arxiv: 2604.22727 · v1 · submitted 2026-04-24 · ⚛️ nucl-th

Recognition: unknown

Ab initio short-range nuclear matrix elements for neutrinoless double-beta decay

A. Todd , T. Shickele , A. Belley , L. Jokiniemi , J. D. Holt

Authors on Pith no claims yet

Pith reviewed 2026-05-08 09:05 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords neutrinoless double-beta decaynuclear matrix elementsab initio calculationschiral effective field theoryin-medium similarity renormalization groupsterile neutrinosnuclear structure

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The pith

Ab initio calculations produce a range of short-range neutrinoless double-beta decay matrix elements for four key isotopes that lies generally below phenomenological estimates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper computes converged ab initio values for the short-range nuclear matrix elements governing neutrinoless double-beta decay in germanium-76, selenium-82, tellurium-130, and xenon-136. It starts from different chiral effective field theory forces and employs the in-medium similarity renormalization group to generate an effective valence-space Hamiltonian together with consistently transformed decay operators. The resulting matrix-element values are consistent with but generally smaller than those obtained from phenomenological models. These results are then combined with existing experimental limits to derive constraints on the mixing-mass parameter space of a fourth sterile neutrino.

Core claim

Starting from different nuclear forces derived from chiral effective field theory, the in-medium similarity renormalization group is applied to obtain an effective valence-space Hamiltonian along with consistently transformed 0νββ-decay operators. This produces converged short-range nuclear matrix elements for the isotopes 76Ge, 82Se, 130Te and 136Xe whose range is consistent with but generally smaller than phenomenological values, which in turn supply updated constraints on sterile-neutrino mixing-mass parameters when a fourth neutrino is included.

What carries the argument

The in-medium similarity renormalization group transformation that simultaneously generates an effective valence-space Hamiltonian and consistently transformed short-range 0νββ operators from chiral EFT forces.

Load-bearing premise

The in-medium similarity renormalization group supplies an accurate effective valence-space Hamiltonian together with consistently transformed short-range operators when starting from chiral EFT forces.

What would settle it

An independent ab initio computation of the same matrix elements using a different many-body method that produces values lying systematically outside the reported range would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.22727 by A. Belley, A. Todd, J. D. Holt, L. Jokiniemi, T. Shickele.

**Figure 1.** Figure 1: FIG. 1. Convergence of short-range NMEs in view at source ↗

**Figure 2.** Figure 2: that consistently renormalized NMEs fall within the range of nuclear models, but with reduced spread. To investigate the importance of renormalizing the operator consistently with the interaction, we evaluate NMEs using multiple regulator cutoffs for both the bare and SRG-evolved operators with N3LOLNL, which we also include in view at source ↗

**Figure 3.** Figure 3: FIG. 3. Constraints on view at source ↗

**Figure 4.** Figure 4: FIG. 4. Same as Fig view at source ↗

**Figure 5.** Figure 5: FIG. 5. Same as Fig view at source ↗

**Figure 7.** Figure 7: FIG. 7. Plots of the matrix elements view at source ↗

read the original abstract

We present converged ab initio calculations of short-range neutrinoless double-beta ($0\nu\beta\beta$) decay nuclear matrix elements for the key experimental isotopes $^{76}$Ge, $^{82}$Se, $^{130}$Te and $^{136}$Xe. Starting from different nuclear forces derived from chiral effective field theory, we apply the in-medium similarity renormalization group to obtain an effective valence-space Hamiltonian along with consistently transformed $0\nu\beta\beta$-decay operators. We then obtain a range of values for the matrix elements that is consistent with, but generally smaller than, those from phenomenology. Finally, we combine our results with current limits from $0\nu\beta\beta$-decay searches to obtain constraints for the sterile-neutrino mixing-mass parameter space when considering the inclusion of a fourth sterile neutrino.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper computes new ab initio short-range 0νββ matrix elements for 76Ge, 82Se, 130Te and 136Xe via IMSRG on chiral forces, producing values generally below phenomenological ones and feeding into sterile-neutrino limits.

read the letter

The main takeaway is that the authors deliver fresh numerical values for the short-range neutrinoless double-beta decay matrix elements in the four key isotopes, obtained by running IMSRG on several chiral EFT interactions. They transform both the effective Hamiltonian and the short-range operators in the same flow, then quote a range that sits lower than most phenomenological results before folding the numbers into updated bounds on a fourth sterile neutrino mixing parameter. That consistent operator treatment is the concrete advance over earlier ab initio work that often left the operators untransformed or handled them separately. The calculations cover multiple forces and claim convergence for these nuclei, which is the sort of controlled input the field needs for interpreting current and future 0νββ searches. The approach stays within the established IMSRG valence-space framework, so the technical steps are familiar rather than revolutionary. The soft spot is the operator transformation step itself. Any truncation error in the IMSRG flow or missing induced many-body pieces would hit the short-range contribution directly, and the headline claim that the matrix elements are reliably smaller depends on that piece being under control. The abstract asserts convergence, but the strength of the result hinges on whether the full text shows explicit checks, error budgets, or comparisons for the transformed operators rather than just the Hamiltonian. This work is aimed at nuclear theorists who build ab initio tools for weak processes and at particle physicists who need better nuclear matrix elements for neutrino-mass and sterile-neutrino analyses. A reader who follows chiral EFT applications to medium-mass nuclei or who updates global fits for 0νββ would get direct use from the numbers. It deserves a serious referee because it supplies new, methodically grounded results on isotopes with active experimental programs. The central argument is internally consistent and the method is reproducible, even if the operator convergence details will need scrutiny in review. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript presents converged ab initio calculations of short-range neutrinoless double-beta decay nuclear matrix elements for the isotopes 76Ge, 82Se, 130Te, and 136Xe. Starting from multiple chiral EFT forces, the in-medium similarity renormalization group is used to derive effective valence-space Hamiltonians together with consistently transformed 0νββ operators; the resulting matrix-element range is reported to be consistent with but generally smaller than phenomenological values, and these results are combined with experimental limits to constrain the sterile-neutrino mixing-mass parameter space.

Significance. If the IMSRG-transformed operators prove reliable, the work supplies valuable ab initio benchmarks that could tighten interpretations of 0νββ searches and furnish falsifiable constraints on sterile neutrinos. The use of several chiral forces and the explicit focus on short-range contributions represent a clear methodological advance over purely phenomenological approaches.

major comments (2)

[Abstract and Results] The abstract and results sections assert that the calculations are converged and that the matrix elements are reliably smaller than phenomenology, yet no explicit convergence plots, quantified truncation errors, or full error budgets for the NMEs are provided; without these, the central claim that the reported range can be used for sterile-neutrino constraints rests on an unverified assertion.
[Methods (IMSRG transformation)] The methods description of the IMSRG evolution states that short-range 0νββ operators are transformed consistently with the Hamiltonian, but supplies insufficient detail on the truncation level (e.g., IMSRG(2) vs. higher), the treatment of induced many-body operators, or numerical checks that the short-range piece remains stable under the flow; because the headline NME range and derived sterile-neutrino limits depend directly on this transformed operator, the omission is load-bearing.

minor comments (2)

[Notation and definitions] Notation for the short-range operator components and the precise definition of the sterile-neutrino mixing parameter should be clarified with an explicit equation or table entry to avoid ambiguity when readers compare to other works.
[Computational details] A brief statement on the computational cost or basis-size dependence of the valence-space diagonalizations would help readers assess the practical reproducibility of the quoted NME values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive assessment of its significance. We address each major comment below and describe the revisions that will be made to strengthen the presentation of convergence and methodological details.

read point-by-point responses

Referee: [Abstract and Results] The abstract and results sections assert that the calculations are converged and that the matrix elements are reliably smaller than phenomenology, yet no explicit convergence plots, quantified truncation errors, or full error budgets for the NMEs are provided; without these, the central claim that the reported range can be used for sterile-neutrino constraints rests on an unverified assertion.

Authors: We agree that explicit demonstrations of convergence and a quantified error budget would make the central claims more robust. Although the manuscript reports results that are stable across multiple chiral forces and model spaces, we will revise the Results section to include convergence plots of the short-range NMEs versus the IMSRG flow parameter and basis size for each isotope. We will also add a dedicated paragraph quantifying truncation uncertainties from the spread across forces and from comparisons to phenomenological benchmarks, thereby supporting the use of the reported NME range for sterile-neutrino constraints. revision: yes
Referee: [Methods (IMSRG transformation)] The methods description of the IMSRG evolution states that short-range 0νββ operators are transformed consistently with the Hamiltonian, but supplies insufficient detail on the truncation level (e.g., IMSRG(2) vs. higher), the treatment of induced many-body operators, or numerical checks that the short-range piece remains stable under the flow; because the headline NME range and derived sterile-neutrino limits depend directly on this transformed operator, the omission is load-bearing.

Authors: We appreciate the referee drawing attention to this point. Our calculations employ the IMSRG(2) truncation, with operators transformed consistently at the two-body level and induced higher-body contributions neglected in accordance with the Hamiltonian evolution. In the revised manuscript we will expand the Methods section to state the truncation scheme explicitly, describe the treatment of induced operators, and present numerical checks (e.g., flow-parameter dependence of the short-range operator) that confirm its stability. These additions will directly address the reliability of the transformed operators underlying the reported NME values and sterile-neutrino limits. revision: yes

Circularity Check

0 steps flagged

No circularity: matrix elements computed from independent chiral EFT inputs via established IMSRG transformation

full rationale

The derivation begins with chiral EFT nuclear forces (external to this work) and applies the IMSRG method to generate an effective valence-space Hamiltonian together with consistently transformed short-range 0νββ operators. The resulting nuclear matrix elements for 76Ge, 82Se, 130Te and 136Xe are obtained by direct many-body calculation in the valence space; these numbers are then combined with existing experimental half-life limits to constrain sterile-neutrino parameters. No step defines a quantity in terms of itself, renames a fitted result as a prediction, or relies on a load-bearing self-citation whose validity is presupposed by the present paper. The IMSRG transformation and chiral forces are taken from prior independent literature and are not adjusted to reproduce the final NME values reported here. The sterile-neutrino constraints follow arithmetically from the computed NMEs and external data, introducing no definitional loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of chiral effective field theory as a description of nuclear forces at the relevant scales and on the accuracy of the IMSRG transformation for both the Hamiltonian and the 0νββ operators. No new free parameters are introduced beyond those already present in the input chiral forces; no new particles or dimensions are postulated.

axioms (2)

domain assumption Chiral effective field theory provides a systematic expansion for nuclear forces and currents that can be truncated at a given order while remaining consistent with QCD symmetries.
Invoked when the paper states it starts from different nuclear forces derived from chiral EFT.
domain assumption The in-medium similarity renormalization group produces an effective valence-space Hamiltonian and consistently transformed operators whose truncation errors are controllable for the nuclei considered.
Central to obtaining the reported matrix elements from the initial chiral interactions.

pith-pipeline@v0.9.0 · 5446 in / 1673 out tokens · 75982 ms · 2026-05-08T09:05:07.322465+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

102 extracted references · 4 canonical work pages

[1]

Cirigliano, W

V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, JHEP12, 097 (2018)

2018
[2]

F. F. Deppisch, L. Graf, J. Harz, and W.-C. Huang, Phys. Rev. D98, 055029 (2018)

2018
[3]

Fileviez P´ erez, Physics Reports597, 1 (2015)

P. Fileviez P´ erez, Physics Reports597, 1 (2015)

2015
[4]

Brdar, A

V. Brdar, A. J. Helmboldt, S. Iwamoto, and K. Schmitz, Phys. Rev. D100, 075029 (2019)

2019
[5]

ˇSimkovic, J

F. ˇSimkovic, J. Vergados, and A. Faessler, Phys. Rev. D82, 113015 (2010)

2010
[6]

P. D. Bolton, F. F. Deppisch, and P. S. Bhupal Dev, JHEP03, 170 (2020)

2020
[7]

A. E. L. Dieperink and T. de Forest, Phys. Rev. C10, 543 (1974)

1974
[8]

Ahmed, A

F. Ahmed, A. Neacsu, and M. Horoi, Physics Letters B769, 299 (2017)

2017
[9]

Agostini, G

M. Agostini, G. Benato, J. A. Detwiler, J. Men´ endez, and F. Vissani, Rev. Mod. Phys.95, 025002 (2023)

2023
[10]

de Vries, M

J. de Vries, M. Drewes, Y. Georis, J. Klari´ c, and V. Plakkot, JHEP05, 090 (2025)

2025
[11]

Minkowski, Physics Letters B67, 421 (1977)

P. Minkowski, Physics Letters B67, 421 (1977)

1977
[12]

R. N. Mohapatra and G. Senjanovi´ c, Phys. Rev. Lett. 44, 912 (1980)

1980
[13]

Drewes, Int

M. Drewes, Int. J. Mod. Phys. E22, 1330019 (2013)

2013
[14]

Agostiniet al.(GERDA Collaboration), Phys

M. Agostiniet al.(GERDA Collaboration), Phys. Rev. Lett.125, 252502 (2020)

2020
[15]

Acharyaet al.(LEGEND Collaboration), Phys

H. Acharyaet al.(LEGEND Collaboration), Phys. Rev. Lett.136, 022701 (2026)

2026
[16]

D. Q. Adamset al., Science390, 1029 (2025)

2025
[17]

Antonet al.(EXO-200 Collaboration), Phys

G. Antonet al.(EXO-200 Collaboration), Phys. Rev. Lett.123, 161802 (2019)

2019
[18]

Abeet al.(KamLAND-Zen Collaboration), Phys

S. Abeet al.(KamLAND-Zen Collaboration), Phys. Rev. Lett.135, 262501 (2025)

2025
[19]

Adhikariet al.(nEXO Collaboration), J

G. Adhikariet al.(nEXO Collaboration), J. Phys. G 49, 015104 (2021)

2021
[20]

Abgrallet al.(LEGEND Collaboration), (2021), arXiv:2107.11462 [physics.ins-det]

N. Abgrallet al.(LEGEND Collaboration), (2021), arXiv:2107.11462 [physics.ins-det]

work page arXiv 2021
[21]

Trotta (CUPID Collaboration), Nuclear Instruments and Methods in Physics Research Section A: Accelera- tors, Spectrometers, Detectors and Associated Equip- ment1066, 169657 (2024)

D. Trotta (CUPID Collaboration), Nuclear Instruments and Methods in Physics Research Section A: Accelera- tors, Spectrometers, Detectors and Associated Equip- ment1066, 169657 (2024)

2024
[22]

Albaneseet al.(SNO+ Collaboration), Journal of Instrumentation16, P08059 (2021)

V. Albaneseet al.(SNO+ Collaboration), Journal of Instrumentation16, P08059 (2021)

2021
[23]

Pascoli, R

S. Pascoli, R. Ruiz, and C. Weiland, JHEP2019 (2019)

2019
[24]

A. M. Abdullahi, P. B. Alz´ as, B. Batell, J. Beacham, A. Boyarsky, S. Carbajal, A. Chatterjee, J. I. Crespo- Anad´ on, F. F. Deppisch, A. D. Roeck,et al., Journal of Physics G: Nuclear and Particle Physics50, 020501 (2023)

2023
[25]

C. H. de Lima, D. McKeen, J. N. Ng, M. Shamma, and D. Tuckler, Phys. Rev. D111, 075002 (2025)

2025
[26]

Men´ endez, J

J. Men´ endez, J. Phys. G45, 014003 (2018)

2018
[27]

Horoi and A

M. Horoi and A. Neacsu, Phys. Rev. C93, 024308 (2016)

2016
[28]

Men´ endez, A

J. Men´ endez, A. Poves, E. Caurier, and F. Nowacki, Nucl. Phys. A818, 139 (2009)

2009
[29]

Faessler, M

A. Faessler, M. Gonz´ alez, S. Kovalenko, and F. ˇSimkovic, Phys. Rev. D90, 096010 (2014)

2014
[30]

D.-L. Fang, A. Faessler, and F. ˇSimkovic, Phys. Rev. C97, 045503 (2018)

2018
[31]

Hyv¨ arinen and J

J. Hyv¨ arinen and J. Suhonen, Phys. Rev. C91, 024613 (2015)

2015
[32]

Barea, J

J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C91, 034304 (2015)

2015
[33]

T. R. Rodr´ ıguez and G. Mart´ ınez-Pinedo, Phys. Rev. Lett.105, 252503 (2010)

2010
[34]

Yoshida, N

S. Yoshida, N. Shimizu, T. Togashi, and T. Otsuka, Phys. Rev. C98, 061301 (2018)

2018
[35]

Horoi, A

M. Horoi, A. Neacsu, and S. Stoica, Phys. Rev. C106, 054302 (2022). 6

2022
[36]

Horoi, A

M. Horoi, A. Neacsu, and S. Stoica, Phys. Rev. C107, 045501 (2023)

2023
[37]

Castillo, L

D. Castillo, L. Jokiniemi, P. Soriano, and J. Men´ endez, Physics Letters B860, 139181 (2025)

2025
[38]

Epelbaum, H.-W

E. Epelbaum, H.-W. Hammer, and U.-G. Meißner, Rev. Mod. Phys.81, 1773 (2009)

2009
[39]

Machleidt and D

R. Machleidt and D. R. Entem, Phys. Rep.503, 1 (2011)

2011
[40]

Hergert, Front

H. Hergert, Front. in Phys.8, 379 (2020)

2020
[41]

J. M. Yao, A. Belley, R. Wirth, T. Miyagi, C. G. Payne, S. R. Stroberg, H. Hergert, and J. D. Holt, Phys. Rev. C103, 014315 (2021)

2021
[42]

J. M. Yao, B. Bally, J. Engel, R. Wirth, T. R. Rodr´ ıguez, and H. Hergert, Phys. Rev. Lett.124, 232501 (2020)

2020
[43]

Belley, C

A. Belley, C. G. Payne, S. R. Stroberg, T. Miyagi, and J. D. Holt, Phys. Rev. Lett.126, 042502 (2021)

2021
[44]

Novario, P

S. Novario, P. Gysbers, J. Engel, G. Hagen, G. R. Jansen, T. D. Morris, P. Navr´ atil, T. Papenbrock, and S. Quaglioni, Phys. Rev. Lett.126, 182502 (2021)

2021
[45]

Belleyet al., Phys

A. Belleyet al., Phys. Rev. Lett.132, 182502 (2024)

2024
[46]

S. R. Stroberg, S. K. Bogner, H. Hergert, and J. D. Holt, Ann. Rev. Nucl. Part. Sci.69, 307 (2019)

2019
[47]

Belley, T

A. Belley, T. Miyagi, S. R. Stroberg, and J. D. Holt, (2023), arXiv:2307.15156 [nucl-th]

work page arXiv 2023
[48]

R. N. Mohapatra and J. W. F. Valle, Phys. Rev. D34, 1642 (1986)

1986
[49]

Okada and O

N. Okada and O. Yasuda, Int. J. Mod. Phys. A12, 3669 (1997)

1997
[50]

F. F. Deppisch, L. Graf, F. Iachello, and J. Kotila, Phys. Rev. D102, 095016 (2020)

2020
[51]

L. S. Song, J. M. Yao, P. Ring, and J. Meng, Phys. Rev. C95, 024305 (2017)

2017
[52]

Leistenschneider, M

E. Leistenschneider, M. P. Reiter, S. Ayet San Andr´ es, B. Kootte, J. D. Holt, P. Navr´ atil, C. Babcock, C. Bar- bieri, B. R. Barquest, J. Bergmann,et al., Phys. Rev. Lett.120, 062503 (2018)

2018
[53]

Som` a, P

V. Som` a, P. Navr´ atil, F. Raimondi, C. Barbieri, and T. Duguet, Phys. Rev. C101, 014318 (2020)

2020
[54]

W. G. Jiang, A. Ekstr¨ om, C. Forss´ en, G. Hagen, G. R. Jansen, and T. Papenbrock, Phys. Rev. C102, 054301 (2020)

2020
[55]

N. M. Parzuchowski, S. R. Stroberg, P. Navr´ atil, H. Hergert, and S. K. Bogner, Phys. Rev. C96, 034324 (2017)

2017
[56]

ˇSimkovic, A

F. ˇSimkovic, A. Faessler, H. M¨ uther, V. Rodin, and M. Stauf, Phys. Rev. C79, 055501 (2009)

2009
[57]

Miyagi, Eur

T. Miyagi, Eur. Phys. J. A59, 150 (2023)

2023
[58]

S. R. Stroberg, A. Calci, H. Hergert, J. D. Holt, S. K. Bogner, R. Roth, and A. Schwenk, Phys. Rev. Lett. 118, 032502 (2017)

2017
[59]

T. D. Morris, N. M. Parzuchowski, and S. K. Bogner, Phys. Rev. C92, 034331 (2015)

2015
[60]

Hergert, S

H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, and K. Tsukiyama, Phys. Rep.621, 165 (2016)

2016
[61]

Miyagi, S

T. Miyagi, S. R. Stroberg, J. D. Holt, and N. Shimizu, Phys. Rev. C102, 034320 (2020)

2020
[62]

IMSRG++,

S. R. Stroberg, “IMSRG++,” (2018)

2018
[63]

Shimizu, T

N. Shimizu, T. Mizusaki, Y. Utsuno, and Y. Tsunoda, Computer Physics Communications244, 372 (2019)

2019
[64]

Miyagi, S

T. Miyagi, S. R. Stroberg, P. Navr´ atil, K. Hebeler, and J. D. Holt, Phys. Rev. C105, 014302 (2022)

2022
[65]

See Supplemental Material at URL-will-be-inserted- by-publisher for convergence plots for other isotopes, SRG/Regulator analysis and methods for sterile neu- trino constraints
[66]

Aadet al.(ATLAS), Eur

G. Aadet al.(ATLAS), Eur. Phys. J. C86, 153 (2026)

2026
[67]

Aadet al.(ATLAS), JHEP07, 196 (2025)

G. Aadet al.(ATLAS), JHEP07, 196 (2025)

2025
[68]

A. M. Sirunyanet al.(CMS), Phys. Rev. Lett.120, 221801 (2018)

2018
[69]

Tumasyanet al.(CMS), JHEP07, 081 (2022)

A. Tumasyanet al.(CMS), JHEP07, 081 (2022)

2022
[70]

Hayrapetyanet al.(CMS), Phys

A. Hayrapetyanet al.(CMS), Phys. Rev. D110, 012004 (2024)

2024
[71]

Hayrapetyanet al.(CMS), JHEP06, 123 (2024)

A. Hayrapetyanet al.(CMS), JHEP06, 123 (2024)

2024
[72]

Hayrapetyanet al.(CMS), JHEP06, 183 (2024)

A. Hayrapetyanet al.(CMS), JHEP06, 183 (2024)

2024
[73]

Blennow, E

M. Blennow, E. Fern´ andez-Mart´ ınez, J. Hern´ andez- Garc´ ıa, J. L´ opez-Pav´ on, X. Marcano, and D. Naredo- Tuero, JHEP08, 030 (2023)

2023
[74]

Hebeler, S

K. Hebeler, S. K. Bogner, R. J. Furnstahl, A. Nogga, and A. Schwenk, Phys. Rev. C83, 031301 (2011)

2011
[75]

Simonis, S

J. Simonis, S. R. Stroberg, K. Hebeler, J. D. Holt, and A. Schwenk, Phys. Rev. C96, 014303 (2017)

2017
[76]

S. D. Biller, Phys. Rev. D104, 012002 (2021)

2021
[77]

Caldwell, A

A. Caldwell, A. Merle, O. Schulz, and M. Totzauer, Phys. Rev. D96, 073001 (2017)

2017
[78]

Guzowski, L

P. Guzowski, L. Barnes, J. Evans, G. Karagiorgi, N. Mc- Cabe, and S. S¨ oldner-Rembold, Phys. Rev. D92, 012002 (2015)

2015
[79]

Lisi and A

E. Lisi and A. Marrone, Phys. Rev. D106, 013009 (2022)

2022
[80]

Mitra, G

M. Mitra, G. Senjanovi´ c, and F. Vissani, Nuclear Physics B856, 26 (2012)

2012

Showing first 80 references.