Analysis of <inline-formula><tex-math id="M1">\begin{document}${{\boldsymbol b}{\bf\rightarrow} {\boldsymbol c}{\boldsymbol\tau}\bar{\boldsymbol\nu}_{\boldsymbol\tau}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2024-0095_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2024-0095_M1.png"/></alternatives></inline-formula> anomalies using weak effective Hamiltonian with complex couplings and their impact on various physical observables

[1]
R. Aaij et al. (LHCb Collaboration), JHEP 06, 133 (2014), arXiv:1403.8044[hep-ex]
[2]
R. Aaij et al. (LHCb Collaboration), JHEP 05, 082 (2014), arXiv:1403.8045[hep-ex]
[3]
R. Aaij et al. (LHCb Collaboration), JHEP 09, 179 (2015), arXiv:1506.08777[hep-ex]
[4]
R. Aaij et al. (LHCb Collaboration), JHEP 02, 104 (2016), arXiv:1512.04442[hep-ex]
[5]
R. Aaij et al. (LHCb Collaboration), JHEP 11 , 047 (2016), [Erratum: JHEP 04, 142 (2017)], arXiv: 1606.04731
[6]
R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 127(15), 151801 (2021), arXiv:2105.14007[hep-ex]
[7]
R. Aaij et al. (LHCb Collaboration), JHEP 11, 043 (2021), arXiv:2107.13428[hep-ex]
[8]
A. Celis, J. Fuentes-Martin, A. Vicente et al., Phys. Rev. D 96(3), 035026 (2017), arXiv:1704.05672[hep-ph]
[9]
D. Buttazzo, A. Greljo, G. Isidori et al., JHEP 11, 044 (2017), arXiv:1706.07808[hep-ph]
[10]
J. Aebischer, W. Altmannshofer, D. Guadagnoli et al., Eur. Phys. J. C 80(3), 252 (2020), arXiv:1903.10434[hep-ph]
[11]
L. Alasfar, A. Azatov, J. de Blas et al., JHEP 12, 016 (2020), arXiv:2007.04400[hep-ph]
[12]
G. Isidori, D. Lancierini, A. Mathad et al., Phys. Lett. B 830, 137151 (2022), arXiv:2110.09882[hep-ph]
[13]
M. Ciuchini, M. Fedele, E. Franco et al., Phys. Rev. D 107(5), 055036 (2023), arXiv:2212.10516[hep-ph]
[14]
J. A. Bailey et al., Phys. Rev. D 92(3), 034506 (2015), arXiv:1503.07237[hep-lat]
[15]
H. Na et al. (HPQCD Collaboration), Phys. Rev. D 92 , 054510 (2015), [Erratum: Phys. Rev. D 93, 119906 (2016)], arXiv: 1505.03925 [hep-lat]
[16]
S. Aoki, Y. Aoki, D. Becirevic et al., Eur. Phys. J. C 77(2), 112 (2017), arXiv:1607.00299[hep-lat]
[17]
S. Fajfer, J. F. Kamenik, and I. Nisandzic, Phys. Rev. D 85, 094025 (2012), arXiv:1203.2654[hep-ph]
[18]
D. Bigi and P. Gambino, Phys. Rev. D 94(9), 094008 (2016), arXiv:1606.08030[hep-ph]
[19]
F. U. Bernlochner, Z. Ligeti, M. Papucci et al. Phys. Rev. D 95 , 115008 (2017), [Erratum: Phys. Rev. D 97, 059902 (2018)], arXiv: 1703.05330[hep-ph]
[20]
D. Bigi, P. Gambino, and S. Schacht, JHEP 11, 061 (2017), arXiv:1707.09509[hep-ph]
[21]
S. Jaiswal, S. Nandi, and S. K. Patra, JHEP 12, 060 (2017), arXiv:1707.09977[hep-ph]
[22]
P. Gambino, M. Jung, and S. Schacht, Phys. Lett. B 795, 386 (2019), arXiv:1905.08209[hep-ph]
[23]
M. Bordone, M. Jung, and D. van Dyk, Eur. Phys. J. C 80(2), 74 (2020), arXiv:1908.09398[hep-ph]
[24]
G. Martinelli, S. Simula, and L. Vittorio, Phys. Rev. D 105(3), 034503 (2022), arXiv:2105.08674[hep-ph]
[25]
J. P. Lees et al., Phys. Rev. Lett. 109, 101802 (2012), arXiv:1205.5442[hep-ex]
[26]
J. P. Lees et al., Phys. Rev. D 88(7), 072012 (2013), arXiv:1303.0571[hep-ex]
[27]
M. Huschle et al., Phys. Rev. D 92(7), 072014 (2015), arXiv:1507.03233[hep-ex]
[28]
G. Caria et al., Phys. Rev. Lett. 124(16), 161803 (2020), arXiv:1910.05864[hep-ex]
[29]
Recent Belle II results on semi leptonic decay anomalies \begin{document}$R(D)$\end{document} and \begin{document}$R(D^{*})$\end{document} Presented at Lepton Photon 2023, https://indico.cern.ch/event/1114856/contributions/5423684/attachments/2685890/4660084/2023-07-04_LP2023_KojimaFinalVer_main.pdf.
[30]
R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 115 , 111803 (2015), [Erratum: Phys. Rev. D 97, 059902 (2018)], arXiv: 1506.08614[hep-ex]
[31]
R. Aaij et al., Phys. Rev. Lett. 120(17), 171802 (2018), arXiv:1708.08856[hep-ex]
[32]
R. Aaij et al., Phys. Rev. D 97(7), 072013 (2018), arXiv:1711.02505[hep-ex]
[33]
R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 131, 111802 (2018)
[34]
R. Aaij et al., Phys. Rev. D 108(1), 012018 (2023), arXiv:2305.01463[hep-ex]
[35]
Y. Amhis et al. (Heavy Flavor Averaging Group Collaboration), Phys. Rev. D 107(1), 052008 (2023)
[36]
Preliminary average of \begin{document}$R(D)$\end{document} and \begin{document}$R(D^{*})$\end{document} for Winter 2023 https://hflav-eos.web.cern.ch/hflav-eos/semi/winter23prel/html/RDsDsstar/RDRDs.html
[37]
Preliminary average of \begin{document}$R(D)$\end{document} and \begin{document}$R(D^{*})$\end{document} for Summer2023, https://hflav-eos.web.cern.ch/hflav-eos/semi/summer23/html/RDsDsstar/RDRDs.html.
[38]
B. Y. Cui, Y. K. Huang, Y. M. Wang et al., arXiv: 2301.12391 [hep-ph]
[39]
S. Hirose et al., Phys. Rev. Lett. 118(21), 211801 (2017), arXiv:1612.00529[hep-ex]
[40]
S. Hirose et al., Phys. Rev. D 97(1), 012004 (2018), arXiv:1709.00129[hep-ex]
[41]
A. Abdesselam et al. (Belle Collaboration), arXiv: 1903.03102 [hep-ex]
[42]
A. K. Alok, D. Kumar, S. Kumbhakar et al., Phys. Rev. D 95(11), 115038 (2017), arXiv:1606.03164[hep-ph]
[43]
S. Iguro and R. Watanabe, JHEP 08(08), 006 (2020), arXiv:2004.10208[hep-ph]
[44]
R. Aaij et al., Phys. Rev. Lett. 120(12), 121801 (2018), arXiv:1711.05623[hep-ex]
[45]
R. Watanabe, Phys. Rev. Lett. 776, 5 (2018),
[46]
J. Harrison et al., Phys. Rev. Lett. 125(22), 222003 (2020), arXiv:2007.06956[hep-lat]
[47]
S. Kamali, Int. J. Mod. Phys. A 34(06n07), 1950036 (2019), arXiv:1811.07393[hep-ph]
[48]
R. Barate et al., Eur. Phys. J. C 19, 213 (2001), arXiv:hep-ex/0010022[hep-ex]
[49]
R. Aaij et al., Phys. Rev. D 89(3), 032001 (2014), arXiv:1311.4823[hep-ex]
[50]
R. Aaij et al., Phys. Rev. Lett. 112, 202001 (2014), arXiv:1403.3606[hep-ex]
[51]
R. Aaij et al., JHEP 07, 103 (2014), arXiv:1406.0755[hep-ex]
[52]
D. O'Hanlon (LHCb Collaboration), arXiv: 1605.06990 [hep-ex]
[53]
R. Aaij et al., JHEP 02, 098 (2018), arXiv:1711.05490[hep-ex]
[54]
R. Aaij et al., Phys. Rev. Lett. 128(19), 191803 (2022), arXiv:2201.03497[hep-ex]
[55]
W. Detmold, C. Lehner, and S. Meinel, Phys. Rev. D 92(3), 034503 (2015), arXiv:1503.01421[hep-lat]
[56]
F. U. Bernlochner, Z. Ligeti, D. J. Robinson et al., Phys. Rev. Lett. 121(20), 202001 (2018), arXiv:1808.09464[hep-ph]
[57]
P. Asadi and D. Shih, Phys. Rev. D 100(11), 115013 (2019), arXiv:1905.03311[hep-ph]
[58]
C. Murgui, A. Peñuelas, M. Jung et al., JHEP 09, 103 (2019), arXiv:1904.09311[hep-ph]
[59]
R. Mandal, C. Murgui, A. Peñuelas et al., JHEP 08(08), 022 (2020), arXiv:2004.06726[hep-ph]
[60]
K. Cheung, Z. R. Huang, H. D. Li et al., Nucl. Phys. B 965, 115354 (2021), arXiv:2002.07272[hep-ph]
[61]
P. Colangelo, F. De Fazio, and F. Loparco, JHEP 11 , 32 (2020), [Erratum: JHEP 12, 098 (2022)], arXiv: 2006.13759 [hep-ph]
[62]
S. Sahoo and R. Mohanta, arXiv: 1910.09269 [hep-ph]
[63]
R. X. Shi, L. S. Geng, B. Grinstein et al., JHEP 12, 065 (2019), arXiv:1905.08498[hep-ph]
[64]
D. Bardhan and D. Ghosh, Phys. Rev. D 100(1), 011701 (2019), arXiv:1904.10432[hep-ph]
[65]
M. Blanke, A. Crivellin, S. de Boer et al., Phys. Rev. D 99(7), 075006 (2019), arXiv:1811.09603[hep-ph]
[66]
M. Fedele, M. Blanke, A. Crivellin et al., Phys. Rev. D 107(5), 055005 (2023), arXiv:2211.14172[hep-ph]
[67]
M. Blanke, A. Crivellin, T. Kitahara et al., Phys. Rev. D 100, 035035 (2019)
[68]
A. K. Alok, D. Kumar, S. Kumbhakar et al., Nucl. Phys. B 953, 114957 (2020), arXiv:1903.10486[hep-ph]
[69]
Z. R. Huang, Y. Li, C. D. Lu et al., Phys. Rev. D 98(9), 095018 (2018), arXiv:1808.03565[hep-ph]
[70]
A. Greljo, D. J. Robinson, B. Shakya et al., JHEP 09, 169 (2018), arXiv:1804.04642[hep-ph]
[71]
A. Azatov, D. Barducci, D. Ghosh et al., JHEP 10, 092 (2018), arXiv:1807.10745[hep-ph]
[72]
J. Heeck and D. Teresi, JHEP 12, 103 (2018), arXiv:1808.07492[hep-ph]
[73]
K. S. Babu, B. Dutta, and R. N. Mohapatra, JHEP 01, 168 (2019), arXiv:1811.04496[hep-ph]
[74]
X. G. He and G. Valencia, Phys. Lett. B 779, 52 (2018), arXiv:1711.09525[hep-ph]
[75]
J. D. Gómez, N. Quintero, and E. Rojas, Phys. Rev. D 100(9), 093003 (2019), arXiv:1907.08357[hep-ph]
[76]
M. Algueró, S. Descotes-Genon, J. Matias et al., JHEP 06, 156 (2020), arXiv:2003.02533[hep-ph]
[77]
R. Dutta, A. Bhol, and A. K. Giri, Phys. Rev. D 88(11), 114023 (2013), arXiv:1307.6653[hep-ph]
[78]
R. Dutta and A. Bhol, Phys. Rev. D 96(7), 076001 (2017), arXiv:1701.08598[hep-ph]
[79]
R. Dutta, arXiv: 1710.00351 [hep-ph]
[80]
R. Dutta and N. Rajeev, Phys. Rev. D 97(9), 095045 (2018), arXiv:1803.03038[hep-ph]
[81]
A. Celis, M. Jung, X. Q. Li et al., Phys. Lett. B 771, 168 (2017), arXiv:1612.07757[hep-ph]
[82]
R. Alonso, B. Grinstein, and J. Martin Camalich, Phys. Rev. Lett. 118(8), 081802 (2017), arXiv:1611.06676[hep-ph]
[83]
S. S. Gershtein, V. V. Kiselev, A. K. Likhoded et al., Phys. Usp. 38, 1 (1995), arXiv:hep-ph/9504319[hep-ph]
[84]
I. I. Y. Bigi, Phys. Lett. B 371, 105 (1996), arXiv:hep-ph/9510325[hep-ph]
[85]
M. Beneke and G. Buchalla, Phys. Rev. D 53, 4991 (1996), arXiv:hep-ph/9601249[hep-ph]
[86]
C. H. Chang, S. L. Chen, T. F. Feng et al., Phys. Rev. D 64, 014003 (2001), arXiv:hep-ph/0007162[hep-ph]
[87]
V. V. Kiselev, A. E. Kovalsky, and A. K. Likhoded, Nucl. Phys. B 585, 353 (2000), arXiv:hep-ph/0002127[hep-ph]
[88]
A. G. Akeroyd and C. H. Chen, Phys. Rev. D 96(7), 075011 (2017), arXiv:1708.04072[hep-ph]
[89]
S. Iguro, T. Kitahara, Y. Omura et al., JHEP 02, 194 (2019), arXiv:1811.08899[hep-ph]
[90]
P. Asadi, M. R. Buckley, and D. Shih, JHEP 09, 010 (2018), arXiv:1804.04135[hep-ph]
[91]
P. Asadi, M. R. Buckley, and D. Shih, Phys. Rev. D 99(3), 035015 (2019), arXiv:1810.06597[hep-ph]
[92]
Z. Ligeti, M. Papucci, and D. J. Robinson, JHEP 01, 083 (2017), arXiv:1610.02045[hep-ph]
[93]
D. J. Robinson, B. Shakya, and J. Zupan, JHEP 02, 119 (2019), arXiv:1807.04753[hep-ph]
[94]
W. Buchmuller and D. Wyler, Nucl. Phys. B 268, 621 (1986)
[95]
B. Grzadkowski, M. Iskrzynski, M. Misiak et al., JHEP 10, 085 (2010), arXiv:1008.4884[hep-ph]
[96]
J. Aebischer, A. Crivellin, M. Fael et al., JHEP 05, 037 (2016), arXiv:1512.02830[hep-ph]
[97]
M. González-Alonso, J. Martin Camalich, and K. Mimouni, Phys. Lett. B 772, 777 (2017), arXiv:1706.00410[hep-ph]
[98]
J. Cardozo, J. H. Muñoz, N. Quintero et al., J. Phys. G 48(3), 035001 (2021), arXiv:2006.07751[hep-ph]
[99]
S. Iguro, T. Kitahara, and R. Watanabe, arXiv: 2210.10751 [hep-ph]
[100]
X. L. Mu, Y. Li, Z. T. Zou et al., Phys. Rev. D 100(11), 113004 (2019), arXiv:1909.10769[hep-ph]
[101]
D. Bečirević, M. Fedele, I. Nišandžić et al., arXiv: 1907.02257 [hep-ph]
[102]
D. Becirevic, S. Fajfer, I. Nisandzic et al., Nucl. Phys. B 946, 114707 (2019), arXiv:1602.03030[hep-ph]
[103]
R. Alonso, A. Kobach, and J. M. Camalich, Phys. Rev. D 94(9), 094021 (2016), arXiv:1602.07671[hep-ph]
[104]
D. Hill, M. John, W. Ke et al., JHEP 11, 133 (2019), arXiv:1908.04643[hep-ph]
[105]
J. Aebischer, T. Kuhr, and K. Lieret JHEP 2020 , 7 (2020), [Erratum: JHEP 2021, 147 (2021)], arXiv: 1909.11088 [hep-ph]
[106]
Y. Sakaki, M. Tanaka, A. Tayduganov et al., Phys. Rev. D 88(9), 094012 (2013), arXiv:1309.0301[hep-ph]
[107]
I. Caprini, L. Lellouch, and M. Neubert, Nucl. Phys. B 530, 153 (1998), arXiv:hep-ph/9712417[hep-ph]
[108]
S. Kumbhakar, Nucl. Phys. B 963, 115297 (2021), arXiv:2007.08132[hep-ph]
[109]
D. Aloni, Y. Grossman, and A. Soffer, Phys. Rev. D 98(3), 035022 (2018), arXiv:1806.04146[hep-ph]
[110]
M. Duraisamy, P. Sharma and A. Datta, Phys. Rev. D 90(7), 074013 (2014), arXiv:1405.3719[hep-ph]
[111]
M. Duraisamy and A. Datta, JHEP 09, 059 (2013), arXiv:1302.7031[hep-ph]
[112]
A. K. Alok, A. Datta, A. Dighe et al., JHEP 11, 122 (2011), arXiv:1103.5344[hep-ph]
[113]
B. Bhattacharya, A. Datta, S. Kamali et al., JHEP 05, 191 (2019), arXiv:1903.02567[hep-ph]
[114]
B. Bhattacharya, A. Datta, S. Kamali et al., JHEP 07(07), 194 (2020), arXiv:2005.03032[hep-ph]
[115]
P. A. Zyla et al., PTEP 2020(8), 083C (2020)
[116]
R. L. Workman et al., PTEP 2022, 083C (2022)