Rare decay modes of the kaons such as $K\ensuremath{\rightarrow}\ensuremath{\mu}\overline{\ensuremath{\mu}}$, $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, $K\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\gamma}\ensuremath{\gamma}$, and $K\ensuremath{\rightarrow}\ensuremath{\pi}e\overline{e}$ are of theoretical interest since here we are observing higher-order weak and electromagnetic interactions. Recent advances in unified gauge theories of weak and electromagnetic interactions allow in principle unambiguous and finite predictions for these processes. The above processes, which are "induced" $|\ensuremath{\Delta}S|=1$ transitions, are a good testing ground for the cancellation mechanism first invented by Glashow, Iliopoulos, and Maiani (GIM) in order to banish $|\ensuremath{\Delta}S|=1$ neutral currents. The experimental suppression of ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\mu}\overline{\ensuremath{\mu}}$ and nonsuppression of ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ must find a natural explanation in the GIM mechanism which makes use of extra quark(s). The procedure we follow is the following: We deduce the effective interaction Lagrangian for $\ensuremath{\lambda}+\mathfrak{N}\ensuremath{\rightarrow}l+\overline{l}$ and $\ensuremath{\lambda}+\overline{\mathfrak{N}}\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\gamma}$ in the free-quark model; then the appropriate matrix elements of these operators between hadronic states are evaluated with the aid of the principles of conserved vector current and partially conserved axial-vector current. We focus our attention on the Weinberg-Salam model. In this model, $K\ensuremath{\rightarrow}\ensuremath{\mu}\overline{\ensuremath{\mu}}$ is suppressed due to a fortuitous cancellation. To explain the small ${K}_{L}\ensuremath{-}{K}_{S}$ mass difference and nonsuppression of ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, it is found necessary to assume $\frac{{m}_{\mathcal{P}}}{{m}_{{\mathcal{P}}^{\ensuremath{'}}}}ll1$, where ${m}_{\mathcal{P}}$ is the mass of the proton quark and ${m}_{{\mathcal{P}}^{\ensuremath{'}}}$, the mass of the charmed quark, and ${m}_{{\mathcal{P}}^{\ensuremath{'}}}l5$ GeV. We present a phenomenological argument which indicates that the average mass of charmed pseudoscalar states lies below 10 GeV. The effective interactions so constructed are then used to estimate the rates of other processes. Some of the results are the following: ${K}_{S}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ is suppressed; ${K}_{S}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\gamma}\ensuremath{\gamma}$ proceeds at a normal rate, but ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\gamma}\ensuremath{\gamma}$ is suppressed; ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ is very much forbidden, and ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ occurs with the branching ratio of ${\mathrm{\ensuremath{\sim}}10}^{\ensuremath{-}10}$; ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}e\overline{e}$ has the branching ratio of ${\mathrm{\ensuremath{\sim}}10}^{\ensuremath{-}6}$, which is comparable to the presently available experimental upper bound. The predictions of other models are briefly discussed. Relevant renormalization procedures and computational details are discussed in appendixes.

http://inspirehep.net/record/89052/files/fermilab-pub-74-021-T.pdf

Rare Decay Modes of the K-Mesons in Gauge Theories

The chiral anomaly provides smoking-gun evidence of a new confining gauge theory. Motivated by a reported event excess in a diphoton invariant mass distribution at the LHC, we discuss a scenario that a pseudo-Nambu-Goldstone (PNG) boson of a new QCD-like theory is produced by gluon fusion and decays into a pair of the standard model gauge bosons. Despite the strong dynamics, the production cross section and the decay widths are determined by an anomaly matching condition. The excess can be explained by the PNG boson with mass of around 750 GeV. The model also predicts exotic hadrons such as a color-octet scalar and baryons. Some of them are within the reach of the LHC experiment.

Footprints of New Strong Dynamics via Anomaly and the 750 GeV Diphoton

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincar\'{e} symmetry) to background gauge fields (and a metric for the Poincar\'{e} symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects 't Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of 't Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary 't Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized 't Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen's superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.

/pdf/anomalies-in-the-space-of-coupling-constants-and-their-41f74bja8k.pdf

Anomalies in the Space of Coupling Constants and Their Dynamical Applications II

We consider general 5d SU(N ) quiver gauge theories whose nodes form an ADE Dynkin diagram of type G. Each node has SU(N
 i
 ) gauge group of general rank, Chern-Simons level κ
 i
 and additional w
 i
 fundamentals. When the total flavor number at each node is less than or equal to 2N
 i
 − 2|κ
 i
 |, we give general rules under which the symmetries associated to instanton currents are enhanced to G × G or a subgroup of it in the UV 5d superconformal theory. When the total flavor number violates that condition at some of the nodes, further enhancement of flavor symmetries occurs. In particular we find a large class of gauge theories interpreted as S1 compactification of 6d superconformal theories which are waiting for string/F-theory realization. We also consider hypermultiplets in (anti-)symmetric representation.

/pdf/instanton-operators-and-symmetry-enhancement-in-5d-4oiggb2ko1.pdf

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

We investigate the continuum spectrum of the SU(2) gauge theory with ${N}_{f}=2$ flavors of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the strongly interacting massive particles (SIMPs). We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the ${w}_{0}$ parameter, and by measuring the relevant renormalization constants nonperturbatively in the regularization-invariant momentum (RI'-MOM) scheme. Our result for the lightest isovector state in the vector channel, in units of the pseudoscalar decay constant, is ${m}_{V}/{F}_{\mathrm{PS}}\ensuremath{\sim}13.1(2.2)$ (combining statistical and systematic errors). For the axial channel our result is ${m}_{A}/{F}_{\mathrm{PS}}\ensuremath{\sim}14.5(3.6)$, which however does include a similarly sized additional systematic error due to residual excited-states contamination. In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are ${m}_{V}g3.2(5)\text{ }\text{ }\mathrm{TeV}$ and ${m}_{A}g3.6(9)\text{ }\text{ }\mathrm{TeV}$, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.

/pdf/su-2-gauge-theory-with-two-fundamental-flavours-a-minimal-1iyivgpmw9.pdf

重雄花輪

Papers

核子構造とcurrent algebra : 素粒子

重雄 花輪

Papers

核子構造とcurrent algebra : 素粒子

重雄花輪