Standard model Definition and 49 Discussions

The Standard Model of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, and not including gravity) in the universe, as well as classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists around the world, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, confirmation of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.
Although the Standard Model is believed to be theoretically self-consistent and has demonstrated huge successes in providing experimental predictions, it leaves some phenomena unexplained and falls short of being a complete theory of fundamental interactions. It does not fully explain baryon asymmetry, incorporate the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the Universe as possibly described by dark energy. The model does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations and their non-zero masses.
The development of the Standard Model was driven by theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigm of a quantum field theory, which exhibits a wide range of phenomena including spontaneous symmetry breaking, anomalies and non-perturbative behavior. It is used as a basis for building more exotic models that incorporate hypothetical particles, extra dimensions, and elaborate symmetries (such as supersymmetry) in an attempt to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.

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  1. G

    I Why does the QFT Lagrangian not already use operators?

    I've learned that in canonical quantization you take a Lagrangian, transform to a Hamiltonian and then "put the hat on" the fields (make them an operator). Then you can derive the equations of motion of the Hamiltonian. What is the reason that you cannot already put hats in the QFT Lagrangian...
  2. A

    A No CP-Violation for coinciding Quark-Masses

    Hello everyone, I know that if two of the quarks (e.g. strange & bottom) had coinciding masses, there would be no CP-violation in the standard model. Apparently the reason lies in the parameters of the CKM-matrix, but I don't understand how to show that. Can someone explain?
  3. S

    I From a false vacuum to a true vacuum?

    In theory (please correct me if I am wrong in any point), if our vacuum were metastable (i.e. in a "false vacuum" state), it could go through a phase transition into a stable state (a "true vacuum" state). Depending on the properties of the new vacuum, fundamental forces and particles could...
  4. F

    I Why are free parameters bad for a theory?

    It is often said that one of the drawbacks of the standard model is that it has many free parameters. My question is two-fold: What exactly is a free parameter? My understanding is that the free parameters of a model/theory are the ones that cannot be predicted by the theory and need to be...
  5. Safinaz

    A How to find the value of the baryon asymmetry in this paper

    I'm trying to understand from this paper What is the value of the baryon to photon ratio ##\eta=n_b/n_\gamma## as named in figure 24.1, but I can't get from the figure or the paper how ##\eta## is of order ##10^{-10}## Any...
  6. Safinaz

    A How Randall-Sundrum model has solved the hierarchy problem?

    I'm trying to understand how the RS model solved the hierarchy problem from this mass relation $$ M^2_p = \frac{M^3}{k} \Large[1- e^{-2k\pi r} \Large],$$ Equ. 16 in their paper: With k as large as the Planck scale, the exponential will be so small and...
  7. J

    A Griffith's Elementary Particles Section 9.7 Electroweak Unification

    1. On pg. 343 Griffith's expresses the weak current in terms of left-handed doublets. jμ± = ##\bar χ_L##γμτ±##χ_L## ##χ_L## = ##\begin{pmatrix} ν_e \\ e \end{pmatrix}_L## ##\tau^+## = ##\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}## , ## \tau^- ## = ##\begin{pmatrix} 0 & 0 \\ 1 & 0...
  8. takunitoche

    A Derivation of the Yang-Mills 3 gauge boson vertex

    Hello everyone, I am stuck in the derivation of the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is $$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term...
  9. D

    I Why does a Lagrangian matter for the standard model?

    Hi, I don't know much about the standard model but I'm asking out of interest. Why do we actually need a Lagrangian for the standard model? Surely when you apply the relevant Euler-Lagrange equations, you end up with a variety of equations like the Maxwell equations or Dirac equations. Why...
  10. A

    A Renormalization (Electron self energy)

    Hello everybody! I have a big question about the renormalization: I do not understand why the "renormalization condition" is to impose the tree level result. Now I will explain it better. Let's take, for example, the electron self energy. The tree-level contribution is the simple fermionic...
  11. A

    A The product of a matrix exponential and a vector

    Hello everybody! I was studying the Glashow-Weinberg-Salam theory and I have found this relation: $$e^{\frac{i\beta}{2}}\,e^{\frac{i\alpha_3}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix}}\, \frac{1}{\sqrt{2}}\begin{pmatrix} 0\\ v \\ \end{pmatrix} =...
  12. S

    I Interpreting SM Lagrangian "differential particle" terms

    The Standard Model Lagrangian contains terms like these: ##-\partial_\mu \phi^+ \partial_\mu\phi^-## ##-\frac{1}{2}\partial_\nu Z^0_\mu\partial_\nu Z^0_\mu## ##-igc_w\partial_\nu Z^0(W^+_\mu W^-_\nu-W^+_\nu W^-_\mu)## How should one interpret the "derivative particle fields" like...
  13. C

    I Is this outline of particle physics right?

    Just a quick query here: Is the outline of particle physics at the link below right? I have found it very helpful in a general way, but I am only just learning this stuff and don't want to be misled. Thanks!
  14. YoungPhysicist

    I Is there a simple explanation for Fermi-Dirac statistics?

    Is there a simple explanation for fermi-dirac statistics? I can't understand how a particle can "follow" a statistic.
  15. A

    B Why is the Higgs boson considered a boson?

    Bosons are described as force carrier particles and, as I understand it, the Higgs mechanism explains why photons are massless, just as all the carriers of the strong nuclear force, the gluons, whereas the weak force bosons have mass. A peculiar type of field is postulated, the ‘Higgs field’. It...
  16. R

    Do photons carry the electric field?

    In basic electrostatics any charged particle will produce an electric field at every point in space, and will have electric filed lines spreading out radially. E = kQ/r^2 The Standard model of particle physics says that the Photon is the force carrier for the Electromagnetic force, just like...
  17. R

    A Electron charge vs quark charge

    I have been trying to understand some of the basic differences in the fundamental nature of leptons and quarks. One article on this issue compares leptons and quarks as "oranges vs apples" to which I basically agree except for one aspect. How can the charges of the quarks be 1/3 or 2/3 the...
  18. heavybuilder

    I Standard Model (Forces interacting with Matter)

    Not the best at physics but trying to understand the standard model. So can someone please tell me if this is right or not and if not, can you explain me why? Higgs bosons reacts with everything that has mass. Electromagnetic force reacts with everything that has charge. Weak force reacts with...
  19. S

    A A symmetric model for leptons

    This is a homework problem in a course in particle physics at Cornell University. Assume the Left Right Symmetric (LRS) model for leptons. The gauge group is GLR = SU(2)L×SU(2)R×U(1)X. The Standard Model group SU(2)L×U(1)Y has to be included in the LRS group. Namely, U(1)Y ⊂ SU(2)R×U(1)X. Find...
  20. mollwollfumble

    A My T-shirt and the Standard Model

    This T-shirt I bought at a physics conference displays the following equation. It looks like the Lagrangian of the Standard Model of particle physics but I only recognise lines 1 (electroweak) and 3 (Higgs mechanism). What are lines 2 and 4 and what is/isn't included? eg. are quarks, gluons...
  21. S

    A Covariant derivative in Standard Model

    The covariant derivative in standard model is given by Dμ = ∂μ + igs Gaμ La + ig Wbμ Tb + ig'BμY where Gaμ are the eight gluon fields, Wbμ the three weak interaction bosons and Bμ the single hypercharge boson. The La's are SU(3)C generators (the 3×3 Gell-Mann matrices ½ λa for triplets, 0...
  22. TAKEDA Hiroki

    I Double sided arrow notation in Dirac Field Lagrangian

    In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...
  23. C

    B Electroweak spontaneous symmetry breaking

    This is a question that I have tried to pose several times without any success but, anyway, I would like to try again for the very last time. Asume for a moment that EW-SSB (electroweak spontaneous symmetry breaking) actually happened in our early universe. Imagine that our Standard Model of...
  24. S

    A How do we know the spins of elementary particles?

    How do we know the spin of an elementary particle? For example, a fermion has spin 1/2; a photon has spin 1; and even the ficticious graviton has spin 2. How do we know these spins? In other words, how are these spins determined?
  25. ohwilleke

    I Do these equations have a non-trivial solution?

    I was reading the following article that tries to use some equations originally proposed by Pauli in 1951 to reason from one of two reasonably plausible axions that there are tight constraints on the fundamental particle content and mass spectrum of the Standard Model together with BSM...
  26. G

    A Divergent Diagrams in the Standard Model

    It is my understanding that the task of enumerating all of the divergent diagrams in a quantum field theory can be reduced to analyzing a hand full of diagrams (well, at the moment I know that this is at least true for QED and phi^4 theory), and that all other divergent diagrams are divergent...
  27. Sophrosyne

    I Why are gluons considered to be elementary particles?

    Gluons are often depicted as fundamental particles in the Standard Model. But in looking at their mechanism, it seems they are not really fundamental particles in the sense that they are fundamental, indivisible, building blocks. They are mesons- a composite quark-antiquark pair, where their...
  28. S

    A Bar on a fermion field, arrows on fermion lines and particle-antiparticle nature of a fermion

    This question is about the use of bar on a fermionic field in a Lagrangian, the use of arrows on external fermion lines and the particle-antiparticle nature of a fermion. For illustration of my question, I will use the following the charged-current interaction of the Standard model...
  29. S

    A Deducing decay processes and Feynman diagrams using Lagrangian and conservation laws

    The decay processes of the ##W## bosons are completely governed by the charged current interaction terms of the Standard model: $$\mathcal{L}_{cc} = ie_{W}\big[W_{\mu}^{+}(\bar{\nu}_{m}\gamma^{\mu}(1-\gamma_{5})e_{m} + V_{mn}\bar{u}_{m}\gamma^{\mu}(1-\gamma_{5})d_{n})\\...
  30. smodak

    Particle The Standard Model in a Nutshell - Goldberg

    Just found this new book on amazon. Looks interesting. I purchased. The TOC, Preface, and intro could be found here I wish they included a sample chapter as well (the book in not cheap), but I...
  31. L

    Other Graduate Research topic involving QFT and General Relativity

    Last year I finished the undergraduate course in Mathematical Physics. This year, more precisely in March, I'm going to start the graduate course to acquire a master's degree in Physics. Now, for this course I must choose a research topic and find an advisor. This is being a little bit...
  32. Q

    Unruh Effect for Standard Model Fields

    I have seen the derivation for Unruh radiation for a massless, non-interacting scalar field (Carroll). Are there interesting differences that arise for more realistic standard model cases. For example, what does QCD look like for an accelerating observer? Any papers that detail this would be...
  33. S

    I Local Gauge invariance

    Hello! Can someone explain to me what exactly a local gauge invariance is? I am reading my first particle physics book and it seems that putting this local gauge invariance to different lagrangians you obtain most of the standard model. The math makes sense to me, I just don't see what is the...
  34. john baez

    Insights Struggles with the Continuum - Conclusion - Comments

    john baez submitted a new PF Insights post Struggles with the Continuum - Conclusion Continue reading the Original PF Insights Post.
  35. john baez

    Insights Struggles with the Continuum - Part 7 - Comments

    john baez submitted a new PF Insights post Struggles with the Continuum - Part 7 Continue reading the Original PF Insights Post.
  36. A

    I Is the SM of particles physics and Cosmology SM

    I'm in a deep discussion with a friend. He says that the Standard Model of particle physics is actually known by Standard Model of cosmology and that both are the same and that the SM of particle physics is in the Minkousky geometry.... I disagree about this, I do think that the SM of particle...
  37. mfb

    Insights LHC Part 4: Searching for New Particles and Decays - Comments

    mfb submitted a new PF Insights post LHC Part 4: Searching for New Particles and Decays Continue reading the Original PF Insights Post.
  38. scientepid

    I How can you visualize the Higgs field, or can you?

    Just when I thought I had finally wrapped my brain around relativity, Quantum theory took off. Then the Higgs Boson was discovered. How does the Higgs field under-pin relativity, namely space-time? How is the Higgs field distributed? Does it have curvature like space time, or is omnipresent...
  39. F

    Pierre Ramond-Journeys Beyond the Standard Model

    Homework Statement I want to diagonalize the quadratic form $$ m_0((m_u+m_d)\pi^3\pi^3+\frac{2}{\sqrt{3}}(m_u-m_d)\pi^3\pi^8+\frac{1}{3}(m_u+m_d+4m_s)\pi^8\pi^8)$$ which can be found under equation 5.47, in order to get the mass of the η and ##\pi^0## pions. This quadratic form is produced by...
  40. dschwie

    Gravity and massless particles

    Just finished reading Sean Carroll's "The Higgs Boson and Beyond". I would be grateful if someone could explain how gravity, which I understand to be a function of mass, can interact with massless particles as evidenced by the phenomenon of gravitational lensing. I understand that gravity is a...
  41. T

    I Ratio of abundance of sub-atomic particles in the universe?

    I was wondering if there is a current hypothesis about the quantities of which matter particles were created? I'm not completely au fait with the standard model, but I've seen the picture...
  42. Samy_A

    Particle Books about the Standard Model (with math)

    I've been trying to learn more about the standard model. Leonard Susskind's lectures have been very helpful for SR, GR and QM. His lectures about the standard model are interesting, I learned a lot, no question. But he doesn't really cover in any depth the mathematical side of it. He mentions...
  43. unknown1111

    A Computing the pole mass from a given MS mass?

    Given a Yukawa coupling as a function of scale and a vev, how can I compute the corresponding pole mas? Understandably most paper explain how from a measured pole mass one can compute the running mass, for example, Eq. 19 here. However I want to compute the pole mass from the running mass. In...
  44. unknown1111

    Top quark mass mt at energy scales μ<mt?

    Does it make sense to talk about the top mass at energies below mt, although in all processes the corresponding energy scale is above mt because of the rest mass energy of the top quark? Using an effective field theory approach, the top quark decouples at energies below the top quark mass and...
  45. thegirl

    Basic interactions in the Standard Model

    Hi, Is there a list of basic interactions in the standard model? Does anyone know where I can find this list of basic interactions in the standard model?
  46. T

    Total mass-energy v nature of forces, particles

    What does the standard model have to say about the relationship between the total mass-energy of the universe and the characteristics of forces and force-carrier particles? That is, if the total mass-energy were different, would the nature, strength, … of the forces and force-carrier particles...

    13 TeV Collisions at the LHC!

    Today is an exciting day, for today will see a new record for the highest energy collisions at the LHC - stable 13 TeV collisions for new physics, signalling the start of the new physics program at the LHC! There are a few ways you can keep track of progress throughout the day. The LHC status...
  48. U

    Why don't a charm-anticharm meson decay to pair of leptons?

    If you consider the ##\chi_0 ## with a mass of ## 3.4 GeV/c^2## meson, why doesn't it decay to a pair of charged leptons? Technically it is possible though the weak interaction (Z boson) or EM interaction, right? Is it because it is so heavily suppressed because the strong interactions are...
  49. B

    Question on the Standard Model

    I read in a magazine (namely Scientific American) that the Standard Model successfully combines Quantum Mechanics with General Relativity, but I also remember reading in The Elegant Universe that the Standard Model fails to do so. What's true and what's not?