Abstract

To measure the helicity of a spin-1 meson from the triple vector product of the three-momenta of its decay products, one needs information about the strong phase of the decay amplitude. In this paper, taking $a_1(1260)$ meson as an example, we present a method to extract information about the strong phase from the triple vector product of the pion momenta in $W \to \nu \tau(\to \nu a_1(\to\pi^\mp \pi^\mp \pi^\pm))$ process, where the $a_1$ helicity is known a priori from electroweak theory. This process is advantageous in that highly-boosted $a_1^-$ mesons from $\tau_L^-$ decays have nearly maximal helicity asymmetry and thus most reflect the strong phase. We revisit the theoretical calculation of the $a_1$ meson helicity in $W \to \nu \tau(\to \nu a_1)$ process. We formulate the differential decay rate of polarized $a_1$ mesons in a manner convenient for the study of the $a_1$ meson helicity asymmetry. Finally, we present the method for extracting information about the strong phase, and assess its feasibility at the LHC.

Highlights

  • The helicity of spin-1 mesons can be a probe for physics beyond the Standard Model (SM)

  • In the B− → K−π−πþγ process induced by b → sγ, the SM predicts that the K−π−πþ system is mostly left-handed because the W boson loop gives an amplitude with a lefthanded photon, while various extensions of the SM contain an extra amplitude with a right-handed photon

  • We have presented a method to extract information about the strong phase of the a−1 → π−π−πþ decay amplitude necessary for the a1 helicity measurement

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Summary

INTRODUCTION

The helicity of spin-1 mesons can be a probe for physics beyond the Standard Model (SM). If the helicity asymmetry of a−1 is known a priori, one can determine ImðA · BÃÞ=Nnor by measuring the asymmetry of the number of events with cos Ψ > 0 and cos Ψ < 0 ImðA · BÃÞ=Nnor is determined from the cos Ψ asymmetry of events, divided by the convolution of theoretically calculated dΓþ dz dΓ− dz and the reweighting function of z under given selection cuts IV D, we estimate statistical uncertainty in a measurement of the right-hand side of Eq (49) with 300 fb−1 of data

Monte Carlo event generation and selection cuts
Statistical uncertainty
Findings
SUMMARY

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