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T-odd asymmetries in top-quark decay

T-odd asymmetries in top-quark decay. Hiroshi Yokoya (Niigata U). in collaboration with Kaoru Hagiwara (KEK) and Kentarou Mawatari (KIAS). KEKPH2007 3/1-3 (2007), KEK. Contents :. Introduction : T-odd asymmetry Top-quark decay Results Summary. What is T-odd asymmetry ?. ~.

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T-odd asymmetries in top-quark decay

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  1. T-odd asymmetries in top-quark decay Hiroshi Yokoya (Niigata U) in collaboration with Kaoru Hagiwara (KEK) and Kentarou Mawatari (KIAS) KEKPH2007 3/1-3 (2007), KEK

  2. Contents : • Introduction : T-odd asymmetry • Top-quark decay • Results • Summary

  3. What is T-odd asymmetry ? ~ • T-transformationis defined as reversing spatial momenta • and spins without interchanging initial and final states. ~ ~ naïve-T T : time-reversal T : parity P : ~ • T-odd means that change sign under T-transformation. • Non-zero T-odd asymmetryneeds P-violating interaction (Weak), • or polarization measurement. : triple product of three momenta e.g. : triple product of two momenta and spin

  4. T-odd asymmetry and Unitarity • Unitarity of S-matrix : Afi : absorptive part forward amplitude (i=f=k) → optical theorem • T-odd quantity (non-forward amplitude) : Time-reversal violating term →T-odd quantitycomes from theabsorptive partof the scattering amplitude in CP conserving theory.

  5. * = Im • sign ? • size ? • shape ? T-odd asymmetry • In perturbation theory, the absorptive part can be predicted • by the imaginary part of loop-diagrams T-odd asymmetry in hard process ⇔ test for the absorptive part of non-forward amplitude

  6. T-odd asymmetry • T-odd asymmetriesin hard processes have been calculated • in the e+e- annihilation, Semi-Inclusive DIS, and DY processes in one-loop level. Semi-Inclusive DIS Hagiwara,Hikasa,Kai (’83) Top-quark decay e+e- → 3-jets Our new calculation! Korner,Kramer,Shcierholz,Fabricius, Schmitt (’80) Brandenburg,Dixon,Shadmi (’96) Drell-Yan (W-jet) Hagiwara,Hikasa,Kai (’84) (Z-jet) Hagiwara,Kuruma,Yamada (’92) • absorptive parts of these processes are related • with each other by crossing and analyticity • so far, no experimental measurements for these processes Korner,Malic,Merebashvili (’00)

  7. Dalitz plot 2. Top-quark decay • We consider the top-quark • decay with one-gluon emission : (mb is neglected) • Kinematics (in top rest frame) physical region of t → bWg is given by

  8. * Top-quark decay • Density matrix (DM) formalism • W-decay DM :

  9. Top-decay density matrix • Top-decay DM : expanding the amplitude as • In leading-order Couture (’89), Barger et al. (’90) • Real part of DM → tree diagrams : • Imaginary part of DM → interference of the tree and • imaginary part of the one-loop diagrams :

  10. One-loop calculation Imaginary part (absorptive part) of the scattering amplitude comes from the on-shell intermediate states. Origin of the imaginary part in the loop integrals; in the integrand We calculate these diagrams by two different methods; 1. analytic calculation by standard Feynman parameter integrals 2. express by loop scalar functions and use the fortran code “FF” and check results by the gauge invariance. Passarino,Veltman (’79), Oldenborgh (’91) • IR divergences are regulated by using gluon mass scheme

  11. Lepton angular distribution • Now, combining Top-decay and W-decay DM’s, the decay rate is • written as the lepton angular distribution. : nine structure functions reflecting the W’s polarization (3x3=9) F7-9 :T-odd (P-odd) ⇔ Imaginary part

  12. 3. Numerical results • Total rate F1 : integrate over lepton angles Contour plot of the F1 with kinematical cuts • Kinematical cuts : Kinematical cuts are needed to avoid the collinear decay, and to select the hard gluon jet event.

  13. T-even and T-odd angular distributions • T-even asymmetries (tree) A2,5 : polar angle distributions, diagonal part of DM A3,4,6: azimuthal angle distributions, off-diagonal part of DM, interference between different polarization states large z2 limit →(t→bW decay) A2→ f0 ~ 0.7, A5 → -2f- ~ -0.6, A3,4,6 vanish • T-odd asymmetries (one-loop, our results) A7 ~ 3%, A8 ~ 1%, A9 ~ ±0.1%

  14. Up-down asymmetry At the LHC experiment, about 800000 of the top-quark events are expected for the “single lepton plus jets” channel (10fb-1) By the branching fraction of top-decay in SM, about 70000 of events may be identified as an event with a hard gluon jet. • Up-down asymmetry : • Lepton direction w.r.t. the top-decay plane

  15. 4. Summary • T-odd asymmetry emerges from the absorptive part of the • scattering amplitudes. In hard process, it can be predicted, • and comparison with experiments would be an interesting test. • We calculate the T-odd asymmetry for the top-quark decay • with one-gluon emission, in one-loop level. • T-odd asymmetries are predicted (~3% at most), • which may be observed at the LHC or in future the ILC.

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