Disconnected contributions to D-meson semi-leptonic decay form factors

Abstract

We calculate the disconnected contribution to the form factor for the semileptonic decay of a D-meson into a final state, containing a flavor singlet eta meson. We use QCDSF n f = 2 + 1 configurations at the flavor symmetric point m u = m d = m s and the partially quenched approximation for the relativistic charm quark. Several acceleration and noise reduction techniques for the stochastic estimation of the disconnected loop are tested.

Ds→η,η′semileptonic decay form factors with disconnected quark loop contributions

“…Despite the statistically noisy and computationally expensive disconnected part, we obtained the form factor at q 2 = 0 within statistical errors of less than 6%. The values at q 2 = 0 are |f Ds→η 0 | = 0.564 (11) fit and θ = −7.7(0.9) stat. (0.8) • fit in the parameterization Eq.…”

“…The parameters for the various techniques are chosen so that the stochastic error is minimized for fixed computational cost, see Ref. [11] for details. Our optimal choices are listed in Table VI.…”

“…Moreover, in the pseudoscalar case the disconnected quark loops couple to the axial anomaly. In spite of the computational expense and the inferior quality of the signal, relative to that of the quark-line connected contribution, the calculation of the disconnected contribution turns out to be feasible and its impact is significant [7,11]. Therefore, these decay modes also provide a perfect playground for testing a variety of techniques for calculating the disconnected quark-line loops.…”

“…c, A1 and A2 are free parameters of the fit. p, q, k × L/(2π) a 2 q 2 f (q [11][12][13] 2exp. + c 1.25 24 (0, 0, 0), (1, 1, 0), (−1, −1, 0) −0.088(17) 0.375(26) 8 [3][4][5], 10[4-7], 16 [10][11][12][13] 1exp.…”

“…p, q, k × L/(2π) a 2 q 2 f (q [11][12][13] 2exp. + c 1.25 24 (0, 0, 0), (1, 1, 0), (−1, −1, 0) −0.088(17) 0.375(26) 8 [3][4][5], 10[4-7], 16 [10][11][12][13] 1exp. + c 0.50 12 (1, 0, 0), (0, 1, 0), (1, −1, 0) −0.000(20) 0.416(36) 8 [3][4][5], 10[5-7], 16 [10][11][12][13] 1exp.…”