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SUMMARY:Phenomenology of GeV-scale Chern-Simons boson
DTSTART;VALUE=DATE-TIME:20201221T111000Z
DTEND;VALUE=DATE-TIME:20201221T113000Z
DTSTAMP;VALUE=DATE-TIME:20240723T064934Z
UID:indico-contribution-175@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Mariia Tsarenkova (Taras Shevchenko National Univers
ity of Kyiv)\nThe Standard Model (SM) is a particle physics theory that is
consistent up to very high energy scales and verified in numerous experi
ments up to $\\sim 14$ TeV. However\, it fails to explain some phenomena
such as massiveness of neutrinos\, dark matter\, dark energy\, baryon asy
mmetry of the Universe etc. Therefore\, SM is incomplete and requires an e
xtension. \n\nOne possible approach is by adding new particles to the theo
ry. There are two possible answers to the question "Why do we not observe
particles of new physics in experiments?" The first answer is the followin
g. The new particles are very heavy and can not be produced in modern a
ccelerators like LHC. To detect them one has to build more powerful and mo
re expensive accelerators. There is another possibility. The particles of
new physics can be light particles that feebly interact with SM particles
.\nThe last case is very interesting for the experimental search of the ne
w physics just now. There are three possible choices of new renormalized i
nteraction Lagrangian of particles of new physics with SM particles. It's
called portals. There are scalar portal\, heavy neutral leptons portal\,
vector portal. There are other portals of high-dimensional operators such
as portal of pseudoscalar particles (axion-like particles)\, or Chern-Simo
ns like (parity odd) interaction of electroweak gauge bosons with a new ve
ctor field [1].\n\n\nIn this paper\, we consider a Chern-Simons (CS) porta
l with new neutral vector particle ($X$) boson. \nThis extension has not
yet been studied sufficiently. This interaction was proposed in [2]. It
origins from non-trivial anomaly cancellations in theory with new heavy fe
rmions. It has gauge-invariant form\n$$\n \\mathcal{L}_1=\\frac{C
_Y}{\\Lambda_Y^2}\\cdot X_\\mu (\\mathfrak D_\\nu H)^\\dagger H B_{\\lambd
a\\rho} \\cdot\\epsilon^{\\mu\\nu\\lambda\\rho}+h.c.\, \\quad \n\
\mathcal{L}_2=\\frac{C_{SU(2)}}{\\Lambda_{SU(2)}^2}\\cdot X_\\mu (\\mathfr
ak D_\\nu H)^\\dagger F_{\\lambda\\rho} H\\cdot\\epsilon^{\\mu\\nu\\lambda
\\rho}+h.c. \n$$\n\nIn the low energy limit (unitary gauge) the effective
renormalized Lagrangian of three particle interaction CS boson with SM pa
rticles is\n$$\n \\mathcal{L}_{CS}=c_z \\epsilon^{\\mu\\nu\\lambda\\rho}
X_\\mu Z_\\nu \\partial_\\lambda Z_\\rho +c_\\gamma \\epsilon^{\\mu\\nu\\l
ambda\\rho} X_\\mu Z_\\nu \\partial_\\lambda A_\\rho+\\left\\{ c_w \\epsil
on^{\\mu\\nu\\lambda\\rho} X_\\mu W_\\nu^- \\partial_\\lambda W_\\rho^+ +
h.c.\\right\\}.\n$$\n\nFor the experimental search of the new particle\, i
t is very important to theoretically consider channels of production and d
ecay of the new particle. We consider the case of experiments on Cern SPS
accelerator\, where CS particles can not be produced from the decay of rea
l $W$\, $Z$ bosons. In this paper\, we consider the production of CS GeV-
scale particles in mesons' decay. \n \nTo do it we get effective Lagrangia
n of CS interaction with different quarks due to presented here loop diagr
am in the form\n$$\n \\mathcal{L}_{CSd}= \\sum_{m\\neq n}\\Theta_{1W}
\\left( C^d_{mn}\\\, \\bar{\\Psi}_{d_n}\\\, \\gamma^{\\mu}\\\,\\hat\n
P_L \\\, \\Psi_{d_m} X_{\\mu}+h.c.\\right)%-\\sum_n\\Theta_W^1
g^2 C^d_{nn}\\\, \\bar{\\Psi}_{d_n}\\\, \\gamma^{\\mu}\\\,\\hat P_L \\\,
\\Psi_{d_n} X_{\\mu}\,\n$$\nwhere $\\Theta_{1W}$ is real part of $c_w$ c
oupling and $C^d_{bs}=1.97\\cdot 10^{-4}$\, $C^d_{bd}=4.43\\cdot 10^{-5}$\
, $C^d_{sd}=1.77\\cdot 10^{-6}$.\nAs it turned out the loop with different
quarks does not suffer from divergence problem and we have to take into a
ccount only interaction with down quarks\, because coefficients of intera
ction with up quarks are sufficiently smaller. \nSo\, we will consider CS
particle production in meson's decay only due to decay of heavy down quark
in the meson. \n\nInitial lightest mesons containing $b$ and $s$ quarks
are $B$-mesons and $K^\\pm$\, $K^0_S$\, $K^0_L$ mesons.\n\nPossible reacti
on of $B$-meson decay with $X$-particle production is decay into pseudosca
lar mesons ($K$ and $\\pi$ mesons)\, scalar mesons ($K^{0\\star}(700)$\,
$K^{0\\star}(1430)$)\, vector mesons ($K^\\star(892)$\, $K^\\star(1410)$\,
$K^\\star(1680)$)\, pseudovector mesons ($K_1(1270)$\, $K_1(1400)$) and t
ensor final meson states ($K_2(1430)$).\n\nFor the initial kaons states\,
the only possible 2-body decay is the process $K \\to \\pi +X$.\nThere are
3 types of the kaons: $K^{\\pm}$\, $K^0_L$\, $K^0_S$. Since $K^0_S$ is th
e $CP$-even eigenstate\, the decay $K^0_S\\to \\pi S$ is proportional to t
he CKM $CP$-violating phase and is strongly suppressed. Further we assume
that the corresponding branching ratio vanishes and consider only reaction
s $K^\\pm \\to \\pi^\\pm +X$ and $K^0_L \\to \\pi^0 +X$.\n\nThe amplitude
of $h$-meson decay into $h'$-meson and $X$-particle has the form\n\n$$\n
M_{h\\rightarrow h'X}=\\Theta_{1W} C^d_{mn} \\\, \\langle h'(p'))|\\
bar d_n\\gamma^{\\mu} \\hat P_L d_m|h(p)\\rangle\\\,\n \\epsilon^{\\sta
r\\lambda_X}_{\\mu}.\n$$\n\nThis quantity can be obtained with help of fo
rmalism summarised in [3].\n\nIn the following\, we plan to complete consi
deration of the production of CS particles by examining direct CS producti
on in $p-p$ collisions. Also\, we plan to consider possible channels of CS
particles' decay. \n\n\nFigure 1. a) loop diagram of quarks interactions
with CS particles\; b) diagram of CS production in meson's decay c) decay
of $B$- and $K$-mesons with CS production.\n\n[1] Sergey Alekhin et al. A
facility to Search for Hidden Particles at the CERN SPS: the SHiP physics
case. *Rept. Prog. Phys.*\, 79(12):124201\, 2016.\n[2] Ignatios Antonia
dis\, Alexey Boyarsky\, Sam Espahbodi\, Oleg Ruchayskiy\, and Jame
s D.Wells. Anomaly driven signatures of new invisible physics at the Lar
ge Hadron Collider. *Nucl. Phys.*\, B824:296–313\, 2010.\n[3] Iryna Bo
iarska\, Kyrylo Bondarenko\, Alexey Boyarsky\, Volodymyr Gorkavenko\
, Maksym Ovchynnikov\, and Anastasia Sokolenko. Phenomenology of GeV-scal
e scalar portal. *JHEP*\, 11:162\, 2019.\n\nhttps://indico.bitp.kiev.ua/ev
ent/7/contributions/175/
LOCATION:Online meeting
URL:https://indico.bitp.kiev.ua/event/7/contributions/175/
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