MainPage:Nuclear:Summer2017:Dannie
Pion and Kaon Strucutre Function
Abstract
- Pions and kaons are some of the main building blocks of nuclear matter and are connected to the Goldstone modes of dynamical chiral symmetry breaking, the mechanism thought
to generate all hadron mass in the visible universe. Because little is known about differences in distribution of quarks and gluons between pions, kaons, and nucleons doubt exists concerning the behavior of the pion's valence quark structure function at large xbj while virtually nothing is known about gluons. The Electron-Ion Collider could provide access to a range of kinematics through which pion and kaon form factors and structure functions could be probed. Over this range, differences in gluon content should become discernible and assumptions in extracting structure functions and form factors could be studied. In the design of such an experiment, feasibility studies and optimization tests for detector design play a critical role. Using Monte Carlo Simulations, suitable kinematics ranges for data collection were evaluated. Additionally, detector simulations allow for determining detector efficiency as well as design optimizations. I will present the prospects of pion and kaon structure function measurements at EIC.
Introduction
What exactly is mass? And where does it come from? In order to answer these deceptively simple questions, matter must be broken down and understood on the smallest levels. Within an atom the major of mass is concentrated in the nucleus while the rest of the atom is mostly free space. To put this in context, if an atom were the size of a football field, the nucleus (the most massive part) would only be the size of a football and electrons would be the size of dinner peas. This means that all matter is mostly free space... yet the universe around us does have mass. As we keep studying mass at smaller scales we uncover more and more conundrums surrounding mass like this.
Even smaller than the atomic level, physicists strive to understand mass on the quantum scale. The study of interactions between quarks and gluons (the partons that make up the protons, neutrons, and electrons of the atom) is called Quantum Chromodynamics. It is under this field of study that this project seeks to elucidate the details of quark gluon interaction and how they contribute to mass. In order to better understand these interactions, pions and kaons are studied for two main reasons. First, as mesons (containing two quarks), these particles are simpler to study and understand than baryons. Secondly, these particle exhibit odd behaviors in terms of mass. As Goldstone bosons, pions and kaons by definition should not have mass, yet they do. It seems logical then that this mysterious mass might be coming from these particle's two constituent quarks. However, when the mass of the quarks are added together, the total constituent mass is greater than the measured mass of the particle. This problem is not just unique to pions and kaons; in fact the the constituent quarks’ mass off protons and neutrons only accounts for ~1% of these baryons’ total mass.
Not only must these discrepancies in mass be explained, however the very origin of most mass remains enigmatic. Arising from the interactions between quarks and massless gluons, the creation of 98% of all mass is still not well understood.
To study quantum interactions, essentially a "microscope" is needed. Such an instrument is currently in the design phases and is called the Electron Ion Collider. From the collision of two beams (a proton and ion beam), the resulting collisions will be studied. An exemplary scattering event is displayed below. From the beam collision as shown there are many possible particles and kinematics that could result, however only interactions creating pions and kaons are of interest in this project. By cutting out all other events that don’t engender a pion or kaon, specific properties of these particles can be determined and used to determine mass in various energy ranges.
Before the EIC is built however, first feasibility studies must occur. In order to conduct feasibility studies, a Monte Carlo simulation of the experiment results over one year is run. If the resulting error bars are said to be reasonable, the experiment is feasible. Additionally, detector design must be optimized to ensure the correct particles can be measured in certain kinematic ranges. This is done using the Geant 4 Monte Carlo (GEMC) program.
Methods
Monte Carlo Simulation
Basic Overview
The Monte Carlo Simulation utilizes random number generation to calculate kinematic quantities (ie angle and momentum) of many scattered particles. Cuts are then implemented to ensure that only data corresponding to scattered pions and kaons passes through. Important values from the data on pions and kaons are calculated like the structure function of pions and kaons in various energy and momentum ranges.
How To Open/Launch the Simluation
TDISMC_EICK.cpp is the c++ file for working with kaons. TDISMC_EIC.cpp is the c++ file for working with pions. TDISMC_EICK.h is the header file for working with kaons. TDISMC_EIC.h is the header file for working with pions. To edit the number of events enter the header file and change the value of NEvts. Typically 35000 was used. Then, in the command line type "root -l batchk.cc"
To work directly from an already generated root file of the simulation, type "root -l readingroot.C". Make sure to change the TFile to the correct directory and name of the root file. This method of working directly through root file allows data to be analyzed in different ways without having to rerun the simulation each time. It allows faster fixing of errors, checking of values, and making of graphs.
GEMC Detector Optimization Design
Details and Changes to Simulation
Variables in readingroot.C
xBj= Bjorken variable
Q2= energy
t= four momentum transfer
F2kMean/f2NMean= mean of structure function in cuts
i, j, k = loop variables for xbj cuts, q2 cuts, and t cuts
delX, delQ2, delt= width of bins
fLuminosity= luminosity
uncerVal= uncertainty value
Tka, invts.xBj, invts.Q2 = data sets for tka, xBj, and Q2
mgt (Multigraph) and f2NMeantka(TGraphError)= for tka vs F2NMean graph
Mgq2 (Multigraph) and fGf2N (TGraphError)= for Q2 vs f2KMean graph
_binsq2 = binning for Q2 vs f2NMean
_binst= binning for t vs f2NMean
ncuts_4q2= number of bins for Q2 vs f2NMean
ncuts_4t= number of bins for t vs f2NMean
Variables in TDISMC_EICK.C
xBj= Bjorken variable
Q2= energy
t= four momentum transfer
F2kMean/f2NMean= mean of structure function in cuts
i, j, k = loop variables for xbj cuts, q2 cuts, and t cuts
delX, delQ2, delt= width of bins
lum= luminosity
uncerVal= uncertainty value
TData, xBjData, Q2Data, F2NData = data sets for tka, xBj, Q2, and F2N
mgt (Multigraph) and f2NMeantka(TGraphError)= for tka vs F2NMean graph
mg (Multigraph), Gf2NQ2 (TGraphError), CG(canvas)= 2D points for Q2 vs f2KMean graph
mg3D(Multigraph), line3d (TGraphErrors), CG3Dl (canvas) = 3D lines for Q2 vs f2KMean graph
g1(TGraph2DErrors), CG3Dp(canvas)= 3D points for Q2 vs f2kMean graph
_binq2 = binning for Q2 vs f2NMean
_bint= binning for t vs f2NMean
_numq2= number of bins for Q2 vs f2NMean
_numt= number of bins for t vs f2NMean
Major Changes Made to Simulation
- The mean of the structure function (F2kMean and f2NMean) are calculated directly using TMath rather than creating a histogram and takings its mean
- mean of a histogram changes with bin number
- uncertainty calculations in .cpp and .h files changed to match calculations in readingroot.C
- unc= lum*∆Q2*∆X*√N/N (*∆t for tka graphs)
- filter out nan (not a number) results for structure function mean
- results from a point in F2N=nan or a bin containing 0 points
- if f2nmean/F2kMean is nan for any reasons listed above, the points is not graphed
- 3D graphs for better visualization were added to TDISMC files but not root files
- tpi and tka were transformed over the y axis (multiplied by -1)
Where I'm Leaving off:(
Kijun has promised a copy of his uncertainty code to look over. Meanwhile I've been reading over the EIC GEMC wiki and trying to understand how exactly it works (where are the .pl files??). Additionally, a newer version of root should fix errors with 3D graphs where axis ranges are unchangeable and titles cannot be added. Ideally the 3D scatter and 3D line graphs for F2kmean and t and F2kmean and x should be consolidated into one line graph with error bars. My final versions of TDISMC_EICK.cpp, TDISMC_EICK.h, TDISMC_EIC.cpp, TDISMC_EIC.h, and readingroot.C were sent via email to Dr. Horn, Richard, Andres, and Salina.