Journal of Theoretics

Transcription

1 Jurnal f Teretis Vlue 6-1, Feb-Mar 00 Te Pssibility f Neutrins Deteted as Tayns Takaaki Musa usa@jda-trdi.g.j usa@jg.ejnet.ne.j M.R.I., , Naiki, Kanazawa-ku Ykaa, , Jaan Abstrat: Reent easureents n eletrn neutrins suggest tat tey igt ae an iaginary rest ass. Tis aer sws tat tey ae a ssibility being eitted fr te ati nuleus as a faster-tan-ligt (FTL) artile alled a tayn. Key Wrds: faster-tan-ligt, tayn, neutrin. Table f Sybls : wae funtin f te ing artile : wae funtin f te artile in a FTL state : rer aeleratin f te artile : ligt seed : entu f te artile : entu f te artile in a FTL state E : energy f te artile : Plank's nstant diided by π : rest ass f te artile T enetratin rbability f artiles trug te ligt barrier L : size f te ati nuleus Λ : traeling distane f te artile in a FTL state

2 INTRODUTION Te rest ass f neutrins as been assued t be zer. Hweer reent easureents n eletrn neutrins suggest tat tey igt ae an iaginary rest ass [1]. Tis eans tat tey are faster-tan-ligt (FTL) artiles, wi were naed tayns by G. Feinberg []. Te urse f tis aer is t exaine te ssibility f eletrn neutrins being eitted fr te ati nuleus as a tayn. WAVE EQUATION FOR THE PARTILE MOVING INSIDE THE ATOMI NULEUS Susing tat te eleentary artile ing inside te nuleus satisfies te equatin desribed as E ( x, t) = A ex i t x, (1) were is a wae funtin, A is an arbitrary nstant and is a Plank's nstant diided by π [3]. E and are energy f te artile and its entu gien by E =, () 1 / =, (3) 1 / were is a rest ass f te artile. Fr Eq.(1), we an btain te relatin gien by i =. () t Wen te ing artile inside te nuleus turns its diretin as swn in Figure 1, Eq.() an be rewritten as = i, (5) by using te rer aeleratin gien by = t t ). (6) ( were is te tie wen te artile is aelerated []. Te slutin f Eq.(5) an be gien by t

3 = 0 lg( ex i, (7) were is an arbitrary nstant. Figure 1. Ming artile inside te nuleus. If te elity f te artile inside nuleus alst equals te ligt seed, te elity f te artile reains alst te sae wen it is aelerated. S te wae equatin fr te ing artile inside te nuleus an be arxiated as fllws by inserting Eq.(3) int Eq.(7). = i lg ex 3. (8) Fr te elity beynd te ligt seed, Eq. (8) an be rewritten as π = ex lg ex 3 3 i, (9) were is a wae funtin f te artile in a FTL state. Fr te unertainty rinile gien by L, te rer aeleratin f te artile ing inside te ati nuleus an be rugly estiated as 0 1 L t =, () were L is a size f te ati nuleus.

4 Arding t te WKB arxiatin [5], te enetratin rbability trug te ligt barrier fr te igly aelerated artile an be estiated by T π L = ex. (11) POSSIBILITY OF THE NEUTRINO EMITTED FROM THE ATOM AS A TAHYON By te unertainty rinile f te entu, te elity f te artile ing inside te ati nuleus an be estiated fr te relatin [6] swn as. (1) 1 / L Fr wi, we ae L, (13) fr te ligt artile wen satisfying L / << 1. Arding t te unertainty rinile, it is nsidered tat te artile enetrated trug te ligt barrier is eritted t aintain te FTL state terarily swn by susing tat energy f te enetrated artile trug te ligt barrier is nsered, te artile ing inside te ati nuleus satisfies E = (in a nn-ftl state), (1) and E = (in a FTL state), (15) were is te entu f te artile and is an abslute alue f te artile s rest ass in a FTL state. If we let =, we ae ( ) =. (16) Ten it is seen tat te FTL artile as an iaginary ass terarily arding t te unertainty rinile. Fr te ase wen >>, an be arxiated as L L = 1 1, (17) L

5 fr / L, wen satisfying L / << 1. Fr te nersatin f energy f te artile trug te ligt barrier swn as =, (18) 1 / / 1 we ae L. (19) Te unertainty relatin fr te tayn an be gien by t, (0) 0 were and is are elities befre and after te easureent [7]. Fr Eq.(17),(19) and (0), te tie interal f te artile eitted fr te ati nuleus traeling in a FTL state an be gien as t (1) 5 3 L if we let. Fr wi, te traeling distane f te artile eitted fr te ati nuleus as a tayn an be estiated as Λ = t () 3 L Hene it is seen tat te ligt artile eitted fr te nuleus as te ssibility t trael in a tayni state witin a finite lengt arding t te unertainty rinile. ALULATION OF EXPERIMENTAL DATA FOR THE ELETRON NEUTRINO and Te square f te eletrn neutrin rest ass easured fr tritiu β deay by any researers are swn in Table 1 belw. β deay, 3 H deay Table 1. Exeriental data f eletrn neutrin. N. Nulear Reatin Exerient (ev ) i (Kg) Λ () Ref. 1 Tritiu β deay ± 8 Tritiu β deay 39 ± H deay 65 ± 85 β deay 17 ± 68 5 Tritiu β deay 130 ± 0 36 i i i i i [8] 1.03 [9] [] [11] [1]

6 Te square f te eletrn neutrin rest ass ilies tat it as an iaginary rest ass swn in Table 1, were is te ean alue f te eletrn neutrin rest ass. Figure sws te enetratin rbability trug te ligt barrier wen we let L 1. If te artiles rest ass satisfies >>, te rbability fr te artile being eitted fr te ati nuleus in a FTL state bees alst a unity as swn in te figure belw. Figure. Prbability f te artile being eitted fr te ati nuleus in a FTL state. Te traeling distane in a FTL state an be alulated by Eq. (), wi is als swn in Tabel.1. Fr tese results, it is nsidered tat eletrn neutrins an be deteted as a tayn near te sure as bsered at te exerients, weer te distane between te sure and te detetr is u larger tan te distane between te Eart and te Sun, wi equals abut ass , tey an be bsered as an rdinary artile wi as a real rest ONLUSION In tis aer, te ssibility f te neutrin being eitted fr te ati nuleus as a tayn as been disussed and te teretial analysis dne gies te result tat eletrn neutrins an be deteted as tayns near teir sure.

7 REFERENES [1] Reai, E., Se infratin abut te fur exeriental setrs f ysis in wi sueruinal tins see t aear, tt://lanl.g/arie/quant-, 000. [] Feinberg, G., Pssibility f faster-tan-ligt artiles, Pys.Re., 159,.89-11, [3] B, D., Quantu Tery, Der Publiatins, N.Y., [] Jyuk, A.I., Intrdutin t te Tery f Relatiity, Natinal ulture Pysis-Mateatis Library, Msw (in Russian), [5] Fren,A.P., Taylr,E.F., An Intrdutin t Quantu Pysis, Te M.I.T Intrdutry Pysis Series,MIT Press, [6] Daies, P..W., Te Aidental Unierse, abridge Uniersity Press, abridge, 198. [7] Park,M., Park,Y., On te fundatin f te relatiisti dynais wit te tayn, IL Nu ient,vl.111,n.11, , [8] Hlzsu,H., Fritsi,M., Kundig,W., Measureent f te eletrn neutrin ass fr tritiu -deay, Pysis Letters B87, , 199. β [9] Weineier.., et al, Ired liit n te eletrn-antineutrin rest ass fr tritiu β -deay, Pysis Letters B300,.-16, [] Kawakai,H., et al, New uer bund n te eletrn anti-neutrin ass, Pysis Letters B, Vl.56, N.1,.5-111, [11] Rbertsn,R.G.H.,et al., Liit n ν e ass bseratin f te β deay f leular tritiu, Pysial Reiew Letters, Vl.67, N.8, , [1] Steffl,W., Dean,D.J., Analus struture in te beta deay f gaseus leular tritiu, Pysial Reiew Letters, Vl.75,N.18, , Jurnal He Page Jurnal f Teretis, In. 00