K-matrix theory of three-body problems

1972 ◽  
Vol 186 (2) ◽  
pp. 417-437 ◽  
Author(s):  
T. Sasakawa
Keyword(s):  
Matrix Theory ◽  
Three Body ◽  
K Matrix

scholarly journals CONVOLUTION FORMULA AND FINITE W BOSON WIDTH EFFECTS IN TOP QUARK WIDTH

2008 ◽  
Vol 23 (22) ◽  
pp. 3525-3533 ◽  
Author(s):  
G. CALDERÓN ◽  
G. LÓPEZ CASTRO
Keyword(s):  
Top Quark ◽  
W Boson ◽  
Matrix Theory ◽  
Finite Width ◽  
Current Limit ◽  
Fermion Masses ◽  
Convolution Formula ◽  
Boson Resonance ◽  
Three Body ◽  
Massless Fermions

In the Standard Model, the top quark decay width Γt is computed from the exclusive t → bW decay. We argue in favor of using the three body decays [Formula: see text] to compute Γt as a sum over these exclusive modes. As dictated by the S-matrix theory, these three body decays of the top quark involve only asymptotic states and incorporate the width of the W boson resonance in a natural way. The convolution formula commonly used to include the finite width effects is found to be valid, in the general case, when the intermediate resonance couples to a conserved current (limit of massless fermions in the case of W bosons). The relation Γt = Γ(t → bW) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of Γt are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher-order radiative corrections.

Diffractive hadron production at ultrahigh energies

2015 ◽  
Vol 30 (11) ◽  
pp. 1550054 ◽  
Author(s):  
V. V. Anisovich ◽  
M. A. Matveev ◽  
V. A. Nikonov
Keyword(s):  
Energy Region ◽  
Hadron Production ◽  
Ultrahigh Energy ◽  
Production Amplitude ◽  
Initial State ◽  
Final State ◽  
Black Disk ◽  
Diffractive Production ◽  
Three Body ◽  
K Matrix

Diffractive production is considered in the ultrahigh energy region where pomeron exchange amplitudes are transformed into black disk ones due to rescattering corrections. The corresponding corrections in hadron reactions h1 + h3 → h1 + h2 + h3 with small momenta transferred [Formula: see text] are calculated in terms of the K-matrix technique modified for ultrahigh energies. Small values of the momenta transferred are crucial for introducing equations for amplitudes. The three-body equation for hadron diffractive production reaction h1 + h3 → h1 + h2 + h3 is written and solved precisely in the eikonal approach. In the black disk regime final state scattering processes do not change the shapes of amplitudes principally but dump amplitudes by a factor ~ ¼; initial state rescatterings result in additional factor ~ ½. In the resonant disk regime initial and final state scatterings damp strongly the production amplitude that corresponds to σ inel /σ tot → 0 at [Formula: see text] in this mode.

scholarly journals K-Matrix Formalism for Three-Body Scattering and Bound-State Scattering

1965 ◽  
Vol 34 (2) ◽  
pp. 284-288 ◽  
Author(s):  
Nobuhiko Mishima ◽  
Miwae Yamazaki
Keyword(s):  
Bound State ◽  
Matrix Formalism ◽  
Three Body ◽  
K Matrix

scholarly journals Developments regarding three-body reaction channels within the R-matrix formalism

2020 ◽  
Vol 239 ◽  
pp. 03002
Author(s):  
Benedikt Raab ◽  
Thomas Srdinko ◽  
Helmut Leeb
Keyword(s):  
Cross Sections ◽  
Matrix Theory ◽  
Resonance Region ◽  
Reaction Cross ◽  
Resonance Structure ◽  
Matrix Formalism ◽  
Matrix Formulation ◽  
R Matrix ◽  
Reaction Channels ◽  
Three Body

At low incident energies of nucleon-induced reaction cross sections exhibit a striking resonance structure which cannot properly be described by (semi-) microscopic models. Usually R-matrix theory is applied which provides a sufficiently accurate but phenomenological description of the resonance region. However, standard R-matrix theory is only suited for two-particle channels. Three- and many-particle channels which may occur at rather low incident energies and are usually treated in approximative or effective way. In this contribution an extension to unequal masses of the R-matrix formulation of Glockle based on the Faddeev equation is performed and proper expressions for numerical implementation are given.

Single Particle Potential in Polarized Nuclear Matter

1974 ◽  
Vol 52 (18) ◽  
pp. 1768-1799 ◽  
Author(s):  
J. Dabrowski ◽  
P. Haensel
Keyword(s):  
Nuclear Matter ◽  
Single Particle ◽  
Optical Potential ◽  
Matrix Theory ◽  
Nucleon Nucleon ◽  
Spin Part ◽  
Spin Polarized ◽  
Particle Potential ◽  
Single Particle Potential ◽  
K Matrix

The problem of the single particle potential U in isospin and spin polarized nuclear matter, i.e. in nuclear matter with neutron excess and nonvanishing spin, is treated within the frame of the K matrix theory. General expressions for the isospin, spin, and spin–isospin parts of U, Uτ, Uσ, and Uστare obtained with the help of K matrices which depend on two Fermi momenta. The σ and στ parts have scalar and tensor components: Uσs and Uσt, and Uστ,s and Uστ,t These general expressions are specialized for nucleons at the Fermi surface. With suitable approximations, numerical values for Uτ(kF), Uσs(kF), and Uστ,s(kF) are obtained for the Brueckner–Gammel–Thaler and the Reid soft core nucleon–nucleon interactions. The tensor components, Uστ and Uστ,t, are estimated to be much smaller than the corresponding scalar components. The rearrangement effects turn out to be very important. At higher nucleon energies the τ, σ, and στ parts of U are calculated in the phase shift approximation with the Yale and Livermore phase shifts. The agreement of the calculated value of U, with experiment is satisfactory. The calculated values of Uσs and Uστ,s suggest that, in certain cases, a scalar spin–spin part of the optical potential is strong compared to other theoretical estimates, which seems to agree with some of the experimental results.

scholarly journals Three-body resonance states just below the antiproton and hydrogen dissociation threshold

2018 ◽  
Vol 181 ◽  
pp. 01034
Author(s):  
Takuma Yamashita ◽  
Yasushi Kino
Keyword(s):  
Matrix Theory ◽  
Resonance State ◽  
Relative Energy ◽  
Positive Energy ◽  
Present Calculation ◽  
Resonance States ◽  
R Matrix ◽  
Hydrogen Dissociation ◽  
Dissociation Threshold ◽  
Three Body

We analyze two shallow resonance states below the antiproton hydrogen dissociation threshold with a non-adiabatic three-body calculation. Rearrangement correlation between initial channel and protonium formation channel is explicitly included in the total wavefunction. The lower resonance state is in good agreement with the resonance position and width calculated with the R-matrix theory. The higher resonance state which is newly found is closer to the threshold and much narrower than the former resonance. A polarization effect of the hydrogen atom is found to be indispensable to support the resonance state. The accuracy of the present calculation is evaluated by the extended virial theorem. The resonance states calculated in the present work gives shallower relative energy below the dissociation threshold than the Born-Oppenheimer calculation, suggesting that the electron motion which is ignored in latter calculation would give positive energy because the electron is unbound inside the distance.

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