A Review of Fundamental Physics in 2012

LHC Discovers Standard Model Higgs Boson

The biggest story in physics in 2012 was the official discovery of a Higgs-like boson which over the course of the year has increasingly been confirmed to have the properties of the Standard Model Higgs boson with a mass of about 126 GeV.  Experimental data in 2012 has confirmed that it has a even parity and intrinsic spin of zero (as predicted), and that the decays that it produces are so far within the range of reasonable statistical and experimental error of the Standard Model Higgs boson (almost all within two sigma, properly calculated, and many closer), although not all of the data are precisely on the money of the Standard Model prediction (which they shouldn't be unless the data has been faked). 

A year or two of additional LHC data should be able to much more definitively confirm that the observed Higgs boson decays match those predicted by the Standard Model and make the mass of the Higgs boson to plus or minus about 0.1 GeV or so, a settled matter.  An additional year or two of LHC data should also rule out (or find) any additional Higgs bosons over a very broad range of masses (i.e. for all masses up to perhaps 600 GeV to more than 1 TeV, perhaps as much as ten times the Higgs boson mass discovered so far).

The observed mass of the Higgs boson is consistent with a universe that is at least "meta-stable" (i.e. has a predicted lifetime arising from quantum instability at least as long as its actual lifetime), and allows Standard Model calculations to remain "unitary" (i.e. compute probabilities that always add up to one for any given computation) to arbitrarily high energy levels, something that would not have been true for all possible Standard Model Higgs boson masses.

Thus, while the Standard Model Higgs boson discovery doesn't solve many unsolved problems in fundamental physics with a "why is nature this way?" character, it does solve most of the unsolved "how can we do physics calculations at extreme energies in a rigorous way?" problems of the Standard Model.

SUSY Looking Less Likely

The two experiments at the Large Hadron Collider have found no evidence of beyond the Standard Model physics despite the fact that the high energies it is testing are excluding many theories that had predicted new particles or new behavior of particles near the TeV scale.

Ongoing exclusions from collider physics, together with the tightening bounds of dark matter searches and neutrino physics, discussed below, in particular, are discouraging for proponents of Supersymmetry (SUSY) and string theory. 

While these theories have a variety of parameters and other "moving parts" that can be adjusted to put the new physics predicted by these theories beyond the range of experimental evidence, any supersymmetry theory that fits the LHC data must have a very high characteristic energy scale (e.g. in some high energy scale SUSY theories most superpartners of ordinary particles predicted under the theory might have masses of 8-20 TeV, with the lighest superpartners having masses of 1 TeV or more, and the theory may not conserve "R-partity" and hence lack the stable superpartner ground state which would otherwise have been a strong dark matter candidate).

SUSY theories with high characteristic energy scales should have theoretical consequences outside collider experiments (like a very heavy dark matter candidate and high rates of neutrinoless double beta decay) that don't seem to be supported by the new experimental evidence.  The non-collider experiment consequences of high energy scale SUSY may ultimately falisfy the theory entirely even though colliders themselves will never be large enough to rule out SUSY directly at all energy scales.

One can, of course, devise SUSY theories that have moving parts that evade these theoretical consequences, but the less "natural" a SUSY theory is, the less well motivated it is as a true theory of nature supported by experimental evidence.  Everyone who devised SUSY expected when the theory was first formulated that it would have been experimentally visible at the energies present at the LHC so far in the experiment, even if they have since revised their opinions.

The problems which motivated SUSY: like the hierarchy problem, the nature of symmetry breaking, and the issue of whether the coupling constants converge until they form a single common force at a "grand unification" energy level are problems that nature doesn't seem too concerned to answer anytime sooon.

Technicolor Dead

SUSY, of course, is not alone.  "Technicolor" models, for example, which were invented to create a Higgsless version of the Standard Model, are pretty much dead now due to the LHC discovery of a Higgs boson.  Technicolor was a theoretical Plan B that turned out not to be necessary.

Dark Matter And Modified Gravity

Dark Matter Effects Are Real, Whatever Their Source, And Unexplained

The universe we observe in our telescopes does not behave the way that the gravitational effects of General Relativity (which are mostly equivalent to Newtonian gravity to the level of precision we can observe with our telescopes) predict that it should.  Galaxies don't fling particles away as they should if their mass were close to the sum of the stars we can observe and central black holes and planetary stuff that we know is there but can't see.  The disparity between masses as measured via relativistic lensing effects and masses estimated from observed luminous material is even greater for galactic clusters.

There are only two possible solutions to this problem, one or both of which must be true.  Either there is a lot of exotic non-baryonic dark matter out there of a type never seen in particle colliders, or the laws of gravity must be different than they are in general relativity, particularly in weak gravitational fields.

New more powerful telescopes and computational capacity is making it possible to precisely quantify the discrepency between the laws of general relativity applied to luminous matter and what we observe in our telescopes.  But, these observations together with direct searches for particles that have the right properties, have ruled out the easiest dark matter theories.  These observations, particularly in galactic clusters, have also ruled out the simplest theories in which all of these effects come from modified gravitational laws.

Direct Searches Find No Dark Matter Particles And Colliders Exclude What Can't Be Seen Directly

Direct searches for dark matter have had contradictory results.  A couple of claimed to see something, but the somethings that they have seen have had different properties.  Other searches have seen nothing at all, effectively ruling out the existence of weakly interacting massive particles of dark matter in the 10 GeV and up mass range. 

Yet, collider tests such as the LHC and LEP have ruled out anything like a weakly interacting neutrino as masses of less than 45 GeV.  SUSY dark matter candidates have been ruled out by the LHC and other collider experiments at masses of 100 GeV and less, as a general matter, and at masses of 600 GeV and less for specific candidates in specific versions of SUSY (such as minimal SUSY). The LHC has also ruled out additional Higgs bosons of the types predicted by SUSY theories to relatively high masses.  No particle discovered so far in particle colliders like the LHC and its predecessors is a good fit to any dark matter particle that could fit the astronomy evidence.

Dark matter theories suffer the curse of being overconstrained. They need particles with properties that aren't found in any kind of matter we have ever observed despite considering extreme situations that have produced all sorts of exotic particles that don't exist in nature. 

Essentially all possible non-baryonic dark matter candidates (other than ordinary neutrinos or perhaps neutrino condensates) are strongly disfavored by some experimental evidence, and there aren't enough neutrinos in the universe to give rise to all of the effects attributed to dark matter.

CDM Models Simulations Don't Reproduce Observed Large Scale Structure In The Universe

Meanwhile, a variety of experimental results, most notably the large scale structure of the universe, appear to be inconsistent with a "cold dark matter" scenario in which dark matter effects observed in nature are due to heavy WIMPS.  Detailed simulations have established that if cold dark matter existed, the large scale structure of the universe would be far more fine grained with far more dwarf galaxies, for example.  The clarity with which this data proved that CDM is a false hypothesis reached critical mass in 2012, although it will take a number of years for this development to be widely assimilated by researchers in the field.

Hot neutrino dark matter also seems inconsistent with the data as well.  Similar simulations show that hot dark matter would virtually eliminate the large scale structure of the universe and reduce it to a homogeneous, amorphous goo.

But "warm dark matter" in the KeV mass range remains consistent with the observed large scale structure of the universe.  If you simulate the formation processs of the universe after its initial moments in high powered computers and add the special sauce of warm dark matter (defined more by speed than the mass assumed to move at that speed in the model), then you get a level of large scale structure in the universe similar to what we actually see, not the goo you see with hot dark matter, or the excessive levels of fine scaled structure you see with cold dark matter.

But, while "warm dark matter" in the KeV range is a hypothesis that fits with the evidence from the large scale structure of the universe, collider experiments and neutrino mass experiments have come close to ruling out the existence of fundamental particles (or composite particles made up of fundamental particles) with masses in that range, or even remotely close.

There are also no good dynamical theories that explain the very consistent shapes of dark matter halos observed in galaxies with dark matter.  Why do galaxies of particular shapes always have the same shaped dark matter halos?  Dark matter theories that stuggle to explain halo shapes even with multiple parameters still perform worse than single parameter modified gravity models in predicting the behavior of observed galaxies.

In particular, cold dark matter theories do not, as a rule, predict that dark matter will be observed with the distribution that must be inferrred from how visible matter in galaxies acts.

Even if dark matter and not modified gravity models are correct, any successful dark matter theory needs to be able to explain the observed data with no more parameters than the modified gravity models, and no dark matter theory has successfully managed this so far.

Sterile Neutrinos?

The Standard Model would admit without great injustice, neutrinos that do not interact via the weak interaction because they have right handed partity, which are called "sterile neutrinos."

Since particles decay via the weak force, there would be no missing matter atributable to sterile neutrinos in collider experiments or radioactive decay experiments. Direct dark matter detection experiments aren't designed to see particles with masses of far less than 1 GeV and so couldn't see any form of warm or hot dark matter. Neutrino detection experiments would either ignore sterile neutrinos entirely, to the extent that they rely on weak force interactions, or would be unable to distinguish "fertile neutrinos" from "sterile neutrinos" to the extent that they rely on contact interactions. So there are reasons why sterile neutrinos would not have been detected directly so far.

But, there is also no positive experimental evidence for the existence of sterile neutrinos (as distinct from dark matter generally). And, there is no precedent for a fermion (or any massive particle, for that matter) that interacts via gravity but not via the weak force, the electromagnetic force, or the strong force. Also, all other Standard Model particles have the same mass regardless of their parity (left handed or right handed intrinsic spins). If this was true, sterile neutrinos would be too light to be the main source of dark matter which is the only experimental motivation for sterile dark matter to exist.

Non-interacting massive sterile neutrinos in the KeV range might help solve warm dark matter problems, but only if one could determine the nature of sterile neutrino leptogenesis and discern how they come to be arranged in the halos in which dark matter seems to arrange itself via gravity alone.

If sterile neutrino leptogenesis took place only a unification scale energies in the early universe, or perhaps also in extreme high energy interactions of the kinds found in galactric clusters, this could explain a relative absence of this kind of dark matter in our local solar system vicinity. And, perhaps the mechanisms that form them, or some analog to the weak force applicable only to right handed particles and much rarer than the observed weak force, could explain why the much lighter particles have KeV sized particle scale momentums. Still, on balance, 2012 ended with less support for sterile neutrinos than there was at the beginning of the year.

Controversial Observations And Calculations Claim Local Dark Matter Is Ruled Out.

One study looking for the gravitational impact of dark matter in the vicinity of the solar system claimed to rule it out, although another study cast doubt on those conclusions.

Controversial Papers Argue That General Relativity Effects Are Larger Than Usually Assumed.

There are also mixed opinions on whether the effects of general relativity are adequately reflected in common models of galactric rotation curves.  Errors in these calculations could significantly overestimate the amount of dark matter that the universe must have to fit astronomy observations.

Dim Matter Discoveries Continue

A steady trickle of results continue to show that material parts of what was previously assumed to be non-baryonic dark matter is, in fact, merely "dim" ordinary matter such as interstellar gasses, very dim stars, and very heavy gas giant planet like objects that aren't quite stars.  Ultra fast objects omitted from central black holes provide a mechanism that could explain some of the distribution of dim matter.

Mainstream dark matter scholarship had failed to catch up with the transfers from the exotic dark matter side of the universe's total mass-energy budget to the ordinary dim matter side of the universe's total mass-energy budget that results from these discoveries, thereby dramatically overstating the amount of dark matter present in the universe, which is closer to 50% than to 75% of all matter in the universe.

MOND Theories With Cluster Dark or Dim Matter Remain Viable

Several considerations have keept the alternative to dark matter, a modification to gravity, alive:

* Large quantities of "dim matter" in galactic clusters that is not present in ordinary galaxies reduces the need for larger quantities of dark matter; failure to account for general relativistic effects in galaxies could also reduce the need to find large quantities of dark matter.
* New theoretical motivations of a cutoff scale for modified gravity effects at levels on the order of the Hubble constant and cosmological constant have been proposed with inspiration for Verlinde's entropic formulation of gravity; essentially modified gravity effects in weak fields starting at just the critical point where modified gravity effects are observed, could arise from the absence of gravity waves longer than the size of the universe.
* Cold dark matter theories have failed to come up with anything approaching the parsimony with which modified gravity theories explain galactric rotation curves with a single parameter gravity modification theories, and cold dark matter theories have made inaccurate predictions about new data that gravity modification theories have accurately predicted.
* There are relativistically consistent formulations of gravity modification theories.
* Forms of baryonic or neutrino dark matter that can't explain rotation curves for a variety of reasons such as the matter budget of the universe, can explain dark matter in galactic clusters which make up a small part of the total amount of mass in the universe.

Evidence from the "bullet cluster" makes clear that modified gravity theories need dark or dim matter to be present in large quantities in galactric clusters where they underestimate dark matter effects.  But, given the large amounts of "dim matter" that improved observational techniques are revealing in galactric clusters that are not present in isolated galaxies, this proposition seems like less of a problem than it did in the past when we thought we understood the composition of galactric clusters better than we actually did.

If non-baryonic dark matter is found principally in galactric clusters with almost all galactic dark matter and some galactic cluster dark matter explained by gravity modifications in weak fields, non-baryonic dark matter only needs to make up something on the order of 3-4% of all of the matter in the universe, instead of 50%-75% of the matter in the universe, since galactric clusters make up only about 10% of the mass in the universe and gravity modifications and newly discovered dim matter in galactric clusters account for some of the deficits even there. 

Sources of non-baryonic dark matter like ordinary "fertile" neutrinos are far more viable in these quantities, given the known proportion of the universe's matter that is in the form of neutrinos, and that there are nuclear processes that take place in galactric clusters much more often than elsewhere that could explain why there might be an excess number of neutrinos there.

Dark Energy Is Still A Solved Problem

The conventional way of describing the matter-energy budget of the universe states that the universe is predominantly composed of "dark energy", a uniform distribution of energy throughout all of the universe that leads it to expand at the rate indicated by the Hubble constant.

All observed dark energy effects in the universe are fully described by the cosmological constant called lambda, a single constant of integration in the equations of general relativity that has been measured fairly precisely.  Experimental efforts to distinguish dark energy conceptualized as a uniformly distributed thin haze of energy in the universe from dark energy conceptualized as one more term in the equations of gravity, has


Dark energy is nothing more than a well understood and simple feature of the formulas of general relativity.  Reifying "dark energy" as a substance, rather than part of the law of gravity is at best a bit of heuristic subterfuge and at its worst, misleading.  It is only moderately tolerable at all because general relativity to some extent reifies the fabric of space-time itself in one common layman's interpretation of the theory.

Neutrino Physics

Mixing Matrixes

Neutrino physics experiments have now put positive non-zero values on all three of the neutrino mixing matrix angles (theta 12, theta 23 and theta 13) although they have not yet determined if there is a non-zero CP-violating phase in the PMNS matrix that governs neutrino oscillation.  These values are know to precisions on the order of 1% to 10%.

Evidence for more than three generations of neutrinos has been quashed by experimental evidence.

Absolute and Relative Neutrino Mass

Evidence regarding the relative and absolute masses of the three neutrino mass eigenstates has also been determined with considerable precision.  The difference in mass between the lighest and next lightest neutrino mass eigenstate is about 0.008 eV.  The difference in mass between second and third neutrino mass eigenstates is about 0.052 eV. 

One study puts the sum of the neutrino mass eigenstates at 0.28 eV or less, implying a electron-neutrino mass of about 0.073 eV or less in an "ordinary hierarchy" (or slightly more in an "inverted hierarchy" of neutrino masses), and improved cosmological observations may be able to pin this number to 0.2 eV of less in the near future (unless the total is between 0.2 and 0.28 eV).  This would imply a muon neutrino mass of about 0.081 eV and and tau neutrino mass of about 0.133 eV. 

But, the relative masses would be far less close to each other (i.e. less "degenerate") if the absolute mass of the electron neutrino were lower, which the experimental data does not rule out.  For example, if the electron-neutrino's mass were 0.001 eV, the muon neutrino mass would be about 0.009 eV, and the tau neutrino mass would be about 0.061 eV, for a sum of the three mass eigenstates of 0.071 eV.  The sum of the three neutrino masses can't be less than about 0.07 eV, so the maximum value of the sum and the minimum value differ by only about a factor of four and experimental evidence could narrow this to a factor of three within just a few years.

Neutrinoless Double Beta Decay Searches And Their Implications

Neutrinoless double beta decay experiments continue to fail to detect any such decays, placing an upper limit on the frequency of such decays (which aren't allowed by the Standard Model), and hence bounding the potential that the neutrino could be a Majorana particle with Majorana mass (in addition to "Dirac mass" of the type found for all other fermions). 

Experimental limits on the Majorana mass of a neutrino, from searches for neutrinoless double beta decays, are 0.140 eV to 0.380 eV.

Neutrinoless double beta decay will either be discovered, or will have an upper limit an order of magnitude or two lower, when the current round of experiments searching for it are completed within a decade or so.

In important consequence of these bounds on neutrino mass is that isolated neutrinos, having masses on the order of a fraction of an electron-volt, cannot be a source of warm dark matter.  Warm dark matter is hypothesized to have a mass on the order of a kiloelectron-volt, about 10,000 heavier than a tau neutrino and 100,000 to 1,000,000 or more times as heavy as the presumably most common electron neutrino.  Yet, warm dark matter is on the order of 100 times lighter than individual electrons.  No Standard Model particles or known composite Standard Model particles have masses anywhere close to the hypothetical warm dark matter mass (a proton or neutron is about 1 GeV) and this mass range is not constrained by the power of state of the art particle colliders which can explore masses in the hundreds of GeV or less.

The failure of credible experimental evidence of neutrinoless double beta decay also disfavors a wide variety of beyond the Standard Model theories in which lepton number is not a conservative quantity and instead baryon number-lepton number is a conserved quantity. Such models, generically predict beyond the Standard Model particles as well as lepton number violations, And, in these models the higher the energy scale of the beyond the Standard Model particles, the more common neutrinoless double beta decay should be. But, as the LHC increasingly pushes up the minimum masses of any beyond the Standard Model particles, and new neutrinoless double beta decay experiments push down the maximum rate of lepton number violations, lepton number violating models are increasingly disfavored.

The failure of models with strong lepton number violations is a big problem for cosmology, because it is quite a bit harder to devise theories that can explain the imbalance of matter and anti-matter in the universe without them.  But, apparently, cosmologists have been forced by collider physicists to deal with this inconvenient reality.

Neutrino Don't Break The Speed Of Light

Late 2011 reports of faster than light neutrinos from the OPERA experiment turned out to be a simple case of a loose cable in the experimental set up.  The corrected results show neutrinos moving at a speed indistinguishable from the speed of light, which implies that they have masses in the low tens of GeV or less (something long know to much greater precision by other means).

Emerging Relationships Between Standard Model Constants

Fundamental Constant Measurements

Lots of the ongoing work in fundamental physics is the process of measuring, every more precisely, the constants of the Standard Model of particle physics, and of cosmology.  But, some of these constants are known much more precisely than others. 

The weak force boson masses, the charge lepton masses, the speed of light in a vacuum, and the coupling constants of the electromagnetic and weak forces are known to astounding precision (parts per million). 

The gravitational constant, strong force constant, top quark mass, Higgs boson mass are known or are on the verge of being known with intermediate precision (perhaps parts per thousand). 

The absolute neutrino masses, the PMNS matrix parameters, the masses of the quarks other than the top quark, and the cosmological constant, however, are know only to one or two significant digits of accuracy.  But, we do know all of the values of all of fundamental physics constants, them with the possible exception of the CP-violating parameter of the PMNS matrix, to at least one significant digit order of magnitude levels of accuracy.

Implications of Fundamental Constant Measurements

As we know these constants with greater precision, it becomes possible to test a variety of possible relationships between them.  Almost everyone in fundamental physics believes that nature does not in fact have dozens of truly fundamental Standard Model constants that don't have deeper sources from which they can be, in principle at least, derived.  But, the deeper connections between those constants remains elusive.

If we knew that some of the Standard Model constants had deepere relationships to each other, we might have better clues about a deeper theory than the Standard Model that could elucidate.  For example, the "coincidental" cancellations of contributions to the Higgs boson mass whose existence has been called the "hierarchy problem" might be transparent if we knew how the fundmental fermion and boson masses were related to each other functionally.

We are close to being able to experimentally test for leading contenders for descriptions of these relationships that could dramatically reduce the number of experimentally measured parameters in the Standard Model and establish that there are deeper relationships between these parameters than the Standard Model itself makes evident.

Koide's Formula

Koide's formula, a simple formula that in its original 1982 version by Yoshio Koide, states a precision relationship between the rest masses of the charged leptons to each other that is still consistent with experimental measurements twenty years later.  A simple extension of this formula has been proposed to derive from the charged lepton masses, the masses of the top, bottom, charm and strange quarks, (also here) the quark masses, although the extended formula seems to imply a higher down quark mass than experimental evidence supports and a near zero up quark mass in some formulations.  

Other extensions of Koide's formula has been proposed for the neutrino masses (one suggests an electron neutrino mass of about 0.0004 eV, a muon neutrino mass of about 0.009 eV and a tau neutrino mass of about 0.510 eV see also by the same author here ) with a negative square root for the electron neutrino mass rather than a positive one, but this can't be tested due to the lack of precision measurements of absolute neutrino masses.  Carl Brannen's 2006 presention in the first link in this paragraph builds up this analysis from a model in which leptons are built from and composed of preons with identical positions in the previous link.  Further analysis of both extensions of the original Koide's formula can be found here. 

Recent scholarship by Yukinari Sumino and François Goffinet has also addresses the criticism of Lubos Motl that the Koide relation is formulated in terms of masses that are themselves dependent upon an energy rather than more fundamental quantities. 

Extended versions of Koide's formula, at their root, if they work, imply that all twelve of the fermion masses in the Standard Model may be determined exactly from the two most exactly measured fermion masses - thereby eliminating the need for ten of the twelve experimentaly measured Standard Model constants.

A Simple Higgs Boson Formula?

The Higgs boson mass continues to be consistent within the bounds of experimental error with a simple formula indeed: 2H=2W+Z (arguably 2H=2W+Z+photon mass, which is equivalent), that almost no one in the theoretical physics community predicted in advance.  The reason for the difference between double the Higgs boson mass (about 252 GeV) and the Higgs field vacuum expectation value (about 246 GeV) remains largely unexplained, but suggestive of a simple formula as well (for example, the difference of 6 GeV is roughly equal to the sum of the quark masses other than the top quark).  The W and Z boson masses, in turn, are related in the Standard Model by the weak mixing angle, and the photon mass in the Standard model is theoretically assumed to be exactly zero.  This relationship, if determined to be valid, would allow the masses of all of the Standard Model bosons to be determined from a single weak force boson mass and a single mixing angle, reducing the number of experimentally measured Standard Model constants by one.

Quark-Lepton Complementarity

A hypothesis known as quark-lepton complementarity (QLC) suggests that the CKM matrix governing quark flavor mixing, and the PMNS matrix governing lepton flavor mixing, when properly parameterized, can be described in terms of angles that sum to 45 degree or other multipes of that angle.  Since the CKM matrix entries are known with precision, and since there are a finite number of sensible ways to parameterized the two matrixes, it is possible to make firm predictions about the PMNS matrix terms predicted by this theory and to compare them against experimental results.  QLC is contrary to experimental evidence for many possible parameterizations, but has not been ruled out for all of them at this time.  Quark-lepton complementarity, if established to be correct, would allow all eight of the experimentally measured mixing matrix parameters of the Standard Model to be determined from just four of those mixing matrix parameters.

Relationships Between Mixing Matrixes and the Square Roots Of Fermion Masses

There have also been suggested relationships between the fermion mass matrixes of the Standard Model (or the matrix of the square roots of Standard Model fermion masses) and the mixing matrixes of the Standard Model that will be possible to test with precision PMNS angle measurements and neutrino masses in hand.

QCD

Quantum chromodynamics which describes the interactions of quarks and gluons in the Standard Model makes only low precision and qualitative predictions relative to the other Standard Model forces.  This is because the mathematical tools used to calculate electroweak force predictions, such as renormalization, don't work well with QCD since gluons have a strong degree of self-interaction.

But, numerical approximations using lattice methods, high power computers and Monte Carlo methods are increasingly making it possible to make solid QCD predictions even in low energy "infrared" contexts where quark confinment serious limits direct measurements.

These approximations are increasingly making it possible to explain how gluons give rise to the vast majority of the mass in the universe, to predict a massive state for gluons which are in motion (gluons have no rest mass), to predict the masses of composite particles made of quarks and gluons, and to predict the existence of composite particles made entirely of gluons without any quarks at all which are called glueballs.

While the mathematics invovled is hard, and the ability to conduct direct experimental measurements of the predicted behavior beyond the nature of the composite particle spectrum observed in nature is modest, QCD has an advantage not shared by beyond the Standard Model theories.  There is wide consensus on the exact form of the equations of QCD and there are moderately accurate experimental measurements of all of the physical constants in those equations.  The theoretical predictions of QCD have not been contradicted by experiment and there is thus high confidence in the ability of elaborate numerical methods that are based on these equations to accurately reproduce nature even in areas where it is very difficult to observe directly.

Quantum Gravity

The Longstanding Challenge Of Unifying Quantum Mechanics and General Relativity

The Standard Model and General Relativity are inconsistent mathematically.  Yet, both theories of fundamental physics perform admirably to the highest levels of precision to which we can experimentally test them in their own respective domains.  Efforts to reconcile the two have been on ongoing area of theoreretical physics research since the 1940s. 

Indeed, the Holy Grail of theoretical physics is a "theory of everything" involves finding a way to reconcile some generalization of Standard Model physics that unifies the three forces and couple of dozens particles in it into a "Grand Unified Theory", and a quantum gravity theory involving a spin-2, massless graviton that carried the gravitational force.  Generalizations of supersymmetry called string theory, in several forms determined to be equivalent descriptions of a larger M theory on a many dimensional brane, were held out for decades to be that TOE.  But, this proved to be a bridge too far.  Neither SUSY, nor M theory, have worked out so far, and they seem to be on the verge of being contradicted by experiment.

Loop Quantum Gravity

The main contender for a quantum gravity theory other than String Theory has been "loop quantum gravity" although half a dozen other names for areas of research using the same paradigm have been developed.  All of these theories start from the premise that space-time is discete rather than continuous, in some carefully defined manner at some sufficiently fine level, typically the Planck scale.  The approaches use toy models connecting nodes of space-time according to rules that look like quantum mechanical rules to formulate a space-time that behaves in the domains where it has been tested like general relativity and to give rise emergently to a four-dimensional space-time.

Efforts are underway to develop a consensus formulation of LQG, to integrate Standard Model particles and interactions into the model, and to explore phenomological distinctions between classical general relativity and the LQG formulations that reduce to it, in those circumstances where classical general relativity gives rise to mathematical inconsistencies with the Standard Model.

In some LQG models, the Standard Model particles themselves are emergent excitations of localized areas of space-time.  It is hoped that quantum gravity could allow us to better understand phenomena like black holes, the Big Bang, the point-like nature of Standard Model particles, and perhaps dark matter and dark energy as well.

LQG remains very much a work in progress, but unlike string theory, it is a work in progress that is showing (in part because these area still early days in the field) real theoretical progress.  No insurmountable dead ends in the LQG research program have emerged yet.

Ad Hoc Efforts To Address Particular Quantum Gravity Questions

Other avenues of quantum gravity research aren't so ambitious. 

Programs to investigate phenomena around black holes, around the Big Bang, in high energy settings (asymptotic gravity) have simply come up with ad hoc and incomplete ansatz approaches to analyzing particular quantum gravity problems on a case by case basis without claiming to have consistent theory of quantum gravity as a whole. 

Notably, one of these approaches, asymptotic gravity, made one of the most accurate of the many dozens of Higgs boson mass predictions.