Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States

S. Nishida; M. Nakao; K. Abe; K. Abe; T. Abe; Byoung Sup Ahn; H. Aihara; M. Akatsu; Y. Asano; T. Aushev; A. M. Bakich; Y. Ban; E. Banas; W. Bartel; A. Bay; I. Bedny; A. Bondar; A. Bozek; M. Bračko; J. Brodzicka; T. E. Browder; B. C.K. Casey; P. Chang; Y. Chao; B. G. Cheon; R. Chistov; S. K. Choi; Y. Choi; M. Danilov; L. Y. Dong; A. Drutskoy; S. Eidelman; V. Eiges; Y. Enari; C. Fukunaga; N. Gabyshev; T. Gershon; A. Gordon; K. Gotow; R. Guo; J. Haba; T. Hara; H. Hayashii; M. Hazumi; E. M. Heenan; I. Higuchi; T. Higuchi; T. Hojo; T. Hokuue; Y. Hoshi; S. R. Hou; W. S. Hou; S. C. Hsu; H. C. Huang; T. Igaki; T. Iijima; K. Inami; A. Ishikawa; H. Ishino; R. Itoh; M. Iwamoto; H. Iwasaki; Y. Iwasaki; P. Jalocha; H. K. Jang; J. H. Kang; P. Kapusta; S. U. Kataoka; N. Katayama; H. Kawai; Y. Kawakami; N. Kawamura; T. Kawasaki; H. Kichimi; D. W. Kim; Heejong Kim; H. J. Kim; H. O. Kim; Hyunwoo Kim; T. H. Kim; K. Kinoshita; P. Križan; P. Krokovny; R. Kulasiri; S. Kumar; Y. J. Kwon; J. S. Lange; G. Leder; S. H. Lee; J. Li; R. S. Lu; J. MacNaughton; G. Majumder; F. Mandl; S. Matsumoto; T. Matsumoto; Y. Mikami; W. Mitaroff; K. Miyabayashi; H. Miyake; H. Miyata; G. R. Moloney; S. Mori; T. Nagamine; Y. Nagasaka; T. Nakadaira; E. Nakano; J. W. Nam; Z. Natkaniec; K. Neichi; O. Nitoh; S. Noguchi; T. Nozaki; S. Ogawa; F. Ohno; T. Ohshima; T. Okabe; S. Okuno; S. L. Olsen; W. Ostrowicz; H. Ozaki; P. Pakhlov; H. Palka; C. W. Park; H. Park; K. S. Park; L. S. Peak; J. P. Perroud; M. Peters; L. E. Piilonen; M. Rozanska; K. Rybicki; H. Sagawa; S. Saitoh; Y. Sakai; H. Sakamoto; M. Satapathy; A. Satpathy; O. Schneider; S. Schrenk; C. Schwanda; S. Semenov; K. Senyo; R. Seuster; M. E. Sevior; H. Shibuya; B. Shwartz; V. Sidorov; J. B. Singh; S. Stanič; A. Sugi; A. Sugiyama; K. Sumisawa; T. Sumiyoshi; K. Suzuki; S. Suzuki; T. Takahashi; F. Takasaki; K. Tamai; N. Tamura; M. Tanaka; G. N. Taylor; Y. Teramoto; S. Tokuda; M. Tomoto; T. Tomura; S. N. Tovey; K. Trabelsi; T. Tsuboyama; T. Tsukamoto; S. Uehara; K. Ueno; S. Uno; Y. Ushiroda; G. Varner; K. E. Varvell; C. C. Wang; C. H. Wang; J. G. Wang; M. Z. Wang; Y. Watanabe; E. Won; B. D. Yabsley; Y. Yamada; A. Yamaguchi; H. Yamamoto; Y. Yamashita; M. Yamauchi; Y. Yuan; Y. Yusa; J. Zhang; Z. P. Zhang; V. Zhilich; D. Žontar

doi:10.1103/PhysRevLett.89.231801

Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States

S. Nishida, M. Nakao, K. Abe, K. Abe, T. Abe, Byoung Sup Ahn, H. Aihara, M. Akatsu, Y. Asano, T. Aushev, A. M. Bakich, Y. Ban, E. Banas, W. Bartel, A. Bay, I. Bedny, A. Bondar, A. Bozek, M. Bračko, J. BrodzickaT. E. Browder, B. C.K. Casey, P. Chang, Y. Chao, B. G. Cheon, R. Chistov, S. K. Choi, Y. Choi, M. Danilov, L. Y. Dong, A. Drutskoy, S. Eidelman, V. Eiges, Y. Enari, C. Fukunaga, N. Gabyshev, T. Gershon, A. Gordon, K. Gotow, R. Guo, J. Haba, T. Hara, H. Hayashii, M. Hazumi, E. M. Heenan, I. Higuchi, T. Higuchi, T. Hojo, T. Hokuue, Y. Hoshi, S. R. Hou, W. S. Hou, S. C. Hsu, H. C. Huang, T. Igaki, T. Iijima, K. Inami, A. Ishikawa, H. Ishino, R. Itoh, M. Iwamoto, H. Iwasaki, Y. Iwasaki, P. Jalocha, H. K. Jang, J. H. Kang, P. Kapusta, S. U. Kataoka, N. Katayama, H. Kawai, Y. Kawakami, N. Kawamura, T. Kawasaki, H. Kichimi, D. W. Kim, Heejong Kim, H. J. Kim, H. O. Kim, Hyunwoo Kim, T. H. Kim, K. Kinoshita, P. Križan, P. Krokovny, R. Kulasiri, S. Kumar, Y. J. Kwon, J. S. Lange, G. Leder, S. H. Lee, J. Li, R. S. Lu, J. MacNaughton, G. Majumder, F. Mandl, S. Matsumoto, T. Matsumoto, Y. Mikami, W. Mitaroff, K. Miyabayashi, H. Miyake, H. Miyata, G. R. Moloney, S. Mori, T. Nagamine, Y. Nagasaka, T. Nakadaira, E. Nakano, J. W. Nam, Z. Natkaniec, K. Neichi, O. Nitoh, S. Noguchi, T. Nozaki, S. Ogawa, F. Ohno, T. Ohshima, T. Okabe, S. Okuno, S. L. Olsen, W. Ostrowicz, H. Ozaki, P. Pakhlov, H. Palka, C. W. Park, H. Park, K. S. Park, L. S. Peak, J. P. Perroud, M. Peters, L. E. Piilonen, M. Rozanska, K. Rybicki, H. Sagawa, S. Saitoh, Y. Sakai, H. Sakamoto, M. Satapathy, A. Satpathy, O. Schneider, S. Schrenk, C. Schwanda, S. Semenov, K. Senyo, R. Seuster, M. E. Sevior, H. Shibuya, B. Shwartz, V. Sidorov, J. B. Singh, S. Stanič, A. Sugi, A. Sugiyama, K. Sumisawa, T. Sumiyoshi, K. Suzuki, S. Suzuki, T. Takahashi, F. Takasaki, K. Tamai, N. Tamura, M. Tanaka, G. N. Taylor, Y. Teramoto, S. Tokuda, M. Tomoto, T. Tomura, S. N. Tovey, K. Trabelsi, T. Tsuboyama, T. Tsukamoto, S. Uehara, K. Ueno, S. Uno, Y. Ushiroda, G. Varner, K. E. Varvell, C. C. Wang, C. H. Wang, J. G. Wang, M. Z. Wang, Y. Watanabe, E. Won, B. D. Yabsley, Y. Yamada, A. Yamaguchi, H. Yamamoto, Y. Yamashita, M. Yamauchi, Y. Yuan, Y. Yusa, J. Zhang, Z. P. Zhang, V. Zhilich, D. Žontar

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We report observations of radiative [Formula presented] meson decays into the [Formula presented] and [Formula presented] final states. In the [Formula presented] channel, we present evidence for decays via an intermediate tensor meson state with a branching fraction of [Formula presented]. We measure the branching fraction [Formula presented], in which the [Formula presented] and [Formula presented] channels dominate. The analysis is based on a data set of [Formula presented] recorded by the Belle experiment at the KEKB collider.

Original language	English
Journal	Physical Review Letters
Volume	89
Issue number	23
DOIs	https://doi.org/10.1103/PhysRevLett.89.231801
Publication status	Published - 2002
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1103/PhysRevLett.89.231801

Cite this

Nishida, S., Nakao, M., Abe, K., Abe, K., Abe, T., Ahn, B. S., Aihara, H., Akatsu, M., Asano, Y., Aushev, T., Bakich, A. M., Ban, Y., Banas, E., Bartel, W., Bay, A., Bedny, I., Bondar, A., Bozek, A., Bračko, M., ... Žontar, D. (2002). Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States. Physical Review Letters, 89(23). https://doi.org/10.1103/PhysRevLett.89.231801

Nishida, S, Nakao, M, Abe, K, Abe, K, Abe, T, Ahn, BS, Aihara, H, Akatsu, M, Asano, Y, Aushev, T, Bakich, AM, Ban, Y, Banas, E, Bartel, W, Bay, A, Bedny, I, Bondar, A, Bozek, A, Bračko, M, Brodzicka, J, Browder, TE, Casey, BCK, Chang, P, Chao, Y, Cheon, BG, Chistov, R, Choi, SK, Choi, Y, Danilov, M, Dong, LY, Drutskoy, A, Eidelman, S, Eiges, V, Enari, Y, Fukunaga, C, Gabyshev, N, Gershon, T, Gordon, A, Gotow, K, Guo, R, Haba, J, Hara, T, Hayashii, H, Hazumi, M, Heenan, EM, Higuchi, I, Higuchi, T, Hojo, T, Hokuue, T, Hoshi, Y, Hou, SR, Hou, WS, Hsu, SC, Huang, HC, Igaki, T, Iijima, T, Inami, K, Ishikawa, A, Ishino, H, Itoh, R, Iwamoto, M, Iwasaki, H, Iwasaki, Y, Jalocha, P, Jang, HK, Kang, JH, Kapusta, P, Kataoka, SU, Katayama, N, Kawai, H, Kawakami, Y, Kawamura, N, Kawasaki, T, Kichimi, H, Kim, DW, Kim, H, Kim, HJ, Kim, HO, Kim, H, Kim, TH, Kinoshita, K, Križan, P, Krokovny, P, Kulasiri, R, Kumar, S, Kwon, YJ, Lange, JS, Leder, G, Lee, SH, Li, J, Lu, RS, MacNaughton, J, Majumder, G, Mandl, F, Matsumoto, S, Matsumoto, T, Mikami, Y, Mitaroff, W, Miyabayashi, K, Miyake, H, Miyata, H, Moloney, GR, Mori, S, Nagamine, T, Nagasaka, Y, Nakadaira, T, Nakano, E, Nam, JW, Natkaniec, Z, Neichi, K, Nitoh, O, Noguchi, S, Nozaki, T, Ogawa, S, Ohno, F, Ohshima, T, Okabe, T, Okuno, S, Olsen, SL, Ostrowicz, W, Ozaki, H, Pakhlov, P, Palka, H, Park, CW, Park, H, Park, KS, Peak, LS, Perroud, JP, Peters, M, Piilonen, LE, Rozanska, M, Rybicki, K, Sagawa, H, Saitoh, S, Sakai, Y, Sakamoto, H, Satapathy, M, Satpathy, A, Schneider, O, Schrenk, S, Schwanda, C, Semenov, S, Senyo, K, Seuster, R, Sevior, ME, Shibuya, H, Shwartz, B, Sidorov, V, Singh, JB, Stanič, S, Sugi, A, Sugiyama, A, Sumisawa, K, Sumiyoshi, T, Suzuki, K, Suzuki, S, Takahashi, T, Takasaki, F, Tamai, K, Tamura, N, Tanaka, M, Taylor, GN, Teramoto, Y, Tokuda, S, Tomoto, M, Tomura, T, Tovey, SN, Trabelsi, K, Tsuboyama, T, Tsukamoto, T, Uehara, S, Ueno, K, Uno, S, Ushiroda, Y, Varner, G, Varvell, KE, Wang, CC, Wang, CH, Wang, JG, Wang, MZ, Watanabe, Y, Won, E, Yabsley, BD, Yamada, Y, Yamaguchi, A, Yamamoto, H, Yamashita, Y, Yamauchi, M, Yuan, Y, Yusa, Y, Zhang, J, Zhang, ZP, Zhilich, V & Žontar, D 2002, 'Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States', Physical Review Letters, vol. 89, no. 23. https://doi.org/10.1103/PhysRevLett.89.231801

@article{ef137935da00452fb567f415cd277885,

title = "Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States",

abstract = "We report observations of radiative [Formula presented] meson decays into the [Formula presented] and [Formula presented] final states. In the [Formula presented] channel, we present evidence for decays via an intermediate tensor meson state with a branching fraction of [Formula presented]. We measure the branching fraction [Formula presented], in which the [Formula presented] and [Formula presented] channels dominate. The analysis is based on a data set of [Formula presented] recorded by the Belle experiment at the KEKB collider.",

author = "S. Nishida and M. Nakao and K. Abe and K. Abe and T. Abe and Ahn, {Byoung Sup} and H. Aihara and M. Akatsu and Y. Asano and T. Aushev and Bakich, {A. M.} and Y. Ban and E. Banas and W. Bartel and A. Bay and I. Bedny and A. Bondar and A. Bozek and M. Bra{\v c}ko and J. Brodzicka and Browder, {T. E.} and Casey, {B. C.K.} and P. Chang and Y. Chao and Cheon, {B. G.} and R. Chistov and Choi, {S. K.} and Y. Choi and M. Danilov and Dong, {L. Y.} and A. Drutskoy and S. Eidelman and V. Eiges and Y. Enari and C. Fukunaga and N. Gabyshev and T. Gershon and A. Gordon and K. Gotow and R. Guo and J. Haba and T. Hara and H. Hayashii and M. Hazumi and Heenan, {E. M.} and I. Higuchi and T. Higuchi and T. Hojo and T. Hokuue and Y. Hoshi and Hou, {S. R.} and Hou, {W. S.} and Hsu, {S. C.} and Huang, {H. C.} and T. Igaki and T. Iijima and K. Inami and A. Ishikawa and H. Ishino and R. Itoh and M. Iwamoto and H. Iwasaki and Y. Iwasaki and P. Jalocha and Jang, {H. K.} and Kang, {J. H.} and P. Kapusta and Kataoka, {S. U.} and N. Katayama and H. Kawai and Y. Kawakami and N. Kawamura and T. Kawasaki and H. Kichimi and Kim, {D. W.} and Heejong Kim and Kim, {H. J.} and Kim, {H. O.} and Hyunwoo Kim and Kim, {T. H.} and K. Kinoshita and P. Kri{\v z}an and P. Krokovny and R. Kulasiri and S. Kumar and Kwon, {Y. J.} and Lange, {J. S.} and G. Leder and Lee, {S. H.} and J. Li and Lu, {R. S.} and J. MacNaughton and G. Majumder and F. Mandl and S. Matsumoto and T. Matsumoto and Y. Mikami and W. Mitaroff and K. Miyabayashi and H. Miyake and H. Miyata and Moloney, {G. R.} and S. Mori and T. Nagamine and Y. Nagasaka and T. Nakadaira and E. Nakano and Nam, {J. W.} and Z. Natkaniec and K. Neichi and O. Nitoh and S. Noguchi and T. Nozaki and S. Ogawa and F. Ohno and T. Ohshima and T. Okabe and S. Okuno and Olsen, {S. L.} and W. Ostrowicz and H. Ozaki and P. Pakhlov and H. Palka and Park, {C. W.} and H. Park and Park, {K. S.} and Peak, {L. S.} and Perroud, {J. P.} and M. Peters and Piilonen, {L. E.} and M. Rozanska and K. Rybicki and H. Sagawa and S. Saitoh and Y. Sakai and H. Sakamoto and M. Satapathy and A. Satpathy and O. Schneider and S. Schrenk and C. Schwanda and S. Semenov and K. Senyo and R. Seuster and Sevior, {M. E.} and H. Shibuya and B. Shwartz and V. Sidorov and Singh, {J. B.} and S. Stani{\v c} and A. Sugi and A. Sugiyama and K. Sumisawa and T. Sumiyoshi and K. Suzuki and S. Suzuki and T. Takahashi and F. Takasaki and K. Tamai and N. Tamura and M. Tanaka and Taylor, {G. N.} and Y. Teramoto and S. Tokuda and M. Tomoto and T. Tomura and Tovey, {S. N.} and K. Trabelsi and T. Tsuboyama and T. Tsukamoto and S. Uehara and K. Ueno and S. Uno and Y. Ushiroda and G. Varner and Varvell, {K. E.} and Wang, {C. C.} and Wang, {C. H.} and Wang, {J. G.} and Wang, {M. Z.} and Y. Watanabe and E. Won and Yabsley, {B. D.} and Y. Yamada and A. Yamaguchi and H. Yamamoto and Y. Yamashita and M. Yamauchi and Y. Yuan and Y. Yusa and J. Zhang and Zhang, {Z. P.} and V. Zhilich and D. {\v Z}ontar",

year = "2002",

doi = "10.1103/PhysRevLett.89.231801",

language = "English",

volume = "89",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "23",

}

TY - JOUR

T1 - Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States

AU - Nishida, S.

AU - Nakao, M.

AU - Abe, K.

AU - Abe, T.

AU - Ahn, Byoung Sup

AU - Aihara, H.

AU - Akatsu, M.

AU - Asano, Y.

AU - Aushev, T.

AU - Bakich, A. M.

AU - Ban, Y.

AU - Banas, E.

AU - Bartel, W.

AU - Bay, A.

AU - Bedny, I.

AU - Bondar, A.

AU - Bozek, A.

AU - Bračko, M.

AU - Brodzicka, J.

AU - Browder, T. E.

AU - Casey, B. C.K.

AU - Chang, P.

AU - Chao, Y.

AU - Cheon, B. G.

AU - Chistov, R.

AU - Choi, S. K.

AU - Choi, Y.

AU - Danilov, M.

AU - Dong, L. Y.

AU - Drutskoy, A.

AU - Eidelman, S.

AU - Eiges, V.

AU - Enari, Y.

AU - Fukunaga, C.

AU - Gabyshev, N.

AU - Gershon, T.

AU - Gordon, A.

AU - Gotow, K.

AU - Guo, R.

AU - Haba, J.

AU - Hara, T.

AU - Hayashii, H.

AU - Hazumi, M.

AU - Heenan, E. M.

AU - Higuchi, I.

AU - Higuchi, T.

AU - Hojo, T.

AU - Hokuue, T.

AU - Hoshi, Y.

AU - Hou, S. R.

AU - Hou, W. S.

AU - Hsu, S. C.

AU - Huang, H. C.

AU - Igaki, T.

AU - Iijima, T.

AU - Inami, K.

AU - Ishikawa, A.

AU - Ishino, H.

AU - Itoh, R.

AU - Iwamoto, M.

AU - Iwasaki, H.

AU - Iwasaki, Y.

AU - Jalocha, P.

AU - Jang, H. K.

AU - Kang, J. H.

AU - Kapusta, P.

AU - Kataoka, S. U.

AU - Katayama, N.

AU - Kawai, H.

AU - Kawakami, Y.

AU - Kawamura, N.

AU - Kawasaki, T.

AU - Kichimi, H.

AU - Kim, D. W.

AU - Kim, Heejong

AU - Kim, H. J.

AU - Kim, H. O.

AU - Kim, Hyunwoo

AU - Kim, T. H.

AU - Kinoshita, K.

AU - Križan, P.

AU - Krokovny, P.

AU - Kulasiri, R.

AU - Kumar, S.

AU - Kwon, Y. J.

AU - Lange, J. S.

AU - Leder, G.

AU - Lee, S. H.

AU - Li, J.

AU - Lu, R. S.

AU - MacNaughton, J.

AU - Majumder, G.

AU - Mandl, F.

AU - Matsumoto, S.

AU - Matsumoto, T.

AU - Mikami, Y.

AU - Mitaroff, W.

AU - Miyabayashi, K.

AU - Miyake, H.

AU - Miyata, H.

AU - Moloney, G. R.

AU - Mori, S.

AU - Nagamine, T.

AU - Nagasaka, Y.

AU - Nakadaira, T.

AU - Nakano, E.

AU - Nam, J. W.

AU - Natkaniec, Z.

AU - Neichi, K.

AU - Nitoh, O.

AU - Noguchi, S.

AU - Nozaki, T.

AU - Ogawa, S.

AU - Ohno, F.

AU - Ohshima, T.

AU - Okabe, T.

AU - Okuno, S.

AU - Olsen, S. L.

AU - Ostrowicz, W.

AU - Ozaki, H.

AU - Pakhlov, P.

AU - Palka, H.

AU - Park, C. W.

AU - Park, H.

AU - Park, K. S.

AU - Peak, L. S.

AU - Perroud, J. P.

AU - Peters, M.

AU - Piilonen, L. E.

AU - Rozanska, M.

AU - Rybicki, K.

AU - Sagawa, H.

AU - Saitoh, S.

AU - Sakai, Y.

AU - Sakamoto, H.

AU - Satapathy, M.

AU - Satpathy, A.

AU - Schneider, O.

AU - Schrenk, S.

AU - Schwanda, C.

AU - Semenov, S.

AU - Senyo, K.

AU - Seuster, R.

AU - Sevior, M. E.

AU - Shibuya, H.

AU - Shwartz, B.

AU - Sidorov, V.

AU - Singh, J. B.

AU - Stanič, S.

AU - Sugi, A.

AU - Sugiyama, A.

AU - Sumisawa, K.

AU - Sumiyoshi, T.

AU - Suzuki, K.

AU - Suzuki, S.

AU - Takahashi, T.

AU - Takasaki, F.

AU - Tamai, K.

AU - Tamura, N.

AU - Tanaka, M.

AU - Taylor, G. N.

AU - Teramoto, Y.

AU - Tokuda, S.

AU - Tomoto, M.

AU - Tomura, T.

AU - Tovey, S. N.

AU - Trabelsi, K.

AU - Tsuboyama, T.

AU - Tsukamoto, T.

AU - Uehara, S.

AU - Ueno, K.

AU - Uno, S.

AU - Ushiroda, Y.

AU - Varner, G.

AU - Varvell, K. E.

AU - Wang, C. C.

AU - Wang, C. H.

AU - Wang, J. G.

AU - Wang, M. Z.

AU - Watanabe, Y.

AU - Won, E.

AU - Yabsley, B. D.

AU - Yamada, Y.

AU - Yamaguchi, A.

AU - Yamamoto, H.

AU - Yamashita, Y.

AU - Yamauchi, M.

AU - Yuan, Y.

AU - Yusa, Y.

AU - Zhang, J.

AU - Zhang, Z. P.

AU - Zhilich, V.

AU - Žontar, D.

PY - 2002

Y1 - 2002

N2 - We report observations of radiative [Formula presented] meson decays into the [Formula presented] and [Formula presented] final states. In the [Formula presented] channel, we present evidence for decays via an intermediate tensor meson state with a branching fraction of [Formula presented]. We measure the branching fraction [Formula presented], in which the [Formula presented] and [Formula presented] channels dominate. The analysis is based on a data set of [Formula presented] recorded by the Belle experiment at the KEKB collider.

AB - We report observations of radiative [Formula presented] meson decays into the [Formula presented] and [Formula presented] final states. In the [Formula presented] channel, we present evidence for decays via an intermediate tensor meson state with a branching fraction of [Formula presented]. We measure the branching fraction [Formula presented], in which the [Formula presented] and [Formula presented] channels dominate. The analysis is based on a data set of [Formula presented] recorded by the Belle experiment at the KEKB collider.

UR - http://www.scopus.com/inward/record.url?scp=85038300311&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038300311&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.89.231801

DO - 10.1103/PhysRevLett.89.231801

M3 - Article

AN - SCOPUS:85038300311

SN - 0031-9007

VL - 89

JO - Physical Review Letters

JF - Physical Review Letters

IS - 23

ER -

Radiative [Formula presented] Meson Decays into [Formula presented] and [Formula presented] Final States

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