Do we have finally found new physics with the latest W boson mass measurement?

If you are interested in particle physics, then you certainly heard about the most recent measurement of the W boson mass by the CDF Collaboration [1], which implies a seven sigma (!) deviation from the Standard Model prediction. Is this finally the sign of new physics, which we all have been hoping for? I fear not (yet).

I started to work on the W boson mass in 2012 and it took us more than five years to publish a first measurement based on data of the ATLAS Experiment [2]. When I applied for funding for this project, one of the referees wrote that "this measurement is too complicated to be done in time and hence (s)he would not recommend funding". Luckily for me the other referees disagreed and I guess I have to thank the DFG and the Volkswagen foundation at this point that they were willing to take the risk. I have another anecdote on the W boson mass measurement, which illustrates its difficulty: We observed for quite some time some features in the our data, which we could not explain. Once one of my PhD students came into my office and told that he finally figured out this feature: the protons in the ATLAS detector do not collide heads-on but under a very small angle, allowing the not interacting protons to continue their travel through the LHC on the other side of the experiment. Indeed he was right - we have not been considering this effect in our simulations, however - after some calculations and speaking to the machine experts - it turned out that this effect induces a feature in our data, which is opposite in sign that we observe; so we have been left with an effect that was twice as large and unexplained. In the end it turned out to be caused by the deformation of the ATLAS detector by its own weight of more than 7000 tons over time. Enough of my memories - I just want to say with this that the W boson mass measurement is a difficult business.

So let's start to look at the new CDF measurement. I just had a brief look, so all what I say needs to be taken with some caution. Clearly it is striking that CDF observes a 7 sigma difference to the Standard Model, which alone would be phenomenal. The main problem, however, is that the new measurement is in disagreement with all other available measurements. I think this could have been presented better in their paper, mainly because the measurements of the LEP experiments have not been combined, secondly because they don't show the latest result from LHCb. Hence I created a new plot (below), which allows for a more fair judgement of the situation. I also made a back-of-envelope combination of all measurements except of CDF, yielding a value of 80371+-14 MeV [3]. It should be pointed out that all these combined measurements rely partly on different methodologies as well as partly on different model uncertainties. The likelihood of the consistency of such a (simple) combination is 0.93. Depending (a bit) on the correlations you assume, this value has a discrepancy of about 4 sigma to the CDF value. So I do not think, we have to discuss which new physics could explain the discrepancy between CDF and the Standard Model - we first have to understand, why the CDF measurement is in strong tension with all others.

Comparison of the CDF measurement with the most precise other W boson mass measurements. The Standard Model (SM) prediction is based on the Gfitter Programm (https://arxiv.org/abs/1803.01853, https://arxiv.org/abs/0811.0009) 

In fact, there are certainly some aspects of the measurement which need to be discussed in more detail (Sorry, now follow some technical aspects, which most likely only people from the field can fully understand): In the context of the LHC Electroweak Working Group, there are ongoing efforts to correctly combine all measurements of the W boson mass; in contrast to what I did above, this is in fact also a complicated business, if you want to do it really statistically sound. My colleague and friend Maarten Boonekamp pointed out in a recent presentation [4], that the Resbos generator (which was used by CDF) has potentially some problems when describing the spin-correlations in the W boson production in hadron collisions. In fact, there are remarkable changes in the predicted relevant spectra between the Resbos program and the new version of the program Resbos2 (and other generators) as seen in the plot below. On first sight, the differences might be small, but you should keep in mind, that these distributions are super sensitive to the W boson mass. I also attached a small PR plot from our last paper, which indicates the changes in those distributions when we change the W boson mass by 50 MeV, i.e. more than ten times than the uncertainty which is stated by CDF. I really don't want to say that this effect was not yet considered by CDF - most likely it was already fixed since my colleagues from CDF are very experienced physicists, who know what they do and it was just not detailed in the paper. I just want to make clear that there are many things to be discussed now within the community to investigate the cause of the tension between measurements. 

 

Difference in the transverse mass spectrum between Resbos and Resbos2 from [4] (left); impact of different W boson mass values on the shapes of transverse mass from [5]

And this brings me to another point, which I consider crucial: I must admit that I am quite disappointed that it was directly submitted to a journal, before uploading the results on a preprint server. We live in 2022 and I think it is by now good practice to do so, simply because the community could discuss these results beforehand - this allows a scientific scrutiny from many scientists which are directly working on similar topics.

Let's not end this comment without two positive thoughts: The experimental part of the analysis is very beautiful. You cannot imagine the amount of work that is necessary to understand your detector with the precision as the colleagues at CDF do. And my last thought: Even if the CDF measurement is too large by 30 MeV and even if the uncertainty is in reality 30% larger, then the new world average would be something like 80386 MeV and a total uncertainty of 9 MeV with a decent consistency of all measurements. And this is still about three sigma from the Standard Model value - so it is certainly worth to look at the W boson mass in future!

Further Information:
[1] CDF Collaboration, High-precision measurement of the W boson mass with the CDF II detector, 2022, https://www.science.org/doi/10.1126/science.abk1781
[2] ATLAS Collaboration, Measurement of the W-boson mass in pp collisions at 7 TeV with the ATLAS detector, https://arxiv.org/abs/1701.07240
[3] Based on a combination with BLUE method, assuming different correlation scenarios ranging from -0.3 to 0.3.
[4] M. Boonekamp: LHC EWK Working Group: https://indico.cern.ch/event/1108518/contributions/4691380/attachments/2392473/4090175/combi_160222_EWWG.pdf

What Physicists can say about the Coronavirus

People in my wider social environment, who are not scientists, start to ask me questions about the spreading of the Corona Virus – clearly I feel flattered, ‘cause, hey, I am a clever scientist and I know about exponentials and also about logistic curves. However, I stop after explaining these fundamental mathematical constructs and I am certainly not starting to judge or recommend actions (to be) taken by governments. I am not an expert on epidemics, I am not an expert on virology, I am not an expert on social behaviors – I just know exponentials.

Why making this obvious statement? Well, I see more and more articles and posts where different nations are compared, and simple data-analyses are performed – either by science journalists or by fellow scientists (and also physicists). Well, I guess people start to get bored. My problem is not that people do data-analysis and explain exponentials or logistic curves. This I find super important (and it is fun too). My problem is, that they draw conclusions and give recommendations or projections.  

I think all these conclusions have all one thing in common: they are certainly too simplistic and most likely plain wrong (apart from the exponential functions which people fit – who would have thought). Nobody of these simple analyses considers obvious factors, e.g. the quality of the underlying data, the differences in the capabilities of the health- and testing-system, differences in the population and their behavior and many others. And all these things definitely matter, when you want to draw any conclusion which goes beyond “Oh look – it is exponential”. And since I am not an expert, I am surely missing hundreds of other factors which matter. Just because one action might or might not have helped in country A does not tell you how this is transferable to country B. The world is complex, if you haven’t noticed yet.

I am certainly convinced that it is important to get the right point in time for the right measure – it must be clear to everybody, that an action that is taken too late can be as harmful as an action that is taken too soon. So, who knows then the best way forward? Everybody agrees that one has to slow down the spread so that your health system doesn’t collapse. Everybody also agrees that simple hygienic measures have to be taken: keep a reasonable distance, wash your damn hands and for god sake cough correctly. But I am afraid there is no definite answer beyond that and we have to live with it. 

It has to be trial and error and from an experimental perspective it might be even useful that different countries try different things – this is the only way how we will learn better in the future. I am just happy that I do not have to take now political decisions, because nobody knows what the optimal answer is – and surely no scientist, who just can fit an exponential and has no other expertise on this topic. However, I get more and more the feeling that far too many people believe they know exactly what should be done. 

And since I am already on it: From time to time, I talk to journalists about my research and I really try to explain things in simple terms. Sometimes journalists even try to summarize some of my papers. In both cases, I am puzzled when I read the first draft of their article. Crucial information is taken out of context or just explained wrongly. Just some days ago, I read about my research that I “study axions, which are the lightest particles in the universe”. People who know my research, understand what’s wrong with this sentence and for all others: naah – I am not doing that. You might think that this is just the case for my research, and I am particularly bad at explaining.

It turns out that all of my colleagues from different fields of sciences have similar experiences. I am sure, the journalists try their best to cook things down so that non experts can easily understand them – however, this is really difficult, and I don’t blame them, that they fail. However, the conclusion for me is also clear: If I read an article from a journalist, even from a journalist with a scientific background, then I should not think that I really understood anything in detail of the underlying research and it certainly doesn’t qualify me to draw any significant conclusion. So, if you read about “a fact in an article” on the Coronavirus, I am almost certain that necessary context is missing for any non-trivial conclusions. So the takeaway message is once again: Ignore all recommendations from people, who have no relevant expertise - and physicists don’t have any of it. For myself: I better go back to work on stuff which I am expert on and extend my knowledge in reconstruction further: install powerlines and lay sewage pipes.

Mini Black Hole Signatures in the Standard Model – Instantons at the LHC

I was recently very lucky and got an ERC grant to search for axion-like particles at colliders. I might write about this topic in the future, but today I want to write about a QCD Instantons. Those have been the topic of my ERC grant proposal two years ago, which was not funded. I don’t take that personal (one never should, since there is a huge portion of luck involved in  all funding decisions), however, I still think that QCD Instantons are a super interesting topic. Hence Instantons will be the first topic of this blog.

I guess most of you have never heard of instantons. Funnily, Instanton processes are known already in non-relativistic quantum mechanics, where they describe tunneling transitions of finite action. As an illustrative example, one can calculate the tunnel processes in a double-well potential shown in Figure 1. These processes are forbidden in classical physics, as they represent solutions to the equation of motion with negative kinetic energy. However, by rotating the real time t to imaginary (Euclidean) time 𝛕=i·t, the potential well changes into a hump, also shown in Figure 1 and a classical solution can be derived. The consequence of this rotation of the time-coordinate becomes clear when interpreting it in the Feynman path integral formalism: Here, every possible path is weighted by 

Although any path is allowed in quantum mechanics, the dominant contribution comes from paths which maximise the weight factor and thereby minimise the classical action. When calculating the solution in Euclidean time, one finds

which is illustrated in Figure 2 along with its imaginary time derivative. These solutions are called (anti)-instanton, depending on the sign. As can be seen, the transition is localized around the time τ0, i.e. the system changes its state rapidly, therefore the name instanton. The corresponding action of this classical solution yields

where λ is the height of the potential well and x0 corresponds to one of its minima. The action is finite, does not depend on τ and therefore non-trivial solutions have been found with a finite transition probability.

Figure 1: Double well potential with two classical states (left); transition for potential to τ = i · t into the double hump potential (right).	Figure 2: Instanton solution in imaginary time (left) and its derivative, illustrating the localisation in time.

The concept of Instanton solutions can be extended to Yang-Mills theories. The non-Abelian nature of Yang-Mills theories implies non-contractable loops in the space of its gauge fields, leading to a non-trivial vacuum structure. The topology of a Yang-Mills vacuum is depicted in Figure 3 by the energy density of the gauge field as a function of the Chern-Simons or winding number NCS, describing the topological charge of a system. In analogy to the quantum-mechanical example, instantons describe tunneling transitions in Minkowski spacetime between classically degenerate vacua, which only differ by their winding number by one unit, i.e. ΔNCS =1. Here, an Instanton solution is not only localized in time, but also in space, i.e. it has a certain spatial extension. There is also a second class of classical solutions, known as Sphalerons, corresponding to a transition from one vacuum by a half-integer winding number on top of the energy barrier (also shown in Figure 3), where its static energy corresponds to the barrier height.

Figure 3: Instanton and Sphaleron processes in the topology of a Yang-Mills vacuum; energy density of the gauge field (y-axis) vs. winding number NCS (x-axis).	Figure 4: Production and decay of an Instanton pseudo-particle

   

These solutions differ significantly from the solutions known from ordinary perturbation theory, where only those field configurations are accessible which correspond to small changes of the vacuum field at NCS = 0, while other minima, which are not accessible by continuous transformation of the gauge field, are ignored. Clearly, this approximation holds only as long as the energy barrier between the vacua is sufficiently large. 

Let’s take a short break and recap: The vacuum structure of the Standard Model – both the QCD but also the electroweak part – is not trivial: there is an infinite number of vacua. The reason, why you probably never heard of these Instanton processes is simple: in perturbation theory, we just choose one specific vacuum, expand around our coupling constants and ignore all other vacua around it, as we assume they are separated by the potential wall in between. 

Nevertheless, Instanton and Sphaleron solutions provide crucial ingredients for an understanding of several aspects in the Standard Model: On the one hand, Instanton and Sphaleron processes in the electroweak sector are associated to baryon+lepton number violation. These become important at high temperatures, as the system has then enough energy to “move” from one vacuum to another [1]. This has a crucial consequence on the evolution of the baryon and lepton asymmetries of the universe (see [2] for a review). On the other hand, such topological fluctuations of the gauge fields in QCD have been argued to play an important role in various long-distance aspects of QCD, and as such provide a possible solution to the axial U(1) problem [3] or are at work in chiral symmetry breaking.

The actual height of the energy barrier between two vacua, sometimes called Sphaleron mass MSp, depends on the type of the underlying Yang-Mills theory. For the electroweak sector, the height is in the order of 10 TeV. For QCD, on the other hand, the barrier height between two vacua is defined by the energy scale parameter Q of the underlying process. It will be large for high energy processes, but it will be small when we reach low energies, e.g. ΛQCD=218 MeV. In fact, the barrier is inversely proportional to the fine-structure constant of the relevant gauge theory. This also means, that Instanton processes play a role in low energy phenomena, which is the reason why they are indeed observed in lattice QCD calculations. 

The question for me as experimental physicists is: Can we find experimental evidence for Instanton (or Sphaleron) processes in the lab? To answer this question, we have to answer two subsequent questions: first, what is the cross-section, i.e. the probability that these processes occur and second, what is their experimental signature. Unfortunately, the answer to both questions is not very pleasant. 

Naively, the cross section of Instanton processes in particle collisions are exponentially suppressed by the height of barrier: for Instanton processes in the electroweak sector, one expects cross sections in the order of 0.001 fb for a 200 TeV proton-proton collider. If you are not familiar with cross sections: This essentially means you will need to measure for many many years at a collider that isn’t even planned by the most ambitious among my colleagues. So, what about QCD? Here things are more promising in proton-proton collisions at 13 TeV, i.e. the energies of the LHC: We expect cross sections in the order of millibarns for processes with energies in the 10 GeV region and still a few pico-barns for processes with a relevant energy scale of 200 GeV. That sounds cool – no? Well, here comes the second question into the game: What are the experimental signatures of an Instanton process? For a reason, which I am happy to admit that I don’t fully understand, an Instanton tunnel processes can be seen as the creation and decay of a pseudo-particle with a certain mass, the latter determined by the barrier height [5].

The leading Feynman diagram for the production and the decay of a QCD Instanton pseudo-particle (let’s call it from now on Instanton for simplicity) in proton-proton collisions is shown in Figure 4. The experimental signature is hence given by the isotropic decay of the pseudo-particle into all accessible quarks in addition to some gluons - very similar to the expected decay of mini black holes. The available energy of these decay processes is given by the associated Instanton mass. The energies of the decay particles are therefore expected to lie in the range between a few hundred MeV and up to several GeV. As an experimentalist you expect therefore lots of charged particle tracks and/or jets in your events – unfortunately that looks pretty much like normal QCD processes, typically known as underlying event (for the low energy regime) or multi-jet processes (for the high energy regime). So, some serious thinking has to be done, how to find ways to discriminate QCD Instantons from all the rest. I think it is totally worth it, as it would be a real breakthrough to proof the non-trivial vacuum structure of the Standard Model and all its associated effects, which are predicted since decades. It might not be as fundamental as the Higgs Boson, but equally spectacular. 

So far, no dedicated search efforts for Instanton processes in proton-proton collisions have never been conducted. I think the main reason for that is, that until very recently, no predictions of their signatures have been available for the LHC. This changed recently, but several concerns on the validity of these predictions have been made [6]. In any case: I think Instantons are cool and certainly among the most promising candidates to observe new effects at the LHC.

What you should take away? Instantons are a fundamental prediction by the Standard Model but have never been observed. While it is extremely challenging to the search for them, I am convinced that it is totally worth the effort. And last but not least: Getting rejections from funding agencies shouldn’t demotivate you.

[1] On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe, V.A. Kuzmin, V.A. Rubakov (Moscow, INR), M.E. Shaposhnikov (ICTP, Trieste), Jan 1985. 7 pp., Published in Phys.Lett. 155B (1985) 36 
[2] Electroweak baryon number nonconservation in the early universe and in high-energy collisions, V.A. Rubakov (Moscow, INR), M.E. Shaposhnikov (CERN & Moscow, INR). Mar 1996. 123 pp. Published in Usp.Fiz.Nauk 166 (1996) 493-537, Phys.Usp. 39 (1996) 461-502 
[3] How Instantons Solve the U(1) Problem, Gerard 't Hooft (Utrecht U.). Apr 1986. 50 pp. Published in Phys.Rept. 142 (1986) 357-387 
[4] A Theory of Light Quarks in the Instanton Vacuum, Dmitri Diakonov, V.Yu. Petrov (St. Petersburg, INP). Apr 1985. 33 pp. Published in Nucl.Phys. B272 (1986) 457-489 
[5] Zooming in on instantons at HERA, A. Ringwald, F. Schrempp (DESY). Dec 2000. 13 pp. Published in Phys.Lett. B503 (2001) 331-340 

[6] Large Effects from Small QCD Instantons: Making Soft Bombs at Hadron Colliders, Valentin V. Khoze, Frank Krauss (Durham U., IPPP), Matthias Schott (University Coll. London & Mainz U.). Nov 21, 2019. 29 pp, e-Print: arXiv:1911.09726 [hep-ph]

What this blog is about?

To be honest, I have no real long-term strategy on the topics that I will cover. This whole thing starts in a train ride from Frankfurt to Nuremberg, which I am frequently on. Typically, I use this time to answer emails, prepare lectures or write grant proposals, however, sometimes I need breaks. So, this will not mainly be written for you, rather than written as a self-entertainment exercise. I am happy to read comments, I almost certainly will think about them, but I don’t plan to get involved into any discussions (as said, I do this as a break, not because I am bored).

So, take my opinion on things as a snapshot at the time when I post them, not as my definite say… Given the nature of this blog, I target, well, mainly myself, but I try to keep it accessible for people with a physics background. Also, I am “only” an experimental physicist hence my wording (and my understanding) might be a little imprecise in the view of my theory colleagues. That’s all for now, as I am arriving in Nuremberg and have to get out ... (btw: the train was on time)