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College of Natural Sciences (자연과학대학)
Dept. of Physics and Astronomy (물리·천문학부)
Physics (물리학전공)
Theses (Ph.D. / Sc.D._물리학전공)

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

- Authors
- 장용철

- Advisor
- 이원종

- Issue Date
- 2015-08

- Publisher
- 서울대학교 대학원

- 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

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