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Register a new userChiral Inflation of the Pion Radius
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We derive expression for the large b_perp asymptotic of the 3D parton distributions q(x,b_perp) in the pion. The asymptotic depends exclusively on the mass scales F_pi and m_pi. Therefore it provides us with a nice example of a strict non-perturbative result for the partonic structure of Nambu-Goldstone bosons in QCD. Analyzing the x-dependent pion transverse radius we reveal a new phenomenon of chiral inflation-- in the parametrically wide region of Bjorken x (m_pi^2/(4 pi F_pi)^2 << x << 1) the pion radius grows exponentially fast with the rapidity eta=ln(1/x). We show that the partons in this interval of Bjorken x contribute to famous logarithmic divergency of the pion radius. In other words, the partonic picture of the classical result of ChPT is provided. The phenomenon of the chiral inflation is at variance with the Gribov diffusion, because of long-range interaction of the Nambu-Goldstone bosons.
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A fundamental property of QCD is the presence of the chiral anomaly, which is the primary component of the $pi^0rightarrowgammagamma$ decay amplitude. Based on this anomaly and its small ($simeq$ 4.5%) chiral correction, a firm prediction of the $pi^0$ lifetime can be used as a test of QCD at confinement scale energies. The interesting experimental and theoretical histories of the $pi^0$ meson are reviewed, from discovery to the present era. Experimental results are in agreement with the theoretical prediction, within the current ($simeq$ 3%) experimental error; however, they are not yet sufficiently precise to test the chiral corrected result, which is a firm QCD prediction and is known to $simeq$ 1% uncertainty. At this level there exist experimental inconsistencies, which require attention. Possible future work to improve the present precision is suggested.
With the aim of extracting the pion charge radius, we analyse extant precise pion+electron elastic scattering data on $Q^2 in [0.015,0.144],$GeV$^2$ using a method based on interpolation via continued fractions augmented by statistical sampling. The scheme avoids any assumptions on the form of function used for the representation of data and subsequent extrapolation onto $Q^2simeq 0$. Combining results obtained from the two available data sets, we obtain $r_pi = 0.640(7),$fm, a value $2.4,sigma$ below todays commonly quoted average. The tension may be relieved by collection and similar analysis of new precise data that densely cover a domain which reaches well below $Q^2 = 0.015,$GeV$^2$. Considering available kaon+electron elastic scattering data sets, our analysis reveals that they contain insufficient information to extract an objective result for the charged-kaon radius, $r_K$. New data with much improved precision, low-$Q^2$ reach and coverage are necessary before a sound result for $r_K$ can be recorded.
The quadratic pion scalar radius, la r^2ra^pi_s, plays an important role for present precise determinations of pipi scattering. Recently, Yndurain, using an Omn`es representation of the null isospin(I) non-strange pion scalar form factor, obtains la
r^2ra^pi_s=0.75pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omn`es equations, la r^2ra^pi_s=0.61pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Yndurains method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input pipi phase shifts, a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is la r^2ra_s^pi=0.65pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0 pipi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.
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J. P. B. C. de Melo (Laboratorio de Fisica Teorica en Computacional
, Universidade Cruzeiro do Sul
, SP
2014
Using the light-front pion wave function based on a Bethe-Salpeter amplitude model, we study the properties of the pion in symmetric nuclear matter. The pion model we adopt is well constrained by previous studies to explain the pion properties in vacuum. In order to consistently incorporate the constituent up and down quarks of the pion immersed in symmetric nuclear matter, we use the quark-meson coupling model, which has been widely applied to various hadronic and nuclear phenomena in a nuclear medium with success. We predict the in-medium modifications of the pion lectromagnetic form factor, charge radius and weak decay constant in symmetric nuclear matter.
The proton radius puzzle has motivated several new experiments that aim to extract the proton charge radius and resolve the puzzle. Recently PRad, a new electron-proton scattering experiment at Jefferson Lab, reported a proton charge radius of $0.831pm 0.007_textnormal{statistical}pm 0.012_textnormal{systematic}$. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using $z$-expansion of the proton charge radius from PRad data. We find that the model-independent statistical error is more than 50% larger compared to the statistical error reported by PRad.
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