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A MAXIMAL MASS MODEL Matey Mateev, University of Sofia Primorsko, 24.06.2010 Matey Mateev 1 V. G. Kadyshevsky, V. N. Rodionov and A. S. Sorin (M. V. Chizhov, P. Danev) Almost all detailes may be found in Towards a Maximal Mass Model hep-ph/30.08.2007 2 We investigate consequences of introduction a new principle in local QFT: Principle of existence of a maximal mass M: m<M 4 On this ground we generalize the Standard Model to a Maximal Mass Model The three main components of the Standard Model are: 1. Local QFT 2. Local gauge SU(3)xSU(2)xU(1) invariance 3. Higgs mechanism for generation of masses SM describes well the existing experimental data. 5 The fundamental physical constants с — velocity of light ħ — Planck constant G — Newton gravitational constant allow simple geometrical or group theoretical interpretation. For instance in special relativity the 3-dimensional velocity space is a Lobachevsky space with curvature -1/с² . v 1 c u , 2 2 v 1 v 1 2 2 c c u02 u 2 1 “Lobachevsky geometry”, 6 (□ m ) ( x) 0 2 ( x) 1 (2 ) 3 2 e ip x ( p)d p 4 ( p x p x p.x ) 0 0 2 (m p ) ( p) 0, p p p 2 2 2 2 0 2 m p p 2 2 0 7 m ≤ M 8 We use Anti-De Sitter geometry of momentum space: 2 2 2 p p p5 M 2 0 2 2 2 p0 p m Here we have: m ≤ M 9 2 2 2 ( p p p5 M ) ( p0 , p, p5 ) 0 2 2 2 2 ~ ( p0 , p, p5 ) ( p0 p p5 M ) ( p0 , p, p5 ) 2 0 ( p, p5 ) 1 ( p) 2 2 ~ ( p0 , p, p5 ) ( p, p5 ) , p5 M p . ( p, p5 ) 2 ( p) The sign of p5 is a new degree of freedom 10 2 (m p p ) ( p0 , p, p5 ) 0 2 2 0 m m p M p M 1 2 M 2 2 2 5 2 2 5 2 2 m cos 1 2 , M ( p5 M cos )( p5 M cos ) ( p, p5 ) 0 11 Klein-Gordon equation in Anti de Sitter momentum space 2M ( p5 M cos ) ( p, p5 ) 0 2M ( p5 M cos )1 ( p) 0, 2M ( p5 M cos ) 2 ( p ) 0, ~ 1 ( p) ( p m )1 ( p) 2 2 2 ( p) 0 12 “Flat” limit is defined as transition from Anti De Sitter to Minkowski momentum space and it corresponds to: M p 2 2 and p5 M In the flat limit: p2 p2 m2 m2 p5 M 1 2 M , cos 1 2 1 2 M 2M M 2M and 2 M ( p5 M cos ) p m 2 2 13 The action may be written in 5-dimensional form: Euclidean formulation De Sitter – O(4, 1) We may integrate over p5 16 ( p) 1 ( p ) 2 ( p) 1 ( p ) p5 M , ( p ) 1 ( p ) 2 ( p) ( p ) p5 M ( p ) 2M , 2 ( p) ( p ) p5 M ( p) 2M S0 ( M ) M d 4 p ( p)( p 2 m 2 ) ( p) ( ( p) M cos ( p)) 2 17 Fourier transform and configuration space: 2M 3 e ipK x K ( pL p L M 2 ) ( p, p5 )d 5 p ( x, x5 ) (2 ) 2 K , L 1,2,3,4,5. 2 2 ( 2 □ M ) ( x, x5 ) 0 x5 18 initial data are given at x5 0 : Why Euclidean formulation? Higgs potential: 2 2 1 2 U ( , ; M ) ( M )( ( x) ( x)) 2 2 2 2 2 ( x) 2 ( x) 2 2 ( ) . 4 2 mo2 m m0 1 4M 2 , m0 2v. 2 m m 0mM 1 2 1 2 M 2M 2 2 0 22 Electromagnetic field Fermion fields Fermion fields I. m 2 p 2 (m pn n )( m pn n ), n 1,2,3.4 2 m 2 2 m p 2M ( p5 M cos ), cos 1 2 M 2M ( p5 M cos ) 2M sin pn n ( p5 M ) 5 2M sin pn n ( p5 M ) 5 2 2 I. II. D( p, M ) pn n ( p5 M ) 5 2M sin 2 2M ( p5 M cos ) pn n 5 ( p5 M ) 2M cos pn n 5 ( p 5 M ) 2M cos 2 2 Dexotic ( p, M ) pn n 5 ( p5 M ) 2M cos 2 31 2 M ( p5 M cos ) n 5 n 5 pn ( p5 M ) 2M sin pn ( p5 M ) 2M sin 2 2 Once more the Dirac’s trick (De Sitter space) : In the flat limit |p|<<M : Chiral fermion fields 1 5 1 5 r ; l 2 2 Weyl spinors In our case: ( p 2 p52 M 2 ) ( p, p5 ) 0 ( pK Г K M )( pN Г N M ) ( p, p5 ) 0 K , N 0,1,2,3,4,5 1 L ( p, p5 ) ( M pK Г K ) ( p, p5 ) 2M 1 R ( p, p5 ) ( M pK Г K ) ( p, p5 ) 2M Chirality depends on energy momentum! 41 In 1956 Lee ,Yang and Wu discovered parity violation in weak interactions i.e. violation of mirror symmetry. From our point of view this effect is a direct consequence of de Sitter geometry of 4-momentum space. 42 Now we have all the bricks to construct a generalization of the SM based on De Sitter momentum space geometry and SU c (3) SU L (2) UY (1) gauge invariance. It is local and naturally incorporates the new physical principle – existence of a maximal mass M of the objects described by quantum fields. 44 For instance the term: becomes: New P-odd effects The new free chirality fields may be represented as: i n ( R , L ) ( x) r ,l ( x) ( x) 2M n and one predicts corrections to all weak interaction processes. A global fit of all SM LEP data gives M ~ 1 TeV 46 New interactions New Higgs decay mode H 2l ( ) 47 MMM 1 2 M a a a 292(63)(58) 10 exp SM 11 M 300GeV 48 • Specific relations between the Youkawa coupling constants and M: M 2 v 4 4 f1 2 8( v m ) 2 f1 2 f1 v 4 f2 2 4 8( v m ) 2 f2 2 f2 ..... 49 Exotic fields Exotic fields are good candidates for dark matter: - they are completely different from ordinary fermions. - in the flat limit they do not have an ordinary analogue. 51 Dark matter production q DM mq mDM M M q H DM Exotic matter is connected to ordinary matter through the same mass generation Higgs mechanism. 52 The new “dark matter” world may happen to be connected with us only through gravitation and Higgs exchange! 53 Conclusions: 1. On the basis of a new physical principle – the existence of a maximal mass M and purely geometrical considerations - a local QFT MMM is constructed. 2. Chirality (parity violation) has clear geometrical origin. New P-odd effects are predicted. 3. New interactions are appearing in the Higgs sector. 4. M is predicted to be in the TeV region. 54 5. We predict “exotic” fermions (candidates for dark matter) coupled to the ordinary matter through the Higgs field. 55 31 Yuri Manin «GEOMETRY IS A SPECIFIC PRESERVATIVE FOR QUICKLY ROTTENING PHYSICS» 56 2 «EXPERIMENT = GEOMETRY + PHYSICS» A. EINSTEIN 57 LHC = Geometry + Physics CERN 58 59 60 THANK YOU! 61