46115571
A proposal for testing quantum gravity in the lab
Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.
119191368
Minimal length in quantum gravity, equivalence principle and holographic entropy bound
A possible discrepancy has been found between the results of a neutron interferometry experiment and quantum mechanics. This experiment suggests that the weak equivalence principle is violated at small length scales, which quantum mechanics cannot explain. In this paper, we investigated whether the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, can explain the violation of the weak equivalence principle at small length scales. We also investigated the consequences of the GUP on the Liouville theorem in statistical mechanics. We have found a new form of invariant phase space in the presence of GUP. This result should modify the density states and affect the calculation of the entropy bound of local quantum field theory, the cosmological constant, black body radiation, etc. Furthermore, such modification may have observable consequences at length scales much larger than the Planck scale. This modification leads to a -type correction to the bound of the maximal entropy of a bosonic field which would definitely shed some light on the holographic theory.
119108040
Quantum Gravity effect on the Quark-Gluon Plasma
The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless quark flavors at the hadron-QGP phase equilibrium and at a vanishing chemical potential. The effective degrees of freedom and MIT bag pressure are utilized to distinguish between the hadronic and partonic phases. We find that GUP makes a non-negligible contribution to all thermodynamic quantities, especially at high temperatures. The asymptotic behavior of corresponding QGP thermodynamic quantities characterized by the Stephan-Boltzmann limit would be approached, when the GUP approach is taken into consideration.
118671611
Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe
The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early universe are studied. Using the GUP approach, the tensorial and scalar density fluctuations in the inflation era are evaluated and compared with the standard case. We find a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-Lemaitre-Robertson-Walker universe which satisfies the boundary condition, the number and entropy densities and the free energy arising form the quantum states are calculated using the GUP approach. A qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities is introduced.
120051381
Discreteness of space from GUP II: Relativistic wave equations
Abstract Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrodinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one-dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this Letter, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein–Gordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.
118350400
The Generalized Uncertainty Principle and Quantum Gravity Phenomenology
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this affects all Hamiltonians, and in particular those which describe low energy experiments. We discuss possible observational consequences. Further, we also show that this indicates that space may be discrete at the fundamental level.
119356068
CP violation and flavour mixing in the Standard Model
SummaryWe review and update the constraints on the parameters of the quark flavour mixing matrixVCKM in the Standard Model and estimate the resultingCP asymmetries in B decays, taking into account recent experimental and theoretical developments. In performing our fits, we use inputs from the measurements of the following quantities: i) |ε|, theCP-violating parameter in K decays, ii) ΔMd, the mass difference due to the
$$B_{d^ - }^0 \bar B_d^0 $$
 mixing, iii) the matrix elements |Vcb| and |Vub|, iv)-v) has improved compared to our previous fits. With the updated CKM matrix we present the currently-allowed range of the ratios |Vtd/Vts| and |Vtd/Vub|, as well as the Standard Model predictions for the
$$B_{s^ - }^0 \bar B_s^0 $$
 mixing parameterxs (or, equivalently, ΔMs) and the quantities sin2α, sin2β and sin2γ, which characterize theCP-asymmetries in B decays. Various theoretical issues related to the so-called «penguin-pollution», which are of importance for the determination of the phases α and γ from theCP-asymmetries in B decays, are also discussed.
119341978
Profiles of the unitarity triangle and CP-violating phases in the standard model and supersymmetric theories
Abstract. We report on a comparative study of the profile of the CKM unitarity triangle, and the resulting CP asymmetries in B decays, in the standard model and in several variants of the minimal supersymmetric standard model (MSSM), characterized by a single phase in the quark flavour mixing matrix. The supersymmetric contributions to the mass differences $\Delta M_d$, $\Delta M_s$ and to the CP-violating quantity $\vert\epsilon\vert$ are, to an excellent approximation, equal to each other in these theories, allowing for a particularly simple way of implementing the resulting constraints on the elements of $V_{CKM}$ from the present knowledge of these quantities. Incorporating the next-to-leading-order corrections and applying the current direct and indirect constraints on the supersymmetric parameters, we find that the predicted ranges of $\sin 2 \beta$ in the standard model and in MSSM models are very similar. However, precise measurements at B-factories and hadron machines may be able to distinguish these theories in terms of the other two CP-violating phases $\alpha$ and $\gamma$. This is illustrated for some representative values of the supersymmetric contributions in $\Delta M_d$, $\Delta M_s$ and $\vert \epsilon\vert$.
1473086
CKM phenomenology and B meson physics: Present status and current issues
We review the status of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and the CP-violating phases in the CKM-unitarity triangle. The emphasis in these lecture notes is on $B$-meson physics, though we also review the current status and issues in the light quark sector of this matrix. Selected applications of theoretical methods in QCD used in the interpretation of data are given and some of the issues restricting theoretical precision on the CKM matrix elements discussed. The overall consistency of the CKM theory with the available data in flavour physics is impressive and we quantify this consistency. Current data also show some anomalies which, however, are not yet statistically significant. They are discussed briefly. Some benchmark measurements that remain to be done in experiments at the $B$-factories and hadron colliders are listed. Together with the already achieved results, they will provide unprecedented tests of the CKM theory and by the same token may lead to the discovery of new physics.