 M log + 2 MδM log π ΛEW π ΛEW 2 (1.6) 2 6λ Λ = m (ΛEW ) old + 2 MδM log π ΛEW from which 2 2 2 2 6λ 2 Λ δM δm (ΛEW ) = m (ΛEW ) − m (ΛEW ) old = 2 M log : (1.7) π ΛEW M 2 In this way, we can define the sensitivity of the observable δm (mpole) with respect to the changes of the high energy, that is to say 2 δm (mpole) δM 2 = ∆ ; (1.8) mpole M where the sensitivity factor is 6λ2 M 2 Λ ∆ = 2 2 log : (1.9) π mpole mpole 2 2 We see that if ∆ 1 ) δm (mpole) =mpole 1, which means that to small changes in the high energy scale correspond large changes in the observables. This goes against the conception of the effective field theory, which should not depend on the details of the high energy theory. 2 6λ2 2 Λ The way to keep the large changes under control is by tuning m (Λ) against 2 M log π ΛEW (which are two unrelated quantities, in principle). This is the hierarchy problem in terms of fine tuning. In the case of SM, if we think of it as an effective field theory where we are integrating out some states with mass MP , the Higgs field interacts with these states and we will have a sensitivity factor given by 2 const MP MP 31 ∆ = 2 2 log ' 10 ; (1.10) 16π mh;P ole mh;P ole so we have a huge tuning. This is the so-called fine tuning problem of the Standard Model. CHAPTER 1. INTRODUCTION 4 The composite Higgs scenario [8,9] addresses the problem by considering the Higgs as a low energy bound state of some more fundamental degree of freedom, so the RGE is valid only up to the energy at which the more fundamental theory kicks in.
Load more

Recommended publications
  • Composite Higgs Sketch
    Composite Higgs Sketch Brando Bellazzinia; b, Csaba Cs´akic, Jay Hubiszd, Javi Serrac, John Terninge a Dipartimento di Fisica, Universit`adi Padova and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy b SISSA, Via Bonomea 265, I-34136 Trieste, Italy c Department of Physics, LEPP, Cornell University, Ithaca, NY 14853 d Department of Physics, Syracuse University, Syracuse, NY 13244 e Department of Physics, University of California, Davis, CA 95616 [email protected], [email protected], [email protected], [email protected], [email protected] Abstract The couplings of a composite Higgs to the standard model fields can deviate substantially from the standard model values. In this case perturbative unitarity might break down before the scale of compositeness, Λ, is reached, which would suggest that additional composites should lie well below Λ. In this paper we account for the presence of an additional spin 1 custodial triplet ρ±;0. We examine the implications of requiring perturbative unitarity up to the scale Λ and find that one has to be close to saturating certain unitarity sum rules involving the Higgs and ρ couplings. Given these restrictions on the parameter space we investigate the main phenomenological consequences of the ρ's. We find that they can substantially enhance the h ! γγ rate at the LHC even with a reduced Higgs coupling to gauge bosons. The main existing LHC bounds arise from di-boson searches, especially in the experimentally clean channel ρ± ! W ±Z ! 3l + ν. We find that a large range of interesting parameter arXiv:1205.4032v4 [hep-ph] 30 Aug 2013 space with 700 GeV .
    [Show full text]
  • Composite Higgs Models with “The Works”
    Composite Higgs models with \the works" James Barnard with Tony Gherghetta, Tirtha Sankar Ray, Andrew Spray and Callum Jones With the recent discovery of the Higgs boson, all elementary particles predicted by the Standard Model have now been observed. But particle physicists remain troubled by several problems. The hierarchy problem Why is the Higgs mass only 126 GeV? Quantum effects naively 16 suggest that mh & 10 GeV would be more natural. Flavour hierarchies Why is the top quark so much heavier than the electron? Dark matter What are the particles that make up most of the matter in the universe? Gauge coupling unification The three gauge couplings in the SM nearly unify, hinting towards a grand unified theory, but they don't quite meet. It feels like we might be missing something. With the recent discovery of the Higgs boson, all elementary particles predicted by the Standard Model have now been observed. However, there is a long history of things that looked like elementary particles turning out not to be Atoms Nuclei Hadrons Splitting the atom Can we really be sure we have reached the end of the line? Perhaps some of the particles in the SM are actually composite. Compositeness in the SM also provides the pieces we are missing The hierarchy problem If the Higgs is composite it is shielded from quantum effects above the compositeness scale. Flavour hierarchies Compositeness in the fermion sector naturally gives mt me . Dark matter Many theories predict other composite states that are stabilised by global symmetries, just like the proton in the SM.
    [Show full text]
  • Composite Higgs
    Lectures on Composite Higgs Adri´anCarmona Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland E-mail: [email protected] Contents 1 Non-Linear Realizations of a Symmetry1 2 Composite Higgs Models6 2.1 General Picture6 2.2 Minimal Composite Higgs Models7 2.2.1 Minimal Composite Higgs model (the real one)7 2.2.2 Minimal Composite Higgs model (the custodial one) 10 1 Non-Linear Realizations of a Symmetry In this lecture, I will mostly follow Jose Santiago's notes, Pokorski [1], the review by Feruglio [2] as well as the original papers by CWZ [3] and CCWZ [4]. Due to several interesting features that we will review in Section2, we will consider theories where the Higgs boson is identified with the pseudo Nambu-Goldstone bosons (pNGB) associated to the spontaneous breaking of some global symmetry G. One of the key ingredients in order to compute the corresponding low energy effective theory is the use of non-linear σ-models, that you have already encountered throughout this course. In the following we will review and introduce some useful concepts, most of which were first introduced in [3,4]. Let us consider a real analytic manifold M, together with a Lie Group G acting on M ' : G × M −! M (1.1) (g; Φ(x)) 7−! T (g) · Φ(x) which we will assume hereinafter to be compact, connected and semi-simple. We will also assume that ' is analytical on its two arguments. The physical situation that we have in mind is that of a manifold of scalar fields Φ(x), with the origin describing the vacuum configuration Σ0, whereas the Lie group G acting on these fields correspond to the symmetry group of the theory1.
    [Show full text]
  • Pseudoscalar Pair Production Via Off-Shell Higgs in Composite Higgs Models
    SciPost Phys. 9, 077 (2020) Pseudoscalar pair production via off-shell Higgs in composite Higgs models 1? 1† 2‡ 3,4,5,6,7 Diogo Buarque Franzosi , Gabriele Ferretti , Li Huang and Jing Shu ◦ 1 Department of Physics, Chalmers University of Technology, Fysikgården, 41296 Göteborg, Sweden 2 Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas, 66045 U.S.A 3 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China 4 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P.R. China 5 CAS Center for Excellence in Particle Physics, Beijing 100049, China 6 Center for High Energy Physics, Peking University, Beijing 100871, China 7 School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China ? [email protected],† [email protected],‡ [email protected], [email protected] ◦ Abstract We propose a new type of search for a pseudoscalar particle η pair produced via an off-shell Higgs, pp h . The search is motivated by a composite Higgs model ∗ ηη in which the η is extremely! ! narrow and decays almost exclusively into Zγ in the mass range 65 GeV ® mη ® 160 GeV. We devise an analysis strategy to observe the novel ZγZγ channel and estimate potential bounds on the Higgs-η coupling. The experimental sensitivity to the signatures depends on the power to identify fake photons and on the ability to predict large photon multiplicities. This search allows us to exclude large values of the compositeness scale f , being thus complementary to other typical processes.
    [Show full text]
  • Flavor and CP Invariant Composite Higgs Models
    CERN-PH-TH/154 DESY 11-109 Flavor and CP Invariant Composite Higgs Models Michele Redi1;2∗ and Andreas Weiler1;3y 1CERN, Theory Division, CH-1211, Geneva 23, Switzerland 2INFN, 50019 Sesto F., Firenze, Italy 3DESY, Notkestrasse 85, D-22607 Hamburg, Germany Abstract The flavor protection in composite Higgs models with partial compositeness is known to be insufficient. We explore the possibility to alleviate the tension with CP odd observables by assuming that flavor or CP are symmetries of the composite sector, broken by the coupling to Standard Model fields. One realization is that the composite sector has a flavor symmetry SU(3) or SU(3)U ⊗ SU(3)D which allows us to realize Minimal Flavor Violation. We show how to avoid the previously problematic tension between a flavor symmetric composite sector and electro-weak precision tests. Some of the light quarks are substantially or even fully composite with striking signals at the LHC. We discuss the constraints from recent dijet mass measurements and give an outlook on the discovery potential. We also present a different protection mechanism where we separate the arXiv:1106.6357v2 [hep-ph] 5 Jul 2011 generation of flavor hierarchies and the origin of CP violation. This can eliminate or safely reduce unwanted CP violating effects, realizing effectively \Minimal CP Violation" and is compatible with a dynamical generation of flavor at low scales. ∗[email protected] [email protected] 1 Introduction The striking phenomenological success of the Standard Model (SM) flavor sector is potentially threat- ened by any new physics that addresses the hierarchy problem.
    [Show full text]
  • Published Version
    PUBLISHED VERSION James Barnard, Daniel Murnane, Martin White, Anthony G. Williams Constraining fine tuning in composite Higgs models with partially composite leptons Journal of High Energy Physics, 2017; 2017(9):049-1-049-31 © 2017, The Author(s). Published in cooperation with JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0 Originally published at: http://doi.org/10.1007/JHEP09(2017)049 PERMISSIONS http://creativecommons.org/licenses/by/4.0/ 7 November 2017 http://hdl.handle.net/2440/109233 Published for SISSA by Springer Received: April 11, 2017 Revised: July 19, 2017 Accepted: August 13, 2017 Published: September 12, 2017 Constraining fine tuning in composite Higgs models with partially composite leptons JHEP09(2017)049 James Barnard,a Daniel Murnane,b Martin Whiteb and Anthony G. Williamsb aARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, University of Melbourne, Victoria 3000, Australia bARC Centre of Excellence for Particle Physics at the Terascale, Department of Physics, University of Adelaide, South Australia 5005, Australia E-mail: [email protected], [email protected], [email protected] Abstract: Minimal Composite Higgs Models (MCHM) have long provided a solution to the hierarchy problem of the Standard Model, yet suffer from various sources of fine tuning that are becoming increasingly problematic with the lack of new physics observations at the LHC. We develop a new fine tuning measure that accurately counts each contribution to fine tuning (single, double, triple, etc) that can occur in a theory with np parameters, that must reproduce no observables.
    [Show full text]
  • Leptons in Composite MFV
    Leptons in Composite MFV Michele Redi∗ INFN, Sezione di Firenze, Via G. Sansone, 1; I-50019 Sesto Fiorentino, Italy Abstract We study the lepton sector of composite Higgs models with partial compositeness. The standard anarchic scenario is in conflict with the absence of observable charged lepton flavor violation. This tension can be completely solved in MFV scenarios that require either left-handed or right-handed SM leptons to be equally composite. Constraints on this scenario are weak and the composite lepton partners could be as light as few hundreds GeVs with interesting LHC signatures. The contribution to the muon (g − 2) in theories where the Higgs is a pseudo Nambu-Goldstone boson is also discussed. arXiv:1306.1525v3 [hep-ph] 21 Jul 2014 ∗michele.redi@fi.infn.it 1 Contents 1 Introduction 2 2 Partially Composite Leptons 3 2.1 Anarchic Leptons . .4 2.2 MFV Leptons . .6 2.3 Beyond MFV . .6 3 Bounds 7 3.1 Compositeness and Precision Tests . .8 3.2 LHC searches . 10 4 Muon g − 2 12 5 Summary 13 1 Introduction The hope that new physics will be discovered at LHC relies on the existence of some special flavor structure of the new degrees of freedom that does not jeopardize the special features of the Standard Model (SM), in particular suppression of flavor changing neutral currents and charged lepton flavor conservation. The simplest hypothesis is that the flavor structure of the new physics is the same as in the SM itself, where flavor symmetries are only broken by the Yukawa couplings. This possibility, known as Minimal Flavor Violation (MFV) [1], is for example automatically realized in supersymmetric theories with gauge or anomaly mediation.
    [Show full text]
  • Composite Higgs Theory
    Third Alpine LHC Physics Summit CompositeComposite HiggsHiggs TheoryTheory CMS LHC LHCb ALICE SPS ATLAS 20.4.2018 FlorianFlorian GoertzGoertz p MPIK Pb PS Physics Beyond the SM SM does not explain everything! ● Gravity SM ● Hierarchy Problem: mh << MPL ● Tiny Neutrino Masses ● Grand Unification of Forces? ● Hierarchical Flavor Structure ● Baryogenesis → Existence of Universe ● Dark Matter SM ● Trigger for Symmetry-Breaking Potential? Mw ● Strong CP Problem ● Some Hints in Flavor/Precision Physics ..... ALPS 2018 2 F. Goertz Physics Beyond the SM Use the Higgs Sector as a unique window to NP! One of the biggest discoveries of mankind CERN LHC Many links to Higgs Sector still least understood... ALPS 2018 3 F. Goertz Physics Beyond the SM Flavor Physics allows to test enormous mass scales ... Neubert, EPS 2011 NP suppressed in SM → large sensitivity to NP And to Flavor!! ALPS 2018 4 F. Goertz The Hierarchy Problem: Running mh Running Higgs Mass Expect coefficient of unprotected D=2 operator H2 to reside at cutoff: Barbieri Phys. Scr. 2013 014006 Jump at threshold of NP → large fine-tuning to achieve ALPS 2018 5 F. Goertz Solving the Hierarchy Problem Hierarchy Problem: Main Classes of Solutions: cancellation ● Supersymmetry → Higgs = symmetry-partner of fermion → elegant protection of mass-term (cancellation of corrections) ● Compositeness ↔ Warped Extra Dimensions → h not fundamental (+Goldstone) both address also several other issues ALPS 2018 6 F. Goertz Composite Higgs Models Kaplan, Georgi, Dimopoulos,. ● Higgs is composite at small distances mH saturated in IR Hierarchy Problem solved ● Higgs = (pseudo) Goldstone Boson mH<<mr like pions in QCD Naturally address ● Hierarchical Flavor Structure 0906.3599 ● Dynamical EWSB ● Tiny Neutrino Masses ● Minimal models: SO(5)→SO(4) Contino, Nomura, Pomarol, ph/0306259 Agashe, Contino, Pomarol, ph/0412089 ● Dark Matter ● → 4 Goldstone dof (SO(5)/SO(4)), custodial symmetry Baryogenesis ..
    [Show full text]
  • Phenomenological Studies on Composite Higgs Models
    Phenomenological Studies on Composite Higgs Models Hesham El Faham Department of Physics and Astronomy Uppsala University A thesis submitted for the degree of Master of Science in Physics Uppsala, Sweden 2018 This thesis is dedicated to My parents, Adel El Faham and Ola Barakat. A special dedication to my mother whom without her support, this work, and future others, would have never been possible. Acknowledgements I am thankful.. to Gunnar Ingelman, who believed that I can do particle theory regardless of my Engineering background. The fuel of my persistence towards accomplishing anything during my master's studies came from knowing that Gunnar was al- ways there1. To my supervisor Rikard Enberg, who taught me a lot of physics in the last two years, and who had recently taught me that you can actually have a non-physics chat with a senior scientist while cycling your way to have dinner2. To Stefan Leupold, for all the fruitful conversations we had during the last two years, and for the advice he happily provided whenever I asked for it. To Gabriele Ferretti, for the great support he dispensed during my master's project work, and for his previous work (among others) that had inspired this work. To all the chats I had with my friend Thomas Mathisen which almost all of the time lead to the realization that we have done a terrible mistake in the model implementation. Well! We eventually (and apparently) got it right. To all the support I received from my good old friends in Egypt. To my sister and my brother, Reham and Mostafa.
    [Show full text]
  • Composite Higgs Models and Extra Dimensions
    International School for Advanced Studies SISSA/ISAS Composite Higgs Models and Extra Dimensions Thesis submitted for the degree of Doctor of Philosophy Candidate: Supervisor: Mahmoud Safari Prof. Marco Serone Acknowledgements I would like to thank my Adviser Marco Serone for his help throughout this project, and Giuliano Panico for collaboration. I am also grateful to Alberto Parolini, Alberto Tonero, Roberto Percacci, and Alessan- dro Codello for discussions on various topics, to the professors of the Theoretical Particle Physics group for their teaching, to the students secretary Riccardo Iancer and Federica Tuniz and in general to all members of SISSA for providing a suitable environment for study and research. I would also like to thank my housemates Jian Zhao and Angelo Russomanno for their patience and sharing the responsibilities of living together. Special thanks to all my friends with whom I have had a great time and who made my stay in Trieste enjoyable, in particular Alireza Alemi neissi, Zhian Asadzadeh, Fahimeh Baftizadeh, Milad Ekram- nia, Marzieh Forough, Zhaleh Ghaemi, Ehsan Hatefi, Majid Moshtagh, Shahab Naghavi, Masoud Nahali, Khadijeh Najafi, Nader Nikbakht, Sahar Pirmoradian, Mohammad Ali Rajabpour, Houman Safaai, Shima Seyed-allaei, Shima Taallohi, Maryam Tavakoli and Mahdi Torabian. Finally I would like to express my deepest gratitude to my parents and my brother and sister for their continuous support and encouragement without which I would have never achieved this goal. Contents 1 Introduction 2 2 Composite Higgs Models 6 2.1 Introduction................................... 6 2.2 TheCCWZprescription ............................ 7 2.3 TheMinimalCompositeHiggsModel . 9 2.4 Composite Higgs and deconstructed models . ..... 13 3 5D Theories and Holography 17 3.1 Gaugefieldsin5D ..............................
    [Show full text]
  • Tera-Zooming in on Light (Composite) ALPS
    Ter a - Z o o m i ng i n on light (composite) ALPS Giacomo Cacciapaglia IP2I Lyon, France Based on: 2104.11064, GC, A. Deandrea, A.Iyer, K. Sridhar Motivation The TeraZ option will produce 10^12 Z’s: does it make sense to search for new light states in Z decays? In composite Higgs models, light (pseudo)scalars are allowed and likely to exist! Composite ALP Lagrangian is “calculable”: predictive power! Access to high composite scales. Ideal physics case for FCC-ee @ 90 GeV! [Synergy with EWPTs] Composite Higgs models 101 Symmetry broken by a condensate (of TC-fermions) Misalignment, Higgs and longitudinal Z/W emergefor a Goldstone-Higgsas mesons (pions) Scales: v f ⇠ f : Higgs decay constant v : EW scale v f m 4⇡f ⌧ ⇢ ⇠ EWPTs + Higgs coupl. limit: v f 4v 1 TeV sin ✓ = Vacuum & f ⇠ misalignment Composite Higgs models 101 How can light states emerge? To p lo o p s Gauge loops TC-fermion masses W, Z top X 2 2 2 2 φ y f g f m f ⇠ t ⇠ ⇠ 2 2 2 = y2v2 2 2 2 2 2 h yt f s✓ t g f s✓ = g v X (h massless for ⇠ vanishing v) ⇠ m f a X X ⇠ This can be small! Composite Higgs models 101 T.Ryttov, F.Sannino 0809.0713 Galloway, Evans, Luty, Tacchi 1001.1361 The EW symmetry is embedded in the global flavour symmetry SU(4) ! The global symmetry is broken: SU(4)/Sp(4) Witten, Kosower 5 Goldstones (pions) arise: 5 (2, 2) (1, 1) Sp(4) ! ⊕ Higgs additional singlet be above 1MeV.
    [Show full text]
  • Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM
    S S symmetry Article Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM Alexander A. Osipov 1 , Brigitte Hiller 2,*, Alex H. Blin 2 and Marcos Sampaio 3 1 Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia; [email protected] 2 CFisUC, Department of Physics, University of Coimbra, P-3004-516 Coimbra, Portugal; [email protected] 3 CCNH Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André 09210-580, SP, Brazil; [email protected] * Correspondence: brigitte@fis.uc.pt Abstract: Here, we use the Schwinger–DeWitt approach to address the four-fermion composite Higgs effective model proposed by Miransky, Tanabashi and Yamawaki (MTY). The surprising benefit of such an approach is that it is possible to ascribe to a SM-type Higgs a quark–antiquark structure of predominantly a bb¯ nature with a small tt¯ admixture, which in turn yields a Higgs mass compatible with the observed value of 125 GeV. We discuss this result in a detailed and pedagogical way, as it goes against the common belief that this model and akin composite descriptions should predict a Higgs mass-of-order of twice the top quark mass, contrary to empirical evidence. A further aspect of this approach is that it highlights the link of the SU(2)L × U(1)R symmetric four-fermion MTY model interactions of the heavy quark family to a specific two-Higgs-doublet model (2HDM), and the necessity to go beyond the one Higgs doublet to obtain the empirical Higgs mass within composite models. By appropriately fixing the symmetry-defining interaction parameters, we show Citation: Osipov, A.A.; Hiller, B.; that the resulting CP-preserving spectrum harbors the following collective states at the electroweak Blin, A.H.; Sampaio, M.
    [Show full text]