Abstract
We discuss the effective field theory (EFT) for nuclear beta decay. The general quark-level EFT describing charged-current interactions between quarks and leptons is matched to the nucleon-level non-relativistic EFT at the \( \mathcal{O}\left(\textrm{MeV}\right) \) momentum scale characteristic for beta transitions. The matching takes into account, for the first time, the effect of all possible beyond-the-Standard-Model interactions at the subleading order in the recoil momentum. We calculate the impact of all the Wilson coefficients of the leading and subleading EFT Lagrangian on the differential decay width in allowed beta transitions. As an example application, we show how the existing experimental data constrain the subleading Wilson coefficients corresponding to pseudoscalar, weak magnetism, and induced tensor interactions. The data display a 3.5 sigma evidence for nucleon weak magnetism, in agreement with the theory prediction based on isospin symmetry.
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References
W. Pauli, Dear radioactive ladies and gentlemen, Phys. Today 31N9 (1978) 27 [INSPIRE].
E. Fermi, An attempt of a theory of beta radiation. I, Z. Phys. 88 (1934) 161 [INSPIRE].
C.L. Cowan et al., Detection of the free neutrino: A Confirmation, Science 124 (1956) 103 [INSPIRE].
T.D. Lee and C.-N. Yang, Question of Parity Conservation in Weak Interactions, Phys. Rev. 104 (1956) 254 [INSPIRE].
C.S. Wu et al., Experimental Test of Parity Conservation in β Decay, Phys. Rev. 105 (1957) 1413 [INSPIRE].
S. Weinberg, V-A was the key, J. Phys. Conf. Ser. 196 (2009) 012002 [INSPIRE].
H. Abele, The neutron. Its properties and basic interactions, Prog. Part. Nucl. Phys. 60 (2008) 1 [INSPIRE].
M. González-Alonso, O. Naviliat-Cuncic and N. Severijns, New physics searches in nuclear and neutron β decay, Prog. Part. Nucl. Phys. 104 (2019) 165 [arXiv:1803.08732] [INSPIRE].
J.C. Hardy and I.S. Towner, Superallowed 0+ → 0+ nuclear β decays: 2020 critical survey, with implications for Vud and CKM unitarity, Phys. Rev. C 102 (2020) 045501 [INSPIRE].
D. Dubbers and B. Märkisch, Precise Measurements of the Decay of Free Neutrons, Ann. Rev. Nucl. Part. Sci. 71 (2021) 139 [arXiv:2106.02345] [INSPIRE].
A. Falkowski, M. González-Alonso and O. Naviliat-Cuncic, Comprehensive analysis of beta decays within and beyond the Standard Model, JHEP 04 (2021) 126 [arXiv:2010.13797] [INSPIRE].
P. Herczeg, Beta decay beyond the standard model, Prog. Part. Nucl. Phys. 46 (2001) 413 [INSPIRE].
J.D. Jackson, S.B. Treiman and H.W. Wyld, Possible tests of time reversal invariance in Beta decay, Phys. Rev. 106 (1957) 517 [INSPIRE].
S. Weinberg, Charge symmetry of weak interactions, Phys. Rev. 112 (1958) 1375 [INSPIRE].
U. van Kolck, Effective field theory of nuclear forces, Prog. Part. Nucl. Phys. 43 (1999) 337 [nucl-th/9902015] [INSPIRE].
B.R. Holstein, Recoil Effects in Allowed beta Decay: The Elementary Particle Approach, Rev. Mod. Phys. 46 (1974) 789 [INSPIRE].
N. Severijns et al., Ft values of the mirror β transitions and the weak-magnetism-induced current in allowed nuclear β decay, Phys. Rev. C 107 (2023) 015502 [arXiv:2109.08895] [INSPIRE].
T. Bhattacharya et al., Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC, Phys. Rev. D 85 (2012) 054512 [arXiv:1110.6448] [INSPIRE].
I. Doršner et al., Physics of leptoquarks in precision experiments and at particle colliders, Phys. Rept. 641 (2016) 1 [arXiv:1603.04993] [INSPIRE].
A. Angelescu et al., Single leptoquark solutions to the B-physics anomalies, Phys. Rev. D 104 (2021) 055017 [arXiv:2103.12504] [INSPIRE].
A. Falkowski, M. González-Alonso and Z. Tabrizi, Reactor neutrino oscillations as constraints on Effective Field Theory, JHEP 05 (2019) 173 [arXiv:1901.04553] [INSPIRE].
J. de Blas, J.C. Criado, M. Perez-Victoria and J. Santiago, Effective description of general extensions of the Standard Model: the complete tree-level dictionary, JHEP 03 (2018) 109 [arXiv:1711.10391] [INSPIRE].
M. Ademollo and R. Gatto, Nonrenormalization Theorem for the Strangeness Violating Vector Currents, Phys. Rev. Lett. 13 (1964) 264 [INSPIRE].
J.F. Donoghue and D. Wyler, Isospin Breaking and the Precise Determination of V (ud), Phys. Lett. B 241 (1990) 243 [INSPIRE].
M. Gell-Mann, The symmetry group of vector and axial vector currents, Physics Physique Fizika 1 (1964) 63 [INSPIRE].
V. Cirigliano et al., Pion-Induced Radiative Corrections to Neutron β Decay, Phys. Rev. Lett. 129 (2022) 121801 [arXiv:2202.10439] [INSPIRE].
Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].
R. Gupta et al., Isovector Charges of the Nucleon from 2 + 1 + 1-flavor Lattice QCD, Phys. Rev. D 98 (2018) 034503 [arXiv:1806.09006] [INSPIRE].
C.C. Chang et al., A per-cent-level determination of the nucleon axial coupling from quantum chromodynamics, Nature 558 (2018) 91 [arXiv:1805.12130] [INSPIRE].
A. Walker-Loud et al., Lattice QCD Determination of gA, PoS CD2018 (2020) 020 [arXiv:1912.08321] [INSPIRE].
M. González-Alonso and J. Martin Camalich, Isospin breaking in the nucleon mass and the sensitivity of β decays to new physics, Phys. Rev. Lett. 112 (2014) 042501 [arXiv:1309.4434] [INSPIRE].
J.F. Donoghue, E. Golowich and B.R. Holstein, Dynamics of the standard model, CUP (2014) [https://doi.org/10.1017/CBO9780511524370] [INSPIRE].
C. Chen, C.S. Fischer, C.D. Roberts and J. Segovia, Nucleon axial-vector and pseudoscalar form factors and PCAC relations, Phys. Rev. D 105 (2022) 094022 [arXiv:2103.02054] [INSPIRE].
RBC and UKQCD collaborations, Domain wall QCD with physical quark masses, Phys. Rev. D 93 (2016) 074505 [arXiv:1411.7017] [INSPIRE].
BMW collaboration, Lattice QCD at the physical point: light quark masses, Phys. Lett. B 701 (2011) 265 [arXiv:1011.2403] [INSPIRE].
BMW collaboration, Lattice QCD at the physical point: Simulation and analysis details, JHEP 08 (2011) 148 [arXiv:1011.2711] [INSPIRE].
C. McNeile et al., High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD, Phys. Rev. D 82 (2010) 034512 [arXiv:1004.4285] [INSPIRE].
A. Bazavov et al., Staggered chiral perturbation theory in the two-flavor case and SU(2) analysis of the MILC data, PoS LATTICE2010 (2010) 083 [arXiv:1011.1792] [INSPIRE].
Fermilab Lattice et al. collaborations, Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD, Phys. Rev. D 98 (2018) 054517 [arXiv:1802.04248] [INSPIRE].
European Twisted Mass collaboration, Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD, Nucl. Phys. B 887 (2014) 19 [arXiv:1403.4504] [INSPIRE].
M. Gorchtein, γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum, Phys. Rev. Lett. 123 (2019) 042503 [arXiv:1812.04229] [INSPIRE].
M. Gorchtein and C.-Y. Seng, Dispersion relation analysis of the radiative corrections to gA in the neutron β-decay, JHEP 10 (2021) 053 [arXiv:2106.09185] [INSPIRE].
S. Ando et al., Neutron beta decay in effective field theory, Phys. Lett. B 595 (2004) 250 [nucl-th/0402100] [INSPIRE].
D.H. Wilkinson, Analysis of neutron beta decay, Nucl. Phys. A 377 (1982) 474 [INSPIRE].
J.D. Jackson, S.B. Treiman and H.W. Wyld, Coulomb corrections in allowed beta transitions, Nucl. Phys. 4 (1957) 206 [INSPIRE].
M. González-Alonso and O. Naviliat-Cuncic, Kinematic sensitivity to the Fierz term of β-decay differential spectra, Phys. Rev. C 94 (2016) 035503 [arXiv:1607.08347] [INSPIRE].
G. Darius et al., Measurement of the Electron-Antineutrino Angular Correlation in Neutron β Decay, Phys. Rev. Lett. 119 (2017) 042502 [INSPIRE].
M.T. Hassan et al., Measurement of the neutron decay electron-antineutrino angular correlation by the aCORN experiment, Phys. Rev. C 103 (2021) 045502 [arXiv:2012.14379] [INSPIRE].
UCNτ collaboration, Improved neutron lifetime measurement with UCNτ , Phys. Rev. Lett. 127 (2021) 162501 [arXiv:2106.10375] [INSPIRE].
T.E. Chupp et al., Search for a T-odd, P-even Triple Correlation in Neutron Decay, Phys. Rev. C 86 (2012) 035505 [arXiv:1205.6588] [INSPIRE].
A. Kozela et al., Measurement of transverse polarization of electrons emitted in free neutron decay, Phys. Rev. C 85 (2012) 045501 [arXiv:1111.4695] [INSPIRE].
J. Ng and S. Tulin, D versus d: CP Violation in Beta Decay and Electric Dipole Moments, Phys. Rev. D 85 (2012) 033001 [arXiv:1111.0649] [INSPIRE].
K.K. Vos, H.W. Wilschut and R.G.E. Timmermans, Symmetry violations in nuclear and neutron β decay, Rev. Mod. Phys. 87 (2015) 1483 [arXiv:1509.04007] [INSPIRE].
S. Alioli et al., Right-handed charged currents in the era of the Large Hadron Collider, JHEP 05 (2017) 086 [arXiv:1703.04751] [INSPIRE].
V. Cirigliano et al., Semileptonic tau decays beyond the Standard Model, JHEP 04 (2022) 152 [arXiv:2112.02087] [INSPIRE].
B.M. Rebeiro et al., Precise branching ratio measurements in 19Neβ decay and fundamental tests of the weak interaction, Phys. Rev. C 99 (2019) 065502 [arXiv:1810.02331] [INSPIRE].
D. Combs et al., A look into mirrors: A measurement of the β-asymmetry in 19Ne decay and searches for new physics, arXiv:2009.13700 [INSPIRE].
M. Beck et al., Improved determination of the β-νe angular correlation coefficient a in free neutron decay with the aSPECT spectrometer, Phys. Rev. C 101 (2020) 055506 [arXiv:1908.04785] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, Scattering amplitudes for all masses and spins, JHEP 11 (2021) 070 [arXiv:1709.04891] [INSPIRE].
W. Mampe et al., Measuring neutron lifetime by storing ultracold neutrons and detecting inelastically scattered neutrons, JETP Lett. 57 (1993) 82.
J. Byrne and P.G. Dawber, A revised Value for the Neutron Lifetime Measured Using a Penning Trap, EPL 33 (1996) 187 [INSPIRE].
A. Serebrov et al., Measurement of the neutron lifetime using a gravitational trap and a low-temperature Fomblin coating, Phys. Lett. B 605 (2005) 72 [nucl-ex/0408009] [INSPIRE].
A. Pichlmaier, V. Varlamov, K. Schreckenbach and P. Geltenbort, Neutron lifetime measurement with the UCN trap-in-trap MAMBO II, Phys. Lett. B 693 (2010) 221 [INSPIRE].
A. Steyerl et al., Quasielastic scattering in the interaction of ultracold neutrons with a liquid wall and application in a reanalysis of the Mambo I neutron-lifetime experiment, Phys. Rev. C 85 (2012) 065503 [INSPIRE].
A.T. Yue et al., Improved Determination of the Neutron Lifetime, Phys. Rev. Lett. 111 (2013) 222501 [arXiv:1309.2623] [INSPIRE].
V.F. Ezhov et al., Measurement of the neutron lifetime with ultra-cold neutrons stored in a magneto-gravitational trap, JETP Lett. 107 (2018) 671 [arXiv:1412.7434] [INSPIRE].
S. Arzumanov et al., A measurement of the neutron lifetime using the method of storage of ultracold neutrons and detection of inelastically up-scattered neutrons, Phys. Lett. B 745 (2015) 79 [INSPIRE].
R.W. Pattie Jr. et al., Measurement of the neutron lifetime using a magneto-gravitational trap and in situ detection, Science 360 (2018) 627 [arXiv:1707.01817] [INSPIRE].
A.P. Serebrov et al., Neutron lifetime measurements with a large gravitational trap for ultracold neutrons, Phys. Rev. C 97 (2018) 055503 [arXiv:1712.05663] [INSPIRE].
P. Bopp et al., The Beta Decay Asymmetry of the Neutron and gA/gV , Phys. Rev. Lett. 56 (1986) 919 [Erratum ibid. 57 (1986) 1192] [INSPIRE].
P. Liaud et al., The measurement of the beta asymmetry in the decay of polarized neutrons, Nucl. Phys. A 612 (1997) 53 [INSPIRE].
B. Erozolimsky, I. Kuznetsov, I. Stepanenko and Y.A. Mostovoi, Corrigendum: Corrected value of the beta-emission asymmetry in the decay of polarized neutrons measured in 1990 [https://doi.org/10.1016/S0370-2693(97)01004-6] [INSPIRE].
D. Mund et al., Determination of the Weak Axial Vector Coupling from a Measurement of the Beta-Asymmetry Parameter A in Neutron Beta Decay, Phys. Rev. Lett. 110 (2013) 172502 [arXiv:1204.0013] [INSPIRE].
UCNA collaboration, New result for the neutron β-asymmetry parameter A0 from UCNA, Phys. Rev. C 97 (2018) 035505 [arXiv:1712.00884] [INSPIRE].
B. Märkisch et al., Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam, Phys. Rev. Lett. 122 (2019) 242501 [arXiv:1812.04666] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
I.A. Kuznetsov et al., Measurements of the anti-neutrino spin asymmetry in beta decay of the neutron and restrictions on the mass of a right-handed gauge boson, Phys. Rev. Lett. 75 (1995) 794 [INSPIRE].
A.P. Serebrov et al., Measurement of the anti-neutrino escape asymmetry with respect to the spin of the decaying neutron, J. Exp. Theor. Phys. 86 (1998) 1074 [INSPIRE].
M. Kreuz et al., A measurement of the antineutrino asymmetry B in free neutron decay, Phys. Lett. B 619 (2005) 263 [INSPIRE].
M. Schumann et al., Measurement of the neutrino asymmetry parameter B in neutron decay, Phys. Rev. Lett. 99 (2007) 191803 [arXiv:0706.3788] [INSPIRE].
Y.A. Mostovoi et al., Experimental value of GA/GV from a measurement of both P-odd correlations in free-neutron decay, Phys. Atom. Nucl. 64 (2001) 1955 [INSPIRE].
C. Stratowa, R. Dobrozemsky and P. Weinzierl, Ratio Ga/Gv Derived from the Proton Spectrum in Free Neutron Decay, Phys. Rev. D 18 (1978) 3970 [INSPIRE].
J. Byrne et al., Determination of the \( electron\overline{n} eutrino \) angular correlation coefficient a0 and the parameter |λ| = |GA/GV| in free neutron beta decay from measurements of the integrated energy spectrum of recoil protons stored in an ion trap, J. Phys. G 28 (2002) 1325 [INSPIRE].
M. Brodeur et al., Precision half-life measurement of 17F, Phys. Rev. C 93 (2016) 025503 [INSPIRE].
N. Severijns, J. Wouters, J. Vanhaverbeke and L. Vanneste, β-decay anisotropies of the mirror nuclei 15O and 17F, Phys. Rev. Lett. 63 (1989) 1050.
N. Severijns, M. Beck and O. Naviliat-Cuncic, Tests of the standard electroweak model in beta decay, Rev. Mod. Phys. 78 (2006) 991 [nucl-ex/0605029] [INSPIRE].
F.P. Calaprice, S.J. Freedman, W.C. Mead and H.C. Vantine, Experimental Study of Weak Magnetism and Second-Class Interaction Effects in the beta Decay of Polarized Ne-19, Phys. Rev. Lett. 35 (1975) 1566 [INSPIRE].
J. Karthein et al., QEC -value determination for 21Na→ 21Ne and 23Mg→ 23Na mirror-nuclei decays using high-precision mass spectrometry with ISOLTRAP at the CERN ISOLDE facility, Phys. Rev. C 100 (2019) 015502 [Erratum ibid. 101 (2020) 049901] [arXiv:1906.01538] [INSPIRE].
P.A. Vetter, J.R. Abo-Shaeer, S.J. Freedman and R. Maruyama, Measurement of the β – ν correlation of 21Na using shakeoff electrons, Phys. Rev. C 77 (2008) 035502 [arXiv:0805.1212] [INSPIRE].
J. Long et al., Precision half-life measurement of 29P , Phys. Rev. C 101 (2020) 015501 [INSPIRE].
G.S. Masson and P.A. Quin, Measurement of the asymmetry parameter for 29P beta decay, Phys. Rev. C 42 (1990) 1110 [INSPIRE].
N. Severijns, M. Tandecki, T. Phalet and I.S. Towner, Ft values of the T = 1/2 mirror β transitions, Phys. Rev. C 78 (2008) 055501 [arXiv:0807.2201] [INSPIRE].
J.D. Garnett, E.D. Commins, K.T. Lesko and E.B. Norman, The Beta Decay Asymmetry Parameter for 35Ar: An Anomaly Resolved, Phys. Rev. Lett. 60 (1988) 499 [INSPIRE].
A. Converse et al., Measurement of the asymmetry parameter for 35Ar β-decay as a test of the CVC hypothesis, Phys. Lett. B 304 (1993) 60 [INSPIRE].
O. Naviliat-Cuncic and N. Severijns, Test of the Conserved Vector Current Hypothesis in T = 1/2 Mirror Transitions and New Determination of |Vud|, Phys. Rev. Lett. 102 (2009) 142302 [arXiv:0809.0994] [INSPIRE].
P.D. Shidling et al., Precision half-life measurement of the β+ decay of 37K, Phys. Rev. C 90 (2014) 032501 [arXiv:1407.1742] [INSPIRE].
B. Fenker et al., Precision measurement of the β-asymmetry in spin-polarized 37K decay, Phys. Rev. Lett. 120 (2018) 062502 [arXiv:1706.00414] [INSPIRE].
D. Melconian et al., Measurement of the neutrino asymmetry in the beta decay of laser-cooled polarized 37K, Phys. Lett. B 649 (2007) 370 [INSPIRE].
ISOLDE collaboration, Positron neutrino correlation in the 0+ → 0+ decay of 32Ar, Phys. Rev. Lett. 83 (1999) 1299 [Erratum ibid. 83 (1999) 3101] [nucl-ex/9903002] [INSPIRE].
A. Gorelov et al., Scalar interaction limits from the β – ν correlation of trapped radioactive atoms, Phys. Rev. Lett. 94 (2005) 142501 [nucl-ex/0412032] [INSPIRE].
M. Butler and J.-W. Chen, Proton proton fusion in effective field theory to fifth order, Phys. Lett. B 520 (2001) 87 [nucl-th/0101017] [INSPIRE].
V. Cirigliano, M.L. Graesser and G. Ovanesyan, WIMP-nucleus scattering in chiral effective theory, JHEP 10 (2012) 025 [arXiv:1205.2695] [INSPIRE].
M. Hoferichter, P. Klos and A. Schwenk, Chiral power counting of one- and two-body currents in direct detection of dark matter, Phys. Lett. B 746 (2015) 410 [arXiv:1503.04811] [INSPIRE].
M.J. Savage et al., Proton-Proton Fusion and Tritium β Decay from Lattice Quantum Chromodynamics, Phys. Rev. Lett. 119 (2017) 062002 [arXiv:1610.04545] [INSPIRE].
H. De-Leon, L. Platter and D. Gazit, Tritium β-decay in pionless effective field theory, Phys. Rev. C 100 (2019) 055502 [arXiv:1611.10004] [INSPIRE].
C. Körber, A. Nogga and J. de Vries, First-principle calculations of Dark Matter scattering off light nuclei, Phys. Rev. C 96 (2017) 035805 [arXiv:1704.01150] [INSPIRE].
NPLQCD collaboration, Axial charge of the triton from lattice QCD, Phys. Rev. D 103 (2021) 074511 [arXiv:2102.03805] [INSPIRE].
W. Detmold and P.E. Shanahan, Few-nucleon matrix elements in pionless effective field theory in a finite volume, Phys. Rev. D 103 (2021) 074503 [arXiv:2102.04329] [INSPIRE].
Acknowledgments
AF and ARS are partially supported by the Agence Nationale de la Recherche (ANR) under grant ANR-19-CE31-0012 (project MORA). AF is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 860881 (HIDDe_ network). MGA is supported by the Generalitat Valenciana (Spain) through the plan GenT program (CIDEGENT/2018/014), and
MCIN/AEI/10.13039/501100011033 Grant No. PID2020-114473GB-I00. The work of AP has received funding from the Swiss National Science Foundation (SNF) through the Eccellenza Professorial Fellowship “Flavor Physics at the High Energy Frontier” project number 186866.
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Falkowski, A., González-Alonso, M., Palavrić, A. et al. Constraints on subleading interactions in beta decay Lagrangian. J. High Energ. Phys. 2024, 91 (2024). https://doi.org/10.1007/JHEP02(2024)091
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DOI: https://doi.org/10.1007/JHEP02(2024)091