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Register a new userPion charge radius from pion+electron elastic scattering data
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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.
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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.
In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_mu$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $gamma^*gamma^*topipi$. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_mu^{pitext{-box}}=-15.9(2)times 10^{-11}$. As an application of the partial-wave formalism, we present a first calculation of $pipi$-rescattering effects in HLbL scattering, with $gamma^*gamma^*topipi$ helicity partial waves constructed dispersively using $pipi$ phase shifts derived from the inverse-amplitude method. In this way, the isospin-$0$ part of our calculation can be interpreted as the contribution of the $f_0(500)$ to HLbL scattering in $(g-2)_mu$. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its $S$-wave rescattering corrections reads $a_mu^{pitext{-box}} + a_{mu,J=0}^{pipi,pitext{-pole LHC}}=-24(1)times 10^{-11}$.
The scattering lengths of a two pion system are the {it golden magnitudes} to test the QCD predictions in the low energy sector. The DIRAC (PS-212) experiment at CERN will obtain a particular combination of the S-wave isospin 0 and 2 scattering lengths by measuring the lifetime of pionium, the hydrogen-like $pi^+ pi^-$ atom. This measurement tests the accurate predictions of the Chiral Perturbation Theory. The most recent experimental results are presented.
The pion distribution amplitude (DA) can be related to the fundamental QCD Greens functions as a function of the quark self-energy and the quark-pion vertex, which in turn are associated with the pion wave function through the Bethe-Salpeter equation. Considering the extreme hard asymptotic behavior in momentum space allowed for a pseudoscalar wave function, which is limited by its normalization condition, we compute the pion DA and its second moment. From the resulting amplitude, representing the field theoretical upper limit on the DA behavior, we calculate the photon-pion transition form factor $F_{pigammagamma^{ast}}(Q^{2})$. The resulting upper limit on the pion transition form factor is compared with existing data published by CLEO, BaBar and Belle collaborations.
It is suggested that proton elastic scattering on atomic electrons allows a precise measurement of the proton charge radius. Very small values of transferred momenta (up to four order of magnitude smaller than the ones presently available) can be reached with high probability.
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