## LHCb’s Flavor Mystery Deepens

Title: Measurement of CP -averaged observables in the B0→ K∗0µ+µ− decay

Authors: LHCb Collaboration

Refference: https://arxiv.org/abs/2003.04831

In the Standard Model, matter is organized in 3 generations; 3 copies of the same family of particles but with sequentially heavier masses. Though the Standard Model can successfully describe this structure, it offers no insight into why nature should be this way. Many believe that a more fundamental theory of nature would better explain where this structure comes from. A natural way to look for clues to this deeper origin is to check whether these different ‘flavors’ of particles really behave in exactly the same ways, or if there are subtle differences that may hint at their origin.

The LHCb experiment is designed to probe these types of questions. And in recent years, they have seen a series of anomalies, tensions between data and Standard Model predictions, that may be indicating the presence of new particles which talk to the different generations. In the Standard Model, the different generations can only interact with each other through the W boson, which means that quarks with the same charge can only interact through more complicated processes like those described by ‘penguin diagrams’.

These interactions typically have quite small rates in the Standard Model, meaning that the rate of these processes can be quite sensitive to new particles, even if they are very heavy or interact very weakly with the SM ones. This means that studying these sort of flavor decays is a promising avenue to search for new physics.

In a press conference last month, LHCb unveiled a new measurement of the angular distribution of the rare B0→K*0μ+μ– decay. The interesting part of this process involves a b → s transition (a bottom quark decaying into a strange quark), where number of anomalies have been seen in recent years.

Rather just measuring the total rate of this decay, this analysis focuses on measuring the angular distribution of the decay products. They also perform this mesaurement in different bins of ‘q^2’, the dimuon pair’s invariant mass. These choices allow the measurement to be less sensitive to uncertainties in the Standard Model prediction due to difficult to compute hadronic effects. This also allows the possibility of better characterizing the nature of whatever particle may be causing a deviation.

The kinematics of decay are fully described by 3 angles between the final state particles and q^2. Based on knowing the spins and polarizations of each of the particles, they can fully describe the angular distributions in terms of 8 parameters. They also have to account for the angular distribution of background events, and distortions of the true angular distribution that are caused by the detector. Once all such effects are accounted for, they are able to fit the full angular distribution in each q^2 bin to extract the angular coefficients in that bin.

This measurement is an update to their 2015 result, now with twice as much data. The previous result saw an intriguing tension with the SM at the level of roughly 3 standard deviations. The new result agrees well with the previous one, and mildly increases the tension to the level of 3.4 standard deviations.

This latest result is even more interesting given that LHCb has seen an anomaly in another measurement (the R_k anomaly) involving the same b → s transition. This had led some to speculate that both effects could be caused by a single new particle. The most popular idea is a so-called ‘leptoquark’ that only interacts with some of the flavors.

LHCb is already hard at work on updating this measurement with more recent data from 2017 and 2018, which should once again double the number of events. Updates to the R_k measurement with new data are also hotly anticipated. The Belle II experiment has also recent started taking data and should be able to perform similar measurements. So we will have to wait and see if this anomaly is just a statistical fluke, or our first window into physics beyond the Standard Model!

Read More:

Symmetry Magazine “The mystery of particle generations”

Cern Courier “Anomalies persist in flavour-changing B decays”

Lecture Notes “Introduction to Flavor Physcis”

## A new anomaly: the electromagnetic duality anomaly

Article: Electromagnetic duality anomaly in curved spacetimes
Authors: I. Agullo, A. del Rio and J. Navarro-Salas
Reference: arXiv:1607.08879

Disclaimer: this blogpost requires some basic knowledge of QFT (or being comfortable with taking my word at face value for some of the claims made :))

Anomalies exists everywhere. Probably the most intriguing ones are medical, but in particle physics they can be pretty fascinating too. In physics, anomalies refer to the breaking of a symmetry. There are basically two types of anomalies:

• The first type, gauge anomalies, are red-flags: if they show up in your theory, they indicate that the theory is mathematically inconsistent.
• The second type of anomaly does not signal any problems with the theory and in fact can have experimentally observable consequences. A prime example is the chiral anomaly. This anomaly nicely explains the decay rate of the neutral pion into two photons.

In this paper, a new anomaly is discussed. This anomaly is related to the polarization of light and is called the electromagnetic duality anomaly.

Chiral anomaly 101
So let’s first brush up on the basics of the chiral anomaly. How does this anomaly explain the decay rate of the neutral pion into two photons? For that we need to start with the Lagrangian for QED that describes the interactions between the electromagnetic field (that is, the photons) and spin-½ fermions (which pions are build from):

$\displaystyle \mathcal L = \bar\psi \left( i \gamma^\mu \partial_\mu - i e \gamma^\mu A_\mu \right) \psi + m \bar\psi \psi$

where the important players in the above equation are the $\psi$s that describe the spin-½ particles and the vector potential $A_\mu$ that describes the electromagnetic field. This Lagrangian is invariant under the chiral symmetry:

$\displaystyle \psi \to e^{i \gamma_5} \psi .$

Due to this symmetry the current density $j^\mu = \bar{\psi} \gamma_5 \gamma^\mu \psi$ is conserved: $\nabla_\mu j^\mu = 0$. This then immediately tells us that the charge associated with this current density is time-independent. Since the chiral charge is time-independent, it prevents the $\psi$ fields to decay into the electromagnetic fields, because the $\psi$ field has a non-zero chiral charge and the photons have no chiral charge. Hence, if this was the end of the story, a pion would never be able to decay into two photons.

However, the conservation of the charge is only valid classically! As soon as you go from classical field theory to quantum field theory this is no longer true; hence, the name (quantum) anomaly.  This can be seen most succinctly using Fujikawa’s observation that even though the field $\psi$ and Lagrangian are invariant under the chiral symmetry, this is not enough for the quantum theory to also be invariant. If we take the path integral approach to quantum field theory, it is not just the Lagrangian that needs to be invariant but the entire path integral needs to be:

$\displaystyle \int D[A] \, D[\bar\psi]\, \int D[\psi] \, e^{i\int d^4x \mathcal L}$ .

From calculating how the chiral symmetry acts on the measure $D \left[\psi \right] \, D \left[\bar \psi \right]$, one can extract all the relevant physics such as the decay rate.

The electromagnetic duality anomaly
Just like the chiral anomaly, the electromagnetic duality anomaly also breaks a symmetry at the quantum level that exists classically. The symmetry that is broken in this case is – as you might have guessed from its name – the electromagnetic duality. This symmetry is a generalization of a symmetry you are already familiar with from source-free electromagnetism. If you write down source-free Maxwell equations, you can just swap the electric and magnetic field and the equations look the same (you just have to send $\displaystyle \vec{E} \to \vec{B}$ and $\vec{B} \to - \vec{E}$). Now the more general electromagnetic duality referred to here is slightly more difficult to visualize: it is a rotation in the space of the electromagnetic field tensor and its dual. However, its transformation is easy to write down mathematically:

$\displaystyle F_{\mu \nu} \to \cos \theta \, F_{\mu \nu} + \sin \theta \, \, ^\ast F_{\mu \nu} .$

In other words, since this is a symmetry, if you plug this transformation into the Lagrangian of electromagnetism, the Lagrangian will not change: it is invariant. Now following the same steps as for the chiral anomaly, we find that the associated current is conserved and its charge is time-independent due to the symmetry. Here, the charge is simply the difference between the number of photons with left helicity and those with right helicity.

Let us continue following the exact same steps as those for the chiral anomaly. The key is to first write electromagnetism in variables analogous to those of the chiral theory. Then you apply Fujikawa’s method and… *drum roll for the anomaly that is approaching*…. Anti-climax: nothing happens, everything seems to be fine. There are no anomalies, nothing!

So why the title of this blog? Well, as soon as you couple the electromagnetic field with a gravitational field, the electromagnetic duality is broken in a deeply quantum way. The number of photon with left helicity and right helicity is no longer conserved when your spacetime is curved.

Physical consequences
Some potentially really cool consequences have to do with the study of light passing by rotating stars, black holes or even rotating clusters. These astrophysical objects do not only gravitationally bend the light, but the optical helicity anomaly tells us that there might be a difference in polarization between lights rays coming from different sides of these objects. This may also have some consequences for the cosmic microwave background radiation, which is ‘picture’ of our universe when it was only 380,000 years old (as compared to the 13.8 billion years it is today!). How big this effect is and whether we will be able to see it in the near future is still an open question.

Further reading

• An introduction to anamolies using only quantum mechanics instead of quantum field theory is “Anomalies for pedestrians” by Barry Holstein
• The beautiful book “Quantum field theory and the Standard Model” by Michael Schwartz has a nice discussion in the later chapters on the chiral anomaly.
• Lecture notes by Adal Bilal for graduate students on anomalies in general  can be found here