Lifetime Difference and Endpoint Effect in the Inclusive Bottom Hadron Decays

Abstract

The lifetime differences of bottom hadrons are known to be properly explained within the framework of heavy quark effective field theory(HQEFT) of QCD via the inverse expansion of the dressed heavy quark mass. In general, the spectrum around the endpoint region is not well behaved due to the invalidity of 1/mQ expansion near the endpoint. The curve fitting method is adopted to treat the endpoint behavior. It turns out that the endpoint effects are truly small and the explanation on the lifetime differences in the HQEFT of QCD is then well justified. The inclusion of the endpoint effects makes the prediction on the lifetime differences and the extraction on the CKM matrix element |V cb | more reliable.

Large Component QCD and Theoretical Framework of Heavy Quark Effective Field Theory

“…For free quark case, taking v = (1, 0, 0, 0), the projected quark fields get the following forms in the momentum space: 15) which shows that in the case |p| E + m Q the effective heavy fieldsQ…”

“…k 0 ∼ |k| ∼Λ m Q ), then LCQCD can be treated as a heavy quark effective field theory (HQEFT) 4,5 via the heavy quark expansion in terms of 1/m Q , which has been applied to deal with heavy-light hadron systems. [6][7][8][9][10][11][12][13][14][15][16][17][18][19] The leading term of effective Lagrangian in HQEFT characterizes the behavior of heavy quarks in the infinite mass limit [20][21][22][23] and coincides with the standard one 24 which explicitly displays the heavy quark spin-flavor symmetry. [25][26][27][28][29][30] The effective Lagrangian in HQEFT 4,5 differs from the widely used one in the literatures b which was shown to be constructed based on the assumption that particle and antiparticle numbers are separately conserved.…”

Heavy quark expansion in 1/\hat{m}_Q and |Vcb| extraction

“…The HQEFT has been applied to explore various processes of heavy hadrons. In particular, the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V cb | and |V ub | are extracted from both inclusive [20][21][22][23] and exclusive [17,[24][25][26][27][28][29] B decays. In the treatment of inclusive B decays, the dressed heavy quark mass mQ = m Q + ¯ as a whole enters the formulation, which implies that a 'dressed heavy quark'-hadron duality is more reasonable than the naive heavy quark-hadron duality.…”

Heavy Quark Expansion in 1/\hat{m}_Q and |V_{cb}| Extraction

“…HQEFT has been applied to explore various processes of heavy hadrons. In particular, the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V cb | and |V ub | are extracted from both inclusive [20][21][22][23] and exclusive [17,[24][25][26][27][28][29] B decays. In the treatment of inclusive B decays, the dressed heavy quark mass mQ = m Q + Λ as a whole enters the formulation, which implies that a "dressed heavy quark"-hadron duality is more reasonable than the naive heavy quark-hadron duality.…”