The Role of the Pion in QCD/SM Model

S.I. SukhoruchkinPetersburg Nuclear Physics Institute

188300 Gatchina Russia

Introduction• Nonstrange pion and $\ro$-meson are well-known participants of nuclear forces

acting between nucleons. Nucleon masses themselves are result of the quark-gluon interaction estimated within QCD-lattice calculations [1]. They are parameters of NRCQM constituent quark model with the meson interaction between quarks ( for example, Goldston-boson interaction [2]). NRCQM is a part of QCD which itself is a part of Standard Model - theory of all interactions.

• Observed universal character of 0+-0+ beta-transitions in many nuclei permitted a conclusion that "the nucleus is one specific case, the coldest and most symmetric one, of hadronic matter" [3]. The mean binding energy of the nucleon in nuclei is about 8 MeV, its mass is about 940-8=932 MeV.

• Recent understanding of a role of pion exchange (and corresponding tensor forces between nucleons) in observed systematic effects of nuclear structure was discussed by T.Otsuka [4] and used in this work during the correlation analysis of binding energies and excitations of a large scope of nuclei [5-8].

• Clustering effects in the nuclear structure [9], unexpected stability of parameters of nucleon residual interaction [10], the interconnection between nuclear parameters and parameters of the Standard Model are considered in light of the suggestion by Y.Nambu [11] that empirical relations in particle masses could be used for the development of the Standard Model.

• Empirical relations in masses discussed [12-15] are considered together with recent result from ATLAS [16] on Higgs boson mass 126GeV (2.5 sigma signif.)

Introduction (continued, references)

• 1. C.D. Roberts et al. Eur. Phys. J. Spec. Topics 140, 53 (2007); M.S. Bhagat et al. 2007 Phys.Rev.C 76 045203• 2. L. Glozman, Nucl. Phys. A 629, 121c (1990).• 3. C.Detraz, Nucl. Phys. A 83, 3 (1995).• 4. T.Otsuka, T. Suzuku, Y.Utsino, Nucl. Phys. A 805, 127c (2008).• 5. Landoldt-Boernstein New Series 2012 vol. I/25A, Ed. H. Schopper (Springer). • 6. S.I. Sukhoruchkin 2008 Int. Rev. Phys. (IREPHY) 2, 239 • 7. S.I. Sukhoruchkin, Nucl. Phys. A 782 37c (2007).• 8. S.I. Sukhoruchkin, Proc. Rutherford Cent. Jubilee Conf. Manchester, 2011 (in press).• 9. S.I. Sukhoruchkin, D.S. Sukhoruchkin, Int. J. Mod. Phys. E 20, 906 , 2011.• 10. Landoldt-Boernstein New Series 2009 vol. I/22A, Ed. H. Schopper (Springer).• 11. Y. Nambu, Nucl. Phys A 629 3c (1998).• 12. S.I. Sukhoruchkin, Proc. 2nd Conf. Neutron Cross Section, 1998, Washington DC vol.2 923. • 13. S.I. Sukhoruchkin 1972, Stat. Properties of Nuclei, Ed. Garg G (Plenum Press) 215. • 14. S. Sukhoruchkin, Proc.XIV Int. Conf. Hadr. Spec. HADRON2011, Munich, eConf C110613, 846 • 15. R. Frosch, Nuovo Cim. 104, 913 (1991). • 16. M. Wielers 2011 ATLAS Results Plans, https://cgc.physics.miami.edn/Miami2011/Wielers.ppt• 17. C. Itoh et al. 1989 Phys. Rev. D 40 3660.• 18. V.V. Belokurov, D.V.Shirkov 1991 The Theory of Particle Interactions, AIP, New York.• 19. I.T. Dyatlov, Phys. Rev. D 45,1636 (1992). 20. J. Bernstein, Elem. Particles and their Currents, Freeman, 1968.• 21. S.I. Sukhoruchkin, DISCRETE’08, IOP Publ. J. Phys. Conf. Ser. 171 (2009) 012064.• 22. S.I. Sukhoruchkin, Hadron2009• 23. S.I. Sukhoruchkin, Symm. Meth. Phys. Dubna 1993, JINR E2-94-347, p.528,536; ibid 1995, JINR E2-96-224,

549• 24. R.P. Feinman, 1985, QED The strange theory of light and matter, Princeton.

Introduction (Plan of contribution)• 1) Study of the tuning effect in nuclear excitation – -- manifestation of stable intervals close to particle mass

splitting (me or me/3, nucleon mass splitting 1293keV or its part 1293keV/8=161keV, pion mass splitting close to 9me).

• 2) Study of the same tunung effect in differences of nuclear binding energies, discretteness of DEb corresponding to different cluster configurations (He-4, 4He-4, He-6 etc.).

• 3) Relations in parameters of NRCQM Nonrelativistic Constituent Quark Model (incl. gluon quark-dressing effect).

• 4) Relations in parameters of Standard Model (masses of fundamental fermions and bosons, radiative corrections with

QED parameters 1/137 and 1/129 (for short distance).

…NEEDS IN INSTRUMENTATION FOR NUCLEAR PHYSICS by S. Devons, Manchester, 1961

• “… it is a natural temptation to make comparisons between the present stage in the study of nuclear structure with the exploration of atomic structure in Rutherford’s time … Rutherford used the bold, direct approach, what one might designate as the “high-energy” approach…”

• “The more subtle “low-energy” investigations, for example the study of optical spectra, only became a fruitful means of examining the refined details of atomic structure after Rutherford’s direct approach led to the Bohr theory, and the subsequent development of quantum mechanics. … distinction between high and low energy phenomena is perhaps not so clear as in atomic structure.

• The existence of highly developed … quantum-mechanics, makes it possible to drow inferences about basic underlying features from observation and sophisticated interpretation of refined detailes.”

• “… since the nucleons of which the nucleus is composed are far from simple entities, one may suspect (or hope?) that there are still to be discovered subtle features of complex nuclei which reflect underlying properties of nucleons, and which may even prove difficult to observe in direct study of the elementary particles themselves.”

• “More directly in such cases as the study of some elementary-particles or high-energy process can be facilitated by observation of phenomena involving complex nuclei, …fullest possible understanding of nuclear structure becomes a pre-requisite.”

• Recent understanding of the role of the pion-exchange dynamics fits this condition.

COMPILATIONS OF NUCLEAR DATA USED IN THE PRESENT DATA ANALYSIS (1), RECENT NEW RESULTS (2)

• 1) LANDOLDT-BOERNSTEIN COMPLEX CATALOG, 2000 by W. Martienssen:• “The importance of collection of selected and easily retrievable data was recognized

long ago and now such activity appears even more important than ever due to the immense production rate of literature and data as well as due to the steady growing interdependence between increasingly differentiated research fields.”

• 16 vols of Landoldt-Boernstein Compilations, Ed. H.Schopper: LB vol. I/16B 1998, LB vol. I/16C 2004, LB vol.1/24 2009 Neutron Resonance Parameters

• LB vol. I/19A1 2004, vol.I/19A2 2005 Nuclear States from Charge Part. Reactions, • LB vol. I/22AB 2009 Nuclear Binding Energies and Atomic Masses,• LB vol. I/19B1 2006, vol.I/19B2 2007, vol.I/19B3 2007, vol.I/19C 2008, • LB vol.I/25A-E, 2012, 5 volumes., Excited Nuclear States Z<29,Z=30-47,Z=48-

60,Z=61-73, 74-102

• 2) Results: Proc. International Seminars on Interaction of Neutrons with Nuclei: • ISINN-19, Compilation of nuclear excited state CRF, S.Sukhoruchkin, Z..Soroko,

D.Sukhoruchkin • ISINN-19, Compilation of nuclear binding energies MDF, S.Sukhoruchkin,

D.Sukhoruchkin (2011)• ISINN-19, Study of nonstatistical effects due to tensor forces, S.Sukhoruchkin,

M.Sukhoruchkina

Table 1. Top: Comparison of E* in near-magic nuclei with multiple values of spin-flip effect in 10B (εo =1022 keV=2me);

Bottom: Excitations in near-magic 101,103Sn close to εo /6=me/3 keV and excitations in 123-133 Sb close to 161 keV=dmN/8=1293 keV/8

• AZ 10B 10B 12C 18Ne 55Co (Fig.2)• 0+,1+ 2- 0+1 0+(T=2) 0+1 0+2 Dij Dij• E*, Dij, keV 1021.8(2) 5110.3 7654.2 27595(2) 3576.2 4590(8) 512 682• n(εo) 1 5 15/2 27 7/2 9/2 1/2 3/4• nx εo 1022 5110 7665 27594 3577 4599 511 683• Diff. 0.2(2) 0.3 1(2) 9(8)

• --------------------------------------------------------------------------------------------------------------------------• 101Sn 103Sn 123Sb 125Sb 125Sb 127Sb 129Sb 131Sb 133Sb• 171.7(6) 168.0(1) 160.3(1) 332.1 643.2 491.2 645.2(1) 798.5 962.3(1)• me/3 me/3 (1/8) δmN (2/8) δmN (4/8) δmN (3/8) δmN (4/8) δmN (5/8) δmN (6/8)δmN

170.3 170.3 161.7 323.3 646.7 485.0 646.7 808.3 970.0

• Suggested by S.Devons manifestation of the nucleon structure in accurately measured nuclear data was observed as stable mass/energy intervals coinciding with the well known nucleon mass splitting 1293 keV shown in the E* distriution that follows as well as in independent E* distributions for nuclei from volumes LB I/25A (Z=2-29) and LB I/25D (Z=60-76) (ISINN-19).

Fig.1 Observed earlier Grouping Effect in Energies of Excited States at E*=2me and nucleon mass differences 1293~keV was named

“tuning effect” in nuclear data.

: Sum distribution of excitations in Z-odd nuclei Z=19-29 at 1293~keV and 2586~keV=2x1293~keV. .

Fig.2 Spacing distribution of levels in 89Y (number of states n=388, ΔE=3 and 5 keV).

Fig.3 D-distribution of levels in 90Y (n=190) at low-energy

and in neutron resonances (n=692).

Fig.4a Distribution of intervals adjacent to D=x=478.5 keV in 90Y neutron resonances (n=692); Fig. 4b D-distribution in low-lying levels of

38Ar

Distribution of isotopes Z=6-100 with stable intervals

• This “tuning effect” was confirmed by maxima at 160 keV and 962 keV=6x160 keV in spacing distributions of levels in 122,124Sb and 133Sb as well as by stable intervals rational to the parameter 6x170 keV=εo=1022 keV found in light nuclei -- near-magic 10B, 12C, 55Co (Table 1, top)..

• New analysis of tuning effects in excitations of all nuclei (situated at different parts of nuclear shells) was performed in this work using compilation of nuclear excitations Springer, LB vol. I/25.

• Numbers of isotopes (for each Z) in which stable intervals D close to D=nx160 keV + mx 170 keV (n,m integers 0,1…12) were observed are presented in Figure that followed as a histogram for different Z.

• Combined D=492 keV=2x160 keV+170 keV, D=672 keV=160keV+3x170 keV are included. Arrows in top part of Figure 5 correspond to closed shells, arrows at bottom show additional maxima in nuclei where a large proton shell 1i9/2 is filled (Z=68,72,76,78).

• Observed in Sb isotopes systematic linear trend corresponds to the same large 1g9/2 neutron shell (with Z=51, valence proton in 1g7/2 shell). In both cases neutron and proton are moving in shells with different spin-orbit orientation.

Fig.5. Isotope distributions for Z=6-100

Fig.6 Sum distributions of excitations in nuclei with Z=79 and Z-84, ΔE=7 keV [6].

Tuning effects in nuclear binding energies • Simultaneously with the above described analysis of tunung

effects in nuclear excitations the same parameter εo=2me and rational to it were found in differences of nuclear binding energies.

• In Sb-isotopes the linear trend in Sp is due to constancy of the residual interaction parameter ep2n=680keV=2/3 εo, see the

Figure that follows, bottom linear dependence of Sp versus N.• Integer values of the parameter εo=2me were observed in two-

and four-proton separation energies and in cluster effects in many nuclei ( see Figures that follow showing the grouping effect at DE_B=46.0 MeV=45 εo and 147.2 MeV=18x8 εo).

• Long-range correlations with the parameter εo=2me are observed in cluster effects (see Table that follows).

Fig.7 Sp Z=51

S2p for Z=78, 84

• The largest maximum in the distribution of numbers of stable intervals in excitations (shown before) corresponds to platinum isotopes (Z=78). A linear dependence of two-proton separation energies (for Z=78,84) as a function of N is shown in Fig that follows. The slope of a trend is 340 keV= εo/3, similar to that in Z=84 isotopes seen in the right part of the same figure.

Fig.8 S2p for Z=78, 84

The linear dependenceof two-proton separation energies (for Z=78,84) as a function of N is shown in Fig 8. The slope of a trend is 340keV= εo/3 in both Z=78,84 isotopes before and after N=126 (x axis).

• Fig. 9 : Distribution of all mutual differences of binding energies in nuclei with Z≤58; position of the maximum at 45εo corresponds to the grouping effect in ΔEB for nuclei differing with He-6 configuration (see Fig that follows) . Parameter εo=1022.0 keV was derived from independent data on excitations and discreteness of two- and four-nucleon separation energies.

He6

• Figure 10: Distribution of observed intervals in nuclear binding energies in nuclei differing with He-6 cluster.

• Figure 11. Observed intervals in nuclear binding energies of light nuclei (Z less 26) differing with 4 alpha.

Table 2. Comparison of experimental ΔEB (in keV) and theoretical estimates in magic nuclei (N=82, N=20) with 10Δ =45εo (6He cluster, left part of Table) and in light nuclei 39K and 36K differing with 4α (values 32Δ =18δ = 144εo ).

Small differences between observed energies and integer numbers of the parameterεo=2me (values Diff.) correspond to the long-range correlations in binding energies.

Z=55 137Cs Z=57 139La Z=58 138Ce 140Ce 39K Z=19

N 80 82 78 80 82 78 80 82 20 17

ΔEB 45946 45970 46018 45927 46024 46087 45997 45996 147160 147152

N·εo 45990 45990 45990 147168 147168

Diff -44 -20 28 -63 34 97 7 6 - 8(2) - 16

FRDM 46620 46340 45950 46820 46970 45960 46850 47160 147450 145950

Diff. 630 350 -40 830 980 -30 860 1170 282 1220

.

Parameters of NRCQM Model Observed tuning effects in nuclear excitations and binding energies (parameter 2me etc.) were compared with relations in

particle masses. Two aspects of this study are connected with NRQM parameters (1) and SM-parameters (2).

1a) Nambu pointed out relations 1:8 between masses of the pion and lambda hyperon (1952), checked in 1972.

1b) Samios (Part. Data Group) found coincidence of pion mass with Omega-Ksi hyperons (the periodic sequence with the period equal to the pion mass, nxmp expression).

1c) Sternheimer noticed that constant splitting in pseudoscalar mesons 409 MeV is p+2mpo 1d) Wick considered stable mass intervals Mq’’=m(omega)/2=(1/2)782 MeV=390 MeV of vector boson

mass (close to three times the pion parameter 3fpi=3x130MeV=390 MeV). 1e) Sternheimer considered stable mass intervals Mq=441 MeV between masses of many particles,

Md=436 MeV was used in NRCQM calculation of strange baryon masses by C. Itoh et al. [17]. 1f) Kropotkin noticed that Sternheimer’s parameter Mq is close to (1/3) of the mass of the Ksi-hyperon 1324 MeV/3=441 MeV. It is the result of a compensaton of the mass increase due to the doubled strangeness (2ms=2x150 MeV) and the mass decrease due to the residual interaction (2x147 MeV) between three initial baryon quarks (with values of 441 MeV each). The initial baryon quark mass M=1324 MeV=3x441 MeV is three times the parameter of the residual

quark interaction DMD=147~MeV well known from nucleon Delta excitation (see the last line of Table 3,4 that follow).

Relations 1a-1f are in agreement with NRQCM where estimates (1/2) and (1/3) are applied to real masses.According to NRCQM (Fig 13 that follows, bottom) three initial quarks (with values explained with QCD

lattice calculations, Fig. 13 top) become Delta-baryon (parralell spins, S=3/2) and nucleons (S=1/2).The baryon quark mass Md=1232 MeV=3x410 is equal to the equidistancy in pseudoscalars (line 1c).

Fig.12 (from [1]). QCD gluon-quark-dressing effect calculated with Dyson-Schwinger Equation, initial masses m; the constituent quark mass arises from a cloud of low-momentum

gluons attaching themselves to the current-quark; this is dynamical chiral symmetry breacking: an nonperturbative effect that generates a quark mass from nothing even at chiral limit m=0 ( bottom).

• Fig.13 (from [2]). Calculation of nonstrange baryon masses (left) and lambda-baryon masses as a function of interaction strength within GBECQM – Goldstone Boson Exchange interaction Constituent Quark Model; initial baryon mass 1350

MeV=3x450 MeV=3Mq is near bottom “+” on left vertical axis.

.

Parameters of NRCQM Model (cont.) Observed tuning effect in nuclear data with parameters 161 keV (equall to 1/8 of nucleon

mass splitting) and 170 keV (equal to 1/3 of the electron mass) was considered in the view of Y. Nambu suggestion to a search for relations in particle masses. The important role of the pion-exchange dynamics permitted to find out the relation in the nucleon masses which are parameters of the NRQM model.

1g) Above mentioned mass parameters (including pion mp and muon mu masses) can be expressed as integers of the doubled value of the pion beta-decay energy (2dmp – 2me) which is close to 16me=d (due to relation 9:1 between pion mass difference and the electron mass, 1968). The observed ratios are:

(mu + me)/2(dmp – me) = 13.00 fp=130.7 MeV (PDG) /2(dmp – me)=16.01 (mp(+-) – me)/ 2(dmp – me)=17.03 DMD/2(dmp-me)=18.02 equidistant interval in pseudiscalar mesons/2(dmp-me)=50.1 neutron mass +me/2(dmp-me)=115.007 1h) The confirmation of NRCQM parameters comes from the stable character of difference of nuclear binding energies

147.2 MeV and 147.0 MeV in light and heavy nuclei, 441 MeV in all odd-odd nuclei.

1i) NRCQM parameters Mq=441 MeV and Mq=M(rho)/2=376 MeV form with vector boson masses (Mz=91,19 GeV and Mw=80.40 GeV) ratios 206.8 and 207.3 which are close to lepton ratio L=mu/me=207=13x18-1=23x9 1j) Using the exactly known ratio between masses of the proton and the electron the shift of neutron mass from 115 periods d=16 me was determined as exactly 161 keV equal to 1/8 of the nucleon mass splitting (see Table that follows). Such relation between particle masses and electron mass ( SM parameter) is supported by analysis by Frosch ( follows).

Fig.14 Tests of the Empirical Mass Rormula m=Nx3me for Leptons and Hadrons, by R.Frosch (in 1967- 1991) Nuovo Cimento v.104A, 6, 913, 1991Deapest maximum in the mean root deviations corresponds to the period 3me

• The experimental set of 47 masses was replaced by set of 47 random numbers… the probability for random masses to fit the 3me formula better than the experimental masses is only 2x10-4 See numbers close to the integers in the 2nd column of the table that follows,

they are marked by asterisk

Table 3. 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

Part. mi, MeV mi/3me N·16me N mi-N·16me Comments

µ 105.658367(4) 68.92* 106.2878 13 -0.6294 -.0511-0.118

πo 134.9766(6) 88,05* 138.9917 17 -4,0174

π± 139.5702(4) 91.04* 17 +0.5762 +0.511+0.065

ηo 547.853(24) 357.38 547.7908 67 0.06(2)

ω 782.65(12) 510.54 784.8943 96 -2.24(12)

φ 1019.46(2) 665.01* 1021.998 125 -2.54(2)

Κ± 493.677(16) 322.03* 490.5590 60 +3.118(16)

p 938.2720(1) 612.05* 940.2380(1) 115 -1.9660 -me-9/8δmN

n 939.5654(1) 612.89* 115 -me-161.6(1) keV

-me-1/8δmN

Σo 1192.64(2) 777.98* 1193.693 146 -1.05(2) -0.51·2=-1.02

Ξo 1314.86(20) 857.71* 1316.333 161 -1.47(20) -0.51·3=-1.53

Table 4. Comparison of particle masses with the period 16me shows an increase of the

shift in masses of neutral octet baryons with incereasing the strangeness S (from 0 up to 2, boxed values in 4-th column) and the

clouseness of neutron Δ-excitation to 2x18x16me (bottom).

Parameters of the Standard Model (I) It was noticed in 1972 that nonstatistical effects in nuclear excitation and spacing

distributions can be presented as three structure (few-particle, fine and super-fine structures) with the corresponding periods 1.022 MeV, 1.2 keV and 1.3 eV related as small QED radiative correction to the doubled value of three-fold Delta-excitions of the nucleon (or the empirical parameter 441 MeV introduced by Sternheimer and Kropotkin which coincides with the estimate of baryon constituent quark in NRCQM model developed many years later).

It was also found later that such well-known factor alpha/2p=115.9x10-5 (QED radiative correction to the magnetic moment of the electron – Schwinger term) exactly coincides with the well-known ratio between two important parameters of the Standard Model mu/Z =115.9x10-5.

It was suggested by Belokurov and Shirkov (see [18]) that the electron mass itself could contain a component proportional to this small factor.

Discussed here empirical relations in particle masses and in nuclear data were represented as the common expression with different powers of such common dimentionless factor to fit a great number of empirically observed stable nuclear intervals (Tables 5-6). An example of such stable nuclear interval is given in Fig 15 and Table 7 for the above discussed (found by Schiffer et al. and explained by Otsuka) linear trend in valence proton excitations in Sb isotopes. Maximum at 160 keV in spacing distribution in two neighbour Sb-isotopes confirm a stable character of intervals related as QED correction to the pion mass mp=140 MeV (excitations were connected with pion-exchange dynamics).

Parameters of the Standard Model (II)

Lepton ratio as the distinguished parameter Earlier, as a realization of Nambu’s suggestion to search for empirical mass relations

needed for SM-development, it was noticed that:1) the well-known lepton ratio L=mμ/me=206.77 becomes the integer 207=9x23=13x16-1 after

a small QED radiative correction applied to me (it becomes mμ/me(1-α/2π)=207.01)2) the same ratio L=207 exists between masses of vector bosons MZ=91.188(2) GeV and

MW=80.40(3) GeV and two discussed estimates of baryon/meson constituent quark masses Mq=441 MeV=mΞ¡/3=(3/2)(mΔ-mN) and M˝ q =mρ/2=775.5(4) MeV/2 =387.8(2) MeV. These ratios are Mz/441 MeV=206.8 and Mw/(mρ/2)=207.3.

The origin of these effects should be considered in the complex analysis of tunung effects in particle masses and in nuclear data which would be performed after the

determination of the mass of the scalar fields. Preliminary result Mh=126 GeV [16] is obtained by ATLAS collaboration (2011).

We do not use earlier obtained results from LEP, namely, Mh=116 GeV (P.Igo-Kemenes, J.Phys G 388, 2006; also: ALEPH collabor. Phys.Lett. B526,

191, 2002; PDG Phys.Lett, B667, 1, 2008; see also: H.Schopper The Lord of the Collider Rings at CERN 1980-2000, Springer 2009).

Table 5. 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 expression (n·16me(α/2π)x)·m with QED parameter α =137-1. Higgs boson and pion masses, the discussed shift in neutron mass nδ-mn-me=161 keV,the parameter of nucleon Delta excitation and me/3 (which related as α/2π) are marked.x m n=1 n=13 n=16 n=17 n=18

-1 3/2 mt=171.2

GeV 1 MZ=91.2 MH=115 MH=126

1/2 ML3=58

0 1 16me=δ mµ=105.7 Fπ =130.7. mπ-me (mΔ-mN) /2=147

MeV 3 Mq˝=mρ/2 Mq΄=420 Mq=441

3 Mq˝΄=mω/2 3ΔMΔ=441

0 1 2Δ-εo 106=ΔEB 130=ΔEB 140=ΔEB 147.2=ΔEB

MeV 3 441.5=ΔEB

1keV

18,

9.5 keV 123 keV nδ-mn-me=161.6(1) δmN=1293.34(1)

170=me/3me=510.99891

2 eV

12

11 eV22 eV

143 eV 187 eV375 eV

Table 6. Parameters of tuning effects

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.

Additional information on stable mass intervals corresponding to systems n=17-18 is given in Tables 1-2 that follow and in Fig.15

X11

Fig.15 Different estimates of constituent quark masses

Figure 15 (continued). Different mass intervals and hadron/lepton masses are shown

here by the two-dimensional mass-presentation with the horizontal axis in units δ=16me close to mω/6. Residuals Mi -

n(16×16me=16δ) are plotted in the vertical direction (y-axis with units of δ =16me). Three values corresponding to different

estimates of constituent quark masses are shown as lines with different slopes:

1) horizontal line corresponds to Wick’s interval mω/2=M´´q=48δ; 2) crossed arrows correspond to MΔq=409 MeV=32+18=50δ and

3) parrallel lines with the large slope – to the interval considered by Sternheimer and Kropotkin Mq=441MeV=3x18=54δ. It is

corresponding to the initial value of the baryon constituent quark which is equal to three-fold value of nucleon Delta-excitation parameter 147 MeV. Mass of the nucleon in nuclear medium which is less than free nucleon mass (N) by about 8 MeV is

located on the stright line from omega-meson mass to the sigma-hyperon mass. This reduced value corresponds to 6x16+18=114δ

.

Fig.16. Spacing distribution in Sb-122,124

Table 7 : Nuclear excitations close to me/3 and n∙δmN/8 in Sn and Sb isotopes

Appearance of stable intervals in nuclear excitations rational to me and δmN (named tuning effect) was found in data for many near-magic nuclei.

Parameters of the Standard Model (III)

It was discussed by many authors [19-21] that radiative correction of the type g/2pi could be useful for comparison of different parameters. A possible example of application of this method was given in [22,23]. Confirmation of preliminary ATLAS data on the SM-scalar mass permitted to check again empirical facts on presence of mass/energy intervals similar to the discussed parameters of NRCQM (147 MeV) and given above intervals multiple to it.

Observed in nuclear data long-range correlations with the parameters me and εo=2me (see Table 2) should be considered as additional argument for a fundamental meaning of earlier found empirical relations in nuclear and neutron resonance data, for example, nonstatistical effects in low-lying and highly excited nuclear states found by V.Andreev, M.Ohkubo, K.Ideno, F.Belyaev and G.Rohr.

Conclusions• Presence of tuning effects in nuclear excitations and nuclear binding

energies is confirmed with new analysis of data from PNPI compilations (Vols. I/19, I/22, I/25 LB Springer) based on the role of pion-exchange.

• Relation between observed stable nuclear intervals and particle masses can be connected with the properties of SM scalars if the preliminary ATLAS results (Mh=126 GeV) will be confirmed. Ratios mu/Mz=alpha/2pi and (1/3me)/Mh=(alpha/2pi)^2 could be a reflection of the fundamental relations between SM-parameters (possible “super-duper” model by Feinman [24]).

• Relation (N·16me – me –mn)/δmN =1/8.000 could be checked with new

more accurate value of the mp/me ratio (this coincidence is important).

• Observed analogy between tuning effects in particle masses and in nuclear data should be theoretically based on QCD as a part of Standard Model and Nambu suggestion about the role of empirical relation for SM development.

• Scientific potential of nuclear physics can be connected with fundamental role of QED parameters including the electron mass and QED corections.