String Dualities and Corrections to Gravity

Based on arXiv:2012.15677 [hep-th]

Figure 1: a torus is an example of a geometry that has T-duality

Physicists have been searching for ways to describe the interplay between gravity and quantum mechanics – quantum gravity – for the last century. The problem of finding a consistent theory of quantum gravity still looms physicists to this day. Fortunately, string theory is the most promising candidate for such a task. 

One of the strengths of string theory is that at low energies, the equations arising from string theory are shown to be precisely Einstein’s theory of general relativity. Let’s break down what this means. First, we must make sure we know the definition of a coupling constant. Theories of physics are typically described by some parameter that signifies the strength of the interaction. This parameter is called the coupling constant of that theory. According to quantum field theory, the value of the coupling constant depends on the energy. We often plot the logarithm of the energy and the coupling constant to understand how the theory behaves at a certain energy scale. The slope of this plot is called the beta function and when this function is zero, that point is called a fixed point. These fixed points are interesting since they imply that the quantum theory does not have any notion of scale.

Back to string theory, its coupling constant is called α′ (said as alpha-prime). At weak coupling, when α′ is small, we can similarly find the beta function for string theory. At the quantum level, string theory must have a vanishing beta function. At the corresponding fixed point, we find that the Einstein’s equations of motion emerge. This is quite remarkable!

We can go even further. Due to the smallness of α′, we can expand the beta function perturbatively. All the subleading terms in α′, which are infinite in number, are considered to be corrections to general relativity. Therefore, we can understand how general relativity is modified via string theory. It becomes technically challenging to compute these corrections and little is known about what the full expansion looks like.

Fortunately for physicists, string theories are interesting in other ways that could help figure us out these corrections to gravity. Particularly, the string energy spectrum that has radii R and radii α′/R look exactly the same. This relation is called T-duality. An example of a geometry that has this duality is the torus, see Figure 1. Because we know that certain dualities for strings must hold, we can use this to guess what the higher order correction must look like. Codina, Hohm and Marques took advantage of this idea to find corrections to the third power of α′. Using a simple scenario where the graviton is the only field in the theory, they were able to predict what the corrections must be.

This method can be applied at higher orders in α′ as well as a theory with more fields than the graviton, although technical challenges still arise. Due to the structure of how T-duality was used, the authors can also use their results to study cosmological models. Finally, the theory result confirms that string theory should be T-duality at all orders of α′.


Measuring the Tau’s g-2 Too

Title : New physics and tau g2 using LHC heavy ion collisions

Authors: Lydia Beresford and Jesse Liu


Since April, particle physics has been going crazy with excitement over the recent announcement of the muon g-2 measurement which may be our first laboratory hint of physics beyond the Standard Model. The paper with the new measurement has racked up over 100 citations in the last month. Most of these papers are theorists proposing various models to try an explain the (controversial) discrepancy between the measured value of the muon’s magnetic moment and the Standard Model prediction. The sheer number of papers shows there are many many models that can explain the anomaly. So if the discrepancy is real,  we are going to need new measurements to whittle down the possibilities.

Given that the current deviation is in the magnetic moment of the muon, one very natural place to look next would be the magnetic moment of the tau lepton. The tau, like the muon, is a heavier cousin of the electron. It is the heaviest lepton, coming in at 1.78 GeV, around 17 times heavier than the muon. In many models of new physics that explain the muon anomaly the shift in the magnetic moment of a lepton is proportional to the mass of the lepton squared. This would explain why we are a seeing a discrepancy in the muon’s magnetic moment and not the electron (though there is a actually currently a small hint of a deviation for the electron too). This means the tau should be 280 times more sensitive than the muon to the new particles in these models. The trouble is that the tau has a much shorter lifetime than the muon, decaying away in just 10-13 seconds. This means that the techniques used to measure the muons magnetic moment, based on magnetic storage rings, won’t work for taus. 

Thats where this new paper comes in. It details a new technique to try and measure the tau’s magnetic moment using heavy ion collisions at the LHC. The technique is based on light-light collisions (previously covered on Particle Bites) where two nuclei emit photons that then interact to produce new particles. Though in classical electromagnetism light doesn’t interact with itself (the beam from two spotlights pass right through each other) at very high energies each photon can split into new particles, like a pair of tau leptons and then those particles can interact. Though the LHC normally collides protons, it also has runs colliding heavier nuclei like lead as well. Lead nuclei have more charge than protons so they emit high energy photons more often than protons and lead to more light-light collisions than protons. 

Light-light collisions which produce tau leptons provide a nice environment to study the interaction of the tau with the photon. A particles magnetic properties are determined by its interaction with photons so by studying these collisions you can measure the tau’s magnetic moment. 

However studying this process is be easier said than done. These light-light collisions are “Ultra Peripheral” because the lead nuclei are not colliding head on, and so the taus produced generally don’t have a large amount of momentum away from the beamline. This can make them hard to reconstruct in detectors which have been designed to measure particles from head on collisions which typically have much more momentum. Taus can decay in several different ways, but always produce at least 1 neutrino which will not be detected by the LHC experiments further reducing the amount of detectable momentum and meaning some information about the collision will lost. 

However one nice thing about these events is that they should be quite clean in the detector. Because the lead nuclei remain intact after emitting the photon, the taus won’t come along with the bunch of additional particles you often get in head on collisions. The level of background processes that could mimic this signal also seems to be relatively minimal. So if the experimental collaborations spend some effort in trying to optimize their reconstruction of low momentum taus, it seems very possible to perform a measurement like this in the near future at the LHC. 

The authors of this paper estimate that such a measurement with a the currently available amount of lead-lead collision data would already supersede the previous best measurement of the taus anomalous magnetic moment and further improvements could go much farther. Though the measurement of the tau’s magnetic moment would still be far less precise than that of the muon and electron, it could still reveal deviations from the Standard Model in realistic models of new physics. So given the recent discrepancy with the muon, the tau will be an exciting place to look next!

Read More:

An Anomalous Anomaly: The New Fermilab Muon g-2 Results

When light and light collide

Another Intriguing Hint of New Physics Involving Leptons