Higgs Modeling using EXPER and Weak Fusion. by Woody Stanford (c) 2016 Stanford Systems.

Transcription

1 iggs Modeling using EXPER and Weak Fusion by Woody Stanford (c) 2016 Stanford Systems. Introduction The EXPER roject, even though its original findings were inconclusive has lead to various ideas as to how the models generated in the original comuter simulations could be used to generate models of other articles. We would recommend reading Understanding EXPER to get a good overview of what the roject was about. In a nutshell... The EXPER series of comuter simulations were designed to exlore the ossibility of structural wave functions (ψ s ) exlaining subatomic henomena. Various geometric models were hyothesized that would have a chance at exlaining mass, energy and the four fundamental forces of nature. These were then taken though various FEM/FEA simulations on a 5 dimensional domain, and the results were interesting. The original EXPER simulations centered around bringing (rimarily) u uark models into close roximity to each other and studying the C/D interference atterns of the matter waves with the intent of exlaining the extreme mass increase during the formation of a W Boson, the force-carrier for the nuclear weak force. An Idea We roduced a W Boson model through interference and interaction of matter waves, so uon further contemlation, we figured, is there a way of roducing more comlex models using the more fundamental models? The iggs Boson was a natural choice for construction. But how do you roduce a iggs? Colliders and EXPER Even though imossible in reality, the bringing of uarks (and other articles) into closer and closer roximity to each other is reminiscent of the rocess that takes lace in real-life atom smashers ; that an EXPER simulation could be a tiny fraction of a collision is hard to dismiss when working with it. In fact, it was the exeriences with ATLAS and the LC that caused me to think of structural wave functions in the first lace. QM and QFT are mathematical models of reality, but in the area of emirical exerimentation, I believe that a hysicist is left thinking These things are real. They either hit or miss each other. I wonder what they actually are. Possible iggs Production Modes

2 Rather than build a comlicated mathematical model to try to figure out a iggs, we decided to take an emirical aroach. ow can iggs bosons be roduced in real life, like in a collider? The first aroach we looked at was exressed in the following Feynman diagram: V iggs Strahlung We figured we had a mechanism for the simulation of a small set of uarks and antiuarks, so we should be able to fuse two to roduce the conditions necessary to roduce a iggs (the in the above diagram). owever, we realized that EXPER isn't currently owerful enough to simulate this tye of interaction. Our second otion was something called gluon fusion : X g t Unfortunately, our exlorations into isolating the gluon wave function in such a way as to interact it was beyond our caability again. Enter otion number 3: Weak Fusion : X Gluon Fusion V V Weak Boson Fusion

3 Since one of EXPER's initial goals was the investigation of W Bosons AND we had various uark models, we felt that this was (1) within the caabilities of EXPER's simulation and (2) we felt we had a good concetual handle on how the interaction should go with structural wave functions. Our Strategy We figured that we could roduce and isolate 2 W boson models, and then interact them with a small Y-axis ositional translation such that it energetically minimized the mass wave function. This would lead to the fusion of two W bosons, and the aearance of a iggs Boson. To correlate this with current science, we decided to look at the masses of the various articles involved. We decided, based on the dynamics of the interaction, to look at the ratio of masses of the various intermediate articles reuired to roduce our iggs model and reort on that. Imlementation of our Strategy The imlementation reuired considerable rework of EXPER:exer6b (exer6.c). That we felt we had roduced a good attern for a W boson in the original EXPER didn't change the fact that we hadn't ulled the article out of the interaction as a stand-alone model. As not to corrut our original code base, we worked on a coy of exer6.c that we named higgs.c (EXPER:higgs). So we came u with a lan, based on regions of comlex mass loss to ma those areas linearly to a second FEM array (fem2). This was difficult to do as the arrays are each 512 Megabytes in size and reuired extensive code dulication to imlement. ere is a sniet of code that exlains how we transferred the isolated W model to the secondary array: //IGGS: we isolate the W Boson by writing the intersection of the two us to the secondary FEM array if ((fem[x][y][z]!=0.00)&&(wf[slot][limitwf((int)(wf_x ))]*sf)!=0.00) utelement2(x,y,z,fem[x][y][z]+wf[slot][limitwf((int)(wf_x ))]*sf); //End of iggs secific code The only way this would work is if we could have regions of the fem eual to zero. We did this by removing the charges from the uarks involved (since we weren't too concerned about EM) and this rovided us the mask necessary to isolate the W Boson structural wave function. Once we isolated a single W Boson, we cleared the rimary FEM array (fem) and rendered a coy of it to the rimary array. We then calculated its real and comlex mass values. To achieve weak fusion, we added (ie. C/D interfered) the W Boson to the rimary array but with a -20 unit Y-axis translation based on our best guess as to how such an interaction would work in our system. This lead to a more comlex region of interference of the mass waves that was consistent with our redictions of what the iggs would look like. At this oint we calculated its real and comlex mass values.

4 Code Examle of Main Loo //for (a=90;a>0;a ) //{ a=0; //single iteration forming good u model clear_fem(); clear_fem2(); render_to_fem(0,200 a,200,200,&dummy1,&dummy2); //u uark to center of array //calculate comlex mass of FEM rintf("\ncomlex mass of U: %E MU\n\n",calculate_comlex_mass()); a=45; //single iteration forming good W Boson at intersection of two us clear_fem(); clear_fem2(); render_to_fem(0,200 a,200,200,&dummy1,&dummy2); //u uark to off center left of array render_to_fem(0,200+a,200,200,&dummy1,&dummy2); //u uark to off center right of array rintf("\n"); snashot("snashot_w_6",a); //create snashot of actual interaction //IGGS: snashot of isolated W Boson snashot2("snashot_fem2.bm"); //transfer fem2 to fem clear_fem(); //clear main fem array addfem(0); //add the w boson model to the main array rintf("\ncomlex mass of W Boson: %E MU\n\n",calculate_comlex_mass()); addfem(20); //add the w boson model again but with a y translation of 20 units rintf("\ncomlex mass of iggs: %E MU\n\n",calculate_comlex_mass()); //create snashot of W W interaction snashot("snashot_higgs_",20); // } This is the main loo for higgs.c. It has a run time of just a few minutes and encasulates the exeriment well. Basically what it does is it renders an u uark model and comutes its comlex mass. Then it renders two u uarks at a distance of searation of 155 units (200-45=155 units) leading to an intersection that is the W Boson model. The W is then isolated to the fem2 array. To comute its comlex mass, we clear fem and add the W Boson model back to fem and then comute its' comlex mass. (We did this so we didn't have to rewrite our comlex mass calculator). To erform the weak fusion, we add the W Boson model a second time (with the Y-axis translation) over the revious W Boson model. Then we calculated the comlex mass of our newly constructed iggs model.

5 The Results ere is a raw dum of the simulation: Starting Exeriment #6b_iggs... Rendering Particle 0 to 3D FEM array: Working...done Comlex mass of U: E+07 MU Rendering Particle 0 to 3D FEM array: Working...done Rendering Particle 0 to 3D FEM array: Working...done Snashot taken through XY Plane (0,0,400,400) thru z=200 lane of the FEM model Snashot taken through XY Plane (0,0,400,400) thru z=200 lane of the FEM2 model Rendering FEM2 to 3D FEM array: Working...done Comlex mass of W Boson: E+07 MU Rendering FEM2 to 3D FEM array: Working...done Comlex mass of iggs: E+08 MU Snashot taken through XY Plane (0,0,400,400) thru z=200 lane of the FEM model The results that we are reorting here is the comlex mass differential between our W Boson model and our iggs model. Comlex Mass of W Boson: 9.19 x 10 7 units Comlex Mass of iggs Boson: x 10 7 units Which leads to a ercentage difference in comlex mass between our two models of 50.2% Comarison with Acceted Values Luckily, we live in a time when both the mass of the W and the iggs are known. The mass of the W Boson is aroximately 80 Gev, and the mass of the iggs Boson is aroximately 125 Gev. This is a mass ratio of 80:125, or the iggs is 56.25% heavier than the W. These values are in rough agreement: 50.2% (simulated) versus 56.25% (actual) and we consider it a good correlation. Potential Sources for Error - The models are really blocky in that we only have about units er article node. - The version of the structural wave function used in simulation is a trigonometric aroximation of a higher derivative. We also think there are some issues on node transition (reference the artifacting in the images taken of our simulations).

6 - the linkage in reasoning of comaring raw comlex mass values directly is missing. ow we are exlaining it is that in the case of the bosons involved that their real masses are the direct result of D- mode loss and thus we can tentatively comare just these two values in this secific case. Downloading iggs.zi This exeriment is not art of the original EXPER ackage, but can be downloaded as exer_higgs.zi from the VERTEX age on the Stanford Systems web site at htt://woodystanford.wordress.com. It runs from a makefile under both Windows and UNIX. If you have any uestions of concerns, feel free to contact me via at woodystanford@yahoo.com. Thank you.

7 Aendix A Outut Images of Interest snashot_w_6_45.bm 2D Slice thru center of FEM array showing two u uarks in close roximity. We believe the W Boson forms at their intersection (the interference atterns in the center) snashot_fem2.bm 2D Slice thru center of FEM2 array showing isolated region of interest: our constructed W Boson model. Artifacting we think caused by coding weakness.

8 snashot_higgs_20.bm 2D Slice thru center of FEM array showing result of weak fusion. This is our iggs boson model. The white circles are the 2 sets of 2 uarks necessary to roduce the interaction. We also think it is sherical.

9 Aendix B iggs Production Modes Possible iggs Production Modes X g t V V X Gluon Fusion Weak Boson Fusion V t t iggs Strahlung tt Introduction to Electroweak theory and iggs-boson hysics at the LC, Carlo Oleari, Universit`a di Milano-Bicocca, Milan. GGI, Firenze, Setember 2007

10 Aendix C Predicted versus Simulated Predicted iggs Boson Structural Wavefunction Simulated iggs Boson Structural Wavefunction

11 Aendix D Comarison of W and iggs Structural Wave Functions W Boson Versus iggs W Boson (M=80 Gev) iggs Boson (M=125 Gev)

12 Aendix E Comarison with other Comlex Models 0.89 fm Down Quark U Quarks Proton7 Mass Distribution Positive Mass Negative Mass Mass Close to Zero A Baryon (a roton model) constructed by interfering 3 uark models of the aroriate flavors (UUD). Comare to Boson functions.

13 Note: we recently came across what we noticed were some minor corrutions in our code base that caused some concerns about the factual foundation for this aer. But, after running several tests on the comlete system, we are still confident of the over-all ideas resented in here. If you should come across any bugs in higgs.c, lease let us know and any hel or suggestions would be welcomed as to how to correct them and make the rogram better.