Annihilation semileptonic decays of B mesons and the model dependence on the choice of the distribution amplitude
- PDF / 137,009 Bytes
- 3 Pages / 612 x 792 pts (letter) Page_size
- 15 Downloads / 166 Views
nihilation Semileptonic Decays of B Mesons and the Model Dependence on the Choice of the Distribution Amplitude1 A. L. Kuznetsova and A. Ya. Parkhomenko* Demidov Yaroslavl State University, Yaroslavl, 150003 Russia *e-mail: [email protected] Abstract—The rare semileptonic B -meson decay B → φ + − is considered. The partial decay rate integrated over the 1–8 GeV2 interval of the dilepton invariant mass squared is computed with a 10% systematic uncertainty arising from the model dependence of the distribution amplitude. The purely perturbative contribution to the decay probability amounts to @ ∼ 10 −12 , which suggests that the LHC experiments could observe the B → φ + − decay in a few years of data taking. DOI: 10.1134/S1063779617060338
B mesons contain a light u or d quark and a heavy b antiquark. A broadly accepted approach to describing such objects in the heavy-quark effective theory (HQET) [1, 2] in which the heavy quark is viewed as a stationary source and the system dynamics is fully determined by the light-quark motion. Note that thereby the heavy meson is treated in the same way as the quantum-mechanical hydrogen-like atom, though in the former case the interaction is strong rather than electromagnetic. As for the hydrogen atom in the nonrelativistic approximation, in HQET the heavy-quark spin does not affect the internal dynamics, and the meson spin structure is reproduced by adding the heavy-quark spin and projecting it to a particular spin state of the meson. In this approximation, the pseudoscalar and vector B and B* mesons are dynamically equivalent up to the 1 mb corrections where mb is the b -quark mass. In quantum field theory, the B -meson wave function is determined by the transition matrix element between the meson and vacuum states of an operator with quantum numbers of the considered particle, referred to as the interpolating current. For the B meson involving only the quark–antiquark interpolating currents in the lowest Fock state, the wave function is fully determined by two functions referred to as the leading and nonleading distribution amplitudes [3]. In the calculation, the transition matrix element is 1 Talk
at the International Session–Conference on the Physics of Fundamental Interactions (JINR Section, Physics Department, Russian Academy of Sciences), Dubna, April 12–15, 2016.
conveniently replaced by the Dirac operator for projecting the two-quark state to that of the B meson [4],
if B mB 4 ⎡ ⎤ ˆ B B B z × ⎢⎢(1 + vˆ ) ϕ + (t ) − ⎣⎡ϕ + (t ) − ϕ − (t )⎦⎤ γ 5 ⎥⎥ , ⎣ 2t ⎦βα 0 q α(z)E (z, 0)hv ,β(0) B (v ) = −
{
}
(1)
where hv (0) is the b -quark quantum field assumed to be stationary, and the reference-frame origin is selected at the heavy-quark position; q(z) is the lightquark field whose mass is neglected; the spacetime interval z μ between the two quarks lies on the light cone ( z 2 = 0); mB and f B are the B-meson mass and leptonic coupling constant, respectively; v μ is the B-meson four-dimensional velocity; t = (v z) is the time in the B-meson rest frame; E (z, 0) is t
Data Loading...
