GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia

Transcription

1 GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv quantum numbrs occurrd in th natur of strongly and wakly intracting particls. Th unusual fatur of such figurs is that during thir building no data about particls ar usd at all but th data about th mntiond spctra though can b found in ths figurs and this can b discovrd with th hlp of spcial coordinat systms. At prsnt w know mor than two hundrd strongly intracting particls and about twnty wakly intracting particls. Som important faturs of ths particls spctra hlp to rval gomtrical phnomna in th physics of subatomic particls. Lt us giv this nam to th gomtrical figurs bing th carrirs of som important charactristics of strongly and wakly intracting particls that ar obsrvd in natur. Th paradox is that whil building ths gomtrical figurs w don t us any data about particls at all. Lt us call a flat gomtrical figur composd of 3 idntical rctilinar hxagons as phnomnon (fig., a). Th cntrs of th hxagons w will call as magic points and dsignat thm as C k whr k is a rfrnc numbr of th magic point. Th positions of ths points in th figur ar markd with yllow circls.. Y. C C C X C C - C -.. a) b) Figur : a) Phnomnon ; b) Phnomnon with its own coordinat systm. In th figur undr considration svral groups of magic points can b singld out and in ach of thm ths points ar locatd quidistantly along th straight lin, and som of ths lins appar to b paralll to ach othr and also locatd quidistantly from ach othr. This allows us to us th magic points as rfrnc points for building diffrnt obliqu-angld coordinat systms with uniform scals along th coordinat axs. In such coordinat systms all th magic points coincid with th nods of th coordinat grids and th valus of ths points coordinats ar qual to intgr numbrs. Ths coordinats can b calld as th propr coordinats of phnomnon. Thy don t chang at diffrnt linar transformations of this figur. On of th propr coordinat systms (systm ) is shown in Fig., b. Th origin of th coordinats in this systm is dcidd to b at th point С. Th coordinats Y and X of th magic points of phnomnon in this systm ar intgr numbrs (Tab. ) as it should b. * -mail addrss: dbastron@yandx.ru

2 Magic points Valus for th coordinats of th magic points in systm and quantum numbrs B and Q for th quark structurs Tabl Valus for th coordinats Valus of th numbrs B and Q for th structurs whny = B, X = Q Valus of th numbrs Q and B for th structurs whn Y = Q, X = B Y X B Q Structur Q B Structur С uuu uuuddd С uud uud С 3 uuuddd uuu С 4 udd u d С 5 ddd d dd С 6 ud u dd С 7 uuu u uuddd С 8 u ud u d С 9 u uuddd uuu С u dd ud С d dd ddd С u d udd С uudd uudd It is paradoxical howvr that th valus of ths coordinat pairs coincid with th valus of th pairs of th rmaining additiv quantum numbrs B and Q, whr B is a barion numbr and Q is an lctric charg in th systm of units whr th modulus of an lctron charg is assumd to b qual to on. Indd, th following accurat qualitis Y = B and X = Q for th quark structurs dsignatd in column 6 of tabl and also qualitis Y = Q and X = B for th quark structurs dsignatd in th last column of th tabl tak plac. Howvr, th group of structurs in th last column diffrs from th group of structurs in th sixth column in only rarrangmnts of th structurs in lins. At first sight it may sm that all th mntiond abov ar th rsult of a good choic of th coordinat systm or a random coincidnc. But it is not tru. Rally, lt us apply anothr propr coordinat systm with numbr to phnomnon (Fig.). Y 3 C X C 3 C - C C - C -3 Figur : Phnomnon with its own coordinat systm.

3 Valus for th coordinats of th magic points in systm and quantum numbrs B and Q for th quark structurs Tabl Numbrs B and Q as Magic Coordinats functions of th coordinats points Y' and X' Structurs Y' X' (Y'X')/3=B (X'Y')/3=Q С 3 uuu С uud С uuuddd С 4 udd С 5 3 ddd С 6 ud С 7 3 uuu С 8 u ud С u uuddd С u dd С 3 d dd С u d С uudd In this systm, as it follows from Tab., th total valus for th coordinats Y' and X' of th magic points diffr from th total valus for th quantum numbrs B and Q. But th dfinit linar combinations of th coordinats Y and X of th magic points coincid with th quantum numbrs B and Q, namly ( Y X )/3= B and (X Y )/3 = Q. This xampl shows that dspit th choic of th propr coordinat systm, phnomnon is indd th carrir of th valu pairs for th numbrs B and Q for th obsrvabl strongly intracting particls, and th coordinat systm allows us to b obviously convincd in it. Ths facts, though, don t xhaust mystrious faturs of phnomnon. Lt s considr th middl part of phnomnon that rmains aftr rmoving xtrnal hxagons of grn colour (Fig. 3). This part of phnomnon contains magic points with only vn numbrs. X C - C - C C Y a) b) Figur 3: a) Th middl part of phnomnon ; b) Th middl part of phnomnon with its own coordinat systm 3. 3

4 On th basis of th magic points of this part of phnomnon w build th propr coordinat systm 3 (Fig. 3, b). Th coordinats X и Y of th magic points in this systm ar intgr numbrs (Tab. 3). Th paradox is that th valus of ths pairs of coordinats coincid with th valus of th pairs of th rmaining additiv quantum numbrs and Q of wakly intracting particls, whr L l is a lpton additiv quantum numbr ( l =, μ, τ ), and Q is an lctric charg in th systm of units whr th modulus of an lctron charg is takn qual to on. L l Tabl 3 Valus for th coordinats of magic points with vn numbrs in coordinat systm 3 and th pairs of additiv quantum numbrs L l and Q of wakly intracting particls Magic points Valus for th coordinats Y X Particls, for which Y = L l, X = Q С, μ, τ Particls, for which Y = Q, X = Ll, μ, С 4 ν, ν μ, ν τ W С 6 ν, ν, ν W μ τ С 8, μ, τ, μ, τ С ν, ν μ, ντ W С ν, ν, ν С Z W μ τ Z τ Indd, th following xact qualitis X = Q and Y = Ll for th particls dsignatd in column 4 of Tab. 3 and also qualitis X = Ll и Y = Qfor th particls dsignatd in th last column of th tabl tak plac. Howvr, th group of particls in th last column diffrs from th group of particls in th 5 th column in only rarrangmnts of th structurs in th lins. Thrfor th constitunt part of phnomnon shown in Fig. 3, a is indd th carrir of th valus of th rmaining additiv quantum numbrs L l and Q of th wakly intracting particls undr considration and th coordinat systm 3 maks it possibl to b dirctly convincd in it. Thr rmains on thing to not that Tab. 3 has all th known wakly intracting particls and dosn t hav any hypothtical particls. Thrfor phnomnon in whol is th carrir of valu pairs for th numbrs B and Q and also L l and Q of th known strongly and wakly intracting particls accordingly. Th cntrs of th rgular hxagons bcom magic points of phnomnon only whn ths hxagons ar connctd into th figur shown in Fig., a. This figur dosn t hav any gomtrical rstrictions on adding nw hxagons to it. For xampl, this figur can b addd svral mor hxagons as is shown in dottd lins in Fig., b. If th coordinats of th cntrs of th addd polygons in th coordinat systm ar takn qual to Y = B and X = Q, thn th coordinats of ths cntrs ar qual to th pairs of th quantum numbrs B =±, Q =, ± and B =, Q =± of six xotic hadrons with xplicit xoticism that havn t bn discovrd during th xprimnt. So thr is a limitation on th magnitud of th modulus of th radius-vctor drawn from th point С to othr magic points of phnomnon. Ths vctors will b dsignatd with th sam 4

5 lttrs as magic points but only in bold typ. Lt us not th following important faturs of ths vctors. Y=B ddd uuuddd uud C udd uuu C,, X=Q ud,, C W - C ddd C C X=Q ud - - C C - udd - uud W - - Z -, -, - C,, Y=L l uuu uuuddd a) b) Figur 4: Distribution of radius-vctors drawn from th figur cntr to th magic points. Th angls btwn random radius-vctors in Fig.4, a ar multipl to π/6. Any radius-vctor С k can b rprsntd as a sum of two othr radius-vctors. For an odd numbr k th qualitis С k = С k С k и С k = С k С k occur. For vn numbrs k th qualitis С k = С k С k occur. Whn choosing th spcific propr coordinat systm, for xampl systm (Fig.4, a), ach magic point of th phnomnon according to th valus of quantum numbrs B = Y and Q=X can b compard to a hadron. Thn th abov writtn qualitis dscrib possibl transmutations of hadrons in which th numbrs B and Q ar rtaind sparatly. For xampl vctor quality С 3 = С 4 С rprsnts th transmutation uuuddd uud udd and th quality С 4 = С 6 С rprsnts th transmutation udd uud ud. Similarly whn choosing th propr coordinat systm 3 for th middl part of phnomnon (Fig. 4, b) ach magic point in accordanc with th valus of quantum numbrs Ll = Y and Q = X can b compard to a wakly intracting particl. Thn th vctor qualitis С k = С k С k dscrib possibl transmutations of th givn particls in which th numbrs Ll и Q ar rtaind sparatly. For xampl th vctor quality С 6 = С 8 С 4 dscribs th transmutation W ν. Thrfor phnomnon rprsnts in a graphic form potntially possibl transmutations of subatomic particls at which th quantum numbrs B and Q or L l and Q rmain. On mor flat gomtrical figur is of intrst, it can b rgardd as phnomnon (Fig. 5). Figur 5: Phnomnon is a carrir of valu pairs for th rtaind additiv quantum numbrs of strongly and wakly intracting particls. 5

6 In fact, having applid coordinat systm 4 (Fig. 5) to phnomnon and having dtrmind th valus for th coordinats Y и X of th magic points of this figur w discovr that Y = B, and X = Q for th quark structurs dsignatd in th 6 th column of Tab.. Y - - C C C C - - C X C Figur 6: Phnomnon with its own coordinat systm 4. On mor phnomnon 3 can b built using six idntical rhombuss, th acut angl of which quals π/3 (Fig. 7). Th vrtics of th rhombuss occur to b th magic points hr. C Y C C X C C C - Figur 7: a) Phnomnon 3; (b) Phnomnon 3 with its own coordinat systm 5. Th coordinat valus for th magic points of phnomnon 3 in th coordinat systm 5 (Fig. 7) fully coincid with th coordinat valus for th magic points of phnomnon in th coordinat systm (Fig., b) rprsntd in Tab.. So phnomnon 3 is fully idntical to phnomnon. Conclusion It was assumd in [] that th distribution of th pairs of th rmaining additiv quantum numbrs of subatomic particls is subjct to th dfinit rgularity that dosn t obviously follow from th modrn thory of particls. This assumption, in our opinion, is confirmd by phnomnal gomtrical figurs, whil building thm w don t us any data of th particls. Howvr thy appar to b th carrirs of th pairs of valus for th rmaining additiv quantum numbrs of th ral strongly and wakly intracting particls. 6

7 Th following rgularitis rsult from distribution of th magic points on any of th phnomna: if a hadron with th valus of quantum numbrs B and Q is ral, thn thr also xists a hadron with th numbr valus B = Q and Q = B ; if a wakly intracting particl with th valus of quantum numbrs Ll and Q is ral, thn thr also xists a particl with th valus of th numbrs Ll = Q and Q = L l. Ths particls can b rgardd as BQ- or LQ-symmtrical partnrs. Finally w not that th striking faturs of th prsntd abov gomtrical figurs indicat that thr is a common law that dtrmins th valus of th rtaind additiv quantum numbrs of th ral quark structurs and wakly intracting particls that is rprsntd in gomtrical form in th producd phnomna. Rfrnc. E.N. Klnov. Structural unit of th mattr and its stat, RGASHM GOU, Rostov-on-Don, 86 (6) 7