updating the xray paper

r15a_xray/tex/abstract.tex

@@ -1,3 +0,0 @@
-\begin{abstract}
-  Abstract
-\end{abstract}

r15a_xray/tex/analysis.tex

@@ -130,7 +130,7 @@ and fractions of muons captured by element of interest are calculated and
 listed in~\cref{tab:capture_frac}.
 \begin{table}[tbp]
   \centering
-  \caption{Nuclear capture probability calculated from mean lifetimes taken
+  \caption{Nuclear capture probabilities calculated from mean lifetimes taken
     from measurements of Suzuki et.al.~\cite{SuzukiMeasday.etal.1987}}
   \label{tab:capture_frac}
   \begin{tabular}{cccc}
@@ -144,3 +144,17 @@ listed in~\cref{tab:capture_frac}.
     \bottomrule
   \end{tabular}
 \end{table}
+
+Number of stopped and captured muons in our targets are:
+\begin{table}[tbp]
+  \centering
+  \caption{Number of muons stopped and captured}
+  \label{}
+  \begin{tabular}{ccc}
+    Target & Number of muons stopped & Number of muons captured \\
+    \midrule
+    \ce{^{nat}Al} & $(2.96002\pm 0.00017) \times 10^8$ & $(1.8041\pm 0.0015) \times 10^8$\\
+    \ce{^{nat}Ti} & $(2.17237\pm 0.00015) \times 10^8$ & $(1.8530\pm 0.0013) \times 10^8$\\
+    \ce{^{nat}W} &   & \\
+  \end{tabular}
+\end{table}

r15a_xray/tex/intro.tex

@@ -1,11 +1,46 @@
 \section{Introduction}
-Why are we even doing this measurement?
+The next generation of charged leption flavor violation (CLFV) experiments
-\begin{itemize}
+(COMET at J-PARC and Mu2e at Fermilab) are going to stop about \num{e18} muons
-  \item targets for mu-e conversion experiments
+in their targets to search for new physics beyond the Standard Model. Knowing
-  \item why did we measure \ce{W}, \ce{H_2O}, \ldots: background for Xrays of
+accurately number of stopped muons in the targets is important as it is the
-    interest in Mu2e
+denominator for the branching ratio of the coherent muon decay to electron
-  \item existing data? focused on nuclear charge radii, did not report muonic
+without a neutrino process these experiments looking for. The proposed way to
-    X-ray yields. This is true for \ce{^{nat}Ti}~\cite{Wohlfahrt1981}
+measure the actual number of stopped muons is infering that from number of
+charateristic muonic X-rays, and gamma rays emitted from excited nuclei after
+muon capture. 
 
-\end{itemize}
+Both COMET and Mu2e will use pulsed proton beam to produce pions which decay in
+flight to muons. The primary beam line of Mu2e would deliver proton pulses
+\SI{1.7}{\micro\second} apart, each pulse contains about \num{4E7} protons.
+Electrons from decays of pions would hit the muon stopping target about
+\SI{100}{\nano\second} earlier than muons do, and produce an intense
+``beam~flash'' (about \SI{51}{\mega\hertz\per\square\centi\meter} of
+bremsstrahlungs with average energy of
+\SI{1.4}{\mega\electronvolt})~\cite{mu2etdr}. It is therefore challenging to
+measure the X-rays and gamma rays mentioned above. The situation in COMET Phase-I
+is similar~\cite{comettdr}.
+
+There are two proposed target materials for COMET and Mu2e, namely aluminum and
+titanium. Most prominent aluminum muonic X-rays at \SI{346.8}{\keV}
+(\twoPoneS~transition) and \SI{412.8}{\keV} (\threePoneS~transition) were
+measured precisely by Measday et
+al.~\cite{Measday2007}. Observing these X-rays in a highly intense pulsed beam
+experiment like COMET and Mu2e would be difficult as they might be buried by
+the ``beam~flash'' described above. A gamma ray of \SI{1808.7}{\keV} from
+\ce{^{26}Mg^*} would provide a better proxy to the number of stopped muons for
+it has a lifetime of muon in aluminium, therefore can be measured out of the
+``beam flash''. The emission rate of this gamma was measured at
+\SI{10}{\percent} uncertainty in~\cite{Measday2007}. 
+
+Knowledge about muonic X-rays and gammas after muon capture on titanium is less
+prehensive. Measurements of titanium were mostly done in context of  either nuclear
+charge radii~\cite{Wohlfahrt1981}, or neutrinoless double beta
+decay~\cite{Zinatulina2019}, and did not report X-ray yeilds. 
+
+To have a more completed picture of the situation, AlCap has carried out
+measurements of photons after muon capture on aluminum and titanium. The goals
+are emission rates of charateristic muonic X-rays from titanium, and improvement
+on the rate of the \SI{1808.7}{\keV} gamma from aluminum. In addion, we have
+measured photons from other materials where muons would stop in the experiments
+to learn about potential background around the gammas and X-rays of interest.
 

r15a_xray/tex/results.tex

@@ -1,17 +1,9 @@
 \section{Results and discussions}
 \subsection{Titanium}
-Number of stopped muons in the natural titanium target was:
+Fitting the peak around \SI{932}{keV} in the photon spectrum gives energies of the $2p_{3/2}-1s$ and $2p_{1/2}-1s$ transitions as \SI{932.5 \pm 0.9}{\keV} and \SI{930.4 \pm 1.1}{\keV}, respectively. These values are consistent with previously reported values by Wohlfahrt et al.~\cite{Wohlfahrt1981} given the isotopic abundance of the natural titanium target used in this experiment. The 
+number of $(2p_{3/2}-1s)$ X-rays is:
 \begin{equation}
-  N_{\mu} = (88296 \pm 9) \times 10^3 \,.
+  N_{2p_{3/2}-1s} = (11881 \pm 591) \,.
-  \label{eqn:Nmu_Ti_Tsc}
-\end{equation}
-
-Fitting the peak around \SI{931}{keV} in the photon spectrum gives the 
-center of gravity at \SI{931.6 \pm 0.7}{keV} (see~\cref{fig:ti_931keV_fit}),
-consistent with previously reported value~\cite{Wohlfahrt1981}.
-Number of $(2p-1s)$ X-rays in the \SI{931.6}{keV} peak is:
-\begin{equation}
-  N_{931.6} = (20750 \pm 764) \,.
 \end{equation}
 
 \begin{figure}[tbp]
@@ -21,8 +13,52 @@ Number of $(2p-1s)$ X-rays in the \SI{931.6}{keV} peak is:
   \label{fig:ti_931keV_fit}
 \end{figure}
 
-The emission rate of the $(2p-1s)$ muonic X-rays is calculated as:
+
-\begin{equation}
+Emission rates of K X-rays from titanium is listed in~\cref{tab:kXraysTi}.
-  R_{Ti} = \frac{N_{931.6}}{A_{931.6} \times N_{\mu} \times f_{capTi}} = 0.90
+
-  \pm 0.04 \,.
+\begin{table}[tbp]
-\end{equation}
+  \centering
+  \caption{Emission rates of K X-rays from titanium}
+  \label{tab:kXraysTi}
+  \begin{tabular}{ccc}
+    Transition & Energy [keV] & Rate [\%] \\
+    $2p-1s$ & 932.4 & \num{78.9\pm2.5}\\
+    $3p-1s$ & 1121.5 & \num{7.5\pm1.7}\\
+    $4p-1s$ & 1187.9 & \num{3.2\pm1.0}\\
+    $5p-1s$ & 1218.5 & \num{2.6\pm1.4}\\
+    $6p-1s$ & 1235.2 & \num{3.2\pm1.9}\\
+  \end{tabular}
+\end{table}
+
+\begin{figure}[tbp]
+  \centering
+  \includegraphics[width=0.8\textwidth]{figs/ti-kXrays.pdf}
+  \caption{Muonic X-rays in the Lyman series from titanium}
+  \label{fig:ti_kXrays}
+\end{figure}
+
+\subsection{Aluminum}
+\label{subsec:result_al}
+
+\begin{figure}[tbp]
+  \centering
+  \includegraphics[width=0.8\textwidth]{figs/al-kXrays.pdf}
+  \caption{Muonic X-rays in the Lyman series from aluminum}
+  \label{fig:al_kXrays}
+\end{figure}
+
+Emission rates of K X-rays from aluminum is listed in~\cref{tab:kXraysAl}.
+
+\begin{table}[tbp]
+  \centering
+  \caption{Emission rates of K X-rays from aluminum}
+  \label{tab:kXraysAl}
+  \begin{tabular}{cccc}
+    Transition & Energy [keV] & Intensity (this experiment) [\%] & Intensity [\%]~\cite{Measday2007}\\
+    $2p-1s$ & 346.8 & \num{83.1\pm3.5} & \num{79.8\pm0.8}\\
+    $3p-1s$ & 412.8 & \num{7.71\pm0.29}& \num{7.6\pm1.5}\\
+    $4p-1s$ & 435.9 & \num{4.79\pm0.18}& \num{4.9\pm1.0}\\
+    $5p-1s$ & 446.6 & \num{3.81\pm0.14}& \num{3.9\pm1.0}\\
+    $6p-1s$ & 452.4 & \num{2.24\pm0.13}& \num{2.2\pm1.0}\\
+  \end{tabular}
+\end{table}

r15a_xray/xray.bib

@@ -45,17 +45,56 @@
   url       = {http://journals.aps.org/prc/abstract/10.1103/PhysRevC.35.2212},
 }
 
-@Article{refId0,
+@Article{ZinatulinaDaniya2018,
   author  = {{Zinatulina, Daniya} and {Brian\c{c}on, Chantal} and {Brudanin, Victor} and {Egorov, Viacheslav} and {Perevoshchikov, Lev} and {Shirchenko, Mark} and {Yutlandov, Igor} and {Petitjean, Claude}},
-  title   = {Electronic catalogue of muonic X-rays},
   journal = {EPJ Web Conf.},
+  title   = {Electronic catalogue of muonic X-rays},
   year    = {2018},
-  volume  = {177},
   pages   = {03006},
+  volume  = {177},
   doi     = {10.1051/epjconf/201817703006},
   url     = {https://doi.org/10.1051/epjconf/201817703006},
 }
 
+@Article{Measday2007,
+  author    = {Measday, David F. and Stocki, Trevor J. and Moftah, Belal A. and Tam, Heywood},
+  journal   = {Phys. Rev. C},
+  title     = {\ensuremath{\gamma} rays from muon capture in $^{27}\mathrm{Al}$ and natural Si},
+  year      = {2007},
+  month     = {Sep},
+  pages     = {035504},
+  volume    = {76},
+  doi       = {10.1103/PhysRevC.76.035504},
+  issue     = {3},
+  numpages  = {17},
+  publisher = {American Physical Society},
+  url       = {https://link.aps.org/doi/10.1103/PhysRevC.76.035504},
+}
+
+@Article{mu2etdr,
+  author      = {L. Bartoszek and E. Barnes and J. P. Miller and J. Mott and A. Palladino and J. Quirk and B. L. Roberts and J. Crnkovic and V. Polychronakos and V. Tishchenko and P. Yamin and C. -h. Cheng and B. Echenard and K. Flood and D. G. Hitlin and J. H. Kim and T. S. Miyashita and F. C. Porter and M. R<>hrken and J. Trevor and R. -Y. Zhu and E. Heckmaier and T. I. Kang and G. Lim and W. Molzon and Z. You and A. M. Artikov and J. A. Budagov and Yu. I. Davydov and V. V. Glagolev and A. V. Simonenko and Z. U. Usubov and S. H. Oh and C. Wang and G. Ambrosio and N. Andreev and D. Arnold and M. Ball and R. H. Bernstein and A. Bianchi and K. Biery and R. Bossert and M. Bowden and J. Brandt and G. Brown and H. Brown and M. Buehler and M. Campbell and S. Cheban and M. Chen and J. Coghill and R. Coleman and C. Crowley and A. Deshpande and G. Deuerling and J. Dey and N. Dhanaraj and M. Dinnon and S. Dixon and B. Drendel and N. Eddy and R. Evans and D. Evbota and J. Fagan and S. Feher and B. Fellenz and H. Friedsam and G. Gallo and A. Gaponenko and M. Gardner and S. Gaugel and K. Genser and G. Ginther and H. Glass and D. Glenzinski and D. Hahn and S. Hansen and B. Hartsell and S. Hays and J. A. Hocker and E. Huedem and D. Huffman and A. Ibrahim and C. Johnstone and V. Kashikhin and V. V. Kashikhin and P. Kasper and T. Kiper and D. Knapp and K. Knoepfel and L. Kokoska and M. Kozlovsky and G. Krafczyk and M. Kramp and S. Krave and K. Krempetz and R. K. Kutschke and R. Kwarciany and T. Lackowski and M. J. Lamm and M. Larwill and F. Leavell and D. Leeb and A. Leveling and D. Lincoln and V. Logashenko and V. Lombardo and M. L. Lopes and A. Makulski and A. Martinez and D. McArthur and F. McConologue and L. Michelotti and N. Mokhov and J. Morgan and A. Mukherjee and P. Murat and V. Nagaslaev and D. V. Neuffer and T. Nicol and J. Niehoff and J. Nogiec and M. Olson and D. Orris and R. Ostojic and T. Page and C. Park and T. Peterson and R. Pilipenko and A. Pla-Dalmau and V. Poloubotko and M. Popovic and E. Prebys and P. Prieto and V. Pronskikh and D. Pushka and R. Rabehl and R. E. Ray and R. Rechenmacher and R. Rivera and W. Robotham and P. Rubinov and V. L. Rusu and V. Scarpine and W. Schappert and D. Schoo and A. Stefanik and D. Still and Z. Tang and N. Tanovic and M. Tartaglia and G. Tassotto and D. Tinsley and R. S. Tschirhart and G. Vogel and R. Wagner and R. Wands and M. Wang and S. Werkema and H. B. White Jr. and J. Whitmore and R. Wielgos and R. Woods and C. Worel and R. Zifko and P. Ciambrone and F. Colao and M. Cordelli and G. Corradi and E. Dane and S. Giovannella and F. Happacher and A. Luca and S. Miscetti and B. Ponzio and G. Pileggi and A. Saputi and I. Sarra and R. S. Soleti and V. Stomaci and M. Martini and P. Fabbricatore and S. Farinon and R. Musenich and D. Alexander and A. Daniel and A. Empl and E. V. Hungerford and K. Lau and G. D. Gollin and C. Huang and D. Roderick and B. Trundy and D. Na. Brown and D. Ding and Yu. G. Kolomensky and M. J. Lee and M. Cascella and F. Grancagnolo and F. Ignatov and A. Innocente and A. L'Erario and A. Miccoli and A. Maffezzoli and P. Mazzotta and G. Onorato and G. M. Piacentino and S. Rella and F. Rossetti and M. Spedicato and G. Tassielli and A. Taurino and G. Zavarise and R. Hooper and D. No. Brown and R. Djilkibaev and V. Matushko and C. Ankenbrandt and S. Boi and A. Dychkant and D. Hedin and Z. Hodge and V. Khalatian and R. Majewski and L. Martin and U. Okafor and N. Pohlman and R. S. Riddel and A. Shellito and A. L. de Gouvea and F. Cervelli and R. Carosi and S. Di Falco and S. Donati and T. Lomtadze and G. Pezzullo and L. Ristori and F. Spinella and M. Jones and M. D. Corcoran and J. Orduna and D. Rivera and R. Bennett and O. Caretta and T. Davenne and C. Densham and P. Loveridge and J. Odell and R. Bomgardner and E. C. Dukes and R. Ehrlich and M. Frank and S. Goadhouse and R. Group and E. Ho and H. Ma and Y. Oksuzian and J. Purvis and Y. Wu and D. W. Hertzog and P. Kammel and K. R. Lynch and J. L. Popp},
+  title       = {Mu2e Technical Design Report},
+  abstract    = {The Mu2e experiment at Fermilab will search for charged lepton flavor violation via the coherent conversion process mu- N --> e- N with a sensitivity approximately four orders of magnitude better than the current world's best limits for this process. The experiment's sensitivity offers discovery potential over a wide array of new physics models and probes mass scales well beyond the reach of the LHC. We describe herein the preliminary design of the proposed Mu2e experiment. This document was created in partial fulfillment of the requirements necessary to obtain DOE CD-2 approval.},
+  date        = {2015-01-21},
+  eprint      = {1501.05241v2},
+  eprintclass = {physics.ins-det},
+  eprinttype  = {arXiv},
+  file        = {:http\://arxiv.org/pdf/1501.05241v2:PDF},
+  keywords    = {physics.ins-det, hep-ex},
+}
+
+@Article{comettdr,
+  author    = {R Abramishvili and G Adamov and R R Akhmetshin and A Allin and J C Ang{\'{e}}lique and V Anishchik and M Aoki and D Aznabayev and I Bagaturia and G Ban and Y Ban and D Bauer and D Baygarashev and A E Bondar and C C{\^{a}}rloganu and B Carniol and T T Chau and J K Chen and S J Chen and Y E Cheung and W da Silva and P D Dauncey and C Densham and G Devidze and P Dornan and A Drutskoy and V Duginov and Y Eguchi and L B Epshteyn and P Evtoukhovitch and S Fayer and G V Fedotovich and M Finger Jr and M Finger and Y Fujii and Y Fukao and J L Gabriel and P Gay and E Gillies and D N Grigoriev and K Gritsay and V H Hai and E Hamada and I H Hashim and S Hashimoto and O Hayashi and T Hayashi and T Hiasa and Z A Ibrahim and Y Igarashi and F V Ignatov and M Iio and K Ishibashi and A Issadykov and T Itahashi and A Jansen and X S Jiang and P Jonsson and T Kachelhoffer and V Kalinnikov and E Kaneva and F Kapusta and H Katayama and K Kawagoe and R Kawashima and N Kazak and V F Kazanin and O Kemularia and A Khvedelidze and M Koike and T Kormoll and G A Kozlov and A N Kozyrev and M Kravchenko and B Krikler and G Kumsiashvili and Y Kuno and Y Kuriyama and Y Kurochkin and A Kurup and B Lagrange and J Lai and M J Lee and H B Li and R P Litchfield and W G Li and T Loan and D Lomidze and I Lomidze and P Loveridge and G Macharashvili and Y Makida and Y J Mao and O Markin and Y Matsuda and A Melkadze and A Melnik and T Mibe and S Mihara and N Miyamoto and Y Miyazaki and F Mohamad Idris and K A Mohamed Kamal Azmi and A Moiseenko and M Moritsu and Y Mori and T Motoishi and H Nakai and Y Nakai and T Nakamoto and Y Nakamura and Y Nakatsugawa and Y Nakazawa and J Nash and H Natori and V Niess and M Nioradze and H Nishiguchi and K Noguchi and T Numao and J O'Dell and T Ogitsu and S Ohta and K Oishi and K Okamoto and T Okamura and K Okinaka and C Omori and T Ota and J Pasternak and A Paulau and D Picters and V Ponariadov and G Qu{\'{e}}mener and A A Ruban and V Rusinov and B Sabirov and H Sakamoto and P Sarin and K Sasaki and A Sato and J Sato and Y K Semertzidis and N Shigyo and Dz Shoukavy and M Slunecka and D St<53>ckinger and M Sugano and T Tachimoto and T Takayanagi and M Tanaka and J Tang and C V Tao and A M Teixeira and Y Tevzadze and T Thanh and J Tojo and S S Tolmachev and M Tomasek and M Tomizawa and T Toriashvili and H Trang and I Trekov and Z Tsamalaidze and N Tsverava and T Uchida and Y Uchida and K Ueno and E Velicheva and A Volkov and V Vrba and W A T Wan Abdullah and P Warin-Charpentier and M L Wong and T S Wong and C Wu and T Y Xing and H Yamaguchi and A Yamamoto and M Yamanaka and T Yamane and Y Yang and T Yano and W C Yao and B Yeo and H Yoshida and M Yoshida and T Yoshioka and Y Yuan and Yu V Yudin and M V Zdorovets and J Zhang and Y Zhang and K Zuber and},
+  journal   = {Progress of Theoretical and Experimental Physics},
+  title     = {{COMET} Phase-I technical design report},
+  year      = {2020},
+  month     = {mar},
+  number    = {3},
+  volume    = {2020},
+  doi       = {10.1093/ptep/ptz125},
+  publisher = {Oxford University Press ({OUP})},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
 
 @Comment{jabref-meta: grouping:

r15a_xray/xray.tex

@@ -1,4 +1,4 @@
-\documentclass[11pt]{article}
+\documentclass[linenumbers]{revtex4-1}
 \usepackage{mhchem}
 \usepackage{booktabs}
 \usepackage{multirow}
@@ -10,14 +10,13 @@
   detect-weight=true,
   per=slash,
   detect-family=true,
-  separate-uncertainty=true]{siunitx}
+  separate-uncertainty=true,multi-part-units=single]{siunitx}
 % \usepackage{listings}
 \usepackage[dvipsnames]{xcolor}
 \usepackage{upquote}
 
 \usepackage[framemethod=tikz]{mdframed}
 \usepackage{adjustbox}
-
 % \definecolor{greybg}{rgb}{0.25,0.25,0.25}
 % \definecolor{yellowbg}{rgb}{0.91, 0.84, 0.42}
 % \definecolor{bananamania}{rgb}{0.98, 0.91, 0.71}
@@ -48,8 +47,12 @@
 % \DeclareSIUnit\eVperc{\eV\per\clight}
 % \DeclareSIUnit\clight{\text{\ensuremath{c}}}
 
+\newcommand\bigO[1]{$\mathcal{O}(#1)$}
+\newcommand{\twoPoneS}{$2p-1s$}
+\newcommand{\threePoneS}{$3p-1s$}
+
 \begin{document}
-\title{Muonic X-rays from aluminum, titanium, ...}
+\title{Muonic X-rays from aluminum, titanium, \ldots}
 \author{Nam H. Tran \\ Boston University}
 \date{\today}
 \maketitle