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We compute an $s$-channel $2to2$ scalar scattering $phiphitoPhitophiphi$ in the Gaussian wave-packet formalism at the tree-level. We find that wave-packet effects, including shifts of the pole and width of the propagator of $Phi$, persist even when we do not take into account the time-boundary effect for $2to2$, proposed earlier. The result can be interpreted that a heavy scalar $1to2$ decay $Phitophiphi$, taking into account the production of $Phi$, does not exhibit the in-state time-boundary effect unless we further take into account in-boundary effects for the $2to2$ scattering. We also show various plane-wave limits.
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We consider scattering processes involving N gluonic massless states of open superstrings with certain Regge slope alpha. At the semi-classical level, the string world-sheet sweeps a disk and N gluons are created or annihilated at the boundary. We present exact expressions for the corresponding amplitudes, valid to all orders in alpha, for the so-called maximally helicity violating configurations, with N=4, 5 and N=6. We also obtain the leading O(alpha^2) string corrections to the zero-slope N-gluon Yang-Mills amplitudes.
The scattering of 1D matter wave bright solitons on attractive potentials enables one to populate bound states, a feature impossible with noninteracting wave packets. Compared to noninteracting states, the populated states are renormalized by the attractive interactions between atoms and keep the same topology. This renormalization can even transform a virtual state into a bound state. By switching off adiabatically the interactions, the trapped wave packets converge towards the true noninteracting bound states. Our numerical studies show how such scattering experiments can reveal and characterize the surface states of a periodic structure whose translational invariance has been broken. We provide evidence that the corresponding 3D regime should be accessible with current techniques.
We determine the $Delta(1232)$ resonance parameters using lattice QCD and the Luscher method. The resonance occurs in elastic pion-nucleon scattering with $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is performed with $N_f=2+1$ flavors of clover fermions on a lattice with $Lapprox 2.8$ fm. The pion and nucleon masses are $m_pi =255.4(1.6)$ MeV and $m_N=1073(5)$ MeV, and the strong decay channel $Delta rightarrow pi N$ is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $vec{P}=frac{2pi}{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass $m_Delta=1378(7)(9)$ MeV and the coupling $g_{Deltatext{-}pi N}=23.8(2.7)(0.9)$.
This review represents a detailed and comprehensive discussion of the Thermal Field Theory (TFT) concepts and key results in Yukawa-type theories. We start with a general pedagogical introduction into the TFT in the imaginary- and real-time formulation. As phenomenologically relevant implications, we present a compendium of thermal decay rates for several typical reactions calculated within the framework of the real-time formalism and compared to the imaginary-time results found in the literature. Processes considered here are those of a neutral (pseudo)scalar decaying into two distinct (pseudo)scalars or into a fermion-antifermion pair. These processes are extended from earlier works to include chemical potentials and distinct species in the final state. In addition, a (pseudo)scalar emission off a fermion line is also discussed. These results demonstrate the importance of thermal effects in particle decay observables relevant in many phenomenological applications in systems at high temperatures and densities.
We find a new contribution in wave-packet scatterings, which has been overlooked in the standard formulation of S-matrix. As a concrete example, we consider a two-to-two scattering of light scalars $phi$ by another intermediate heavy scalar $Phi$, in the Gaussian wave-packet formalism: $phiphitoPhitophiphi$. This contribution can be interpreted as an in-time-boundary effect of $Phi$ for the corresponding $Phitophiphi$ decay, proposed by Ishikawa et al., with a newly found modification that would cure the previously observed ultraviolet divergence. We show that such an effect can be understood as a Stokes phenomenon in an integral over complex energy plane: The number of relevant saddle points and Lefschetz thimbles (steepest descent paths) discretely changes depending on the configurations of initial and final states in the scattering.
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