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High Precision Test of the Standard Model using $\varepsilon_K$ and $V_{cb}$ in Lattice QCD

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Authors
장용철
Advisor
이원종
Issue Date
2015-08
Publisher
서울대학교 대학원
Keywords
standard model, CP violation, lattice QCD, heavy quarks, meson spectrum
Description
학위논문(박사)--서울대학교 대학원 :자연과학대학 물리·천문학부,2015. 8. 이원종.
Abstract
In the Standard Model (SM), CP violation is described by the single Kobayashi-
Maskawa (KM) phase. By the generalization of the Cabibbo mixing angle for
the first and second quark generations, the Cabibbo-Kobayashi-Maskawa (CKM)
matrix $V_{CKM}$ defines quark
avor mixing amplitudes in the electroweak processes
among the three quark generations. The precise determination of the CKM matrix
elements is a central part of the SM
avor physics, because it allows a test of the
SM by observing CP violating processes. Moreover, some of electroweak processes
with the W boson exchange are sensitive to the new physics (NP) effects and
they can be used to constrain the model space of the NP beyond the SM. By
the a lot of dedicated works both from theory and experiment, testing the CKM
mechanism enters into the precision era. Among progresses in the theory such as
the higher order perturbative calculations, the lattice QCD plays the essential role
by providing precise values for the nonperturbative hadronic matrix elements.
In the first part of this thesis, the current status of the indirect CP violation
parameter in neutral kaon system, $varepsilon_K$, in the SM is discussed in detail. The SM
evaluation of the $varepsilon_K$ uses inputs from lattice QCD: the kaon bag parameter $\hat{B}_K$, $\xi_0$, $
V_{us}
$ from the $K\ell3$ and $K\mu2$ decays, and $
V_{cb}
$ from the axial current form factor
for the exclusive decay $\bar{B}\to D^{\ast}\ell\nu$ at zero-recoil. The theoretical expression for $varepsilon_K$
is thoroughly reviewed to give an estimate of the size of the neglected corrections,
including long distance effects. The Wolfenstein parametrization ($
V_{cb}
$; $\lambda$, $\bar{\rho}$, $\bar{\eta}$)
is adopted for CKM matrix elements which enter through the short-distance
contribution of the box diagrams. It is found that the SM prediction of $varepsilon_K$ with
exclusive $V_{cb}$ and the Unitarity Triangle apex ($\bar{eta}$, $\bar{\rho}$) from the angle-only fit is
lower than the experimental value by 3.4$\sigma$. However, with inclusive $V_{cb}, there
is no gap between the SM prediction of $varepsilon_K$ and its experimental value. The
importance of a specific CKM matrix element $V_{cb}$ is reemphasized in this context.
The determination of $V_{cb}$ in a sub-precent level is needed for a decisive test
of the SM with $varepsilon_K$. To meet the target precision for the $V_{cb}$, the heavy quark
discretization effect on the lattice, which dominates the error for form factor
calculations for the $b\to c$ transition, should be controlled with a similar precision.
Thus, in the second part, a discussion on the treatment of the heavy quarks on
the lattice follows. A numerical test of a highly improved lattice action for heavy quarks, so-called the Oktay-Kronfeld (OK) action, is performed by assessing improvements
on the meson spectrums of heavy-strange systems and quarkonia. The
OK action is an extension to higher order of the Fermilab improvement program
for massive Wilson fermions, a lattice description of the fermion fields. The OK action
includes dimension-six and -seven operators necessary for tree-level matching
to QCD through order O($\Lambda^3/m_Q^3$) for heavy-light mesons and O($v^6$) for quarkonium,
or, with Symanzik power counting, O($a^2$) with some O($a^3$) terms. Data
is generated with the tadpole-improved Fermilab and OK actions on 500 gauge
configurations from a MILC coarse (a $\approx$ 0.12 fm) $N_f$ = 2 + 1 flavors, asqtad staggered
ensemble. From the analysis of the inconsistency parameter and the
hyperfine splittings for the rest and kinetic masses, it is clearly shown that, with
one exception, the results obtained with the tree-level matched OK action are
significantly closer to the continuum limits than the results obtained with the
Fermilab action. The exception occurs for the hyperfine splitting of the bottom strange
system, where statistics are too low to draw a firm conclusion, though
a similar improvement is expected. An optimization of the conjugate gradient
inverter code for the OK action is also discussed. It promotes the OK action to
the practical level of use.
Language
eng
URI
http://dcollection.snu.ac.kr:80/jsp/common/DcLoOrgPer.jsp?sItemId=000000066973
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College of Natural Sciences (자연과학대학)Dept. of Physics and Astronomy (물리·천문학부)Physics (물리학전공)Theses (Ph.D. / Sc.D._물리학전공)
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