QUANTUM STABILITY OF THE MUON, TAU, ELECTRON LEPTONS IN RELATION TO PLANCK MAGNITUDES AND VACUUM

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1 ANTM STABILITY O THE MON TA ELECTRON LEPTONS IN RELATION TO PLANCK MANITDES AND VACM zal A. M Jéz Mah 00 Apd.9. C.P.900. Códba. Spa gzala@gal. th study f th spatal agtud apaty as a sufft f ts lat wth th Plak agtuds th fat ad dvlpt f bsvabl ad al psss suh as ltal hag ad st ass th ls xstg latshps ag Tau Mu ad Elt lpt patls a dtald as wll as th dft f Tau ad Mu patls as sytal pts f a dly athatal fawk dfd by spatal latshps whh ly pts th fat f s stutus by a ly ad pdubl way. Th valus btad f th dvlpd thtal uats f u ad tau lpts st ass uvalt a: µ (8) [Mv] (0) [Mv]. Takg th f f xptal u st ass valu () du t auay ass asut th latv s µ Kywds: u ass tau ass lpts thgss spatal agtud uatzat f lt hag ltay patl Plak ass Plak stats syty. INDEX. uatzat f lt hag... uatzat f lt hag. Suppltay dts.. Thtal suppt ad lat wth lt ass.. Tau Mu latshps. Rst ass valus alulat ad luss. () udatal Physal stats su: Pt J. Mh ad Bay N. Tayl CODATA Rdd Valus f th udatal Physal Cstats: Jual f Physal ad Chal Rf Data Vl. 8 N ad Rvws f Md Physs Vl. 7 N ANTIZATION O ELECTRIC CHARE. Adg t pvus hypthss whh th valu f stgth / was datd as a fg pus f st ass ppty ad kpg d th valu f th assatd spa latd t vauu dlt stat ad agt pablty

2 x() w a supps that suh a stgth/ts ts at up th du s als pld th appaa f th ppty alld lt hag. I ths way by applyg th valu f th abv td pus f t th du f lgth uplg spa : x ( Plak spa) ad by ualzg t t th Culb s Law d t bsv th lt hag valus latd t th sa s that t uld ly pssss uatzd hag valus: hag(/) [b] w wll bsv th apaty that th du f dfd lgth ffs t au th abv td ppty f th at f th f whh was alady latd t th apaty f th du d t au th ppty stg ass : Plak x h x π ( ) ( ) S x π h π Plak Wh a sphal sufa valu wth adus x s ad:. x π S h h π [.] Oh. : Ω Ω vs f th vauu pda s th ] [ ( ) Ω h π.. ANTIZATION O ELECTRIC CHARE. SPPLEMENTARY CONDITIONS. Exptally th a vds f th xst f fats f th sdd ltay hag "" whh at fst d t tu ut t b ddud th uat [.]. It s f t that th xt ddut s fllwd d t sd th xst t f th abv td lat:

3 - By takg valus f "": 0... t s bsvd th apaty f atalzat f th uat [.] f vy valu f ta (thugh lat t wll b dvlpd f th valus f "" w stat f th valu f ts pstatv ddut): ay valu f "": πh πh I ths way f ay valu f "" fs ad sdg valus f 0... a suppltay uatzat pssblty a b bsvd f th ltal hag: πh [.] ( ) πh

4 S that f th sdat f th xst f a suppltay uatzat dt fally xpssd adg t th uat [.] th atalzat xptally bsvd th abv td hag appas. By assgg atual ubs 0 9 w hav th fllwg valus f ltal hag agtud: ( ) πh ( 85 ) 0 8 [b] Thtal valus xptal valus latv ( 9) (0) (0) ( 9) () () ( 9) (6) (6) I th thtal alulat f f() valu th xstg stadad utaty th xptal valu f Plak stat h has b daggd alg (). (h (5)0 - [J s] [s - ] µ π0-7 [NA]). IRE. Study f syty th fut f() f ts fst dvatv d/d t bsv th pssbl lat btw th allwd ltal hag syty ad stablty.

5 . THEORETICAL SPPORT AND RELATION WITH ELECTRON MASS. I lat t th uat xf()() f whh th spatal agtud s dtfd ass th f xf() whh psssss assatd haatsts wth th ltal hag by applyg th sa ppl dvlpd st 8..[]: π π [.] Idtal uat t th lassal lt adus wth ly th plat f th hag f th lt hag ad ts spdg ass. By ag x du t th spd ths as wth a sphal ppty th spatal vaabls appa dpdg th ass: π x h (Cpt wavlgth f a ass ). x: Assatd spa t ass. (S st 8.. []: Bg a pht that s fud tappd th uvatu pdud by a ass s that t tats aud t t a dsta pttg a stuat f ulbu wh t tasfs th syst dfd by pht t a tal syst wth stat vlty Th pht wuld a tappd by th tal putual ass ly t a dsta whs valu wll b th assatd spa t : x/ whh s dpdt f th pht ass. ). Th fllwg luss a bsvd as f d uplgs ag th pvus agtuds: h (S st 8.. []). / ( ) - π π (7) 0 [b kg ] π h [.] fd ltal hag. / uplg s sufft. Wh t s alld ufd ltal hag : t th valu f th sultat hag f th th spatal lats ualty ad th ualty f ass wth th s alld uplg ass: (dt wth Plak ass). Ths valu f ltal hag s th whh

6 appas th asg f th pt. That luds wth th uat [.] dtal t [.] xpt f th uatzat. As t was s pt. th valu f s vlvd lkws th ltal f valu dtal wth / as wll as th f th sphal sufa valu πx ( x dt wth Plak spa). T bsv th uatzabl fat t s substtutd th Cpt wavlgth f ass agtud appag a uty spatal lat t: π h πh [.] µ If [.] ds wth [.] th that pls a uatzd ltal hag valus dpdg f a spatal paats lat ad ts uplg sult. I ths way th spatal lats appas lat wth ltal ppts lk ass ad ltal hag: x (S s.9..[]) [.] x h x uplg spa. Cdt wth Plak agtud. Studyg w th bd lats f th lt d t lat ts ltal hag: h π π ( ) [.5] Lkws f ay stg ass t s fulflld: [.6] π By bg [.5] wth th st gal [.6] [.] /. / l π h l [.7] [.6]

7 By bg th uats (E.6.. [] xx xx xx lat th t [.7]: (EE. 9.. SSSSSSSS)) d t h l t T h t x / x x T l l x l l x x [.8] Adg t th uat [.7] th st ass ppty appas lk a adat whs g s th Plak f ad a ltal f f( ) tat bth f th ht t th vauu ( T / : Ts f a stg wth la dsty µ/l whh a wav wth spd v s tasttd Lx/ ) that affts t th Plak ass valu d t au kw valus assatd t patls ths valus d t tak ay uatty as wll as t us wth th lt hag Natu alty. If w wat t bta th lt st ass valu f th uat [.7] by applatg uatzd valus ths valu appas wth a uatzat f th typ: l / κ κ [.9] That s t say by uatzg th ltal f a sla way t th stablshd ltal hag. I ths way as wll as t us wth valu f whh th lt hag aus th atalzat xptally bsvd wth spt t lt hag th st ass valu that ds wth th td patl ass s btad f th valu κ 9. [.9]: ( κ 9) ( 58 ) 0 Kg uat [.] ad by uval wth th 9 5 [.0] / 9 (f lt) l a ltal f f appas uatzd.

8 Th stadad utaty xstg xptal Plak stat valu h () has b tak t aut f lt st ass thtal valu slvd klgas. Nt that statd latv s f th lt hag ad ass pst sla valus d t 0 -. (h (5)0 - [Js] (6)0-9 [b]) () (0) [Mv] () [Mv] () (9) Wth th thtal valus btad f lt/pst ltal hag ad st ass th at /- / aus th fllwg valus: (8) 0 [ kkkk ] (7) 0 [ kkkk ] (). TA MON RELATIONSHIPS. REST MASS VALES CALCLATION AND CONCLSIONS. W sd th asss f tw patls wh th dsgat ds wth lt/pst assgg t th spatal agtud dfd by [.] uat ad t th Cpt wavlgth whh haatzs that s latd tslf wth at th sa t. [.] d t [.] f th valus whh lt hag ds wth th lt hag ad ts atpatl: [.] Adg t th uat [.] th xstg lat ag th ass f tw patls s assatd t th tw lats a spatal s fd t a sgl patl as t was alady s [.] ad ath btw bsvabl lt hag ad lt hag assatd t Plak agtuds. Lkws th uats [.] ad [.] a π h π /

9 tasfd t [.] (f ) ad [.] sptvly f th spatal lat fs t a sgl patl. Adg t [.] at / s a asd t sua fut f paat s / wuld b abl t b fut f s that th spatal lat b a glbal fut. Mu ad tau lpts hav b hs as patls ths study s that ludg th lt thy f a tally latd t as bs f ths gup ad wth dtal ltstat hag pssss. I fat ust as w had atpatd tw sytal lats xst that df th tault ad u-lt lats wth spt t ass akg a glbal lat /. As wll as that fat assgd t / ths xpsss a asd t sua ad thy a afftd by s dft paats whh a udld f ts tg subsut lats. Ths xpsss a th fllwg s: [.] [.] S th xpss that lats th asss f th th patls psts a sytal lat: [.5] Ad th asss f tau ad u patls appa laly td: [.6] [.7] ( ) ( ). 9

10 Th ffts that w pfd f tg hav b dstbutd wth th dats ad as wll as t th fft s that wh thy a substtutd f valus that dt th at btw th tau ad u asss adg t th uat [.7] thy dsplay th xstg syty suh uat ad th tat lat ag th tw patls as sytal pts f a wll aagd athatal fawk dfd by spatal lats paalll t D.N.A. stuts that ly pts th fat f ta stutus a uu ad pdubl way. Th valus btad f th pvus uats [.] [.] ad [.7] a: µ.. / µ sd uats & valus (8) Mv * (0) (6) [.][.]()[kg]() (6) [.7] (5) Mv () (9) Mv () (7) () Cdata () * I ada wth CLEO[] 997 llabat (778.7±.6±. Mv). Th CLEO[][] bd sult s: (778.±. Mv) DELPHI llabat: (778.7±.±. Mv) ad utlss day sults []. [.] [.] ad [.] by btag th uats (/µ) / (/ ) / t a b vfd that th uat [.7] has a gat pta baus t dsbs lkws th spatal lat btw Cpt wavlgths wavlgths f ay vlty (whv vµv ) f th tw asss: [.8][.7] µ µ 0 0 µ µ

11 W a tdu ad study a dsal dulat fat that w wll a syty fat: S d t pst a spatal syty wth spt t authzd Cpt wavlgth valus btw ± uatts. S S S S S BIBLIORAPHY [] CLEO Cllabat R. Balst t al. Phys. Rv. D 7 R67 (99). [] CLEO Cllabat A. Aastassv t al. Phys. Rv. D 55 R559 (997). [] axv: hp-x/000v Ot 00. Study f CMS sstvty t utlss day at LHC. R. Satll. 7 th Itatal Wkshp Tau Lpt Physs (Tau0) Sata Cuz CA 0- Sptb00. [] Jual f Thts Extsv paps. A Study f Egy Ad Its Iplats. Spa Tpal Stutu Of Egy. zal A. M Jéz. Otb Th Auth.

Handout 30. Optical Processes in Solids and the Dielectric Constant

Handout 30. Optical Processes in Solids and the Dielectric Constant Haut Otal Sl a th Dlt Ctat I th ltu yu wll la: La ut Ka-Kg lat Dlt tat l Itba a Itaba tbut t th lt tat l C 47 Sg 9 Faha Raa Cll Uty Chag Dl, Dl Mt, a lazat Dty A hag l t a gat a a t hag aat by ta: Q Q