Physics beyond the Standard Model

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Beyond the Standard Model
CMS Higgs-event.jpg
Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
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 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.

Contents

Problems with the Standard Model [edit]

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

The Standard Model of elementary particles

Experimental observations not explained [edit]

There are experimental observations of nature that the Standard Model does not adequately explain:

  • Gravity. The standard model does not explain gravity. Moreover, it is incompatible with the most successful theory of gravity to date, general relativity.[3]
  • Dark matter and dark energy. Cosmological observations tell us the standard model explains about 4% of the energy present in the universe. Of the missing 96%, about 24% should be dark matter, which would behave just like other matter, but which only interacts weakly with the standard model fields. The rest should be dark energy, a constant energy density for the vacuum. Attempts to explain dark energy in terms of vacuum energy of the standard model lead to a mismatch of 120 orders of magnitude.[4]
  • Neutrino masses. According to the standard model, 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 one another as the universe cooled.

Theoretical predictions not observed [edit]

Observation at particle colliders of all of the particles predicted by the Standard Model has been confirmed. The Higgs boson 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 125 GeV/c2 and 126 GeV/c2,[5] although simple extensions to the Standard Model allow for a mass between 185 GeV/c2 and about 250 GeV/c2. On July 4, 2012, CERN scientists using the Large Hadron Collider announced the discovery of a particle consistent with the Higgs boson; it has not yet been formally identified as being the Higgs boson.

Theoretical problems [edit]

Some features of the standard model are added in an ad hoc way. These are not problems 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.
  • Time-Reversal Violation The Stanford BaBar data observed Time-Reversal Violation in the B Meson System. The rule of symmetric activity in relation to time has been a foundational concept. Using data from the nonzero results represent the first direct observation of T violation through the exchange of initial and final states in transitions that can only be connected by a T-symmetry transformation. BABAR is a multi-year particle physics experiment designed to study some of the most fundamental questions about the universe by exploring its smallest and most basic constituents – elementary particles. [6]
  • BaBar Data Suggests Possible Flaws in the Standard Model - Results from a BaBar experiment may suggest a surplus over Standard Model predictions of a type of particle decay called “B to D-star-tau-nu.” In this, an electron and positron collide, resulting in a B meson and an antimatter B-bar meson, which then decays into a D meson and a tau lepton as well as a smaller antineutrino. While the level of certainty of the excess (3.4 sigma in statistical language) is not enough to claim a break from the Standard Model, the results are a potential sign of something amiss and are likely to impact existing theories, including those attempting to deduce the properties of Higgs bosons. [7]

Grand unified theories [edit]

Main article: Grand Unified Theory

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 1016 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.[8] 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).[9]

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,[10] and instability of the proton.[11] Neither of which have been observed, and this absence of observation puts limits on the possible GUTs.

Supersymmetry [edit]

Main article: supersymmetry

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 may not be powerful enough to produce them.

Neutrinos [edit]

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.[12] 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.[13] This necessitates an extension of the standard model, which not only needs to explain how neutrinos get their mass, but also why the mass is so tiny.[14]

One approach to add masses to the neutrinos, the so-called seesaw mechanism, 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 unpredictable. The standard model fermion masses differ by many orders of magnitude; the Dirac neutrino mass has at least the same uncertainty. The Majorana mass for the right-handed neutrinos should arise through the Standard Model Higgs and is therefore expected to be tied to some energy scale of new physics beyond the standard model.[15] Therefore, any process involving right-handed neutrinos will be suppressed at low energies. The correction due to these suppressed processes effectively gives the left-handed neutrinos a mass that is inversely proportional to the right-handed Majorana mass, a mechanism known as the see-saw.[16] 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. However, due to the uncertainty in the Dirac neutrino masses, the right-handed neutrino masses can lie anywhere. For example, they could be as light as keV and be dark matter,[17] they can have a mass in the LHC energy range[18][19] and lead to observable lepton number violation,[20] or they can be near the GUT scale, linking the right-handed neutrinos to the possibility of a grand unified theory.[21][22]

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.[23] 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.[24]

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.[25]

Theories of everything [edit]

Theory of everything [edit]

Main article: Theory of everything

Theoretical physics continues to strive toward a theory of everything, a theory that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle. In practical terms the immediate goal in this regard is to develop a theory which would unify the Standard Model with General Relativity in a theory of quantum gravity. Additional features, such as overcoming conceptual flaws in either theory or accurate prediction of particle masses, would be desired. The challenges in putting together such a theory are not just conceptual - they include the experimental aspects of the very high energies needed to probe exotic realms.

Several notable attempts in this direction are supersymmetry, string theory, and loop quantum gravity.

String theory [edit]

Main article: 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 think 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 thought by some to be promising candidates to the mathematical unification of quantum field theory and general relativity, requiring less drastic changes to existing theories.[26] However recent work places stringent limits on the putative effects of quantum gravity on the speed of light, and disfavours some current models of quantum gravity.[27]

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 by physicists Brian Greene and Stephen Hawking. Though a full mathematical description is not yet known, solutions to the theory exist for specific cases.[28] 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.[29][30]

See also [edit]

References [edit]

  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. ^ A. O. Sushkov, W. J. Kim, and D. A. R. Dalvit and S. K. Lamoreaux, "New Experimental Limits on Non-Newtonian Forces in the Micrometer Range", Phys. Rev. Lett. 107, 171101 (2011) DOI: 10.1103/PhysRevLett.107.171101 (the first sentence of the paper reads: "It is remarkable that two of the greatest successes on 20th century physics, General Relativity and the Standard Model, appear to be fundamentally incompatible.") http://arxiv.org/pdf/1108.2547.pdf. But see John F. Donoghue, "The effective field theory treatment of quantum gravity" (Presented at the Sixth International School on Field Theory and Gravitation, Petropolis, Brazil, April 2012, to be published in the proceedings 2012) ("One can find thousands of statements in the literature to the effect that “general relativity and quantum mechanics are incompatible”. These are completely outdated and no longer relevant. Effective field theory shows that general relativity and quantum mechanics work together perfectly normally over a range of scales and curvatures, including those relevant for the world that we see around us. However, effective field theories are only valid over some range of scales. General relativity certainly does have problematic issues at extreme scales. There are important problems which the effective field theory does not solve because they are beyond its range of validity. However, this means that the issue of quantum gravity is not what we thought it to be. Rather than a fundamental incompatibility of quantum mechanics and gravity, we are in the more familiar situation of needing a more complete theory beyond the range of their combined applicability. The usual marriage of general relativity and quantum mechanics is fine at ordinary energies, but we now seek to uncover the modifications that must be present in more extreme conditions. This is the modern view of the problem of quantum gravity, and it represents progress over the outdated view of the past.") http://arxiv.org/pdf/1209.3511v1.pdf
  4. ^ Krauss, Lawrence. A Universe from Nothing. AAI Conference, 2009.
  5. ^ Taylor, Lucas (2012-07-04). "Observation of a New Particle with a Mass of 125 GeV". CMS Public Website. CERN. 
  6. ^ Multiple Authors. "Observation of Time-Reversal Violation in the B0 Meson System". 
  7. ^ Multiple Authors. "Evidence for an excess of B -> D(*) Tau Nu decays". 
  8. ^ Peskin, Michael Edward; Schroeder, Daniel V. (1995). An introduction to quantum field theory. Addison-Wesley. pp. 786–791. ISBN 978-0-201-50397-5. 
  9. ^ Buchmüller (2002). "Neutrinos, Grand Unification and Leptogenesis". arXiv:hep-ph/0204288v2 [hep-ph].
  10. ^ Milstead, D.; Weinberg, E.J. (2009). "Magnetic Monopoles". Particle Data Group. Retrieved 2010-12-20. 
  11. ^ Pran Nath; Pavel Fileviez Perez (2006). "Proton stability in grand unified theories, in strings, and in branes". arXiv:hep-ph/0601023v3 [hep-ph].
  12. ^ Peskin, Michael Edward; Schroeder, Daniel V. (1995). An introduction to quantum field theory. Addison-Wesley. pp. 713–715. ISBN 978-0-201-50397-5. 
  13. ^ K. Nakamura et al. (Particle Data Group) (2010). "Neutrino Properties". Particle Data Group. Retrieved 2010-12-20. 
  14. ^ Mohapatra, R. N.; Pal, P. B. (2004). Massive neutrinos in physics and astrophysics, second edition. World Scientific Lecture Notes in Physics, Vol. 60. ISBN 98123807101 Check |isbn= value (help). 
  15. ^ G. Senjanovic (2011). "Probing the Origin of Neutrino Mass: from GUT to LHC". arXiv:1107.5322 [hep-ph].
  16. ^ Yuval Grossman (2003). "TASI 2002 lectures on neutrinos". arXiv:hep-ph/0305245v1 [hep-ph].
  17. ^ Scott Dodelson; Lawrence M. Widrow (1993). "Sterile neutrinos as dark matter". Physical Review Letters 72: 17. arXiv:hep-ph/9303287.  Unknown parameter |class= ignored (help)
  18. ^ Peter Minkowski (1977). "mu --> e gamma at a Rate of One Out of 1-Billion Muon Decays?". Physics Letters B 67: 421. 
  19. ^ R.N. Mohapatra and G. Senjanovic (1980). "Neutrino mass and spontaneous parity nonconservation". Physical Review Letters 44: 912. 
  20. ^ W.-Y. Keung and G. Senjanovic (1983). "Majorana Neutrinos And The Production Of The Right-handed Charged Gauge Boson". Physical Review Letters 50: 1427. 
  21. ^ M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, ed. by D. Freedman et al., North Holland (1979).
  22. ^ S.L. Glashow, in Quarks and Leptons, Cargese 1979, ed. by M. Levy, Plenum, NY (1979).
  23. ^ Guido Altarelli (2007). "Lectures on Models of Neutrino Masses and Mixings". arXiv:0711.0161 [hep-ph].
  24. ^ Buchmüller (2002). "Neutrinos, Grand Unification and Leptogenesis". arXiv:hep-ph/0204288v2 [hep-ph].
  25. ^ Hitoshi Murayama (2007). "Physics Beyond the Standard Model and Dark Matter". arXiv:0704.2276v1 [hep-ph].
  26. ^ L. Smolin (2001). Three Roads to Quantum Gravity. Basic Books. ISBN 0-465-07835-4. 
  27. ^ 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. 
  28. ^ 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. 
  29. ^ 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. 
  30. ^ 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 [edit]

External resources [edit]

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