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Reply to the Comment on "Resonant Spectra and the Time Evolution of the Survival and Nonescape Probabilities"  [PDF]
G. Garcia-Calderon,J. L. Mateos,M. Moshinsky
Physics , 1998, DOI: 10.1103/PhysRevLett.80.4354
Abstract: In our paper [Phys. Rev. Lett. 74, 337 (1995)], we derived an exact expression for the survival and nonescape probabilities as an expansion in terms of resonant states. It was shown that these quantities exhibit at long times a different behavior. Although both decay as a power law, they have different exponents. In this paper we show that, contrary to the claim in the Comment of R. M. Cavalcanti (quant-ph/9704023), the nonescape probability decay for long times as an inverse power law.
Comment on ``Resonant Spectra and the Time Evolution of the Survival and Nonescape Probabilities''  [PDF]
R. M. Cavalcanti
Physics , 1997, DOI: 10.1103/PhysRevLett.80.4353
Abstract: In [G. Garcia-Calderon, J. L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995)], the time evolution of the quantum decay of a state initially located within an interaction region of finite range was investigated. In particular, it was shown that the survival and nonescape probabilities behave differently at very large times. The purpose of this Comment is to show that they have the same asymptotic behavior.
Free initial wave packets and the long-time behavior of the survival and nonescape probabilities  [PDF]
Manabu Miyamoto
Physics , 2002, DOI: 10.1103/PhysRevA.68.022702
Abstract: The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both S(t) and P(t) asymptotically exhibit the same power-law decrease at long times, when the initial wave packet in momentum representation behaves as O(1) or O(k) at small momentum. On the other hand, if the integer m becomes greater than 1, S(t) and P(t) decrease in different power-laws at long times.
Resonant and nonresonant D+ -> K- pi+ l+ nu(l) semileptonic decays  [PDF]
B. Bajc,S. Fajfer,R. J. Oakes,T. N. Pham
Physics , 1997, DOI: 10.1103/PhysRevD.58.054009
Abstract: We analyse the semileptonic decay D+ -> K- pi+ l+ nu(l) using an effective Lagrangian developed previously to describe the decays D -> P l nu(l) and D -> V l nu(l). Light vector mesons are included in the model which combines the heavy quark effective Lagrangian and chiral perturbation theory approach. The nonresonant and resonant contributions are compared. With no new parameters the model correctly reproduces the measured ratio Gamma(nres)/Gamma(nres + res). We also present useful nonresonant decay distributions. Finally, a similar model, but with a modified current which satisfies the soft pion theorems at the expense of introducing another parameter, is analyzed and the results of the models are compared.
Complementarity of Resonant and Nonresonant Strong $WW$ Scattering at the LHC  [PDF]
Michael S. Chanowitz,William Kilgore
Physics , 1993, DOI: 10.1016/0370-2693(94)90503-7
Abstract: We exhibit a complementary relationship between resonant $WZ$ and nonresonant $W^+W^+$ scattering in a chiral Lagrangian model of the electroweak symmetry breaking sector with a dominant ``$\rho$'' meson. We use the model to estimate the minimum luminosity for the LHC to ensure a ``no-lose'' capability to observe the symmetry breaking sector.
Resonant and nonresonant new phenomena of four-fermion operators for experimental searches  [PDF]
She-Sheng Xue
Physics , 2015, DOI: 10.1016/j.physletb.2015.03.038
Abstract: In the fermion content and gauge symmetry of the standard model (SM), we study the four-fermion operators in the torsion-free Einstein-Cartan theory. The collider signatures of irrelevant operators are suppressed by the high-energy cutoff (torsion-field mass) $\Lambda$, and cannot be experimentally accessible at TeV scales. Whereas the dynamics of relevant operators accounts for (i) the SM symmetry-breaking in the domain of infrared-stable fixed point with the energy scale $v\approx 239.5$ GeV and (ii) composite Dirac particles restoring the SM symmetry in the domain of ultraviolet-stable fixed point with the energy scale ${\mathcal E}\gtrsim 5$ TeV. To search for the resonant phenomena of composite Dirac particles with peculiar kinematic distributions in final states, we discuss possible high-energy processes: multi-jets and dilepton Drell-Yan process in LHC $p\,p$ collisions, the resonant cross-section in $e^-e^+$ collisions annihilating to hadrons and deep inelastic lepton-hadron $e^-\,p$ scatterings. To search for the nonresonant phenomena due to the form-factor of Higgs boson, we calculate the variation of Higgs-boson production and decay rate with the CM energy in LHC. We also present the discussions on four-fermion operators in the lepton sector and the mass-squared differences for neutrino oscillations in short baseline experiments.
Minimization of nonresonant effects in a scalable Ising spin quantum computer  [PDF]
G. P. Berman,D. I. Kamenev,V. I. Tsifrinovich
Physics , 2003,
Abstract: The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing the gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.
Charmless 3-body B Decays: Resonant and Nonresonant Contributions
Cheng, Hai-Yang
High Energy Physics - Phenomenology , 2007, DOI: 10.1142/S0217751X08041888
Abstract: Charmless 3-body decays of $B$ mesons are studied using a simple model based on the framework of the factorization approach. We have identified a large source of the nonresonant signal in the matrix elements of scalar densities, e.g. $$. This explains the dominance of the nonresonant background in $B\to KKK$ decays, the sizable nonresonant fraction of order $(35\sim 40)%$ in $K^-\pi^+\pi^-$ and $\bar K^0\pi^+\pi^-$ modes and the smallness of nonresonant rates in $B\to \pi\pi\pi$ decays. We have computed the resonant and nonresonant contributions to charmless 3-body decays and determined the rates for the quasi-two-body decays $B\to VP$ and $B\to SP$. Time-dependent CP asymmetries $\sin2\beta_{\rm eff}$ and $A_{CP}$ in $K^+K^-K_S,K_SK_SK_S,K_S\pi^+\pi^-$ and $K_S\pi^0\pi^0$ modes are estimated.
Charmless 3-body B Decays: Resonant and Nonresonant Contributions  [PDF]
Hai-Yang Cheng
Physics , 2007, DOI: 10.1142/S0217751X08041888
Abstract: Charmless 3-body decays of $B$ mesons are studied using a simple model based on the framework of the factorization approach. We have identified a large source of the nonresonant signal in the matrix elements of scalar densities, e.g. $$. This explains the dominance of the nonresonant background in $B\to KKK$ decays, the sizable nonresonant fraction of order $(35\sim 40)%$ in $K^-\pi^+\pi^-$ and $\bar K^0\pi^+\pi^-$ modes and the smallness of nonresonant rates in $B\to \pi\pi\pi$ decays. We have computed the resonant and nonresonant contributions to charmless 3-body decays and determined the rates for the quasi-two-body decays $B\to VP$ and $B\to SP$. Time-dependent CP asymmetries $\sin2\beta_{\rm eff}$ and $A_{CP}$ in $K^+K^-K_S,K_SK_SK_S,K_S\pi^+\pi^-$ and $K_S\pi^0\pi^0$ modes are estimated.
Nonresonant Semileptonic Heavy Quark Decay  [PDF]
Nathan Isgur
Physics , 1999, DOI: 10.1103/PhysRevD.60.074030
Abstract: In both the large N_c limit and the valence quark model, semileptonic decays are dominated by resonant final states. Using Bjorken's sum rule in an "unquenched" version of the quark model, I demonstrate that in the heavy quark limit nonresonant final states should also be produced at a significant rate. By calculating the individual strengths of a large number of exclusive two-body nonresonant channels, I show that the total rate for such processes is highly fragmented. I also describe some very substantial duality-violating suppression factors which reduce the inclusive nonresonant rate to a few percent of the total semileptonic rate for the finite quark masses of B decay, and comment on the importance of nonresonant decays as testing grounds for very basic ideas on the structure, strength, and significance of the quark-antiquark sea and on quark-hadron duality in QCD.
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