Abstract
The lifetimes of bottom and charmed hadrons are analyzed within the framework of the heavy quark expansion (HQE). Lifetime differences arise from the spectator effects such as weak W-annihilation and Pauli interference. Spectator effects originating from dimension-7 four-quark operators are derived. Hadronic matrix elements of four-quark operators are parameterized in a model-independent way. Using the dimension-6 bag parameters recently determined from HQET sum rules and the vacuum insertion approximation for meson matrix elements of dimension-7 operators, the calculated B meson lifetime ratios τ(B+)/τ(B 0 d ) = 1.074 + 0.017− 0.016 and τ(B 0 s )/τ(B 0 d ) = 0.9962 ± 0.0024 are in excellent agreement with experiment. Likewise, based on the quark model evaluation of baryon matrix elements, the resulting baryon lifetime ratios τ(Ξ − b )/τ(Λ 0 b ), τ(Ξ − b )/τ(Ξ 0 b ), τ(Ω − b )/τ(Ξ − b ) and the Λb − B0 lifetime ratio τ(Λ 0 b )/τ(B 0 d ) = 0.953 also agree well with the data. Contrary to the bottom hadron sector where the HQE in 1/mb works well, the HQE to 1/m 3 c fails to give a satisfactory description of the lifetimes of both charmed mesons and charmed baryons. This calls for the subleading 1/mQ corrections to spectator effects. The relevant dimension-7 spectator effects are in the right direction for explaining the large lifetime ratio of τ(Ξ + c )/τ(Λ + c ). However, the destructive 1/mc corrections to Γ(Ω 0 c ) are too large to justify the validity of the HQE, namely, the predicted Pauli interference and semileptonic rates for Ω 0 c become negative. Demanding these rates to be positive for a sensible HQE, we find the lifetime pattern τ(Ξ + c ) > τ(Ω 0 c ) > τ(Λ + c ) > τ(Ξ 0 c ), contrary to the current hierarchy τ(Ξ + c ) > τ(Λ + c ) > τ(Ξ 0 c ) > τ(Ω 0 c ). We conclude that the Ω 0 c , which is naively expected to be shortest-lived in the charmed baryon system owing to the large constructive Pauli interference, could live longer than the Λ + c due to the suppression from 1/mc corrections arising from dimension-7 four-quark operators. The new charmed baryon lifetime pattern needs to be tested in forthcoming experiments.
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References
I.I.Y. Bigi, N.G. Uraltsev and A.I. Vainshtein, Nonperturbative corrections to inclusive beauty and charm decays: QCD versus phenomenological models, Phys. Lett. B 293 (1992) 430 [Erratum ibid. B 297 (1992) 477] [hep-ph/9207214] [INSPIRE].
B. Blok and M.A. Shifman, The rule of discarding 1/N c in inclusive weak decays. 1, Nucl. Phys. B 399 (1993) 441 [hep-ph/9207236] [INSPIRE].
B. Blok and M.A. Shifman, The rule of discarding 1/N c in inclusive weak decays. 2, Nucl. Phys. B 399 (1993) 459 [hep-ph/9209289] [INSPIRE].
B. Blok and M.A. Shifman, Lifetimes of charmed hadrons revisited. Facts and fancy, in Tau charm factory. Proceedings, 3rd Workshop, Marbella, Spain, 1–6 June 1993, J. Kirkby and R. Kirkby eds., Editions Frontieres, France, (1994) [hep-ph/9311331] [INSPIRE].
N. Bilic, B. Guberina and J. Trampetic, Pauli interference effect in D + lifetime, Nucl. Phys. B 248 (1984) 261 [INSPIRE].
M.A. Shifman and M.B. Voloshin, Preasymptotic effects in inclusive weak decays of charmed particles, Sov. J. Nucl. Phys. 41 (1985) 120 [Yad. Fiz. 41 (1985) 187] [INSPIRE].
B. Guberina, R. Rückl and J. Trampetic, Charmed baryon lifetime differences, Z. Phys. C 33 (1986) 297 [INSPIRE].
A. Lenz, Lifetimes and heavy quark expansion, Int. J. Mod. Phys. A 30 (2015) 1543005 [arXiv:1405.3601] [INSPIRE].
J. Chay, H. Georgi and B. Grinstein, Lepton energy distributions in heavy meson decays from QCD, Phys. Lett. B 247 (1990) 399 [INSPIRE].
J. Chay and S.-J. Rey, Instanton contribution to \( B\to {X}_{\mu }e\overline{\nu} \) decay, Z. Phys. C 68 (1995) 431 [hep-ph/9404214] [INSPIRE].
M.E. Luke, Effects of subleading operators in the heavy quark effective theory, Phys. Lett. B 252 (1990) 447 [INSPIRE].
M. Neubert and C.T. Sachrajda, Spectator effects in inclusive decays of beauty hadrons, Nucl. Phys. B 483 (1997) 339 [hep-ph/9603202] [INSPIRE].
Particle Data Group collaboration, M. Tanabashi et al., Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
Particle Data Group collaboration, R.M. Barnett et al., Review of particle physics, Phys. Rev. D 54 (1996) 1 [INSPIRE].
LEP B lifetime working group webpage, http://lepbosc.web.cern.ch/LEPBOSC/archive_LEPBOSC/lifetimes/lepblife.html.
Heavy Flavor Averaging Group (HFAG) collaboration, J. Alexander et al., Averages of b-hadron properties as of summer 2004, hep-ex/0412073 [INSPIRE].
G. Altarelli, G. Martinelli, S. Petrarca and F. Rapuano, Failure of local duality in inclusive nonleptonic heavy flavor decays, Phys. Lett. B 382 (1996) 409 [hep-ph/9604202] [INSPIRE].
H.-Y. Cheng, A phenomenological analysis of heavy hadron lifetimes, Phys. Rev. D 56 (1997) 2783 [hep-ph/9704260] [INSPIRE].
T. Ito, M. Matsuda and Y. Matsui, New possibility of solving the problem of lifetime ratio τ(Λb)/τ(B d), Prog. Theor. Phys. 99 (1998) 271 [hep-ph/9705402] [INSPIRE].
D0 collaboration, V.M. Abazov et al., Measurement of the Λ 0 b lifetime in the decay Λ 0 b → J/ψΛ0 with the DO detector, Phys. Rev. Lett. 94 (2005) 102001 [hep-ex/0410054] [INSPIRE].
CDF collaboration, A. Abulencia et al., Measurement of the Λ 0 b lifetime in Λ 0 b → J/ψΛ0 in \( p\overline{p} \) collisions at \( \sqrt{s}=1.96 \) TeV, Phys. Rev. Lett. 98 (2007) 122001 [hep-ex/0609021] [INSPIRE].
M. Kirk, A. Lenz and T. Rauh, Dimension-six matrix elements for meson mixing and lifetimes from sum rules, JHEP 12 (2017) 068 [arXiv:1711.02100] [INSPIRE].
F. Gabbiani, A.I. Onishchenko and A.A. Petrov, Λb lifetime puzzle in heavy quark expansion, Phys. Rev. D 68 (2003) 114006 [hep-ph/0303235] [INSPIRE].
F. Gabbiani, A.I. Onishchenko and A.A. Petrov, Spectator effects and lifetimes of heavy hadrons, Phys. Rev. D 70 (2004) 094031 [hep-ph/0407004] [INSPIRE].
M. Beneke, G. Buchalla and I. Dunietz, Width difference in the \( {B}_s-{\overline{B}}_s \) system, Phys. Rev. D 54 (1996) 4419 [Erratum ibid. D 83 (2011) 119902] [hep-ph/9605259] [INSPIRE].
A. Lenz and T. Rauh, D-meson lifetimes within the heavy quark expansion, Phys. Rev. D 88 (2013) 034004 [arXiv:1305.3588] [INSPIRE].
M. Neubert, B decays and CP-violation, Int. J. Mod. Phys. A 11 (1996) 4173 [hep-ph/9604412] [INSPIRE].
E.E. Jenkins, Heavy baryon masses in the 1/m Q and 1/N c expansions, Phys. Rev. D 54 (1996) 4515 [hep-ph/9603449] [INSPIRE].
E.E. Jenkins, Update of heavy baryon mass predictions, Phys. Rev. D 55 (1997) 10 [hep-ph/9609404] [INSPIRE].
P. Gambino, K.J. Healey and S. Turczyk, Taming the higher power corrections in semileptonic B decays, Phys. Lett. B 763 (2016) 60 [arXiv:1606.06174] [INSPIRE].
A.F. Falk, Z. Ligeti, M. Neubert and Y. Nir, Heavy quark expansion for the inclusive decay \( \overline{B}\to \tau \overline{\nu}X \), Phys. Lett. B 326 (1994) 145[hep-ph/9401226] [INSPIRE].
T. Mannel, A.V. Rusov and F. Shahriaran, Inclusive semitauonic B decays to order \( \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^3/{m}_b^3\right) \), Nucl. Phys. B 921 (2017) 211 [arXiv:1702.01089] [INSPIRE].
M.A. Shifman and M.B. Voloshin, On annihilation of mesons built from heavy and light quark and \( {\overline{B}}^0\leftrightarrow {B}^0 \) oscillations, Sov. J. Nucl. Phys. 45 (1987) 292 [Yad. Fiz. 45 (1987) 463] [INSPIRE].
M.B. Voloshin, Spectator effects in semileptonic decay of charmed baryons, Phys. Lett. B 385 (1996) 369 [hep-ph/9604335] [INSPIRE].
T. Mannel, S. Turczyk and N. Uraltsev, Higher order power corrections in inclusive B decays, JHEP 11 (2010) 109 [arXiv:1009.4622] [INSPIRE].
H.-K. Quang and X.-Y. Pham, Mass effects in QCD corrections of weak decays, Phys. Lett. B 122 (1983) 297 [INSPIRE].
H.-K. Quang and X.-Y. Pham, Exact one gluon corrections for inclusive weak processes, Annals Phys. 155 (1984) 202 [INSPIRE].
Y. Nir, The mass ratio m c /m b in semileptonic B decays, Phys. Lett. B 221 (1989) 184 [INSPIRE].
T. Becher, H. Boos and E. Lunghi, Kinetic corrections to \( B\to {X}_c\ell \overline{\nu} \) at one loop, JHEP 12 (2007) 062 [arXiv:0708.0855] [INSPIRE].
A. Alberti, T. Ewerth, P. Gambino and S. Nandi, Kinetic operator effects in \( \overline{B}\to {X}_c\ell \nu \) at O(α s), Nucl. Phys. B 870 (2013) 16 [arXiv:1212.5082] [INSPIRE].
A. Alberti, P. Gambino and S. Nandi, Perturbative corrections to power suppressed effects in semileptonic B decays, JHEP 01 (2014) 147 [arXiv:1311.7381] [INSPIRE].
T. Mannel, A.A. Pivovarov and D. Rosenthal, Inclusive weak decays of heavy hadrons with power suppressed terms at NLO, Phys. Rev. D 92 (2015) 054025 [arXiv:1506.08167] [INSPIRE].
M. Beneke and V.M. Braun, Heavy quark effective theory beyond perturbation theory: renormalons, the pole mass and the residual mass term, Nucl. Phys. B 426 (1994) 301 [hep-ph/9402364] [INSPIRE].
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev and A.I. Vainshtein, The pole mass of the heavy quark. Perturbation theory and beyond, Phys. Rev. D 50 (1994) 2234 [hep-ph/9402360] [INSPIRE].
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev and A.I. Vainshtein, Sum rules for heavy flavor transitions in the SV limit, Phys. Rev. D 52 (1995) 196 [hep-ph/9405410] [INSPIRE].
I.I.Y. Bigi, M.A. Shifman, N. Uraltsev and A.I. Vainshtein, High power n of m b in beauty widths and n = 5 → ∞ limit, Phys. Rev. D 56 (1997) 4017 [hep-ph/9704245] [INSPIRE].
A.H. Hoang, Z. Ligeti and A.V. Manohar, B decay and the ϒ mass, Phys. Rev. Lett. 82 (1999) 277 [hep-ph/9809423] [INSPIRE].
F. Krinner, A. Lenz and T. Rauh, The inclusive decay \( b\to c\overline{c}s \) revisited, Nucl. Phys. B 876 (2013) 31 [arXiv:1305.5390] [INSPIRE].
V. Chernyak, Calculation of the D and B meson lifetimes and the unitarity triangle parameters, Nucl. Phys. B 457 (1995) 96 [hep-ph/9503208] [INSPIRE].
P. Colangelo and F. De Fazio, Role of four quark operators in the inclusive Λb decays, Phys. Lett. B 387 (1996) 371 [hep-ph/9604425] [INSPIRE].
M.S. Baek, J. Lee, C. Liu and H.S. Song, Four quark operators relevant to B meson lifetimes from QCD sum rules, Phys. Rev. D 57 (1998) 4091 [hep-ph/9709386] [INSPIRE].
H.-Y. Cheng and K.-C. Yang, Nonspectator effects and B meson lifetimes from a field theoretic calculation, Phys. Rev. D 59 (1999) 014011 [hep-ph/9805222] [INSPIRE].
UKQCD collaboration, M. Di Pierro and C.T. Sachrajda, A lattice study of spectator effects in inclusive decays of B mesons, Nucl. Phys. B 534 (1998) 373 [hep-lat/9805028] [INSPIRE].
D. Becirevic, Theoretical progress in describing the B meson lifetimes, PoS(HEP2001)098, (2001) [hep-ph/0110124] [INSPIRE].
A.G. Grozin and R.N. Lee, Three-loop HQET vertex diagrams for \( {B}^0\hbox{-} {\overline{B}}^0 \) mixing, JHEP 02 (2009) 047 [arXiv:0812.4522] [INSPIRE].
A.G. Grozin, R. Klein, T. Mannel and A.A. Pivovarov, \( {B}^0\hbox{-} {\overline{B}}^0 \) mixing at next-to-leading order, Phys. Rev. D 94 (2016) 034024 [arXiv:1606.06054] [INSPIRE].
G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380] [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 77 (2017) 112 [arXiv:1607.00299] [INSPIRE].
B. Guberina, S. Nussinov, R.D. Peccei and R. Rückl, D meson lifetimes and decays, Phys. Lett. B 89 (1979) 111 [INSPIRE].
Y. Koide, Inclusive studies of charmed meson decays and SU(4) 20-plet dominance model, Phys. Rev. D 20 (1979) 1739 [Erratum ibid. D 21 (1980) 853] [INSPIRE].
A. Chodos, R.L. Jaffe, K. Johnson and C.B. Thorn, Baryon structure in the bag theory, Phys. Rev. D 10 (1974) 2599 [INSPIRE].
T.A. DeGrand, R.L. Jaffe, K. Johnson and J.E. Kiskis, Masses and other parameters of the light hadrons, Phys. Rev. D 12 (1975) 2060 [INSPIRE].
T.A. DeGrand and R.L. Jaffe, Excited states of confined quarks, Annals Phys. 100 (1976) 425 [INSPIRE].
T.A. DeGrand, Excited states of confined quarks. 2, Annals Phys. 101 (1976) 496 [INSPIRE].
M. Beneke, G. Buchalla, C. Greub, A. Lenz and U. Nierste, The B + ‐ B 0 d lifetime difference beyond leading logarithms, Nucl. Phys. B 639 (2002) 389 [hep-ph/0202106] [INSPIRE].
H.-Y. Cheng and B. Tseng, Nonleptonic weak decays of charmed baryons, Phys. Rev. D 46 (1992) 1042 [Erratum ibid. D 55 (1997) 1697] [INSPIRE].
A. De Rujula, H. Georgi and S.L. Glashow, Hadron masses in a gauge theory, Phys. Rev. D 12 (1975) 147 [INSPIRE].
J.L. Cortes and J. Sanchez Guillen, The lifetimes of charmed baryons, Phys. Rev. D 24 (1981) 2982 [INSPIRE].
J.L. Rosner, Enhancement of the Λb decay rate, Phys. Lett. B 379 (1996) 267 [hep-ph/9602265] [INSPIRE].
D. Ebert, R.N. Faustov and V.O. Galkin, Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture, Phys. Rev. D 84 (2011) 014025 [arXiv:1105.0583] [INSPIRE].
H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.C. Lin, T.-M. Yan and H.-L. Yu, Heavy flavor conserving nonleptonic weak decays of heavy baryons, Phys. Rev. D 46 (1992) 5060 [INSPIRE].
H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.-C. Lin, T.-M. Yan and H.-L. Yu, Heavy-flavor-conserving hadronic weak decays of heavy baryons, JHEP 03 (2016) 028 [arXiv:1512.01276] [INSPIRE].
LHCb collaboration, Evidence for the strangeness-changing weak decay Ξ − b → Λ 0 b π −, Phys. Rev. Lett. 115 (2015) 241801 [arXiv:1510.03829] [INSPIRE].
HFLAV collaboration, Y. Amhis et al., 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].
Heavy Flavor Averaging Group (HFLAV) online update webpage, http://www.slac.stanford.edu/xorg/hfag.
A. Le Yaouanc et al., Hadron transitions in the quark model, Gordon and Breach, New York, U.S.A., (1987).
G.S. Abrams et al., Observation of charmed baryon production in e + e − annihilation, Phys. Rev. Lett. 44 (1980) 10 [INSPIRE].
BESIII collaboration, M. Ablikim et al., Measurement of the absolute branching fraction of the inclusive semileptonic Λ + c decay, arXiv:1805.09060 [INSPIRE].
M.A. Shifman and M.B. Voloshin, Hierarchy of lifetimes of charmed and beautiful hadrons, Sov. Phys. JETP 64 (1986) 698 [Zh. Eksp. Teor. Fiz. 91 (1986) 1180] [INSPIRE].
G. Bellini, I.I.Y. Bigi and P.J. Dornan, Lifetimes of charm and beauty hadrons, Phys. Rept. 289 (1997) 1 [INSPIRE].
B. Guberina and B. Melić, Inclusive charmed baryon decays and lifetimes, Eur. Phys. J. C 2 (1998) 697 [hep-ph/9704445] [INSPIRE].
B. Guberina, B. Melić and H. Stefancic, Lifetime difference pattern of heavy hadrons, Phys. Lett. B 484 (2000) 43 [hep-ph/0004264] [INSPIRE].
B. Guberina and H. Stefancic, Cabibbo suppressed decays and the Ξ + c lifetime, Phys. Rev. D 65 (2002) 114004 [hep-ph/0202080] [INSPIRE].
A. Babic, B. Guberina, B. Melić and H. Stefancic, Cabibbo-suppressed decays of the Ω 0 c : feedback to the Ξ + c lifetime, Phys. Rev. D 70 (2004) 117501 [hep-ph/0406183] [INSPIRE].
LHCb collaboration, Measurement of the Ω 0 c baryon lifetime, Phys. Rev. Lett. 121 (2018) 092003 [arXiv:1807.02024] [INSPIRE].
H.Y. Cheng, Charmed hadronic decay, talk presented at the International Workshop on Physics at Future High Intensity Collider @2–7 GeV, http://cicpi.ustc.edu.cn/hiepa2018, Huairou, Beijing, China, 19–21 March 2018.
LHCb collaboration, Measurement of the lifetime of the doubly charmed baryon Ξ + + cc , Phys. Rev. Lett. 121 (2018) 052002 [arXiv:1806.02744] [INSPIRE].
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Cheng, HY. Phenomenological study of heavy hadron lifetimes. J. High Energ. Phys. 2018, 14 (2018). https://doi.org/10.1007/JHEP11(2018)014
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DOI: https://doi.org/10.1007/JHEP11(2018)014