Martin Bauer
@martinmbauer.bsky.social
I'm a theoretical physicist at Durham University
A more careful formulation requires the embedding of the SM in a GUT (to get rid off the Landau pole) and can be found in the introduction of this nice paper (from which I also stole the figure)
arxiv.org/pdf/1305.6939
arxiv.org/pdf/1305.6939
arxiv.org
October 25, 2025 at 3:31 PM
A more careful formulation requires the embedding of the SM in a GUT (to get rid off the Landau pole) and can be found in the introduction of this nice paper (from which I also stole the figure)
arxiv.org/pdf/1305.6939
arxiv.org/pdf/1305.6939
From this geometric perspective the Hierarchy problem is the question of whether there is a mechanism in some meow fundamental version of the Standard Model that selects or stabilises this very special trajectory
11/11
11/11
October 25, 2025 at 3:31 PM
From this geometric perspective the Hierarchy problem is the question of whether there is a mechanism in some meow fundamental version of the Standard Model that selects or stabilises this very special trajectory
11/11
11/11
But from the point of view of the high energy fixed point, this trajectory is exponentially close to generic trajectories that fall directly into on of the RG attractors.
The SM trajectory requires very specific, highly fine-tuned initial conditions to realise this trajectory
10/11
The SM trajectory requires very specific, highly fine-tuned initial conditions to realise this trajectory
10/11
October 25, 2025 at 3:31 PM
But from the point of view of the high energy fixed point, this trajectory is exponentially close to generic trajectories that fall directly into on of the RG attractors.
The SM trajectory requires very specific, highly fine-tuned initial conditions to realise this trajectory
10/11
The SM trajectory requires very specific, highly fine-tuned initial conditions to realise this trajectory
10/11
The SM as realised in nature corresponds to a very special trajectory in this theory space
It stays for very long RG-time almost on the scaleless trajectory only to branch off into the broken phase
9/ 11
It stays for very long RG-time almost on the scaleless trajectory only to branch off into the broken phase
9/ 11
October 25, 2025 at 3:31 PM
The SM as realised in nature corresponds to a very special trajectory in this theory space
It stays for very long RG-time almost on the scaleless trajectory only to branch off into the broken phase
9/ 11
It stays for very long RG-time almost on the scaleless trajectory only to branch off into the broken phase
9/ 11
Importantly, both the mu^2>0 and mu^2<0 asymptotic low-energy theories are RG attractors
But the mu^2=0 theory is a repulsive fixed point. It is unstable
(Technically this is defined by the sign of the beta function).
8/11
But the mu^2=0 theory is a repulsive fixed point. It is unstable
(Technically this is defined by the sign of the beta function).
8/11
October 25, 2025 at 3:31 PM
Importantly, both the mu^2>0 and mu^2<0 asymptotic low-energy theories are RG attractors
But the mu^2=0 theory is a repulsive fixed point. It is unstable
(Technically this is defined by the sign of the beta function).
8/11
But the mu^2=0 theory is a repulsive fixed point. It is unstable
(Technically this is defined by the sign of the beta function).
8/11
the mu^2<0 branch corresponds to a broken electroweak symmetry phase
The mu^2=0 option is special, because it corresponds to the trajectory on which all particles remain massless and the theory remains scale-invariant (all operators are marginal)
7/11
The mu^2=0 option is special, because it corresponds to the trajectory on which all particles remain massless and the theory remains scale-invariant (all operators are marginal)
7/11
October 25, 2025 at 3:31 PM
the mu^2<0 branch corresponds to a broken electroweak symmetry phase
The mu^2=0 option is special, because it corresponds to the trajectory on which all particles remain massless and the theory remains scale-invariant (all operators are marginal)
7/11
The mu^2=0 option is special, because it corresponds to the trajectory on which all particles remain massless and the theory remains scale-invariant (all operators are marginal)
7/11
But there're different low energy fixed points.
They correspond to the three different options for the Higgs mass term mu^2<0, mu^2=0 and mu^2>0
The mu^2>0 branch corresponds to the SM in which the electroweak gauge symmetry remains unbroken
6/11
They correspond to the three different options for the Higgs mass term mu^2<0, mu^2=0 and mu^2>0
The mu^2>0 branch corresponds to the SM in which the electroweak gauge symmetry remains unbroken
6/11
October 25, 2025 at 3:31 PM
But there're different low energy fixed points.
They correspond to the three different options for the Higgs mass term mu^2<0, mu^2=0 and mu^2>0
The mu^2>0 branch corresponds to the SM in which the electroweak gauge symmetry remains unbroken
6/11
They correspond to the three different options for the Higgs mass term mu^2<0, mu^2=0 and mu^2>0
The mu^2>0 branch corresponds to the SM in which the electroweak gauge symmetry remains unbroken
6/11
One can then view the Standard Model as a specific trajectory in theory space from the high-energy fixed point to a low energy fixed point
5/11
5/11
October 25, 2025 at 3:31 PM
One can then view the Standard Model as a specific trajectory in theory space from the high-energy fixed point to a low energy fixed point
5/11
5/11
Now imagine the SM in the opposite limit: almost 0 energy. In the effective field theory approach you have successively integrated out every massive particle and you're left with a theory of only massless states, which is also scale-invariant.
4/11
4/11
October 25, 2025 at 3:31 PM
Now imagine the SM in the opposite limit: almost 0 energy. In the effective field theory approach you have successively integrated out every massive particle and you're left with a theory of only massless states, which is also scale-invariant.
4/11
4/11
In the 'map of theories', this is a fixed point. Because it doesn't matter what the values if the mass parameters of the theory were different, in the limit of very high energies, physical observables would all look the same
3/11
3/11
October 25, 2025 at 3:31 PM
In the 'map of theories', this is a fixed point. Because it doesn't matter what the values if the mass parameters of the theory were different, in the limit of very high energies, physical observables would all look the same
3/11
3/11
For this it is important to understand the SM at different energy scales.
At very, very high energies, all the mass terms in the SM are irrelevant. The SM looks scale invariant in this limit, because all effects from dimensionful parameters (scales) can be ignored.
2/11
At very, very high energies, all the mass terms in the SM are irrelevant. The SM looks scale invariant in this limit, because all effects from dimensionful parameters (scales) can be ignored.
2/11
October 25, 2025 at 3:31 PM
For this it is important to understand the SM at different energy scales.
At very, very high energies, all the mass terms in the SM are irrelevant. The SM looks scale invariant in this limit, because all effects from dimensionful parameters (scales) can be ignored.
2/11
At very, very high energies, all the mass terms in the SM are irrelevant. The SM looks scale invariant in this limit, because all effects from dimensionful parameters (scales) can be ignored.
2/11
The Nobel laureates were the first to show this effect for systems containing billions of Cooper pairs. 'Macroscopic' objects described by a collective wavefucntion. Their work laid the foundations for superconducting qubits
They also showed other properties like energy quantisation
7/7
They also showed other properties like energy quantisation
7/7
October 8, 2025 at 8:17 PM
The Nobel laureates were the first to show this effect for systems containing billions of Cooper pairs. 'Macroscopic' objects described by a collective wavefucntion. Their work laid the foundations for superconducting qubits
They also showed other properties like energy quantisation
7/7
They also showed other properties like energy quantisation
7/7
In superconductors you can build have states where many, many Cooper pairs (pairs of electrons) are described by the same wavefunction, which allows them collectively to tunnel through thin insulator barriers called Josephson junctions
6/7
6/7
October 8, 2025 at 8:17 PM
In superconductors you can build have states where many, many Cooper pairs (pairs of electrons) are described by the same wavefunction, which allows them collectively to tunnel through thin insulator barriers called Josephson junctions
6/7
6/7
But in quantum mechanics one wavefunction doesn't mean one particle. Many particles can be described by the same wavefunction. Entanglement is an example in which multiple particles are described by one wavefunction
5/7
5/7
October 8, 2025 at 8:17 PM
But in quantum mechanics one wavefunction doesn't mean one particle. Many particles can be described by the same wavefunction. Entanglement is an example in which multiple particles are described by one wavefunction
5/7
5/7
It is also responsible for field electron emission, used in electron microscopes and tunnel diodes, nuclear fusion in stars, etc
4/7
4/7
October 8, 2025 at 8:17 PM
It is also responsible for field electron emission, used in electron microscopes and tunnel diodes, nuclear fusion in stars, etc
4/7
4/7
This effect isn't uncommon in nature
It explains radioactive alpha-decay where a whole Helium nucleus is emitted from a heavy decaying element even if the binding forces wouldn't allow this process classically
3/7
It explains radioactive alpha-decay where a whole Helium nucleus is emitted from a heavy decaying element even if the binding forces wouldn't allow this process classically
3/7
October 8, 2025 at 8:17 PM
This effect isn't uncommon in nature
It explains radioactive alpha-decay where a whole Helium nucleus is emitted from a heavy decaying element even if the binding forces wouldn't allow this process classically
3/7
It explains radioactive alpha-decay where a whole Helium nucleus is emitted from a heavy decaying element even if the binding forces wouldn't allow this process classically
3/7
..is on the other side of the barrier (unless its an infinitely strong force field)
If you measure the position of the particle there is a finite probability it's outside the trap even if it never had enough kinetic energy to overcome the barrier. It 'tunnels' through the barrier
2/7
If you measure the position of the particle there is a finite probability it's outside the trap even if it never had enough kinetic energy to overcome the barrier. It 'tunnels' through the barrier
2/7
October 8, 2025 at 8:17 PM
..is on the other side of the barrier (unless its an infinitely strong force field)
If you measure the position of the particle there is a finite probability it's outside the trap even if it never had enough kinetic energy to overcome the barrier. It 'tunnels' through the barrier
2/7
If you measure the position of the particle there is a finite probability it's outside the trap even if it never had enough kinetic energy to overcome the barrier. It 'tunnels' through the barrier
2/7
These results use Run 2 data. By the end of Run 4, the much larger dataset would push the significance beyond discovery thresholds, if the central value holds
In the plot below we were at the blue, we are now at the red and could be as sensitive as the green markers
6/6
In the plot below we were at the blue, we are now at the red and could be as sensitive as the green markers
6/6
September 9, 2025 at 6:48 PM
These results use Run 2 data. By the end of Run 4, the much larger dataset would push the significance beyond discovery thresholds, if the central value holds
In the plot below we were at the blue, we are now at the red and could be as sensitive as the green markers
6/6
In the plot below we were at the blue, we are now at the red and could be as sensitive as the green markers
6/6
This type of new physics would have the properties of a new vector boson (like the Z boson) or a leptoquark, a completely new state that connects color-charged quarks with color-neutral muons
5/6
5/6
September 9, 2025 at 6:48 PM
This type of new physics would have the properties of a new vector boson (like the Z boson) or a leptoquark, a completely new state that connects color-charged quarks with color-neutral muons
5/6
5/6
If it is indeed physics beyond the standard model, the data points toward the same types of interactions that have already been shown to consistently explain several other anomalies in B-meson decays
4/6
4/6
September 9, 2025 at 6:48 PM
If it is indeed physics beyond the standard model, the data points toward the same types of interactions that have already been shown to consistently explain several other anomalies in B-meson decays
4/6
4/6
It's an open question whether there is a systematic effect here that shows up in both experiments in the same way, or a theoretical uncertainty that has been underestimated or whether this is a genuine signal that the Standard Model cannot account for
3/6
3/6
September 9, 2025 at 6:48 PM
It's an open question whether there is a systematic effect here that shows up in both experiments in the same way, or a theoretical uncertainty that has been underestimated or whether this is a genuine signal that the Standard Model cannot account for
3/6
3/6