Heavy-quark opportunities and challenges at FCC-ee

The abundant production of beauty and charm hadrons in the $$5 \times 10^{12}$$ 5 × 10 12 $$Z^0$$ Z 0 decays expected at FCC-ee offers outstanding opportunities in flavour physics that in general exceed those available at Belle II and are complementary to the heavy-flavour programme of the LHC. A wide range of measurements will be possible in heavy-flavour spectroscopy, rare decays of heavy-flavoured particles and $$C\!P$$ C P -violation studies, which will benefit from the low-background experimental environment, the high Lorentz boost and the availability of the full spectrum of hadron species. This essay first surveys the important questions in heavy-flavour physics and assesses the likely theoretical and experimental landscape at the turn-on of FCC-ee. From this certain, measurements are identified where the impact of FCC-ee will be particularly important. A full exploitation of the heavy-flavour potential of FCC-ee places specific constraints and challenges on detector design, which in some cases are in tension with those imposed by the other physics goals of the facility. These requirements and conflicts are discussed.

Brownian Motion at the Speed of Light: A New Lorentz Invariant Family of Processes

We consider here a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the surface of a sphere of radius c and its trajectories only may connect points of this variety. A process can be constructed both by considering jumps from one point to another (velocity changes discontinuously) and by continuous velocity trajectories on the surface. We recently proposed to follow this second strategy assuming that the velocity is described by a Wiener process (which is isotropic only in the ’rest frame’) on the surface of the sphere. Using both Ito calculus and Lorentz boost rules, we succeed here in characterizing the entire Lorentz-invariant family of processes. Moreover, we highlight and describe the short-term ballistic behavior versus the long-term diffusive behavior of the particles in the 3D physical space.

Euler–Heisenberg waves propagating in a magnetic background

We derive the Euler–Heisenberg solutions that describe electromagnetic waves propagating through very intense uniform magnetic or electric background, with the effective metric approach. We first explore the case of a magnetic background: as a result of the interaction between the wave and the background there is birefringence and a longitudinal electric field component arises. The two phase velocities depend on the intensity of the external magnetic field and on the polarization of the wave; phase velocities can be slowed down up to the order of hundred thousandths for fields $$B/B_\mathrm{cr}<< 1$$ B / B cr < < 1 . The analogous study is done when the wave propagates through a uniform electric field. We then consider the situation when the background is in movement by means of a Lorentz boost, modeling then a magnetized flowing medium. We determined how this motion affects the speed of propagation of the electromagnetic wave, in this case the phase velocities depend on both the magnetic background and the direction and velocity of the boost.

Enhancement of superluminal weak values under Lorentz boost

The local group velocity defined as the weak value of the velocity operator in (1 + 1)-dimensional Klein-Gordon and Dirac theory is studied. As shown by Berry [J. Phys. A 45, 185308 (2012)], when the pre- and post-selected states for evaluating the weak value are chosen at random from an ensemble of available states, it gives rise to a universal probability distribution for the local group velocity which can have both subluminal and superluminal components. In this work, we explore the possibility of enhancement of the superluminal fraction of this total probability distribution by applying a Lorentz boost and show that it can indeed be enhanced both in the case of Klein–Gordon and Dirac theories.

Helicity rotation induced by Lorentz boosts

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

One Universe, Many Spaces: A Non-Local, Relativistic Quantum Spacetime

The nonlocality of entangled quantum mechanical systems is incompatible with the standard interpretation of special relativity as a single 4D Minkowskian metric spacetime. The difficulty is that the definition of a spacetime interval between any pair of events precludes any form of nonlocal interaction, even the relatively benign non-signaling correlations. By an application of the relativity principle, and the use of the space &larr;&rarr; time symmetry of the Lorentz boost I propose here a reinterpretation of special relativistic spacetime. This new ontology consists of a set of coexisting 3+1D spaces (&lsquo;framespaces&rsquo;), each containing unique content in the form of a complex density. These spaces are related by the Lorentz boost, and coupled pairwise in a manner dictated by the Lorentz transformation. The inter-space coupling acting on the spacetime content gives rise to a nonlocal wave phenomenon, which is identified as quantum wave mechanics. The interspace coupling strength is then inversely proportional to Planck&rsquo;s constant. The coexistence of multiple spaces is interpreted as momentum superposition, implying that momentum is the fundamental physical basis of quantum superposition. This new spacetime interpretation of quantum mechanics has many consequences, including explanations of quantum non-locality, the spacetime role of Planck&rsquo;s constant, quantum measurement as a symmetry-breaking process and the redundancy of description of gauge theory.

Covariant response theory and the boost transform of the dielectric tensor

After a short critique of the Minkowski formulae for the electromagnetic constitutive laws in moving media, we argue that in actual fact the problem of Lorentz-covariant electromagnetic response theory is automatically solved within the framework of modern microscopic electrodynamics of materials. As an illustration, we first rederive the well-known relativistic transformation behavior of the microscopic conductivity tensor. Thereafter, we deduce from first principles the transformation law of the wavevector- and frequency-dependent dielectric tensor under Lorentz boost transformations.