Hadron tomography by generalized distribution amplitudes in the pion-pair production process γ*γ→π0π0

Abstract

Hadron tomography can be investigated by three-dimensional structure functions such as generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions, and generalized distribution amplitudes (GDAs). Here, we extract the GDAs, which are s-t crossed quantities of the GPDs, from cross-section measurements of hadron-pair production process γ Ã γ → π 0 π 0 at KEKB. This work is the first attempt to obtain the GDAs from the actual experimental data. The GDAs are expressed by a number of parameters and they are determined from the data of γ Ã γ → π 0 π 0 by including intermediate scalar-and tensor-meson contributions to the cross section. Our results indicate that the dependence of parton-momentum fraction z in the GDAs is close to the asymptotic one. The timelike gravitational form factors Θ 1 and Θ 2 are obtained from our GDAs, and they are converted to the spacelike ones by the dispersion relation. From the spacelike Θ 1 and Θ 2 , gravitational densities of the pion are calculated. Then, we obtained the mass (energy) radius and the mechanical (pressure and shear force) radius from Θ 2 and Θ 1 , respectively. They are calculated as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hr 2 i mass p ¼ 0.32-0.39 fm, whereas the mechanical radius is larger ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi hr 2 i mech p ¼ 0.82-0.88 fm. This is the first report on the gravitational radius of a hadron from actual experimental measurements. It is interesting to find the possibility that the gravitational mass and mechanical radii could be different from the experimental charge radius ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi hr 2 i charge q ¼ 0.672 AE 0.008 fm for the charged pion. For drawing a clear conclusion on the GDAs of hadrons, accurate experimental data are needed, and it should be possible, for example, by future measurements of super-KEKB and international linear collider. Accurate measurements will not only provide important information on hadron tomography but also possibly shed light on gravitational physics in the quark and gluon level.

Gravitational form factors of light mesons

“…All radii are in fm, the mass quadrupole moment is in units of m ρ -fm 2 , and the electric quadrupole moment is in e-fm 2 . the extraction in [16], where a dispersive analysis of KEKB data for γ * γ → π 0 π 0 was done to extract gravitational form factors.…”

“…The formula used in [16] was the same as our Eq. (66) for the squared light cone pion mass radius, but with a factor 6 instead of 4.…”

Poincaré constraints on the gravitational form factors for massive states with arbitrary spin

“…(41) 6 Here we use the convention ǫ0123 = +1. 7 The explicit form for the covariant spin matrices in terms of the non-conserved ones Σ i m ′ m (k) is given by: 8 Given these definitions of W µ and B µ the general Lorentz generator can be written in the following form:…”

“…In the case of the energy-momentum tensor (EMT) these matrix elements encode a wide variety of different phenomena, from the quantum corrections which arise in the gravitational motion of particles, to the distribution of mass and angular momentum within hadrons [1][2][3][4][5][6]. Although there is a significant breadth of literature on these objects, most of these studies have chosen to focus on particular cases where the states have lower spin (generally spin 0, 1 2 , or 1 [2][3][4][5][6][7][8][9][10][11]) or correspond to specific particles, as opposed to analysing the constraints imposed for arbitrary states. Whilst this approach has proven to be successful phenomenologically, it potentially risks obscuring the underlying properties governing these constraints, preventing one from separating model-specific and general QFT effects.…”

Universality of the Poincaré gravitational form factor constraints

“…The form factors that appear in the Lorentz covariant decomposition of the energy-momentum tensor (EMT), the so-called gravitational form factors (GFFs), enter into the physics of many different phenomena, including gravitational scattering [1,2] and the internal properties of hadrons, such as mass, spin and pressure [3][4][5][6][7][8][9][10][11][12][13][14][15]. In recent years there has been a significant drive to characterise the properties of these objects for target states of different spin [6,7,10,12,13,[16][17][18][19][20], due to their connection to generalised parton distributions (GPDs) [21]. By constraining GPDs via the GFFs, this could help, for example, in providing new insights into the dynamics of quarks and gluons within composite states.…”