Search for the decay $B^{0}\rightarrow K^{\ast 0}τ^{+}τ^{-}$ at the Belle 
experiment

Belle Collaboration,; Dong, T.V.; Luo, T.; Adachi, I.; Aihara, H.; Asner, D.M.; Atmacan, H.; Aulchenko, V.; Aushev, T.; Ayad, R.; Babu, V.; Bahinipati, S.; Behera, P.; Belous, K.; Bernlochner, F.; Bessner, M.; Bhuyan, B.; Bilka, T.; Biswal, J.; Bobrov, A.; Bozek, A.; Bračko, M.; Branchini, P.; Browder, T.E.; Budano, A.; Campajola, M.; Červenkov, D.; Chang, M.-C.; Chang, P.; Chen, A.; Cheon, B.G.; Chilikin, K.; Cho, H.E.; Cho, K.; Cho, S.-J.; Choi, S.-K.; Choi, Y.; Choudhury, S.; Cinabro, D.; Cunliffe, S.; Czank, T.; Das, S.; De Nardo, G.; De Pietro, G.; Dhamija, R.; Di Capua, F.; Dingfelder, J.; Doležal, Z.; Dubey, S.; Epifanov, D.; Ferber, T.; Ferlewicz, D.; Fulsom, B.G.; Garg, R.; Gaur, V.; Gabyshev, N.; Garmash, A.; Giri, A.; Goldenzweig, P.; Graziani, E.; Gu, T.; Gudkova, K.; Hara, T.; Hartbrich, O.; Hayasaka, K.; Hernandez Villanueva, M.; Hou, W.-S.; Hsu, C.-L.; Inami, K.; Inguglia, G.; Ishikawa, A.; Itoh, R.; Iwasaki, M.; Jacobs, W.W.; Jang, E.-J.; Jia, S.; Jin, Y.; Joo, K.K.; Kahn, J.; Kang, K.H.; Kichimi, H.; Kiesling, C.; Kim, C.H.; Kim, D.Y.; Kim, K.T.; Kim, S.H.; Kim, Y.-K.; Kimmel, T.D.; Kodyš, P.; Konno, T.; Korobov, A.; Korpar, S.; Kovalenko, E.; Križan, P.; Kroeger, R.; Krokovny, P.; Kuhr, T.; Kulasiri, R.; Kumar, M.; Kumar, R.; Kumara, K.; Kuzmin, A.; Kwon, Y.-J.; Laurenza, M.; Lee, S.C.; Li, J.; Li, L.K.; Li, Y.B.; Li Gioi, L.; Libby, J.; Lieret, K.; Liventsev, D.; MacQueen, C.; Masuda, M.; Matsuda, T.; Matvienko, D.; Merola, M.; Metzner, F.; Miyabayashi, K.; Mizuk, R.; Mohanty, G.B.; Nakao, M.; Natochii, A.; Nayak, L.; Niiyama, M.; Nisar, N.K.; Nishida, S.; Nishimura, K.; Ono, H.; Onuki, Y.; Oskin, P.; Pakhlov, P.; Pakhlova, G.; Pardi, S.; Park, H.; Park, S.-H.; Patra, S.; Paul, S.; Pedlar, T.K.; Pestotnik, R.; Piilonen, L.E.; Podobnik, T.; Popov, V.; Prencipe, E.; Prim, M.T.; Rostomyan, A.; Rout, N.; Russo, G.; Sahoo, D.; Sandilya, S.; Sangal, A.; Santelj, L.; Sanuki, T.; Savinov, V.; Schnell, G.; Schueler, J.; Schwanda, C.; Seino, Y.; Senyo, K.; Sevior, M.E.; Shapkin, M.; Sharma, C.; Shiu, J.-G.; Simon, F.; Solovieva, E.; Starič, M.; Sumihama, M.; Sumisawa, K.; Sumiyoshi, T.; Takizawa, M.; Tamponi, U.; Tanida, K.; Tenchini, F.; Trabelsi, K.; Uchida, M.; Unno, Y.; Uno, S.; Van Tonder, R.; Varner, G.; Varvell, K.E.; Waheed, E.; Wang, C.H.; Wang, E.; Wang, P.; Watanabe, M.; Watanuki, S.; Werbycka, O.; Won, E.; Yabsley, B.D.; Yan, W.; Yang, S.B.; Ye, H.; Yin, J.H.; Zhang, Z.P.; Zhilich, V.; Zhukova, V.

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Journal Article

Search for the decay $B^{0}\rightarrow K^{\ast 0}τ^{+}τ^{-}$ at the Belle experiment

MPS-Authors

Belle Collaboration,
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Dong, T.V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Luo, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Adachi, I.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Aihara, H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Asner, D.M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Atmacan, H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Aulchenko, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Aushev, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Ayad, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Babu, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bahinipati, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Behera, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Belous, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bernlochner, F.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bessner, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bhuyan, B.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bilka, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Biswal, J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bobrov, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bozek, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Bračko, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Branchini, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Browder, T.E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Budano, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Campajola, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Červenkov, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Chang, M.-C.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Chang, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Chen, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Cheon, B.G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Chilikin, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Cho, H.E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Cho, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Cho, S.-J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Choi, S.-K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Choi, Y.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Choudhury, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Cinabro, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Cunliffe, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Czank, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Das, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

De Nardo, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

De Pietro, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Dhamija, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Di Capua, F.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Dingfelder, J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Doležal, Z.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Dubey, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Epifanov, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Ferber, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Ferlewicz, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Fulsom, B.G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Garg, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Gaur, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Gabyshev, N.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Garmash, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Giri, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Goldenzweig, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Graziani, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Gu, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Gudkova, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hara, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hartbrich, O.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hayasaka, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hernandez Villanueva, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hou, W.-S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Hsu, C.-L.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Inami, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Inguglia, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Ishikawa, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Itoh, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Iwasaki, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Jacobs, W.W.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Jang, E.-J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Jia, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Jin, Y.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Joo, K.K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kahn, J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kang, K.H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kichimi, H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kiesling, C.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kim, C.H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kim, D.Y.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kim, K.T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kim, S.H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kim, Y.-K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kimmel, T.D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kodyš, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Konno, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Korobov, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Korpar, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kovalenko, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Križan, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kroeger, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Krokovny, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kuhr, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kulasiri, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kumar, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kumar, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kumara, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kuzmin, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Kwon, Y.-J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Laurenza, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Lee, S.C.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Li, J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Li, L.K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Li, Y.B.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Li Gioi, L.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Libby, J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Lieret, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Liventsev, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

MacQueen, C.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Masuda, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Matsuda, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Matvienko, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Merola, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Metzner, F.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Miyabayashi, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Mizuk, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Mohanty, G.B.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Nakao, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Natochii, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Nayak, L.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Niiyama, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Nisar, N.K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Nishida, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Nishimura, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Ono, H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Onuki, Y.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Oskin, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Pakhlov, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Pakhlova, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Pardi, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Park, H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Park, S.-H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Patra, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Paul, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Pedlar, T.K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Pestotnik, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Piilonen, L.E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Podobnik, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Popov, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Prencipe, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Prim, M.T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Rostomyan, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Rout, N.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Russo, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sahoo, D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sandilya, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sangal, A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Santelj, L.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sanuki, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Savinov, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Schnell, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Schueler, J.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Schwanda, C.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Seino, Y.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Senyo, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sevior, M.E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Shapkin, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sharma, C.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Shiu, J.-G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Simon, F.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Solovieva, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Starič, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sumihama, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sumisawa, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sumiyoshi, T.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Takizawa, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Tamponi, U.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Tanida, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Tenchini, F.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Trabelsi, K.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Uchida, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Unno, Y.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Uno, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Van Tonder, R.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Varner, G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Varvell, K.E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Waheed, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Wang, C.H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Wang, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Wang, P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Watanabe, M.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Watanuki, S.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Werbycka, O.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Won, E.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Yabsley, B.D.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Yan, W.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Yang, S.B.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Ye, H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Yin, J.H.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Zhang, Z.P.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Zhilich, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Zhukova, V.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

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Citation

Belle Collaboration, Dong, T., Luo, T., Adachi, I., Aihara, H., Asner, D., et al. (2023). Search for the decay $B^{0}\rightarrow K^{\ast 0}τ^{+}τ^{-}$ at the Belle experiment. Physical Review D, 108, L011102. Retrieved from https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2021-371.

Cite as: https://hdl.handle.net/21.11116/0000-000F-113E-9

Abstract

This letter presents a search for the rare flavor-changing neutral current process $B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}$ using data taken with the Belle detector at the KEKB asymmetric energy $e^{+}e^{-}$ collider. The analysis is based on the entire $\Upsilon(4S)$ resonance data sample of 711 $\rm fb^{-1}$, corresponding to $772\times 10^{6} B \bar{B}$ pairs. In our search we fully reconstruct the companion $B$ meson produced in the process $e^{+}e^{-}\rightarrow\Upsilon(4S)\rightarrow B\bar{B}$ from its hadronic decay modes, and look for the decay $B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}$ in the rest of the event. No evidence for a signal is found. We report an upper limit on the branching fraction $\mathcal{B}({B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}})<2.0\times 10^{-3}$ at 90\% confidence level. This is the first direct limit on $\mathcal{B}({B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}})$.