DOCSLIB.ORG

Mass Generation Via the Higgs Boson and the Quark Condensate of the QCD Vacuum

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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. Quantitatively, we obtain the experimental tory as long as we consider the vacuum as an empty masses of the nucleons after including a binding energy space. The QCD vacuum contains a condensate of up- of 19.6 MeV and 20.5 MeV per constituent quark for and down-quarks. Condensate means that the qq¯ pairs the proton and neutron, respectively, again in analogy to the nuclear case where the binding energies are are correlated via interquark forces mediated by gluon 3 exchanges. As part of the vacuum structure, the qq¯ pairs 2.83 MeV per nucleon for 1H and 2.57 MeV per 3 have to be in a scalar–isoscalar configuration. This nucleon for 2He. suggests that the vacuum condensate may be described In the present work we extend our previous [9] inves- tigation by exploring in more detail the rules according in terms√ of a scalar–isoscalar particle, |σ=(|uu¯+ to which the effects of electroweak (EW) and strong |dd¯)/ 2, providing the σ field. These two descriptions, interaction symmetry breaking combine in order to in terms of a vacuum condensate or a σ field, are essen- generate the masses of hadrons. As a test of the con- tially equivalent and are the bases of the Nambu–Jona- cept, the mass of the π meson is precisely predicted on σ σ Lasinio (NJL) model [1–7] and the linear model (L M) an absolute scale. In the strange-quark sector the Higgs [8], respectively. Furthermore, it is possible to write boson is responsible for about 1/3 of the constituent down a bosonized version of the NJL model where quark mass, so that effects of the interplay of the two the vacuum condensate is replaced by the vacuum components of mass generation become essential. expectation value of the σ field. Progress is made by taking into account the predicted In the QCD vacuum the largest part of the mass M second σ meson, σ (1344) =|ss¯ [6]. It is found that of an originally massless quark, up (u) or down (d), is the coupling constant of the s-quark coupling to the σ generated independent of the presence of the Higgs field meson is larger than the corresponding quantity of the and amounts to M = 326 MeV [9]. The Higgs field only u and d quarks coupling to the σ meson by a factor 1 44 Page 2 of 11 Pramana – J. Phys. (2016) 87: 44 √ of 2. This leads to a considerable increase of the vacuum or the Higgs field of the EW vacuum. As long constituent quark masses in the strange quark sector as we consider the two symmetry breaking processes in comparison with the ones in the non-strange sector separately we can write down [9] already in the chiral limit, i.e. without the effects of the M = gvcl, (1) Higgs boson. There is an additional sizable increase of σ the mass generation mediated by the Higgs boson due 0 = × −5 mu 2.03 10 vH, (2) to ∼20 times stronger coupling of the s quark to the 0 = × −5 Higgs boson in comparison to the u and d quarks. md 3.66 10 vH. (3) In addition to the progress made in [9] as described above, this paper contains a history of the subject from The quantity g is the quark-σ coupling√ constant which = Schwinger’s seminal work of 1957 [10] to the dis- has been derived to be g 2π/ 3. This quantity leads = covery of the Brout–Englert–Higgs (BEH) mechanism, via eq. (1) to the constituent quark mass M 326 MeV with emphasis on the Nobel prize awarded to Nambu in in the chiral limit (cl), i.e. without the effects of the cl ≡ cl = 2008. This is the reason why paper [9] has been pub- Higgs boson. The quantity vσ fπ 89.8 MeV is the lished as a supplement of the Nobel lectures of Englert pion decay constant in the chiral limit, serving as vac- = [11] and Higgs [12]. uum expectation value, vσ . The quantity vH 246 GeV is the vacuum expectation value of the Higgs field, lead- 0 = 0 = ing to the current quark masses mu 5 MeV and md 2. Symmetry breaking in the non-strange sector 9 MeV. These values are the well-known current quark masses entering into low-energy QCD via explicit sym- In figure 1 the symmetry breaking process is illustrated. metry breaking. The coupling constants in eqs (2) and Figure 1a corresponds to the LσM and figure 1b to the (3) are chosen such that these values are reproduced. bosonized NJL model, together with their EW counter- In the following we study the laws according to parts. In figure 1a symmetry breaking provides us with which the two sources of mass generation combine in v H v a vacuum expectation H of the Higgs field and σ order to generate the observable particle masses. For σ of the -field. Without the effects of the Higgs field, the this purpose, we write down the well-known NJL equa- π strong-interaction Nambu–Goldstone bosons, ,are tion and refer to [9] for more details massless. The π mesons generate mass via the interac- tion with the Higgs field in the presence of the QCD G L = ψ(i/¯ ∂ −m )ψ + [(ψψ)¯ 2 +(ψiγ¯ τψ)2]. (4) quark condensate, as will be outlined below. The EW NJL 0 2 5 counterparts of the π mesons are the longitudinal com- In eq. (4) the interaction between the fermions is para- ponents W of the weak vector bosons W. These lon- l metrized by the four-fermion interaction constant G. gitudinal components are transferred into the originally Explicit symmetry breaking as mediated by the Higgs massless weak vector bosons W via the Brout–Englert– m = m0 + m0 Higgs (BEH) mechanism. In figure 1b, the view of the boson is represented by the trace 0 u d of bosonized NJL model is presented. The originally mass- the current quark mass matrix [4]. From eq. (4) the less quarks interact via the exchange of a σ meson or constituent quark mass in the chiral limit (cl) may be a Higgs boson with the respective σ field of the QCD derived via the relation M = G|ψψ¯ |cl. (5) V(Φ) σ, Η The bosonization of eq. (4) is obtained by replacing G by a propagator g2 G → ,q2 → 0, (6) cl 2 − 2 (mσ ) q σ,Η σ Η cl π, v where m is the mass of the σ meson in the chiral limit WL q σ (a) (b) and q is the momentum carried by the σ meson, and by Figure 1. Strong-interaction and EW interaction symme- introducing the σ and π fields via try breaking. (a)TheLσM together with the EW counterpart G ¯ G ¯ and (b) the bosonized NJL model together with the EW σ =− ψψ, π =− ψiγ5 τψ. (7) counterpart. g g Pramana – J. Phys. (2016) 87: 44 Page 3 of 11 44 cl = with Using the Nambu relation√mσ 2M, the quark-σ g = π/ M = gf cl f cl = coupling constant 2 3, π and π μ2 89.8 MeV we arrive at π = 0, σ= ≡ vcl ≡ f cl. (14) λ σ π π | ¯ |cl = √8 cl 3 = 3 ψψ (fπ ) (219 MeV) , 3 It is of interest to compare the self-coupling strengths of strong interaction symmetry breaking with the one 1 −5 −2 G = = 3.10 × 10 MeV . (8) of EW symmetry breaking. The σ meson mass in the 4(f cl)2 π chiral limit may be expressed in two ways [9]: In the present case of small current quark masses it is cl = cl cl = cl straightforward to arrive at a version which includes mσ 2gvσ ,mσ 2λσ vσ , (15) cl the effects of the Higgs boson by replacing fπ with where the first version corresponds to the NJL model fπ .
Load more

Recommended publications
  • 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.
    [Show full text]
  • Conformal Symmetry in Field Theory and in Quantum Gravity
    universe Review Conformal Symmetry in Field Theory and in Quantum Gravity Lesław Rachwał Instituto de Física, Universidade de Brasília, Brasília DF 70910-900, Brazil; [email protected] Received: 29 August 2018; Accepted: 9 November 2018; Published: 15 November 2018 Abstract: Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented. Keywords: quantum gravity; conformal gravity; quantum field theory; non-local gravity; super- renormalizable gravity; UV-finite gravity; conformal anomaly; scattering amplitudes; conformal symmetry; conformal supergravity 1. Introduction From the beginning of research on theories enjoying invariance under local spacetime-dependent transformations, conformal symmetry played a pivotal role—first introduced by Weyl related changes of meters to measure distances (and also due to relativity changes of periods of clocks to measure time intervals).
    [Show full text]
  • The Particle World
    The Particle World ² What is our Universe made of? This talk: ² Where does it come from? ² particles as we understand them now ² Why does it behave the way it does? (the Standard Model) Particle physics tries to answer these ² prepare you for the exercise questions. Later: future of particle physics. JMF Southampton Masterclass 22–23 Mar 2004 1/26 Beginning of the 20th century: atoms have a nucleus and a surrounding cloud of electrons. The electrons are responsible for almost all behaviour of matter: ² emission of light ² electricity and magnetism ² electronics ² chemistry ² mechanical properties . technology. JMF Southampton Masterclass 22–23 Mar 2004 2/26 Nucleus at the centre of the atom: tiny Subsequently, particle physicists have yet contains almost all the mass of the discovered four more types of quark, two atom. Yet, it’s composite, made up of more pairs of heavier copies of the up protons and neutrons (or nucleons). and down: Open up a nucleon . it contains ² c or charm quark, charge +2=3 quarks. ² s or strange quark, charge ¡1=3 Normal matter can be understood with ² t or top quark, charge +2=3 just two types of quark. ² b or bottom quark, charge ¡1=3 ² + u or up quark, charge 2=3 Existed only in the early stages of the ² ¡ d or down quark, charge 1=3 universe and nowadays created in high energy physics experiments. JMF Southampton Masterclass 22–23 Mar 2004 3/26 But this is not all. The electron has a friend the electron-neutrino, ºe. Needed to ensure energy and momentum are conserved in ¯-decay: ¡ n ! p + e + º¯e Neutrino: no electric charge, (almost) no mass, hardly interacts at all.
    [Show full text]
  • Effects of Scalar Mesons in a Skyrme Model with Hidden Local Symmetry
    Effects of scalar mesons in a Skyrme model with hidden local symmetry 1, 2, 1, Bing-Ran He, ∗ Yong-Liang Ma, † and Masayasu Harada ‡ 1Department of Physics, Nagoya University, Nagoya, 464-8602, Japan 2Center of Theoretical Physics and College of Physics, Jilin University, Changchun, 130012, China (Dated: March 5, 2018) We study the effects of light scalar mesons on the skyrmion properties by constructing and ex- amining a mesonic model including pion, rho meson, and omega meson fields as well as two-quark and four-quark scalar meson fields. In our model, the physical scalar mesons are defined as mixing states of the two- and four-quark fields. We first omit the four-quark scalar meson field from the model and find that when there is no direct coupling between the two-quark scalar meson and the vector mesons, the soliton mass is smaller and the soliton size is larger for lighter scalar mesons; when direct coupling is switched on, as the coupling strength increases, the soliton becomes heavy, and the radius of the baryon number density becomes large, as the repulsive force arising from the ω meson becomes strong. We then include the four-quark scalar meson field in the model and find that mixing between the two-quark and four-quark components of the scalar meson fields also affects the properties of the soliton. When the two-quark component of the lighter scalar meson is increased, the soliton mass decreases and the soliton size increases. PACS numbers: 11.30.Rd, 12.39.Dc, 12.39.Fe, 14.40.Be I.
    [Show full text]
  • Effective Field Theories, Reductionism and Scientific Explanation Stephan
    To appear in: Studies in History and Philosophy of Modern Physics Effective Field Theories, Reductionism and Scientific Explanation Stephan Hartmann∗ Abstract Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effec- tive field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispens- able. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. Keywords: Effective Field Theory; Quantum Field Theory; Renormalisation; Reductionism; Explanation; Pluralism. ∗Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pitts- burgh, PA 15260, USA (e-mail: [email protected]) (correspondence address); and Sektion Physik, Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany. 1 1 Introduction There is little doubt that effective field theories are nowadays a very popular tool in quantum physics.
    [Show full text]
  • Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 12: Hadron Decays
    Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 12: Hadron Decays !Resonances !Heavy Meson and Baryons !Decays and Quantum numbers !CKM matrix 1 Announcements •No lecture on Friday. •Remaining lectures: •Tuesday 13 March •Friday 16 March •Tuesday 20 March •Friday 23 March •Tuesday 27 March •Friday 30 March •Tuesday 3 April •Remaining Tutorials: •Monday 26 March •Monday 2 April 2 From Friday: Mesons and Baryons Summary • Quarks are confined to colourless bound states, collectively known as hadrons: " mesons: quark and anti-quark. Bosons (s=0, 1) with a symmetric colour wavefunction. " baryons: three quarks. Fermions (s=1/2, 3/2) with antisymmetric colour wavefunction. " anti-baryons: three anti-quarks. • Lightest mesons & baryons described by isospin (I, I3), strangeness (S) and hypercharge Y " isospin I=! for u and d quarks; (isospin combined as for spin) " I3=+! (isospin up) for up quarks; I3="! (isospin down) for down quarks " S=+1 for strange quarks (additive quantum number) " hypercharge Y = S + B • Hadrons display SU(3) flavour symmetry between u d and s quarks. Used to predict the allowed meson and baryon states. • As baryons are fermions, the overall wavefunction must be anti-symmetric. The wavefunction is product of colour, flavour, spin and spatial parts: ! = "c "f "S "L an odd number of these must be anti-symmetric. • consequences: no uuu, ddd or sss baryons with total spin J=# (S=#, L=0) • Residual strong force interactions between colourless hadrons propagated by mesons. 3 Resonances • Hadrons which decay due to the strong force have very short lifetime # ~ 10"24 s • Evidence for the existence of these states are resonances in the experimental data Γ2/4 σ = σ • Shape is Breit-Wigner distribution: max (E M)2 + Γ2/4 14 41.
    [Show full text]
  • 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]
  • Fully Strange Tetraquark Sss¯S¯ Spectrum and Possible Experimental Evidence
    PHYSICAL REVIEW D 103, 016016 (2021) Fully strange tetraquark sss¯s¯ spectrum and possible experimental evidence † Feng-Xiao Liu ,1,2 Ming-Sheng Liu,1,2 Xian-Hui Zhong,1,2,* and Qiang Zhao3,4,2, 1Department of Physics, Hunan Normal University, and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha 410081, China 2Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha 410081, China 3Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China 4University of Chinese Academy of Sciences, Beijing 100049, China (Received 21 August 2020; accepted 5 January 2021; published 26 January 2021) In this work, we construct 36 tetraquark configurations for the 1S-, 1P-, and 2S-wave states, and make a prediction of the mass spectrum for the tetraquark sss¯s¯ system in the framework of a nonrelativistic potential quark model without the diquark-antidiquark approximation. The model parameters are well determined by our previous study of the strangeonium spectrum. We find that the resonances f0ð2200Þ and 2340 2218 2378 f2ð Þ may favor the assignments of ground states Tðsss¯s¯Þ0þþ ð Þ and Tðsss¯s¯Þ2þþ ð Þ, respectively, and the newly observed Xð2500Þ at BESIII may be a candidate of the lowest mass 1P-wave 0−þ state − 2481 0þþ 2440 Tðsss¯s¯Þ0 þ ð Þ. Signals for the other ground state Tðsss¯s¯Þ0þþ ð Þ may also have been observed in PC −− the ϕϕ invariant mass spectrum in J=ψ → γϕϕ at BESIII. The masses of the J ¼ 1 Tsss¯s¯ states are predicted to be in the range of ∼2.44–2.99 GeV, which indicates that the ϕð2170Þ resonance may not be a good candidate of the Tsss¯s¯ state.
    [Show full text]
  • An Introduction to the Quark Model
    An Introduction to the Quark Model Garth Huber Prairie Universities Physics Seminar Series, November, 2009. Particles in Atomic Physics • View of the particle world as of early 20th Century. • Particles found in atoms: –Electron – Nucleons: •Proton(nucleus of hydrogen) •Neutron(e.g. nucleus of helium – α-particle - has two protons and two neutrons) • Related particle mediating electromagnetic interactions between electrons and protons: Particle Electric charge Mass – Photon (light!) (x 1.6 10-19 C) (GeV=x 1.86 10-27 kg) e −1 0.0005 p +1 0.938 n 0 0.940 γ 0 0 Dr. Garth Huber, Dept. of Physics, Univ. of Regina, Regina, SK S4S0A2, Canada. 2 Early Evidence for Nucleon Internal Structure • Apply the Correspondence Principle to the Classical relation for q magnetic moment: µ = L 2m • Obtain for a point-like spin-½ particle of mass mp: qqeq⎛⎞⎛⎞ µ == =µ ⎜⎟ ⎜⎟ N 2222memepp⎝⎠ ⎝⎠ 2 Experimental values: µp=2.79 µN (p) µn= -1.91 µN (n) • Experimental values inconsistent with point-like assumption. • In particular, the neutron’s magnetic moment does not vanish, as expected for a point-like electrically neutral particle. This is unequivocal evidence that the neutron (and proton) has an internal structure involving a distribution of charges. Dr. Garth Huber, Dept. of Physics, Univ. of Regina, Regina, SK S4S0A2, Canada. 3 The Particle Zoo • Circa 1950, the first particle accelerators began to uncover many new particles. • Most of these particles are unstable and decay very quickly, and hence had not been seen in cosmic ray experiments. • Could all these particles be fundamental? Dr. Garth Huber, Dept.
    [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]
  • 1 Quark Model of Hadrons
    1 QUARK MODEL OF HADRONS 1 Quark model of hadrons 1.1 Symmetries and evidence for quarks 1 Hadrons as bound states of quarks – point-like spin- 2 objects, charged (‘coloured’) under the strong force. Baryons as qqq combinations. Mesons as qq¯ combinations. 1 Baryon number = 3 (N(q) − N(¯q)) and its conservation. You are not expected to know all of the names of the particles in the baryon and meson multiplets, but you are expected to know that such multiplets exist, and to be able to interpret them if presented with them. You should also know the quark contents of the simple light baryons and mesons (and their anti-particles): p = (uud) n = (udd) π0 = (mixture of uu¯ and dd¯) π+ = (ud¯) K0 = (ds¯) K+ = (us¯). and be able to work out others with some hints. P 1 + Lowest-lying baryons as L = 0 and J = 2 states of qqq. P 3 + Excited versions have L = 0 and J = 2 . Pauli exclusion and non existence of uuu, ddd, sss states in lowest lying multiplet. Lowest-lying mesons as qq¯0 states with L = 0 and J P = 0−. First excited levels (particles) with same quark content have L = 0 and J P = 1−. Ability to explain contents of these multiplets in terms of quarks. J/Ψ as a bound state of cc¯ Υ (upsilon) as a bound state of b¯b. Realization that these are hydrogenic-like states with suitable reduced mass (c.f. positronium), and subject to the strong force, so with energy levels paramaterized by αs rather than αEM Top is very heavy and decays before it can form hadrons, so no top hadrons exist.
    [Show full text]
  • Neutrino Mass Models: a Road Map
    Neutrino Mass Models: a road map S.F.King School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK E-mail: [email protected] Abstract. In this talk we survey some of the recent promising developments in the search for the theory behind neutrino mass and mixing, and indeed all fermion masses and mixing. The talk is organized in terms of a neutrino mass models road map according to which the answers to experimental questions provide sign posts to guide us through the maze of theoretical models eventually towards a complete theory of flavour and uni¯cation. 1. Introduction It has been one of the long standing goals of theories of particle physics beyond the Standard Model (SM) to predict quark and lepton masses and mixings. With the discovery of neutrino mass and mixing, this quest has received a massive impetus. Indeed, perhaps the greatest advance in particle physics over the past decade has been the discovery of neutrino mass and mixing involving two large mixing angles commonly known as the atmospheric angle θ23 and the solar angle θ12, while the remaining mixing angle θ13, although unmeasured, is constrained to be relatively small [1]. The largeness of the two large lepton mixing angles contrasts sharply with the smallness of the quark mixing angles, and this observation, together with the smallness of neutrino masses, provides new and tantalizing clues in the search for the origin of quark and lepton flavour. However, before trying to address such questions, it is worth recalling why neutrino mass forces us to go beyond the SM.
    [Show full text]