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36 changes: 18 additions & 18 deletions section/1_Intro.tex
Original file line number Diff line number Diff line change
Expand Up @@ -245,7 +245,7 @@ \section{Parton Model}
where $e_i$ is the charge carried by the quark and antiquark of flavor $i$. Since the
gluon does not carry any charge, it does not enter the cross section at leading
order. The ability to write the structure function and the cross section as a
convolution of the non-perturbative PDF and pertubative short range interaction
convolution of the non-perturbative PDF and perturbative short range interaction
is known as the factorization theorem~\cite{collins1989}. These PDFs are also
expected to be universal and independent of the details of the scattering
process, as they describe the dynamics of the partons in a given hadron.
Expand Down Expand Up @@ -523,7 +523,7 @@ \chapter{Drell-Yan Process}
\begin{subfigure}{0.45\linewidth}
\centering
\input{images/NLO_gb1}
\caption{Gluon bremstrahlung.}
\caption{Gluon bremsstrahlung.}
\label{subfig:DY_gb}
\end{subfigure}
\begin{subfigure}{0.45\linewidth}
Expand Down Expand Up @@ -697,7 +697,7 @@ \subsection{Chiral Quark Model}
\begin{equation}
q_{\pm} \rightarrow GB + q^\prime_\mp \rightarrow \left(q q^\prime\right)_0 q_{\mp}^\prime.
\end{equation}
For example, after one emission, the $u$ quark wavefuction would have the following components
For example, after one emission, the $u$ quark wavefunction would have the following components
\begin{equation}
\Psi\left(u\right) \sim \left[d\pi^+ + s K^+ + u \left(\frac{\pi^0}{\sqrt{2}} + \frac{\eta}{\sqrt{6}}\right)\right],
\end{equation}
Expand All @@ -706,7 +706,7 @@ \subsection{Chiral Quark Model}
\begin{equation}
Prob\left[ u_+ \rightarrow \pi^+d_-\right] \equiv a,
\end{equation}
and using charge asymmetry to determine the $d$ quark wavefucntion, the number of antiquark after one emission
and using charge asymmetry to determine the $d$ quark wavefunction, the number of antiquark after one emission
by the initial $(2u+d)$ valence quarks in the proton is given by
\begin{equation}
\begin{aligned}
Expand Down Expand Up @@ -791,7 +791,7 @@ \subsection{Five-quark Intrinsic Sea Model}

Recent global analysis from NNPDF~\cite{ball2022} and measurement from the LHCb~\cite{aaij2022}
have suggested evidence of intrinsic charm in the proton. This has led to many recent theory
development in understanding the nonperturbative charm in the proton~\cite{guzzi2023}. There are
development in understanding the non-perturbative charm in the proton~\cite{guzzi2023}. There are
also suggestions that SeaQuest kinematic would be ideal for testing limits on intrinsic charm~\cite{vogt2021}.

\subsection{Lattice QCD}
Expand Down Expand Up @@ -865,7 +865,7 @@ \chapter{Charmonium Production}
and is calculated with perturbative QCD (pQCD). CEM then assumes a constant
probability $F$ for the $c\bar{c}$ pairs to hadronize into a specific quarkonium
state and this probability is independent of the kinematics or the production
subprocess. The $J/\psi$ production cross section in the CEM framework can be
sub-process. The $J/\psi$ production cross section in the CEM framework can be
expressed as
\begin{equation}
\begin{split}
Expand Down Expand Up @@ -932,16 +932,16 @@ \chapter{Charmonium Production}
orbital angular momentum $L$, total angular momentum $J$, and color state $a=1,8$.
The coefficient $C^{ij}_{c\bar{c}\left[n\right]}$ describes the production of $c\bar{c}$ pair in state $n$,
from partons $i$ and $j$ and is calculated perturbatively in powers of $\alpha_s$ using pQCD.
The LDME $\expval{O^H_n}$ accounts for the hardronization probability for a specfic $c\bar{c}$ state $n$ into the
The LDME $\expval{O^H_n}$ accounts for the hadronization probability for a specific $c\bar{c}$ state $n$ into the
charmonium state $H$.
This formalaism suggests that the $c\bar{c}$ pairs can be produced in color-octet state,
then evlove into physical color-singlet quarkonia by nonperturbative emission of soft gluons.
This formalism suggests that the $c\bar{c}$ pairs can be produced in color-octet state,
then evolve into physical color-singlet quarkonia by non-perturbative emission of soft gluons.

The LDMEs discribe the hadronization process,
The LDMEs describe the hadronization process,
and are assumed to be universal and independent of beam or target hadrons and the energy scale.
As the LDMEs describe the non-pertubative interactions,
As the LDMEs describe the non-perturbative interactions,
they cannot be calculated using pQCD, and have to be extracted from models or experiments.
For example, the color-singlet LDMEs are typically estmated using the potential model~\cite{eichten1995}.
For example, the color-singlet LDMEs are typically estimated using the potential model~\cite{eichten1995}.
Using the potential model, the wavefunction of the heavy quark pair can be calculated,
and the color-singlet LDMEs can be estimated from the wavefunction at the origin
\begin{equation}
Expand All @@ -956,7 +956,7 @@ \chapter{Charmonium Production}
Some existing LDMEs for direct $J/\psi$ and $\psi'$ productions are tabulated in \cref{tab:LDMEs}.
The values of some LDMEs from different groups are very different, in some cases, even the signs are different.
This is partly due to the choice of data sets used in their global fits. The
SeaQuest experiment can provide additonal constraints on these LDMEs. Some
SeaQuest experiment can provide additional constraints on these LDMEs. Some
existing data are shown in \cref{fig:charm_cs}.
Unlike most previous fixed-target charmonium experiments, which utilized nuclear
targets, SeaQuest have both hydrogen and deuterium targets.
Expand Down Expand Up @@ -1002,11 +1002,11 @@ \chapter{Charmonium Production}
where $B$ is the branching ratio for $\psi'$ or $\chi_{cJ}$ to decay into $J/\psi$.

The relationship between the LDMEs and the $c\bar{c}$ produced via different
subprocesses up to $\mathcal{O}\left(\alpha_s^3\right)$ are shown in \cref{tab:LDME_order}.
For $q\bar{q}$ subprocess, the $c\bar{c}$ pairs are produced in
sub-processes up to $\mathcal{O}\left(\alpha_s^3\right)$ are shown in \cref{tab:LDME_order}.
For $q\bar{q}$ sub-process, the $c\bar{c}$ pairs are produced in
$S$-wave color-octet states at $\mathcal{O}\left(\alpha_s^2\right)$,
which then hadronize into various charmonium states with the LDMEs $\expval{O^H\left[^3 S_1^{[8]}\right]}$.
The $J/\psi$ and $\psi'$ mesons can also be produced via $GG$ subprocess.
The $J/\psi$ and $\psi'$ mesons can also be produced via $GG$ sub-process.
The $c\bar{c}$ pairs produced are either in color-singlet
state at $\mathcal{O}\left(\alpha_s^3\right)$ or color-octet state at $\mathcal{O}\left(\alpha_s^2\right)$.

Expand All @@ -1021,7 +1021,7 @@ \chapter{Charmonium Production}
\begin{table}[h!]
\centering
\caption{Relationship of the LDMEs and the associated order of $\alpha_s$ to
the scattering subprocesses for various charmonium states.}
the scattering sub-processes for various charmonium states.}
\label{tab:LDME_order}
\input{table/LDME_order.tex}
\end{table}
Expand All @@ -1037,7 +1037,7 @@ \chapter{Charmonium Production}
The calculated cross sections for $J/\psi$ and $\psi'$ production using NRQCD for
$p+p$ at 120 GeV are shown in \cref{fig:NRQCD_cs}. In this model, quark-antiquark
annihilation is more important than suggested by CEM. This model also suggests
that the relative importance of the two subprocesses depend on the charmonium state.
that the relative importance of the two sub-processes depend on the charmonium state.
In particular, \cref{fig:NRQCD_cs} shows that the quark-antiquark annihilation
is the dominant process for $\psi^\prime$ production.
\begin{figure}[h!]
Expand Down
6 changes: 3 additions & 3 deletions section/2_seaquest.tex
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Expand Up @@ -157,7 +157,7 @@ \subsection{Magnets}
The upstream focusing magnet (FMag) is a solid iron magnet, shown in \cref{fig:fmag}.
It measures at \SI{503}{\cm} by \SI{302.4}{\cm} tall by \SI{160}{\cm} wide.
The magnet consists of a stack of high purity iron, recovered from
the Columbia University Nevis Laboratory Cyclotron, and the aluminium coils from the E866
the Columbia University Nevis Laboratory Cyclotron, and the aluminum coils from the E866
SM3 magnet. The coils are excited to \SI{2000}{\ampere} and generate an \SI{1.9}{\tesla}
magnetic field within the iron block. This corresponds to a transverse momentum kick of
\SI{3.07}{\GeV}. FMag serves three main purposes: focusing high mass muon pairs, beam
Expand Down Expand Up @@ -320,8 +320,8 @@ \section{Trigger System}
modules. The 9 modules are separated into three levels from level 0 to level
2, as illustrated in \cref{fig:trigger}.
Four FPGA modules form the level 0, with one module for each hodoscope
``quadrant'' (upper bend plane, lower bend plane, upper nonbend plane and
lower nonbend plane). During data taking, level 0 simply passes the input signal
``quadrant'' (upper bend plane, lower bend plane, upper non-bend plane and
lower non-bend plane). During data taking, level 0 simply passes the input signal
to level 1. The level 0 can also act as a pulser for diagnostic purpose.
At level 1, four FPGA modules are used to search for four-hit track
candidates in each quadrant and compared with a preselected list of hit
Expand Down
10 changes: 5 additions & 5 deletions section/3_analysis.tex
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Expand Up @@ -411,7 +411,7 @@ \subsection{Track Finding}
St.~2 is approximately a constant and is determined using Monte Carlo simulation. Using this fact,
the search window on St.~1 is constrained by this ratio.

\pdfmargincomment{kalment filter}
\pdfmargincomment{kalman filter}
Once the hits are identified, the Kalman track fitting can begin~\cite{kalman1960}. A list of nodes are created
from the hits. Each node corresponds to a hit and also contain the drift distance of the particular hit.
The Kalman filter parametrizes a track based on the five parameters (the momentum, x-, y-slope, x- and y-position)
Expand All @@ -420,7 +420,7 @@ \subsection{Track Finding}
to the prediction. At each iteration, the Kalman filter preforms three steps: predict, filter, and smoothing,
as depicted in \cref{fig:kalman_flowchart}.
The Kalman filter loops over all the nodes, using the current estimate of the track parameters
from the previous node and calculates the expected hit location using Geant4. This predicted location
from the previous node and calculates the expected hit location using GEANT4. This predicted location
is then compared with measured location. During the filter step, the track parameters at the current node is
adjusted based on the difference between the predicted and measured hit location in order to minimized
the $\chi^2$. Kalman filter will then move on to the next node. This is illustrated in \cref{fig:kalman_node}.
Expand Down Expand Up @@ -453,9 +453,9 @@ \subsection{Track Finding}
\subsection{Vertex Finding}
Once all the tracks are found in each event, the reconstruction of the dimuon vertex can begin using kVertex.
For MATRIX-1 events, all possible combinations of $\mu^+$ and $\mu^-$ tracks are tested to see if they can form
a dimuon. The vertex is determined using the same Kalment filter with the tracks acting as measurements.
a dimuon. The vertex is determined using the same Kalman filter with the tracks acting as measurements.

\pdfmargincomment{kalment filter, refitting if it the pair originate from target to account for multiple scattering }
\pdfmargincomment{Kalman filter, refitting if it the pair originate from target to account for multiple scattering }
To account for multiple scattering of the muons while traversing FMag, dimuon pairs that are
determined to be likely originating from the target are refitted by requiring the dimuon vertex to
fall within the target. Due to the length of the target and the acceptance of the spectrometer,
Expand Down Expand Up @@ -657,7 +657,7 @@ \section{Beam Luminosity Normalization}\pdfmargincomment{might move this section
\label{fig:deadtime}
\end{figure}

During regular data-taking, the minimum width of the inhibit signal is controled by a programmable
During regular data-taking, the minimum width of the inhibit signal is controlled by a programmable
register, and is typically set to 16, meaning when bucket $i$ is above the threshold, buckets $i-8$
to $i+8$ (inclusive) will be inhibited. The length of the inhibit can be longer if a series
of high intensity buckets arrive in succession. In this situation, the inhibit will extend till 8
Expand Down
4 changes: 2 additions & 2 deletions section/4_1_result_DY.tex
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Expand Up @@ -214,10 +214,10 @@ \subsection{Comparison with global PDF analysis}
The isovector PDF $\bar{d}-\bar{u}$ over the region $0.13<x<0.45$
can also be calculated from the extracted $\bar{d}/\bar{u}$ ratio by taking the $\bar{d}+\bar{u}$
distribution from CT18.
As a flavor nonsinglet quantity, the integral, $\int^1_0 \left[\bar{d}\left(x\right) - \bar{u}\left(x\right)\right] \dd{x}$,
As a flavor non-singlet quantity, the integral, $\int^1_0 \left[\bar{d}\left(x\right) - \bar{u}\left(x\right)\right] \dd{x}$,
is expected to be independent of $Q^2$, even though the $x$ dependence might differ at different $Q^2$.
As the perturbative processes should not produce a significant $\bar{d},\,\bar{u}$ difference,
the $\bar{d}-\bar{u}$ values can provide a direct measure on the nonperturbative contributions.
the $\bar{d}-\bar{u}$ values can provide a direct measure on the non-perturbative contributions.
The values of $\bar{d}-\bar{u}$ derived from the SeaQuest data are shown in \cref{fig:e906_e866_dbarMubar} and tabulated in \cref{tab:dbarubar_e906},
and are also compared with results from E866~\cite{towell2001} and HERMES~\cite{ackerstaff1998},
and with predictions from meson cloud and statistical models.
Expand Down
2 changes: 1 addition & 1 deletion section/4_2_result_jpsi.tex
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Expand Up @@ -142,7 +142,7 @@ \subsection{\texorpdfstring{$x_F$}{x\_F} distributions}
is representing the increasing importance of the $q\bar{q}$ annihilation process for the $\psi'$
production.
It is also worth pointing out that in the CEM framework, the hadronization probability only depends on
the final charmonium state, but not the underlying subprocess. Therefore, the CEM framework would predict
the final charmonium state, but not the underlying sub-process. Therefore, the CEM framework would predict
the $x_F$ distributions for $J/\psi$ and $\psi'$ to be very similar, with a smaller total cross section
for $\psi'$ production. Hence the predicted $\sigma_{\psi'}/\sigma_{J/\psi}$ from CEM would be
largely independent of $x_F$, inconsistent with the trend of the data.
Expand Down
2 changes: 1 addition & 1 deletion table/cuts/track.tex
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Expand Up @@ -19,7 +19,7 @@
$\chi^2/(\mathrm{nHits}-5)$ & $\chi^2/\mathrm{ndf}$ & $<12$ \\ \hline
$y_1/y_3$ & y position of track at St.~1 and St.~3 & $<1$ \\ \hline
$y_1\times y_3$ & & $>0$ \\ \hline
$| |px_1 - px_3| -0.416|$ & difference in x momentum at St.~1 and St.~3 accounting for the Kmag kick & $<\SI{0.008}{\GeV}$ \\ \hline
$| |px_1 - px_3| -0.416|$ & difference in x momentum at St.~1 and St.~3 accounting for the KMag kick & $<\SI{0.008}{\GeV}$ \\ \hline
$|py_1 - py_3|$ & difference in y momentum at St.~1 and St.~3 & $<\SI{0.008}{\GeV}$ \\ \hline
$|pz_1 - pz_3|$ & difference in z momentum at St.~1 and St.~3 & $<\SI{0.08}{\GeV}$ \\ \hline
$|py_1 |$ & absolute value of the y momentum at St.~1 & $>\SI{0.02}{\GeV}$ \\ \hline
Expand Down

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