Abstract
We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
H.P. Nilles, Supersymmetry, Supergravity and Particle Physics, Phys. Rept. 110 (1984) 1 [INSPIRE].
H.E. Haber and G.L. Kane, The Search for Supersymmetry: Probing Physics Beyond the Standard Model, Phys. Rept. 117 (1985) 75 [INSPIRE].
N. Chamoun, F. Domingo and H.K. Dreiner, Nucleon decay in the R-parity violating MSSM, arXiv:2012.11623 [INSPIRE].
A.D. Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Sov. Phys. Usp. 34 (1991) 392 [INSPIRE].
L. Canetti, M. Drewes and M. Shaposhnikov, Matter and Antimatter in the Universe, New J. Phys. 14 (2012) 095012 [arXiv:1204.4186] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
D. Harlow and H. Ooguri, Constraints on Symmetries from Holography, Phys. Rev. Lett. 122 (2019) 191601 [arXiv:1810.05337] [INSPIRE].
P. Langacker, Grand Unified Theories and Proton Decay, Phys. Rept. 72 (1981) 185 [INSPIRE].
S. Raby, Proton decay, in 10th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY02), (2002) [hep-ph/0211024] [INSPIRE].
P. Nath and P. Fileviez Perez, Proton stability in grand unified theories, in strings and in branes, Phys. Rept. 441 (2007) 191 [hep-ph/0601023] [INSPIRE].
J. Ellis, J.L. Evans, N. Nagata, K.A. Olive and L. Velasco-Sevilla, Supersymmetric proton decay revisited, Eur. Phys. J. C 80 (2020) 332 [arXiv:1912.04888] [INSPIRE].
Super-Kamiokande collaboration, Search for proton decay via p → e+π0 and p → μ+π0 in 0.31 megaton · years exposure of the Super-Kamiokande water Cherenkov detector, Phys. Rev. D 95 (2017) 012004 [arXiv:1610.03597] [INSPIRE].
K. Abe et al., Calibration of the Super-Kamiokande Detector, Nucl. Instrum. Meth. A 737 (2014) 253 [arXiv:1307.0162] [INSPIRE].
Super-Kamiokande collaboration, The Super-Kamiokande detector, Nucl. Instrum. Meth. A 501 (2003) 418 [INSPIRE].
C. Jarlskog and F.J. Yndurain, Matter instability in the SU(5) unified model of strong, weak and electromagnetic interactions, Nucl. Phys. B 149 (1979) 29.
M. Machacek, The Decay Modes of the Proton, Nucl. Phys. B 159 (1979) 37 [INSPIRE].
J.T. Goldman and D.A. Ross, How Accurately Can We Estimate the Proton Lifetime in an SU(5) Grand Unified Model?, Nucl. Phys. B 171 (1980) 273 [INSPIRE].
M.B. Gavela, A. Le Yaouanc, L. Oliver, O. Pene and J.C. Raynal, Calculation of Proton Decay in the Nonrelativistic Quark Model, Phys. Rev. D 23 (1981) 1580 [INSPIRE].
P. Salati and J.C. Wallet, Proton and Neutron Decay Rates in Conventional and Supersymmetric GUTs, Nucl. Phys. B 209 (1982) 389 [INSPIRE].
A.M. Din, G. Girardi and P. Sorba, A Bag Model Calculation of the Nucleon Lifetime in Grand Unified Theories, Phys. Lett. B 91 (1980) 77 [INSPIRE].
J.F. Donoghue, Proton Lifetime and Branching Ratios in SU(5), Phys. Lett. B 92 (1980) 99 [INSPIRE].
E. Golowich, Two-body Decays of the Nucleon, Phys. Rev. D 22 (1980) 1148 [INSPIRE].
J.F. Donoghue and E. Golowich, Proton decay via three quark fusion, Phys. Rev. D 26 (1982) 3092 [INSPIRE].
M. Wakano, Static Bag Model Predictions of the Proton Lifetime and Branching Ratios in the SU(5) Grand Unified Theory, Prog. Theor. Phys. 67 (1982) 909 [INSPIRE].
T. Okazaki and K. Fujii, An Extended Application of the Bag Model: The Proton Decay, Phys. Rev. D 27 (1983) 188 [INSPIRE].
V.S. Berezinsky, B.L. Ioffe and Y.I. Kogan, The Calculation of Matrix Element for Proton Decay, Phys. Lett. B 105 (1981) 33 [INSPIRE].
M. Claudson, M.B. Wise and L.J. Hall, Chiral Lagrangian for Deep Mine Physics, Nucl. Phys. B 195 (1982) 297 [INSPIRE].
N. Isgur and M.B. Wise, On the Consistency of Chiral Symmetry and the Quark Model in Proton Decay, Phys. Lett. B 117 (1982) 179 [INSPIRE].
S. Chadha and M. Daniel, Chiral Lagrangian Calculation of Nucleon Decay Modes Induced by d = 5 Supersymmetric Operators, Nucl. Phys. B 229 (1983) 105 [INSPIRE].
O. Kaymakcalan, C.-H. Lo and K.C. Wali, Chiral Lagrangian for Proton Decay, Phys. Rev. D 29 (1984) 1962 [INSPIRE].
Y. Aoki, C. Dawson, J. Noaki and A. Soni, Proton decay matrix elements with domain-wall fermions, Phys. Rev. D 75 (2007) 014507 [hep-lat/0607002] [INSPIRE].
M.B. Gavela, S.F. King, C.T. Sachrajda, G. Martinelli, M.L. Paciello and B. Taglienti, A Lattice Computation of Proton Decay Amplitudes, Nucl. Phys. B 312 (1989) 269 [INSPIRE].
JLQCD collaboration, Nucleon decay matrix elements from lattice QCD, Phys. Rev. D 62 (2000) 014506 [hep-lat/9911026] [INSPIRE].
CP-PACS and JLQCD collaborations, Lattice QCD calculation of the proton decay matrix element in the continuum limit, Phys. Rev. D 70 (2004) 111501 [hep-lat/0402026] [INSPIRE].
QCDSF collaboration, Nucleon distribution amplitudes and proton decay matrix elements on the lattice, Phys. Rev. D 79 (2009) 034504 [arXiv:0811.2712] [INSPIRE].
Y. Aoki, E. Shintani and A. Soni, Proton decay matrix elements on the lattice, Phys. Rev. D 89 (2014) 014505 [arXiv:1304.7424] [INSPIRE].
Y. Aoki, T. Izubuchi, E. Shintani and A. Soni, Improved lattice computation of proton decay matrix elements, Phys. Rev. D 96 (2017) 014506 [arXiv:1705.01338] [INSPIRE].
J.-S. Yoo, Y. Aoki, T. Izubuchi and S. Syritsyn, Proton decay matrix element on lattice at physical pion mass, PoS LATTICE2018 (2019) 187 [arXiv:1812.09326] [INSPIRE].
Super-Kamiokande collaboration, Review of Nucleon Decay Searches at Super-Kamiokande, in 51st Rencontres de Moriond on EW Interactions and Unified Theories, (2016) [arXiv:1605.03235] [INSPIRE].
J. Heeck and V. Takhistov, Inclusive Nucleon Decay Searches as a Frontier of Baryon Number Violation, Phys. Rev. D 101 (2020) 015005 [arXiv:1910.07647] [INSPIRE].
S. Girmohanta and R. Shrock, Improved Lower Bounds on Partial Lifetimes for Nucleon Decay Modes, Phys. Rev. D 100 (2019) 115025 [arXiv:1910.08106] [INSPIRE].
M. Ruhdorfer, J. Serra and A. Weiler, Effective Field Theory of Gravity to All Orders, JHEP 05 (2020) 083 [arXiv:1908.08050] [INSPIRE].
G. Durieux and C.S. Machado, Enumerating higher-dimensional operators with on-shell amplitudes, Phys. Rev. D 101 (2020) 095021 [arXiv:1912.08827] [INSPIRE].
M.B. Wise, R. Blankenbecler and L.F. Abbott, Three-body Decays of the Proton, Phys. Rev. D 23 (1981) 1591 [INSPIRE].
USQCD collaboration, The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics, Eur. Phys. J. A 55 (2019) 197 [arXiv:1904.09704] [INSPIRE].
E.C. Poggio, H.R. Quinn and S. Weinberg, Smearing the Quark Model, Phys. Rev. D 13 (1976) 1958 [INSPIRE].
M.A. Shifman, Quark hadron duality, in 8th International Symposium on Heavy Flavor Physics, Singapore, World Scientific (2000) [DOI] [hep-ph/0009131] [INSPIRE].
K.G. Wilson, Nonlagrangian models of current algebra, Phys. Rev. 179 (1969) 1499 [INSPIRE].
P. Colangelo and A. Khodjamirian, QCD sum rules, a modern perspective, hep-ph/0010175 [INSPIRE].
B.L. Ioffe, On the choice of quark currents in the QCD sum rules for baryon masses, Z. Phys. C 18 (1983) 67 [INSPIRE].
D.B. Leinweber, Nucleon properties from unconventional interpolating fields, Phys. Rev. D 51 (1995) 6383 [nucl-th/9406001] [INSPIRE].
I.I. Balitsky and V.M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989) 541 [INSPIRE].
V.M. Braun and I.E. Filyanov, Conformal Invariance and Pion Wave Functions of Nonleading Twist, Z. Phys. C 48 (1990) 239 [INSPIRE].
V.M. Braun, A. Khodjamirian and M. Maul, Pion form-factor in QCD at intermediate momentum transfers, Phys. Rev. D 61 (2000) 073004 [hep-ph/9907495] [INSPIRE].
S.S. Agaev, V.M. Braun, N. Offen and F.A. Porkert, Light Cone Sum Rules for the pi0-gamma*-gamma Form Factor Revisited, Phys. Rev. D 83 (2011) 054020 [arXiv:1012.4671] [INSPIRE].
D.B. Leinweber, QCD sum rules for skeptics, Annals Phys. 254 (1997) 328 [nucl-th/9510051] [INSPIRE].
A. Khodjamirian, B. Melić, Y.-M. Wang and Y.-B. Wei, The D*Dπ and B*Bπ couplings from light-cone sum rules, JHEP 03 (2021) 016 [arXiv:2011.11275] [INSPIRE].
P. Ball, Theoretical update of pseudoscalar meson distribution amplitudes of higher twist: The Nonsinglet case, JHEP 01 (1999) 010 [hep-ph/9812375] [INSPIRE].
P. Ball and R. Zwicky, New results on B → π, K, η decay formfactors from light-cone sum rules, Phys. Rev. D 71 (2005) 014015 [hep-ph/0406232] [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
M. Gell-Mann, R.J. Oakes and B. Renner, Behavior of current divergences under SU(3) × SU(3), Phys. Rev. 175 (1968) 2195 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and Resonance Physics. Theoretical Foundations, Nucl. Phys. B 147 (1979) 385 [INSPIRE].
V.M. Braun, A. Lenz, N. Mahnke and E. Stein, Light cone sum rules for the nucleon form-factors, Phys. Rev. D 65 (2002) 074011 [hep-ph/0112085] [INSPIRE].
V.M. Braun, A. Lenz and M. Wittmann, Nucleon Form Factors in QCD, Phys. Rev. D 73 (2006) 094019 [hep-ph/0604050] [INSPIRE].
M.C. Chu, J.M. Grandy, S. Huang and J.W. Negele, Correlation functions of hadron currents in the QCD vacuum calculated in lattice QCD, Phys. Rev. D 48 (1993) 3340 [hep-lat/9306002] [INSPIRE].
D.B. Leinweber, Testing QCD sum rule techniques on the lattice, Phys. Rev. D 51 (1995) 6369 [nucl-th/9405002] [INSPIRE].
K.G. Chetyrkin, J.H. Kühn 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].
J. Bordes, C.A. Dominguez, P. Moodley, J. Penarrocha and K. Schilcher, Chiral corrections to the SU(2) × SU(2) Gell-Mann-Oakes-Renner relation, JHEP 05 (2010) 064 [arXiv:1003.3358] [INSPIRE].
B.L. Ioffe, Condensates in quantum chromodynamics, Phys. Atom. Nucl. 66 (2003) 30 [hep-ph/0207191] [INSPIRE].
T. Nihei and J. Arafune, The Two loop long range effect on the proton decay effective Lagrangian, Prog. Theor. Phys. 93 (1995) 665 [hep-ph/9412325] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, FeynCalc 9.3: New features and improvements, Comput. Phys. Commun. 256 (2020) 107478 [arXiv:2001.04407] [INSPIRE].
M. Jamin and M.E. Lautenbacher, TRACER: Version 1.1: A Mathematica package for gamma algebra in arbitrary dimensions, Comput. Phys. Commun. 74 (1993) 265 [INSPIRE].
T. Ohl, Drawing Feynman diagrams with Latex and Metafont, Comput. Phys. Commun. 90 (1995) 340 [hep-ph/9505351] [INSPIRE].
A. Khodjamirian, T. Mannel, N. Offen and Y.M. Wang, B → πℓνl Width and |Vub| from QCD Light-Cone Sum Rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].
Jefferson Lab collaboration, Charged pion form-factor between Q2 = 0.60 and 2.45 GeV2. II. Determination of, and results for, the pion form-factor, Phys. Rev. C 78 (2008) 045203 [arXiv:0809.3052] [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].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2103.13928
Rights and permissions
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.
About this article
Cite this article
Haisch, U., Hala, A. Light-cone sum rules for proton decay. J. High Energ. Phys. 2021, 258 (2021). https://doi.org/10.1007/JHEP05(2021)258
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2021)258