Physics beyond the Standard Model

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), and 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. A large share of the published output of theoretical physicists consists of proposals for various forms of "Beyond the Standard Model" new physics proposals that would modify the Standard Model in ways subtle enough to be consistent with existing data, yet address its imperfections materially enough to predict non-Standard Model outcomes of new experiments that can be proposed.

Phenomena not explained

The Standard Model is inherently an incomplete theory. There are fundamental physical phenomena in nature that the Standard Model does not adequately explain:

• Quantum gravity. The standard model does not explain gravity. The approach of simply adding a graviton to the Standard Model does not recreate what is observed experimentally without other modifications, as yet undiscovered, to the Standard Model. Moreover, the Standard Model is widely considered to be incompatible with the most successful theory of gravity to date, general relativity.
• Cosmic inflation. The early universe underwent an enormous and quick expansion that supercooled the cosmos. Following the inflationary period, the universe continued to expand, but at a slower rate. At the end of inflation the driving field converted its energy into particles, leading to a quark-soup phase of the universe. The hypothetical field thought to be responsible for inflation is called inflaton, but the detailed particle-physics mechanism and the nature of this hypothetical field is unknown.
• Dark matter. Assuming that general relativity and Lambda CDM are true, cosmological observations show that the Standard Model explains about 5% of the mass-energy present in the universe. About 26% should be dark matter (the remaining 69% being dark energy) which would behave just like other matter, but which only interacts weakly (if at all) with the Standard Model fields. Yet the Standard Model does not supply any fundamental particles that are good dark matter candidates (e.g. axions, WIMPs or primordial black holes).
• Dark energy. As mentioned, the remaining 69% of the universe's energy should consist of the so-called 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.
• Neutrino oscillations. According to the Standard Model, neutrinos do not oscillate. However, experiments and astronomical observations have shown that neutrino oscillation does occur. These are typically explained by postulating that neutrinos have mass. Neutrinos do not have mass in the Standard Model, and 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 and it is not clear if the neutrino masses would arise in the same way that the masses of other fundamental particles do in the Standard Model. There are also other extensions of the Standard Model for neutrino oscillations which do not assume massive neutrinos, such as Lorentz-violating neutrino oscillations.
• Matter–antimatter asymmetry. The universe is made out of mostly matter. However, the Standard Model predicts that matter and antimatter should have been created in (almost) equal amounts if the initial conditions of the universe did not involve disproportionate matter relative to antimatter. The Standard Model can incorporate baryogenesis through sphalerons in a thermodynamic imbalance during the early universe, though the amount of net baryons (and leptons) thus created may not be sufficient to account for the present baryon asymmetry. Thus, there might be no mechanism in the Standard Model to sufficiently explain this asymmetry.

Experimental results not explained

No experimental result is accepted as definitively contradicting the Standard Model at the 5 σ level, widely considered to be the threshold of a discovery in particle physics. Because every experiment contains some degree of statistical and systemic uncertainty, and the theoretical predictions themselves are also almost never calculated exactly and are subject to uncertainties in measurements of the fundamental constants of the Standard Model (some of which are tiny and others of which are substantial), it is to be expected that some of the hundreds of experimental tests of the Standard Model will deviate from it to some extent, even if there were no new physics to be discovered.

At any given moment there are several experimental results standing that significantly differ from a Standard Model-based prediction. In the past, many of these discrepancies have been found to be statistical flukes or experimental errors that vanish as more data has been collected, or when the same experiments were conducted more carefully. On the other hand, any physics beyond the Standard Model would necessarily first appear in experiments as a statistically significant difference between an experiment and the theoretical prediction. The task is to determine which is the case.

In each case, physicists seek to determine if a result is merely a statistical fluke or experimental error on the one hand, or a sign of new physics on the other. More statistically significant results cannot be mere statistical flukes but can still result from experimental error or inaccurate estimates of experimental precision. Frequently, experiments are tailored to be more sensitive to experimental results that would distinguish the Standard Model from theoretical alternatives.

Some of the most notable examples include the following:

• B meson decay etc. – results from a BaBar experiment may suggest a surplus over Standard Model predictions of a type of particle decay ( B → D^(*) τ⁻ ν_τ ). In this, an electron and positron collide, resulting in a B meson and an antimatter B meson, which then decays into a D meson and a tau lepton as well as a tau antineutrino. While the level of certainty of the excess (3.4 σ in statistical jargon) is not enough to declare a break from the Standard Model, the results are a potential sign of something amiss and are likely to affect existing theories, including those attempting to deduce the properties of Higgs bosons. In 2015, LHCb reported observing a 2.1 σ excess in the same ratio of branching fractions. The Belle experiment also reported an excess. In 2017 a meta analysis of all available data reported a cumulative 5 σ deviation from SM.
• Neutron lifetime puzzle – Free neutrons are not stable but decay after some time. Currently there are two methods used to measure this lifetime ("bottle" versus "beam") that give different values not within each other's error margin. Currently the lifetime from the bottle method is at ${\displaystyle {\tau }_n=877.75s}$ with a difference of 10 seconds below the beam method value of ${\displaystyle {\tau }_n=887.7s}$. This problem may be solved by taking into account neutron scattering which decreases the lifetime of the involved neutrons. This error occurs in the bottle method and the effect depends on the shape of the bottle – thus this might be a bottle method only systematic error.

Theoretical predictions not observed

Observation at particle colliders of all of the fundamental particles predicted by the Standard Model has been confirmed. The Higgs boson is predicted by the Standard Model's explanation of the Higgs mechanism, which describes how the weak SU(2) gauge symmetry is broken and how fundamental particles obtain mass; it was the last particle predicted by the Standard Model to be observed. On July 4, 2012, CERN scientists using the Large Hadron Collider announced the discovery of a particle consistent with the Higgs boson, with a mass of about 126 GeV/c². A Higgs boson was confirmed to exist on March 14, 2013, although efforts to confirm that it has all of the properties predicted by the Standard Model are ongoing.

A few hadrons (i.e. composite particles made of quarks) whose existence is predicted by the Standard Model, which can be produced only at very high energies in very low frequencies have not yet been definitively observed, and "glueballs" (i.e. composite particles made of gluons) have also not yet been definitively observed. Some very low frequency particle decays predicted by the Standard Model have also not yet been definitively observed because insufficient data is available to make a statistically significant observation.

Unexplained relations

• Koide formula – an unexplained empirical equation remarked upon by Yoshio Koide in 1981, and later by others. It relates the masses of the three charged leptons: ${\displaystyle Q=\frac{m_e+m_{\mu }+m_{\tau }}{(\sqrt{m_e}+\sqrt{m_{\mu }}+\sqrt{m_{\tau }}{)}^2}=0.666661(7)\approx \frac{2}{3}}$. The Standard Model does not predict lepton masses (they are free parameters of the theory). However, the value of the Koide formula being equal to 2/3 within experimental errors of the measured lepton masses suggests the existence of a theory which is able to predict lepton masses.
• The CKM matrix, if interpreted as a rotation matrix in a 3-dimensional vector space, "rotates" a vector composed of square roots of down-type quark masses ${\displaystyle (\sqrt{m_d},\sqrt{m_s},\sqrt{m_b})}$ into a vector of square roots of up-type quark masses ${\displaystyle (\sqrt{m_u},\sqrt{m_c},\sqrt{m_t})}$, up to vector lengths, a result due to Kohzo Nishida.
• The sum of squares of the Yukawa couplings of all Standard Model fermions is approximately 0.984, which is very close to 1. To put it another way, the sum of squares of fermion masses is very close to half of squared Higgs vacuum expectation value. This sum is dominated by the top quark.
• The sum of squares of boson masses (that is, W, Z, and Higgs bosons) is also very close to half of squared Higgs vacuum expectation value, the ratio is approximately 1.004.
• Consequently, the sum of squared masses of all Standard Model particles is very close to the squared Higgs vacuum expectation value, the ratio is approximately 0.994.

It is unclear if these empirical relationships represent any underlying physics; according to Koide, the rule he discovered "may be an accidental coincidence".

Theoretical problems

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 the ad hoc insertions), but they imply a lack of understanding. These contrived features have motivated theorists to look for more fundamental theories with fewer parameters. Some of the contrivances 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 particle 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. The problem cannot be formulated in the strict context of the Standard Model, for the Higgs mass cannot be calculated. In a sense, the problem amounts to the worry that a future theory of fundamental particles, in which the Higgs boson mass will be calculable, should not have excessive fine-tunings.
• Number of parameters – the Standard Model depends on 19 parameter numbers. 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 or calculating particle masses, such as in asymptotic safety scenarios.
• Strong CP problem – it can be argued theoretically that the Standard Model should contain a term in the strong interaction that breaks CP symmetry, causing slightly different interaction rates for matter vs. antimatter. Experimentally, however, no such violation has been found, implying that the coefficient of this term – if any – would be suspiciously close to zero.