International Journal of Modern Physics A

To better understand the role of CDD poles in modern field theories, we investigate the effects of CDD poles on the $P_{33}$ channel in $\pi -n$ scattering. We use the non-crossing Chew–Low model for this investigation. The Chew–Low model is the simplest phenomenological model of $\pi -n$ scattering. In the no crossing limit, the $P_{33}$ channel can be easily solved and displays the predominate $\mathrm{\Delta }$ resonance. It has been shown that the denominator function, used in the $N∕D$ method of solution, is a generalized R-function. Our research centers on two investigations. The first is whether one can readily associate a CDD pole with the $\mathrm{\Delta }$ resonance. We find that one cannot, since the CDD pole forces the phases to disagree with the experimental values. The second investigation is into the nature of the redundant solutions one can generate by adding CDD pole to the denominator function. We find that the solutions with the added CDD pole cannot reproduce the phases of the original Chew–Low Model at low energies. Thus, there are no redundant solutions to this model. These results are contrary to what is generally assumed. We question the use of adding a CDD pole to produce resonances and the ideal that adding such poles do not effect the low energy phases.

In this paper, the potentials of two different processes $e^{+}{e}^{-}\to W^{-}{W}^{+}\gamma$ and $e^{+}{e}^{-}\to e^{+}{\gamma }^{\ast }{e}^{-}\to e^{+}{W}^{-}Z{\nu }_e$ at the Compact Linear Collider (CLIC) are examined to probe the anomalous quartic $WWZ\gamma$ gauge couplings. For $\sqrt{s}=0.5$, 1.5 and 3TeV energies at the CLIC, 95% confidence level limits on the anomalous coupling parameters defining the dimension-six operators are found via the effective Lagrangian approach in a model independent way. The best limits on the anomalous couplings $\frac{k_0^W}{{\Lambda }^2}$, $\frac{k_c^W}{{\Lambda }^2}$, $\frac{k_2^m}{{\Lambda }^2}$ and $\frac{a_n}{{\Lambda }^2}$ which can be achieved with the integrated luminosity of $L_{\mathrm{\text{int}}}=590{\mathrm{\text{fb}}}^{-1}$ at the CLIC with $\sqrt{s}=3\mathrm{\text{TeV}}$ are $[-8.80;8.73]\times 10^{-8}{\mathrm{\text{GeV}}}^{-2}$, $[-1.53;1.51]\times 10^{-7}{\mathrm{\text{GeV}}}^{-2}$, $[-3.75;3.74]\times 10^{-7}{\mathrm{\text{GeV}}}^{-2}$ and $[-9.13;9.09]\times 10^{-7}{\mathrm{\text{GeV}}}^{-2}$, respectively.

We consider the Higgs and Yukawa parts of the Noncommutative Standard Model (NCSM). We explore the NC-action to give all Feynman rules for couplings of the Higgs boson to electroweak gauge fields and fermions.

Anticipating future precise measurements of the D- and B-like (semi)leptonic and hadronic decays for alternative determinations of the CKM mixing angles, we pursue our program on the D- and B-like mesons by improving the estimates of $f_{D_{(s)}^{\ast }}$ and $f_{B_{(s)}^{\ast }}$ (analogue to $f_{\pi }$) by using the well-established (inverse) Laplace sum rules (LSR) and/or their suitable ratios less affected by the systematics, which are known to N2LO pQCD and where the complete $d=6$ nonperturbative condensate contributions are included. The convergence of the PT series is analyzed by an estimate of the N3LO terms based on geometric growth of the coefficients. In addition to the standard LSR variable $\tau$ and the QCD continuum threshold $t_c$ stability criteria, we extract our optimal results by also requiring stability on the variation of the arbitrary QCD subtraction point $\mu$ which reduces the errors in the analysis. We complete the study of the open bottom states by an estimate of $f_{B_c}$. Our results summarized in Tables 3 and 4 are compared with some other recent sum rules and lattice estimates.

We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one $(0+1)$-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.

In this paper, we first understand the classical $G_2$-structure and $G_2$-geometry from the viewpoint of spinor, which is a more familiar framework for physicists. Explicit construction of invariant spinor is given via the Dirac gamma matrices. We introduce a notion of multispinor bundle associated with invariant spinor and differential operator on the section of this bundle. Then we study the vector fields satisfy some additional properties on $G_2$-manifold, more precisely, we prove some no-go theorems corresponding to the vector field preserving the associated 4-form on $G_2$-manifold, and we also consider the nowhere-vanishing vector field which induces an integrable complex structure on the vertical direction of tangent bundle. Next we discuss the relation between the variation of metric and that of effective action on the moduli space of integrable $G_2$-structures. In the last section, we deal with the structure operators on generalized $G_2$-manifold after describing the integrability of generalized $G_2$-structure, some identities of structure operators are derived, which are analogues of Kähler-type and Weitzenböck-type identities under the classical case. And finally, we introduce a flow of which a generalized $G_2$-manifold can be realized as the fixed point.

The yield of $\mathrm{\Upsilon }$ associated with open charm has been estimated with different approaches. The crucial differences between SPS and DPS predictions are discussed.

We categorize new physics signatures that manifest themselves as a “dip” structure at colliders. One potential way to realize a dip is to require interactions to be zero when all particles are mass on-shell, but not if one or more are mass off-shell. For three particle interactions, we have found three interesting cases: one massive gauge boson with two identical scalars; one massless gauge boson with two different scalars; one massive gauge boson with two identical massless gauge bosons. For each case, we identify the relevant effective operators to explore its dip signature at the LHC. Unfortunately, the unstable particle with a vanishing mass-on-shell interaction has a complex mass which is coincident with the complex pole in its propagator. As a result, a contact-like amplitude without a dip is produced. Some interesting collider signatures for “fermion-phobic” vector bosons are also discussed.