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Andrea Signori | Nikhef | Netherlands

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[email protected]: Going beyond the collider

Tuesday, April 7th, 2015

While everybody is excited by the coming “phase 2” of the LHC, someone else is already looking beyond it, thinking: “what are the possible future scenarios for our beloved Large Hadron Collider?”

The community of “phenomenologists”, theoreticians who like to play with data, closely collaborate with experimentalists to plan new experiments. We are hoping to get the most out of a set-up and think about future stages and improvements.

In the last months there has been a lot of interest around a proposal for a new experiment at the LHC: [email protected], namely A Fixed Target ExpeRiment at the LHC. This means that we do not have particles running in opposite directions within two rings (the collider setting), crashing head-on; rather, there is just one ring where particles run coherently and are then extracted by means of a crystal and smashed against a fixed target, like hitting a wall.


You may actually wonder: “Why should I prefer this instead of the super nice and Nobel-prize-generator collider?”

In the LHC protons are accelerated at approximately the speed of light and collide along the ring. The protons are made out of quarks and gluons, so each proton-proton collision can be interpreted as a smashing among their elementary constituents. In particular, since gluons are the most relevant elementary constituents at the LHC energy, the latter can be thought as a collider of gluons.

As I partly discussed in a previous post, we can study the structure of the proton with 3D probability distributions (transverse-momentum-dependent distributions, TMDs) which allow you to access all the possible spin and momentum configurations of the constituents. For example, quark and gluons can be investigated with and without their spin state, and the proton where they live in can be polarized or not. There are several of these combinations and each one represents a fundamental piece in the puzzle of the proton structure.

The LHC is currently running with beam of unpolarized protons only. Meaning we do not consider their spin in analyses. For those who want to investigate the puzzle of a proton’s structure, this is a limitation. We are able to access only two out of the eight (under certain assumptions) configurations of polarizations, namely the unpolarized and the linearly polarized gluons. So there are six options we don’t get to study!

In this table the eight available TMD (transverse-momentum-dependent) distributions shaping the physics of (un)polarized gluons inside (un)polarized protons are listed. At the LHC we can access the first row only, at AFTER more combinations will be investigated.

In this table the eight available TMD distributions shaping the physics of (un)polarized gluons inside (un)polarized protons are listed. At the LHC we can access the first row only, at AFTER more combinations will be investigated.

And here is the answer to our question. The fixed target at AFTER could be easily polarized, allowing us to study the physics of gluons inside polarized protons, which would be impossible at the present collider! There is only another machine in the world where hadrons can be polarized: the Relativistic Heavy Ion Collider – RHIC at Brookhaven National Lab.

For this reason, AFTER could access novel phenomena intrinsically related to the polarization of hadrons and, at the same time, allow us to study processes already available at the LHC but in different physical regions. For example, there is the possibility of accessing the simple 1D probability distributions in a region where they are still poorly known.

A particularly interesting observable which AFTER could look at is the so-called “Sivers” distribution for gluons, namely the probability of extracting unpolarized gluons from a proton whose spin is transverse with respect to the direction of the beam. Part of its core features cannot be calculated from first principles in the theory, so a good way to explore it would be extraction from experimental data. In the past years physicists got indications that the Sivers effect for gluons could be small, but an experimental insight at AFTER would be really important.

As you can see, there could be a lot of cool physics going on. We are in the early stages, where all the possible (including economic) constraints need to be taken into account and where a good scientific motivational plan is fundamental.

When you try to give birth to an experiment you face a lot of problems, like “What’s a realistic estimate of its scientific impact? Do we really need a new machine or not?” Some of these questions have already been addressed and the answers are collected in scientific publications, which you can partly find here.

If everything goes according to plan and desires, [email protected] will bring very good insight and contributions to the study of the proton structure: stay tuned for updates!


United for peace

Monday, January 12th, 2015

The past week saw extremely sad events in Paris, reminding us that our society relies on a fragile equilibrium. This is just the most recent episode over the last years in a long list of events around the world – and also in Amsterdam, the city where I now live.

We have been flooded through the mass media by analyses, considerations, speeches and public actions. I don’t think it is necessary to add more here, because what we mostly need is time to think: about us as individuals and as active parts of a complex society.

Nevertheless, I would like to remind myself – and everyone who will read these thoughts – about what we can do as men and women of science. Even though fear and anger may knock at our doors, we need to find what could keep us united across different countries, cultures, religions and faiths. And fight for it.

As scientists, we are privileged: our job is to generate knowledge, the common heritage of mankind. Science is a universal endeavor involving people from every country, social background and culture. No matter what we think and believe, we collaborate daily to reach a high goal. Science, like any other intercultural enterprise, is a training for peace, and we are in extreme need of it and anything else that keeps us united in purity of interests, freedom and friendship.

The "tree of peace" in The Hague, which carries people's wishes for a better and peaceful world.

The “tree of peace” in The Hague (NL), which carries people’s wishes for a better and peaceful world.

The quest for peace is not just a hand-waving argument, nor fantasy of hopeful people: it is clearly stated even in the original documents of CERN – the European Center for Nuclear Research – signed by the founding members and shared by every single scientist working and studying there.

I. I. Rabi, an American scientist among the first supporters of CERN, greeted the 30th anniversary of CERN foundation with these words(*): “I hope all the scientists at CERN will remember to have more duties than just doing research in particle physics. They represent the results of centuries of research and study, showing the powers of the human mind. I hope they will not consider themselves technicians, but guardians of the European unity, so that Europe can protect peace in the world.”

Let’s build together a future of peace: we can do it.

(*) translated from the Italian version available here.


A transverse look into the proton

Friday, December 19th, 2014

Protons and neutrons (alias, the nucleons) constitute the building blocks of matter, accounting for almost all the mass of our world. Even if we are still far from understanding their physical inner structure, many efforts have been made to deepen our knowledge about them.

Over the past few years, thanks to a fruitful synergy of theoretical and experimental progress, we have started opening the study of new multi-dimensional images of the structure of proton, investigating the behavior of its fundamental constituents, the quarks and gluons.

When we look into nucleons with extremely high resolution, we are in the regime of perturbative QCD (in other words, a regime where we can really work out mathematical calculations) and quarks and gluons appear almost free. With the due caveats, we can compare the situation to observing water at extreme magnifications, and seeing quasi-free water molecules. As we reduce the magnification, we realize that the molecules clump together in heavier, composite droplets. Eventually, at low magnification they form a single object, like the proton.

Pursuing the analogy, when we are looking at a proton at rest (not smashed inside a collider, for example) it is as if we were unable to describe water starting from the dynamics of molecules. This is because confinement, the reason for quarks and gluons being inescapably bound inside a proton, is left without any rigorous mathematical justification. Confinement is the most crucial characteristic of the theory and represents one of the hardest physics problems of today.

What we can do is to just describe this jam of quarks and gluons giving rise to a proton through mathematical objects specifically introduced in order to “parametrize” our ignorance about its structure: these are what are called parton distribution functions (PDFs), which shape the probability of finding quarks and gluons within a proton.

The knowledge of the multi-dimensional structure of protons allows the analysis of properties otherwise inaccessible. The situation may be compared to diagnostic studies: electrocardiography, for example, gives us mono-dimensional information about the hearth activity. It is of fundamental importance, but it does not give detailed information about the multidimensional inner structure. Instead, more important for this purpose are multi-dimensional tomographies of heart activity (MRI, CT and others). The enormous advantages of medical diagnostic imaging literally revolutionized medicine and surgery. In a similar way, the latest “multi-dimensional” pictures of the nucleon obtained with QCD phenomenology can improve the current status of hadronic physics and aim at better understanding particle physics in general.

Although one-dimensional (collinear) parton distribution functions are extremely useful for studying any process involving hadrons (including the proton-proton collisions taking place at the LHC), from the point of view of nucleon tomography they are rather limited, because they describe the distribution of partons in a single dimension.

More informative distributions are the so-called transverse-momentum-dependent distributions (TMDs). They represent pictures of three-dimensional probabilities in momentum space. The distributions change depending on the energy scale at which they are probed (in a way that is calculable using evolution equations from perturbative QCD) and on the value of the longitudinal fractional momentum.

Partons (quarks and gluons) are like fishes confined inside a fishbowl (the proton). Each parton has its own collinear and transverse velocity, indicated by black and colored arrows respectively. Different colors indicate different flavors for quarks.

Partons (quarks and gluons) are like fishes confined inside a fishbowl (the proton). Each parton has its own collinear and transverse velocity, indicated by black and colored arrows respectively. Different colors indicate different flavors for quarks and external excitations (like photons) can extract partons from inside the proton. (credit: A. Signori)

There are many nontrivial questions concerning TMDs that do not have an answer yet, like their most truthful mathematical representation. At present, we know that experimental data form proton-proton and electron-proton collisions point towards Gaussian shapes (if the spin of quarks is neglected), but other forms could do the job as well.

An important question concerns the flavor dependence of transverse-momentum-dependent distributions: are up quarks moving in the nucleon with greater velocity than the down ones, or vice versa? What about sea quarks? Are they faster than the other ones? Part of my research activity is devoted to the investigation of this topic, which could be quite relevant both from the theoretical and experimental point of view. After lot of struggling with data analysis, we now know that sea quarks are likely to be faster than up quarks, which are then faster than down ones.

The statistical analysis of the huge amount of data collected at hadron colliders like the Tevatron and the LHC strongly relies on the detailed knowledge of parton distribution functions, both in 1D and 3D (the TMDs!). Before now, data analysis has been carried out assuming that quarks have all the same velocity, but we now know that this is not the case! This means that it will be important to refine the knowledge of quark (and gluons too, in the future) velocities, in order to improve the accuracy and reliability of data analysis. That’s what a PhD student can do during his/her amazing time in scientific research!


Geometry and interactions

Tuesday, November 25th, 2014

Or, how do we mathematically describe the interaction of particles?

In my previous post, I addressed some questions concerning the nature of the wavefunction, the most truthful mathematical representation of a particle. Now let us make this simple idea more complete, getting closer to the deep mathematical structure of particle physics. This post is a bit more “mathematical” than the last, and will likely make the most sense to those who have taken a calculus course. But if you bear with me, you may also come to discover that this makes particle interactions even more attractive!

The field theory approach considers wavefunctions as fields. In the same way as the temperature field \(T(x,t)\) gives the value of the temperature in a room at space \(x\) and time \(t\), the wavefunction \(\phi (x,t)\) quantifies the probability of presence of a particle at space point \(x\) and time \(t\).
Cool! But if this sounds too abstract to you, then you should remember what Max Planck said concerning the rise of quantum physics: “The increasing distance between the image of the physical world and our common-sense perception of it simply indicates that we are gradually getting closer to reality”.

Almost all current studies in particle physics focus on interactions and decays of particles. How does the concept of interaction fit into the mathematical scheme?

The mother of all the properties of particles is called the Lagrangian function. Through this object a lot of properties of the theory can be computed. Here let’s consider the Lagrangian function for a complex scalar field without mass (one of the simplest available), representing particles with electric charge and no spin:

\(L(x) = \partial_\mu \phi(x)^* \partial^\mu \phi(x) \).

Mmm… Is it just a bunch of derivatives of fields? Not really. What do we mean when we read \(\phi(x)\)? Mathematically, we are considering \(\phi\) as a vector living in a vector space “attached” to the space-time point \(x\). For the nerds of geometry, we are dealing with fiber bundles, structures that can be represented pictorially in this way:


Click on image for larger version

The important consequence is that, if \(x\) and \(y\) are two different space-time points, a field \(\phi(x)\) lives in a different vector space (fiber) with respect to \(\phi(y)\)! For this reason, we are not allowed to perform operations with them, like taking their sum or difference (it’s like comparing a pear with an apple… either sum two apples or two pears, please). This feature is highly non-trivial, because it changes the way we need to think about derivatives.

In the \(L\) function we have terms containing derivatives of the field \(\phi(x)\). Doing this, we are actually taking the difference of the value of the field at two different space-time points. But … we just outlined that we are not allowed to do it! How can we solve this issue?

If we want to compare fields pertaining to the same vector space, we need to slightly modify the notion of derivative introducing the covariant derivative \(D\):

\( D_\mu = \partial_\mu + ig A_\mu(x) \).

Here, on top of the derivative \(\partial\), there is the action of the “connection” \(A(x)\), a structure which takes care of “moving” all the fields in the same vector space, and eventually allows us to compare apples with apples and pears with pears.
So, a better way to write down the Lagrangian function is:

\(L(x) = D_\mu \phi(x)^* D^\mu \phi(x) \).

If we expand \(D\) in terms of the derivative and the connection, \(L\) reads:

\(L(x) = \partial_\mu \phi(x)^* \partial^\mu \phi(x) +ig A_\mu (\partial^\mu \phi^* \phi – \phi^* \partial^\mu \phi) + g^2 A^2 \phi^* \phi \).

Do you recognize the role of these three terms? The first one represents the propagation of the field \(\phi\). The last two are responsible for the interactions between the fields \(\phi, \phi^*\) and the \(A\) field, referred to as the “photon” in this context.


Click on image for larger version

This slightly hand-waving argument involving fields and space-time is a simple handle to understand how the interactions among particles emerge as a geometric feature of the theory.

If we consider more sophisticated fields with spin and color charges, the argument doesn’t change. We need to consider a more refined “connection” \(A\), and we could see the physical interactions among quarks and gluons (namely QCD, Quantum Chromo Dynamics) emerging just from the mathematics.

 Probably the professor of geometry in my undergrad course would call this explanation “Spaghetti Mathematics”, but I think it can give you a flavor of the mathematical subtleties involved in the theory of particle physics.


From wavefunctions to detectors: how to think about particles

Sunday, November 9th, 2014

This blog is all about particle physics and particle physicists. We can all agree, I suppose, on the notion of the particle physicist, right? There are even plenty of nice pictures up here! But do we know or are we aware of what a particle really is? This fundamental question tantalized me from the very beginning of my studies and before addressing more involved topics I think it is worth spending some time on this concept. Through the years I probably changed my opinion several times, according to the philosophy underlying the topic that I was investigating. Moreover, there’s probably not a single answer to this question.

  1. The Standard Model: from geometry to detectors

The human mind conceived the Standard Model of Particle Physics to give a shape on the blackboard to the basic ingredients of particle physics: it is a field theory, with quantization rules, namely a quantum field theory and its roots go deep down to differential geometry.
But we know that “particles” like the Higgs boson have been discovered through complex detectors, relying on sophisticated electronic systems, tons of Monte Carlo simulations and data analysis. Quite far away from geometry, isn’t it?
So the question is: how do we fill this gap between theory and experiment? What do theoreticians think about and experimentalists see through the detectors? Furthermore, does a particle’s essence change from its creation to its detection?

  1. Essence and representation: the wavefunction

 Let’s start with simple objects, like an electron. Can we imagine it as a tiny thing floating here and there? Mmm. Quantum mechanics already taught us that it is something more: it does not rotate around an atomic nucleus like the Earth around the Sun (see, e.g., Bohr’s model). The electron is more like a delocalized “presence” around the nucleus quantified by its “wavefunction”, a mathematical function that gives the probability of finding the electron at a certain place and time.
Let’s think about it: I just wrote that the electron is not a localized entity but it is spread in space and time through its wavefunction. Fine, but I still did not say what an electron is.

I have had long and intensive discussions about this question. In particular I remember one with my housemate (another theoretical physicist) that was about to end badly, with the waving of frying pans at each other. It’s not still clear to me if we agreed or not, but we still live together, at least.

Back to the electron, we could agree on considering its essence as its abstract definition, namely being one of the leptons in the Standard Model. But the impossibility of directly accessing it forces me to identify it with its most trustful representation, namely the wavefunction. I know its essence, but I cannot directly (i.e. with my senses) experience it. My human powers stop to the physical manifestation of its mathematical representation: I cannot go further.
Renè Magritte represented the difference between the representation of an object and the object itself in a famous painting “The treachery of images”:


“Ceci n’est pas une pipe”, it says, namely “This is not a pipe”. He is right, the picture is its representation. The pipe is defined as “A device for smoking, consisting of a tube of wood, clay, or other material with a small bowl at one end” and we can directly experience it. So its representation is not the pipe itself.

As I explained, this is somehow different in the case of the electron or other particles, where experience stops to the representation. So, according to my “humanity”, the electron is its wavefunction. But, to be consistent with what I just claimed: can we directly feel its wavefunction? Yes, we can. For example we can see its trace in a cloud chamber, or more elaborate detectors. Moreover, electricity and magnetism are (partly) manifestations of electron clouds in matter, and we experience those in everyday life.


You may wonder why I go through all these mental wanderings: just write down your formulas, calculate and be happy with (hopefully!) discoveries.

I do it because philosophy matters. And is nice. And now that we are a bit more aware of the essence of things that we are investigating, we can move a step forward and start addressing Quantum Chromo Dynamics (QCD), from its basic foundations to the latest results released by the community. I hope to have sufficiently stimulated your curiosity to follow me during the next steps!

Again, I want to stress that this is my own perspective, and maybe someone else would answer these questions in a different way. For example, what do you think?


I feel it mine

Tuesday, October 21st, 2014

On Saturday, 4 October, Nikhef – the Dutch National Institute for Subatomic Physics where I spend long days and efforts – opened its doors, labs and facilities to the public. In addition to Nikhef, all the other institutes located in the so-called “Science Park” – the scientific district located in the east part of Amsterdam – welcomed people all day long.

It’s the second “Open Day” that I’ve attended, both as a guest and as guide. Together with my fellow theoreticians we provided answers and explanations to people’s questions and curiosities, standing in the “Big Bang Theory Corner” of the main hall. Each department in Nikhef arranged its own stand and activities, and there were plenty of things to be amazed at to cover the entire day.

The research institutes in Science Park (and outside it) offer a good overview of the concept of research, looking for what is beyond the current status of knowledge. “Verder kijken”, or looking further, is the motto of Vrije Universiteit Amsterdam, my Dutch alma mater.

I deeply like this attitude of research, the willingness to investigating what’s around the corner. As they like to define themselves, Dutch people are “future oriented”: this is manifest in several things, from the way they read the clock (“half past seven” becomes “half before eight” in Dutch) to some peculiarities of the city itself, like the presence of a lot of cultural and research institutes.

This abundance of institutes, museums, exhibitions, public libraries, music festivals, art spaces, and independent cinemas makes me feel this city as cultural place. People interact with culture in its many manifestations and are connected to it in a more dynamic way than if they were only surrounded by historical and artistic.

Back to the Open Day and Nikhef, I was pleased to see lots of people, families with kids running here and there, checking out delicate instruments with their curious hands, and groups of guys and girls (also someone who looked like he had come straight from a skate-park) stopping by and looking around as if it were their own courtyard.

The following pictures give some examples of the ongoing activities:

We had a model of the ATLAS detector built with Legos: amazing!


Copyright Nikhef

And not only toy-models. We had also true detectors, like a cloud chamber that allowed visitors to see the traces of particles passing by!


Copyright Nikhef

Weak force and anti-matter are also cool, right?


Copyright Nikhef

The majority of people here (not me) are blond and/or tall, but not tall enough to see cosmic rays with just their eyes… So, please ask the experts!


Copyright Nikhef

I think I can summarize the huge impact and the benefit of such a cool day with the words of one man who stopped by one of the experimental setups. He listened to the careful (but a bit fuzzy) explanation provided by one of the students, and said “Thanks. Now I feel it mine too.”

Many more photos are available here: enjoy!


Why pure research?

Thursday, October 2nd, 2014

With my first post on Quantum Diaries I will not address a technical topic; instead, I would like to talk about the act (or art) of “studying” itself. In particular, why do we care about fundamental research, pure knowledge without any practical purpose or immediate application?

A. Flexner in 1939 authored a contribution to Harper’s Magazine (issue 179) named “The usefulness of useless knowledge”. He opens the discussion with an interesting question: “Is it not a curios fact that in a world steeped in irrational hatreds which threaten civilization itself, men and women – old and young – detach themselves wholly or partly from the angry current of daily life to devote themselves to the cultivation of beauty, to the extension of knowledge […] ?”

Nowadays this interrogative is still present, and probably the need for a satisfactory answer is even stronger.

From a pragmatic point of view, we can argue that there are many important applications and spin-offs of theoretical investigations into the deep structure of Nature that did not arise immediately after the scientific discoveries. This is, for example, the case of QED and antimatter, the theories for which date back to the 1920s and are nowadays exploited in hospitals for imaging purposes (like in PET, positron emission tomography). The most important discoveries affecting our everyday life, from electricity to the energy bounded in the atom, came from completely pure and theoretical studies: electricity and magnetism, summarized in Maxwell’s equations, and quantum mechanics are shining examples.

It may seem that it is just a matter of time: “Wait enough, and something useful will eventually pop out of these abstract studies!” True. But that would not be the most important answer. To me this is: “Pure research is important because it generates knowledge and education”. It is our own contribution to the understanding of Nature, a short but important step in a marvelous challenge set up by the human mind.

Personally, I find that research into the yet unknown aspects of Nature responds to some partly conscious and partly unconscious desires. Intellectual achievements provide a genuine ‘spiritual’ satisfaction, peculiar to the art of studying. For sake of truth I must say that there are also a lot of dark sides: frustration, stress, graduate-depression effects, geographical and economic instability and so on. But leaving for a while all these troubles aside, I think I am pretty lucky in doing this job.


Books, the source of my knowledge

During difficult times from the economic point of view, it is legitimate to ask also “Why spend a lot of money on expensive experiments like the Large Hadron Collider?” or “Why fund abstract research in labs and universities instead of investing in more socially useful studies?”

We could answer by stressing again the fact that many of the best innovations came from the fuzziest studies. But in my mind the ultimate answer, once for all, relies in the power of generating culture, and education through its diffusion. Everything occurs within our possibilities and limitations. A willingness to learn, a passion for teaching, blackboards, books and (super)computers: these are our tools.

Citing again Flexner’s paper: “The mere fact spiritual and intellectual freedoms bring satisfaction to an individual soul bent upon its own purification and elevation is all the justification that they need. […] A poem, a symphony, a painting, a mathematical truth, a new scientific fact, all bear in themselves all the justification that universities, colleges and institutes of research need or require.”

Last but not least, it is remarkable to think about how many people from different parts of the world may have met and collaborated while questing together after knowledge. This may seem a drop in the ocean, but research daily contributes in generating a culture of peace and cooperation among people with different cultural backgrounds. And that is for sure one of the more important practical spin-offs.