Astronomy:MINERνA

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Short description: Neutrino scattering experiment at Fermilab in Illinois, USA
MINERνA
Websitehttps://minerva.fnal.gov
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Main Injector Experiment for ν-A, or MINERνA, is a neutrino scattering experiment which uses the NuMI beamline at Fermilab. MINERνA seeks to measure low energy neutrino interactions both in support of neutrino oscillation experiments and also to study the strong dynamics of the nucleon and nucleus that affect these interactions.[1]

Name

MINERvA's name combines several things. "MI" stands for the Main Injector, a Fermilab accelerator that provides high-energy protons which are targeted to create the neutrino beam. "NER" comes from "Neutrino ExpeRiment." The conventional symbol for the neutrino is the Greek letter nu, which resembles a lowercase "v". Finally, "A" represents the mass number of the target material. MINERvA studies neutrino interactions with several materials, in particular helium, carbon, iron or lead, each having a different value of A.

Physicists describe these interactions where a neutrino collides with a nucleus as a "nu-A interaction," but spell MINERvA with a Roman "v" and pronounce it with a "v". The name also evokes Minerva, the Roman goddess of wisdom.[2]

Status

The experiment that became MINERvA was proposed to Fermilab by two separate groups in 2002.[3] MINERvA's detector was assembled 107 meters underground, in a portion of the same hall that housed the Near Detector of the MINOS experiment. The first detector module was completed in early 2006,[1] and the first events were observed by the partially assembled detector in April 2009.[4][5] MINERvA started taking data regularly in November 2009 with a partially complete detector, and started taking data with the full detector in March 2010.[6]

At times, the NuMI beamline would provide either neutrino or antineutrino beams, tuned to particular energies. MINERvA acquired data in both a low energy (peaked at ~2.5 GeV) tune and a medium energy (peaked at ~6 GeV) tune.[7] The physics run was completed in February 2019.[3] Years of data analysis have followed.

Approximately 65 scientists collaborate on MINERvA.[8] As of the end of 2022, 51 students had earned their Ph.D.s for MINERvA-related work, and 32 students had earned Master's Degrees. The scientific co-spokespersons of the MINERvA experiment are Prof. Laura Fields of University of Notre Dame and Prof. Deborah Harris of York University.[3]

Detector

Diagram of neutrino detector in the MINERvA experiment. Left, front view of a single detector module. Right, elevation view of complete detector.

The detector used for the MINERνA experiment is made of many layers of parallel scintillator strips.[9] Each strip is connected to a photomultiplier tube which is used to detect the amount of energy deposited into the strip. The orientation of the strips varies from layer to layer so that three-dimensional information about where particles interact with the strip can be determined. The detector consists of a middle region, the active tracker, which is made of just the scintillator strips, and is surrounded by scintillator strips interspersed with lead and iron absorbers to provide surrounding calorimetry. Upstream of the active tracker is a nuclear target region of scintillator strips in which passive targets of liquid helium, carbon, water, iron, and lead are interspersed in order to allow comparisons of interactions of neutrinos in different materials.[10]

Scientific Results

MINERvA has published results on a wide variety of topics related to neutrino interactions and on other aspects of accelerator neutrino experiments.

Neutrino Flux Measurements

In order to measure neutrino interaction probabilities, MINERvA has needed to precisely understand the flux of incoming neutrinos. Through techniques such as studying the precisely predicted but rare interactions of neutrinos on atomic electrons,[11][12][13][14] improving the simulation of the production of neutrinos in the beamline,[15][16] and studying the most elastic interactions of neutrinos,[17] MINERvA has been able to predict its flux with a fractional uncertainty of approximately 4%.[14] MINERvA's techniques provide a proof of principle for applications expected to result in higher precision in future experiments.[18]

Charged-Current Quasielastic-like Reactions

MINERvA has extensively studied charged-current quasielastic-like reactions. In such reactions, one or more nucleons are knocked out of a nucleus by a neutrino as the muon neutrino or muon antineutrino is transformed into a muon or antimuon. MINERvA's first scientific results measured the rate of these processes in correlation with the visible energy from knocked-out protons. They suggested that about 20% of the quasielastic-like rate on carbon was from events in which multiple nucleons were ejected.[19][20] This technique—correlating the observed muon either with the total observed energy,[21][22][23][24][25] or with an individual proton [26][27][28][29] or neutron[30][31]—has allowed MINERvA to infer the rate of these multinucleon processes and also to measure details of the momentum and energy of the target nucleon before it is struck.[32]

Production of Pions and Kaons

MINERvA has also measured production of charged and neutral pions in both neutrino and antineutrino scattering.[33][34][35][36][37][38][39] One of the main conclusions of that work is that the production of pions from nuclei appears to be suppressed in low-momentum transfer reactions.[40] MINERvA has also precisely measured a rare process, coherent pion production, which involves scattering off the entire nucleus, leaving it intact.[41][42][43][44]

MINERvA has studied production of charged kaons,[45][46][47] a process that is an important background to searches for proton decay. MINERvA was also the first experiment to observe coherent kaon production.[48]

Nuclear Dependence of Neutrino Interactions

MINERvA has used its passive nuclear targets to compare reactions on different nuclei in inclusive scattering and in deep inelastic scattering.[49][50] Work in pre-publication form as of 2022 has expanded these comparisons to include quasielastic scattering [51] and charged pion production.[52]

This recent data provides evidence that the low-momentum transfer suppression of the reaction occurs in many nuclei. They show the effect of intranuclear rescattering increasing as expected in heavier nuclei.

Interactions of Electron Neutrinos compared to Muon Neutrinos

Using the 1% contamination of electron neutrinos in the neutrino beam, MINERvA has measured quasielastic-like scattering of electron neutrinos.[53] Differences between muon neutrino and electron neutrino interactions would significantly impact present and future oscillation measurements.[54] In making these measurements, a surprising number of events with neutral pions and little else visible in the detector were found. These were attributed to a larger than expected rate of coherent production of these neutral pions from hydrogen.[55][56]

Data Preservation and Release

MINERvA is designing a general release of its data with a software package to allow anyone to analyze this preserved data.[57]

Neutrino communication

On March 14, 2012, MINERνA submitted a preprint demonstrating communication using neutrinos. Though not a part of the experiment's physics program, this is the first reported instance of a message being transmitted by neutrinos. Scientists used ASCII code to represent the word "neutrino" as a series of 1s and 0s. Over a period of 6 minutes, this sequence was delivered by either the presence (1) or absence (0) of a neutrino pulse, over a distance of about a kilometer. The data communication speed was 0.1 bit per second, with an error rate of 1%.[58][59][60]

References

  1. ↑ 1.0 1.1 MINERνA home page , retrieved 5 Oct 2007
  2. ↑ Michelle Mo (2016-09-08). "Providing precise neutrino measurements with MINERvA". Fermilab. https://news.fnal.gov/2016/09/providing-precise-neutrino-measurements-minerva/. Retrieved 2023-01-24. 
  3. ↑ 3.0 3.1 3.2 Buongiorno, Caitlyn (April 5, 2019). MINERvA Successfully Completes Its Physics Run. https://news.fnal.gov/2019/04/minerva-successfully-completes-its-physics-run/. 
  4. ↑ Wisniewski, Rhianna (2009-04-03). "MINERvA opens eyes to neutrino data". Fermilab Today. http://www.fnal.gov/pub/today/archive_2009/today09-04-03.html. Retrieved 2010-06-11. 
  5. ↑ "MINERvA Sees!". MINERvA at Fermilab. 2009-04-01. Archived from the original on 2010-05-27. https://web.archive.org/web/20100527205755/http://minerva.fnal.gov//news/MINERvA-Sees/minerva-sees.html. Retrieved 2010-06-11. 
  6. ↑ "Intensity Frontier". Fermilab. 2010-03-24. http://www.fnal.gov/pub/science/experiments/intensity/minerva.html. Retrieved 2010-06-11. 
  7. ↑ Aliaga Soplin, Leonidas (March 2016). Neutrino Flux Prediction for the NuMI Beamline. https://lss.fnal.gov/archive/thesis/2000/fermilab-thesis-2016-03.pdf. 
  8. ↑ "Collaboration". MINERvA Collaboration. https://minerva.fnal.gov/collaboration/. Retrieved 2023-01-24. 
  9. ↑ "Fermilab Today". http://www.fnal.gov/pub/today/archive_2006/today06-02-15.html. 
  10. ↑ L. Aliaga (11 April 2014). "Design, calibration, and performance of the MINERvA detector". Nuclear Instruments and Methods 743: 130–159. doi:10.1016/j.nima.2013.12.053. Bibcode: 2014NIMPA.743..130A. https://doi.org/10.1016/j.nima.2013.12.053. 
  11. ↑ J. Park (10 June 2016). "Measurement of Neutrino Flux from Neutrino-Electron Elastic Scattering". Physical Review D 93 (11): 112007. doi:10.1103/PhysRevD.93.112007. Bibcode: 2016PhRvD..93k2007P. https://doi.org/10.1103/PhysRevD.93.112007. 
  12. ↑ E. ValenciaExpression error: Unrecognized word "et". (5 November 2019). "Constraint of the MINERvA medium energy neutrino flux using neutrino-electron elastic scattering". Physical Review D 100 (1): 092001. doi:10.1103/PhysRevD.100.092001. Bibcode: 2019PhRvD.100i2001V. https://doi.org/10.1103/PhysRevD.100.092001. 
  13. ↑ D. Ruterbories (23 November 2021). "Constraint of the MINERvA medium energy neutrino flux using neutrino-electron elastic scattering". Physical Review D 104 (9): 092010. doi:10.1103/PhysRevD.104.092010. https://doi.org/10.1103/PhysRevD.104.092010. 
  14. ↑ 14.0 14.1 L. Zazueta (11 January 2023). "Constraint of the MINERvA medium energy neutrino flux using neutrino-electron elastic scattering". Physical Review D 107 (1). doi:10.1103/PhysRevD.107.012001. https://doi.org/10.1103/PhysRevD.107.012001. 
  15. ↑ L. Aliaga (29 November 2016). "Neutrino Flux Predictions for the NuMI Beam". Physical Review D 94 (9): 092005. doi:10.1103/PhysRevD.94.092005. Bibcode: 2016PhRvD..94i2005A. https://doi.org/10.1103/PhysRevD.94.092005. 
  16. ↑ L. Aliaga (15 February 2017). "Neutrino Flux Predictions for the NuMI Beam". Physical Review D 95 (3). doi:10.1103/PhysRevD.95.039903. https://doi.org/10.1103/PhysRevD.95.039903. 
  17. ↑ A. BashyalExpression error: Unrecognized word "et". (31 August 2021). "Use of Neutrino Scattering Events with Low Hadronic Recoil to Inform Neutrino Flux and Detector Energy Scale". Journal of Instrumentation 16 (P08068): P08068. doi:10.1088/1748-0221/16/08/P08068. Bibcode: 2021JInst..16P8068B. https://doi.org/10.1088/1748-0221/16/08/P08068. 
  18. ↑ Chris M. Marshall; Kevin S. McFarland; Callum Wilkinson (5 February 2020). "Neutrino-electron elastic scattering for flux determination at the DUNE oscillation experiment". Physical Review D 101 (3): 032002. doi:10.1103/PhysRevD.101.032002. Bibcode: 2020PhRvD.101c2002M. https://doi.org/10.1103/PhysRevD.101.032002. 
  19. ↑ G.A. FiorentiniExpression error: Unrecognized word "et". (11 July 2013). "Measurement of Muon Neutrino Quasielastic Scattering on a Hydrocarbon Target at Neutrino Energy ~3.5 GeV". Physical Review Letters 111 (2): 022502. doi:10.1103/PhysRevLett.111.022502. PMID 23889389. https://doi.org/10.1103/PhysRevLett.111.022502. 
  20. ↑ L. FieldsExpression error: Unrecognized word "et". (11 July 2013). "Measurement of Muon Antineutrino Quasielastic Scattering on a Hydrocarbon Target at Neutrino Energy ~3.5 GeV". Physical Review Letters 111 (2): 022501. doi:10.1103/PhysRevLett.111.022501. PMID 23889388. https://doi.org/10.1103/PhysRevLett.111.022501. 
  21. ↑ P.A. Rodrigues (17 February 2016). "Identification of nuclear effects in neutrino-carbon interactions at low three-momentum transfer". Physical Review Letters 116 (7): 071802. doi:10.1103/PhysRevLett.116.071802. PMID 26943528. Bibcode: 2016PhRvL.116g1802R. https://doi.org/10.1103/PhysRevLett.116.071802. 
  22. ↑ P.A. Rodrigues (15 November 2018). "Identification of nuclear effects in neutrino-carbon interactions at low three-momentum transfer (Addendum)". Physical Review Letters 121 (20): 209902. doi:10.1103/PhysRevLett.121.209902. PMID 30500228. https://doi.org/10.1103/PhysRevLett.121.209902. 
  23. ↑ M.V. AscencioExpression error: Unrecognized word "et". (1 August 2022). "Measurement of inclusive charged-current νμ scattering on hydrocarbon at ⟨Eν⟩ ~ 6 GeV with low three-momentum transfer". Physical Review D 106 (3): 032001. doi:10.1103/PhysRevD.106.032001. Bibcode: 2022PhRvD.106c2001A. https://doi.org/10.1103/PhysRevD.106.032001. 
  24. ↑ R. GranExpression error: Unrecognized word "et". (1 June 2018). "Antineutrino Charged-Current Reactions on Hydrocarbon with Low Momentum Transfer". Physical Review Letters 120 (22): 221805. doi:10.1103/PhysRevLett.120.221805. PMID 29906174. Bibcode: 2018PhRvL.120v1805G. https://doi.org/10.1103/PhysRevLett.120.221805. 
  25. ↑ D. Ruterbories (6 July 2022). "Simultaneous Measurement of Proton and Lepton Kinematics in Quasielasticlike Muon Neutrino-Hydrocarbon Interactions from 2 to 20 GeV". Physical Review Letters 129 (2): 021803. doi:10.1103/PhysRevLett.129.021803. PMID 35867435. https://doi.org/10.1103/PhysRevLett.129.021803. 
  26. ↑ T. WaltonExpression error: Unrecognized word "et". (1 April 2015). "Measurement of muon plus proton final states in νμ interactions on hydrocarbon at ⟨Eν⟩ = 4.2 GeV". Physical Review D 91 (7): 071301. doi:10.1103/PhysRevD.91.071301. Bibcode: 2015PhRvD..91g1301W. https://doi.org/10.1103/PhysRevD.91.071301. 
  27. ↑ Betancourt, Minerba (May 16, 2014). A neutrino tale as told by a proton. https://news.fnal.gov/2014/05/a-neutrino-tale-as-told-by-a-proton/. 
  28. ↑ X.G. LuExpression error: Unrecognized word "et". (11 July 2018). "Measurement of muon plus proton final states in νμ interactions on hydrocarbon at ⟨Eν⟩ = 4.2 GeV". Physical Review Letters 121 (2): 022504. doi:10.1103/PhysRevLett.121.022504. PMID 30085714. https://doi.org/10.1103/PhysRevLett.121.022504. 
  29. ↑ Lu, Xianguo (February 4, 2019). CSI: Neutrinos Cast No Shadows. https://news.fnal.gov/2019/02/csi-neutrinos-cast-no-shadows/. 
  30. ↑ M. ElkinsExpression error: Unrecognized word "et". (5 September 2019). "Neutron measurements from antineutrino hydrocarbon reactions". Physical Review D 100 (5): 052002. doi:10.1103/PhysRevD.100.052002. Bibcode: 2019PhRvD.100e2002E. https://doi.org/10.1103/PhysRevD.100.052002. 
  31. ↑ Hesla, Leah (June 18, 2018). The secret to measuring the energy of an antineutrino. https://news.fnal.gov/2018/06/the-secret-to-measuring-the-energy-of-an-antineutrino/. 
  32. ↑ T. CaiExpression error: Unrecognized word "et". (1 May 2020). "Nucleon binding energy and transverse momentum imbalance in neutrino-nucleus reactions". Physical Review D 101 (9): 092001. doi:10.1103/PhysRevD.101.092001. Bibcode: 2020PhRvD.101i2001C. https://doi.org/10.1103/PhysRevD.101.092001. 
  33. ↑ T. LeExpression error: Unrecognized word "et". (7 October 2015). "Single neutral pion production by charged-current νμ interactions on hydrocarbon at ⟨Eν⟩ = 3.6 GeV". Physics Letters B 749: 130–136. doi:10.1016/j.physletb.2015.07.039. https://doi.org/10.1016/j.physletb.2015.07.039. 
  34. ↑ O. AltinokExpression error: Unrecognized word "et". (17 October 2017). "Measurement of νμ charged-current single π0 production on hydrocarbon in the few-GeV region using MINERvA". Physical Review D 96 (7): 072003. doi:10.1103/PhysRevD.96.072003. Bibcode: 2017PhRvD..96g2003A. https://doi.org/10.1103/PhysRevD.96.072003. 
  35. ↑ T. Le (16 September 2019). "Measurement of νμ charged-current single π− production on hydrocarbon in the few-GeV region using MINERvA". Physical Review D 100 (5): 052008. doi:10.1103/PhysRevD.100.052008. https://doi.org/10.1103/PhysRevD.100.052008. 
  36. ↑ B. Eberly (23 November 2015). "Charged Pion Production in νμ Interactions on Hydrocarbon at ⟨Eν⟩ = 4.0GeV". Physical Review D 92 (9): 092008. doi:10.1103/PhysRevD.92.092008. Bibcode: 2015PhRvD..92i2008E. https://doi.org/10.1103/PhysRevD.92.092008. 
  37. ↑ C. L. McGivernExpression error: Unrecognized word "et". (6 September 2016). "Cross Sections for νμ and νμ induced pion production on hydrocarbon in the few-GeV region using MINERvA". Physical Review D 94 (5): 052005. doi:10.1103/PhysRevD.94.052005. https://doi.org/10.1103/PhysRevD.94.052005. 
  38. ↑ McGivern, Carrie (4 February 2014). What happens in hydrocarbon stays in hydrocarbon (sometimes). https://news.fnal.gov/2014/02/what-happens-in-hydrocarbon-stays-in-hydrocarbon-sometimes/. 
  39. ↑ Yaeggy, Barbara (8 September 2017). Neutral-pion production at MINERvA, or how to cope with cases of mistaken identity. https://news.fnal.gov/2017/09/neutral-pion-production-minerva-cope-cases-mistaken-identity/. 
  40. ↑ P. StowellExpression error: Unrecognized word "et". (14 October 2019). "Tuning the GENIE Pion Production Model with MINERvA Data". Physical Review D 100 (7): 072005. doi:10.1103/PhysRevD.100.072005. https://doi.org/10.1103/PhysRevD.100.072005. 
  41. ↑ A. Higuera (23 December 2014). "Measurement of Coherent Production of π± in Neutrino and Antineutrino Beams on Carbon from Eν of 1.5 to 20 GeV". Physical Review Letters 113 (26): 261802. doi:10.1103/PhysRevLett.113.261802. PMID 25615308. Bibcode: 2014PhRvL.113z1802H. https://doi.org/10.1103/PhysRevLett.113.261802. 
  42. ↑ A. MislevicExpression error: Unrecognized word "et". (2018). "Measurement of total and differential cross sections of neutrino and antineutrino coherent π± production on carbon". Physical Review D 97 (3): 032014. doi:10.1103/PhysRevD.97.032014. Bibcode: 2018PhRvD..97c2014M. https://doi.org/10.1103/PhysRevD.97.032014. 
  43. ↑ Mislivec, Aaron (1 August 2014). Pion on the break shot. https://news.fnal.gov/2014/08/pion-on-the-break-shot/. 
  44. ↑ A. Mislevic; A. Higuera; et al. (MINERvA Collaboration) (2022). "Neutrino-induced coherent π+ production in C, CH, Fe and Pb at ⟨Eν⟩ ≈ 6 GeV". arXiv:2210.01285 [hep-ex].
  45. ↑ C.M. Marshall (14 July 2016). "Measurement of K+ production in charged-current νμ interactions". Physical Review D 94 (1): 012002. doi:10.1103/PhysRevD.94.012002. Bibcode: 2016PhRvD..94a2002M. https://doi.org/10.1103/PhysRevD.94.012002. 
  46. ↑ C.M. Marshall (7 July 2017). "Measurement of neutral-current K+ production by neutrinos using MINERvA". Physical Review Letters 119 (1): 011802. doi:10.1103/PhysRevLett.119.011802. PMID 28731762. Bibcode: 2017PhRvL.119a1802M. https://doi.org/10.1103/PhysRevLett.119.011802. 
  47. ↑ Fine, Robert (1 February 2016). MC Truth drops new track: kaons at MINERvA. https://news.fnal.gov/2016/02/mc-truth-drops-new-track-kaons-at-minerva/. 
  48. ↑ Z. WangExpression error: Unrecognized word "et". (5 August 2016). "First evidence of coherent K+ meson production in neutrino-nucleus scattering". Physical Review Letters 117 (6): 061802. doi:10.1103/PhysRevLett.117.061802. PMID 27541459. https://doi.org/10.1103/PhysRevLett.117.061802. 
  49. ↑ B.G. TiceExpression error: Unrecognized word "et". (9 June 2014). "Measurement of Ratios of νμ Charged-Current Cross Sections on C, Fe, and Pb to CH at Neutrino Energies 2-20 GeV". Physical Review Letters 112 (23): 231801. doi:10.1103/PhysRevLett.112.231801. PMID 24972195. Bibcode: 2014PhRvL.112w1801T. https://doi.org/10.1103/PhysRevLett.112.231801. 
  50. ↑ J. Mousseau (19 April 2016). "Measurement of Partonic Nuclear Effects in Deep-Inelastic Neutrino Scattering using MINERvA". Physical Review D 93 (7): 071101. doi:10.1103/PhysRevD.93.071101. Bibcode: 2016PhRvD..93g1101M. https://doi.org/10.1103/PhysRevD.93.071101. 
  51. ↑ J. Kleykamp; et al. (MINERvA Collaboration) (2023). "Simultaneous measurement of muon neutrino quasielastic-like cross sections on CH, C, water, Fe, and Pb as a function of muon kinematics at MINERvA". arXiv:2301.02272 [hep-ex].
  52. ↑ A. Bercellie; et al. (MINERvA Collaboration) (2022). "Simultaneous measurement of muon neutrino νμ charged-current single π+ production in CH, C, H2O, Fe, and Pb targets in MINERvA". arXiv:2209.07852 [hep-ex].
  53. ↑ J. Wolcott (23 February 2016). "Measurement of electron neutrino quasielastic and quasielasticlike scattering on hydrocarbon at ⟨Eν⟩ = 3.6 GeV". Physical Review Letters 116 (8): 081802. doi:10.1103/PhysRevLett.116.081802. PMID 26967410. Bibcode: 2016PhRvL.116h1802W. https://doi.org/10.1103/PhysRevLett.116.081802. 
  54. ↑ O. Tomalak; Q. Chen; R.J. Hill; K.S. McFarland (8 September 2022). "QED radiative corrections for accelerator neutrinos". Nature Communications 13 (1): 5286. doi:10.1038/s41467-022-32974-x. PMID 36075927. PMC 9458660. Bibcode: 2022NatCo..13.5286T. https://doi.org/10.1038/s41467-022-32974-x. 
  55. ↑ J. Wolcott (7 September 2016). "Evidence for Neutral-Current Diffractive π0 Production from Hydrogen in Neutrino Interactions on Hydrocarbon". Physical Review Letters 117 (11): 111801. doi:10.1103/PhysRevLett.117.111801. PMID 27661679. Bibcode: 2016PhRvL.117k1801W. https://doi.org/10.1103/PhysRevLett.117.111801. 
  56. ↑ Marshall, Chris (18 September 2015). The one-percenters and those who fake it. https://news.fnal.gov/2015/09/the-one-percenters-and-those-who-fake-it/. 
  57. ↑ B. Messerly; R. Fine; A. Olivier (23 August 2021). "An Error Analysis Toolkit for Binned Counting Experiments". European Physical Journal Web of Conferences 251: 03046. doi:10.1051/epjconf/202125103046. Bibcode: 2021EPJWC.25103046M. https://doi.org/10.1051/epjconf/202125103046. 
  58. ↑ "Message Encoded in Neutrino Beam Transmitted through Solid Rock". Scientific American. 2012-03-16. http://blogs.scientificamerican.com/observations/2012/03/16/message-encoded-in-neutrino-beam-transmitted-through-solid-rock. Retrieved 2012-03-16. 
  59. ↑ "Neutrino-based communication is a first". Physics World. 2012-03-19. https://physicsworld.com/a/neutrino-based-communication-is-a-first/. Retrieved 2020-05-17. 
  60. ↑ Stancil, D. D. et al. (2012-03-14). "Demonstration of Communication Using Neutrinos". Modern Physics Letters A 27 (12): 1250077-1-1250077-10. doi:10.1142/S0217732312500770. Bibcode: 2012MPLA...2750077S. 




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