Abstract
We present a detailed theoretical analysis of very rare, exclusive hadronic decays of the electroweak gauge bosons V = W, Z from first principles of QCD. Our main focus is on the radiative decays V → Mγ, in which M is a pseudoscalar or vector meson. At leading order in an expansion in powers of ΛQCD/m V the decay amplitudes can be factorized into convolutions of calculable hard-scattering coefficients with the leading-twist light-cone distribution amplitude of the meson M. Power corrections to the decay rates arise first at order (ΛQCD/m V )2. They can be estimated in terms of higher-twist distribution amplitudes and are predicted to be tiny. We include one-loop \( \mathcal{O}\left({\alpha}_s\right) \) radiative corrections to the hard-scattering coefficients and perform the resummation of large logarithms (α s ln(m 2 v /μ 20 ))n (with μ 0 ∼ 1 GeV a typical hadronic scale) to all orders in perturbation theory. Evolution effects have an important impact both numerically and conceptually, since they reduce the sensitivity to poorly determined hadronic parameters. We present detailed numerical predictions and error estimates, which can serve as benchmarks for future precision measurements. We also present an exploratory study of the weak radiative decays Z → MW. Some of the decay modes studied here have branching ratios large enough to be accessible in the high-luminosity run of the LHC. Many of them can be measured with high accuracy at a future lepton collider. This will provide stringent tests of the QCD factorization formalism and enable novel searches for new physics.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
G.P. Lepage and S.J. Brodsky, Exclusive Processes in Quantum Chromodynamics: Evolution Equations for Hadronic Wave Functions and the Form-Factors of Mesons, Phys. Lett. B 87 (1979) 359 [INSPIRE].
G.P. Lepage and S.J. Brodsky, Exclusive Processes in Perturbative Quantum Chromodynamics, Phys. Rev. D 22 (1980) 2157 [INSPIRE].
A.V. Efremov and A.V. Radyushkin, Asymptotical Behavior of Pion Electromagnetic Form-Factor in QCD, Theor. Math. Phys. 42 (1980) 97 [INSPIRE].
A.V. Efremov and A.V. Radyushkin, Factorization and Asymptotical Behavior of Pion Form-Factor in QCD, Phys. Lett. B 94 (1980) 245 [INSPIRE].
V.L. Chernyak and A.R. Zhitnitsky, Asymptotic Behavior of Exclusive Processes in QCD, Phys. Rept. 112 (1984) 173 [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for B → ππ decays: Strong phases and CP-violation in the heavy quark limit, Phys. Rev. Lett. 83 (1999) 1914 [hep-ph/9905312] [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for exclusive, nonleptonic B meson decays: General arguments and the case of heavy light final states, Nucl. Phys. B 591 (2000) 313 [hep-ph/0006124] [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization in B → πK, ππ decays and extraction of Wolfenstein parameters, Nucl. Phys. B 606 (2001) 245 [hep-ph/0104110] [INSPIRE].
M. Beneke and M. Neubert, QCD factorization for B → PP and B → PV decays, Nucl. Phys. B 675 (2003) 333 [hep-ph/0308039] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [INSPIRE].
M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].
S.S. Agaev, V.M. Braun, N. Offen and F.A. Porkert, Light Cone Sum Rules for the π 0 γ * γ Form Factor Revisited, Phys. Rev. D 83 (2011) 054020 [arXiv:1012.4671] [INSPIRE].
M. Mangano and T. Melia, Rare exclusive hadronic W decays in a \( t\overline{t} \) environment, arXiv:1410.7475 [INSPIRE].
A. Blondel, A. Chao, W. Chou, J. Gao, D. Schulte and K. Yokoya, Report of the ICFA Beam Dynamics Workshop ‘Accelerators for a Higgs Factory: Linear vs. Circular’ (HF2012), arXiv:1302.3318 [INSPIRE].
G. Isidori, A.V. Manohar and M. Trott, Probing the nature of the Higgs-like Boson via h → Vℱ decays, Phys. Lett. B 728 (2014) 131 [arXiv:1305.0663] [INSPIRE].
G.T. Bodwin, F. Petriello, S. Stoynev and M. Velasco, Higgs boson decays to quarkonia and the \( H\overline{c}c \) coupling, Phys. Rev. D 88 (2013) 053003 [arXiv:1306.5770] [INSPIRE].
A.L. Kagan, G. Perez, F. Petriello, Y. Soreq, S. Stoynev and J. Zupan, An Exclusive Window onto Higgs Yukawa Couplings, Phys. Rev. Lett. 114 (2015) 101802 [arXiv:1406.1722] [INSPIRE].
G.T. Bodwin, H.S. Chung, J.-H. Ee, J. Lee and F. Petriello, Relativistic corrections to Higgs boson decays to quarkonia, Phys. Rev. D 90 (2014) 113010 [arXiv:1407.6695] [INSPIRE].
D.-N. Gao, A note on Higgs decays into Z boson and J/Ψ(Υ), Phys. Lett. B 737 (2014) 366 [arXiv:1406.7102] [INSPIRE].
B. Bhattacharya, A. Datta and D. London, Probing New Physics in Higgs Couplings to Fermions using an Angular Analysis, Phys. Lett. B 736 (2014) 421 [arXiv:1407.0695] [INSPIRE].
ATLAS collaboration, Search for Higgs and Z Boson Decays to J/ψγ and Υ(nS)γ with the ATLAS Detector, arXiv:1501.03276 [INSPIRE].
L. Arnellos, W.J. Marciano and Z. Parsa, Radiative Decays W ± → ρ ± γ and Z 0 → ρ 0 γ, Nucl. Phys. B 196 (1982) 378 [INSPIRE].
A.V. Manohar, The decays Z → Wπ and Z → γπ, Phys. Lett. B 244 (1990) 101 [INSPIRE].
B. Guberina, J.H. Kuhn, R.D. Peccei and R. Ruckl, Rare decays of the Z 0, Nucl. Phys. B 174 (1980) 317 [INSPIRE].
T.-C. Huang and F. Petriello, Rare exclusive decays of the Z-boson revisited, arXiv:1411.5924 [INSPIRE].
M. Jacob and T.T. Wu, The Decay Z → π 0 γ, Phys. Lett. B 232 (1989) 529 [INSPIRE].
Y.Y. Keum and X.-Y. Pham, Possible huge enhancement in the radiative decay of the weak W boson into the charmed D s meson, Mod. Phys. Lett. A 9 (1994) 1545 [hep-ph/9303300] [INSPIRE].
C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
R.J. Hill and M. Neubert, Spectator interactions in soft collinear effective theory, Nucl. Phys. B 657 (2003) 229 [hep-ph/0211018] [INSPIRE].
M. Beneke and M. Neubert, Flavor singlet B decay amplitudes in QCD factorization, Nucl. Phys. B 651 (2003) 225 [hep-ph/0210085] [INSPIRE].
M. König and M.Neubert, in preparation.
S.W. Bosch, R.J. Hill, B.O. Lange and M. Neubert, Factorization and Sudakov resummation in leptonic radiative B decay, Phys. Rev. D 67 (2003) 094014 [hep-ph/0301123] [INSPIRE].
T. Becher, R.J. Hill and M. Neubert, Factorization in B → Vγ decays, Phys. Rev. D 72 (2005) 094017 [hep-ph/0503263] [INSPIRE].
T. Becher, R.J. Hill and M. Neubert, Soft collinear messengers: A new mode in soft collinear effective theory, Phys. Rev. D 69 (2004) 054017 [hep-ph/0308122] [INSPIRE].
T. Becher, R.J. Hill, B.O. Lange and M. Neubert, External operators and anomalous dimensions in soft collinear effective theory, Phys. Rev. D 69 (2004) 034013 [hep-ph/0309227] [INSPIRE].
V.M. Braun and I.E. Filyanov, Conformal Invariance and Pion Wave Functions of Nonleading Twist, Z. Phys. C 48 (1990) 239 [INSPIRE].
A. Ali, V.M. Braun and H. Simma, Exclusive radiative B decays in the light cone QCD sum rule approach, Z. Phys. C 63 (1994) 437 [hep-ph/9401277] [INSPIRE].
P. Ball and V.M. Braun, The ρ meson light cone distribution amplitudes of leading twist revisited, Phys. Rev. D 54 (1996) 2182 [hep-ph/9602323] [INSPIRE].
P. Ball, V.M. Braun, Y. Koike and K. Tanaka, Higher twist distribution amplitudes of vector mesons in QCD: Formalism and twist 3 distributions, Nucl. Phys. B 529 (1998) 323 [hep-ph/9802299] [INSPIRE].
M. Beneke and T. Feldmann, Symmetry breaking corrections to heavy to light B meson form-factors at large recoil, Nucl. Phys. B 592 (2001) 3 [hep-ph/0008255] [INSPIRE].
S. Wandzura and F. Wilczek, Sum Rules for Spin Dependent Electroproduction: Test of Relativistic Constituent Quarks, Phys. Lett. B 72 (1977) 195 [INSPIRE].
R. Arthur et al., Lattice Results for Low Moments of Light Meson Distribution Amplitudes, Phys. Rev. D 83 (2011) 074505 [arXiv:1011.5906] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001.
M. Neubert and B. Stech, Nonleptonic weak decays of B mesons, Adv. Ser. Direct. High Energy Phys. 15 (1998) 294 [hep-ph/9705292] [INSPIRE].
M. Dimou, J. Lyon and R. Zwicky, Exclusive Chromomagnetism in heavy-to-light FCNCs, Phys. Rev. D 87 (2013) 074008 [arXiv:1212.2242] [INSPIRE].
P. Ball and G.W. Jones, Twist-3 distribution amplitudes of K * and ϕ mesons, JHEP 03 (2007) 069 [hep-ph/0702100] [INSPIRE].
P. Ball and R. Zwicky, SU(3) breaking of leading-twist K and K * distribution amplitudes: A reprise, Phys. Lett. B 633 (2006) 289 [hep-ph/0510338] [INSPIRE].
P. Ball, V.M. Braun and A. Lenz, Higher-twist distribution amplitudes of the K meson in QCD, JHEP 05 (2006) 004 [hep-ph/0603063] [INSPIRE].
P. Ball and R. Zwicky, Operator relations for SU(3) breaking contributions to K and K * distribution amplitudes, JHEP 02 (2006) 034 [hep-ph/0601086] [INSPIRE].
A.P. Bakulev, K. Passek-Kumericki, W. Schroers and N.G. Stefanis, Pion form-factor in QCD: From nonlocal condensates to NLO analytic perturbation theory, Phys. Rev. D 70 (2004) 033014 [Erratum ibid. D 70 (2004) 079906] [hep-ph/0405062] [INSPIRE].
A.P. Bakulev, S.V. Mikhailov and N.G. Stefanis, QCD based pion distribution amplitudes confronting experimental data, Phys. Lett. B 508 (2001) 279 [Erratum ibid. B 590 (2004) 309-310] [hep-ph/0103119] [INSPIRE].
S.S. Agaev, V.M. Braun, N. Offen and F.A. Porkert, BELLE Data on the π 0 γ * γ Form Factor: A Game Changer?, Phys. Rev. D 86 (2012) 077504 [arXiv:1206.3968] [INSPIRE].
BaBar collaboration, B. Aubert et al., Measurement of the γγ * → π 0 transition form factor, Phys. Rev. D 80 (2009) 052002 [arXiv:0905.4778] [INSPIRE].
Belle collaboration, S. Uehara et al., Measurement of γγ * → π 0 transition form factor at Belle, Phys. Rev. D 86 (2012) 092007 [arXiv:1205.3249] [INSPIRE].
W.E. Caswell and G.P. Lepage, Effective Lagrangians for Bound State Problems in QED, QCD and Other Field Theories, Phys. Lett. B 167 (1986) 437 [INSPIRE].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
V.V. Braguta, A.K. Likhoded and A.V. Luchinsky, The study of leading twist light cone wave function of η c meson, Phys. Lett. B 646 (2007) 80 [hep-ph/0611021] [INSPIRE].
G.T. Bodwin, H.S. Chung, D. Kang, J. Lee and C. Yu, Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium, Phys. Rev. D 77 (2008) 094017 [arXiv:0710.0994] [INSPIRE].
H.S. Chung, J. Lee and C. Yu, NRQCD matrix elements for S-wave bottomonia and Γ[η b (nS) → γγ] with relativistic corrections, Phys. Lett. B 697 (2011) 48 [arXiv:1011.1554] [INSPIRE].
A. Czarnecki and K. Melnikov, Two loop QCD corrections to the heavy quark pair production cross-section in e + e − annihilation near the threshold, Phys. Rev. Lett. 80 (1998) 2531 [hep-ph/9712222] [INSPIRE].
M. Beneke, A. Signer and V.A. Smirnov, Two loop correction to the leptonic decay of quarkonium, Phys. Rev. Lett. 80 (1998) 2535 [hep-ph/9712302] [INSPIRE].
M. Beneke et al., Leptonic decay of the Υ(1S) meson at third order in QCD, Phys. Rev. Lett. 112 (2014) 151801 [arXiv:1401.3005] [INSPIRE].
M. Neubert, Heavy quark symmetry, Phys. Rept. 245 (1994) 259 [hep-ph/9306320] [INSPIRE].
A.G. Grozin and M. Neubert, Asymptotics of heavy meson form-factors, Phys. Rev. D 55 (1997) 272 [hep-ph/9607366] [INSPIRE].
S.J. Lee and M. Neubert, Model-independent properties of the B-meson distribution amplitude, Phys. Rev. D 72 (2005) 094028 [hep-ph/0509350] [INSPIRE].
V.M. Braun, D.Y. Ivanov and G.P. Korchemsky, The B meson distribution amplitude in QCD, Phys. Rev. D 69 (2004) 034014 [hep-ph/0309330] [INSPIRE].
P. Ball, G.W. Jones and R. Zwicky, B → Vγ beyond QCD factorisation, Phys. Rev. D 75 (2007) 054004 [hep-ph/0612081] [INSPIRE].
HPQCD collaboration, R.J. Dowdall, C.T.H. Davies, R.R. Horgan, C.J. Monahan and J. Shigemitsu, B-Meson Decay Constants from Improved Lattice Nonrelativistic QCD with Physical u, d, s and c Quarks, Phys. Rev. Lett. 110 (2013) 222003 [arXiv:1302.2644] [INSPIRE].
ALPHA collaboration, F. Bernardoni et al., Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks, Phys. Lett. B 735 (2014) 349 [arXiv:1404.3590] [INSPIRE].
B.O. Lange and M. Neubert, Renormalization group evolution of the B meson light cone distribution amplitude, Phys. Rev. Lett. 91 (2003) 102001 [hep-ph/0303082] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
G. Bonneau, Preserving Canonical Ward Identities in Dimensional Regularization With a Nonanticommuting γ 5, Nucl. Phys. B 177 (1981) 523 [INSPIRE].
T.L. Trueman, Chiral Symmetry in Perturbative QCD, Phys. Lett. B 88 (1979) 331 [INSPIRE].
B. Melic, B. Nizic and K. Passek, BLM scale setting for the pion transition form-factor, Phys. Rev. D 65 (2002) 053020 [hep-ph/0107295] [INSPIRE].
F.M. Dittes and A.V. Radyushkin, TWo Loop Contribution To The Evolution Of The Pion Wave Function, Phys. Lett. B 134 (1984) 359 [INSPIRE].
S.V. Mikhailov and A.V. Radyushkin, Evolution Kernels in QCD: Two Loop Calculation in Feynman Gauge, Nucl. Phys. B 254 (1985) 89 [INSPIRE].
D. Mueller, Conformal constraints and the evolution of the nonsinglet meson distribution amplitude, Phys. Rev. D 49 (1994) 2525 [INSPIRE].
D. Mueller, The evolution of the pion distribution amplitude in next-to-leading-order, Phys. Rev. D 51 (1995) 3855 [hep-ph/9411338] [INSPIRE].
S.J. Brodsky, P. Damgaard, Y. Frishman and G.P. Lepage, Conformal Symmetry: Exclusive Processes Beyond Leading Order, Phys. Rev. D 33 (1986) 1881 [INSPIRE].
T. Feldmann, P. Kroll and B. Stech, Mixing and decay constants of pseudoscalar mesons, Phys. Rev. D 58 (1998) 114006 [hep-ph/9802409] [INSPIRE].
T. Feldmann, Quark structure of pseudoscalar mesons, Int. J. Mod. Phys. A 15 (2000) 159 [hep-ph/9907491] [INSPIRE].
E. Braaten, Quantum-chromodynamic corrections to meson-photon transition form factors, Phys. Rev. D 28 (1983) 524 [INSPIRE].
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].
K.G. Chetyrkin et al., Charm and Bottom Quark Masses: An Update, Phys. Rev. D 80 (2009) 074010 [arXiv:0907.2110] [INSPIRE].
K. Hagiwara, T. Kuruma and Y. Yamada, Three jet distributions from the one loop Z g g vertex at e + e − colliders, Nucl. Phys. B 358 (1991) 80 [INSPIRE].
ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group and SLD Heavy Flavour Group collaborations, S. Schael et al., Precision electroweak measurements on the Z resonance, Phys. Rept. 427 (2006) 257 [hep-ex/0509008] [INSPIRE].
UTfit collaboration, M. Bona et al., Model-independent constraints on ΔF = 2 operators and the scale of new physics, JHEP 03 (2008) 049 [arXiv:0707.0636] [INSPIRE].
ETM collaboration, V. Bertone et al., Kaon Mixing Beyond the SM from N f =2 tmQCD and model independent constraints from the UTA, JHEP 03 (2013) 089 [Erratum ibid. 1307 (2013) 143] [arXiv:1207.1287] [INSPIRE].
ETM collaboration, N. Carrasco et al., B-physics from N f = 2 tmQCD: the Standard Model and beyond, JHEP 03 (2014) 016 [arXiv:1308.1851] [INSPIRE].
R. Harnik, J. Kopp and J. Zupan, Flavor Violating Higgs Decays, JHEP 03 (2013) 026 [arXiv:1209.1397] [INSPIRE].
A. Sirlin, Current Algebra Formulation of Radiative Corrections in Gauge Theories and the Universality of the Weak Interactions, Rev. Mod. Phys. 50 (1978) 573 [Erratum ibid. 50 (1978) 905] [INSPIRE].
W.J. Marciano and A. Sirlin, Electroweak Radiative Corrections to τ Decay, Phys. Rev. Lett. 61 (1988) 1815 [INSPIRE].
E. Braaten and C.-S. Li, Electroweak radiative corrections to the semihadronic decay rate of the τ lepton, Phys. Rev. D 42 (1990) 3888 [INSPIRE].
J. Erler, Calculation of the QED coupling \( \widehat{\alpha} \)(M Z ) in the modified minimal subtraction scheme, Phys. Rev. D 59 (1999) 054008 [hep-ph/9803453] [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
ArXiv ePrint: 1501.06569
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Grossman, Y., König, M. & Neubert, M. Exclusive radiative decays of W and Z bosons in QCD factorization. J. High Energ. Phys. 2015, 101 (2015). https://doi.org/10.1007/JHEP04(2015)101
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)101