Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new user$pipi$ scattering in a renormalized Hamiltonian matrix
138
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A Wilsonian approach to $pipi$ scattering based in the Glazek-Wilson Similarity Renormalization Group (SRG) for Hamiltonians is analyzed in momentum space up to a maximal CM energy of $sqrt{s}=1.4$ GeV. To this end, we identify the corresponding relativistic Hamiltonian by means of the 3D reduction of the Bethe-Salpeter equation in the Kadyshevsky scheme, introduce a momentum grid and provide an isospectral definition of the phase-shift based on a spectral shift of a Chebyshev angle. We also propose a new method to integrate the SRG equations based on the Crank-Nicolson algorithm with a single step finite difference so that isospectrality is preserved at any step of the calculations. We discuss issues on the unnatural high momentum tails present in the fitted interactions and reaching far beyond the maximal CM energy of $sqrt{s}=1.4$ GeV and how these tails can be integrated out explicitly by using Block-Diagonal generators of the SRG.
rate research
Read More
We develop a numerical method to nonperturbatively study scattering and gluon emission of a quark from a colored target using a light-front Hamiltonian approach. The target is described as a classical color field, as in the Color Glass Condensate effective theory. The Fock space of the scattering system is restricted to the $ket{q}+ket{qg}$ sectors, but the time evolution of this truncated system is solved exactly. This method allows us to study the interplay between coherence and multiple scattering in gluon emission. It could be applied both to studying subeikonal effects in high energy scattering and to understanding jet quenching in a hot plasma.
In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space-time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit-Fermi spin couplings in the effective quark-antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.
The weak two-pion form factor $F_V^{pipi}$ is described as the product of a weak kernel $cal{K}_W$ by a strong function $Theta_{pipi}^P$, determined directly from $pipi$ scattering data. As the latter accounts at once for all effects associated with resonances, intermediate $Kbar{K}$ loops, and other possible inelasticities present in $pipi$ scattering, the need of modeling is restricted to $cal{K}_W$ only. The procedure proposed allows one to asses the weak kernel directly, which has a dominant cut beginning at the $Kbar{K}$ threshold. Even the simplest vector-meson-dominance choice for $cal{K}_W$ already yields a good qualitative description of $F_V^{pipi}$. The energy sector below $0.8$ GeV is quite well reproduced when a precise theoretical chiral perturbation $pipi$ amplitude is used as input, together with the single free parameter $F_V G_V/F^2=1.20$. The inclusion of kaon loops, along well established lines and using few parameters, produces a good description of the form factor in the entire energy range allowed by $tau$ decays. This indicates that the replacement of modeling by direct empirical scattering information can also be useful in the construction of theoretical tools to be used in analysesof hadronic heavy meson decay data.
The physical meaning of bare and dressed scattering matrix singularities has been investigated. Special attention has been attributed to the role of well known invariance of scattering matrix with respect to the field transformation of the effective Lagrangian. Examples of evaluating bare and dressed quantities in various models are given.
A Wilsonian approach based on the Similarity Renormalization Group to $pipi$ scattering is analyzed in the $JI=$00, 11 and 02 channels in momentum space up to a maximal CM energy of $sqrt{s}=1.4$ GeV. We identify the Hamiltonian by means of the 3D reduction of the Bethe-Salpeter equation in the Kadyschevsky scheme. We propose a new method to integrate the SRG equations based in the Crank-Nicolson algorithm with a single step finite difference so that isospectrality is preserved at any step of the calculations. We discuss issues on the high momentum tails present in the fitted interactions hampering calculations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
