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Figure 3 : Observed intervals in nuclear binding energies

Constituent Quark Masses and Standard Model Parameters S. I. Sukhoruchkin Petersburg Nuclear Physics Institute 188300 Gatchina Russia.

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Figure 3 : Observed intervals in nuclear binding energies

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  1. Constituent Quark Masses and Standard Model ParametersS. I. Sukhoruchkin Petersburg Nuclear Physics Institute 188300 Gatchina Russia We review a recent state of nuclear physics as a part of the QCD and the Standard Model -theory of all interactions. Collected in PNPI nuclear data files on binding energies, excitations and neutron resonance parameters (NRF-3,4) were used to check a suggestion that in the accurately measured nuclear data one can find manifestations of nucleon structure. We study the stabilizing effect of major nuclear shells in values of binding energies corresponding to well-known nuclear clusters like α and (differences of totalbinding energies ofnuclei differing with ΔZ=2, Δ N=2 or Δ Z=2, Δ N=4)

  2. We check the suggestions by Y.Nambu that empirical relation in particle masses can be used for further development of the Standard Model and by F.Wilchek that top quark mass is a distinguished hadronic parameter. • Starting from the observation that values of quark mass from QCD quark gluon-dressing effect (about 420 MeV) and constituent quark masses in NRCQM (436 MeV from strange baryon masses, 450 MeV from Goldstone boson exchange model etc.) are close to values 441 MeV and 3x147 MeV in the grouping effects at 147 and 441 MeV in nuclear binding energies we find out the closeness of the ratios between vector boson masses (Mz=91 GeV, Mw=83 GeV) and QCD-based estimates of the constituent quark masses Mq=441~MeV and Mq''=Mρ/2(half of ρ-meson mass). • After that from 3:2:1 relation between the top quark mass (Mt) and parameters of mass grouping effects (115 GeV and 58 GeV) found earlier in data from LEPP-2 and LEP(L3) experiments we observe a closeness of the ratio between (1/3)Mt and Mq to 1/129 (QED parameter for the short distance). • We come to the conclusion that Nambu/Wilchek suggestions could really reflect the important role of QCD-based hadronic effects.

  3. Top Calculation of nonstrange baryon and Λ-hyperon masses as a function of interaction strength within Goldstone Boson Exchange Constituent Quark Model; the initial baryon mass 1350MeV=3·450MeV=3Mq is marked "+" on the left vertical axis].Bottom:QCD gluon-quark-dressing effect calculated with DSE, initial masses mq=0 (bottom), 30 and 70MeV (top). The quark-parton acquires a momentum-dependent mass function that at infrared momentum (p=0) is larger by two-orders-of-magnitude than the current-quark mass (several MeV) due to a cloud of gluons that closes a low-momentum quark.Right: Schematic view of nucleon structure used in CQM calculations ( top), larger radius rN and smaller rmatter correspond to the nucleon size and the space of the baryon matter.

  4. Figure 1: Distribution of all mutual differences of binding energies in nuclei with Z≤58; positionof the maximum at 45εo corresponds to the grouping effect in ΔEB for nuclei differing with configuration. Parameter εo=1022.0 keV was derived from independent data on excitation.

  5. Figure 2: The same distribution of ΔEB in nuclei with Z≤58 calculated with the FRDM-model;the position of the maximum is shifted by 0.8 MeV relative to that in the experimental data.

  6. Figure 3: Observed intervals in nuclear binding energies

  7. Figure 4: Observed intervals in nuclear binding energies

  8. Top: ΔEB-distribution in nuclei Z≤26 differing by two and four α-clusters: marked: ΔEB = 73.6 MeV= 16Δ = 9δ, 147.2 MeV = 32Δ = 18δ with Δ=9me=4.599keV and 16me=δ. Bottom: ΔEB-distributions in N=even=50-82 nuclei, maximum at 46.0 MeV=10Δ=45εo ( left) the same for odd-odd nuclei, maximum at 441 MeV=3·147MeV=3·18δ.

  9. Table 1. Comparison of experimental ΔEB (in keV) and theoretical estimates in magic nuclei (N=82, N=20) with 10Δ =45εo (6He cluster) and 32Δ =18δ = 144εo (4α 39,36K).

  10. Tuning effects in nuclear excitationsDistribution of parameters εn2n=ΔSn(ΔN=2) and εn2p=Δ Sn(ΔZ=2) in N-odd and odd-odd nuclei. Center: Spacing distribution in all excited states of 42Ca (left), number of levels n=543 including resonances from 41K(p,γ)42Ca and 38Ar(α,γ)42Ca reactions) left: Spacing distribution in levels of 38Ar (right}.

  11. Spacing distribution of levels in 89Y (number of states n=388, ΔE=3 and 5 keV).

  12. Spacing distribution in F-18 (two nucleons above O-16). Stable intervals of 162 keV, 480 keV, 642 keV, 1288 keV are integer (n= 1, 3, 4, 8).

  13. Spacing distribution in F-18 adjacent to D=x=162 keV. Stable intervals 642, 1452, 1611, 1769, 1932 keV are integer (n= 4, 9, 10, 11, 12).

  14. Spacing distruibution of F-18levels adjacent to D=x=642 keV, x=1932 keV. Intervals 162, 479, 1288 and 1769 keV are integer (n = 1, 3, 8, 11).

  15. Figure 6:Spacing distribution in Sb Appearance of stable intervals in nuclear excitations rational to me and δmN (named tuning effect) was found in data for near-magic nuclei, see Fig.6. • Data from recent compilation of nuclear excitations CRF5 permit confirmation of tuning effect. In Table 2 it is shown that stable excitations of low-lying levels of Sn are close to (1/3)me =170 keV and in sequence of Sb isotopes (Z=51, N=72-82) excitations increase as n∙δmN/8=n∙161 keV. The interval 160 keV is seen in spacing of Sb (Fig.6 top) Table 2: Nuclear excitations close to me/3 and n∙δmN/8 (in CRF5)

  16. Spacing distribution in levels of Pd-97, 98.

  17. Top : Momentum transfer evolution of QED effective electron charge squared. Monotonously rising theoretical curves is confronted with the precise measurements (left). ALEPH results with about 3 standard deviation at mass 115 GeV, observed (solid line) and expected behavior of the test statistic (sharer region) (right).Bottom: The measured at LEP two photon invariant mass spectrum from L3 (left) and DELPHI (right) compared with Monte Carlo expectations (channel contributions are indicated).

  18. Table 2a. Presentation of parameters of tuning effects in particle masses (three upper parts with x = -1,0,1) and in nuclear data (separately in binding energies x=0 and excitations x = 1,2) by the expression (n·16me(α/2π)x)·m with QED parameter α =137-1. Values related to (2/3)mt=MH with QED parameter αZ=129-1 (mπ-me, me/3) and the shift in neutron mass nδ-mn-me are boxed.

  19. Table 2b. Presentation of parameters of tuning effects in particle masses (three upper parts with x = -1,0,1) and in nuclear data (separately in binding energies x=0 and excitations x = 1,2) by the expression (n·16me(α/2π)x)·m with QED parameter α =137-1. Values related to (2/3)mt=MH with QED parameter αZ=129-1 (mπ-me, me/3) and the shift in neutron mass nδ-mn-me are boxed.

  20. Table 3a. Comparison of particle masses (PDG 2008) with periods 3me and 16me = δ = 8175.9825(2) (N - number of the period δ, me=510.998910(13) keV

  21. Table 3b. Comparison of particle masses (PDG 2008) with periods 3me and 16me = δ = 8175.9825(2) (N - number of the period δ, me=510.998910(13) keV.

  22. Table 3: Presentation of parameters of tuning effects in particle masses (three upper parts, lines marked with X= -1, 0, 1 at left) and parameters of tuning effects in nuclear data (lines with X=0,1,2 in central and bottom parts) by the common expression n·16me(α/2π) M with the QED parameter α=137 . Boxed are values related to (2/3)mt=MH with the QED parameter αZ=129 (mπ-me, me/3) and the neutron mass shift nδ-mn-me discussed in text. Asterisks mark stable intervals observed in E* and neutron resonance data.

  23. Table 4a. Comparison of particle masses (PDG 2008) with periods 3me and 16me = δ = 8175.9825(2) (N - number of the period δ, me=510.998910(13) keV

  24. Conclusions • Presence of tuning effects in nuclear excitations and nuclear binding energies is confirmed with new data from PNPI compilations (Vols. I/19, I/22 Springer Landoldt-Boernstein Library) • Relation 3 : 2 : 1 = mt : MH : ML3 between masses of top quark, possible mass of Higgs boson and the grouping effect in L3 LEP experiment could be checked with the future LHC data. • Relation (N·16me – me –mn)/δmN =1/8.000 could be checked with new more accurate value of the mp/me ratio. • Observed analogy between tuning effects in particle masses and in nuclear data should be theoretically based on QCD as a part of the Standard Model (Nambu’s suggestion about the important role of empirical relations in particle masses for the SM development).

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