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.
Highlights
IntroductionA straightforward way to consider this problem is to reduce a doubly heavy baryon into a two-body system, where two of the three quarks are treated as a point-like diquarks
One year later, LHCb has successfully measured the +cc+’s lifetime [3], and reconstructed this resonance from the
When using diquark effective theory (DiET) to study doubly heavy baryon decays BbQ → BcQlν, for instance when the bb diquark turns into the bc diquark through the V − A current cγμ(1 − γ5)b, or electromagnetic transitions BQ1 Q2 → BQ1 Q2 γ ∗ induced by the vector current Qγμ Q, one needs to express the corresponding currents in terms of the diquark fields instead of the heavy quark fields
Summary
A straightforward way to consider this problem is to reduce a doubly heavy baryon into a two-body system, where two of the three quarks are treated as a point-like diquarks. J. C (2020) 80:398 ever, for a doubly heavy baryon, it is more reasonable to treat the two heavy quarks behave as static color sources and as a diquark. For the transition form factors we will assume the applicability of HDiET, and by assuming the diquark to be a point-like particle, we can construct the weak and electromagnetic transition currents of the diquarks according to the SU(2) heavy flavor symmetry and U(1) symmetry. We show that the six transition form factors of doubly heavy baryon semi-leptonic decay can be reduced into only one soft function.
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