Abstract
We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe−e− amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n(p1)n(p2)W+(k) → \( p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k) \), in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon (NN) scattering in the 1S0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1S0 NN scattering lengths. While our analysis is performed in the \( \overline{\mathrm{MS}} \) scheme, we express our final result in terms of the scheme-independent renormalized amplitude \( {\mathcal{A}}_{\nu}\left(\left|\mathbf{p}\right|,\left|\mathbf{p}^{\prime}\right|\right) \) at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for \( {\mathcal{A}}_{\nu } \), one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W.H. Furry, On transition probabilities in double beta-disintegration, Phys. Rev. 56 (1939) 1184 [INSPIRE].
J. Schechter and J.W.F. Valle, Neutrinoless double beta decay in SU(2) × U(1) theories, Phys. Rev. D 25 (1982) 2951 [INSPIRE].
S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].
W. Rodejohann, Neutrino-less double beta decay and particle physics, Int. J. Mod. Phys. E 20 (2011) 1833 [arXiv:1106.1334] [INSPIRE].
KamLAND-Zen collaboration, Search for Majorana neutrinos near the inverted mass hierarchy region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503 [Addendum ibid. 117 (2016) 109903] [arXiv:1605.02889] [INSPIRE].
NEMO-3 collaboration, Measurement of the 2νββ decay half-life of 150Nd and a search for 0νββ decay processes with the full exposure from the NEMO-3 detector, Phys. Rev. D 94 (2016) 072003 [arXiv:1606.08494] [INSPIRE].
EXO collaboration, Search for neutrinoless double-beta decay with the Upgraded EXO-200 detector, Phys. Rev. Lett. 120 (2018) 072701 [arXiv:1707.08707] [INSPIRE].
Majorana collaboration, Search for neutrinoless double-β decay in 76Ge with the Majorana demonstrator, Phys. Rev. Lett. 120 (2018) 132502 [arXiv:1710.11608] [INSPIRE].
CUORE collaboration, Improved limit on neutrinoless double-beta decay in 130Te with CUORE, Phys. Rev. Lett. 124 (2020) 122501 [arXiv:1912.10966] [INSPIRE].
GERDA collaboration, Final results of GERDA on the search for neutrinoless double-β decay, Phys. Rev. Lett. 125 (2020) 252502 [arXiv:2009.06079] [INSPIRE].
F.T. Avignone, III, S.R. Elliott and J. Engel, Double beta decay, Majorana neutrinos, and neutrino mass, Rev. Mod. Phys. 80 (2008) 481 [arXiv:0708.1033] [INSPIRE].
J. Menéndez, A. Poves, E. Caurier and F. Nowacki, Disassembling the nuclear matrix elements of the neutrinoless beta beta decay, Nucl. Phys. A 818 (2009) 139 [arXiv:0801.3760] [INSPIRE].
J.D. Vergados, H. Ejiri and F. Šimkovic, Theory of neutrinoless double beta decay, Rept. Prog. Phys. 75 (2012) 106301 [arXiv:1205.0649] [INSPIRE].
F. Šimkovic, V. Rodin, A. Faessler and P. Vogel, 0νββ and 2νββ nuclear matrix elements, quasiparticle random-phase approximation, and isospin symmetry restoration, Phys. Rev. C 87 (2013) 045501 [arXiv:1302.1509] [INSPIRE].
N. López Vaquero, T.R. Rodríguez and J.L. Egido, Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements, Phys. Rev. Lett. 111 (2013) 142501 [arXiv:1401.0650] [INSPIRE].
J. Barea, J. Kotila and F. Iachello, 0νββ and 2νββ nuclear matrix elements in the interacting boson model with isospin restoration, Phys. Rev. C 91 (2015) 034304 [arXiv:1506.08530] [INSPIRE].
R.A. Sen’kov and M. Horoi, Shell-model calculation of neutrinoless double-β decay of 76Ge, Phys. Rev. C 93 (2016) 044334 [arXiv:1512.06157] [INSPIRE].
J. Engel and J. Menéndez, Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review, Rept. Prog. Phys. 80 (2017) 046301 [arXiv:1610.06548] [INSPIRE].
M.J. Dolinski, A.W.P. Poon and W. Rodejohann, Neutrinoless double-beta decay: status and prospects, Ann. Rev. Nucl. Part. Sci. 69 (2019) 219 [arXiv:1902.04097] [INSPIRE].
S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].
S. Weinberg, Nuclear forces from chiral Lagrangians, Phys. Lett. B 251 (1990) 288 [INSPIRE].
S. Weinberg, Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces, Nucl. Phys. B 363 (1991) 3 [INSPIRE].
D.B. Kaplan, M.J. Savage and M.B. Wise, Nucleon-nucleon scattering from effective field theory, Nucl. Phys. B 478 (1996) 629 [nucl-th/9605002] [INSPIRE].
D.B. Kaplan, M.J. Savage and M.B. Wise, A new expansion for nucleon-nucleon interactions, Phys. Lett. B 424 (1998) 390 [nucl-th/9801034] [INSPIRE].
D.B. Kaplan, M.J. Savage and M.B. Wise, Two nucleon systems from effective field theory, Nucl. Phys. B 534 (1998) 329 [nucl-th/9802075] [INSPIRE].
E. Epelbaum, H.-W. Hammer and U.-G. Meißner, Modern theory of nuclear forces, Rev. Mod. Phys. 81 (2009) 1773 [arXiv:0811.1338] [INSPIRE].
R. Machleidt and D.R. Entem, Chiral effective field theory and nuclear forces, Phys. Rept. 503 (2011) 1 [arXiv:1105.2919] [INSPIRE].
H.-W. Hammer, S. König and U. van Kolck, Nuclear effective field theory: status and perspectives, Rev. Mod. Phys. 92 (2020) 025004 [arXiv:1906.12122] [INSPIRE].
J.M. Yao, B. Bally, J. Engel, R. Wirth, T.R. Rodríguez and H. Hergert, Ab initio treatment of collective correlations and the neutrinoless double beta decay of 48Ca, Phys. Rev. Lett. 124 (2020) 232501 [arXiv:1908.05424] [INSPIRE].
A. Belley, C.G. Payne, S.R. Stroberg, T. Miyagi and J.D. Holt, Ab initio neutrinoless double-beta decay matrix elements for 48Ca, 76Ge, and 82Se, Phys. Rev. Lett. 126 (2021) 042502 [arXiv:2008.06588] [INSPIRE].
S.J. Novario et al., Coupled-cluster calculations of neutrinoless double-beta decay in 48Ca, Phys. Rev. Lett. 126 (2021) 182502 [arXiv:2008.09696] [INSPIRE].
I.S. Towner, Quenching of spin matrix elements in nuclei, Phys. Rept. 155 (1987) 263 [INSPIRE].
S. Pastore et al., Quantum Monte Carlo calculations of weak transitions in A = 6–10 nuclei, Phys. Rev. C 97 (2018) 022501 [arXiv:1709.03592] [INSPIRE].
P. Gysbers et al., Discrepancy between experimental and theoretical β-decay rates resolved from first principles, Nature Phys. 15 (2019) 428 [arXiv:1903.00047] [INSPIRE].
G. Prézeau, M. Ramsey-Musolf and P. Vogel, Neutrinoless double beta decay and effective field theory, Phys. Rev. D 68 (2003) 034016 [hep-ph/0303205] [INSPIRE].
J. Menéndez, D. Gazit and A. Schwenk, Chiral two-body currents in nuclei: Gamow-Teller transitions and neutrinoless double-beta decay, Phys. Rev. Lett. 107 (2011) 062501 [arXiv:1103.3622] [INSPIRE].
V. Cirigliano, W. Dekens, J. de Vries, M.L. Graesser and E. Mereghetti, Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven, JHEP 12 (2017) 082 [arXiv:1708.09390] [INSPIRE].
V. Cirigliano, W. Dekens, E. Mereghetti and A. Walker-Loud, Neutrinoless double-β decay in effective field theory: The light-Majorana neutrino-exchange mechanism, Phys. Rev. C 97 (2018) 065501 [Erratum ibid. 100 (2019) 019903] [arXiv:1710.01729] [INSPIRE].
S. Pastore, J. Carlson, V. Cirigliano, W. Dekens, E. Mereghetti and R.B. Wiringa, Neutrinoless double-β decay matrix elements in light nuclei, Phys. Rev. C 97 (2018) 014606 [arXiv:1710.05026] [INSPIRE].
V. Cirigliano et al., New Leading Contribution to Neutrinoless Double-β Decay, Phys. Rev. Lett. 120 (2018) 202001 [arXiv:1802.10097] [INSPIRE].
L.-J. Wang, J. Engel and J.M. Yao, Quenching of nuclear matrix elements for 0νββ decay by chiral two-body currents, Phys. Rev. C 98 (2018) 031301 [arXiv:1805.10276] [INSPIRE].
V. Cirigliano, W. Dekens, J. de Vries, M.L. Graesser and E. Mereghetti, A neutrinoless double beta decay master formula from effective field theory, JHEP 12 (2018) 097 [arXiv:1806.02780] [INSPIRE].
V. Cirigliano et al., Renormalized approach to neutrinoless double-β decay, Phys. Rev. C 100 (2019) 055504 [arXiv:1907.11254] [INSPIRE].
W. Dekens, J. de Vries, K. Fuyuto, E. Mereghetti and G. Zhou, Sterile neutrinos and neutrinoless double beta decay in effective field theory, JHEP 06 (2020) 097 [arXiv:2002.07182] [INSPIRE].
M. Pavón Valderrama and D.R. Phillips, Power counting of contact-range currents in effective field theory, Phys. Rev. Lett. 114 (2015) 082502 [arXiv:1407.0437] [INSPIRE].
V. Cirigliano, W. Detmold, A. Nicholson and P. Shanahan, Lattice QCD inputs for nuclear double beta decay, arXiv:2003.08493 [INSPIRE].
G.A. Miller and J.E. Spencer, A survey of pion charge-exchange reactions with nuclei, Annals Phys. 100 (1976) 562 [INSPIRE].
F. Šimkovic, A. Faessler, H. Müther, V. Rodin and M. Stauf, The 0νββ decay nuclear matrix elements with self-consistent short-range correlations, Phys. Rev. C 79 (2009) 055501 [arXiv:0902.0331] [INSPIRE].
J. Engel, J. Carlson and R.B. Wiringa, Jastrow functions in double-β decay, Phys. Rev. C 83 (2011) 034317 [arXiv:1101.0554] [INSPIRE].
O. Benhar, R. Biondi and E. Speranza, Short-range correlation effects on the nuclear matrix element of neutrinoless double-β decay, Phys. Rev. C 90 (2014) 065504 [arXiv:1401.2030] [INSPIRE].
F. Šimkovic, A. Faessler, V. Rodin, P. Vogel and J. Engel, Anatomy of nuclear matrix elements for neutrinoless double-beta decay, Phys. Rev. C 77 (2008) 045503 [arXiv:0710.2055] [INSPIRE].
X. Feng, L.-C. Jin, X.-Y. Tuo and S.-C. Xia, Light-neutrino exchange and long-distance contributions to 0ν2β decays: an exploratory study on ππ → ee, Phys. Rev. Lett. 122 (2019) 022001 [arXiv:1809.10511] [INSPIRE].
X.-Y. Tuo, X. Feng and L.-C. Jin, Long-distance contributions to neutrinoless double beta decay π− → π+ee, Phys. Rev. D 100 (2019) 094511 [arXiv:1909.13525] [INSPIRE].
W. Detmold and D. Murphy, Neutrinoless double beta decay from lattice QCD: the long-distance π− → π+e−e− amplitude, arXiv:2004.07404 [INSPIRE].
X. Feng, L.-C. Jin, Z.-Y. Wang and Z. Zhang, Finite-volume formalism in the \( 2\overset{\left({H}_I+{H}_I\right)}{\to }2 \) transition: an application to the lattice QCD calculation of double beta decays, Phys. Rev. D 103 (2021) 034508 [arXiv:2005.01956] [INSPIRE].
Z. Davoudi et al., Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes, Phys. Rept. 900 (2021) 1 [arXiv:2008.11160] [INSPIRE].
Z. Davoudi and S.V. Kadam, Path from lattice QCD to the short-distance contribution to 0νββ decay with a light Majorana neutrino, Phys. Rev. Lett. 126 (2021) 152003 [arXiv:2012.02083] [INSPIRE].
T.R. Richardson, M.R. Schindler, S. Pastore and R.P. Springer, Large-Nc analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms, arXiv:2102.02184 [INSPIRE].
V. Cirigliano, W. Dekens, J. de Vries, M. Hoferichter and E. Mereghetti, Toward complete leading-order predictions for neutrinoless double β decay, Phys. Rev. Lett. 126 (2021) 172002 [arXiv:2012.11602] [INSPIRE].
W.N. Cottingham, The neutron proton mass difference and electron scattering experiments, Annals Phys. 25 (1963) 424 [INSPIRE].
H. Harari, Superconvergent dispersion relations and electromagnetic mass differences, Phys. Rev. Lett. 17 (1966) 1303 [INSPIRE].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The role of resonances in chiral perturbation theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].
W.A. Bardeen, J. Bijnens and J.M. Gerard, Hadronic matrix elements and the π+π0 mass difference, Phys. Rev. Lett. 62 (1989) 1343 [INSPIRE].
J.F. Donoghue, B.R. Holstein and D. Wyler, Electromagnetic selfenergies of pseudoscalar mesons and Dashen’s theorem, Phys. Rev. D 47 (1993) 2089 [INSPIRE].
R. Baur and R. Urech, On the corrections to Dashen’s theorem, Phys. Rev. D 53 (1996) 6552 [hep-ph/9508393] [INSPIRE].
J.F. Donoghue and A.F. Pérez, The electromagnetic mass differences of pions and kaons, Phys. Rev. D 55 (1997) 7075 [hep-ph/9611331] [INSPIRE].
J. Gasser and H. Leutwyler, Implications of scaling for the proton-neutron mass difference, Nucl. Phys. B 94 (1975) 269.
J. Gasser and H. Leutwyler, Quark masses, Phys. Rept. 87 (1982) 77 [INSPIRE].
A. Walker-Loud, C.E. Carlson and G.A. Miller, The electromagnetic self-energy contribution to Mp − Mn and the isovector nucleon magneticpolarizability, Phys. Rev. Lett. 108 (2012) 232301 [arXiv:1203.0254] [INSPIRE].
A.W. Thomas, X.G. Wang and R.D. Young, Electromagnetic contribution to the proton-neutron mass splitting, Phys. Rev. C 91 (2015) 015209 [arXiv:1406.4579] [INSPIRE].
F.B. Erben, P.E. Shanahan, A.W. Thomas and R.D. Young, Dispersive estimate of the electromagnetic charge symmetry violation in the octet baryon masses, Phys. Rev. C 90 (2014) 065205 [arXiv:1408.6628] [INSPIRE].
J. Gasser, M. Hoferichter, H. Leutwyler and A. Rusetsky, Cottingham formula and nucleon polarisabilities, Eur. Phys. J. C 75 (2015) 375 [Erratum ibid. 80 (2020) 353] [arXiv:1506.06747] [INSPIRE].
J. Gasser, H. Leutwyler and A. Rusetsky, On the mass difference between proton and neutron, Phys. Lett. B 814 (2021) 136087 [arXiv:2003.13612] [INSPIRE].
J. Gasser, H. Leutwyler and A. Rusetsky, Sum rule for the Compton amplitude and implications for the proton-neutron mass difference, Eur. Phys. J. C 80 (2020) 1121 [arXiv:2008.05806] [INSPIRE].
S. Borsányi et al., Ab initio calculation of the neutron-proton mass difference, Science 347 (2015) 1452 [arXiv:1406.4088] [INSPIRE].
D.A. Brantley et al., Strong isospin violation and chiral logarithms in the baryon spectrum, arXiv:1612.07733 [INSPIRE].
CSSM, QCDSF, UKQCD collaboration, Isospin splittings in the decuplet baryon spectrum from dynamical QCD+QED, J. Phys. G 46 (2019) 115004 [arXiv:1904.02304] [INSPIRE].
S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].
R.J. Furnstahl, H.-W. Hammer and N. Tirfessa, Field redefinitions at finite density, Nucl. Phys. A 689 (2001) 846 [nucl-th/0010078] [INSPIRE].
M.L. Goldberger and K.M. Watson, Collision theory, Wiley, New York U.S.A (1964).
R.J. Hill, P. Kammel, W.J. Marciano and A. Sirlin, Nucleon axial radius and muonic hydrogen — A new analysis and review, Rept. Prog. Phys. 81 (2018) 096301 [arXiv:1708.08462] [INSPIRE].
J. Arrington and I. Sick, Precise determination of low-Q nucleon electromagnetic form factors and their impact on parity-violating e-p elastic scattering, Phys. Rev. C 76 (2007) 035201 [nucl-th/0612079] [INSPIRE].
I.T. Lorenz, U.-G. Meißner, H.-W. Hammer and Y.B. Dong, Theoretical constraints and systematic effects in the determination of the proton form factors, Phys. Rev. D 91 (2015) 014023 [arXiv:1411.1704] [INSPIRE].
M. Hoferichter, B. Kubis, J. Ruiz de Elvira, H.-W. Hammer and U.-G. Meißner, On the ππ continuum in the nucleon form factors and the proton radius puzzle, Eur. Phys. J. A 52 (2016) 331 [arXiv:1609.06722] [INSPIRE].
Z. Ye, J. Arrington, R.J. Hill and G. Lee, Proton and neutron electromagnetic form factors and uncertainties, Phys. Lett. B 777 (2018) 8 [arXiv:1707.09063] [INSPIRE].
M. Srivastava and D. Sprung, Off-shell behavior of the nucleon-nucleon interaction, Springer, Germany (1975).
D.B. Kaplan and J.V. Steele, The long and short of nuclear effective field theory expansions, Phys. Rev. C 60 (1999) 064002 [nucl-th/9905027] [INSPIRE].
R.V. Reid, Jr., Local phenomenological nucleon-nucleon potentials, Annals Phys. 50 (1968) 411 [INSPIRE].
R.B. Wiringa, V.G.J. Stoks and R. Schiavilla, An accurate nucleon-nucleon potential with charge independence breaking, Phys. Rev. C 51 (1995) 38 [nucl-th/9408016] [INSPIRE].
A. Nicholson et al., Heavy physics contributions to neutrinoless double beta decay from QCD, Phys. Rev. Lett. 121 (2018) 172501 [arXiv:1805.02634] [INSPIRE].
M.J. Savage, Pionic matrix elements in neutrinoless double Beta decay, Phys. Rev. C 59 (1999) 2293 [nucl-th/9811087] [INSPIRE].
V. Cirigliano, W. Dekens, M. Graesser and E. Mereghetti, Neutrinoless double beta decay and chiral SU(3), Phys. Lett. B 769 (2017) 460 [arXiv:1701.01443] [INSPIRE].
J. Bijnens and G. Ecker, Mesonic low-energy constants, Ann. Rev. Nucl. Part. Sci. 64 (2014) 149 [arXiv:1405.6488] [INSPIRE].
G. Colangelo, M. Hoferichter, M. Procura and P. Stoffer, Dispersion relation for hadronic light-by-light scattering: theoretical foundations, JHEP 09 (2015) 074 [arXiv:1506.01386] [INSPIRE].
G. Colangelo, M. Hoferichter, M. Procura and P. Stoffer, Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon, Phys. Rev. Lett. 118 (2017) 232001 [arXiv:1701.06554] [INSPIRE].
G. Colangelo, M. Hoferichter, M. Procura and P. Stoffer, Dispersion relation for hadronic light-by-light scattering: two-pion contributions, JHEP 04 (2017) 161 [arXiv:1702.07347] [INSPIRE].
H.A. Bethe, Theory of the effective range in nuclear scattering, Phys. Rev. 76 (1949) 38 [INSPIRE].
J.D. Jackson and J.M. Blatt, The interpretation of low energy proton-proton scattering, Rev. Mod. Phys. 22 (1950) 77 [INSPIRE].
X. Kong and F. Ravndal, Coulomb effects in low-energy proton proton scattering, Nucl. Phys. A 665 (2000) 137 [hep-ph/9903523] [INSPIRE].
E. Epelbaum and U.-G. Meißner, Charge independence breaking and charge symmetry breaking in the nucleon-nucleon interaction from effective field theory, Phys. Lett. B 461 (1999) 287 [Erratum ibid. 467 (1999) 308] [nucl-th/9902042] [INSPIRE].
J.R. Bergervoet, P.C. van Campen, W.A. van der Sanden and J.J. de Swart, Phase shift analysis of 0–30 MeV pp scattering data, Phys. Rev. C 38 (1988) 15 [INSPIRE].
P. Reinert, H. Krebs and E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order, Eur. Phys. J. A 54 (2018) 86 [arXiv:1711.08821] [INSPIRE].
S. Klarsfeld, J. Martorell and D.W.L. Sprung, Deuteron properties and the nucleon nucleon interaction, J. Phys. G 10 (1984) 165 [INSPIRE].
R. Machleidt, The high precision, charge dependent Bonn nucleon-nucleon potential (CD-Bonn), Phys. Rev. C 63 (2001) 024001 [nucl-th/0006014] [INSPIRE].
Q. Chen et al., Measurement of the neutron-neutron scattering length using the π−d capture reaction, Phys. Rev. C 77 (2008) 054002 [INSPIRE].
K.M. Watson, Some general relations between the photoproduction and scattering of π mesons, Phys. Rev. 95 (1954) 228 [INSPIRE].
H.-W. Hammer, A. Nogga and A. Schwenk, Three-body forces: from cold atoms to nuclei, Rev. Mod. Phys. 85 (2013) 197 [arXiv:1210.4273] [INSPIRE].
K. Hebeler, Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter, Phys. Rept. 890 (2021) 1 [arXiv:2002.09548] [INSPIRE].
J.M. Yao et al., Ab initio benchmarks of neutrinoless double-β decay in light nuclei with a chiral Hamiltonian, Phys. Rev. C 103 (2021) 014315 [arXiv:2010.08609] [INSPIRE].
M. Hoferichter, J. Menéndez and A. Schwenk, Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses, Phys. Rev. D 102 (2020) 074018 [arXiv:2007.08529] [INSPIRE].
NEMO-3, SuperNEMO collaboration, Latest results from NEMO-3 and commissioning status of the SuperNEMO demonstrator, J. Phys. Conf. Ser. 1342 (2020) 012029 [INSPIRE].
LEGEND collaboration, LEGEND: the future of neutrinoless double-beta decay search with germanium detectors, J. Phys. Conf. Ser. 1468 (2020) 012111 [INSPIRE].
CUPID collaboration, First data from the CUPID-Mo neutrinoless double beta decay experiment, J. Phys. Conf. Ser. 1468 (2020) 012129 [arXiv:1911.10426] [INSPIRE].
nEXO collaboration, The nEXO detector: design overview, J. Phys. Conf. Ser. 1468 (2020) 012131 [INSPIRE].
CANDLES, low temperature group collaboration, Status of 48Ca double beta decay search and its future prospect in CANDLES, J. Phys. Conf. Ser. 1468 (2020) 012132 [INSPIRE].
SNO+ collaboration, Background analysis for the SNO+ experiment, J. Phys. Conf. Ser. 1468 (2020) 012135 [INSPIRE].
KamLAND-Zen collaboration, First results of KamLAND-Zen 800, J. Phys. Conf. Ser. 1468 (2020) 012142 [INSPIRE].
E. Epelbaum, U.-G. Meißner, W. Glöckle and C. Elster, Resonance saturation for four nucleon operators, Phys. Rev. C 65 (2002) 044001 [nucl-th/0106007] [INSPIRE].
G. Colangelo, M. Hoferichter and P. Stoffer, Two-pion contribution to hadronic vacuum polarization, JHEP 02 (2019) 006 [arXiv:1810.00007] [INSPIRE].
G. Colangelo, M. Hoferichter and P. Stoffer, Constraints on the two-pion contribution to hadronic vacuum polarization, Phys. Lett. B 814 (2021) 136073 [arXiv:2010.07943] [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: 2102.03371
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
Cirigliano, V., Dekens, W., de Vries, J. et al. Determining the leading-order contact term in neutrinoless double β decay. J. High Energ. Phys. 2021, 289 (2021). https://doi.org/10.1007/JHEP05(2021)289
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2021)289