Electromagnetic properties of singly heavy baryons

TL;DR

This paper investigates the electromagnetic properties of the baryon decuplet, especially the $
$ baryon, using the SU(3) chiral quark-soliton model, and compares results with lattice data.

Contribution

It provides new calculations of electromagnetic form factors of decuplet baryons considering SU(3) symmetry breaking effects.

Findings

Electromagnetic form factors of $
$ baryon are computed.

Results show consistency with lattice data.

Explicit SU(3) symmetry breaking effects are significant.

Abstract

In the present talk, we report recent results on electromagnetic properties of the baryon decuplet within the SU(3) chiral quark-soliton model, taking into account the effects of explicit flavor SU(3) symmetry breaking. We focus on the comparison of the present results on the electromagnetic form factors of the $\Delta^{+}$ baryon with the lattice data.

Tables

Table 1. Table 1: Electromagnetic properties of Δ + superscript Δ \Delta^{+} baryon.

	${⟨r^2⟩}_E^{{\Delta }^{+}}$$\left[{\mathrm{fm}}^2\right]$	${\mu }_{{\Delta }^{+}}$[${\mu }_N$]	$Q_{{\Delta }^{+}}\left[e\cdot {\mathrm{fm}}^2\right]$
$\chi$QSM ($m_s=180$)	0.79	2.33	0.043
$\chi$QSM ($m_s=0$)	0.83	2.47	0.053
Exp. Kotulla:2002cg	-	${2.7}_{-1.3}^{+1.0}\pm 1.5\pm 3$	-
LQCD Boinepalli:2009sq	0.41(6)	1.6(3)	-

Full text

Electroagnetic properties of the $\Delta$ isobar, pion mean-field approach, SU(3) chiral quark-soliton model, explicit flavor SU(3) symmetry breakingm

††preprint: INHA-NTG-04/2019

I Introduction

When we investigate the structure of a baryon, its electromagnetic (EM) properties are the first subject to study, since it reveals how the quarks are distributed inside it. While the EM properties of the baryon octet have been extensively studied both experimentally and theoretically, those of the baryon decuplet have been examined mainly theoretically. Except for the $\Omega^{-}$ baryon, all the members of the baryon decuplet decay strongly, so that it is extremely difficult to measure the EM form factors of the baryon decuplet. Nevertheless, using the electron and photon beams, experimentalists put a great deal of efforts on extracting information on the EM properties of the $\Delta$ isobar Kotulla:2002cg ; Sparveris:2013ena . On the other hand, recent investigations in the lattice QCD produce more and more quantitative results on the structure of the baryon decuplet Alexandrou:2008bn ; Alexandrou:2010jv .

In the present talk, we will report recent results on the electromagnetic form factors of the baryon decuplet  JYKim , derived from the self-consistent chiral quark-soliton model ($\chi$QSM) Diakonov:1987ty ; Blotz:1992pw ; Christov:1995vm . The $\chi$QSM provides a simple but useful theoretical framework for investigating the structure of the baryon decuplet, since the decuplet representation naturally appears from the constraint imposed by the valence quarks. In fact, the EM form factors of the $\Delta$ were already studied within the $\chi$QSM Ledwig:2008es with exact flavor SU(3) symmetry considered. In the present talk, we focus on the effects from explicit breaking of flavor SU(3) symmetry. The results of the $\Delta$ EM form factors will be compared with the recent lattice data.

II Result and Discussion

The detailed formalism for deriving the EM form factors of the baryon decuplet within the $\chi$QSM will appear elsewhere JYKim . In the present talk, we will concentrate on the results from the model.

In Fig. 1, we show the numerical result of the electric monopole form factor of the $\Delta^{+}$ baryon as a function of $Q^{2}$ in comparison with the lattice data Alexandrou:2007we ; Alexandrou:2008bn . The positive-definite $Q^{2}$ is defined as $Q^{2}=-q^{2}$ in which $q^{2}$ is the square of the momentum transfer. It is rather well known that when higher unphysical pion masses are employed the lattice calculation of the nucleon EM form factor yield the results of hadronic form factors, which fall off more slowly, compared with the experimental data. Keeping in mind this, we find that indeed the present result decreases more rapidly than the lattice data, as shown clearly in Fig. 1. What is interesting is that the present result even falls off faster than the lattice data with physical extrapolation.

In Fig. 2, the numerical result of the $\Delta$ magnetic dipole form factor is drawn, compared with the lattice data. The result exhibits a similar tendency as shown in the case of the electric form factor presented in Fig. 1. Again, the reason can be found in the large value of the pion mass adopted by the lattice QCD.

Figure 3 depicts the result of the electric quadrupole form factor of the $\Delta^{+}$, again compared with those of the lattice QCD. Unfortunately, the lattice results show large uncertainty, so that one can not draw any meaning conclusion from this comparison. However, the general dependence on $Q^{2}$ of the present result seems similar to the lattice one.

In Tab. 1, we list the numerical results on the squared electric charge radius, the magnetic dipole moment, and the electric quadrupole moment of the $\Delta^{+}$ with the SU(3) symmetry breaking taken into account. The inclusion of the SU(3) symmetry-breaking effects lessens slightly the squared electric charge radius. It indicates that the SU(3) breaking makes the $\Delta^{+}$ a little bit more compact. As already expected from Fig. 1, the lattice data produces a smaller value of $\langle r^{2}\rangle_{E}$. The contribution from the flavor SU(3) symmetry breaking also reduces the value of the $\Delta^{+}$ magnetic dipole moment, which is opposite the case of the nucleon Kim:1995mr . Note that the nucleon mass for the nuclear magneton is replaced by the classical soliton mass in the present model in order to keep a consistency, as already pointed out by Ledwig et al. Ledwig:2008es . When it comes to the electric quadrupole moment, the effects of the explicit flavor SU(3) symmetry breaking turns out to be much large in contrast to the previous observables such as the electric charge radius and magnetic dipole moment. The reason will be discussed elsewhere in detail JYKim .

We want to mention that the magnetic quadrupole form factor vanishes within the present framework. This is already well known that in any chiral model with hedgehog symmetry the magnetic octupole form factor becomes null. However, it indicates that the magnetic octupole form factor will be negligibly small in nature. Finally, we find that $U$-spin symmetry is preserved in the whole form factors of the baryon decuplet in the flavor SU(3) symmetric case.

III Summary and conclusion

In this talk, we presented recent results of the electromagnetic form factors of the $\Delta^{+}$ isobar in comparison with the lattice QCD data, and discuss the related observables with the effects of flavor SU(3) symmetry breaking. While the present talk concentrates on the electromagnetic properties of the $\Delta^{+}$ isobar, we can easily extend the present work to examine those of all other members belonging to the baryon decuplet. A more complete article will soon appear JYKim .

Acknowledgment

The work is supported by Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Korean government (Ministry of Education, Science and Technology(MEST)): Grant No. NRF-2018R1A2B2001752.