LHC 750 GeV diphoton excess and muon (g−2)(g-2)

We consider implications of the diphoton excess recently observed at the LHC on the anomalous magnetic dipole moment of the muon $(g-2)_\mu = 2 a_\mu$, hypothesizing that the possible 750 GeV resonance is a (pseudo)scalar particle. The (pseudo)scalar-$\gamma$-$\gamma$ interaction implied by the diphoton events might generically contribute to $a_\mu$ via 2-loop Barr-Zee type diagrams in a broad class of models. If the scalar is an $SU(2)_L$ singlet, the new contribution to $a_\mu$ is much smaller than the current anomaly, $\Delta a_\mu \equiv a_\mu^{\rm exp}-a_\mu^{\rm SM} \approx (30 \pm 10) \times 10^{-10}$, since the scalar can complete the Barr-Zee diagrams only through its mixing with the Standard Model Higgs boson. If the (pseudo)scalar belongs to an $SU(2)_L$ doublet in an extended Higgs sector, then by contrast, $\Delta a_\mu$ can be easily accommodated with the aid of an enhanced Yukawa coupling of the (pseudo)scalar to the muon such as in the Type-II or -X two Higgs doublet model.Comment: 16 pages, added discussions about UV completions with vector-like fermions as well as consequences for heavy Higgs searches and B-physics, journal versio

Reconfiguring Graph Homomorphisms on the Sphere

Given a loop-free graph $H$, the reconfiguration problem for homomorphisms to $H$ (also called $H$-colourings) asks: given two $H$-colourings $f$ of $g$ of a graph $G$, is it possible to transform $f$ into $g$ by a sequence of single-vertex colour changes such that every intermediate mapping is an $H$-colouring? This problem is known to be polynomial-time solvable for a wide variety of graphs $H$ (e.g. all $C_4$-free graphs) but only a handful of hard cases are known. We prove that this problem is PSPACE-complete whenever $H$ is a $K_{2,3}$-free quadrangulation of the $2$-sphere (equivalently, the plane) which is not a $4$-cycle. From this result, we deduce an analogous statement for non-bipartite $K_{2,3}$-free quadrangulations of the projective plane. This include several interesting classes of graphs, such as odd wheels, for which the complexity was known, and $4$-chromatic generalized Mycielski graphs, for which it was not. If we instead consider graphs $G$ and $H$ with loops on every vertex (i.e. reflexive graphs), then the reconfiguration problem is defined in a similar way except that a vertex can only change its colour to a neighbour of its current colour. In this setting, we use similar ideas to show that the reconfiguration problem for $H$-colourings is PSPACE-complete whenever $H$ is a reflexive $K_{4}$-free triangulation of the $2$-sphere which is not a reflexive triangle. This proof applies more generally to reflexive graphs which, roughly speaking, resemble a triangulation locally around a particular vertex. This provides the first graphs for which $H$-Recolouring is known to be PSPACE-complete for reflexive instances.Comment: 22 pages, 9 figure

Business Groups and Tunneling: Evidence from Private Securities Offerings by Korean Chaebols

Using a comprehensive sample of equity-linked private securities offerings by Korean firms from 1989 to 2000, we examine whether such offerings can be used as a mechanism for wealth transfer between issuers and acquirers. For deals involving issuers and acquirers in the same business group (chaebol), the announcement returns for chaebol-affiliated issuers with good past performance are lower than those for other types of issuers if the price discount is larger. In contrast, this deal leads to more value creation for chaebol-affiliated acquirers than other types of acquirers. Furthermore, well-performing chaebol-affiliated acquirers experience a larger wealth loss than other types of acquirers if they buy securities from poorly performing issuers in the same chaebol. We also find that chaebol firms with good past performance tend to sell private securities at a low price to their member firms. This evidence is consistent with tunneling within business groups.

Disconnected Common Graphs via Supersaturation

A graph $H$ is said to be common if the number of monochromatic labelled copies of $H$ in a $2$-colouring of the edges of a large complete graph is asymptotically minimized by a random colouring. It is well known that the disjoint union of two common graphs may be uncommon; e.g., $K_2$ and $K_3$ are common, but their disjoint union is not. We investigate the commonality of disjoint unions of multiple copies of $K_3$ and $K_2$. As a consequence of our results, we obtain an example of a pair of uncommon graphs whose disjoint union is common. Our approach is to reduce the problem of showing that certain disconnected graphs are common to a constrained optimization problem in which the constraints are derived from supersaturation bounds related to Razborov's Triangle Density Theorem. We also improve bounds on the Ramsey multiplicity constant of a triangle with a pendant edge and the disjoint union of $K_3$ and $K_2$.Comment: 31 page

Preservice Teachers’ Algebraic Reasoning and Symbol Use on a Multistep Fraction Word Problem

Previous research on preservice teachers’ understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors’ solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems) when combining fractions with algebra on a multistep word problem. In this article, we identify and describe common strategy clusters and approaches present in the preservice teachers’ written work. Our results indicate that preservice teachers’ understanding of algebra include arithmetic methods, proportions, and is related to their understanding of a whole