Abstract
Recent LHCb data shows that the direct CP asymmetries of the decay modes D0 → π+π− and D0 → K+K− have the same sign, violating an improved U-spin limit sum rule in an unexpected way at 2.1σ. From the new data, we determine for the first time the imaginary part of the CKM-subleading, U-spin breaking ∆U = 1 correction to the U-spin limit ∆U = 0 amplitude. The imaginary part of the ∆U = 0 amplitude is determined by \( \Delta {a}_{\textrm{CP}}^{\textrm{dir}} \). The corresponding strong phases are yet unknown and could be extracted in the future from time-dependent measurements. Assuming \( \mathcal{O}(1) \) strong phases due to non-perturbative rescattering, we find the ratio of U-spin breaking to U-spin limit contributions to the CKM-subleading amplitudes to be \( \left({173}_{\hbox{--} 74}^{+85}\right)\% \). This highly exceeds the Standard Model (SM) expectation of ~ 30% U -spin breaking, with a significance of 1.95σ. If this puzzle is confirmed with more data in the future, in the SM it would imply the breakdown of the U -spin expansion in CKM-subleading amplitudes of charm decays. The other solution are new physics models that generate an additional ∆U = 1 operator, leaving the U-spin power expansion intact. Examples for the latter option are an extended scalar sector or flavorful Z′ models.
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References
LHCb collaboration, Observation of CP Violation in Charm Decays, Phys. Rev. Lett. 122 (2019) 211803 [arXiv:1903.08726] [INSPIRE].
S. Maccolini, Direct CPV in charm hadrons at LHCb, talk at the XLI International Conference on High Energy Physics (ICHEP 2022), Bologna, Italy, 6–13 July 2022 [https://agenda.infn.it/event/28874/contributions/169315/].
Belle collaboration, Measurement of the charm-mixing parameter yCP in \( {D}^0\to {K}_S^0\omega \) decays at Belle, Phys. Rev. D 102 (2020) 071102 [arXiv:1912.10912] [INSPIRE].
LHCb collaboration, Search for CP violation in \( {D}_{(s)}^{+}\to {h}^{+}{\pi}^0 \) and \( {D}_{(s)}^{+}\to {h}^{+}\eta \) decays, JHEP 06 (2021) 019 [arXiv:2103.11058] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetry in \( {D}^0\to {K}_S^0{K}_S^0 \) decays, Phys. Rev. D 104 (2021) L031102 [arXiv:2105.01565] [INSPIRE].
LHCb collaboration, Search for time-dependent CP violation in D0 → K+K− and D0 → π+π− decays, Phys. Rev. D 104 (2021) 072010 [arXiv:2105.09889] [INSPIRE].
LHCb collaboration, Observation of the Mass Difference Between Neutral Charm-Meson Eigenstates, Phys. Rev. Lett. 127 (2021) 111801 [arXiv:2106.03744] [INSPIRE].
LHCb collaboration, Simultaneous determination of CKM angle γ and charm mixing parameters, JHEP 12 (2021) 141 [arXiv:2110.02350] [INSPIRE].
LHCb collaboration, Measurement of the charm mixing parameter \( {y}_{CP}-{y}_{CP}^{K\pi} \) using two-body D0 meson decays, Phys. Rev. D 105 (2022) 092013 [arXiv:2202.09106] [INSPIRE].
HFLAV collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2021, Phys. Rev. D 107 (2023) 052008 [arXiv:2206.07501] [INSPIRE].
Y. Grossman and S. Schacht, The emergence of the ∆U = 0 rule in charm physics, JHEP 07 (2019) 020 [arXiv:1903.10952] [INSPIRE].
M. Chala, A. Lenz, A.V. Rusov and J. Scholtz, ∆ACP within the Standard Model and beyond, JHEP 07 (2019) 161 [arXiv:1903.10490] [INSPIRE].
H.-N. Li, C.-D. Lü and F.-S. Yu, Implications on the first observation of charm CPV at LHCb, arXiv:1903.10638 [INSPIRE].
A. Soni, Resonance enhancement of Charm CP, arXiv:1905.00907 [INSPIRE].
H.-Y. Cheng and C.-W. Chiang, Revisiting CP violation in D → PP and VP decays, Phys. Rev. D 100 (2019) 093002 [arXiv:1909.03063] [INSPIRE].
F. Buccella, A. Paul and P. Santorelli, SU(3)F breaking through final state interactions and CP asymmetries in D → PP decays, Phys. Rev. D 99 (2019) 113001 [arXiv:1902.05564] [INSPIRE].
A. Dery and Y. Nir, Implications of the LHCb discovery of CP violation in charm decays, JHEP 12 (2019) 104 [arXiv:1909.11242] [INSPIRE].
L. Calibbi, T. Li, Y. Li and B. Zhu, Simple model for large CP violation in charm decays, B-physics anomalies, muon g – 2 and dark matter, JHEP 10 (2020) 070 [arXiv:1912.02676] [INSPIRE].
A. Dery, Y. Grossman, S. Schacht and A. Soffer, Probing the ∆U = 0 rule in three body charm decays, JHEP 05 (2021) 179 [arXiv:2101.02560] [INSPIRE].
R. Bause, H. Gisbert, M. Golz and G. Hiller, Exploiting CP -asymmetries in rare charm decays, Phys. Rev. D 101 (2020) 115006 [arXiv:2004.01206] [INSPIRE].
A.L. Kagan and L. Silvestrini, Dispersive and absorptive CP violation in \( {D}^0-{\overline{D}}^0 \) mixing, Phys. Rev. D 103 (2021) 053008 [arXiv:2001.07207] [INSPIRE].
A.J. Buras, P. Colangelo, F. De Fazio and F. Loparco, The charm of 331, JHEP 10 (2021) 021 [arXiv:2107.10866] [INSPIRE].
H. Acaroğlu and M. Blanke, Tasting flavoured Majorana dark matter, JHEP 05 (2022) 086 [arXiv:2109.10357] [INSPIRE].
S. Schacht and A. Soni, Enhancement of charm CP violation due to nearby resonances, Phys. Lett. B 825 (2022) 136855 [arXiv:2110.07619] [INSPIRE].
M. Gavrilova, Y. Grossman and S. Schacht, The mathematical structure of U-spin amplitude sum rules, JHEP 08 (2022) 278 [arXiv:2205.12975] [INSPIRE].
M.B. Einhorn and C. Quigg, Nonleptonic Decays of Charmed Mesons: Implications for e+ e- Annihilation, Phys. Rev. D 12 (1975) 2015 [INSPIRE].
L.F. Abbott, P. Sikivie and M.B. Wise, Cabibbo suppressed nonleptonic D decays, Phys. Rev. D 21 (1980) 768 [INSPIRE].
A.J. Buras, J.M. Gerard and R. Ruckl, 1/n Expansion for Exclusive and Inclusive Charm Decays, Nucl. Phys. B 268 (1986) 16 [INSPIRE].
M. Golden and B. Grinstein, Enhanced CP Violations in Hadronic Charm Decays, Phys. Lett. B 222 (1989) 501 [INSPIRE].
F. Buccella et al., CP Violating asymmetries in charged D meson decays, Phys. Lett. B 302 (1993) 319 [hep-ph/9212253] [INSPIRE].
A.F. Falk, Y. Grossman, Z. Ligeti and A.A. Petrov, SU(3) breaking and \( {D}^0-{\overline{D}}^0 \) mixing, Phys. Rev. D 65 (2002) 054034 [hep-ph/0110317] [INSPIRE].
J. Brod, Y. Grossman, A.L. Kagan and J. Zupan, A Consistent Picture for Large Penguins in D → π+π−, K+K−, JHEP 10 (2012) 161 [arXiv:1203.6659] [INSPIRE].
B. Bhattacharya, M. Gronau and J.L. Rosner, CP asymmetries in singly-Cabibbo-suppressed D decays to two pseudoscalar mesons, Phys. Rev. D 85 (2012) 054014 [arXiv:1201.2351] [INSPIRE].
E. Franco, S. Mishima and L. Silvestrini, The Standard Model confronts CP violation in D0 → π+π− and D0 → K+K−, JHEP 05 (2012) 140 [arXiv:1203.3131] [INSPIRE].
G. Hiller, M. Jung and S. Schacht, SU(3)-flavor anatomy of nonleptonic charm decays, Phys. Rev. D 87 (2013) 014024 [arXiv:1211.3734] [INSPIRE].
U. Nierste and S. Schacht, Neutral D → KK∗ decays as discovery channels for charm CP violation, Phys. Rev. Lett. 119 (2017) 251801 [arXiv:1708.03572] [INSPIRE].
U. Nierste and S. Schacht, CP Violation in D0 → KSKS, Phys. Rev. D 92 (2015) 054036 [arXiv:1508.00074] [INSPIRE].
S. Müller, U. Nierste and S. Schacht, Topological amplitudes in D decays to two pseudoscalars: A global analysis with linear SU(3)F breaking, Phys. Rev. D 92 (2015) 014004 [arXiv:1503.06759] [INSPIRE].
S. Müller, U. Nierste and S. Schacht, Sum Rules of Charm CP Asymmetries beyond the SU(3)F Limit, Phys. Rev. Lett. 115 (2015) 251802 [arXiv:1506.04121] [INSPIRE].
Y. Grossman and S. Schacht, U-Spin Sum Rules for CP Asymmetries of Three-Body Charmed Baryon Decays, Phys. Rev. D 99 (2019) 033005 [arXiv:1811.11188] [INSPIRE].
F. Buccella et al., Nonleptonic weak decays of charmed mesons, Phys. Rev. D 51 (1995) 3478 [hep-ph/9411286] [INSPIRE].
Y. Grossman, A.L. Kagan and Y. Nir, New physics and CP violation in singly Cabibbo suppressed D decays, Phys. Rev. D 75 (2007) 036008 [hep-ph/0609178] [INSPIRE].
M. Artuso, B. Meadows and A.A. Petrov, Charm Meson Decays, Ann. Rev. Nucl. Part. Sci. 58 (2008) 249 [arXiv:0802.2934] [INSPIRE].
A. Khodjamirian and A.A. Petrov, Direct CP asymmetry in D → π−π+ and D → K−K+ in QCD-based approach, Phys. Lett. B 774 (2017) 235 [arXiv:1706.07780] [INSPIRE].
F. Buccella, M. Lusignoli, A. Pugliese and P. Santorelli, CP violation in D meson decays: Would it be a sign of new physics?, Phys. Rev. D 88 (2013) 074011 [arXiv:1305.7343] [INSPIRE].
H.-Y. Cheng and C.-W. Chiang, Direct CP violation in two-body hadronic charmed meson decays, Phys. Rev. D 85 (2012) 034036 [Erratum ibid. 85 (2012) 079903] [arXiv:1201.0785] [INSPIRE].
T. Feldmann, S. Nandi and A. Soni, Repercussions of Flavour Symmetry Breaking on CP Violation in D-Meson Decays, JHEP 06 (2012) 007 [arXiv:1202.3795] [INSPIRE].
H.-N. Li, C.-D. Lu and F.-S. Yu, Branching ratios and direct CP asymmetries in D → PP decays, Phys. Rev. D 86 (2012) 036012 [arXiv:1203.3120] [INSPIRE].
D. Atwood and A. Soni, Searching for the Origin of CP violation in Cabibbo Suppressed D-meson Decays, PTEP 2013 (2013) 093B05 [arXiv:1211.1026] [INSPIRE].
Y. Grossman and D.J. Robinson, SU(3) Sum Rules for Charm Decay, JHEP 04 (2013) 067 [arXiv:1211.3361] [INSPIRE].
F.-S. Yu, D. Wang and H.-N. Li, CP asymmetries in charm decays into neutral kaons, Phys. Rev. Lett. 119 (2017) 181802 [arXiv:1707.09297] [INSPIRE].
J. Brod, A.L. Kagan and J. Zupan, Size of direct CP violation in singly Cabibbo-suppressed D decays, Phys. Rev. D 86 (2012) 014023 [arXiv:1111.5000] [INSPIRE].
D. Pirtskhalava and P. Uttayarat, CP Violation and Flavor SU(3) Breaking in D-meson Decays, Phys. Lett. B 712 (2012) 81 [arXiv:1112.5451] [INSPIRE].
W. Altmannshofer, R. Primulando, C.-T. Yu and F. Yu, New Physics Models of Direct CP Violation in Charm Decays, JHEP 04 (2012) 049 [arXiv:1202.2866] [INSPIRE].
Y. Grossman, A.L. Kagan and J. Zupan, Testing for new physics in singly Cabibbo suppressed D decays, Phys. Rev. D 85 (2012) 114036 [arXiv:1204.3557] [INSPIRE].
M. Gronau, U spin symmetry in charmless B decays, Phys. Lett. B 492 (2000) 297 [hep-ph/0008292] [INSPIRE].
R. Fleischer, New strategies to extract β and γ from Bd → π+π− and BS → K+K−, Phys. Lett. B 459 (1999) 306 [hep-ph/9903456] [INSPIRE].
M. Gronau and J.L. Rosner, The Role of Bs → Kπ in determining the weak phase γ, Phys. Lett. B 482 (2000) 71 [hep-ph/0003119] [INSPIRE].
M. Jung and T. Mannel, General Analysis of U-Spin Breaking in B Decays, Phys. Rev. D 80 (2009) 116002 [arXiv:0907.0117] [INSPIRE].
M. Gell-Mann, The Eightfold Way: A Theory of strong interaction symmetry, CTSL-20 (1961) [https://doi.org/10.2172/4008239] [INSPIRE].
Y. Ne’eman, Derivation of strong interactions from a gauge invariance, Nucl. Phys. 26 (1961) 222 [INSPIRE].
W. Greiner and B. Muller, Theoretical physics. Vol. 2: Quantum mechanics. Symmetries, (1989) [INSPIRE].
S. Okubo, Note on unitary symmetry in strong interactions, Prog. Theor. Phys. 27 (1962) 949 [INSPIRE].
Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].
M.J. Savage, SU(3) violations in the nonleptonic decay of charmed hadrons, Phys. Lett. B 257 (1991) 414 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
H.-Y. Cheng and C.-W. Chiang, Two-body hadronic charmed meson decays, Phys. Rev. D 81 (2010) 074021 [arXiv:1001.0987] [INSPIRE].
B. Bhattacharya and J.L. Rosner, Charmed meson decays to two pseudoscalars, Phys. Rev. D 81 (2010) 014026 [arXiv:0911.2812] [INSPIRE].
Y. Grossman, Y. Nir and G. Perez, Testing New Indirect CP Violation, Phys. Rev. Lett. 103 (2009) 071602 [arXiv:0904.0305] [INSPIRE].
A.L. Kagan and M.D. Sokoloff, On Indirect CP Violation and Implications for \( {D}^0-{\overline{D}}^0 \) and \( {B}_s-{\overline{B}}_s \) mixing, Phys. Rev. D 80 (2009) 076008 [arXiv:0907.3917] [INSPIRE].
T. Pajero and M.J. Morello, Mixing and CP violation in D0 → K−π+ decays, JHEP 03 (2022) 162 [arXiv:2106.02014] [INSPIRE].
BaBar collaboration, Search for CP violation in the decays D0 → K−K+ and D0 → π−π+, Phys. Rev. Lett. 100 (2008) 061803 [arXiv:0709.2715] [INSPIRE].
CDF collaboration, Measurement of the difference of CP-violating asymmetries in D0 → K+K− and D0 → π+π− decays at CDF, Phys. Rev. Lett. 109 (2012) 111801 [arXiv:1207.2158] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetry in D0 → K−K+ and D0 → π−π+ decays, JHEP 07 (2014) 041 [arXiv:1405.2797] [INSPIRE].
LHCb collaboration, Measurement of the difference of time-integrated CP asymmetries in D0 → K−K+ and D0 → π−π+ decays, Phys. Rev. Lett. 116 (2016) 191601 [arXiv:1602.03160] [INSPIRE].
Belle collaboration, Measurement of CP asymmetry in Cabibbo suppressed D0 decays, Phys. Lett. B 670 (2008) 190 [arXiv:0807.0148] [INSPIRE].
Belle collaboration, Measurement of \( {D}^0-\overline{D^0} \) mixing and search for CP violation in D0 → K+K−, π+π− decays with the full Belle data set, Phys. Lett. B 753 (2016) 412 [arXiv:1509.08266] [INSPIRE].
Y. Grossman, Z. Ligeti and D.J. Robinson, More Flavor SU(3) Tests for New Physics in CP Violating B Decays, JHEP 01 (2014) 066 [arXiv:1308.4143] [INSPIRE].
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Schacht, S. A U-spin anomaly in charm CP violation. J. High Energ. Phys. 2023, 205 (2023). https://doi.org/10.1007/JHEP03(2023)205
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DOI: https://doi.org/10.1007/JHEP03(2023)205