Self-interaction mass formula that relates all leptons and quarks to the electron

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1 Slf-intraction mass formula that rlats all lptons and quarks to th lctron GERALD ROSEN (a) Dpartmnt of Physics, Drxl Univrsity Philadlphia, PA 19104, USA PACS Ff Quark and lpton modls spcific thoris particl systmatics Abstract. An accurat mpirical slf-intraction mass formula has bn obtaind for all twlv lptons and quarks, in which th baryon numbr B and th charg numbr Q ntr as ignvalu surrogats for th strong and th lctromagntic slf-intractions. All lpton and quark masss appar dirctly rlatd to th lctron mass.. Rcntly vry dtaild high-prcision calculations hav stablishd th masss of th up and down quarks and as m 2.01 u = (10) MV m d = (15) MV (1) at th most appropriat 2 GV nrgy-scal in th MS rnormalization schm [1]. Thus th masss of th first-gnration lptons and quarks ar givn by th slf-intraction mass formula m = m (8B Q) 2 (2) in which m is th xprimntal mass of th lctron (takn as mpirical input) and B, Q ar commuting quantum oprators that giv th baryon numbr B B (ignvalu surrogat for th strong intraction) and th charg numbr Q Q (ignvalu surrogat for th lctromagntic intraction), with BQ = BQ, B 2 =, and Q 2 Q + ε whr ε B 2 = 2 = drivs from th virtual charg-distribution around a nutrino du to ( a ) grald.h.rosn@drxl.du

2 lctrowak closd-loop procsss [2, ]. Hnc from (2) w obtain m ν = ε m = V 1 m = MV () m u = MV m d = MV Comparing (1) and (), w s that th mpirical formula (2) yilds accurat valus for th u and d masss. Lpton and quark slf-intraction mass givn by (2) for th first gnration has an absolut physical charactr, nrgy-scal indpndnt lik pol mass [4] but with a physical maning that dos not involv prturbation-rnormalization thory ( ). Th slf-intraction mass formula (2) can b gnralizd for th scond and third gnrations. Lt ξ = ξ = (0, 1, +1) b th gnration quantum numbr, with ξ = 0 for th first, ξ = 1 for th scond, and ξ = + 1 for th third. By mploying data-fitting tchniqus [6,7], w find ( ) Existnc of a Higgs boson to brak th lctrowak symmtry and ngndr th zro-mass photon and th massiv ± W and o Z bosons is of cours likly. Howvr, it is uncrtain whthr th Higgs should also gnrat lpton and quark masss through a hirarchy of Yukawa couplings [5]. Whil th four fundamntal bosons H, γ, ± W and o Z most probably rlat to ach othr, th twlv fundamntal frmions appar to rlat through th slf-intractions mass formula (4). Th lpton and quark mass valus subsquntly ntr th standard modl Lagrangian as pr-stablishd input, with th mixing of quark stats, as wll as th mixing of nutrino stats, viwd to b a standard modl fild-intraction phnomnon.

3 m = m (nb Q) 2 ξ 4 ξ +ξ (4.1) (4) in which th vn-intgr valud cofficint of B is 1 + (P+ ) ξ+ (2P ) ξ 2 2 P( ξ ξ) / 2 n = 2 (5) Apparing in (5) is th projction quantum numbr 2 P = P B + Q which quals zro for 1 2 Q = 0 or and quals unity for Q = or 1. Hnc (5) rducs to n= 2 n= 2 + ( ξ ξ ) / 2 + (ξ+ ξ ) / 2 ( ξ ξ) / 2 for P=0 for P=1 (6) In th final trm in (4), th bas factor (4.1) = (41/10) appars for th mass scaling of th thr gnrations, as in arlir mpirical invstigations that wr rstrictd to th chargd-lptons [8,9]. Th logical simplicity and quantum-thortic charactr of th mass formula (4) ar clarly vidnt, with all lpton and quark masss manifstly rlatd to that of th lctron. Th quantum numbrs for lptons and quarks appar with thir slf-intraction masss (4) in th TABLE. Th ovrall agrmnt with th xprimntal masss [10,11] is quit striking. In particular, w hav th fractional dviations δm μ / m μ = and δ m τ / m τ = Acknowldgmnts. Th author would lik to thank Christin Davis for svral illuminating communications rgarding th work of hr group [1]. At Drxl, Margart Dominy hlpd with a litratur survy, and Jacqulin Sampson assistd with th manuscript prparation.

4 REFERENCES [1] MCNEILE C. t al., arxiv: , v1 (2010). [2] BERNABÉU J. t al., Phys Rv. Ltt., 89 (2002) [] FUJIKAWA K. and SHROCK R., Phys Rv. D, 69 (2004) [4] KRONFELD A.S., Phys Rv. D, 58 (1998) [5] BABU K.S. t al., Phys Rv. Ltt., 67 (199) 545. [6] TARANTOLA A., Invrs Problm Thory - Mthods for Data Fixing and Modl Paramtr Estimation (Elsvir, Amstrdam) [7] VAPNIK V.N., Statistical Larning Thory (Wily, Nw York) [8] SIRLIN A., Comm. Nucl. Part. Phys., 21 (1994) 227. [9] ROSEN G., Europhys. Ltt., 62 (200) 47. [10] NAKAMURA K. t al., J. Phys. G, 7 (2010) [11] PARTICLE DATA GROUP (2012)

5 TABLE - Quantum mmbrs and slf-intraction masss for th lptons and quarks. Masss from (4) ar in MV xcpt for th nutrinos, whr V magnituds ar indicatd. ξ B Q P n m ν V u 0 ⅓ ⅔ d 0 ⅓ ⅓ ν V μ c 1 ⅓ ⅔ s 1 ⅓ ⅓ ν V τ t 1 ⅓ ⅔ ,607 b 1 ⅓ ⅓

Standard Model - Electroweak Interactions. Standard Model. Outline. Weak Neutral Interactions. Electroweak Theory. Experimental Tests.

Standard Model - Electroweak Interactions. Standard Model. Outline. Weak Neutral Interactions. Electroweak Theory. Experimental Tests. Standard Modl - Elctrowak Intractions Outlin ak Nutral Intractions Nutral Currnts (NC) Elctrowak Thory ± and Z and γ Discovry of ± Exprimntal Tsts LEP Z Boson Mass and idth Numbr of Nutrinos ± Boson ±