HOMELEGALKIT

D2: Non-perturbative parameter within the HQE

Principal Investigator
Prof. Alexander Lenz University of Siegen

Subject

The project will increase the theoretical precision in the description of lifetimes of heavy mesons, containing a heavy $b$ or $c$ quark and light $u, d, s$ quarks. The total decay rate of such a hadron can be expressed as

$$ \displaystyle \Gamma = \Gamma_0 + \Gamma_2 \frac{ \langle {\cal O}_5 \rangle }{m_b^2} + \Gamma_3 \frac{\langle {\cal O}_6 \rangle}{m_b^3} + \ldots + 16 \pi^2 \Big{[} \tilde{\Gamma}_3 \frac{\langle \tilde{\mathcal{O}}_6 \rangle}{m_b^3} + \tilde{\Gamma}_4 \frac{\langle \tilde{\mathcal{O}}_7\rangle}{m_b^4} + \ldots \Big{]}. \label{eq:HQE} $$

We plan to determine the non-perturbative matrix elements $\langle {\cal O}_6 \rangle$, $\langle \tilde{\mathcal{O}}_6 \rangle$ and $\langle \tilde{\mathcal{O}}_7\rangle$ with sum rules using the Heavy Quark Effective Theory (HQET) for different observables, like $\tau (B_s)/ \tau (B_d)$, $\tau (D_s^+)/ \tau (D_0)$ and the decay rate difference $\Delta \Gamma_s$. All these quantities are experimentally well-known and they will be measured even more precisely in the future.

Key features of studied quantities:

Research Topics

  1. Determination of the matrix element of the Darwin operator for $D$ mesons
    • will give one of the dominant contributions to the lifetime ratio $\tau (D_s^+)/ \tau (D^0)$ which is measured very precisely
    • will allow a convergence test of the HQE in the charm sector
  2. Determination of strange quark mass corrections to the Bag parameter of four quark operators triggering the $D_s^+$ lifetime
    • will allow a convergence test of the HQE in the charm sector
  3. Determination of dimension seven Bag parameter of four quark operators triggering the $B_s$ mixing
    • tests the formalism HQE
    • reduces the dominant uncertainty in $\Delta \Gamma_s$
  4. Determination of dimension seven Bag parameter of four quark operators contribution to the $B_s$ lifetime
    • will reduce the theory uncertainty in the lifetime ratio $\tau (B_s) / \tau (B_d) $ which is measured to a precision of four per mille
    • will allow a precision test of the HQE
    • can be used to look for invisible decay channels of the $B_s$ meson
This website uses cookies. By using the website, you agree with storing cookies on your computer. Also you acknowledge that you have read and understand our Privacy Policy. If you do not agree leave the website.More information about cookies