Physics beyond the Standard Model

Physics beyond the Standard Model

Physics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy.[1] Another problem lies within the mathematical framework of the Standard Model itself – the Standard Model is inconsistent with that of general relativity to the point that one or both theories break down in their descriptions under certain conditions (for example within known space-time singularities like the Big Bang and black hole event horizons).

Theories that lie beyond the Standard Model include various extensions of the standard model through supersymmetry, such as the Minimal Supersymmetric Standard Model (MSSM) and Next-to-Minimal Supersymmetric Standard Model (NMSSM), or entirely novel explanations, such as string theory, M-theory and extra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the "best step" towards a Theory of Everything, can only be settled via experiments and is one of the most active areas of research in both theoretical and experimental physics.


Problems with the Standard Model

Despite being the most successful theory of particle physics to date, the Standard Model is not perfect.[2]

Experimental observations not explained

There are a number of experimental observations of Nature for which the Standard Model does not give an adequate explanation.

  • Gravity. The standard model does not provide an explanation of gravity. Moreover it is incompatible with the most successful theory of gravity to date, general relativity.
  • Dark matter and dark energy Cosmological observations tell us that the standard model is able to explain only about 4% of the energy present in the universe. Of the missing 96% percent about 24% should be dark matter, i.e. matter that behaves just like the other matter we know, but which interacts only weakly with the standard model fields. The rest should be dark energy, a constant energy density for the vacuum. Attempts to explain the dark energy in terms of vacuum energy of the standard model lead to a mismatch of 120 orders of magnitude.
  • Neutrino masses According to the standard model the neutrinos are massless particles. However, neutrino oscillation experiments have shown that neutrinos do have mass. Mass terms for the neutrinos can be added to the standard model by hand, but these lead to new theoretical problems. (For example, the mass terms need to be extraordinarily small).
  • Matter–antimatter asymmetry The universe is made out of mostly matter. However, the standard model predicts that matter and anti-matter should have been created in (almost) equal amounts, which would have annihilated each other as the universe cooled.

Theoretical predictions not observed

Most of the particles predicted by the Standard Model have been observed at particle colliders. The exception is the Higgs boson, which is predicted by the Standard Model's explanation of the Higgs mechanism that describes how the weak SU(2) gauge symmetry is broken and how fundamental particles obtain mass. Experimental searches have determined that if the Standard Model is correct and the Higgs boson exists, then it most likely has a mass between 114 GeV/c2 and 157 GeV/c2,[3] although simple extensions to the Standard Model allow for a mass between 185 GeV/c2 and about 250 GeV/c2. If the Higgs boson exists, experiments at the CERN Large Hadron Collider should find it; if the Higgs boson is not found at the LHC, then SU(2) breaking and mass generation must involve physics beyond the Standard Model.

Theoretical problems

Some features of the standard model are added in an ad hoc way. These are not a problem per se (i.e. the theory works fine with these ad hoc features), but they imply a lack of understanding. These ad hoc features have motivated theorists to look for more fundamental theories with fewer parameters. Some of the ad hoc features are:

  • Hierarchy problem The standard model introduces particle masses through a process known as spontaneous symmetry breaking caused by the Higgs field. Within the standard model, the mass of the Higgs gets some very large quantum corrections due to the presence of virtual particles (mostly virtual top quarks). These corrections are much larger than the actual mass of the Higgs. This means that the bare mass parameter of the Higgs in the standard model must be fine tuned in such a way that almost completely cancels the quantum corrections. This level of fine tuning is deemed unnatural by many theorists.
  • Strong CP problem Theoretically it can be argued that the standard model should contain a term that breaks CP symmetry —relating matter to antimatter— in the strong interaction sector. Experimentally, however, no such violation has been found, implying that the coefficient of this term is very close to zero. This fine tuning is also considered unnatural.
  • Number of parameters The standard model depends on 19 numerical parameters. Their values are known from experiment, but the origin of the values is unknown. Some theorists have tried to find relations between different parameters, for example, between the masses of particles in different generations.

Grand unified theories

The standard model has three gauge symmetries; the colour SU(3), the weak isospin SU(2), and the hypercharge U(1) symmetry, corresponding to the three fundamental forces. Due to renormalization the coupling constants of each of these symmetries vary with the energy at which they are measured. Around 1019 GeV these couplings become approximately equal. This has led to speculation that above this energy the three gauge symmetries of the standard model are unified in one single gauge symmetry with a simple group gauge group, and just one coupling constant. Below this energy the symmetry is spontaneously broken to the standard model symmetries.[4] Popular choices for the unifying group are the special unitary group in five dimensions SU(5) and the special orthogonal group in ten dimensions SO(10).[5]

Theories that unify the standard model symmetries in this way are called Grand Unified Theories (or GUTS), and the energy scale at which the unified symmetry is broken is called the GUT scale. Generically, grand unified theories predict the creation of magnetic monopoles in the early universe,[6] and instability of the proton.[7] Neither of which have been observed, and this absence of observation puts limits on the possible GUTs.


Supersymmetry extends the Standard Model by adding an additional class of symmetries to the Lagrangian. These symmetries exchange fermionic particles with bosonic ones. Such a symmetry predicts the existence of supersymmetric particles, abbreviated as sparticles, which include the sleptons, squarks, neutralinos and charginos. Each particle in the Standard Model would have a superpartner whose spin differs by 1/2 from the ordinary particle. Due to the breaking of supersymmetry, the sparticles are much heavier than their ordinary counterparts; they are so heavy that existing particle colliders would not be powerful enough to produce them. However, some physicists believe that sparticles will be detected when the Large Hadron Collider at CERN begins running.


In the standard model neutrinos have exactly zero mass. This is a consequence of the standard model containing only left handed neutrinos. With no suitable right handed partner it is impossible to add a renormalizible mass term to the standard model.[8] Measurements however indicated that neutrinos spontaneously change flavour, which implies that neutrinos have a mass. These measurements only give the relative masses of the different flavours. The best constraint on the absolute mass of the neutrinos comes from precision measurements of tritium decay, providing an upper limit 2 eV, which makes them at least five orders of magnitude lighter than the other particles in the standard model.[9] This means that extension of the standard model, not only need to explain how neutrinos get their mass, but also why it is so tiny.[10]

One approach to add masses to the neutrinos is to add right-handed neutrinos and have these couple to left-handed neutrinos with a Dirac mass term. The right-handed neutrinos have to be sterile, meaning that they do not participate in any of the standard model interactions. Because they have no charges the right-handed neutrinos can act as their own anti-particles, and have a Majorana mass term. Like the other Dirac masses in the standard model, the neutrino Dirac mass is expected to be generated through the Higgs mechanism, and is therefore expected to be of a similar order of magnitude as the other masses. The Majorana mass for the right-handed neutrinos should arise through a different method and is expect to be tied to some energy scale of new physics beyond the standard model.[11] Therefore, any process involving right-handed neutrinos will be suppressed at low energies. The correction due these suppressed processes, effectively give the left-handed neutrinos a mass that is inversely proportional to the right-handed Majorana mass, a mechanism known as the see-saw.[12] The presence of heavy right-handed neutrinos thereby explains both the small mass of the left-handed neutrinos, and the absence of the right-handed neutrinos in observations. To get effective neutrino masses in the observed range with Dirac masses similar to the other standard model masses, the right-handed neutrino masses must be near the GUT scale, linking the right-handed neutrinos to the possibility of a grand unified theory.[13]

The mass terms mix neutrinos of different generations. This mixing is parameterized by the PMNS matrix, which is the neutrino analogue of the CKM quark mixing matrix. Unlike the quark mixing, which is almost minimal, the mixing of the neutrinos appears to be almost maximal. This has led to various speculations of symmetries between the various generations that could explain the mixing patterns.[14] The mixing matrix could also contain several complex phases that break CP invariance, although there has been no experimental probe of these. These phases could potentially create a surplus of leptons over anti-leptons in the early universe, a process known as leptogenesis. This asymmetry could then at a later stage be converted in an excess of baryons over anti-baryons, and explain the matter-antimatter asymmetry in the universe.[15]

The light neutrinos cannot explain the missing dark matter, because they do not have enough mass. Moreover, simulations of structure formation show that they are too hot —i.e. their kinetic energy is large compared to their mass— while formation of structures similar to the galaxies in our universe requires cold dark matter. The simulations show that neutrinos can at best explain a few percent of the missing dark matter. The heavy sterile right-handed neutrinos, are however a possible candidate for a dark matter WIMP.[16]

Theories of Everything

String theory

Extensions, revisions, replacements, and reorganizations of the Standard Model exist in attempt to correct for these and other issues. String theory is one such reinvention, and many theoretical physicists believe that such theories are the next theoretical step toward a true Theory of Everything. Theories of quantum gravity such as loop quantum gravity and others are believed by some to be promising candidates to the mathematical unification of quantum field theory and general relativity, requiring less drastic changes to existing theories.[17] However a recent paper submitted to Nature places stringent limits on the putative effects of quantum gravity on the speed of light, and disfavours current models of quantum gravity.[18][19]

Among the numerous variants of String Theory, M-theory, whose mathematical existence was first proposed at a String Conference in 1995, is believed by many to be a proper "ToE" candidate, notably physicists Brian Greene and Stephen Hawking. Though a full mathematical description is not yet known, solutions to the theory exist for specific cases.[20] Recent works have also proposed alternate string models, some of which lack the various harder-to-test features of M-theory (e.g. the existence of Calabi–Yau manifolds, many extra dimensions, etc) including works by well-published physicists such as Lisa Randall.[21][22]

See also


  1. ^ J. Womersley (February 2005). "Beyond the Standard Model". Symmetry Magazine. Retrieved 2010-11-23. 
  2. ^ Lykken (2010). "Beyond the Standard Model". arXiv:1005.1676 [hep-ph]. 
  3. ^ "Higgs bosons: Theory and Searches". Particle Data Group. 
  4. ^ Peskin, Michael Edward; Schroeder, Daniel V. (1995). An introduction to quantum field theory. Addison-Wesley. pp. 786–791. ISBN 9780201503975. 
  5. ^ Buchmüller (2002). "Neutrinos, Grand Unification and Leptogenesis". arXiv:hep-ph/0204288v2 [hep-ph]. 
  6. ^ Milstead, D.; Weinberg, E.J. (2009). "Magnetic Monopoles". Particle Data Group. Retrieved 2010-12-20. 
  7. ^ Pran Nath; Pavel Fileviez Perez (2006). "Proton stability in grand unified theories, in strings, and in branes". arXiv:hep-ph/0601023v3 [hep-ph]. 
  8. ^ Peskin, Michael Edward; Schroeder, Daniel V. (1995). An introduction to quantum field theory. Addison-Wesley. pp. 713–715. ISBN 9780201503975. 
  9. ^ K. Nakamura et al. (Particle Data Group) (2010). "Neutrino Properties". Particle Data Group. Retrieved 2010-12-20. 
  10. ^ Wells (2009). "Lectures on Higgs Boson Physics in the Standard Model and Beyond". arXiv:0909.4541 [hep-ph]. 
  11. ^ Wells (2009). "Lectures on Higgs Boson Physics in the Standard Model and Beyond". arXiv:0909.4541 [hep-ph]. 
  12. ^ Yuval Grossman (2003). "TASI 2002 lectures on neutrinos". arXiv:hep-ph/0305245v1 [hep-ph]. 
  13. ^ Guido Altarelli; Ferruccio Feruglio (2004). "Models of Neutrino Masses and Mixings". arXiv:hep-ph/0405048v2 [hep-ph]. 
  14. ^ Guido Altarelli (2007). "Lectures on Models of Neutrino Masses and Mixings". arXiv:0711.0161 [hep-ph]. 
  15. ^ Buchmüller (2002). "Neutrinos, Grand Unification and Leptogenesis". arXiv:hep-ph/0204288v2 [hep-ph]. 
  16. ^ Hitoshi Murayama (2007). "Physics Beyond the Standard Model and Dark Matter". arXiv:0704.2276v1 [hep-ph]. 
  17. ^ L. Smolin, R. Sundrum (2001). Three Roads to Quantum Gravity. Basic Books. ISBN 0465078354. 
  18. ^ A. A. Abdo et al. (Fermi GBM/LAT Collaborations) (2009). "A limit on the variation of the speed of light arising from quantum gravity effects". Nature 462 (7271): 331. arXiv:0908.1832. Bibcode 2009Natur.462..331A. doi:10.1038/nature08574. PMID 19865083. 
  19. ^ A. A. Abdo et al. (Fermi GBM/LAT Collaborations) (2009). "Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510". arXiv:0908.1832 [astro-ph]. 
  20. ^ J. Maldacena, A. Strominger, E. Witten (1997). "Black hole entropy in M-Theory". Journal of High Energy Physics 1997 (12): 002. arXiv:hep-th/9711053. Bibcode 1997JHEP...12..002M. doi:10.1088/1126-6708/1997/12/002. 
  21. ^ L. Randall, R. Sundrum (1999). "Large Mass Hierarchy from a Small Extra Dimension". Physical Review Letters 83 (17): 3370–3373. arXiv:hep-ph/9905221. Bibcode 1999PhRvL..83.3370R. doi:10.1103/PhysRevLett.83.3370. 
  22. ^ L. Randall, R. Sundrum (1999). "An Alternative to Compactification". Physical Review Letters 83 (23): 4690–4693. arXiv:hep-th/9906064. Bibcode 1999PhRvL..83.4690R. doi:10.1103/PhysRevLett.83.4690. 

Further reading

  • L. Randall (2005). Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. HarperCollins. ISBN 0060531088. 

External resources

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