A Modified Rishon Model Patrick S. Walters AAPT-CPS Spring Meeting 2009 Penn State – Mont Alto March 27 th – 28 th 2009

Rishon Theory First proposed in 1979 by Haim Harari Quarks, leptons, gauge bosons are composite particles in Rishon Theory. Two fundamental particles, T and V, and antiparticles  T and  V. T is charged -1/3 e, V is neutral. [1]

Haim Harari Ph.D. in Physics from the Hebrew University of Jerusalem. In 1967, became the youngest Professor ever to teach at the Weizmann Institute. Predicted the existence of bottom and top quarks in President of the Wiezmann Institute of Science from 1988 to In 2001, received the Harnack Medal from the Max Planck Institute [3].

Implications Electron (TTT), up quark (  T  T  V), down quark (TVV), and neutrino (  V  V  V) are each three-Rishon states. Additional generations formed by adding T  T pairs, i.e. b quark is TVVT  TT  T. Photons and gluons are four-Rishon states (TV  T  V). W bosons TTTVVV and  T  T  T  V  V  V.

Assumptions Rishons are bound by an SU(3) H hypercolor mechanism [2]. T is massive, V is massless. T and V have opposite hypercharge (±1/3). 4 th generation or higher fermions allowed. No Higgs mechanism is necessary.

Downfalls No explanation of mass origin. Hypercharge assignments are inconsistent, and isospin is ambiguous. No certain explanation of attraction between Rishons. No direct explanation of color forces. Massless photons, gluons, and Z mass are unexplained.

Proposed Modifications T   P,  T  P, V  N,  V   N, changing the names and particle/antiparticle assignment slightly. Assume that we start out with two equally massive non-natural Rishons P′ and N′ which mix at nearly 45 degrees to produce natural Rishons P (massive) and N (nearly massless). Rishons are attracted strongly to each other, but Rishons and anti-Rishons repel even more strongly, proportional to their masses.

Proposed Modifications P has positive isospin and hypercharge.  P has negative isospin and hypercharge. N has negative isospin and positive hypercharge.  N has positve isospin and negative hypercharge. Isospin comes in units of 1/6, hypercharge in units of 1/3, intrinsic spin is ±1/2. SU(3) color charges a, b, and c for Rishons.

Color Charges

SU(3) Color for Composites

Methodology for Rishon Composites Bag model may be effective for finding masses of composite states, such as quarks, leptons, and bosons. Since chiral symmetry is broken by the bag contents, and not arbitrarily at the edge of the bag, the earlier problems with bag model may be resolved. PP attraction is strong enough to cancel out a P mass, the P  P repulsion is even stronger.

N  N versus P  P N  N repulsion is much weaker than P  P repulsion, proportional to the much smaller N mass. N  N contributes little mass to a composite state, while P  P contributes most of the mass to its composite states. States with N  N pairs will have the same or similar mass to states without it.

Modified Rishon Model Structure

Interactions in Modified Model Rishon interactions come in two types Type 1  (Δg 8 ) 2 + (Δg 3 ) 2 – ΔI 2 = 1/3 Type 2  (Δg 8 ) 2 + (Δg 3 ) 2 – ΔI 2 = 0 Weak nuclear processes proceed via one Type 1 and two Type 2 processes Strong nuclear processes proceed via two Type 1 processes

Weak Interactions

Strong Interactions

Transitions in Modified Model P  N transitions naturally occur 50% of the time in a 45° mixing scheme. Natural mixing between quarks occurs for odd numbers of Rishons changing simultaneously in W-mediated processes 3-Rishon processes = 1/2 3 = 1/8 5-Rishon processes = 1/2 5 = 1/32 7-Rishon processes = 1/2 7 = 1/128 Such as t  b W + or s  u e -  v e

Transitions in Modified Model Natural mixing between quarks occurs for even numbers of Rishons changing simultaneously in Z-mediated processes 2-Rishon processes = 1/2 2 = 1/4 4-Rishon processes = 1/2 4 = 1/16 Such as t  c Z or b  d u  u Fourth-generation composites would instantly fall apart into three first-generation composites; hence, they do not exist.

Quark Transitions by Rishon Mixing

Particle Physics Implications All particle decays and decay ratios can be derived from Rishon Model, and current experimental data may be sufficient to show this. Quark mixing in the CKM matrix can be derived from Rishon Model. Neutrino mixing can be derived from Rishon Model. No new generations of quarks or leptons exist beyond the current three.

Particle Physics Implications Pure B and W 3 fields in electro-weak model mix due to Rishon mixing to form natural photon and Z fields. Z is massive and photon massless due to Rishon mixing. Z branching ratios can be derived from Rishon Model. Isospin symmetry is completely broken, while hypercharge is always conserved. Higgs sector may exist, but is not necessary to explain mass.

Cosmological Implications Natural Abundance; electron plus proton plus neutron plus neutrino. Natural Abundance gives equal numbers of P and N Rishons. Natural Abundance gives equal portions of Rishons and anti-Rishons; matter- antimatter symmetry. 1:3:3:1 structure of matter and antimatter; natural repulsion between matter and antimatter.

Testing the Modified Model Using the quark mixing tables from the modified model, reconstruct the CKM matrix. Using the modified model, compare the generated Z branching ratios to the experimental Z branching ratios. Parameters include probabilities of  PP and  NN production, P and N exchange. Using parameters and phase space, compare generated hadronic branching ratios with experimental hadronic branching ratios.

References [1] H. Harari, Phys. Lett. B86, 83 (1979) [2] H. Harari and N. Seiberg, Phys. Lett. B98, 269 (1981) [3] Wikipedia, (2009)

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