https://madrid.hostmaster.org/articles/physics_beyond_the_standard_model/en.html
By 2012, with the Higgs boson confirmed at CERN’s Large Hadron Collider, the Standard Model (SM) was, on paper, complete. Every predicted particle had been found. Its equations had passed every experimental test with staggering precision.
And yet, the feeling in physics was not one of closure, but of incompleteness. Like Newton’s laws before Einstein, or classical physics before quantum mechanics, the Standard Model was too successful at the scales we can test, but incapable of answering deeper questions. It was an almost perfect map - but only of a small part of the landscape.
The most glaring omission is gravity.
This is more than just an oversight. General relativity treats gravity as the curvature of spacetime, a smooth geometric field, while the SM treats forces as quantum fields mediated by particles. Attempts to quantize gravity in the same way run into infinities that cannot be renormalized.
The Standard Model and GR are like two different operating systems - brilliant in their own domains, but fundamentally incompatible. Reconciling them is perhaps the greatest challenge in physics today.
The SM predicts neutrinos to be massless. But experiments, beginning with the Super-Kamiokande detector in Japan (1998) and confirmed worldwide, showed that neutrinos oscillate between flavors (electron, muon, tau). Oscillations require mass.
This was the first confirmed evidence of physics beyond the Standard Model. The discovery won the 2015 Nobel Prize for Kajita and McDonald.
Neutrinos are extremely light, at least a million times lighter than the electron. Their masses are not explained by the SM - but they might hint at new physics, like the seesaw mechanism, sterile neutrinos, or connections to the early universe. In some scenarios, heavy seesaw neutrinos enable leptogenesis, where an early-universe lepton asymmetry is created and later converted into the observed matter–antimatter asymmetry.
The visible matter described by the SM makes up less than 5% of the universe. The rest is invisible.
Theories propose new particles: WIMPs (weakly interacting massive particles), axions, sterile neutrinos, or something stranger. But despite decades of searches - underground detectors, collider experiments, astrophysical surveys - dark matter remains elusive.
Even more mysterious is dark energy, the force driving the accelerating expansion of the universe.
This cosmological constant problem is arguably the sharpest clash between quantum field theory and gravity. The Standard Model has nothing to say about dark energy. It is a gaping hole in our understanding of the cosmos.
Another deep puzzle lies within the Higgs boson itself.
The Higgs mass is measured to be 125 GeV. But quantum corrections should push it up to near the Planck scale (\(10^{19}\) GeV), unless there are miraculous cancellations. Why is it so light compared to the natural energy scales of gravity?
This is the hierarchy problem: the Higgs appears unnaturally fine-tuned. Physicists suspect new physics, such as supersymmetry (SUSY), which could stabilize the Higgs mass by introducing partner particles that cancel out the dangerous corrections. (Debates around naturalness include ideas from dynamical solutions to anthropic reasoning in a possible “landscape” of vacua.)
The SM includes some CP violation, but not nearly enough to explain why the universe today is filled with matter rather than equal amounts of matter and antimatter. As noted above, mechanisms like leptogenesis (often tied to the seesaw origin of neutrino masses) provide one compelling path where physics beyond the SM tips the balance.
The Standard Model is sometimes called “the most successful theory in physics.” Its predictions match experiment to 10–12 decimal places. It explains nearly everything we see in particle accelerators and laboratories.
But it is incomplete:
Physicists now face a familiar moment in history. Just as Newtonian mechanics gave way to relativity, and classical physics to quantum mechanics, the SM must eventually give way to something deeper.
The ultimate goal is a Grand Unified Theory (GUT) or even a Theory of Everything (ToE): a framework that unites all four forces, explains all particles, and works consistently from the smallest scales (quantum gravity) to the largest (cosmology).
This is the holy grail of modern physics. It is why researchers push colliders to higher energies, build massive neutrino detectors, map the cosmos with telescopes, and invent bold new mathematics.
The next chapters will explore the leading candidates:
Each of these ideas arose not as dogma, but as science at its best: noticing cracks, building new theories, and testing them against reality.
Physics has a long history of unification through symmetry. Maxwell’s equations unified electricity and magnetism. Special relativity unified space and time. Electroweak theory unified two of the four fundamental forces. Each leap forward came from uncovering a hidden symmetry in nature.
Supersymmetry - or SUSY, as physicists affectionately call it - is the bold proposal that the next great symmetry links two seemingly distinct categories of particles: matter and forces.
In the Standard Model, particles fall into two broad families:
Fermions (spin 1/2): These include quarks and leptons, the building blocks of matter. Their half-integer spin means they obey the Pauli exclusion principle: no two identical fermions can occupy the same state. This is why atoms have structured shells and why matter is stable.
Bosons (integer spin): These include photons, gluons, W and Z bosons, and the Higgs. Bosons mediate forces. Unlike fermions, they can pile into the same state, which is why lasers (photons) and Bose–Einstein condensates exist.
In short: fermions make up matter, bosons carry forces.
Supersymmetry proposes a symmetry that links fermions and bosons. For every known fermion, there exists a bosonic partner. For every known boson, a fermionic partner.
(“Photino” and “zino” are older gauge-eigenstate nicknames; experiments actually search for the mass eigenstates listed above.)
Why propose such a radical doubling of the particle world? Because SUSY promises elegant solutions to some of the deepest problems left by the Standard Model.
One of SUSY’s greatest appeals is its ability to address the hierarchy problem: why the Higgs boson is so light compared to the Planck scale.
In the Standard Model, quantum corrections from virtual particles should drive the Higgs mass up to enormous values. Supersymmetry introduces sparticles whose contributions cancel out these divergences. The result: the Higgs mass is stabilized naturally, without fine-tuning (at least in “natural” SUSY spectra).
Another motivation for SUSY comes from unification of forces.
This suggests that at extremely high energies, all three forces may unify into a single Grand Unified Theory (GUT).
Supersymmetry also provides a natural candidate for dark matter.
If SUSY is correct, one of the sparticles should be stable and electrically neutral. A leading candidate is the lightest neutralino, a mixture of the bino, wino, and higgsinos.
Neutralinos would interact only weakly, fitting the profile of WIMPs (weakly interacting massive particles). If discovered, they could explain the missing 27% of the universe’s matter.
For decades, physicists hoped that supersymmetric particles would appear just above the energy scales already probed.
The lack of SUSY discoveries at the LHC has been disappointing. Many of the simplest versions of SUSY, such as the “minimal supersymmetric Standard Model” (MSSM), are now heavily constrained. “Natural” spectra are pushed heavier, implying more tuning if SUSY lives near the TeV scale.
Still, SUSY has not been ruled out. More elaborate models predict heavier or more subtle sparticles, perhaps beyond the LHC’s reach, or with interactions too weak to be easily detected.
Beyond its phenomenological motivations, SUSY has deep mathematical elegance.
Even if nature does not realize SUSY at accessible energies, its mathematics has already enriched physics.
Today, SUSY occupies a curious position.
If the LHC and its successors continue to find nothing, SUSY may be realized only at energy scales far beyond our reach - or perhaps nature took a different path altogether.
Supersymmetry illustrates the scientific method in action.
Physicists identified problems: the hierarchy issue, unification, dark matter. They proposed a bold new symmetry that solves them all. They designed experiments to test it. So far, the results are negative - but that does not mean the idea was wasted. SUSY sharpened our tools, clarified what we seek, and guided whole generations of research.
Like the aether or epicycles before it, SUSY may prove a stepping stone toward deeper truth, whether or not it survives as the final word.
Physics beyond the Standard Model is often motivated by patches: solve the hierarchy problem, explain dark matter, unify gauge couplings. String theory is different. It does not begin with a particular puzzle. Instead, it begins with mathematics - and ends up reshaping our entire conception of space, time, and matter.
String theory began, surprisingly, not as a theory of everything, but as a failed attempt to understand the strong nuclear force.
In the late 1960s, before QCD was fully developed, physicists were trying to explain the zoo of hadrons. They noticed patterns in scattering data that suggested resonances could be modeled by vibrating strings.
The “dual resonance model,” introduced by Veneziano in 1968, described strong interactions as if hadrons were excitations of tiny strings. It was elegant but quickly abandoned once QCD emerged as the true theory of the strong force.
Yet string theory refused to die. Hidden within its equations were remarkable features that seemed to point far beyond nuclear physics.
When theorists quantized string vibrations, they discovered that the spectrum inevitably included a massless spin-2 particle.
This was shocking. Quantum field theory had shown that a massless spin-2 particle is unique: it must be the quantum of gravity, the graviton.
As John Schwarz later remarked: “But a startling fact emerged: the mathematics of string theory inevitably contained a massless spin-2 particle - a graviton.”
What began as a theory of hadrons had accidentally produced the building block of quantum gravity.
At its heart, string theory replaces point particles with tiny one-dimensional objects: strings.
Strings can be open (with two endpoints) or closed (loops).
Different vibration modes of the string correspond to different particles.
This simple shift - from points to strings - resolves many of the infinities that plague quantum gravity. The string’s finite size smears out interactions that would otherwise blow up at zero distance.
Early versions of string theory had problems: they contained tachyons (instabilities) and required unrealistic features. The breakthrough came with the introduction of supersymmetry, leading to superstring theory in the 1970s and 1980s.
Superstrings eliminated tachyons, incorporated fermions, and brought new mathematical consistency.
But there was a catch: string theory only works in higher dimensions. Specifically, 10 dimensions of spacetime.
This idea, radical as it seems, was not entirely new. In the 1920s, Kaluza–Klein theory had already hinted that extra dimensions could unify gravity and electromagnetism. String theory revived and vastly expanded this idea.
By the mid-1980s, physicists found that string theory was not unique, but came in five distinct versions:
Each seemed mathematically consistent, but why should nature pick one?
In 1984, Michael Green and John Schwarz showed that string theory could cancel quantum anomalies automatically - something quantum field theories had to carefully engineer. This discovery triggered the first superstring revolution, with thousands of physicists turning to string theory as a candidate for a unified theory of all forces.
It was the first serious framework in which quantum gravity was not only consistent but inevitable.
In the mid-1990s, a second revolution unfolded. Edward Witten and others discovered that the five different string theories were not rivals, but different limits of a single, deeper theory: M-theory.
M-theory is believed to live in 11 dimensions and includes not just strings but higher-dimensional objects called branes (short for membranes).
These branes gave rise to rich new possibilities: entire universes could exist as 3-branes floating in higher-dimensional space, with gravity leaking into the bulk while other forces remain confined. This picture inspired modern extra-dimensional models like Randall–Sundrum.
Kaluza–Klein (1920s): Proposed an extra fifth dimension to unify gravity and electromagnetism. The idea was shelved for decades, but string theory revived it in grander form. Compactified extra dimensions remain a core feature of string models.
Randall–Sundrum (1999): Proposed “warped” extra dimensions, where our universe is a 3-brane embedded in higher dimensions. Gravity propagates in the bulk, explaining why it is weaker than other forces. Such models predict possible signals in particle colliders or deviations from Newton’s law at very short distances.
String theory makes bold claims, but testing them is extraordinarily difficult.
Despite the challenges, string theory has provided fertile ground for mathematics, inspiring progress in geometry, topology, and dualities like AdS/CFT (connecting gravity in higher dimensions to quantum field theory without gravity).
Supporters argue that string theory is the most promising path to a unified theory: it includes quantum gravity, unifies all forces, and explains why a graviton must exist.
Critics argue that without experimental confirmation, string theory risks becoming detached from empirical science. Its vast “landscape” of possible solutions (as many as \(10^{500}\)) makes it hard to extract unique predictions.
Both sides agree on one thing: string theory has changed how we think about physics, providing a new language for unification.
If supersymmetry is the next step beyond the Standard Model, string theory is the step after that: a candidate for the long-sought Theory of Everything.
Its boldest claim is not just that it includes the Standard Model and gravity, but that these are inevitable consequences of vibrating strings in higher dimensions. The graviton is not an add-on - it is built in.
Whether nature has chosen this path remains to be discovered.
Theories are the lifeblood of physics, but experiments are its heartbeat. Supersymmetry, string theory, and extra dimensions are beautiful mathematical constructions, but they live or die by evidence. If they are to be more than speculation, they must leave footprints in the data.
Physicists have devised ingenious ways to look for these footprints - in colliders, in the cosmos, and in the structure of spacetime itself.
The Large Hadron Collider (LHC) at CERN is the world’s most powerful particle accelerator, colliding protons at energies up to 13.6 TeV (design: 14 TeV). It has been humanity’s primary tool for probing physics beyond the Standard Model.
Some theories suggest that if gravity becomes strong at the TeV scale, tiny black holes could form in LHC collisions, evaporating in bursts of particles. No such events have been seen.
If extra dimensions exist, Newton’s law of gravity could break down at short distances.
These tabletop experiments are remarkably sensitive, probing scales inaccessible to colliders.
The discovery of gravitational waves by LIGO in 2015 opened a new frontier.
So far, observations are consistent with GR within current uncertainties, but higher precision may uncover surprises.
The cosmos itself is the ultimate particle accelerator.
So far, the sky is silent. Dark matter remains undetected, and cosmological data fit the ΛCDM model with no clear stringy fingerprints.
Decades of searching have not confirmed SUSY, extra dimensions, or stringy signals. But absence of evidence is not evidence of absence:
A few precision anomalies (e.g., the muon (g-2) measurement and some flavor-physics tensions) remain intriguing but unsettled; they motivate continued scrutiny without yet overturning the SM.
What experiments have done is narrow the parameter space. They have told us where SUSY is not, how small extra dimensions must be, and how strongly dark matter can or cannot interact.
Future experiments promise to push deeper:
The experimental story of BSM physics is not one of failure, but of process.
Just as Rutherford’s gold foil experiment shattered the plum pudding model, or LIGO shattered doubts about gravitational waves, the next big discovery may come suddenly - and change everything.
For centuries, physics has advanced by unification. Newton united the heavens and Earth under one law of gravitation. Maxwell unified electricity and magnetism. Einstein united space and time. The electroweak theory showed that two very different forces are aspects of one.
The natural next step is the boldest yet: to unify all four fundamental interactions - strong, weak, electromagnetic, and gravitational - into a single, self-consistent framework. This is the holy grail of physics: the Theory of Everything (ToE).
A complete unification is not just philosophical elegance; it addresses deep practical and conceptual problems:
A ToE would not just unify forces - it would unify scales, from the tiniest strings of quantum theory to the largest cosmic structures.
Supersymmetry (SUSY), if realized in nature, provides a stepping stone to a ToE.
SUSY-inspired GUTs (such as SU(5), SO(10), or E₆) envision that at ultra-high energies, quarks and leptons are unified into larger multiplets, and forces are merged into a single gauge group.
But SUSY has yet to appear in experiments. If it exists only at scales beyond our reach, its unifying power may remain tantalizing but hidden.
String theory goes further. Instead of patching the Standard Model, it rewrites the foundation:
In this vision, unification is not an accident - it is geometry. Forces differ because strings vibrate in different ways, shaped by the topology of extra dimensions.
The discovery that the five string theories are connected by dualities led to M-theory, an even grander framework:
M-theory is still incomplete, but it represents the most ambitious step toward a ToE ever attempted.
String theory and M-theory are not the only paths. Physicists are exploring multiple frameworks, each with different strengths:
While none yet rival string theory’s unifying scope, they exemplify the richness of the search.
A ToE must ultimately be testable. Though the Planck scale is far beyond current experiments, physicists search for indirect evidence:
So far, the ToE remains out of reach, but every null result prunes the possibilities.
A true ToE would not just unify physics - it would unify human knowledge. It would bridge quantum mechanics and relativity, micro and macro, particle and cosmos.
Yet it faces a paradox: the very scale at which unification happens may forever lie beyond experimental reach. A 100 TeV collider probes only a fraction of the way to the Planck scale. We may have to rely on cosmology, mathematical consistency, or indirect signatures.
The dream remains alive because of the profound elegance of the frameworks. As Witten remarked, string theory is not just “a set of equations” but “a new framework for physics.”
The quest for a ToE is not about declaring string theory, SUSY, or any single idea “true.” It is about the scientific method:
The story is far from finished. But it is precisely this openness - the refusal to treat any theory as sacred - that makes physics a living science, not a dogma.
The next century of physics may reveal:
Or perhaps the real ToE is something no one has yet imagined.
But the quest itself - the drive to unify, to explain, to see nature whole - is as much a part of humanity as the equations themselves.