Standard Model of Particle Physics |

**In General** > s.a. cosmological standard model;
history of particle physics; particle physics [context].

* __Particles__: Classified
by representations of the symmetry group SU(3) × SU(2) × U(1);
Presently known particles can be divided into quarks (*u*, *d*; *c*, *s*; *t*, *d*)
(each in 3 colors), leptons (*e*, *ν*_{e}; *μ*,
*ν*_{μ}; *τ*, *ν*_{τ}),
and gauge bosons (graviton, 8 gluons, *W*^{ ±},
*Z*); Others are predicted by various extensions, like Higgs scalars (from spontaneous gauge
symmetry breaking), gravitinos (> see supergravity),
etc; Cosmology puts an upper bound of 4 on the number of generations.

* __Interactions__: Four of them explain all presently known phenomena.

Interaction |
Strength |
Range |
Exchange particles |
Theory |
See also |

gravitational | 10^{–40} |
∞ | graviton | > general relativity | > other theories, quantum gravity |

weak | 10^{–15} |
10^{–15} cm |
W^{ ±}, Z |
> electroweak | |

electromagnetic | 10^{–2} |
∞ | photon | > electroweak | > other theories, QED |

strong | 1 | 10^{–13} cm |
gluons | > QCD |

The weak and electromagnetic interactions have in fact been unified by
the Weinberg-Salam electroweak theory, which has been experimentally tested;
aka hypercharge force;
There could be additional forces (> see fifth force).

* __Theoretical problems__:
Why do weak interactions couple differently to left-handed and right-handed
particles? The theoretical basis for the Cabibbo-Kobayashi-Maskawa matrix (too many
parameters); The standard model is not enough to account for
baryogenesis (GUTs or supersymmetry of some type are needed); > s.a. Landau
Pole and Hierarchy Problem.

@ __General references__: Leader & Predazzi 95; Cahn RMP(96) [18 parameters];
Herrero hp/98-ln;
Riles CP(98) [tests];
Bertin et al RNC(00) [CKM matrix];
Quigg AIP(00)hp;
Rosner AJP(03)apr [RL];
Particle Data Group PLB(04) [reference];
Morii et al 04;
Oerter 05 [I];
Burgess & Moore 06; Cottingham & Greenwood 07;
McCabe ed-PFP(07) [structure and interpretation];
Mann 09; Langacker 09;
Perović SHPMP(11) [missing experimental challenges];
Robinson 11 [introduction];
Schwartz 13,
Han 14 [and qft];
Becchi & Ridolfi 14 [II];
Donoghue et al 14;
Kibble a1412-conf [rev];
Butterworth PTRS(16)-a1601-conf [successes and challenges];
Maiani & Rolandi ed-16;
't Hooft IJMPA(16).

@ __Number of generations__: van der Bij PRD(07) [three generations and the topology of the universe];
Gould a1011 [anthropic argument for three generations];
Kaplan & Sun PRL(12) [spacetime as a topological insulator];
He et al a1408
[algebraic geometry and the phenomenology of generations];
> s.a. beyond the standard model [beyond three generations].

**Theoretical Aspects** > s.a. group
theory; Hypercharge;
renormalization of gauge theories; unified theories.

* __Isospin__:
A quantum number associated with an SU(2) group, related to a transformation
between the *u* and *d* quarks; The isospin SU(2) is a symmetry
group for strong interactions, but is broken when electromagnetic interactions are turned
on, since *Q* = \(1\over2\)*B* + *I*_{3},
so [*Q*, *I*_{1,2}] ≠ 0;
Usually though *H*_{em} \(\ll\) *H*_{strong},
and the breaking is small.

* __Cabibbo angle__: The parameter
*θ*_{C} that allows to obtain the weakly
interacting eigenstates as linear combinations of the quark mass eigenstates, like

*d*' = *d* cos *θ*_{C} +
*s* sin *θ*_{C}, *s*'
= –*d* sin *θ*_{C} + *s* cos
*θ*_{C} .

@ __General references__: Iliopoulos a1101-conf [Cabibbo angle, history].

@ __Hamiltonian / Dirac treatment__: Lusanna NPPS(97)ht,
ht/97-conf;
Lusanna & Valtancoli IJMPA(98)ht/97.

@ __Other theoretical aspects__: Grigore a1506-conf [perturbation theory up to second order (in the causal approach)];
Todorov & Dubois-Violette a1806 [and the exceptional Jordan algebra].

> __Related topics__:
see Calabi-Yau Spaces; CKM Matrix;
clifford algebra; conformal symmetry;
fine-structure constant [variation]; Fine Tuning;
Krajewski Diagrams; PMNS Matrix.

**Phenomenology and Experiment** > s.a. experimental physics
and particle physics / early-universe cosmology;
QCD phenomenology.

* __And experiment__: 1989, So far seems
to be ok with experiment down to 10^{–16} cm; Some
predictions confirmed to 10^{–12}; No problem including
a fourth family, and can accommodate *ν* oscillations; Possible problems include
same sign dileptons; The decay *Z*^{0} →
*l*^{+}* l*^{–}
*γ*, and, Where is the Higgs particle? 2002, The experimental value of the CP violation
parameter sin 2*β* approaches prediction, but the *g*–2 problem remains.

@ __Cosmology__: Kusenko & Langacker PLB(97) [vacuum];
Bjorken PRD(01) [and Λ],
PRD(03)ht/02; > s.a. vacuum phenomenology.

@ __Particle physics__: Froggatt et al NPB(94) [fermion masses];
Dolgov NPB(97) [mass corrections in expanding universe];
Gynther & Vepsäläinen JHEP(06) [high-*T*, pressure];
Mangano IJMPA(08)-a0802-in [LHC preview];
news symm(11)jul [Ξ_{b} discovery by CDF];
Blümlein a1205-proc [perturbative precision calculations];
> s.a. astrophysics; atomic physics;
electroweak theory [including *W* and *Z *bosons, Higgs particle];
higgs field; Regge Trajectory;
Sum Rules.

**Variations / Generalizations** > s.a. physics
beyond the standard model [including non-commutative geometry].

@ __Variations__: Spaans gq/97 [topological];
Lombardo hp/01-ln [at finite temperature, phase transitions];
Srivastava & Brodsky PRD(02) [light front];
Blaha ht/02 [as quantum computer];
Davoudiasl et al PLB(05)hp/04 [new minimal model];
Ziino MPLA(07) [with neutrino masses and oscillations];
Zubkov PLB(07) [extra discrete symmetry];
Grinstein et al PRD(08)-a0704 [Lee-Wick, with Higgs mass stabilization];
Alberghi et al a0804 [vacuum energy and additional particles];
Sannino MPLA(11)
[as the magnetic dual of a gauge theory with only fermionic matter];
Masina & Sannino a1110 [dark-sector modifications];
Senjanović MPLA(17)-a1610-proc [left-right symmetric theory].

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