Date: Thu, 28 Mar 2024 10:42:16 -0400 (EDT)
Message-ID: <2105600528.2835.1711636936523@3844c1e05b81>
Subject: Exported From Confluence
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This project uses virtual =
reality (VR) and other visualization tools to model the mechanical and quan=
tum mechanical properties of the partons inside the proton. The quark=
and gluon dynamics are responsible for more than 98% of all mass around us=
. Still, it is not clear how this motion manifests and how the energy densi=
ty and composition of the proton changes under various states. For ex=
ample, the proton can be polarized so the spin is oriented along some parti=
cular axis. This will naturally change the dynamics and the partons s=
tate as well. Quarks and gluon=
s can spin, and can have linear and circular motion, and can appear and dis=
appear continuously and sporadically. This project has two overarchin=
g goals. One is to visualize the complex internal structure of the pr=
oton. We intend to do this with Unity-based VR with help from other t=
ools like Blender, and Niagara from unreal engine 5, and other ways to test=
and explore visualizing this information. The second goal is to deve=
lop a detailed and accurate simulation of these dynamics and the proton's i=
nternal structure using data from experiments, lattice QCD, and phenomenolo=
gy. These simulations should be able to evolve in time and should be =
able to contain much of what we presently understand about the proton's ins=
ides, like charge variations, flux tube geometry, the density of sea-quarks=
, and gluons at various Q2 and momentum fractions. In the end,=
these two goals should be merged and the visualization studio should be co=
mbined with the simulation and modeling package.
For the VR visualization studio, we are still testing and exploring but =
the basic approach is to develop assets =
using 3D modeling =
of quantum mechanical objects in a somewhat classical and intuitive represe=
ntation while also utilizing standard and costume =
span>phys=
ics engine capabilities.=
The development of a specialized physics engine to manage the electr=
icity and magnetism, the energy and momentum, and the color charge will be =
required. There are also many quantum mechanical dynamics that requir=
e a costume physics engine. Right now the platform is Oculus Quest 2,=
but we are likely going to need more computational power to achieve the lo=
ng-term goals.
You can learn about some aspects of the experimental effort and the piec=
ing of these results together here:
Some details on how information is extracted experimentally for the futu=
re:
https://www.bnl.gov/eic/rhic-eic-comparison.ph=
p
https://indico.cern.ch/event/797767/contributions/3682425/a=
ttachments/1965703/3268608/BNL-EIC_Mumbai_2020.pdf
A write-up by Jinge Zhou discusses some hypothetical ways to address som=
e of the goals of the Unity Project:
A high-level write-up to introduce some of the basic goals of the Unity =
Project:
The repository of the project is here:
https://github.com/uva-spin/VR-Unity/
The group Discord page is here:
https://discord.gg/pwExfsum
Other reading about models:
https://physicstoday.sci=
tation.org/doi/10.1063/PT.3.4743
https://physicstoday.sci=
tation.org/doi/10.1063/PT.3.4871
On Projects:
Layer 1: Three valance quarks orbiting inside the proton. Th=
eir dynamics are largely random following a turbulent path driven by quantu=
m fluctuations and
momentum as well as the tension that binds them together. These ar=
e called flux tubes. When polarized the dynamics are much more orderl=
y and follow a
path around the center of the proton. A swarm of gluons exists in =
the space around the valance quarks along with sea-quarks with are virtual =
quarks that pop
in and out of existence continuously.
Physics Implementation:
Flux tube (String) tension on quarks
Flux tube pushing away gluon swarm
forces between gluons and quarks
forces between gluons and gluons
Electricity and magnetism between all quarks
Layer 2: Here we want to zoom in on a region, either a valance qua=
rk, a flux tube region, the edge of the proton, or an open region where sea=
-quarks and gluons
are swarming.
Layer 3: In this layer, we are zoomed in even further than any other one=
. Things are so zoomed in on the quantum fluctuations that the gluons=
start to look like
an ever-evolving network connected into space that continuously fluctuat=
es varying in gluon density creating a massive network of interacting gluon=
s in some regions and low-density pockets in other regions.
Status video:
https://d=
rive.google.com/file/d/11u1zmO5MYS-LrW_mVfVrKlADVq_nACMT/view?usp=3Dsharing=
Description of Pa=
rton Dynamics
This tool is intended for the visualization of different models of dynam=
ics so we ultimately want to be able to switch between the various models u=
sing the UI.
The f=
ollowing is true for all models:
Forces: There is a centrifugal force on the quarks=
as they orbit with some momentum. This force should manifest natural=
ly due to the fact that the quarks have some intrinsic energy which means t=
hey must be given an initial momentum. There is the color charge forc=
e (strong force) which is the flux tube that binds the quarks together.&nbs=
p; There is electricity and magnetism that are applied to all of the charge=
d quarks. Th=
e force between valance quarks should go as F(r)=3DAr+BrCr. In other words,=
at small r where the quarks=
are close together, there is a spring constant A. As r gets bigge=
r (beyond the diameter of the proton) then the attractive force gets strong=
er and stronger very fast (try A=3D0.3, B=
=3D0.1 C=3D2.9). The sea quarks should go as F(r)=3Da/r2+b where =
r is again the distance between them. Both a&nb=
sp;and =
;b are constants that play=
a role in the spatial region that each term kicks in. The sea quarks actually u=
ndergo a gluon-mediated scattering interaction governed by an inverse squar=
e law just like Coulomb=E2=80=99s law. The difference is that there=E2=80=
=99s a second term in the equation, and it=E2=80=99s a constant. Regardless of the distance between them, two =E2=80=9Cunpaired=
=E2=80=9D quarks will be attracted to each other with a constant force on t=
op of the inverse square law which is 137 times stronger than the electroma=
gnetic force. So a is 137 times the scale of the for=
ce between two charges (Coulomb's Law) and b should be on =
the same scale as a. Here I've provided some startin=
g parameters but we should have these parameters be something that we can c=
hange in our menu by at least 10%.
FluxTubes: Quarks are connected via the flux tubes.&nbs=
p; The flux tube can be modeled as just a string holding the valence quarks=
together. The three valence quarks should be orbiting around the cen=
ter of the proton with a momentum that wants to send them flying off but th=
e string tension of the flux tube keeps them bound to each other. The=
string tension and the valence quark momentum should be control parameters=
that can be changed in the UI. The flux tube should get smaller (nar=
rower) as its stretches and the tension tighten. The flux tube is a t=
hree-dimensional geometry that has an empty volume inside. Gluons can=
pass through the volume changing the color of the quarks as they make an e=
xchange. This happens exactly the same in both valence and sea quarks=
. The valence will always have three flux tube arms while the sea can=
have two or three or more but normally only two.
Gluons: Each Gluon has two colors as indicated on=
the Wikipedia page under Color Charge. All combinations of gluon col=
ors should be represented. There are three colors and three anti-colo=
rs red, gluon, blue, and anti-red, anti-green, and anti-blue. You can=
use the same color representation as what you see on Wikipedia. Each gluon=
can float around and interact with other gluons and quarks. Gluons c=
an attract one another and annihilate turning into two photons. They =
can only annihilate if the total color charge of the two gluons is color-ne=
utral. Only gluons that can form white will interact. For example, a =
red and anti-red can interact with another red and anti-red gluon. Th=
ree gluons all of different colors can form two color-neutral states. =
In this way, gluons can interact with each other to make pure gluon states=
. Other than that all they do is swarm around and interact with the q=
uarks. When they make contact, they can bounce off each other =
changing from attracting to repelling, or they can pass right through each =
other. When the gluon density is large more sea quarks pop in and out=
of the vacuum. Space is full of fluctuating waves/swarms of gluons i=
ncreasing and decreasing the likelihood of QCD making something happen.&nbs=
p; The gluons continuously pop in and out of existence but the swarm is alw=
ays present. As the flux tubes move in space they clear out the fluct=
uating gluons in the vacuum. The probability of gluon sea-quark inter=
action is inversely proportional to the sea-quark virtuality.
Quarks: The quarks are charged so besides the col=
or force there is an electromagnetic force as well. This is true for =
the sea quarks and valence quarks. The Up quark has a charge of +2/3,=
and the Down quark is -1/3. This is important in the physics of thei=
r dynamics because when charges move, they make magnetic fields. &nbs=
p; The force from the electromagnetic charge scales as 1/r^2, where r is th=
e distance between the quarks (charges). The color force on the other=
hand does not diminish as fast over distance, it is the same between quark=
s but will normally only act between two (sea-quarks) or three (valence qua=
rks). The strength of the color force is roughly 137 times that of th=
e electromagnetic force. When the proton is polarized the orbital motion is correlated to the proton's spin when th=
e proton is not polarized the spin direction is chaotic. The up quark=
and the down quark rotate in opposite directions. The up quark has a=
mass of about 2 MeV while the down quark has a mass of about 4.8 MeV so th=
e up quark is about 2.4 times faster than the down quark. The =
momentum of the quarks is faster when the quarks are closer together in the=
center of the proton and slow when they are farther apart. The valen=
ce quarks orbit the center of the proton with Up and Down going in differen=
t directions but also following chaotic and wild paths when unpolarized.&nb=
sp; Polarized protons have much more order with the valence quarks always o=
rbiting the central axis. The sea quarks can also orbit the central a=
xis and follow and interact with the valence quarks. There are sum-ru=
les that govern the exchange between orbital angular momentum, and partonic=
spin, and how all of this is shared between all the pieces.
Models of Dynamics<=
/strong>:
Spin Sum Rule: All of the components of parton =
spin and dynamics must lead to a total proton spin of 1/2. Its not po=
ssible to make this work without imposing some model dependence so its very=
important that all the above aspects are addressed first. Since the =
famous EMC experiments revealed that only a small fraction of the nucleon s=
pin is due to quark spins, there has been a great interest in =E2=80=98solv=
ing the spin puzzle=E2=80=99, i.e. in decomposing the nucleon spin into con=
tributions from quark/gluon spin and orbital degrees of freedom. In this ef=
fort, the Ji decomposition:
not only the quark spin contributions ?q but also=
the quark total angular momenta. Charged particles in a magnetic fie=
ld are governed by a velocity EXB an orbi=
tal angular momentum L=3DrXEXB =
strong>where r is the position vector [ref]. This means that the charges will orbit the center of =
the proton in opposite directions. This however is a very classical p=
icture. The terms in the above equation are defined as quantum mechan=
ical expectation values of the corresponding terms in the angular momentum =
tensor. A representation of this decomposition should start with the =
valence quarks and include the intrinsic spin of the quarks that hold the k=
now spin percentage (randomly oriented otherwise). Then the OAM is re=
presented classically as rotating charges in a B-field.
Meson Cloud Model: At any given instant, the proton might really be a neutron (ddu) plus a=
positively charged pion (ud- ud-)=E2=80=94or another proton (uud) plus a neutral pi=
on. This violates energy conserva=
tion but it is allowed, for a fleeting moment, by the Heisenberg uncertaint=
y principle. By adding up the contributions from all the possible channels,=
the theorists can model the composition of the sea.
Constituent Quark: Most basic isospin configuratio=
n.
Pauli-blocking: Pauli exclusion principle suppress=
ed the formation of quarks of a certain color and flavor since two like qua=
nta can not be in the same state.
Effective 4-quark Langrangian: =E2=80=99t Hooft ef=
fective four-quark Lagrangian =
is =E2=80=9Cflavor nondiagonal,=E2=80=9D leading to processes u=E2=86=92u(d=
d-). In a way, the effect is also due to the Pauli exclusion pri=
nciple, but at a different level. Topological tunneling events, known as in=
stantons, create fields so strong that they fix the color and spin states o=
f participating quarks uniquely. Instead of six possibilities, there remain=
s only one, thus a complete blocking. Since the proton has two valence u qu=
arks and only one valence d quark, that mechanism would suggest that the ra=
tio of anti d to anti u is 2 rather than 1.
Sivers Effect: Map the distribution of unpolarized quar=
ks in 3-dimensional momentum space. A simple first test sea quark mod=
el might be to make a single 0++ state with both sea-quark spins=
pointing down and the OAM pointing up. These should orbit the centra=
l axis just like the valence in the pattern extracted from the data. =
We should make the sum rule worked by forcing spin, OAM and momentum be con=
served.
UI and Controls:
We also want a nice User Interface that is transparent so you can still =
see what's going on behind it and provides the option of controlling all of=
the dynamics and
quantum mechanical parameters. This should be able to help the use=
r navigate but also provide analysis tools and plots of the system given va=
rious parameter adjustments.
One example is plotting the Sivers function of the various partons (quar=
ks and gluons). The Sivers function correlates the transverse momentu=
m of the partons with the
polarization of the proton.
Task List and Assignm=
ents:
Member |
Year |
Unity |
Major |
Project |
Team |
Notes |
Duncan Beauch |
3rd year |
Novice |
Physics/CS |
Views and UI and Expanding 3D representation (+ =
physics team work) |
Physics |
|
Wyndham White |
3rd year |
Novice |
Physics/CS |
Unity Fluid simulation tests (+ physics team wor=
k) |
Physics |
|
Bryant Lisk |
2nd year |
Novice |
CS |
gluon-quark/gluon-gluon/fluxtube force |
Modeling |
|
Jared Conway |
2nd year |
2 years |
CS |
Electricity and Magnetism of quarks (Unity EM en=
gine) |
Modeling |
|
Sam Colvin |
2nd year |
Novice |
CS |
Optimization for high particle density |
Modeling |
|
Ethan Hanover |
4th year |
3 years |
CS |
Sea-quark, gluon, fluxtube interactions |
Dynamics/Modeling |
|
Ishan Mathur |
MS student |
|
CS |
CS Integration and communication |
Systems Organization |
|
Ishara Fernando |
Postdoc |
|
Physics |
Physics Integration and communication |
Systems Organization |
|
Liliet Diaz |
Phd student |
|
Physics |
Physics team lead |
Physics |
|
Misc. documents
- GitHub_Steps.pdf
- https://www.uni-muenster.de/Physik.TP/archive/fileadmin/lehre/Quan=
tenmechanik_Friedrich_/book1_01.pdf
- https://arxiv.org/abs/1907.11903
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