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8HIGGS AND STANDARD MODEL
Rzaeva S.
Sumgait State University
ABSTRACT
The possibility of construction of the electroweak model based on spontaneously broken gauge su(3)c0su(3)l®u(1)x'®u(1)x' group symmetry has been investigated. In the case of arbitrary values of Higgs and fermions fields' hypercharges, the expressions for the gauge bosons masses, neutral fields and the interactions lagrangian of leptons and quarks with gauge vector bosons are calculated. Keywords: Gauge Models, Electroweak interaction, Higgs fields.
On July 4th 2012 the ATLAS and CMS experiments at CERN presented their results in the search for the Higgs boson. The data collected at the Large Had-ron Collider (LHC) during the first run clearly indicated that a new particle had been observed: the illustrious and long sought after Higgs boson. The search for this particle was one of the main reasons the LHC was constructed as the Higgs boson. It is not 'just' a new particle in particle physics, but really forms one of the foundations of the (electroweak sector of the) Standard Model: it allows to give masses to both fermions and gauge bosons in a local gauge invariance theory, it is at the heart of electroweak unification, quark mixing etc.
Though the Standard Model is a good phenome-nological theory and coincides very well with all experimental results [2], it leaves several unanswered questions which suggest that SM should be an effective model at low energies, originated from a more fundamental theory.
Note that the possibilities of construction of elec-troweak interaction models (both usual, and supersym-metric) based on su(2)l ®u(1)x' ®u(1)x' group symmetry have been considered in [5-7]. In this paper the possibility of construction of the electroweak model based on
spontaneously broken gauge
su(3)c0su(3)l®u(1)x'®u(1)x' group symmetry has been investigated (3-3-1-1 - model).
Phenomenology of the 3-3-1 model in the version that includes right-handed neutrinos with two Higgs triplets is a subject of this study.
The su(3)c®su(3)l®u(1)x'®u(1)x' gauge group is broken spontaneously via three steps. In the first step, it is embedded in that of the SM via a Higgs scalar triplet
X =
x 0
va y
\i,3,xx x x \
acquired with VEV given by
42
(o \
V y
(1)
In the last steps, to embed the gauge group of the SM in U(1)x', U(1)x", another Higgs scalar triplet
P =
fP + ^
Yi,3,Xp X P A
and
n =
(i,s,Xn X n).
n
y
is needed with the VEV as follows
(0 ]
(2)
1
<P>=T2
u
V 0 y
1
42
and
0
V 0 y
(3)
The Yukawa interactions which induce masses for the fermions can be written in the most general form as ly — (ly + ly + ^y*) + ^y' The covariant derivative of a triplet is given by
Du№ = d№ -iP№>
(4)
where tyj - Higgs fields. The P^ matrix appeared
in the above covariant derivative is rewritten in a convenient form
P
"Sp
43
W8p 2
+ J ~/tXBM + u >
42W '
42X'°°*
4~W
Wo
-p;
r8p 2 - W3p +7f j l(tXBp+ tX'Cu;
42Y';
2W,
42X'0 f
42Y' -
fs
\
8p 12
u +J-(XBu + t'X'Cp )
y
X
1
0
0
t+
ft
V
here t = g'/ g, t' = g"/ g and
W + iW W + iW W - iW
w± = LM 2M Y'+ = 6M X0 - 4m 5m (6)
m V2 ' m ' m v2 '
In this case taking into account (1) and (3) in (4) for the masses of gauge bosons we have the following masses
mw - ¿- {u2 + u2 ), m2 . ¿. (v2 + u2 ), m^x - ^ {v2 + u2 ). (7) Taking into account V >> u >> u from (15) we have MX, MY >> MW .
The interactions lagrangian, containing the mass of the neutral (Hermitian) gauge bosons in this case, looks
like:
lng - LVTM2V, V - (W ,W ,B ,C ). (8)
mass 2 3m 8m M M
For the mass lagrangian of the neutral gauge bosons we have (the field remains massless)
LNG - L(M2 Z Z + M2 Z Z + M2 Z Z ), (9)
mass 2 Zj iM iM Z^ 2m 2m Z 3m 3m
Neutral gauge bosons masses are
2 2
2 g a 2 g an
M2 - —(fncos- + f ), M2 - —[fncos(- ± - ) + f ]. (10)
Z j 2 0 3 1 Z2Z3 2 0 3 3 1
- f2 where cos— --. and
3 3f3 J0
f0 - 2(x0 + 4x, + x - 2x3 - 3x4)L2 ¡9,
fi - [2(V2 + u2 + u2) + V2yi + u2y2 + v2y3]/9,
8
f2 - — [(V2 + u2 + u2)2 + xJ[11(V2u2 + V2u2 + u2u2) - 8(V4 + u4 + u4) - (11)
8
- 8x1 - 2x2 + 9x4 + 2x5] - — x6.
2 2 2
Expression of quantities xi and yi, in neutral M^ , M^ and M^ - bosons masses have the form: x0 - 4(V4 + u4 + u4) - [V2 (u2 + u2) + u2u2},
ir4 4 4 ir4 2 4 2 4 2
xi - V yi + u4y2 + u4y3, x2 - V4yL + u4y2 + u4y23,
x3 - V2u2(yl + y2 - y^t) + V2u2(yi + y3 - y,y3) + u2u2(y2 + y3 - y2y3),
9 9 9 9 9 9
x4 - u u n + V u n + V u n,
x5 - V2u2(5yi + 5y2 - 2yj2) +V2u2(5yi + 5y3 - 2yj3) + u2u2(5y2 +5^ - 2y2y3),
2t2t2
x6 - V2u2u2x7, x7 [Zi(Zi + z2) + z2(z2 + Z3) + z3(z3 - Zi)] + t2P23 + t'2P2,
where
yi - t2X2x + t'2X'2x, y2 - t2X2 + t'2X2, y3 - t2X2p + t'2X'2p, z. - XX' -X 'X , z, - XX ' -X 'X , z, -XX ' -X 'X,
1 p n p n ' 2 X n X n ' 3 X p X p '
r,i - t2t'2zL + 2t2XpXn + 2t'2XpX , n2 - t2t'2zl + 2t2XxX, + 2t'2XXX'„,
In the case of M7 >> M7 >> M7 corresponding to the modern experimental data [1], for neutral bos-\ 2 Z3
ons masses, we have
M
M
2
21 * t[y2(2 + yl} + U (2 + У2) + и (2 + y3)], 2 V2v2(3 + ) + V2u2(3 + ) + u2v2(3 + )
g
Z-
V2(2 + y}) + u2(2 + y2) + и 2 (2 + y3)
M
g
Zr
6 V2и2(3 + n ) + V2u2(3 + n_) + U2v2(3 + n )
'4'
'5'
'6'
The Conclusion: Taking into account the arbitrary values of fermions and Higgs fields hypercharges the possibility of construction of electroweak interactions model, based on spontaneously broken symmetry group by three Higgs fields have been investigated. Masses of gauge bosons, arising in the considered model are calculated. Diagonalization of mass matrix of neutral fields has been performed and expressions for eigenstates of neutral fields are obtained.
References
1. Particle Data Group, W. - M. Yao et al., Journal of Phys., G33, p.1, 2006.
2. P. Langacker, Phys. Rep., 72, p.185, 1981.
3. P. Fayet, hep-ph/9812300, 1998; S. Martin, hep-ph/9709356; M. Green, J. Schwarz and
4. K. Kang, J. E. Kim. Lett. Nuono Cim., 16, p.252. 1976.
5. Ф. Т. Халил-заде. Препринт № 315 ИФАН Азерб. ССР Баку, 1989.
6. O.B. Abdinov, F.T. Khalil-zade, S.S. Rzaeva. Reports of NAS of Azerbaijan Republic. XXVII, № 5, p.20, 2007.
7. H. N. Long, Phys. Rev., D53, p.437, 1996.
8. W. A. Ponce, D. A. Gutierrez , L. A. Sanchez. hep - ph/031243v3, 2004.
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О «КАЖУЩЕМСЯ ИЗМЕНЕНИИ ВЕСА» В ОПЫТАХ ФАРАДЕЯ ПО ВЛИЯНИЮ ЗЕМНОГО МАГНЕТИЗМА НА ПРОВОДНИКИ С
ЭЛЕКТРИЧЕСКИМ ТОКОМ
Ромм Я.Е.
д-р техн. наук, профессор, зав. кафедрой информатики Таганрогского института им. А.П. Чехова (филиал) ФГБОУВО "РГЭУ (РИНХ)",
Ерохин Н. Ф.
канд. физ.-мат. наук, доцент кафедры теоретической, общей физики и технологии Таганрогского института им. А.П. Чехова (филиал) ФГБОУ ВО "РГЭУ (РИНХ)"
ABOUT «SEEMING WEIGHT CHANGE» IN FARADAY EXPERIMENT ON THE INFLUENCE OF TERRESTRIAL MAGNETISM ON THE CURRENT-CARRYING CONDUCTORS
Romm Ya.E.
Doctor of Engineering Science, Professor, Chair of the department of Information Science
of the A.P. Chekhov Taganrog Institute (branch) RSUE,
Erokhin N.F.
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Theoretical, General Physics and Technology of the A.P. Chekhov Taganrog Institute (branch) RSUE
АННОТАЦИЯ
При изучении влияния земного магнетизма на проводники с током М. Фарадей наблюдал «кажущееся изменение веса» проводников в замкнутой электрической цепи. Частичное объяснение состояло в действии электрокапиллярности ртути на медные концы подвижного контакта. В статье описываются видоизменения опыта М. Фарадея, выполненные с целью исключения побочных эффектов. Показано, что в реальных условиях устойчиво воспроизводится действие на проводники и соленоиды с переменным то-
