Abstract
We present a systematic analysis of the angular distribution of \( \overline B \to {\overline K^*}\left( { \to \overline K \pi } \right){l^{+} }{l^{-} } \) decays with l = e, μ in the low recoil region (i.e. at high dileptonin variant masses of the order of the mass of the b-quark) to account model-independently for CP violation beyond the Standard Model, working to next-to-leading order QCD. From the employed heavy quark effective theory framework we identify the key CP observables with reduced hadronic uncertainties. Since some of the CP asymmetries are CP-odd they can be measured without B -flavour tagging. This is particularly beneficial for \( {\overline B_s},{B_s} \to \phi \left( { \to {K^{+} }{K^{-} }} \right){l^{+} }{l^{-} } \) decays, which are not self-tagging, and we work out the corresponding time-integrated CP asymmetries. Presently available experimental constraints allow the proposed CP asymmetries to be sizeable, up to values of the order ~ 0.2, while the corresponding Standard Model values receive a strong parametric suppression at the level of \( \mathcal{O}\left( {{{10}^{ - 4}}} \right) \). Furthermore, we work out the allowed ranges of the short-distance (Wilson) coefficients \( {\mathcal{C}_{9,10}} \) in the presence of CP violation beyond the Standard Model but no further Dirac structures. We find the \( {\overline B_s} \to {\mu^{+} }{\mu^{-} } \) branching ratio to be below 10 × 10−9 (at 95% CL). Possibilities to check the performance of the theoretical low recoil framework are pointed out.
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References
F. Krüger, L.M. Sehgal, N. Sinha and R. Sinha, Angular distribution and CP asymmetries in the decays \( \overline B \to {K^{-} }{\pi^{+} }{e^{-} }{e^{+} } \) and \( \overline B \to {\pi^{-} }{\pi^{+} }{e^{-} }{e^{+} } \), Phys. Rev. D 61 (2000) 114028 [Erratum ibid D 63 (2001) 019901] [hep-ph/9907386] [SPIRES].
M. Beneke, T. Feldmann and D. Seidel, Systematic approach to exclusive B → V ℓ+ℓ− ,Vγ decays, Nucl. Phys. B 612 (2001) 25 [hep-ph/0106067] [SPIRES].
M. Beneke, T. Feldmann and D. Seidel, Exclusive radiative and electroweak b → d and b → s penguin decays at NLO, Eur. Phys. J. C 41 (2005) 173 [hep-ph/0412400] [SPIRES].
C. Bobeth, G. Hiller and G. Piranishvili, CP Asymmetries in \( \overline B \to {\overline K^*}\left( { \to \overline K \pi } \right)\overline \ell \ell \) Untagged \( {\overline B_s},{B_s} \to \phi \left( { \to {K^{+} }{K^{-} }} \right)\overline \ell \ell \) Decays at NLO, JHEP 07 (2008) 106 [arXiv:0805.2525] [SPIRES].
U. Egede, T. Hurth, J. Matias, M. Ramon and W. Reece, New observables in the decay mode \( \overline B \to {\overline K^{*0}}{\ell^{+} }{\ell^{-} } \), JHEP 11 (2008) 032 [arXiv:0807.2589] [SPIRES].
W. Altmannshofer et al., Symmetries and Asymmetries of B → K ∗ μ+μ− Decays in the Standard Model and Beyond, JHEP 01 (2009) 019 [arXiv:0811.1214] [SPIRES].
C. Bobeth, G. Hiller and G. Piranishvili, Theoretical Status of Rare B Decays with Muons, PoS(BEAUTY 2009)047 [arXiv:0911.4054] [SPIRES].
U. Egede, T. Hurth, J. Matias, M. Ramon and W. Reece, New physics reach of the decay mode \( \overline B \to {\overline K^{*0}}{\ell^{+} }{\ell^{-} } \), JHEP 10 (2010) 056 [arXiv:1005.0571] [SPIRES].
A. Khodjamirian, T. Mannel, A.A. Pivovarov and Y.M. Wang, Charm-loop effect in B → K (*) ℓ+ ℓ- and B → K *γ, JHEP 09 (2010) 089 [arXiv:1006.4945] [SPIRES].
B. Grinstein and D. Pirjol, Precise |V(ub)| determination from exclusive B decays: Controlling the long-distance effects, Phys. Rev. D 70 (2004) 114005 [hep-ph/0404250] [SPIRES].
M. Beylich, G. Buchalla and T. Feldmann, Theory of B → K (∗)ℓ+ℓ- decays at high q 2 : OPE and quark-hadron duality, Eur. Phys. J. C 71 (2011) 1635 [arXiv:1101.5118] [SPIRES].
B. Grinstein and D. Pirjol, Symmetry-breaking corrections to heavy meson form-factor relations, Phys. Lett. B 533 (2002) 8 [hep-ph/0201298] [SPIRES].
J.L. Hewett, et al., The Discovery potential of a Super B Factory, proceedings of SLAC Workshops, Stanford U.S.A. (2003), hep-ph/0503261 [SPIRES].
C. Bobeth, G. Hiller and D. van Dyk, The Benefits of B → K ∗ ℓ+ℓ- Decays at Low Recoil, JHEP 07 (2010) 098 [arXiv:1006. 013] [SPIRES].
CKMfitter Group collaboration, J. Charles et al., CP violation and the CKM matrix: Assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [SPIRES]. We use the numerical results as presented at ICHEP2010, Paris France, July 22–28, 2010.
F. Krüger and L.M. Sehgal, Lepton Polarization in the Decays B → X s μ+μ− and B → X s τ+τ−, Phys. Lett. B 380 (1996) 199 [hep-ph/9603237] [SPIRES].
Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [SPIRES].
A. Ali, P. Ball, L.T. Handoko and G. Hiller, A Comparative study of the decays B → (K,K ∗)ℓ+ℓ- in standard model and supersymmetric theories, Phys. Rev. D 61 (2000) 074024 [hep-ph/9910221] [SPIRES].
G. Buchalla, G. Hiller and G. Isidori, Phenomenology of nonstandard Z couplings in exclusive semileptonic b → s transitions, Phys. Rev. D 63 (2000) 014015 [hep-ph/0006136] [SPIRES].
F. Krüger and E. Lunghi, Looking for novel CP-violating effects in \( \overline B \to {K^*}{\ell^{+} }{\ell^{-} } \), Phys. Rev. D 63 (2001) 014013 [hep-ph/0008210] [SPIRES].
A.K. Alok et al., New Physics in b → sμ+μ− : CP-Violating Observables, arXiv:1103.5344 [SPIRES].
R. Fleischer and I. Dunietz, CP violation and CKM phases from angular distributions for B s decays into admixtures of CP eigenstates, Phys. Rev. D 55 (1997) 259 [hep-ph/9605220] [SPIRES].
Heavy Flavor Averaging Group collaboration, E. Barberio et al., Averages of b − hadron and c − hadron Properties at the End of 2007, arXiv:0808.1297 [SPIRES], online from March 2010 http://www.slac.stanford.edu/xorg/hfag.
M. Misiak et al., The first estimate of \( B\left( {\overline B \to {X_s}\gamma } \right) \) at O(α s 2), Phys. Rev. Lett. 98 (2007) 022002 [hep-ph/0609232] [SPIRES].
T. Becher and M. Neubert, Analysis of \( B\left( {\overline B \to {X_s}\gamma } \right) \) at NNLO with a cut on photon energy, Phys. Rev. Lett. 98 (2007) 022003 [hep-ph/0610067] [SPIRES].
D. van Dyk et al., online: http://project.het.physik.tu-dortmund.de/source/eos/tag/lowrecoil-cp.
HPQCD collaboration, E. Gamiz, C.T.H. Davies, G.P. Lepage, J. Shigemitsu and M. Wingate, Neutral B Meson Mixing in Unquenched Lattice QCD, Phys. Rev. D 80 (2009) 014503 [arXiv:0902.1815] [SPIRES].
Fermilab Lattice and MILC collaborations, J. Simone et al., T he decay constants f (D/s),f (D +),f (B/s) and f (B) from lattice QCD, PoS(Lattice 2010)317 [SPIRES].
M. Palutan, Rare decays results and prospects with LHCb, on behalf of the LHCb collaboration at BEAUTY 2011, 13th International Conference on B-Physics at Hadron Machines, Amsterdam The Netherlands, April 4th–8th, 2011.
BABAR collaboration, B. Aubert et al., Direct CP, Lepton Flavor and Isospin Asymmetries in the Decays B → K (∗)ℓ+ℓ-, Phys. Rev. Lett. 102 (2009) 091803 [arXiv:0807.4119] [SPIRES].
BELLE collaboration, J.T. Wei et al., Measurement of the Differential Branching Fraction and Forward-Backword Asymmetry for B → K (∗)ℓ+ℓ-, Phys. Rev. Lett. 103 (2009) 171801 [arXiv:0904.0770] [SPIRES].
CDF collaboration, T. Aaltonen et al., Measurement of the Forward-Backward Asymmetry in the B → K (∗)μ+μ− Decay and First Observation of the B s 0 → φμ+μ− Decay, Phys. Rev. Lett. 106 (2011) 161801 [arXiv:1101.1028] [SPIRES].
D. Seidel, Analytic two-loop virtual corrections to b → dℓ+ℓ-, Phys. Rev. D 70 (2004) 094038 [hep-ph/0403185] [SPIRES].
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ArXiv ePrint:1105.0376
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Bobeth, C., Hiller, G. & van Dyk, D. More benefits of semileptonic rare B decays at low recoil: CP violation. J. High Energ. Phys. 2011, 67 (2011). https://doi.org/10.1007/JHEP07(2011)067
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DOI: https://doi.org/10.1007/JHEP07(2011)067