International Journal of Modern Physics A

Since 2010 there has been a rich harvest of results on standard model physics by the ATLAS and CMS experiments operating on the Large Hadron Collider. In the summer of 2012, a spectacular discovery was made by these experiments of a new, heavy particle. All the subsequently analysed data point strongly to the properties of this particle as those expected for the Higgs boson associated with the Brout–Englert–Higgs mechanism postulated to explain the spontaneous symmetry breaking in the electroweak sector, thereby explaining how elementary particles acquire mass. This article focuses on the CMS experiment, the technological challenges encountered in its construction, describing some of the physics results obtained so far, including the discovery of the Higgs boson, and searches for the widely anticipated new physics beyond the standard model, and peer into the future involving the high-luminosity phase of the LHC. This article is complementary to the one by Peter Jenni⁴ that focuses on the ATLAS experiment.

We review what is currently known about the transverse spin structure of hadrons, in particular from observables that can be analyzed within a collinear framework. These effects have been around for 40 years and represent a critical test of perturbative QCD. We look at both proton–proton and lepton–nucleon collisions for various final states. While the main focus is on transverse single-spin asymmetries, we also discuss how longitudinal-transverse double-spin asymmetries offer a complimentary, yet equally important, source of information on the quark–gluon content of hadrons. We also summarize some recent progress in solidifying the theoretical formalism behind these observables and give an outlook on future directions of research.

We begin with a few words about Salam’s contribution to the growth of String Theory in India. In the technical talk we review results in $SU(N)$ Chern–Simons plus vector matter theories in 2+1 dim in the large $N$ limit. The dressing of charged matter by Chern–Simons gauge fields leads to anyons that interpolate between fermions and bosons and lead to a duality symmetry between fermionic and bosonic theories. The S-matrix (defined in the large $N$ limit) besides exhibiting this duality, also exhibits novel properties due to the presence of anyons. The S-matrix is not analytic, like in Aharonov–Bohm scattering, and satisfies modified crossing symmetry relations.

The calculation of the mass of light scalar isosinglet meson within the Shifman–Vainshtein–Zakharov (SVZ) sum rules is revisited. We develop simple analytical methods for estimation of hadron masses in the SVZ approach and try to reveal the origin of their numerical values. The calculations of hadron parameters in the SVZ sum rules are known to be heavily based on a choice of the perturbative threshold. This choice requires some important ad hoc information. We show analytically that the scalar mass under consideration has a lower and upper bound which are independent of this choice: $0.78\lesssim m_s\lesssim 1.28$ GeV.

In this paper, we calculate rare top quark 2-body and 3-body decays in the littlest Higgs Model with T-parity (LHT). We find that the branching ratios of $t\to cX$ $(X=g,\gamma ,Z,H)$ and $t\to c{X}_1{X}_2$ $(X=g,\gamma ,Z,H,f)$ can be greatly enhanced in the LHT model in the allowed parameter space. The recent measurements of the decay $t\to cg$ can give a strong constraint on the LHT parameters and the decays of $t\to cgg$ and $t\to cb\bar{b}$ can be accessible at the LHC.

The polymer quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincaré invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincaré invariant Fock quantization. The resulting symmetry group of such polymer quantization is the subgroup $\mathrm{\text{SDiff}}({ℝ}^4)$ which is a subgroup of $\mathrm{\text{Diff}}({ℝ}^4)$ formed by spatial volume preserving diffeomorphisms. In consequence, this yields an entirely different irreducible representation of the canonical commutation relations, nonunitary equivalent to the standard Fock representation. We also compared the Poincaré invariant Fock vacuum with the polymer Fourier vacuum.

This paper is based on the framework of a two-dimensional universe considering it to be a lattice structure. The Ising model has been used to show that there is a spontaneous phase transition from the Planck scale to the Compton scale. Also, a mean field theoretic approach has been considered to delve into the statistical properties of such a lattice-structured universe.

We have long speculated,${}^{2,12,50-62}$ that 6 top + 6 antitop quarks due to the relatively large size of the top-Yukawa coupling would bind exceptionally strongly by mainly Higgs exchange. Here we present a surprisingly simple “calculation” of the mass of this speculated bound state. Even a possible resonance in scattering of two such bound states is speculated. For the “calculation” of the masses it is crucial to assume, that our since long speculated principle “multiple point principle,”${}^{5-18}$ is true. This principle says: there are several vacua all having almost zero energy density. Further, we make an approximation of the Higgs Yukawa potential essentially replacing the exponential in it by a step-function. The new result means that there are now two independent calls for our bound state having the mass around 750 GeV required by our “new law of nature” the Multiple Point Principle. It should be remarked that in our picture there is no new physics in the sense of new fundamental particles, but the “multiple point principle” is new in the sense of being not yet accepted. Further, we get the same mass within uncertainties as earlier² but now from a completely different assumption, except for being from our “multiple point principle.” But the two masses are gotten from using different (speculative) vacua occurring in the pure Standard Model.

The three-loop ladder diagram is a graph with six links and four cubic vertices that contributes to the $D^{12}{{ℛ}}^4$ amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one-, two- and three-loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five-point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples.

Elaborating on our previous presentation, where the term dipolar quantization was introduced, we argue here that adopting $L_0-(L_1+L_{-1})/2+{\bar{L}}_0-({\bar{L}}_1+{\bar{L}}_{-1})/2$ as the Hamiltonian instead of $L_0+{\bar{L}}_0$ yields an infinite circumference limit in two-dimensional conformal field theory. The new Hamiltonian leads to dipolar quantization instead of radial quantization. As a result, the new theory exhibits a continuous and strongly degenerated spectrum in addition to the Virasoro algebra with a continuous index. Its Hilbert space exhibits a different inner product than that obtained in the original theory. The idiosyncrasy of this particular Hamiltonian is its relation to the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The appearance of the infinite circumference explains why the vacuum states of sine-square deformed systems are coincident with those of the respective closed-boundary systems.

The generalized version of a lower dimensional model where vector and axial vector interactions get mixed up with different weights is considered. The bosonized version of which does not possess the local gauge symmetry. An attempt has been made here to construct the BRST invariant reformulation of this model using Batalin–Fradlin and Vilkovisky formalism. It is found that the extra field needed to make it gauge invariant turns into Wess–Zumino scalar with appropriate choice of gauge fixing. An application of finite field-dependent BRST and anti-BRST transformation is also made here in order to show the transmutation between the BRST symmetric and the usual nonsymmetric version of the model.

In this paper, we have considered the thermodynamics of a photon gas subject to the presence of a minimal measurable length following from a covariant extension of the original generalized uncertainty principle (GUP). After consistently establishing a generalized dynamics, we define a GUP deformed Maxwell invariant which serves as the basis for our study. In order to highlight the GUP effects, we compute the one- and two-loop order contribution to the partition function at the high-temperature limit. Afterwards, by computing the internal energy density, we conclude that the additional terms can be seen as corrections $\delta {\sigma }_{\mathrm{\text{GUP}}}$ to the Stefan–Boltzmann law due to GUP effects.

Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein–Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to $\frac{\hslash }{2}$, i.e. proton spin decomposition has no meaning in this approach.