The Masses of elementary particles and hadrons. Ding-Yu Chung

Transcription

1 The Msses of elementry prticles nd hdrons Ding-Yu Chung The msses of elementry prticles nd hdrons cn be clculted from the periodic tble of elementry prticles. The periodic tble is derived from dimensionl hierrchy for the seven extr sptil dimensions. As molecule is the composite of toms with chemicl bonds, hdron is the composite of elementry prticles with hdronic bonds. The msses of elementry prticles nd hdrons cn be clculted using the periodic tble with only four known constnts: the number of the extr sptil dimensions in the superstring, the mss of electron, the mss of Z, nd α e. The clculted msses re in good greement with the observed vlues. For exmples, the clculted msses for the top qurk, neutron, nd pion re GeV, MeV, nd MeV in excellent greement with the observed msses, 176 ± 13 GeV, MeV, nd MeV, respectively. The msses of 110 hdrons re clculted. The overll verge difference between the clculted msses nd the observed msses for ll hdrons is 0.29 MeV. The periodic tble of elementry prticles provides the most comprehensive explntion nd clcultion for the msses of elementry prticles nd hdrons. PACS number(s): Sq, Pb, Kt, Yx Keywords: string field theory, supersymmetry, mss reltions, hdron mss models nd clcultions 1

2 1. Introduction The mss hierrchy of elementry prticles is one of the most difficult problems in prticle physics. There re vrious pproches to solve the problem. In this pper, the pproch is to use periodic tble. The properties of toms cn be expressed by the periodic reltionships in the periodic tble of the elements. The periodic tble of the elements is bsed on the tomic orbitl structure. Do elementry prticles possess orbitl structure? In this pper, the orbitl structure for elementry prticles is constructed from the superstring. The extr dimensions in the superstring become the orbits with dimensionl hierrchy. The energy is ssumed to be distributed differently in different dimensions in such wy tht the energy increses with incresed number of spcetime dimensions. All elementry prticles re plced in the periodic tble of elementry prticles [1]. As molecule is the composite of toms with chemicl bonds, hdron is the composite of elementry prticles with hdronic bonds. The msses of elementry prticles nd hdrons cn be clculted using only four known constnts: the number of the extr sptil dimensions in the superstring, the mss of electron, the mss of Z, nd α e. The clculted msses of elementry prticles nd hdrons re in good greement with the observed vlues. For exmples, the clculted msses for the top qurk, neutron, nd pion re GeV, MeV, nd MeV in excellent greement with the observed msses, 176 ± 13 GeV [2], MeV, nd MeV, respectively. 2. Dimensionl hierrchy A supermembrne cn be described s two dimensionl object tht moves in n eleven dimensionl spce-time [3]. This supermembrne cn be converted into the ten dimensionl superstring with the extr dimension curled into circle to become closed superstring. Bsed on this eleven-dimensionl supermembrne, the seven extr spce dimension ssumes dimensionl hierrchy. Ech extr spce-time dimension cn be described by fermion nd boson. The msses of fermion nd its boson prtner re not the sme. This supersymmetry breking is in the form of energy hierrchy with incresing energies from the dimension five to the dimension eleven s F 5 B 5 F 6 B 6 F 7 B 7 F 8 B 8 F 9 B 9 F 10 B 10 F 11 B 11 where B nd F re boson nd fermion in ech spcetime dimension. The probbility to trnsforming fermion into its boson prtner in the djcent dimension is sme s the fine structure constnt, α, the probbility of fermion emitting or bsorbing boson. The probbility to trnsforming boson into its fermion prtner in the sme dimension is lso the fine structure constnt, α. This hierrchy cn be expressed in term of the dimension number, D, 2

3 E D-1, B = E D,F α D,F, (1) E D, F = E D, B α D, B, (2) where E D,B nd E D,F re the energies for boson nd fermion, respectively, nd α D, B or α D,F is the fine structure constnt, which is the rtio between the energies of boson nd its fermionic prtner. All fermions nd bosons re relted by the order 1/α. (In some mechnism for the dynmicl supersymmetry breking, the effects of order exp(-4π 2 / g 2 ) where g is some smll coupling, give rise to lrge mss hierrchies [4].) Assuming α D,B = α D,F, the reltion between the bosons in the djcent dimensions, then, cn be expressed in term of the dimension number, D, or E D-1, B = E D, B α 2 D, (3) E D, B = E α D 1, B 2 D, (4) where D= 6 to 11, nd E 5,B nd E 11,B re the energies for the dimension five nd the dimension eleven, respectively. The lowest energy is the Coulombic field, E 5,B E 5, B = α M 6,F = α M e, (5) where M e is the rest energy of electron, nd α = α e, the fine structure constnt for the mgnetic field. The bosons generted re clled "dimensionl bosons" or "B D ". Using only α e, the mss of electron, the mss of Z 0, nd the number of extr dimensions (seven), the msses of B D s the guge boson cn be clculted s shown in Tble 1. Tble 1. The Energies of The Dimensionl Bosons B D = dimensionl boson, α = α e B D E D GeV Guge Boson Interction B 5 M e α 3.7x10-6 A electromgnetic B 6 M e /α 7x10-2 π 1/2 strong B 7 E 6 /α 2 w cos θ w Z L wek (left) B 8 E 7 /α 2 1.7x10 6 X R CP (right) nonconservtion B 9 E 8 /α 2 3.2x10 10 X L CP (left) nonconservtion B 10 E 9 /α 2 6.0x Z R wek (right) B 11 E 10 /α 2 1.1x

4 In Tble 1, α w is not sme s α of the rest, becuse there is symmetry group mixing between B 5 nd B 7 s the symmetry mixing in the stndrd theory of the electrowek interction, nd sinθ w is not equl to 1. As shown ltter, B 5, B 6, B 7, B 8, B 9, nd B 10 re A (mssless photon), π 1/2, Z L 0, X R, X L, nd Z R 0, respectively, responsible for the electromgnetic field, the strong interction, the wek (left hnded) interction, the CP (right hnded) nonconservtion, the CP (left hnded) nonconservtion, nd the P (right hnded) nonconservtion, respectively. The clculted vlue for θ w is in good greement with for the observed vlue of θ w [5]. The totl energy of the eleven dimensionl superstring is the sum of ll energies of both fermions nd bosons. The clculted totl energy is 1.1x10 19 GeV in good greement with the Plnck mss, 1.2x10 19 GeV, s the totl energy of the superstring. As shown lter, the clculted msses of ll guge bosons re lso in good greement with the observed vlues. Most importntly, the clcultion shows tht exctly seven extr dimensions re needed for ll fundmentl interctions. In dimensionl hierrchy, the bosons nd the fermions in the dimensions > 5 gin msses in the four dimensionl spcetime by combining with sclr Higgs bosons in the four dimensionl spcetime. Without combining with sclr Higgs bosons, neutrino nd photon remin mssless. Grviton, the mssless boson from the vibrtion of the superstring, remins mssless. 3. The Internl Symmetries And The Interctions All six non-grvittionl dimensionl bosons re represented by the internl symmetry groups, consisting of two sets of symmetry groups, U(1), U(1), nd SU(2) with the left-right symmetry. Ech B D is represented by n internl symmetry group s follows. B 5 : U(1), B 6 : U(1), B 7 : SU(2) L, B 8 : U(1) R, B 9 : U(1) L, B 10 : SU(2) R The dditionl symmetry group, U(1) X SU(2) L, is formed by the "mixing" of U(1) in B 5 nd SU(2) L in B 7. This mixing is sme s in the stndrd theory of the electrowek interction. As in the stndrd theory to the electrowek interction, the boson mixing of U(1) nd SU(2) L is to crete electric chrge nd to generte the bosons for leptons nd qurks by combining isospin nd hyperchrge. The hyperchrges for both e + nd ν re 1, while for both u nd d qurks, they re 1/3 [6]. The electric chrges for e + nd ν re 1 nd 0, respectively, while for u nd d qurks, they re 2/3 nd - 1/3, respectively. There is no strong interction from the internl symmetry for the dimensionl bosons, originlly. The strong interction is generted by "leptoniztion" [7], which mens qurks hve to behve like leptons. Leptons hve integer electric chrges nd hyperchrges, while qurks hve frctionl electric chrges nd hyperchrges. The leptoniztion is to mke qurks behve like 4

5 leptons in terms of "pprent" integer electric chrges nd hyperchrges. Obviously, the result of such leptoniztion is to crete the strong interction, which binds qurks together in order to mke qurks to hve the sme "pprent" integer electric chrges nd hyperchrges s leptons. There re two prts for this strong interction: the first prt is for the chrge, nd the second prt is for the hyperchrge. The first prt of the strong interction llows the combintion of qurk nd n ntiqurk in prticle, so there is no frctionl electric chrge. It involves the conversion of π 1/2 boson in B 6 into the electriclly chrgeless meson field by combining two π 1/2, nlogous to the combintion of e + nd e - fields, so the meson field becomes chrgeless. (The mss of π, 135 MeV, is twice of the mss of hlf-pion boson, 70 MeV, minus the binding energy. π 1/2 becomes pseudosclr up or down qurk in pion.) In the meson field, no frctionl chrge of qurk cn pper. The second prt of the strong interction is to combine three qurks in prticle, so there is no frctionl hyperchrge. It involves the conversion of B 5 (π 1/2 ) into the gluon field with three colors. The number of colors (three) in the gluon field is equl to the rtio between the lepton hyperchrge nd qurk hyperchrge. There re three π 1/2 in the gluon field, nd t ny time, only one of the three colors ppers in qurk. Qurks pper only when there is combintion of ll three colors or color-nticolor. In the gluon field, no frctionl hyperchrge of qurks cn pper. By combining both of the meson field nd the gluon field, the strong interction is the three-color gluon field bsed on the chrgeless vector meson field from the combintion of two π 1/2 's. The totl number of π 1/2 is 6, so the fine structure constnt, α s, for the strong force is α S = 6α e = (6) which is in good greement with the observed vlue, [8]. The dimensionl boson, B 8, is CP violting boson, becuse B 8 is ssumed to hve the CP-violting U(1) R symmetry. The rtio of the force constnts between the CP-invrint W L in B 8 nd the CP-violting X R in B 8 is α G W G = E 7 αw E = 5.3 X 10, cos Θ (7) which is in the sme order s the rtio of the force constnts between the CPinvrint wek interction nd the CP-violting interction with S = 2. The dimensionl boson, B 9 (X L ), hs the CP-violting U(1) L symmetry. The lepton (l 9 ) nd the qurk (q 9 ) re outside of the three fmilies for leptons nd qurks, so bryons in dimension nine do not hve to hve the bryon number conservtion. The bryon which does not conserve bryon number hs the bryon number of zero. The combintion of the CP-nonconservtion nd the 5

6 bryon number of zero leds to the bryon, p 9, with the bryon number of zero nd the bryon, p + 9, with the bryon number of 1. The decy of p 9 is s follows. p 9 l 9 l 9 The combintion this p 9 nd p 9 + s well s leptons, l 9 l 9 results in p + 9 p 9 + l 9 l 9 p l 9 l 9 + l 9 l 9 p l 9 + rdition + l 9 n 9 + rdition Consequently, excess bryons, n 9, re generted in the dimension nine. These excess bryons, n 9, become the predecessors of excess neutrons in the low energy level. The rtio of force constnts between X R with CP-independent bryon number nd X L with CP-dependent bryon number is α α (8) 2 G9 8 2 G = E 8 E 9-9 = 2.8 X 10, which is in the sme order s the observed rtio of the numbers between the left hnded bryons (proton or neutron) nd photons in the universe. 4. The periodic tble of elementry prticles Leptons nd qurks re complementry to ech other, expressing different spects of superstring. The model for leptons nd qurks is shown in Fig. 1. The periodic tble for elementry prticles is shown in Tble 2. 6

7 Lepton ν e e ν µ ν τ l 9 l 10 µ 7 τ 7 µ 8 D = = d 7 s 7 c 7 b 7 t 7 b 8 t 8 u 7 u d 3µ µ q 9 q 10 Qurk Fig. 1. Leptons nd qurks in the dimensionl orbits D = dimensionl number, = uxiliry dimensionl number Tble 2. The Periodic Tble of Elementry Prticles D = dimensionl number, = uxiliry dimensionl number D = = Lepton Qurk Boson 5 l 5 = ν e q 5 = u = 3ν e B 5 = A 6 l 6 = e q 6 = d = 3e B 6 = π 1/2 7 l 7 = ν µ µ 7 τ 7 q 7 = 3µ u 7 /d 7 s 7 c 7 b 7 t 7 0 B 7 = Z L 8 l 8 = ν τ µ 8 q 8 = µ' b 8 t 8 B 8 = X R 9 l 9 q 9 B 9 = X L 10 0 B 10 = Z R 11 B 11 D is the dimensionl orbitl number for the seven extr spce dimensions. The uxiliry dimensionl orbitl number,, is for the seven extr uxiliry spce dimensions. All guge bosons, leptons, nd qurks re locted on the seven dimensionl orbits nd seven uxiliry orbits. Most leptons re dimensionl fermions, while ll qurks re the sums of subqurks from the loops round the tori from the compcified extr dimensions. ν e, e, ν µ, nd ν τ re dimensionl fermions for dimension 5, 6, 7, nd 8, respectively. All neutrinos hve zero mss becuse of chirl symmetry. The dimensionl fermions for D = 5 nd 6 re neutrino (l 5 ) nd electron (l 6 ). Other fermions re generted, so there re more thn one fermion in the sme dimension. These extr fermions include qurks nd hevy leptons (µ nd τ). To generte qurk whose mss is higher thn the lepton in the sme dimension is to dd the lepton to the boson from the combined lepton-ntilepton, so the mss of 7

8 the qurk is three times of the mss of the corresponding lepton in the sme dimension. The eqution for the qurk mss is M qd = 3 M (9) ld The mixing between the fifth nd the seventh dimensionl orbits which is sme s the symmetry mixing in the stndrd model llows the seventh dimensionl orbit to be the strting dimensionl orbit for the dditionl orbits, uxiliry orbits with quntum number. (The totl number of the uxiliry orbits is lso seven s the seven dimensionl orbits.) A hevy lepton (µ or τ) is the combintion of the dimensionl leptons nd the uxiliry dimensionl leptons. In the sme wy, hevy qurk is the combintion of the dimensionl qurks from Eq.(9) nd the uxiliry qurks. The mss of the uxiliry dimensionl fermion (AF for both hevy lepton nd hevy qurk) is generted from the corresponding dimensionl boson s follows. M AFD, = M BD 10, 4 α = 0, (10) where α = uxiliry dimensionl fine structure constnt, nd = uxiliry dimension number = 0 or integer. The first term, M BD 1, 0, of the mss formul α (Eq.(10)) for the uxiliry dimensionl fermions is derived from the mss eqution, Eq. (1), for the dimensionl fermions nd bosons. The second term, =0 4, of the mss formul is for Bohr-Sommerfeld quntiztion for chrge - dipole interction in circulr orbit s described by A. Brut [9]. 1/α is 3/2. The coefficient, 3/2, is to convert the dimensionl boson mss to the mss of the uxiliry dimensionl fermion in the higher dimension by dding the boson mss to its fermion mss which is one-hlf of the boson mss. The formul for the mss of uxiliry dimensionl fermions (AF) becomes M = AF D, = = M α M M B D-1,0 BD 10, = 0 FD, 0 =0 α D = 0 When the mss of this uxiliry dimensionl fermion is dded to the sum of msses from the corresponding dimensionl fermions (zero uxiliry dimension (11) 8

9 number) with the sme electric chrge nd the sme dimension, the fermion mss formul for hevy leptons nd qurks is derived s follows. M = M + M FD, FD, 0 AFD, 3 = MF + MB D, 0 D 1, 0 2 = 0 3 = MF + MF α D D, 0 D, = 0 4 (12) Ech fermion cn be defined by dimensionl numbers (D's) nd uxiliry dimensionl numbers ('s). Hevy leptons nd qurks consist of one or more D's nd 's. The compositions nd clculted msses of leptons nd qurks re listed in Tble 3. Tble 3. The Compositions nd the Constituent Msses of Leptons nd Qurks D = dimensionl number nd = uxiliry dimensionl number Clc. Mss D Composition Leptons D for leptons ν e 5 0 ν e 0 e 6 0 e 0.51 MeV (given) ν µ 7 0 ν µ 0 ν τ 8 0 ν τ 0 µ e + ν µ + µ MeV τ e + ν µ + τ MeV µ' e + ν µ + µ 7 + ν τ + µ GeV Qurks D for qurks u u 5 + q 7 + u MeV d d 6 + q 7 + d MeV s d 6 + q 7 + s MeV c u 5 + q 7 + c MeV b d 6 + q 7 + b MeV t u 5 + q 7 + t 7 + q 8 + t GeV The lepton for dimension five is ν e, nd the qurk for the sme dimension is u 5, whose mss is equl to 3 Mν e from Eq. (9). The lepton for the dimension six is e, nd the qurk for this dimension is d 6. u 5 nd d 6 represent the light qurks or current qurks which hve low msses. The dimensionl lepton for the dimensions seven is ν µ. All ν's become mssless by the chirl symmetry to preserve chirlity. The uxiliry dimensionl leptons (Al) in the dimension seven re µ 7 nd τ 7 whose msses cn be clculted by Eq. (13) derived from Eq. (11). 9

10 M = 3 2 M Al 7, B6,0 =0 4 = M π / 2, =0 4 (13) where = 1, 2 for µ 7 nd τ 7, respectively. The mss of µ is the sum of e nd µ 7, nd the mss of τ is the sum of e + τ 7, s in Eq.(12). For hevy qurks, q 7 (the dimensionl fermion, F 7, for qurks in the dimension seven) is 3µ insted of mssless 3ν s in Eq. (9). According to the Aq 7, q7 7 M = 3 2 M α =0 4 = 3 w 2 (3 M µ ) α, =0 4 (14) mss formul, Eq. (11), of the uxiliry fermion, the mss formul for the uxiliry qurks, Aq 7,, is s follows. where α 7 = α w, nd = 1, 2, 3, 4, nd 5 for u 7 /d 7, s 7, c 7, b 7, nd t 7, respectively. The dimensionl lepton for the dimension eight is ν τ, whose mss is zero to preserve chirlity. The hevy lepton for the dimensionl eight is µ s the sum of e, µ, nd µ 8 (uxiliry dimensionl lepton). Becuse there re only three fmilies for leptons, µ' is the extr lepton, which is "hidden". µ' cn pper only s µ + photon. The piring of µ + µ from the hidden µ' nd regulr µ my ccount for the occurrence of sme sign dilepton in the high energy level [10]. For the dimension eight, q 8 (the F 8 for qurks) is µ' insted of 3µ', becuse the hiding of µ' llows q 8 to be µ'. The hiding of µ' for leptons is blnced by the hiding of b 8 for qurks. The clculted msses re in good greement with the observed constituent msses of leptons nd qurks [2,11]. The mss of the top qurk found by Collider Detector Fcility is 176 ± 13 GeV [2] in good greement with the clculted vlue, GeV. 5. Hdrons As molecules re the composites of toms, hdrons re the composites of elementry prticles. Hdron cn be represented by elementry prticles in mny different wys. One wy to represent hdron is through the nonreltivistic constituent qurk model where the mss of hdron is the sum of the msses of qurks plus reltively smll binding energy. π 1/2 (u or d pseudosclr qurk), u, d, s, c, b, nd t qurks mentioned bove re nonreltivistic constituent qurks. On 10

11 the other hnd, except proton nd neutron, ll hdrons re unstble, nd decy eventully into low-mss qurks nd leptons. Is hdron represented by ll nonreltivistic qurks or by low-mss qurks nd leptons? This pper proposes dul formul: the full qurk formul for ll nonreltivistic constituent qurks (π 1/2, u, d, s, c, nd b) nd the bsic fermion formul for the lowest- mss qurk (π 1/2 nd u) nd lepton (e). The clcultion of the msses of hdrons requires both formuls. The full qurk formul sets the initil mss for hdron. This initil mss is mtched by the mss resulted from the combintion of vrious prticles in the bsic fermion formul. The mss of hdron is the mss plus the binding energy in the bsic fermion formul. M full qurk formul M bsic fermion formul M hdron = M bsic fermion formul + binding energy (15) This dul representtion of hdrons by the full qurk formul nd the bsic qurk formul is seen in the tretment of nucleons [12] s mixture of the qurk model nd the vector meson dominnce model which cn be represented by π 1/2 nd u. The full qurk formul consists of the vector qurks (u, d, s, c, nd b) nd pseudosclr qurk, π 1/2 (70.03 MeV), which is B 6 (dimension boson in the dimension six). The strong interction converts B 6 (π 1/2 ) into pseudosclr u nd d qurk in pseudosclr π meson. The combintion of the pseudosclr qurk (π 1/2 ) nd vector qurks (q) results in hybrid qurks (q' ) whose mss is the verge mss of pseudosclr qurk nd vector qurk. Mq' = 1/2 ( Mq + Mπ 1/2 ) (16) Hybrid qurks include u', d', nd s' whose msses re , , nd MeV, respectively. For bryons other thn n nd p, the full qurk formul is the combintion of vector qurks, hybrid qurks (u' nd d'), nd pseudosclr qurk (π 1/2 ). For exmple, Λ (uds) is u'd's3, where 3 denotes 3 π 1/2. For pseudosclr mesons (J = 0), the full qurk formul is the combintion of π 1/2 nd q' (u', d' nd s') or π 1/2 lone. For vector mesons (J > 0), the full qurk formul is the combintion of vector qurks (u, d, s, c, nd b) nd π 1/2. For exmples, π is 2, η (1295,J =0) is u'u'd'd'8, nd K 1 (1400, J=1) is ds8. The compositions of hdrons from the prticles of the full qurk formul re listed in Tble 4. 11

12 Tble 4. Prticles for the full qurk formul π 1/2 u, d s u, d s c, b mss (MeV) , , , 5318 n nd p bryons other thn n nd p mesons (J = 0) except c c nd b b mesons (J > 0) nd c c nd b b Different energy sttes in hdron spectroscopy re the results of differences in the numbers of π 1/2. The higher the energy stte, the higher the number of π 1/2. The number of π 1/2 ttched to q or q' in the full qurk formul is restricted. The number of π 1/2 cn be 0, ±1, ±3, ±4, ±7, nd ±3n (n>2). This is the π 1/2 series. The number, 3, is indictive of bryon-like (3 qurks in bryon) number. The number, 4, is the combintion of 1 nd 3, while the number, 7, is the combintion of 3 nd 4. Since π 1/2 is essentilly pseudosclr u nd d qurks, the π 1/2 series is closely relted to u nd d qurks. Since s is close to u nd d, the π 1/2 series is lso relted to s qurk.. Ech presence of u, d, nd s ssocites with one single π 1/2 series. The single π 1/2 series ssocites with bryons nd the mesons with u u d d s s, s s, d c, u c, d b, u b, s c, nd s b. The combintion of two single π 1/2 series is the double π 1/2 series (0, ±2, ±6, ±8, ±14, nd ±6n) ssociting with u d nd d s mesons. For the mesons (c c nd b b) without u, d, or s, the numbers of π 1/2 ttched to qurks cn be from the single π 1/2 series or the double π 1/2 series. The bsic fermion formul is similr to M. H. McGregor's light qurk model [13], whose clculted msses nd the predicted properties of hdrons re in very good greement with observtions. In the light qurk model, the mss building blocks re the "spinor" (S with mss MeV) nd the mss quntum (mss = 70MeV). S hs 1/2 spin nd neutrl chrge, while the bsic quntum hs zero spin nd neutrl chrge. For the bsic fermion formul, S is u, the qurk with the lowest mss ( MeV), nd the bsic quntum is π 1/2 (mss = MeV). In the bsic fermion formul, u nd π 1/2 hve the sme spins nd chrge s S nd the bsic quntum, respectively. For exmples, in the bsic fermion formul, neutron is SSS, nd K 1 (1400, J=1) is S 2 11, where S 2 denotes two S, nd 11 denotes 11 π 1/2 's. In dditionl to S nd π 1/2, the bsic fermion formul includes P (positive chrge) nd N (neutrl chrge) with the msses of proton nd neutron. As in 12

13 the light qurk model, the mss ssocited with positive or negtive chrge is the electromgnetic mss, MeV, which is nine times the mss of electron. This mss (nine times the mss of electron) is derived from the bryon-like electron tht represents three qurks in bryon nd three electron in d 6 qurk s in Tble 2. This electromgnetic mss is observed in the mss difference between π (2) nd π + (2+) where + denotes positive chrge. The clculted mss different is one electromgnetic mss, MeV, in good greement with the observed mss difference, MeV, between π nd π +. (The vlues for observed msses re tken from "Prticle Physics Summry "[14].) The prticles in the bsic fermion formul re listed in Tble 5. Tble 5. Prticles in the bsic fermion formul mss (MeV) S π 1/2 N P electromgnetic mss Hdrons re the composites of qurks s molecules composing of toms. As toms re bounded together by chemicl bonds, hdrons re bounded by hdronic bonds, connecting the prticles in the bsic fermion formul. These hdronic bonds re similr to the hdronic bonds in the light qurk model. The hdronic bonds re the overlppings of the uxiliry dimensionl orbits. As in Eq (11), the energy derived from the uxiliry orbit for S (u qurk) is E = (3/2) (3 M µ ) α w = MeV (17) The uxiliry orbit is chrge - dipole interction in circulr orbit s described by A. Brut [9], so fermion for the circulr orbit nd n electron for the chrge re embedded in this hdronic bond. The fermion for the circulr orbit is the supersymmetricl fermion for the uxiliry dimensionl orbit ccording to Eq (2). M f = E α w (18) The binding energy (negtive energy) for the bond (S!S) between two S's is twice of MeV minus the msses of the supersymmetricl fermion nd electron. E S -S = - 2 (E - M f - M e ) = MeV (19) It is similr to the binding energy (-26 MeV) in the light qurk model. An exmple of S!S bond is in neutron (S S S) which hs two S S bonds. The mss of neutron cn be clculted s follows. 13

14 M n = 3M S + 2E S-S = MeV, (20) which is in excellent greement with the observed mss, MeV. The mss of proton is the mss of neutron minus the mss difference (three times of electron mss = M 3e ) between u nd d qurk s shown in Tble 2. Proton is represented s S S (S -3e). The clcultion of the mss of proton is s follows. E for (S-3e) = (3/2) (3 (M µ - M 3e )) α w M f = E α w M p = 2 M S + M (S-3e) + E S!S + E S!(S-3e) = MeV (21) The clculted mss is in good greement with the observed mss, MeV. The binding energy for π 1/2 π 1/2 bond cn be derived in the sme wy s Eqs (17), (18), nd (19). E = (3/2) Mπ 1/2 α w M f = E α w E π 1/2 - π 1/2 = - 2 (E - M f - M e ) = MeV (22) It is similr to the binding energy (-5 MeV) in the light qurk model. An exmple for the binding energy of π 1/2 π 1/2 bond is in π. The mss of π cn be clculted s follows. M π = 2 Mπ 1/2 + E π 1/2 - π 1/2 = MeV. (23) The clculted mss of π is in excellent greement with the observed vlue, MeV. There is one π 1/2 π 1/2 bond per pir of π 1/2 s, so there re two π 1/2 π 1/2 bonds for 4 π 1/2 s, nd three π 1/2 π 1/2 bonds for 6 π 1/2 s. Another bond is N π 1/2 or P π 1/2, the bond between neutron or proton nd π 1/2. Since N is SSS, N π 1/2 bond is derived from S π 1/2. The binding energy of S π 1/2 is the verge between S S nd π 1/2 π 1/2. E S - π 1/2 = 1/2 ( E S-S + E π 1/2 - π 1/2 ) (24) An dditionl dipole (e + e - ) is needed to connected S π 1/2 to neutron. E N - π 1/2 = E S - π 1/2 + 2 M e = MeV. (25) 14

15 It is similr to -15 MeV in the light qurk model. An exmple for P π 1/2 is Σ + which is represented by P4 whose structure is 2 P 2. The 4 π 1/2 's re connected to P with two P π 1/2 bonds. The mss of Σ + is s follows. M Σ + = M P + 4 Mπ 1/2 + 2 E N - π 1/2 = MeV. (26) The clculted mss is in good greement with the observed mss, ± 0.07 MeV. There is N N hdronic bond between two N s. N hs the structure of S S S. N N hs hexgonl structure shown in Fig. 2. S S S S S S Fig. 2. The structure of N - N There re two dditionl S S for ech N. The totl number of S S bonds between two N s is 4. An exmple is Ω c (ssc) which hs the bsic fermion formul of N 2 S9 with the structure of 3 N N 6 S. The mss of Ω c cn be clculted s follows. M = 2M N + M S + 9Mπ 1/2 + 4 E S S + 2 E N - π 1/2 = MeV (27) The clculted mss for Ω c is in good greement with the observed mss (2704 ± 4 MeV). For bryons other thn p nd n, there re two or three N - π 1/2 or P - π 1/2 bonds per bryon. It is used to distinguish J = ½ nd J 3/2. For J = ½ which hve symmetricl spins (two up nd one down), there re two bonds for three S in bryon to represent the symmetricl spins. For J 3/2, there re three bonds for three S in bryon except if there is only one π 1/2, only two bonds exists for bryon. Among the prticles in the bsic fermion formul, there re hdronic bonds, but not ll prticles hve hdronic bonds. In the bsic fermion formul, hdronic bonds pper only mong the prticles tht relte to the prticles in the corresponding full qurk formul. The relted prticles re the core prticles tht hve hdronic bonds, nd the unrelted prticles re filler prticles tht hve no hdronic bonds. In the bsic fermion formul, for bryons other thn p nd n, the core prticles re P, N, nd π 1/2. For the mesons consisting of u nd d qurks, the core prticles re π 1/2, S, nd N. For the mesons contining one u, 15

16 d, or s long with s, c, or b, the core prticles re S nd N, nd no hdronic bond exist mong π 1/2 's, which re the filler prticles. For the mesons (c c nd b b), the only hdronic bond is N N. The occurrences of hdronic bonds re listed in Tble 6. Tble 6. Hdronic bonds in hdrons S S π 1/2 - π 1/2 N(P) - π 1/2 N N binding energy (MeV) S S per N bryons other thn n nd p mesons with u nd d only mesons contining one u, d, or s long with s, c, or b c c or b b mesons An exmple is the difference between π nd f 0. The decy modes of f 0 include the mesons of s qurks from K meson. Consequently, there is no π 1/2 - π 1/2 for f 0. The bsic fermion formul for f 0 is 14. The mss of f 0 is s follows. M = 14Mπ 1/2 = MeV (28) The observed mss is 980 ± 10 MeV. In dditionl to the binding energies for hdronic bonds, hdrons hve Coulomb energy (-1.2 MeV) between positive nd negtive chrges nd mgnetic binding energy (±2MeV per interction) for S S from the light qurk model [13]. In the light qurk model, the dipole moment of hdron cn be clculted from the mgnetic binding energy. Since in the bsic fermion formul, mgnetic binding energy becomes prt of hdronic binding energy s shown in Eq (19), mgnetic binding energy for other bryons is the difference in mgnetic binding energy between bryon nd n or p. If bryon hs similr dipole moment s p or n, there is no mgnetic binding energy for the bryon. An exmple for Coulomb energy nd mgnetic binding energy is Λ (uds, J=1/2) whose formul is P3- with the structure of 2 P 1- where "-" denotes negtive chrge. The dipole moment of Λ is 6.13 µ N, while the dipole moment of proton (P) is 2.79 µ N [13]. According to the light qurk model, this difference in dipole moment represents -6 MeV mgnetic binding energy. The Coulomb energy between the positive chrge P nd the negtive chrge 1- is 1.2 MeV. The electromgnetic mss for 1- is MeV. The mss of Λ is clculted s follows. 16

17 M Λ = M P + 3Mπ 1/2 + M e.m. + 2 E N - π 1/2 + E mg + E coul = MeV (29) The observed mss is ± MeV. An exmple of the dul representtion of the full qurk formul nd the bsic fermion formul s expressed by Eq. (15) is Λ (uds). The full qurk formul for Λ is u d s 3 with mss of MeV. This mss is mtched by the mss of the bsic fermion formul, P3- with the mss of MeV. The finl mss of Λ is MeV plus the vrious binding energies. Tble 7 is the results of clcultion for the msses of bryons selected from Ref. (18). The hdrons selected re the hdrons with precise observed msses nd known quntum sttes such s isospin nd spin. 17

18 Tble 7. The msses of bryons Bryons I(J P ) Full qurk formul Bsic fermion formul Clculted mss Observed mss Difference n nd p n 1/2(½ + ) udd SSS p ½(½ + ) uud SSS-3e uds, uus, dds Λ 0(½ + ) u'd's3 P (½ + ) u'u's4 P (½ + ) u'd's4 P (½ + ) d'd's4 N (3/2 + ) u'u's7 P (3/2 + ) u'd's7 P (3/2 + ) d'd's7 N Λ (s 01 ) 0(½-) u'd's7 P Λ (D 03 ) 0(3/2 - ) u'd's9 N uss, dss Ξ ½(½ + ) u'ss NS Ξ - ½(½ + ) d'ss NS Ξ ½(3/2 + ) u'ss4 N Ξ - ½(3/2 + ) d'ss4 N Ξ ½(3/2 - ) u'ss9 N udc, ddc, uuc Λ + c 0(½ + ) u'd'c3 PS (½ + ) d'd'c7 N (½ + ) u'u'c7 N (½ - ) u'd'c7 N Λ + c 0(½ - ) u'd'c9 N usc, dsc Ξ + c ½(½ + ) u'sc1 NS Ξ c ½(½ + ) d'sc1 N S sss Ω - 0(3/2 + ) sss NS ssc Ω c 0(½ + ) ssc N 2 S udb Λ b 0(½ + ) u'd'b1 N 2 S c ++ c + c The full qurk formul for bryons other thn p nd n involves hybrid qurks (u nd d ), vector qurks (s, c, nd b), nd pseudosclr qurk (π 1/2 ). The whole spectrum of bryons (other thn p nd n) follows the single π 1/2 series 18

19 with 0, 1, 3, 4, 7, nd 3n. π 1/2 is closely relted to u nd d, so the lowest energy stte bryons (Λnd Σ) tht contin low mss qurk nd high number of u or d hve high number of π 1/2.. On the contrry, the lowest energy stte bryons (Ω, Ω c, nd Λ b ) tht contin high mss qurks nd no or low number of u nd d hve low number of π 1/2 or no π 1/2. π 1/2 's re dded to the lowest energy stte bryons to form the high-energy stte bryons. The bsic fermion formul includes P, N, S, nd π 1/2. If the dominnt decy mode includes p, the bsic fermion formul includes P. If the dominnt decy mode includes n, the bsic fermion formul includes N. If the decy mode does not include either n or p directly, the bryon with the dipole moment similr to p or n hs the bsic fermion formul with P or N, respectively. If the dipole moment is not known, the designtion of P or N for the higher energy stte bryon follows the designtion of P or N for the corresponding lower energy stte bryon. Only N is used in the multiple nucleons such s N 2 (two N s). The result of clculted msses for light unflvored mesons is listed in Tble 8. Light unflvored mesons hve zero strnge, chrm, nd bottom numbers. 19

20 Tble 8. Light unflvored mesons Meson I (J pc ) Full qurk formul Bsic fermion formul Clculted mss. Observed mss Difference J =0, only u, d, or lepton in decy mode π 1 (0 -+ ) π ± 1 (0 - ) 2 2± η 0 (0 -+ ) η 0 (0 -+ ) η 0 (0 -+ ) u'u'u'd'd'd'2 S f 0 0 (0 ++ ) u'u'u'd'd'd'6 S J >0, only u, d, or lepton in decy modes ρ 1 (1 -- ) ud2 S ω 0 (1 -- ) ud2 S h 1 0 (1 +- ) ud8 S ω 0 (1 -- ) uudd2 S ω 0 (1 -- ) uudd6 S ω 3 0 (3 -- ) uudd6 S J = 0, u nd d in mjor decy modes, s in minor decy modes f 0 0 (0 ++ ) u'd's' O 1 (0 ++ ) u'd's' η 0 (0 -+ ) u'u'd'd's's' S J >o, u nd d in mjor decy modes, s in minor decy mode 1 1 (1 ++ ) uds S b 1 1 (1 +- ) uds S f 2 0 (2 ++ ) uds1 S f 1 0 (1 ++ ) uds1 S (2 ++ ) uds1 S f 1 0 (1 ++ ) uds4 S ρ 1 (1 -- ) uds4 S π 2 1 (2 -+ ) uds7 S ρ 3 1 (3 -- ) uds7 S ρ 1 (1 -- ) uds7 S f 4 0 (4++) uds12 S s in mjor decy modes Φ 0 (1 -- ) ss-1 S f 1 0 (1 ++ ) ss7 S (2 ++ ) ss7 S Φ 0 (1 -- ) ss9 S Φ 3 0 (3 -- ) ss12 S f 2 0 (2 ++ ) ss15 S f 2 0 (2 ++ ) ss18 N S f 2 0 (2 ++ ) ss18 N S f 2 20

21 The full qurk formuls for light unflvored mesons re different for different decy modes. There re three different types of the full qurk formul for light unflvored mesons. Firstly, when the decy mode is ll leptons or ll mesons with u nd d qurks, the full qurk formul consists of π 1/2, u, d, u, nd d qurks, Secondly, when u, d, nd leptons re in the mjor decy modes, nd s is in the minor decy modes, the full qurk formul consists of π 1/2, u, d, s, u, d, nd s qurks. The most common full qurk formul for such mesons is uds, which is essentilly ½ (u u d d s s). Finlly, when s qurks re in the mjor or ll decy mode, the full qurk formul consists of π 1/2 s nd s qurks. When J = 0, the full qurk formul includes π 1/2 s nd hybrid qurks (u, d, nd s ). When J > 0, the full qurk formul includes π 1/2 s nd vector qurks (u, d, nd s). Since there re double presence of u nd d qurks for the full qurk formul with u nd d qurk, it follows the double π 1/2 series: 0, 2, 6, 8, 14, nd 6n. The full qurk formul with odd presence of u, d, nd s follows the single π 1/2 series: 0, ±1, ±3, ±4, ±7, nd ±3n. The bsic fermion formul includes π 1/2 s, S, nd N. π 1/2 π 1/2 hdronic bond exists in the full qurk formul with u nd d qurks, nd does not exist in the full qurk formul with s qurk. S S bond exists in ll formul. Light unflvored mesons decy into symmetricl low mss mesons, such s 2γ, 3π o, nd π 0 2γ from η, or symmetricl high nd low mss mesons, such s symmetricl π + πη, ρ 0 γ, nd π 0 π 0 η from η. To distinguish the symmetricl decy modes from the symmetricl decy modes, one counter π 1/2 π 1/2 hdronic bond is introduced in η [13]. The binding energy for the counter π 1/2 π 1/2 hdronic bond is 5.04 MeV, directly opposite to 5.04 MeV for the π 1/2 π 1/2 hdronic bond. All light unflvored mesons with symmetricl decy modes include this counter π 1/2 π 1/2 hdronic bonds. For n exmple, the mss of η (14+-) is clculted s follows. M η = 14 Mπ 1/2 + 2 M e.m. + E e.m. + 7Eπ 1/2 π 1/2 - Eπ 1/2 π 1/2 = MeV (30) The observed mss is ± 0.14 MeV. The result of the mss clcultion for the mesons consisting of u, d, or s with s, c, or b is listed in Tble 9. 21

22 Tble 9. Mesons with s, c, nd b Meson J pc Full qurk formul Bsic fermion formul Clculted mss. Observed mss Difference Light strnge mesons K ± 0-7 7± K K* 0 + d's'14 S K* 1 - us S8± K* 1 - ds S K ds6 S K ds8 S K* 1 - ds8 S K* ± 2 + us8 N7± K* 2 + ds8 N K* 1 - ddss S K ddss N K 3* 3 - ddss N K ds14 S K 4* 4 + ds18 S Chrmed mesons D 0 - u'c1 S D ± 0 - d'c1 S 6 ± D * o 1 - uc1 S D* ± 1 - dc1 S 6 2± D uc7 S D 2* 2 + uc7 N S D 2* ± 2 + dc7 N S 4 4± Chrmed strnge mesons D s 0 - s'c1 S D s1 1 + sc4 NS Bottom mesons B ± 0 - u'b N 4 S20± B 0 - d'b N 4 S B* 1 - db N Bs 0 - s'b N 5 S The full qurk formul for these mesons contins π 1/2 s, u, d, s, u, d, s, c, nd b. The full qurk formul for the mesons with J = 0 contins π 1/2, hybrid qurks (u, d, nd s ), c, nd b qurks. The full qurk formul with J > 0 contins π 1/2 s nd vector qurks (u, d, s, c, nd b). Strnge mesons hve double presence of d nd s, so it follows the double π 1/2 series. All other mesons hve 22

23 single presence of u, d, or s, so they follow the single π 1/2 series. The bsic fermion formul consists of π 1/2 s, S, nd N. There is no π 1/2 π 1/2 bond. There re S S nd N N bonds. For exmple, the mss of B s (N 5 S 3 ) is clculted s follows. M = 5M N + 3M S + (10+ 2) M S S = MeV (31) There re 10 S S bonds for N 5 (two S S bonds for ech N) nd 2 S S bonds for S 3. The observed mss is ± 2 MeV. The result of mss clcultion for c c nd b b mesons is listed in Tble 10. Tble 10. c c nd b b mesons Meson J pc Full qurk formul Bsic fermion formul Clculted mss. Observed mss Difference c c mesons η c (1s) 0 -+ cc-6 N S J/ψ 1 -- cc-3 N 2 S χ c (1p) 0 ++ cc2 N 2 S χ c (1p) 1 ++ cc3 N 2 S χ c2 (1p) 2 ++ cc4 N 2 S U 2s 1 -- cc6 N 3 S ψ 1 -- cc7 N 3 S ψ 1 -- cc12 N ψ 1 -- cc14 N 4 S ψ 1 -- cc18 N 4 S b b mesons ϒ (1s) 1 -- bb-12 N 7 S χ b (1p) 0 ++ bb-4 N 10 S χ b1 (1p) 1 ++ bb-3 N 10 S χ b2 (1p) 2 ++ bb-3 N ϒ (2s) 1 -- bb-1 N 10 S χ b0 (1p) 0 ++ bb2 N 10 S χ b1 (2p) 1 ++ bb2 N 10 S χ b2 (2p) 2 ++ bb2 N 10 S ϒ (3s) 1 -- bb3 N 10 S ϒ (4s) 1 -- bb7 N 11 S ϒ 1 -- bb12 N ϒ 1 -- bb14 N 11 S The full qurk formul contins c or b. Since it contins no u, d, or s relted to π 1/2, it follows mixed π 1/2 series from both the single π 1/2 series nd the double 23

24 π 1/2 series. Since c nd b re high mss qurks unlike the low mss u nd d qurks tht relte to π 1/2, the π 1/2 series ctully strts from negtive π 1/2. The bsic fermion formul contins π 1/2 s, S, nd N. The only hdronic bond is N N. An exmple is J/ψ (N 2 S 4 ) whose mss ( ± 0.04 MeV) is clculted s follows. M = 2 M N + 4 M S + 4 M S S = MeV (32) 6. Conclusion The periodic tble of elementry prticles (Fig. 1 nd Tble 2) is constructed from dimensionl hierrchy. All leptons, qurks, nd guge bosons cn be plced in the periodic tble. The msses of elementry prticles cn be clculted using only four known constnts: the number of the extr sptil dimensions in the eleven dimensionl membrne, the mss of electron, the mss of Z, nd α e. The clculted msses (Tbles 1 nd 3) of elementry prticles derived from the periodic tble re in good greement with the observed vlues. For n exmple, the clculted mss (176.5 GeV) of the top qurk hs n excellent greement with the observed mss (176 ± 13 GeV). A hdron cn be represented by the full qurk formul (Tble 4) nd the bsic qurk formul (Tble 5). The full qurk formul consists of ll qurks, pseudosclr qurk in pion, nd the hybrid qurks. The bsic qurk formul consists of the lowest mss qurks. The reltion between these two formuls is expressed by Eq. (15). As molecule is the composite of toms with chemicl bonds, hdron is the composite of elementry prticles with "hdronic bonds" (Tble 6) which re the overlppings of the uxiliry dimensionl orbits. The clculted msses (Tbles 7, 8, 9, nd 10) of hdrons re in good greement with the observed vlues. For exmples, the clculted msses for neutron nd pion re nd MeV in excellent greement with the observed msses, nd MeV, respectively. The overll verge difference between the clculted msses nd the observed msses for ll hdrons (110 hdrons) is 0.29 MeV, nd the stndrd devition for such differences is 5.06 MeV. The verge observed error for the msses of the hdrons is ± 6.41 MeV. The periodic tble of elementry prticles provides the most comprehensive explntion nd clcultion for the msses of elementry prticles nd hdrons. 24

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