From My Vast Repertoire ...

The following sections are included:

• Preface
• Contents

Guido Altarelli is a giant of particle physics, and I use the present tense advisedly, as his outstanding contributions to the discipline make his marks everlasting and as relevant today as ever. The breadth and depth of his scientific output are evidenced by the range of topics covered by the many distinguished physicists writing in this volume. From my vast repertoire is indeed a fitting title, since Guido’s work ranged from QCD to deep inelastic scattering and neutrino physics, and from HERA to LEP, the LHC and beyond. There were very few areas of particle physics that did not interest him, or to which he did not contribute.

Guido was my dearest friend. Our friendship lasted more than 60 years.

Our families knew each other before we did; our fathers had met and become close friends during their military service. His father was best man at my wedding as I was for Guido and Monica 20 years after…

The following sections are included:

• Introduction
• The early period
• The Rome period and the Altarelli–Parisi equations
• The CERN period
• The last period, conclusion
• Acknowledgements

The following sections are included:

• Introduction
• NLO corrections
  • Cancelling singularities
  • Current status
• NNLO
  • Loop amplitudes
  • Combination techniques
  • Physical results
• N³LO
• Resummation
  • Collinear resummation
  • Transverse momentum resummation
  • Recent progress in resummations
• Epilogue and Conclusions
• Acknowledgements

Scientifically, the notion of precision relates to the reproducibility and repeatability of a measurement or a prediction. In practical terms, it relates to the degree of consistency of repeated measurements, i.e. to the spread of such results around their average or mean value. The term precision measurements usually implies that one expects significantly higher precision, i.e. smaller spread, than previous measurements. In absolute terms, the attribute precise is often used for results with precisions below the percent level, but this boundary also depends on the current and commonly accepted level of consistency. For instance, measurements or predictions in the field of Quantum Chromodynamics, the gauge field theory of the strong interaction, are regarded to be precise if they reach precisions of 1% or less, while in Quantum Electrodynamics, “precision” would require levels of at least sub-per-mille to even parts-per-million.

Soon after Guido Altarelli’s passing away, the H1 and ZEUS collaborations published their final paper combining all measurements of inclusive deep inelastic scattering cross sections into a coherent data set. These data have a richness of physics, providing results for student textbooks and will provide the backbone of parametrisations of the structure of the proton for years to come. There is no doubt that Guido’s influence on these final HERA results was far reaching; as such the paper was dedicated to his memory. A summary of the highlights of this paper form the bulk of the work presented in this chapter on HERA physics and is a fitting tribute to Guido’s contribution to science.

The strong coupling, α_s, is one of the fundamental parameters of the Standard Model. It enters into all cross-section calculations for processes at the Large Hadron Collider (LHC), whether directly at leading order, or through higher order QCD calculations. It also enters indirectly through the evolution of parton distribution functions (PDFs) and their correlation with the strong coupling. Consequently, as the LHC experiments’ work evolves towards precision physics, accurate knowledge of the strong coupling is becoming increasingly important. The value of the coupling matters also for the question of gauge coupling unification at high scales and for the stability of the universe in any given particle-physics scenario.

The following sections are included:

• Introduction
• The top mass problem
  • The “Perturbative” argument
  • The “Non-Perturbative” argument
  • Summary of the issue
  • What to do
• The renormalon problem
  • A simplified description of the renormalon problem
  • The full story
• Conclusions
• A personal note
• Acknowledgements

I discuss selected topics of Standard Model (SM) physics at the LHC and their connection to the work of Guido Altarelli. An overarching connection is given by Guido’s fundamental contributions to our understanding of the strong force, parton distribution functions and their evolution, and techniques to calculate theoretical predictions through perturbative Quantum Chromodynamics. The increasingly precise LHC measurements of diverse processes can be confronted with SM predictions relying on these foundations to test the SM and contribute to the knowledge of the proton structure. The LHC experiments have also started to perform precise measurements of SM parameters, such as the mass of the W-boson, and have measured a variety of processes sensitive to interactions of multiple electroweak bosons. The discovery of the Higgs boson in 2012 and the measurements of its properties are crucial to establish the nature of the mechanism of electroweak symmetry breaking and the status of these studies is summarised.

The following sections are included:

• Introduction
• Multi-Regge kinematics, multiple gluon emission and t-channel ladders
• k_T factorisation, off-shell cross section and unintegrated gluon distribution function
• From factorisation to resummation, the generalised ladder expansion and duality
• Evolution kernels beyond LO: the ABF approach
• Small-x techniques at the LHC: Higgs physics beyond the heavy top approximation
• Conclusions
• Acknowledgements

We discuss spin physics, Guido’s contribution to it, and what we still have to learn. We set out in particular a programme for incorporating constraints from semi-inclusive data into global fits of polarised PDFs, and discuss the need for the EIC to increase the precision and kinematic coverage of current measurements.

We explore a new class of supersymmetric models for lepton masses and mixing angles where the role of flavour symmetry is played by modular invariance. The building blocks are modular forms of level N and matter supermultiplets, both transforming in representations of a finite discrete group Γ_N. In the simplest version of these models, Yukawa couplings are just modular forms and the only source of flavour symmetry breaking is the vacuum expectation value of a single complex field, the modulus. In the special case where modular forms are constant functions the whole construction collapses to a supersymmetric flavour model invariant under Γ_N, the case treated so far in the literature. The framework has a number of appealing features. Flavon fields other than the modulus might not be needed. Neutrino masses and mixing angles are simultaneously constrained by the modular symmetry. As long as supersymmetry is exact, modular invariance determines all higher-dimensional operators in the superpotential. We discuss the general framework and we provide complete examples of the new construction. The most economical model predicts neutrino mass ratios, lepton mixing angles, Dirac and Majorana phases uniquely in terms of the modulus vacuum expectation value, with all the parameters except one within the experimentally allowed range. As a byproduct of the general formalism we extend the notion of non-linearly realised symmetries to the discrete case.

In an imaginary conversation with Guido Altarelli, I express my views on the status of particle physics beyond the Standard Model and its future prospects.

As a way to recall and honour Guido Altarelli I contribute to the discussion on the prospects for the future of particle physics. I do this because I am sure that Guido would have liked the discussion, even though I am not equally sure that he would have agreed on all the opinions I express here.

For nearly a decade, Guido Altarelli accompanied the Large Hadron electron Collider project, as invited speaker, referee and member of the International Advisory Committee. This text summarises the status and prospects of the development of the LHeC, with admiration for a one-time scientist and singular leader whom I met first nearly 40 years ago under the sun shining for the “Herceg Novi School” in Kupari, where we both lectured about the beautiful science of deep inelastic scattering and enjoyed life under a yellow moon.

I had the great fortune to interact with Guido Altarelli on several occasions. As everyone knows, he was a leader in the theoretical physics community and a founder of the modern approach to understanding hadronic structure. His evolution equation for parton densities as a function of momentum scale [Altarelli and Parisi (1977); Gribov and Lipatov (1972a); Dokshitzer (1977)] will be forever enshrined in our textbooks on particle physics. As an experimental physicist active in the HERA electron-proton collider programme at the DESY laboratory, I had many opportunities to discuss with Guido a wide range of topics related to structure functions, diffractive scattering, and other topics in strong interactions. But there was also a second area where we discussed in depth, and that was related to an early fluctuation in HERA data that had us excited about the possibility of having seen leptoquarks, a new form of matter. Guido came to DESY and explained to us why our data was most likely not a sign of new physics, and he was right. His manner of explaining was at once completely understandable and also completely convincing, on this topic and in general. He was a real pleasure to be around and discuss with, and we miss him greatly.

The following sections are included:

• Foreword
• Introduction
• The FCC operation scenarios
• Studies of Higgs couplings
  • Higgs studies at FCC-ee
  • Higgs studies at FCC-hh
• The precision frontier at the FCC
• The high-mass reach of the FCC
• The possible role of the HE-LHC
• Conclusions

13 July 2011: the day after Guido’s 70^th birthday. This is when our life was turned upside down. I was by chance in Guido’s office at CERN, at the moment in which he casually opened a pdf file with the results of a routine blood test that he had taken the day before. Everything was perfect, as usual, with many parameters literally as good as those of a young man, which always triggered the compliments of our general practitioner and the comment that he was destined to a very long life, just like his parents. Except for … in the middle of the last page, in bold characters, a PSA level of 14.72 ng/mL, while normal values should be between 0 and 4. We were flabbergasted …. How could it be? Guido had checked his PSA only one and a half years before and it was completely normal. I remember he said to me, “Mop (a funny contraction between my first and last names, which he often used), I’m doomed” (“Mop, sono fottuto”). Guido used to keep a journal, in which he jotted down a few lines every day. On that day he wrote “Terrore”. A doctor told us “But cancer does not manifest itself like this!”, and another “The PSA is too low for the tumour to have metastasised”. In the following days, we went through the stress of a second PSA test, and then biopsy, skeletal scintigraphy, MRI, PET…. Before every test, doctors described possible options, some of which were much more favourable than others, giving us hope. At some point we made plans for an operation. But Guido was not lucky and at every step the worst-case scenario always prevailed. The tumour was particularly aggressive, had already metastasised to lymph nodes and bones, and could not be operated on nor irradiated. It could only be treated pharmacologically with a limited number of weapons: a couple of hormonal treatments and two types of chemo (therapy).

The following section is included:

• References