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Register a new userThe slope of the hadron spin-flip amplitude and the determination of rho(s,t)
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We re-examine the extraction of rho(s,t), the ratio of the real part to the imaginary part of the scattering amplitude, and of the spin-flip amplitude, from the existing experimental data in the Coulomb-hadron interference region. We show that it is not possible to find reasonable assumptions about the structure of the scattering amplitude of proton-proton and proton-antiproton elastic scattering at high energy that would lead, in proton-antiproton scattering for 3.8 < p_L <6 GeV/c, to an agreement between data and an analysis based on dispersion relations.
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Using interpolators with different SU(2)_L times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $qbargamma^i{tau}q$ and $qbarsigma^{0i}{tau}q$ interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ~1 fm. In the ground state rho meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1) + (1,0) and (1/2,1/2)_b chiral representations with the former being the leading contribution. In contrast, in the rho meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)_b. Using a unitary transformation from the chiral basis to the {2S +1}L_J basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The rho meson is practically a 3S_1 state with no obvious trace of a spin crisis. The rho meson has a sizeable contribution of the 3D_1 wave, which implies that the rho meson cannot be considered as a pure radial excitation of the rho meson.
Using the soft pion theorem, crossing, and the dispersion relations for the two pion distribution amplitude ($2pi$DA) we argue that the second Gegenbauer moment the $rho$-meson DA ($a_2^{(rho)}$) most probably is negative. This result is at variance with the majority of the model calculations for $a_2^{(rho)}$. Using the instanton theory of the QCD vacuum, we computed $a_2^{(rho)}$ at a low normalisation point and obtain for the ratio $ a_2^{(rho)}/M_3^{(pi)}$ {it definitely negative value} in the range of $a_2^{(rho)}/M_3^{(pi)}in [-2, -1]$. The range of values corresponds to a generous variation of the parameters of the instanton vacuum. The value of the second Gegenbauer moment of pion DA is positive in the whole range and is compatible with its the most advanced lattice measurement. It seems that the topologically non-trivial field configurations in the QCD vacuum (instantons) lead to qualitatively different shapes of the pion and the $rho$-meson DAs.
A new method for the determination of the real part of the elastic scattering amplitude is examined for high energy proton-proton at small momentum transfer. This method allows us to decrease the number of model assumptions, to obtain the real part in a narrow region of momentum transfer and to test different models. The possible non-exponential behavior of the real part was found on the base of the analysis of the ISR experimental data.
A new method for the determination of the real part of the elastic scattering amplitude is examined for high energy proton-proton elastic scattering at small momentum transfer. This method allows us to decrease the number of model assumptions, to obtain the real part in a narrow region of momentum transfer and to test different models. The real part is computed at a given point t_min near t=0 from the known Coulomb amplitude. Hence one obtains an important constraint on the real part of the forward scattering amplitude and therefore on the rho-parameter (measuring the ratio of the real to imaginary part of the scattering amplitude at t=0), which can be tested at LHC.
The entanglement entropy of two-body elastic scattering at high energies is studied by using the model-independent Levy imaging method for investigating the hadron structure. It is considered the finite entropy in the momentum Hilbert space properly regularized and results are compared to recent evaluation using the diffraction peak approximation. We present the entropy for RHIC, Tevatron and LHC energies pointing out the underlying uncertainties.
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