DOCSLIB.ORG

Higgs Bosons and Supersymmetry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Higgs Bosons and Supersymmetry Higgs bosons and Supersymmetry 1. The Higgs mechanism in the Standard Model | The story so far | The SM Higgs boson at the LHC | Problems with the SM Higgs boson 2. Supersymmetry | Surpassing Poincar´e | Supersymmetry motivations | The MSSM 3. Conclusions & Summary D.J. Miller, Edinburgh, July 2, 2004 page 1 of 25 1. Electroweak Symmetry Breaking in the Standard Model 1. Electroweak Symmetry Breaking in the Standard Model Observation: Weak nuclear force mediated by W and Z bosons • M = 80:423 0:039GeV M = 91:1876 0:0021GeV W Z W couples only to left{handed fermions • Fermions have non-zero masses • Theory: We would like to describe electroweak physics by an SU(2) U(1) gauge theory. L ⊗ Y Left{handed fermions are SU(2) doublets Chiral theory ) right{handed fermions are SU(2) singlets f There are two problems with this, both concerning mass: gauge symmetry massless gauge bosons • SU(2) forbids m)( ¯ + ¯ ) terms massless fermions • L L R R L ) D.J. Miller, Edinburgh, July 2, 2004 page 2 of 25 1. Electroweak Symmetry Breaking in the Standard Model Higgs Mechanism Introduce new SU(2) doublet scalar field (φ) with potential V (φ) = λ φ 4 µ2 φ 2 j j − j j Minimum of the potential is not at zero 1 0 µ2 φ = with v = h i p2 v r λ Electroweak symmetry is broken Interactions with scalar field provide: Gauge boson masses • 1 1 2 2 MW = gv MZ = g + g0 v 2 2q Fermion masses • Y ¯ φ m = Y v=p2 f R L −! f f 4 degrees of freedom., 3 become longitudinal components of W and Z, one left over the Higgs boson D.J. Miller, Edinburgh, July 2, 2004 page 3 of 25 1. Electroweak Symmetry Breaking in the Standard Model The Higgs boson mass is not predicted in the SM LEP limits (e+e ZH) M > 114:4 GeV at 95% C.L. − ! ) H Electroweak Precision tests: 6 Theory uncertainty (5) ∆αhad = 5 0.02761±0.00036 0.02747±0.00012 4 incl. low Q2 data 2 3 ∆χ 2 1 Excluded Preliminary 0 20 100 400 mH [GeV] +60 MH = 96 38 GeV MH < 219 GeV at 95% C.L. − D.J. Miller, Edinburgh, July 2, 2004 page 4 of 25 1. Electroweak Symmetry Breaking in the Standard Model Summer 2003 2421 Winter 2004 ΓZ ΓZ [GeV] σ0 had σ0 [nb] R0 had l 0 0,l Rl Afb A0,l Al(Pτ) fb 0 Rb Al(Pτ) R0 0 c Rb 0,b A 0 fb R 0,c c Afb 0,b Afb Ab 0,c Afb Ac A Al(SLD) b 2 lept sin θeff (Qfb) Ac m W Al(SLD) 2 lept ΓW sin θeff (Qfb) mW [GeV] QW(Cs) 2 − − ΓW [GeV] sin θMS−−(e e ) 2 sin θW(νN) 2 2 '$NuTeV gL(νN) sin θW(νN) g2 (νN) R QW(Cs) 0 0 1 2 3 4 5 2 &%3 theo meas 10 10 10 Sensitivity |∂O /∂logMH|/σ MH [GeV] logarithmic sensitivity to MH [c.f. top mass] Not clear how to combine different measurements D.J. Miller, Edinburgh, July 2, 2004 page 5 of 25 1. Electroweak Symmetry Breaking in the Standard Model The Large Hadron Collider (LHC) will switch on in 2007 • main goal: discover the mechanism of Electroweak Symmetry Breaking Guaranteed to see something W W scattering at LHC will violate unitarity without Higgs boson (or something else) W- W- H W+ W+ 2 8πp2 2 MH . (780 GeV) ) 5GF D.J. Miller, Edinburgh, July 2, 2004 page 6 of 25 1. Electroweak Symmetry Breaking in the Standard Model SM Higgs production at the LHC σ(pp→H+X) [pb] 2 10 √s = 14 TeV M = 175 GeV Main production channel is gg H gg→H t ! 10 CTEQ4M 1 + ¥ -1 _ qq→Hqq 10 qq'→HW ¡ ¢¤£ -2 10 ¥ _ _ gg,qq→Htt -3 10 _ _ _ gg,qq→Hbb qq→HZ -4 10 0 200 400 600 800 1000 MH [GeV] D.J. Miller, Edinburgh, July 2, 2004 page 7 of 25 0 100 200 300 400 500 600 700 800 900 1000 1. Electroweak Symmetry Breaking in the Standard Model SM Higgs branching ratios D.J. Miller, Edinburgh, July 2, 2004 page 8 of 25 1. Electroweak Symmetry Breaking in the Standard Model H → γ γ + WH, ttH (H → γ γ ) ttH (H → bb) ATLAS H → ZZ(*) → 4 l H → WW(*) → lνlν (*) 2 WH → WWW 10 H → ZZ → llνν H → WW → lνjj Total significance Signal significance 10 5 σ ∫ L dt = 100 fb-1 (no K-factors) 1 2 3 10 10 mH (GeV) D.J. Miller, Edinburgh, July 2, 2004 page 9 of 25 1. Electroweak Symmetry Breaking in the Standard Model Is the Standard Model valid to all energies? V (φ) = λ(φ φ)2 µ2(φ φ) M = 2λ(v2)v y − y H p Coupling λ runs with energy, t log Q2=v2: ≡ dλ = 3 (4λ2 + λm2v2 m4v4=4) dt 16π2 t − t Triviality upper bound on MH • 2 Large λ: λ(Q2) λ(v2)=(1 3λ(v ) log Q2=v2) < ≈ − 4π2 1 2 M 2 8π2v2=3 log Q −! H ≤ v2 [this triviality problem is endemic to scalar theories] Vacuum stability lower bound on M • H 2 Small λ: large mt pulls λ(Q ) < 0 electroweak vacuum unstable −! D.J. Miller, Edinburgh, July 2, 2004 page 10 of 25 1. Electroweak Symmetry Breaking in the Standard Model If no new physics up to M 1016 GeV GUT ≈ M 130{170 GeV ) H ≈ Fits well with Electroweak precision tests... D.J. Miller, Edinburgh, July 2, 2004 page 11 of 25 1. Electroweak Symmetry Breaking in the Standard Model The Hierarchy Problem The Standard Model (SM) has a fundamental flaw: The parameters of the model must be fine tuned The Higgs mass gains corrections from fermion loops f Quadratic divergence: 2 2 λf 2 δM = 2 j j Λ + ::: H H H − 16π2 Λ Scale of new physics 1016 GeV (?) ∼ ∼ δM 2 1030 GeV ! ) H ∼ must arrange for parameters to cancel to one part in 1026 Is this a hint that new physics will be seen at the LHC? D.J. Miller, Edinburgh, July 2, 2004 page 12 of 25 2. Supersymmetry 2. Supersymmetry The new physics most favoured by theorists is Supersymmetry | a symmetry between particles with different spins Coleman-Mandula theorem: Most general symmetries of the S matrix are boosts, rotations and translations of the Poincar´e group • symmetries of compact Lie groups (e.g. U(1), SU(2), E6...) • But they didn't consider groups with anti-commuting generators Supersymmetry enlarges the Poincar´e group by introducing new fermionic coordinates of space-time, θ; θ¯ [anticommuting Weyl spinors] promoted fields φ(x) −!superfields Ψ(x; θ; θ¯) D.J. Miller, Edinburgh, July 2, 2004 page 13 of 25 2. Supersymmetry Expand superfields in powers of θ and θ¯: Since θ only has two components, terms like θθθ must vanish θαθβ = θβθα − e.g. a chiral superfield (D¯αΨ = 0) Ψ(x; θ; θ¯) = φ(x~) + θ (x~) + θθF (x~) [x~µ = xµ + iθσµθ¯] 6 @I @ @ @ @ @ scalar fermion auxilliary field Supersymmetry is just a rotation in the new enlarged space-time (x; θ; θ¯) quarks, leptons squarks, sleptons gauge bosons ! gauginos neutralinos & charginos Higgs bosons ! higgsinos ! g \extra" particles are just different facets of the known SM particles D.J. Miller, Edinburgh, July 2, 2004 page 14 of 25 2. Supersymmetry The Hierarchy Problem Revisited f ~f H H H H 2 2 λf 2 2 λf~ 2 δM = +2 j j Λ + ::: δM = 2 Λ + ::: H 16π2 H − 16π2 2 Supersymmetry λ = λ ~ ) j f j f quadratic divergence cancels (to all orders in perturbation theory) Higgs mass stabilized! ) D.J. Miller, Edinburgh, July 2, 2004 page 15 of 25 2. Supersymmetry Supersymmetry breaking Clearly supersymmetry is not a true symmetry of nature | it must be broken How supersymmetry is broken is not known but it might go something like this... Hidden Sector E Visible Sector 6 Exact Supersymmetry Gravitational interactions with hidden Gauge theory becomes gravity - sector produce soft supersymmetry strongly interacting 2 Condensates form F F MΛ h i breaking terms: φyφ MPlanck logarithmic running ? Low energy softly broken supersymmetry D.J. Miller, Edinburgh, July 2, 2004 page 16 of 25 2. Supersymmetry More motivations for Supersymmetry Local supersymmetry Supergravity } An essential ingredient of String Theory } Both of the above very exciting but only imply SuSy at some (high?) scale They are no motivation for low (TeV) scale SuSy Gauge coupling unification } 60 If we want to unify the 3 forces at −1 50 α 1 SM MGUT, need to unify their couplings 40 Supersymmetry more compatible −1 α 30 with gauge unification −1 α 2 3 20 SuSy Desert between MEW 10 GeV 16≈ and MGUT 10 GeV 10 −1 ≈ α3 0 2 4 6 8 10 12 14 16 18 Log10(Q/1 GeV) D.J. Miller, Edinburgh, July 2, 2004 page 17 of 25 2. Supersymmetry \Natural" mechanism of electroweak symmetry breaking } d 6 16π2 M 2 6h2(M 2 + M 2 + M 3 ) 6g2M 2 g2M 2 dt Hu ≈ t Hu Q3 u3 − 2 2 − 5 1 1 [t = log Q ] MGUT ~g ~q 600 ~ L qR ~ 2 t large top mass pulls M < 0, L Hu ~t breaking Electroweak Symmetry 400 R 2 2 µ + M0 Hd m ~ 1/2 Explains why we have a L 200 \mexican hat" potential ~W M0 ~ B Running Mass (GeV) 0 [Still doesn't explain why Hu M (MGUT) MGUT] H –200 2 4 6 8 10 12 14 16 5–97 Log10Q (GeV) 8303A15 D.J.
Load more

Recommended publications
  • 1 Standard Model: Successes and Problems
    Searching for new particles at the Large Hadron Collider James Hirschauer (Fermi National Accelerator Laboratory) Sambamurti Memorial Lecture : August 7, 2017 Our current theory of the most fundamental laws of physics, known as the standard model (SM), works very well to explain many aspects of nature. Most recently, the Higgs boson, predicted to exist in the late 1960s, was discovered by the CMS and ATLAS collaborations at the Large Hadron Collider at CERN in 2012 [1] marking the first observation of the full spectrum of predicted SM particles. Despite the great success of this theory, there are several aspects of nature for which the SM description is completely lacking or unsatisfactory, including the identity of the astronomically observed dark matter and the mass of newly discovered Higgs boson. These and other apparent limitations of the SM motivate the search for new phenomena beyond the SM either directly at the LHC or indirectly with lower energy, high precision experiments. In these proceedings, the successes and some of the shortcomings of the SM are described, followed by a description of the methods and status of the search for new phenomena at the LHC, with some focus on supersymmetry (SUSY) [2], a specific theory of physics beyond the standard model (BSM). 1 Standard model: successes and problems The standard model of particle physics describes the interactions of fundamental matter particles (quarks and leptons) via the fundamental forces (mediated by the force carrying particles: the photon, gluon, and weak bosons). The Higgs boson, also a fundamental SM particle, plays a central role in the mechanism that determines the masses of the photon and weak bosons, as well as the rest of the standard model particles.
    [Show full text]
  • A Young Physicist's Guide to the Higgs Boson
    A Young Physicist’s Guide to the Higgs Boson Tel Aviv University Future Scientists – CERN Tour Presented by Stephen Sekula Associate Professor of Experimental Particle Physics SMU, Dallas, TX Programme ● You have a problem in your theory: (why do you need the Higgs Particle?) ● How to Make a Higgs Particle (One-at-a-Time) ● How to See a Higgs Particle (Without fooling yourself too much) ● A View from the Shadows: What are the New Questions? (An Epilogue) Stephen J. Sekula - SMU 2/44 You Have a Problem in Your Theory Credit for the ideas/example in this section goes to Prof. Daniel Stolarski (Carleton University) The Usual Explanation Usual Statement: “You need the Higgs Particle to explain mass.” 2 F=ma F=G m1 m2 /r Most of the mass of matter lies in the nucleus of the atom, and most of the mass of the nucleus arises from “binding energy” - the strength of the force that holds particles together to form nuclei imparts mass-energy to the nucleus (ala E = mc2). Corrected Statement: “You need the Higgs Particle to explain fundamental mass.” (e.g. the electron’s mass) E2=m2 c4+ p2 c2→( p=0)→ E=mc2 Stephen J. Sekula - SMU 4/44 Yes, the Higgs is important for mass, but let’s try this... ● No doubt, the Higgs particle plays a role in fundamental mass (I will come back to this point) ● But, as students who’ve been exposed to introductory physics (mechanics, electricity and magnetism) and some modern physics topics (quantum mechanics and special relativity) you are more familiar with..
    [Show full text]
  • New Physics of Strong Interaction and Dark Universe
    universe Review New Physics of Strong Interaction and Dark Universe Vitaly Beylin 1 , Maxim Khlopov 1,2,3,* , Vladimir Kuksa 1 and Nikolay Volchanskiy 1,4 1 Institute of Physics, Southern Federal University, Stachki 194, 344090 Rostov on Don, Russia; [email protected] (V.B.); [email protected] (V.K.); [email protected] (N.V.) 2 CNRS, Astroparticule et Cosmologie, Université de Paris, F-75013 Paris, France 3 National Research Nuclear University “MEPHI” (Moscow State Engineering Physics Institute), 31 Kashirskoe Chaussee, 115409 Moscow, Russia 4 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Russia * Correspondence: [email protected]; Tel.:+33-676380567 Received: 18 September 2020; Accepted: 21 October 2020; Published: 26 October 2020 Abstract: The history of dark universe physics can be traced from processes in the very early universe to the modern dominance of dark matter and energy. Here, we review the possible nontrivial role of strong interactions in cosmological effects of new physics. In the case of ordinary QCD interaction, the existence of new stable colored particles such as new stable quarks leads to new exotic forms of matter, some of which can be candidates for dark matter. New QCD-like strong interactions lead to new stable composite candidates bound by QCD-like confinement. We put special emphasis on the effects of interaction between new stable hadrons and ordinary matter, formation of anomalous forms of cosmic rays and exotic forms of matter, like stable fractionally charged particles. The possible correlation of these effects with high energy neutrino and cosmic ray signatures opens the way to study new physics of strong interactions by its indirect multi-messenger astrophysical probes.
    [Show full text]
  • MIT at the Large Hadron Collider—Illuminating the High-Energy Frontier
    Mit at the large hadron collider—Illuminating the high-energy frontier 40 ) roland | klute mit physics annual 2010 gunther roland and Markus Klute ver the last few decades, teams of physicists and engineers O all over the globe have worked on the components for one of the most complex machines ever built: the Large Hadron Collider (LHC) at the CERN laboratory in Geneva, Switzerland. Collaborations of thousands of scientists have assembled the giant particle detectors used to examine collisions of protons and nuclei at energies never before achieved in a labo- ratory. After initial tests proved successful in late 2009, the LHC physics program was launched in March 2010. Now the race is on to fulfill the LHC’s paradoxical mission: to complete the Stan- dard Model of particle physics by detecting its last missing piece, the Higgs boson, and to discover the building blocks of a more complete theory of nature to finally replace the Standard Model. The MIT team working on the Compact Muon Solenoid (CMS) experiment at the LHC stands at the forefront of this new era of particle and nuclear physics. The High Energy Frontier Our current understanding of the fundamental interactions of nature is encap- sulated in the Standard Model of particle physics. In this theory, the multitude of subatomic particles is explained in terms of just two kinds of basic building blocks: quarks, which form protons and neutrons, and leptons, including the electron and its heavier cousins. From the three basic interactions described by the Standard Model—the strong, electroweak and gravitational forces—arise much of our understanding of the world around us, from the formation of matter in the early universe, to the energy production in the Sun, and the stability of atoms and mit physics annual 2010 roland | klute ( 41 figure 1 A photograph of the interior, central molecules.
    [Show full text]
  • Introduction to Supersymmetry
    Introduction to Supersymmetry Pre-SUSY Summer School Corpus Christi, Texas May 15-18, 2019 Stephen P. Martin Northern Illinois University [email protected] 1 Topics: Why: Motivation for supersymmetry (SUSY) • What: SUSY Lagrangians, SUSY breaking and the Minimal • Supersymmetric Standard Model, superpartner decays Who: Sorry, not covered. • For some more details and a slightly better attempt at proper referencing: A supersymmetry primer, hep-ph/9709356, version 7, January 2016 • TASI 2011 lectures notes: two-component fermion notation and • supersymmetry, arXiv:1205.4076. If you find corrections, please do let me know! 2 Lecture 1: Motivation and Introduction to Supersymmetry Motivation: The Hierarchy Problem • Supermultiplets • Particle content of the Minimal Supersymmetric Standard Model • (MSSM) Need for “soft” breaking of supersymmetry • The Wess-Zumino Model • 3 People have cited many reasons why extensions of the Standard Model might involve supersymmetry (SUSY). Some of them are: A possible cold dark matter particle • A light Higgs boson, M = 125 GeV • h Unification of gauge couplings • Mathematical elegance, beauty • ⋆ “What does that even mean? No such thing!” – Some modern pundits ⋆ “We beg to differ.” – Einstein, Dirac, . However, for me, the single compelling reason is: The Hierarchy Problem • 4 An analogy: Coulomb self-energy correction to the electron’s mass A point-like electron would have an infinite classical electrostatic energy. Instead, suppose the electron is a solid sphere of uniform charge density and radius R. An undergraduate problem gives: 3e2 ∆ECoulomb = 20πǫ0R 2 Interpreting this as a correction ∆me = ∆ECoulomb/c to the electron mass: 15 0.86 10− meters m = m + (1 MeV/c2) × .
    [Show full text]
  • Light Higgs Production in Hyperon Decay
    Light Higgs Production in Hyperon Decay Xiao-Gang He∗ Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei. Jusak Tandean† Department of Mathematics/Physics/Computer Science, University of La Verne, La Verne, CA 91750, USA G. Valencia‡ Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA (Dated: July 8, 2018) Abstract A recent HyperCP observation of three events in the decay Σ+ pµ+µ− is suggestive of a new particle → with mass 214.3 MeV. In order to confront models that contain a light Higgs boson with this observation, it is necessary to know the Higgs production rate in hyperon decay. The contribution to this rate from penguin-like two-quark operators has been considered before and found to be too large. We point out that there are additional four-quark contributions to this rate that could be comparable in size to the two-quark contributions, and that could bring the total rate to the observed level in some models. To this effect we implement the low-energy theorems that dictate the couplings of light Higgs bosons to hyperons at leading order in chiral perturbation theory. We consider the cases of scalar and pseudoscalar Higgs bosons in the standard model and in its two-Higgs-doublet extensions to illustrate the challenges posed by existing experimental constraints and suggest possible avenues for models to satisfy them. arXiv:hep-ph/0610274v3 16 Apr 2008 ∗Electronic address: [email protected] †Electronic address: [email protected] ‡Electronic address: [email protected] 1 I. INTRODUCTION Three events for the decay mode Σ+ pµ+µ− with a dimuon invariant mass of 214.3 0.5 MeV → ± have been recently observed by the HyperCP Collaboration [1].
    [Show full text]
  • Exotic Quarks in Twin Higgs Models
    Prepared for submission to JHEP SLAC-PUB-16433, KIAS-P15042, UMD-PP-015-016 Exotic Quarks in Twin Higgs Models Hsin-Chia Cheng,1 Sunghoon Jung,2;3 Ennio Salvioni,1 and Yuhsin Tsai1;4 1Department of Physics, University of California, Davis, Davis, CA 95616, USA 2Korea Institute for Advanced Study, Seoul 130-722, Korea 3SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA 4Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742, USA E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The Twin Higgs model provides a natural theory for the electroweak symmetry breaking without the need of new particles carrying the standard model gauge charges below a few TeV. In the low energy theory, the only probe comes from the mixing of the Higgs fields in the standard model and twin sectors. However, an ultraviolet completion is required below ∼ 10 TeV to remove residual logarithmic divergences. In non-supersymmetric completions, new exotic fermions charged under both the standard model and twin gauge symmetries have to be present to accompany the top quark, thus providing a high energy probe of the model. Some of them carry standard model color, and may therefore be copiously produced at current or future hadron colliders. Once produced, these exotic quarks can decay into a top together with twin sector particles. If the twin sector particles escape the detection, we have the irreducible stop-like signals. On the other hand, some twin sector particles may decay back into the standard model particles with long lifetimes, giving spectacular displaced vertex signals in combination with the prompt top quarks.
    [Show full text]
  • Scalar Portal and Its Connection to Higgs Physics from a Theory Viewpoint
    Scalar portal and its connection to Higgs physics from a theory viewpoint Stefania Gori UC Santa Cruz FIPs 2020 - Feebly Interacting Particles 2020 September 4, 2020 The scalar portal & open problems in particle physics S.Gori 2 The scalar portal & open problems in particle physics Baryon anti-baryon asymmetry Origin of neutrino masses; Electroweak phase Flavor puzzle; transitions … Higgs hierarchy problem SUSY; Neutral naturalness; Origin of DM Relaxion models; … Possible existence of a dark sector Dark scalar responsible of DM mass A broad topic. Apology for the omissions… S.Gori 2 Dark sectors & the Higgs portal “Portals”: Dark photon Higgs dark Neutrino fermions? Not charged under the generically mediators SM gauge symmetries small parameters The Higgs portal is one of the three renormalizable portals connecting the SM to the dark sector S.Gori 3 Dark sectors & the Higgs portal “Portals”: Dark photon Higgs dark Neutrino fermions? Not charged under the generically mediators SM gauge symmetries small parameters The Higgs portal is one of the three renormalizable portals connecting the SM to the dark sector In this talk, we will discuss the phenomenology of three simplified models: Minimal model (SM+S): 1) ms < mh / 2; 2) heavy ms; + more complete 3) Non minimal model (SM+S+DM): ms > 2mDM theories S.Gori 3 Simplified models Minimal model (SM+S): 1) ms < mh / 2; 2) heavy ms; 3) Non minimal model (SM+S+DM): ms > 2mDM from symmetry magazine 1) ms < mh / 2 How to probe the Higgs portal (light ms)? S.Gori 4 1) ms < mh / 2 How to probe the Higgs portal (light ms)? 1.
    [Show full text]
  • Higgs-Like Boson at 750 Gev and Genesis of Baryons
    BNL-112543-2016-JA Higgs-like boson at 750 GeV and genesis of baryons Hooman Davoudiasl, Pier Paolo Giardino, Cen Zhang Submitted to Physical Review D July 2016 Physics Department Brookhaven National Laboratory U.S. Department of Energy USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25) Notice: This manuscript has been co-authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
    [Show full text]
  • Mass Generation Via the Higgs Boson and the Quark Condensate of the QCD Vacuum
    Pramana – J. Phys. (2016) 87: 44 c Indian Academy of Sciences DOI 10.1007/s12043-016-1256-0 Mass generation via the Higgs boson and the quark condensate of the QCD vacuum MARTIN SCHUMACHER II. Physikalisches Institut der Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany E-mail: [email protected] Published online 24 August 2016 Abstract. The Higgs boson, recently discovered with a mass of 125.7 GeV is known to mediate the masses of elementary particles, but only 2% of the mass of the nucleon. Extending a previous investigation (Schumacher, Ann. Phys. (Berlin) 526, 215 (2014)) and including the strange-quark sector, hadron masses are derived from the quark condensate of the QCD vacuum and from the effects of the Higgs boson. These calculations include the π meson, the nucleon and the scalar mesons σ(600), κ(800), a0(980), f0(980) and f0(1370). The predicted second σ meson, σ (1344) =|ss¯, is investigated and identified with the f0(1370) meson. An outlook is given on the hyperons , 0,± and 0,−. Keywords. Higgs boson; sigma meson; mass generation; quark condensate. PACS Nos 12.15.y; 12.38.Lg; 13.60.Fz; 14.20.Jn 1. Introduction adds a small additional part to the total constituent- quark mass leading to mu = 331 MeV and md = In the Standard Model, the masses of elementary parti- 335 MeV for the up- and down-quark, respectively [9]. cles arise from the Higgs field acting on the originally These constituent quarks are the building blocks of the massless particles. When applied to the visible matter nucleon in a similar way as the nucleons are in the case of the Universe, this explanation remains unsatisfac- of nuclei.
    [Show full text]
  • The Effective Action for Gauge Bosons Arxiv:1810.06994V1 [Hep-Ph]
    October 2018 The effective action for gauge bosons Jeremie Quevillon1 , Christopher Smith2 and Selim Touati3 Laboratoire de Physique Subatomique et de Cosmologie, Universit´eGrenoble-Alpes, CNRS/IN2P3, Grenoble INP, 38000 Grenoble, France. Abstract By treating the vacuum as a medium, H. Euler and W. Heisenberg estimated the non-linear interactions between photons well before the advent of Quantum Electrodynamics. In a modern language, their result is often presented as the archetype of an Effective Field Theory (EFT). In this work, we develop a similar EFT for the gauge bosons of some generic gauge symmetry, valid for example for SU(2), SU(3), various grand unified groups, or mixed U(1) ⊗ SU(N) and SU(M) ⊗ SU(N) gauge groups. Using the diagrammatic approach, we perform a detailed matching procedure which remains manifestly gauge invariant at all steps, but does not rely on the equations of motion hence is valid off-shell. We provide explicit analytic expressions for the Wilson coefficients of the dimension four, six, and eight operators as induced by massive scalar, fermion, and vector fields in generic representations of the gauge group. These expressions rely on a careful analysis of the quartic Casimir invariants, for which we provide a review using conventions adapted to Feynman diagram calculations. Finally, our computations show that at one loop, some operators are redundant whatever the representation or spin of the particle being arXiv:1810.06994v1 [hep-ph] 16 Oct 2018 integrated out, reducing the apparent complexity of the operator basis that can be constructed solely based on symmetry arguments. 1 [email protected] 2 [email protected] 3 [email protected] Contents 1 Introduction 1 2 Photon effective interactions3 3 Gluon effective interactions6 4 SU(N) effective interactions 11 4.1 Reduction to SU(3) and SU(2) .
    [Show full text]
  • Higgs Boson(S) and Supersymmetry
    Higgs Boson(s) and Supersymmetry Quantum Electrodynamics • Mass for the photon forbidden (gauge invariance). • Mass for the electron allowed. Anomalous magnetic moment of the electron: D. Hanneke et.al. (2011) M. Hayakawa Weak Interactions • Still cannot give mass to the gauge boson B, thus, neither to the Z gauge boson! • Cannot write a mass term for the electron neither, due to the splitting between the left and right component. • Need Brout-Englert-Higgs mechanism. Higgs Mechanism It does not explain why the masses are so different. Simultaneous work: Englert y Brout. Higgs Potential The field must have spin 0, and a non-zero vacuum expectation value. Buttazzo et.al. (2013) But, lifetime of meta-stable vacuum is very large! Higgs Boson It is well established the existence of a scalar with Standard Model couplings and a mass ≈ 125 GeV. Evidence points to spin cero and couplings to fermions as well as gauge bosons. Supersymmetry Neutralino Gravitino SM MSSM Rp Conserving Rp Violating Dark Matter De Boer et.al. (2004) Supersymmetric Searches Squarks, sleptons, and gluinos seem to be heavier than ~1 TeV. Mysteries Triple Higgs coupling: • ããbb-bar channel. • hhh in SM is too low to be seen by the LHC. • Hhh in 2HDM may be seen (excess?). • arXiv:1406.5053 CMS and LHCb observe the rare decay BS to mu mu (arXiv:1411.4413). ~2.5 σ (CMS PAS HIG-14-005) B(B→μμ) / B(BS→μμ) too large! Heavy squarks and gluinos and low tan(β) (arXiv:1501.02044)? Heavy Supersymmetry Split Supersymmetry hep-th/0405159, hep-ph/0406088 High Scale Supersymmetry • Gauge coupling unification • All supersymetry partners are heavy.
    [Show full text]