Towards a heavy diquark effective theory for weak decays of doubly heavy baryons

Abstract

We construct a leading-order effective field theory for both scalar and axial-vector heavy diquarks, and consider its power expansion in the heavy diquark limit. By assuming the transition from QCD to diquark effective theory, we derive the most general form for the effective diquark transition currents based on the heavy diquark symmetry. The short-distance coefficients between QCD and heavy diquark effective field theory are also obtained by a tree level matching. With the effective currents in the heavy diquark limit, we perform a reduction of the form factors for semi-leptonic decays of doubly heavy baryons, and find that only one nonperturbative function is remaining. It is shown that this soft function can be related to the Isgur–Wise function in heavy meson transitions. As a phenomenological application, we take a single pole structure for the reduced form factor, and use it to calculate the semi-leptonic decay widths of doubly heavy baryons. The obtained results are consistent with others given in the literature, and can be tested in the future.

Effective field theory for double heavy baryons at strong coupling

“…Interestingly, upon implementing chiral symmetry to this EFT and the expansion of the fields in the eigenstates of the Schrördinger equations, our EFT will match the standard chiral hadronic theories. These EFTs have been used abundantly to discuss threshold effects and decays [43,44,61].…”

QCD sum rules analysis of weak decays of doubly heavy baryons: the $$b\rightarrow c$$ processes

“…The discovery of the doubly charmed baryon has triggered many related theoretical researches on the masses, lifetimes, strong coupling constants, and decay widths of doubly heavy baryons. They are based on various model calculations , SU(3) symmetry analysis [27][28][29], effective theories [30][31][32][33][34][35][36][37][38][39][40], QCD sum rules [41][42][43] and light-cone sum rules [44][45][46][47][48][49][50][51][52]. For a recent review, see [53].…”

“…However, the heavy quark limit can still be taken from the full theory results, as can be seen in [56][57][58]. Some efforts were made to develop the effective theory for doubly heavy baryons in [37].…”

QCD sum rules analysis of weak decays of doubly heavy baryons: the $b\to c$ processes

“…The discovery of the doubly charmed baryon has triggered many related theoretical researches on the masses, lifetimes, strong coupling constants, and decay widths of doubly heavy baryons. They are based on various model calculations , SU(3) symmetry analysis [27][28][29], effective theories [30][31][32][33][34][35][36][37][38][39][40], QCD sum rules [41][42][43]and light-cone sum rules [44][45][46][47][48][49][50][51][52]. For a recent review, see [53].…”

“…However, the heavy quark limit can still be taken from the full theory results, as can be seen in [56][57][58]. Some efforts were made to develop the effective theory for doubly heavy baryons in [37].…”