Abstract
In this work, we study the C P asymmetry in the angular distribution of τ → KSπντ decays, taking into account the known C P violation in \( {K}^0-{\overline{K}}^0 \) mixing. It is pointed out for the first time that, once the well-measured C P violation in the neutral kaon system is invoked, a non-zero C P asymmetry would appear in the angular observable of the decays considered, even within the Standard Model. By employing the reciprocal basis, which is most convenient when a KS(L) is involved in the final state, the C P -violating angular observable is derived to be two times the product of the time-dependent C P asymmetry in K → π+π− and the mean value of the angular distribution in \( {\tau}^{\pm}\to {K}^0\left({\overline{K}}^0\right){\pi}^{\pm }{\overline{\nu}}_{\tau}\left({\nu}_{\tau}\right) \) decays. Compared with the Belle results measured in four different bins of the K π invariant mass, our predictions lie within the margins of these measurements, except for a 1.7 σ deviation for the lowest mass bin. While being below the current Belle detection sensitivity that is of \( \mathcal{O} \)(10−3), our predictions are expected to be detectable at the Belle II experiment, where \( \sqrt{70} \) times more sensitive results will be obtained with a 50 ab−1 data sample.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Evidence for the 2π Decay of the \( {K}_2^0 \)Meson, Phys. Rev. Lett. 13 (1964) 138 [INSPIRE].
KTeV collaboration, Observation of direct CP-violation in KS,L → ππ decays, Phys. Rev. Lett. 83 (1999) 22 [hep-ex/9905060] [INSPIRE].
NA48 collaboration, A Precise measurement of the direct CP-violation parameter Re(ϵ′ /ϵ), Eur. Phys. J. C 22 (2001) 231 [hep-ex/0110019] [INSPIRE].
BaBar collaboration, Observation of CP-violation in the B0 meson system, Phys. Rev. Lett. 87 (2001) 091801 [hep-ex/0107013] [INSPIRE].
Belle collaboration, Observation of large CP-violation in the neutral B meson system, Phys. Rev. Lett. 87 (2001) 091802 [hep-ex/0107061] [INSPIRE].
BaBar collaboration, Observation of direct CP-violation in B0 → K + π− decays, Phys. Rev. Lett. 93 (2004) 131801 [hep-ex/0407057] [INSPIRE].
Belle collaboration, Evidence for direct CP-violation in B0 → K + π− decays, Phys. Rev. Lett. 93 (2004) 191802 [hep-ex/0408100] [INSPIRE].
LHCb collaboration, Observation of CP-violation in B± → DK ± decays, Phys. Lett. B 712 (2012) 203 [Erratum ibid. B 713 (2012) 351] [arXiv:1203.3662] [INSPIRE].
LHCb collaboration, First observation of C P violation in the decays of \( {B}_s^0 \)mesons, Phys. Rev. Lett. 110 (2013) 221601 [arXiv:1304.6173] [INSPIRE].
LHCb collaboration, Observation of CP-violation in Charm Decays, Phys. Rev. Lett. 122 (2019) 211803 [arXiv:1903.08726] [INSPIRE].
N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].
A. Pich, Precision Tau Physics, Prog. Part. Nucl. Phys. 75 (2014) 41 [arXiv:1310.7922] [INSPIRE].
M. Davier, A. Hocker and Z. Zhang, The Physics of Hadronic Tau Decays, Rev. Mod. Phys. 78 (2006) 1043 [hep-ph/0507078] [INSPIRE].
Y.S. Tsai, Search for new mechanism of CP-violation through tau decay and semileptonic decay of hadrons, Nucl. Phys. Proc. Suppl. C 55 (1997) 293 [hep-ph/9612281] [INSPIRE].
I.I. Bigi, Probing CP-violation in τ − → ν(K π/K 2π/3K/K 3π)− Decays, arXiv:1204.5817 [INSPIRE].
I.I. Bigi, CP Violation in τ Decays at SuperB & Super-Belle II Experiments — like Finding Signs of Dark Matter, Nucl. Phys. Proc. Suppl. 253–255 (2014) 91 [arXiv:1210.2968] [INSPIRE].
K. Kiers, CP violation in hadronic τ decays, Nucl. Phys. Proc. Suppl. 253–255 (2014) 95 [arXiv:1212.6921] [INSPIRE].
CLEO collaboration, First search for CP-violation in tau lepton decay, Phys. Rev. Lett. 81 (1998) 3823 [hep-ex/9805027] [INSPIRE].
CLEO collaboration, Search for CP-violation in τ → K πντ decays, Phys. Rev. Lett. 88 (2002) 111803 [hep-ex/0111095] [INSPIRE].
Belle collaboration, Search for CP-violation in \( \tau \to {K}_S^0{\pi \nu}_{\tau } \)decays at Belle, Phys. Rev. Lett. 107 (2011) 131801 [arXiv:1101.0349] [INSPIRE].
BaBar collaboration, Search for CP-violation in the Decay \( {\tau}^{-}\to {\pi}^{-}{K}_S^0\left(\ge 0{\pi}^0\right){\nu}_{\tau } \), Phys. Rev. D 85 (2012) 031102 [Erratum ibid. D 85 (2012) 099904] [arXiv:1109.1527] [INSPIRE].
I.I. Bigi and A.I. Sanda, A ‘Known’ CP asymmetry in tau decays, Phys. Lett. B 625 (2005) 47 [hep-ph/0506037] [INSPIRE].
G. Calderon, D. Delepine and G.L. Castro, Is there a paradox in CP asymmetries of τ ± → KL,S π± ν, Phys. Rev. D 75 (2007) 076001 [hep-ph/0702282] [INSPIRE].
Y. Grossman and Y. Nir, CP Violation in τ → νπKS and D → πKS : The Importance of KS − KL Interference, JHEP 04 (2012) 002 [arXiv:1110.3790] [INSPIRE].
Particle Data Group, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
H.Z. Devi, L. Dhargyal and N. Sinha, Can the observed CP asymmetry in τ → K πντ be due to nonstandard tensor interactions?, Phys. Rev. D 90 (2014) 013016 [arXiv:1308.4383] [INSPIRE].
L. Dhargyal, Full angular spectrum analysis of tensor current contribution to Acp (τ → Ks πντ ), LHEP 1 (2018) 9 [arXiv:1605.00629] [INSPIRE].
L. Dhargyal, New tensor interaction as the source of the observed CP asymmetry in τ → KSπντ , Springer Proc. Phys. 203 (2018) 329 [arXiv:1610.06293] [INSPIRE].
A. Dighe, S. Ghosh, G. Kumar and T.S. Roy, Tensors for tending to tensions in τ decays, arXiv:1902.09561 [INSPIRE].
V. Cirigliano, A. Crivellin and M. Hoferichter, No-go theorem for nonstandard explanations of the τ → KSπντ CP asymmetry, Phys. Rev. Lett. 120 (2018) 141803 [arXiv:1712.06595] [INSPIRE].
J. Rendón, P. Roig and G. Toledo S´anchez, Effective-field theory analysis of the τ − → (K π)− ντ decays, Phys. Rev. D 99 (2019) 093005 [arXiv:1902.08143] [INSPIRE].
F.-Z. Chen, X.-Q. Li, Y.-D. Yang and X. Zhang, CP asymmetry in τ → KSπντ decays within the Standard Model and beyond, Phys. Rev. D 100 (2019) 113006 [arXiv:1909.05543] [INSPIRE].
Belle-II collaboration, The Belle II Physics Book, Prog. Theor. Exp. Phys. 2019 (2019) 123C01 [Erratum ibid. 2020 (2020) 029201] [arXiv:1808.10567] [INSPIRE].
J.H. Kuhn and A. Santamaria, Tau decays to pions, Z. Phys. C 48 (1990) 445 [INSPIRE].
J.H. Kuhn and E. Mirkes, CP violation in semileptonic tau decays with unpolarized beams, Phys. Lett. B 398 (1997) 407 [hep-ph/9609502] [INSPIRE].
D. Kimura, K.Y. Lee, T. Morozumi and K. Nakagawa, CP violation in tau decays, in proceedings of the Heavy Quarks and Leptons 2008 (HQ&L08), Melbourne, Australia, 5–9 June 2008, arXiv:0905.1802 [INSPIRE].
D. Kimura, K.Y. Lee and T. Morozumi, The Form factors of τ → K π(η)ν and the predictions for CP-violation beyond the standard model, Prog. Theor. Exp. Phys. 2013 (2013) 053B03 [Erratum ibid. 2013 (2013) 099201] [arXiv:1201.1794] [INSPIRE].
D. Delepine, G. Lopez Castro and L.T. Lopez Lozano, CP violation in semileptonic tau lepton decays, Phys. Rev. D 72 (2005) 033009 [hep-ph/0503090] [INSPIRE].
R.G. Sachs, Methods for Testing the CPT Theorem, Phys. Rev. 129 (1963) 2280 [INSPIRE].
C.P. Enz and R.R. Lewis, On the phenomenological description of CP-violation for K mesons and its consequences, Helv. Phys. Acta 38 (1965) 860 [INSPIRE].
L. Wolfenstein, S-matrix formulation of KL and KS decays and unitarity relations, Phys. Rev. 188 (1969) 2536 [INSPIRE].
G.C. Branco, L. Lavoura and J.P. Silva, CP Violation, Int. Ser. Monogr. Phys. 103 (1999) 1 [INSPIRE].
J.P. Silva, On the use of the reciprocal basis in neutral meson mixing, Phys. Rev. D 62 (2000) 116008 [hep-ph/0007075] [INSPIRE].
J.P. Silva, Phenomenological aspects of CP-violation, in proceedings of the Central European School in Particle Physics, Prague, Czech Republic, 14–24 September 2004, hep-ph/0410351 [INSPIRE].
Belle collaboration, Study of τ − → KS π− ντ decay at Belle, Phys. Lett. B 654 (2007) 65 [arXiv:0706.2231] [INSPIRE].
BaBar collaboration, Selected topics in tau physics from BaBar, in proceedings of the Meeting of the Division of Particles and Fields of the American Physical Society (DPF 2009), Detroit, Michigan, U.S.A., 26–31 July 2009, arXiv:0910.2884 [INSPIRE] and online pdf version at http://www-public.slac.stanford.edu/sciDoc/docMeta.aspx?slacPubNumber=SLAC-PUB-14932.
M. Finkemeier and E. Mirkes, Tau decays into kaons, Z. Phys. C 69 (1996) 243 [hep-ph/9503474] [INSPIRE].
M. Finkemeier and E. Mirkes, The Scalar contribution to τ → K πντ , Z. Phys. C 72 (1996) 619 [hep-ph/9601275] [INSPIRE].
D.R. Boito, R. Escribano and M. Jamin, K pi vector form-factor, dispersive constraints and τ → ντ K π decays, Eur. Phys. J. C 59 (2009) 821 [arXiv:0807.4883] [INSPIRE].
D.R. Boito, R. Escribano and M. Jamin, K π vector form factor constrained by τ → K πντ and Kℓ3 decays, JHEP 09 (2010) 031 [arXiv:1007.1858] [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, S wave K π scattering in chiral perturbation theory with resonances, Nucl. Phys. B 587 (2000) 331 [hep-ph/0006045] [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, Strangeness changing scalar form-factors, Nucl. Phys. B 622 (2002) 279 [hep-ph/0110193] [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, Scalar K π form factor and light quark masses, Phys. Rev. D 74 (2006) 074009 [hep-ph/0605095] [INSPIRE].
L. Beldjoudi and T.N. Truong, τ → πK ντ decay and πK scattering, Phys. Lett. B 351 (1995) 357 [hep-ph/9411423] [INSPIRE].
J. Erler, Electroweak radiative corrections to semileptonic tau decays, Rev. Mex. Fis. 50 (2004) 200 [hep-ph/0211345] [INSPIRE].
J.H. Kuhn and E. Mirkes, Structure functions in τ decays, Z. Phys. C 56 (1992) 661 [Erratum ibid. C 67 (1995) 364] [INSPIRE].
D.-N. Gao and X.-F. Wang, On the angular distributions of τ − → KS π− ντ decay, Phys. Rev. D 87 (2013) 073016 [arXiv:1212.5978] [INSPIRE].
M. Moulson, Experimental determination of Vus from kaon decays, PoS(CKM2016)033 (2017) [arXiv:1704.04104] [INSPIRE].
R. Escribano, S. Gonz´alez-Soĺıs, M. Jamin and P. Roig, Combined analysis of the decays τ − → KS π− ντ and τ − → K − ηντ , JHEP 09 (2014) 042 [arXiv:1407.6590] [INSPIRE].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].
G. Ecker, J. Gasser, H. Leutwyler, A. Pich and E. de Rafael, Chiral Lagrangians for Massive Spin 1 Fields, Phys. Lett. B 223 (1989) 425 [INSPIRE].
M. Jamin, A. Pich and J. Portoles, Spectral distribution for the decay τ → ντ K π, Phys. Lett. B 640 (2006) 176 [hep-ph/0605096] [INSPIRE].
M. Jamin, A. Pich and J. Portoles, What can be learned from the Belle spectrum for the decay τ − → ντ KS π− , Phys. Lett. B 664 (2008) 78 [arXiv:0803.1786] [INSPIRE].
S. Gonzàlez-Solís and P. Roig, A dispersive analysis of the pion vector form factor and τ − → K − KS ντ decay, Eur. Phys. J. C 79 (2019) 436 [arXiv:1902.02273] [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, Light quark masses from scalar sum rules, Eur. Phys. J. C 24 (2002) 237 [hep-ph/0110194] [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, Order p6 chiral couplings from the scalar K π form-factor, JHEP 02 (2004) 047 [hep-ph/0401080] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2003.05735
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Chen, FZ., Li, XQ. & Yang, YD. CP asymmetry in the angular distribution of τ → KSπντ decays. J. High Energ. Phys. 2020, 151 (2020). https://doi.org/10.1007/JHEP05(2020)151
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2020)151