Study of the decay asymmetry parameter and CP violation parameter in the ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}$ decay

Abstract

Using data from the FOCUS (E831) experiment at Fermilab, we present a new measurement of the weak decay-asymmetry parameter ${\alpha }_{{\Lambda }_c}$ in ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}$ decay. Comparing particle with antiparticle decays, we obtain the first measurement of the CP violation parameter $\mathcal{A}\equiv \frac{{\alpha }_{{\Lambda }_c}+{\alpha }_{{\overline{\Lambda }}_c}}{{\alpha }_{{\Lambda }_c}-{\alpha }_{{\overline{\Lambda }}_c}}$. We obtain ${\alpha }_{{\Lambda }_c}=-0.78\pm 0.16\pm 0.19$ and $\mathcal{A}=-0.07\pm 0.19\pm 0.24$ where errors are statistical and systematic.

Introduction

Parity violation in the weak decay of a spin $\frac{1}{2}$ hyperon into a spin $\frac{1}{2}$ baryon and a pseudoscalar meson is well known. An example is $\Lambda \to p{\pi }^{-}$ [1], where the angular distribution of the proton in the Λ rest frame is given by

$$\frac{dW}{d\cos \theta }=\frac{1}{2}(1+P{\alpha }_{\Lambda }\cos \theta ),$$

where P is the polarization of Λ along the z direction, θ is the polar angle and ${\alpha }_{\Lambda }$ is the weak decay-asymmetry parameter. The latter is defined as

$${\alpha }_{\Lambda }\equiv \frac{2\mathcal{R}e(A_{+}^{\ast }{A}_{-})}{{|A_{+}|}^2+{|A_{-}|}^2},$$

where $A_{+}$ and $A_{-}$ are the parity-even and parity-odd decay amplitudes. In a non-relativistic picture, they correspond to the $L=0$ and $L=1$ orbital angular momenta of the proton–π system, respectively.

Eq. (1) can be generalized for the case of a baryon double decay chain like ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}$ with $\Lambda \to p{\pi }^{-}$ in which each baryon weak decay is a ${\frac{1}{2}}^{+}\to {\frac{1}{2}}^{+}+0^{-}$ process. If the ${\Lambda }_c^{+}$ is produced unpolarized, Eq. (1) for the Λ decay becomes

$$\frac{dW}{d\cos \theta }=\frac{1}{2}(1+{\alpha }_{{\Lambda }_c}{\alpha }_{\Lambda }\cos \theta ),$$

where ${\alpha }_{{\Lambda }_c}$ is the weak-decay asymmetry parameter of the ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}$ process and θ is the helicity angle of the proton in the Λ rest frame, i.e. it is the supplement of the angle (i.e., π minus the angle) in the Λ rest frame between the proton and the direction of the ${\Lambda }_c^{+}$. The distribution of the helicity angle, θ, determines the product ${\alpha }_{{\Lambda }_c}{\alpha }_{\Lambda }$, and, since ${\alpha }_{\Lambda }$ is known (in this analysis we assume ${\alpha }_{\Lambda }=-{\alpha }_{\overline{\Lambda }}=0.642\pm 0.013$ [2]), one can extract ${\alpha }_{{\Lambda }_c}$.

If CP were conserved exactly, ${\alpha }_{{\Lambda }_c}$ of the ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}$ process would be the negative of ${\alpha }_{{\overline{\Lambda }}_c}$ in ${\overline{\Lambda }}_c^{-}\to \overline{\Lambda }{\pi }^{-}$ decay. Just as with the Λ decay, there is the possibility of CP violation in ${\Lambda }_c^{+}$ decay (a weak decay with possible final state interactions). In this Letter we (1) measure ${\alpha }_{{\Lambda }_c}$ and ${\alpha }_{{\overline{\Lambda }}_c}$ separately, (2) use them for the first measurement of the CP asymmetry parameter

$$\mathcal{A}\equiv \frac{{\alpha }_{{\Lambda }_c}+{\alpha }_{{\overline{\Lambda }}_c}}{{\alpha }_{{\Lambda }_c}-{\alpha }_{{\overline{\Lambda }}_c}},$$

and (3) having established that the difference is negligible within our errors, combine the data for particle and antiparticle decays to obtain the best value of the asymmetry parameter. In this analysis the ${\Lambda }_c^{+}$ is assumed to be unpolarized and thus the Λ longitudinal polarization (polarization along the Λ momentum direction in the ${\Lambda }_c^{+}$ rest frame) is ${\alpha }_{{\Lambda }_c}$. As discussed later, if the polarization is the maximum allowed in our data, the effect on our measurement is negligible.

FOCUS is a charm photoproduction experiment, an upgraded version of E687 [3], which collected data during the 1996–1997 fixed target run at Fermilab. Electron and positron beams obtained from the $800\text{GeV}/c$ Tevatron proton beam produce, by means of bremsstrahlung, a photon beam (with typically $300\text{GeV}$ endpoint energy) which interacts with a segmented BeO target [4]. The mean photon energy for triggered events is ∼180 GeV. A system of three multicell threshold Čerenkov counters is used to perform the charged particle identification, separating kaons from pions up to $60\text{GeV}/c$ of momentum. Two systems of silicon microvertex detectors are used to track particles: the first system consists of 4 planes of microstrips interleaved with the experimental target [3], [5] and the second system consists of 12 planes of microstrips located downstream of the target. These detectors provide high resolution in the transverse plane (approximately 9 μm on the track position), allowing the identification and separation of charm production and decay vertices. The charged particle momentum is determined by measuring the deflections in two magnets of opposite polarity through five stations of multiwire proportional chambers.