Abstract
Based on recent HQET sum rule and lattice calculations we present updated Standard Model predictions for the mass differences of neutral B mesons: \( \varDelta {M}_s^{\mathrm{SM}}=\left({18.4}_{-1.2}^{+0.7}\right){\mathrm{ps}}^{-1} \) and \( \varDelta {M}_d^{\mathrm{SM}}=\left({0.533}_{-0.036}^{+0.022}\right){\mathrm{ps}}^{-1} \) study their impact onnew physics models that address the present hints of anomalous data in b → sℓℓ transitions. We also examine future prospects of further reducing the theory uncertainties and discuss the implications of a 2025 scenario with \( \varDelta {M}_s^{\mathrm{SM}\;2025}=\left(18.4\pm 0.5\right) \) ps−1. In particular, the latter yields upper bounds MZ′ ≲ 9TeV and \( {M}_{S_3}\lesssim 30\mathrm{TeV} \)for the minimal Z′ and S3 lepto-quark explanations of the b → sℓℓ anomalies, respectively.
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References
M. Artuso, G. Borissov and A. Lenz, CP violation in the \( {B}_s^0 \)system, Rev. Mod. Phys.88 (2016) 045002 [arXiv:1511.09466] [INSPIRE].
HFLAV collaboration, Averages of b-hadron, c-hadron and τ -lepton properties as of summer 2016, Eur. Phys. J.C 77 (2017) 895 [arXiv:1612.07233] [INSPIRE].
ARGUS collaboration, Observation of \( {B}^0-{\overline{B}}^0 \)Mixing, Phys. Lett.B 192 (1987) 245 [INSPIRE].
CDF collaboration, Observation of \( {B}^0-{\overline{B}}^0 \)Oscillations, Phys. Rev. Lett.97 (2006) 242003 [hep-ex/0609040] [INSPIRE].
LHCb collaboration, Measurement of the \( {B}_s^0-{\overline{B}}_s^0 \)oscillation frequency ∆m sin \( {B}_s^0\to {D}_s^{-}(3)\uppi \)decays, Phys. Lett.B 709 (2012) 177 [arXiv:1112.4311] [INSPIRE].
LHCb collaboration, Opposite-side flavour tagging of B mesons at the LHCb experiment, Eur. Phys. J.C 72 (2012) 2022 [arXiv:1202.4979] [INSPIRE].
LHCb collaboration, Measurement of the \( {B}^0-{\overline{B}}^0 \)oscillation frequency ∆m dwith the decaysio B 0 → D −π+and B 0 → JψK ∗0, Phys. Lett.B 719 (2013) 318 [arXiv:1210.6750] [INSPIRE].
LHCb collaboration, Precision measurement of the \( {B}_s^0-{\overline{B}}_s^0 \)oscillation frequency with the decay \( {B}_s^0\to {D}_s^{-}{\uppi}^{+} \), New J. Phys.15 (2013) 053021 [arXiv:1304.4741] [INSPIRE].
LHCb collaboration, Observation of \( {B}_s^0-{\overline{B}}_s^0 \)mixing and measurement of mixing frequencies using semileptonic B decays, Eur. Phys. J.C 73 (2013) 2655 [arXiv:1308.1302] [INSPIRE].
LHCb collaboration, Precision measurement of C P violation in \( {B}_s^0\to J/\psi {K}^{+}{K}^{-} \)− decays, Phys. Rev. Lett.114 (2015) 041801 [arXiv:1411.3104] [INSPIRE].
S. Aoki et al., Review of Lattice Results Concerning Low-Energy Particle Physics, Eur. Phys. J.C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].
Fermilab Lattice and MILC collaborations, \( {B}_{(s)}^0 \)-mixing matrix elements from lattice QCD for the Standard Model and beyond, Phys. Rev.D 93 (2016) 113016 [arXiv:1602.03560] [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019, arXiv:1902.08191 [INSPIRE].
M. Blanke and A.J. Buras, Universal Unitarity Triangle 2016 and the tension between ∆M s,dand ε Kin CMFV models, Eur. Phys. J.C 76 (2016) 197 [arXiv:1602.04020] [INSPIRE].
A.J. Buras and F. De Fazio, 331 Models Facing the Tensions in ∆F = 2 Processes with the Impact on ε ε ′ /ε, B s → μ +μ −and K ∗ → μ +μ −, JHEP08 (2016) 115 [arXiv:1604.02344] [INSPIRE].
C. Bobeth, A.J. Buras, A. Celis and M. Jung, Yukawa enhancement of Z -mediated new physics in ∆S = 2 and ∆B = 2 processes, JHEP07 (2017) 124 [arXiv:1703.04753] [INSPIRE].
M. Blanke and A.J. Buras, Emerging ∆M d-anomaly from tree-level determinations of |V cb| and the angle γ, Eur. Phys. J.C 79 (2019) 159 [arXiv:1812.06963] [INSPIRE].
Q.-Y. Hu, X.-Q. Li, Y.-D. Yang and M.-D. Zheng, \( {B}_{s(d)}-{\overline{B}}_{s(d)} \)Mixing and B s→ μ +μ −Decay in the NMSSM with the Flavour Expansion Theorem, JHEP06 (2019) 133 [arXiv:1903.06927] [INSPIRE].
L. Di Luzio, M. Kirk and A. Lenz, Updated B s-mixing constraints on new physics models for b → sℓ+ ℓ−anomalies, Phys. Rev.D 97 (2018) 095035 [arXiv:1712.06572] [INSPIRE].
A.G. Grozin, R. Klein, T. Mannel and A.A. Pivovarov, \( {B}^0-{\overline{B}}^0 \)mixing at next-to-leading order, Phys. Rev.D 94 (2016) 034024 [arXiv:1606.06054] [INSPIRE].
A.G. Grozin, T. Mannel and A.A. Pivovarov, Towards a Next-to-Next-to-Leading Order analysis of matching in \( {B}^0-{\overline{B}}^0 \)mixing, Phys. Rev.D 96 (2017) 074032 [arXiv:1706.05910] [INSPIRE].
A.G. Grozin, T. Mannel and A.A. Pivovarov, \( {B}^0-{\overline{B}}^0 \)mixing: Matching to HQET at NNLO, Phys. Rev.D 98 (2018) 054020 [arXiv:1806.00253] [INSPIRE].
M. Kirk, A. Lenz and T. Rauh, Dimension-six matrix elements for meson mixing and lifetimes from sum rules, JHEP12 (2017) 068 [arXiv:1711.02100] [INSPIRE].
D. King, A. Lenz and T. Rauh, B smixing observables and |V td/V ts| from sum rules, JHEP05 (2019) 034 [arXiv:1904.00940] [INSPIRE].
R.J. Dowdall et al., Neutral B-meson mixing from full lattice QCD at the physical point, arXiv:1907.01025 [INSPIRE].
RBC/UKQCD collaboration, SU(3)-breaking ratios for D (s)and B (s)mesons, arXiv:1812.08791 [INSPIRE].
Belle-II collaboration, The Belle II Physics Book, arXiv:1808.10567 [INSPIRE].
LHCb collaboration, Physics case for an LHCb Upgrade II — Opportunities in flavour physics and beyond, in the HL-LHC era, arXiv:1808.08865 [INSPIRE].
T. Inami and C.S. Lim, Effects of Superheavy Quarks and Leptons in Low-Energy Weak Processes and \( {L}_L\to \mu \overline{\mu},{K}^{+}\to {\pi}^{+}v\overline{v} \) and \( {K}^0\leftrightarrow {\overline{K}}^0 \), Prog. Theor. Phys.65 (1981) 297 [Erratum ibid.65 (1981) 1772] [INSPIRE].
A.J. Buras, M. Jamin and P.H. Weisz, Leading and Next-to-leading QCD Corrections to E Parameter and \( {B}^0-{\overline{B}}^0 \)Mixing in the Presence of a Heavy Top Quark, Nucl. Phys.B 347 (1990) 491 [INSPIRE].
ETM collaboration, B-physics from N f = 2 tmQCD: the Standard Model and beyond, JHEP03 (2014) 016 [arXiv:1308.1851] [INSPIRE].
ETM collaboration, Mass of the b quark and B-meson decay constants from N f = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev.D 93 (2016) 114505 [arXiv:1603.04306] [INSPIRE].
C. Hughes, C.T.H. Davies and C.J. Monahan, New methods for B meson decay constants and form factors from lattice NRQCD, Phys. Rev.D 97 (2018) 054509 [arXiv:1711.09981] [INSPIRE].
A. Bazavov et al., B- and D-meson leptonic decay constants from four-flavor lattice QCD, Phys. Rev.D 98 (2018) 074512 [arXiv:1712.09262] [INSPIRE].
A.G. Grozin and R.N. Lee, Three-loop HQET vertex diagrams for \( {B}^0-{\overline{B}}^0 \)mixing, JHEP02 (2009) 047 [arXiv:0812.4522] [INSPIRE].
RBC/UKQCD collaboration, Neutral Kaon Mixing Beyond the Standard Model with n f = 2 + 1 Chiral Fermions Part 1: Bare Matrix Elements and Physical Results, JHEP11 (2016) 001 [arXiv:1609.03334] [INSPIRE].
A. Cerri et al., Opportunities in Flavour Physics at the HL-LHC and HE-LHC, arXiv:1812.07638 [INSPIRE].
J.G. Korner, A.I. Onishchenko, A.A. Petrov and A.A. Pivovarov, \( {B}^0-{\overline{B}}^0 \)mixing beyond factorization, Phys. Rev. Lett.91 (2003) 192002 [hep-ph/0306032] [INSPIRE].
T. Mannel, B.D. Pecjak and A.A. Pivovarov, Sum rule estimate of the subleading non-perturbative contributions to \( {B}_s-{B}_s^{\ast } \)mixing, Eur. Phys. J.C 71 (2011) 1607 [hep-ph/0703244] [INSPIRE].
LHCb collaboration, Test of lepton universality using B +→ K + ℓ+ ℓ −decays, Phys. Rev. Lett.113 (2014) 151601 [arXiv:1406.6482] [INSPIRE].
LHCb collaboration, Test of lepton universality with B 0→ K *0 ℓ+ ℓ −decays, JHEP08 (2017) 055 [arXiv:1705.05802] [INSPIRE].
LHCb collaboration, Search for lepton-universality violation in B +→ K + ℓ+ ℓ −decays, Phys. Rev. Lett.122 (2019) 191801 [arXiv:1903.09252] [INSPIRE].
LHCb collaboration, Angular analysis and differential branching fraction of the decay \( {B}_s^0\to \phi {\mu}^{+}{\mu}^{-} \), JHEP09 (2015) 179 [arXiv:1506.08777] [INSPIRE].
CMS collaboration, Angular analysis of the decay B 0→ K ∗0μ +μ −from pp collisions at \( \sqrt{s} \)= 8 TeV, Phys. Lett.B 753 (2016) 424 [arXiv:1507.08126] [INSPIRE].
BaBar collaboration, Measurement of angular asymmetries in the decays B → K ∗ ℓ+ ℓ− , Phys. Rev.D 93 (2016) 052015 [arXiv:1508.07960] [INSPIRE].
Belle collaboration, Measurement of the Differential Branching Fraction and Forward-Backword Asymmetry for B → K (∗)ℓ + ℓ− , Phys. Rev. Lett.103 (2009) 171801 [arXiv:0904.0770] [INSPIRE].
CDF collaboration, Measurements of the Angular Distributions in the Decays B → K (∗)μ +μ −at CDF, Phys. Rev. Lett.108 (2012) 081807 [arXiv:1108.0695] [INSPIRE].
LHCb collaboration, Angular analysis of the B 0→ K ∗0μ +μ −decay using 3 fb −1of integrated luminosity, JHEP02 (2016) 104 [arXiv:1512.04442] [INSPIRE].
Belle collaboration, Angular analysis of B 0→ K ∗ (892)0 ℓ+ ℓ − , in Proceedings, LHCSki 2016— A First Discussion of 13 TeV Results, Obergurgl, Austria, 10–15 April 2016 (2016) [arXiv:1604.04042] [INSPIRE].
Belle collaboration, Lepton-Flavor-Dependent Angular Analysis of B → K * ℓ+ ℓ − , Phys. Rev. Lett.118 (2017) 111801 [arXiv:1612.05014] [INSPIRE].
CMS collaboration, Measurement of angular parameters from the decay B0→ K ∗0μ +μ −in proton-proton collisions at \( \sqrt{s} \) = 8 TeV, Phys. Lett.B 781 (2018) 517 [arXiv:1710.02846] [INSPIRE].
ATLAS collaboration, Angular analysis of \( {B}_d^0\to {K}^{\ast }{\mu}^{+}{\mu}^{-} \)decays in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, JHEP10 (2018) 047 [arXiv:1805.04000] [INSPIRE].
LHCb collaboration, Differential branching fractions and isospin asymmetries of B→K (*)𝜇+ 𝜇- decays, JHEP 06 (2014) 133 [arXiv:1403.8044] [INSPIRE].
J. Aebischer, W. Altmannshofer, D. Guadagnoli, M. Reboud, P. Stangl and D.M. Straub, B-decay discrepancies after Moriond 2019, arXiv:1903.10434 [INSPIRE].
M. Algueró et al., Emerging patterns of New Physics with and without Lepton Flavour Universal contributions, Eur. Phys. J.C 79 (2019) 714 [arXiv:1903.09578] [INSPIRE].
K. Kowalska, D. Kumar and E.M. Sessolo, Implications for new physics in b → sμμ transitions after recent measurements by Belle and LHCb, Eur. Phys. J.C 79 (2019) 840 [arXiv:1903.10932] [INSPIRE].
M. Ciuchini et al., New Physics in b → sℓ+ ℓ−confronts new data on Lepton Universality, Eur. Phys. J.C 79 (2019) 719 [arXiv:1903.09632] [INSPIRE].
P. Arnan, A. Crivellin, M. Fedele and F. Mescia, Generic loop effects of new scalars and fermions in b → sℓ + ℓ −and a vector-like 4thgeneration, JHEP06 (2019) 118 [arXiv:1904.05890] [INSPIRE].
G. D’Amico et al., Flavour anomalies after the R K ∗measurement, JHEP09 (2017) 010 [arXiv:1704.05438] [INSPIRE].
A.K. Alok, A. Dighe, S. Gangal and D. Kumar, Continuing search for new physics in b → sμμ decays: two operators at a time, JHEP06 (2019) 089 [arXiv:1903.09617] [INSPIRE].
J.A. Bagger, K.T. Matchev and R.-J. Zhang, QCD corrections to flavor changing neutral currents in the supersymmetric standard model, Phys. Lett.B 412 (1997) 77 [hep-ph/9707225] [INSPIRE].
I. Doršner, S. Fajfer, A. Greljo, J.F. Kamenik and N. Košnik, Physics of leptoquarks in precision experiments and at particle colliders, Phys. Rept.641 (2016) 1 [arXiv:1603.04993] [INSPIRE].
W. Altmannshofer, S. Gori, J. Martín-Albo, A. Sousa and M. Wallbank, Neutrino Tridents at DUNE, arXiv:1902.06765 [INSPIRE].
CCFR collaboration, Neutrino tridents and W Z interference, Phys. Rev. Lett.66 (1991) 3117 [INSPIRE].
DUNE collaboration, The DUNE Far Detector Interim Design Report Volume 1: Physics, Technology and Strategies, arXiv:1807.10334 [INSPIRE].
ATLAS collaboration, Search for new high-mass phenomena in the dilepton final state using 36 fb −1of proton-proton collision data at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP10 (2017) 182 [arXiv:1707.02424] [INSPIRE].
CMS collaboration, Search for third-generation scalar leptoquarks and heavy right-handed neutrinos in final states with two tau leptons and two jets in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, JHEP07 (2017) 121 [arXiv:1703.03995] [INSPIRE].
L. Di Luzio and M. Nardecchia, What is the scale of new physics behind the B-flavour anomalies?, Eur. Phys. J.C 77 (2017) 536 [arXiv:1706.01868] [INSPIRE].
L. Di Luzio, J.F. Kamenik and M. Nardecchia, Implications of perturbative unitarity for scalar di-boson resonance searches at LHC, Eur. Phys. J.C 77 (2017) 30 [arXiv:1604.05746] [INSPIRE].
B.C. Allanach, B. Gripaios and T. You, The case for future hadron colliders from B → K (∗)μ +μ −decays, JHEP03 (2018) 021 [arXiv:1710.06363] [INSPIRE].
Y. Afik, J. Cohen, E. Gozani, E. Kajomovitz and Y. Rozen, Establishing a Search for b → sℓ+ ℓ−Anomalies at the LHC, JHEP08 (2018) 056 [arXiv:1805.11402] [INSPIRE].
L. Di Luzio, M. Kirk and A. Lenz, \( {B}_s-{\overline{B}}_s \)mixing interplay with B anomalies, in 10th International Workshop on the CKM Unitarity Triangle (CKM 2018), Heidelberg, Germany, 17–21 September 2018 (2018) [arXiv:1811.12884] [INSPIRE].
A. Lenz and U. Nierste, Theoretical update of \( {B}_s-{\overline{B}}_s \)mixing, JHEP06 (2007) 072 [hep-ph/0612167] [INSPIRE].
HFLAV collaboration, HFLAV PDG 2018 results, http://www.slac.stanford.edu/xorg/hflav/osc/PDG_2018/.
CKMfitter collaboration, CKMfitter Summer 2018 results, http://ckmfitter.in2p3.fr/www/results/plots summer18/ckm_res summer18.html.
A.K. Alok, B. Bhattacharya, D. Kumar, J. Kumar, D. London and S.U. Sankar, New physics in b → sμ +μ −: Distinguishing models through CP-violating effects, Phys. Rev.D 96 (2017) 015034 [arXiv:1703.09247] [INSPIRE].
J. Alda, J. Guasch and S. Penaranda, Some results on Lepton Flavour Universality Violation, Eur. Phys. J.C 79 (2019) 588 [arXiv:1805.03636] [INSPIRE].
D.M. Straub, flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond, arXiv:1810.08132 [INSPIRE].
W. Altmannshofer, C. Niehoff, P. Stangl and D.M. Straub, Status of the B → K ∗μ +μ −anomaly after Moriond 2017, Eur. Phys. J.C 77 (2017) 377 [arXiv:1703.09189] [INSPIRE].
G. Hiller and M. Schmaltz, Diagnosing lepton-nonuniversality in b → sℓℓ, JHEP02 (2015) 055 [arXiv:1411.4773] [INSPIRE].
A. Carmona and F. Goertz, Recent B physics anomalies: a first hint for compositeness?, Eur. Phys. J.C 78 (2018) 979 [arXiv:1712.02536] [INSPIRE].
M. Bordone, C. Cornella, J. Fuentes-Martín and G. Isidori, Low-energy signatures of the PS3model: from B-physics anomalies to LFV, JHEP10 (2018) 148 [arXiv:1805.09328] [INSPIRE].
L. Di Luzio, A. Greljo and M. Nardecchia, Gauge leptoquark as the origin of B-physics anomalies, Phys. Rev.D 96 (2017) 115011 [arXiv:1708.08450] [INSPIRE].
L. Calibbi, A. Crivellin and T. Li, Model of vector leptoquarks in view of the B-physics anomalies, Phys. Rev.D 98 (2018) 115002 [arXiv:1709.00692] [INSPIRE].
M. Bordone, C. Cornella, J. Fuentes-Martin and G. Isidori, A three-site gauge model for flavor hierarchies and flavor anomalies, Phys. Lett.B 779 (2018) 317 [arXiv:1712.01368] [INSPIRE].
R. Barbieri and A. Tesi, B-decay anomalies in Pati-Salam SU(4), Eur. Phys. J.C 78 (2018) 193 [arXiv:1712.06844] [INSPIRE].
M. Blanke and A. Crivellin, B Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background, Phys. Rev. Lett.121 (2018) 011801 [arXiv:1801.07256] [INSPIRE].
L. Di Luzio, J. Fuentes-Martin, A. Greljo, M. Nardecchia and S. Renner, Maximal Flavour Violation: a Cabibbo mechanism for leptoquarks, JHEP11 (2018) 081 [arXiv:1808.00942] [INSPIRE].
CKMfitter Group collaboration, CP violation and the CKM matrix: Assessing the impact of the asymmetric B factories, Eur. Phys. J.C 41 (2005) 1 [hep-ph/0406184] [INSPIRE].
CKMfitter collaboration, CKMlive, http://ckmlive.in2p3.fr.
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].
Particle Data Group collaboration, PDG 2019 update, http://pdg.lbl.gov/.
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, RunDec: A Mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun.133 (2000) 43 [hep-ph/0004189] [INSPIRE].
F. Herren and M. Steinhauser, Version 3 of RunDec and CRunDec, Comput. Phys. Commun.224 (2018) 333 [arXiv:1703.03751] [INSPIRE].
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Di Luzio, L., Kirk, M., Lenz, A. et al. ∆Ms theory precision confronts flavour anomalies. J. High Energ. Phys. 2019, 9 (2019). https://doi.org/10.1007/JHEP12(2019)009
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DOI: https://doi.org/10.1007/JHEP12(2019)009