CP Reach

In table 2 is a comparison of the statistical precision that BaBar (and BELLE) and HERA-B claim can be achieved in measuring $\sin 2\alpha$ and $\sin 2\beta$ for one year's running at design luminosity. The two experiments are comparable in the $B^0 \rightarrow J/\Psi K_s^0$ channel, but there are other channels that BaBar can use, because of the clean event environment, to extract the angle $\alpha.$ For measuring $\sin 2\beta$ at first glance the two experiments are again comparable, but the figures quoted in the table are for zero background. HERA-B will have a background in $B^0 \rightarrow \pi^+ \pi^-$ channel and the quoted figures need to be modified by a factor $\sqrt{1+B/S}$ where B/S is the ratio of background to signal. It is thought that a value of B/S < 1 can be achieved [17].

 

 

Decay Channel BaBar HERA-B

$$J/\Psi K_s^0$$

$$\Delta \sin 2\beta \pm 0.10 \pm 0.13$$ All channels

$$\Delta \sin 2\beta \pm 0.06 \pm 0.13$$

$$\pi^+ \pi^-$$

$$\Delta \sin 2\alpha \pm 0.20 \pm 0.14$$

$$\rho^{\pm}\pi^{\pm}$$

$$\Delta \sin 2\alpha \pm 0.11$$ All channels

$$\Delta \sin 2\alpha \pm 0.085 \pm 0.14$$

Table 3 reviews the accuracy that the experiments at hadron colliders hope to achieve from 10⁷ seconds running. Besides the accuracy on $\sin(2\alpha)$ and $\sin(2\beta),$ the measurement precision and upper limit of $\gamma$ and x_s (comparable to x in the B_d system) are listed, which need the B_s mesons to be detected and tagged. The figures show that the dedicated experiment at the LHC, LHC-B, has by far the best reach in measuring the parameters of CP violation. It is also worth noting that the performance of the Tevatron general purpose detectors are comparable to result expected from HERA-B and thus the e⁺e^- B factories. (It should be noted though the clean experimental environment in e⁺e^- allows them to make a more complete study of rare B-decays.)

 

 

CDF/D0 HERA-B ATLAS/CMS LHC-B BTeV

$$\Delta \sin(2\alpha) \sim 0.10 \sim 0.14$$ 0.10/0.07 0.039 0.1

$$\Delta \sin(2\beta) \sim 0.10 \sim 0.13$$ 0.02/0.07 0.023 0.042

$$\Delta \gamma 6-16^{\circ}$$

$$\le 17 \le 34 \le 55 \le 30$$ x_s