Exact solutions of quantum field theories are very rare and, normally, refer to toy models and pathological cases. Quite recently, I put on arxiv a pair of papers presenting exact solutions both of the Higgs sector of the Standard Model and the Yang-Mills theory made just of gluons. The former appeared a few month ago (see here) while the latter has been accepted for publication a few days ago (see here). I have updated the latter just today and the accepted version will appear on arxiv on 2 January next year.

What does it mean to solve exactly a quantum field theory? A quantum field theory is exactly solved when we know all its correlation functions. From them, thanks to LSZ reduction formula, we are able to compute whatever observable in principle being these cross sections or decay times. The shortest way to correlation functions are the Dyson-Schwinger equations. These equations form a set with the former equation depending on the higher order correlators and so, they are generally very difficult to solve. They were largely used in studies of Yang-Mills theory provided some truncation scheme is given or by numerical studies. Their exact solutions are generally not known and expected too difficult to find.

The problem can be faced when some solutions to the classical equations of motion of a theory are known. In this way there is a possibility to treat the Dyson-Schwinger set. Anyhow, before to enter into their treatment, it should be emphasized that in literature the Dyson-Schwinger equations where managed just in one way: Using their integral form and expressing all the correlation functions by momenta. It was an original view by Carl Bender that opened up the way (see here). The idea is to write the Dyson-Schwinger equations into their differential form in the coordinate space. So, when you have exact solutions of the classical theory, a possibility opens up to treat also the quantum case!

This shows unequivocally that a Yang-Mills theory can display a mass gap and an infinite spectrum of excitations. Of course, if nature would have chosen the particular ground state depicted by such classical solutions we would have made bingo. This is a possibility but the proof is strongly related to what is going on for the Higgs sector of the Standard Model that I solved exactly but without other matter interacting. If the decay rates of the Higgs particle should agree with our computations we will be on the right track also for Yang-Mills theory. Nature tends to repeat working mechanisms.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model Eur. Phys. J. Plus (2016) 131: 199 arXiv: 1504.02299v3

Marco Frasca (2015). Quantum Yang-Mills field theory arXiv arXiv: 1509.05292v1

Carl M. Bender, Kimball A. Milton, & Van M. Savage (1999). Solution of Schwinger-Dyson Equations for ${\cal PT}$-Symmetric Quantum Field Theory Phys.Rev.D62:085001,2000 arXiv: hep-th/9907045v1

Filed under: Applied Mathematics, Mathematical Physics, Particle Physics, Physics, QCD Tagged: Correlation functions, Dyson-Schwinger equations, Exact solutions, Exact solutions of nonlinear PDEs, Mass Gap, Quantum Field Theory, Yang-Mills spectrum, Yang-Mills theory ]]>

I hope this will go properly evaluated by the scientific community moving to a more serious addressing of this effect.

**Update**: The links were removed from the subreddit’s moderator. I have copies of these files but I do not mean to publish them in any form.

**Update**: Here is the published paper.

Filed under: Astronautics, News Tagged: Eagleworks Labs, EmDrive, Harold White, NASA ]]>

ATLAS and CMS nuked our illusions on that bump. More than 500 papers were written on it and some of them went through Physical Review Letters. Now, we are contemplating the ruins of that house of cards. This says a lot about the situation in hep in these days. It should be emphasized that people at CERN warned that that data were not enough to draw a conclusion and if they fix the threshold at a reason must exist. But carelessness acts are common today if you are a theorist and no input from experiment is coming for long.

It should be said that the fact that LHC could confirm the Standard Model and nothing else is one of the possibilities. We should hope that a larger accelerator could be built, after LHC decommissioning, as there is a long way to the Planck energy that we do not know how to probe yet.

What does it remain? I think there is a lot yet. My analysis of the Higgs sector is still there to be checked as I will explain in a moment but this is just another way to treat the equations of the Standard Model, not beyond it. Besides, for the end of the year they will reach , almost triplicating the actual integrated luminosity and something interesting could ever pop out. There are a lot of years of results ahead and there is no need to despair. Just to wait. This is one of the most important activities of a theorist. Impatience does not work in physics and mostly for hep.

About the signal strength, things seem yet too far to be settled. I hope to see better figures for the end of the year. ATLAS is off the mark, going well beyond unity for WW, as happened before. CMS claimed for WW decay, worsening their excellent measurement of reached in Run I. CMS agrees fairly well with my computations but I should warn that the error bar is yet too large and now is even worse. I remember that the signal strength is obtained by the ratio of the measured cross section to the one obtained from the Standard Model. The fact that is smaller does not necessarily mean that we are beyond the Standard Model but that we are just solving the Higgs sector in a different way than standard perturbation theory. This solution entails higher excitations of the Higgs field but they are strongly depressed and very difficult to observe now. The only mark could be the signal strength for the observed Higgs particle. Finally, the ZZ channel is significantly less sensible and error bars are so large that one can accommodate whatever she likes yet. Overproduction seen by ATLAS is just a fluctuation that will go away in the future.

The final sentence to this post is what we have largely heard in these days: Standard Model rules.

Filed under: Particle Physics, Physics Tagged: 750 GeV, ATLAS, CERN, CMS, Higgs particle, ICHEP 2016, LHC ]]>

LHCP2016 is running yet with further analysis on 2015 data by people at CERN. We all have seen the history unfolding since the epochal event on 4 July 2012 where the announcement of the great discovery happened. Since then, also Kibble passed away. What is still there is our need of a deep understanding of the Higgs sector of the Standard Model. Quite recently, LHC restarted operations at the top achievable and data are gathered and analysed in view of the summer conferences.

The scalar particle observed at CERN has a mass of about 125 GeV. Data gathered on 2015 seem to indicate a further state at 750 GeV but this is yet to be confirmed. Anyway, both ATLAS and CMS see this bump in the data and this seems to follow the story of the discovery of the Higgs particle. But we have not a fully understanding of the Higgs sector yet. The reason is that, in run I, gathered data were not enough to reduce the error bars to such small values to decide if Standard Model wins or not. Besides, as shown by run II, further excitations seem to pop up. So, several theoretical proposals for the Higgs sector still stand up and could be also confirmed already in August this year.

Indeed, there are great news already in the data presented at LHCP2016. As I pointed out here, there is a curious behavior of the strengths of the signals of Higgs decay in and some tension, even if small, appeared between ATLAS and CMS results. Indeed, ATLAS seemed to have seen more events than CMS moving these contributions well beyond the unit value but, as CMS had them somewhat below, the average was the expected unity agreeing with expectations from the Standard Model. The strength of the signals is essential to understand if the propagator of the Higgs field is the usual free particle one or has some factor reducing it significantly with contributions from higher states summing up to unity. In this case, the observed state at 125 GeV would be just the ground state of a tower of particles being its excited states. As I showed recently, this is not physics beyond the Standard Model, rather is obtained by solving exactly the quantum equations of motion of the Higgs sector (see here). This is done considering the other fields interacting with the Higgs field just a perturbation.

So, let us do a recap of what was the situation for the strength of the signals for the decays of the Higgs particle. At LHCP2015 the data were given in the following slide

From the table one can see that the signal strengths for decays in ATLAS are somewhat beyond unity while in CMS these are practically unity for but, more interestingly, 0.85 for . But we know that data gathered for decay are largely more than for decay. The error bars are large enough to be not a concern here. The value 0.85 is really in agreement with the already cited exact computations from the Higgs sector but, within the error, in overall agreement with the Standard Model. This seems to point toward on overestimated number of events in ATLAS but a somewhat reduced number of events in CMS, at least for decay.

At LHCP2016 new data have been presented from the two collaborations, at least for the decay. The results are striking. In order to see if the scenario provided from the exact solution of the Higgs sector is in agreement with data, these should be confirmed from run II and those from ATLAS should go down significantly. This is indeed what is going on! This is the corresponding slide

This result is striking *per se* as shows a tendency toward a decreasing value when, in precedence, it was around unity. Now it is aligned with the value seen at CMS for the decay! The value seen is again in agreement with that given in the exact solution of the Higgs sector. And ATLAS? This is the most shocking result: They see a significant reduced set of events and the signal strength they obtain is now aligned to the one of CMS (see Strandberg’s talk at page 11).

What should one conclude from this? If the state at 750 GeV should be confirmed, as the spectrum given by the exact solution of the Higgs sector is given by an integer multiplied by a mass, this would be at . Together with the production strengths, if further data will confirm them, the proper scenario for the breaking of electroweak symmetry is exactly the one described by the exact solution. Of course, this should be obviously true but an experimental confirmation is essential for a lot of reasons, last but not least the form of the Higgs potential that, if the numbers are these, the one postulated in the sixties would be the correct one. An other important reason is that coupling with other matter does not change the spectrum of the theory in a significant way.

So, to answer to the question of the title remains to wait a few weeks. Then, summer conferences will start and, paraphrasing Coleman: God knows, I know and by the end of the summer we all know.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model Eur. Phys. J. Plus (2016) 131: 199 arXiv: 1504.02299v3

Filed under: Particle Physics, Physics Tagged: ATLAS, CERN, CMS, Higgs decay, Higgs particle, LHC, Standard Model ]]>

This is a great moment in history of physics: Gravitational waves were directly detected by the merging of two black holes by the LIGO Collaboration. This is a new world we arrived at and there will be a lot to be explored and understood. I do not know if it is for the direct proof of existence of gravitational waves or black holes that fixes this great moment forever in the memory of mankind. But by today we have both!

You can find an excellent recount here. This is the paper

Thank you for this great work!

Abbott, B., Abbott, R., Abbott, T., Abernathy, M., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R., Adya, V., Affeldt, C., Agathos, M., Agatsuma, K., Aggarwal, N., Aguiar, O., Aiello, L., Ain, A., Ajith, P., Allen, B., Allocca, A., Altin, P., Anderson, S., Anderson, W., Arai, K., Arain, M., Araya, M., Arceneaux, C., Areeda, J., Arnaud, N., Arun, K., Ascenzi, S., Ashton, G., Ast, M., Aston, S., Astone, P., Aufmuth, P., Aulbert, C., Babak, S., Bacon, P., Bader, M., Baker, P., Baldaccini, F., Ballardin, G., Ballmer, S., Barayoga, J., Barclay, S., Barish, B., Barker, D., Barone, F., Barr, B., Barsotti, L., Barsuglia, M., Barta, D., Bartlett, J., Barton, M., Bartos, I., Bassiri, R., Basti, A., Batch, J., Baune, C., Bavigadda, V., Bazzan, M., Behnke, B., Bejger, M., Belczynski, C., Bell, A., Bell, C., Berger, B., Bergman, J., Bergmann, G., Berry, C., Bersanetti, D., Bertolini, A., Betzwieser, J., Bhagwat, S., Bhandare, R., Bilenko, I., Billingsley, G., Birch, J., Birney, R., Birnholtz, O., Biscans, S., Bisht, A., Bitossi, M., Biwer, C., Bizouard, M., Blackburn, J., Blair, C., Blair, D., Blair, R., Bloemen, S., Bock, O., Bodiya, T., Boer, M., Bogaert, G., Bogan, C., Bohe, A., Bojtos, P., Bond, C., Bondu, F., Bonnand, R., Boom, B., Bork, R., Boschi, V., Bose, S., Bouffanais, Y., Bozzi, A., Bradaschia, C., Brady, P., Braginsky, V., Branchesi, M., Brau, J., Briant, T., Brillet, A., Brinkmann, M., Brisson, V., Brockill, P., Brooks, A., Brown, D., Brown, D., Brown, N., Buchanan, C., Buikema, A., Bulik, T., Bulten, H., Buonanno, A., Buskulic, D., Buy, C., Byer, R., Cabero, M., Cadonati, L., Cagnoli, G., Cahillane, C., Bustillo, J., Callister, T., Calloni, E., Camp, J., Cannon, K., Cao, J., Capano, C., Capocasa, E., Carbognani, F., Caride, S., Diaz, J., Casentini, C., Caudill, S., Cavaglià, M., Cavalier, F., Cavalieri, R., Cella, G., Cepeda, C., Baiardi, L., Cerretani, G., Cesarini, E., Chakraborty, R., Chalermsongsak, T., Chamberlin, S., Chan, M., Chao, S., Charlton, P., Chassande-Mottin, E., Chen, H., Chen, Y., Cheng, C., Chincarini, A., Chiummo, A., Cho, H., Cho, M., Chow, J., Christensen, N., Chu, Q., Chua, S., Chung, S., Ciani, G., Clara, F., Clark, J., Cleva, F., Coccia, E., Cohadon, P., Colla, A., Collette, C., Cominsky, L., Constancio, M., Conte, A., Conti, L., Cook, D., Corbitt, T., Cornish, N., Corsi, A., Cortese, S., Costa, C., Coughlin, M., Coughlin, S., Coulon, J., Countryman, S., Couvares, P., Cowan, E., Coward, D., Cowart, M., Coyne, D., Coyne, R., Craig, K., Creighton, J., Creighton, T., Cripe, J., Crowder, S., Cruise, A., Cumming, A., Cunningham, L., Cuoco, E., Canton, T., Danilishin, S., D’Antonio, S., Danzmann, K., Darman, N., Da Silva Costa, C., Dattilo, V., Dave, I., Daveloza, H., Davier, M., Davies, G., Daw, E., Day, R., De, S., DeBra, D., Debreczeni, G., Degallaix, J., De Laurentis, M., Deléglise, S., Del Pozzo, W., Denker, T., Dent, T., Dereli, H., Dergachev, V., DeRosa, R., De Rosa, R., DeSalvo, R., Dhurandhar, S., Díaz, M., Di Fiore, L., Di Giovanni, M., Di Lieto, A., Di Pace, S., Di Palma, I., Di Virgilio, A., Dojcinoski, G., Dolique, V., Donovan, F., Dooley, K., Doravari, S., Douglas, R., Downes, T., Drago, M., Drever, R., Driggers, J., Du, Z., Ducrot, M., Dwyer, S., Edo, T., Edwards, M., Effler, A., Eggenstein, H., Ehrens, P., Eichholz, J., Eikenberry, S., Engels, W., Essick, R., Etzel, T., Evans, M., Evans, T., Everett, R., Factourovich, M., Fafone, V., Fair, H., Fairhurst, S., Fan, X., Fang, Q., Farinon, S., Farr, B., Farr, W., Favata, M., Fays, M., Fehrmann, H., Fejer, M., Feldbaum, D., Ferrante, I., Ferreira, E., Ferrini, F., Fidecaro, F., Finn, L., Fiori, I., Fiorucci, D., Fisher, R., Flaminio, R., Fletcher, M., Fong, H., Fournier, J., Franco, S., Frasca, S., Frasconi, F., Frede, M., Frei, Z., Freise, A., Frey, R., Frey, V., Fricke, T., Fritschel, P., Frolov, V., Fulda, P., Fyffe, M., Gabbard, H., Gair, J., Gammaitoni, L., Gaonkar, S., Garufi, F., Gatto, A., Gaur, G., Gehrels, N., Gemme, G., Gendre, B., Genin, E., Gennai, A., George, J., Gergely, L., Germain, V., Ghosh, A., Ghosh, A., Ghosh, S., Giaime, J., Giardina, K., Giazotto, A., Gill, K., Glaefke, A., Gleason, J., Goetz, E., Goetz, R., Gondan, L., González, G., Castro, J., Gopakumar, A., Gordon, N., Gorodetsky, M., Gossan, S., Gosselin, M., Gouaty, R., Graef, C., Graff, P., Granata, M., Grant, A., Gras, S., Gray, C., Greco, G., Green, A., Greenhalgh, R., Groot, P., Grote, H., Grunewald, S., Guidi, G., Guo, X., Gupta, A., Gupta, M., Gushwa, K., Gustafson, E., Gustafson, R., Hacker, J., Hall, B., Hall, E., Hammond, G., Haney, M., Hanke, M., Hanks, J., Hanna, C., Hannam, M., Hanson, J., Hardwick, T., Harms, J., Harry, G., Harry, I., Hart, M., Hartman, M., Haster, C., Haughian, K., Healy, J., Heefner, J., Heidmann, A., Heintze, M., Heinzel, G., Heitmann, H., Hello, P., Hemming, G., Hendry, M., Heng, I., Hennig, J., Heptonstall, A., Heurs, M., Hild, S., Hoak, D., Hodge, K., Hofman, D., Hollitt, S., Holt, K., Holz, D., Hopkins, P., Hosken, D., Hough, J., Houston, E., Howell, E., Hu, Y., Huang, S., Huerta, E., Huet, D., Hughey, B., Husa, S., Huttner, S., Huynh-Dinh, T., Idrisy, A., Indik, N., Ingram, D., Inta, R., Isa, H., Isac, J., Isi, M., Islas, G., Isogai, T., Iyer, B., Izumi, K., Jacobson, M., Jacqmin, T., Jang, H., Jani, K., Jaranowski, P., Jawahar, S., Jiménez-Forteza, F., Johnson, W., Johnson-McDaniel, N., Jones, D., Jones, R., Jonker, R., Ju, L., Haris, K., Kalaghatgi, C., Kalogera, V., Kandhasamy, S., Kang, G., Kanner, J., Karki, S., Kasprzack, M., Katsavounidis, E., Katzman, W., Kaufer, S., Kaur, T., Kawabe, K., Kawazoe, F., Kéfélian, F., Kehl, M., Keitel, D., Kelley, D., Kells, W., Kennedy, R., Keppel, D., Key, J., Khalaidovski, A., Khalili, F., Khan, I., Khan, S., Khan, Z., Khazanov, E., Kijbunchoo, N., Kim, C., Kim, J., Kim, K., Kim, N., Kim, N., Kim, Y., King, E., King, P., Kinzel, D., Kissel, J., Kleybolte, L., Klimenko, S., Koehlenbeck, S., Kokeyama, K., Koley, S., Kondrashov, V., Kontos, A., Koranda, S., Korobko, M., Korth, W., Kowalska, I., Kozak, D., Kringel, V., Krishnan, B., Królak, A., Krueger, C., Kuehn, G., Kumar, P., Kumar, R., Kuo, L., Kutynia, A., Kwee, P., Lackey, B., Landry, M., Lange, J., Lantz, B., Lasky, P., Lazzarini, A., Lazzaro, C., Leaci, P., Leavey, S., Lebigot, E., Lee, C., Lee, H., Lee, H., Lee, K., Lenon, A., Leonardi, M., Leong, J., Leroy, N., Letendre, N., Levin, Y., Levine, B., Li, T., Libson, A., Littenberg, T., Lockerbie, N., Logue, J., Lombardi, A., London, L., Lord, J., Lorenzini, M., Loriette, V., Lormand, M., Losurdo, G., Lough, J., Lousto, C., Lovelace, G., Lück, H., Lundgren, A., Luo, J., Lynch, R., Ma, Y., MacDonald, T., Machenschalk, B., MacInnis, M., Macleod, D., Magaña-Sandoval, F., Magee, R., Mageswaran, M., Majorana, E., Maksimovic, I., Malvezzi, V., Man, N., Mandel, I., Mandic, V., Mangano, V., Mansell, G., Manske, M., Mantovani, M., Marchesoni, F., Marion, F., Márka, S., Márka, Z., Markosyan, A., Maros, E., Martelli, F., Martellini, L., Martin, I., Martin, R., Martynov, D., Marx, J., Mason, K., Masserot, A., Massinger, T., Masso-Reid, M., Matichard, F., Matone, L., Mavalvala, N., Mazumder, N., Mazzolo, G., McCarthy, R., McClelland, D., McCormick, S., McGuire, S., McIntyre, G., McIver, J., McManus, D., McWilliams, S., Meacher, D., Meadors, G., Meidam, J., Melatos, A., Mendell, G., Mendoza-Gandara, D., Mercer, R., Merilh, E., Merzougui, M., Meshkov, S., Messenger, C., Messick, C., Meyers, P., Mezzani, F., Miao, H., Michel, C., Middleton, H., Mikhailov, E., Milano, L., Miller, J., Millhouse, M., Minenkov, Y., Ming, J., Mirshekari, S., Mishra, C., Mitra, S., Mitrofanov, V., Mitselmakher, G., Mittleman, R., Moggi, A., Mohan, M., Mohapatra, S., Montani, M., Moore, B., Moore, C., Moraru, D., Moreno, G., Morriss, S., Mossavi, K., Mours, B., Mow-Lowry, C., Mueller, C., Mueller, G., Muir, A., Mukherjee, A., Mukherjee, D., Mukherjee, S., Mukund, N., Mullavey, A., Munch, J., Murphy, D., Murray, P., Mytidis, A., Nardecchia, I., Naticchioni, L., Nayak, R., Necula, V., Nedkova, K., Nelemans, G., Neri, M., Neunzert, A., Newton, G., Nguyen, T., Nielsen, A., Nissanke, S., Nitz, A., Nocera, F., Nolting, D., Normandin, M., Nuttall, L., Oberling, J., Ochsner, E., O’Dell, J., Oelker, E., Ogin, G., Oh, J., Oh, S., Ohme, F., Oliver, M., Oppermann, P., Oram, R., O’Reilly, B., O’Shaughnessy, R., Ott, C., Ottaway, D., Ottens, R., Overmier, H., Owen, B., Pai, A., Pai, S., Palamos, J., Palashov, O., Palomba, C., Pal-Singh, A., Pan, H., Pan, Y., Pankow, C., Pannarale, F., Pant, B., Paoletti, F., Paoli, A., Papa, M., Paris, H., Parker, W., Pascucci, D., Pasqualetti, A., Passaquieti, R., Passuello, D., Patricelli, B., Patrick, Z., Pearlstone, B., Pedraza, M., Pedurand, R., Pekowsky, L., Pele, A., Penn, S., Perreca, A., Pfeiffer, H., Phelps, M., Piccinni, O., Pichot, M., Pickenpack, M., Piergiovanni, F., Pierro, V., Pillant, G., Pinard, L., Pinto, I., Pitkin, M., Poeld, J., Poggiani, R., Popolizio, P., Post, A., Powell, J., Prasad, J., Predoi, V., Premachandra, S., Prestegard, T., Price, L., Prijatelj, M., Principe, M., Privitera, S., Prix, R., Prodi, G., Prokhorov, L., Puncken, O., Punturo, M., Puppo, P., Pürrer, M., Qi, H., Qin, J., Quetschke, V., Quintero, E., Quitzow-James, R., Raab, F., Rabeling, D., Radkins, H., Raffai, P., Raja, S., Rakhmanov, M., Ramet, C., Rapagnani, P., Raymond, V., Razzano, M., Re, V., Read, J., Reed, C., Regimbau, T., Rei, L., Reid, S., Reitze, D., Rew, H., Reyes, S., Ricci, F., Riles, K., Robertson, N., Robie, R., Robinet, F., Rocchi, A., Rolland, L., Rollins, J., Roma, V., Romano, J., Romano, R., Romanov, G., Romie, J., Rosińska, D., Rowan, S., Rüdiger, A., Ruggi, P., Ryan, K., Sachdev, S., Sadecki, T., Sadeghian, L., Salconi, L., Saleem, M., Salemi, F., Samajdar, A., Sammut, L., Sampson, L., Sanchez, E., Sandberg, V., Sandeen, B., Sanders, G., Sanders, J., Sassolas, B., Sathyaprakash, B., Saulson, P., Sauter, O., Savage, R., Sawadsky, A., Schale, P., Schilling, R., Schmidt, J., Schmidt, P., Schnabel, R., Schofield, R., Schönbeck, A., Schreiber, E., Schuette, D., Schutz, B., Scott, J., Scott, S., Sellers, D., Sengupta, A., Sentenac, D., Sequino, V., Sergeev, A., Serna, G., Setyawati, Y., Sevigny, A., Shaddock, D., Shaffer, T., Shah, S., Shahriar, M., Shaltev, M., Shao, Z., Shapiro, B., Shawhan, P., Sheperd, A., Shoemaker, D., Shoemaker, D., Siellez, K., Siemens, X., Sigg, D., Silva, A., Simakov, D., Singer, A., Singer, L., Singh, A., Singh, R., Singhal, A., Sintes, A., Slagmolen, B., Smith, J., Smith, M., Smith, N., Smith, R., Son, E., Sorazu, B., Sorrentino, F., Souradeep, T., Srivastava, A., Staley, A., Steinke, M., Steinlechner, J., Steinlechner, S., Steinmeyer, D., Stephens, B., Stevenson, S., Stone, R., Strain, K., Straniero, N., Stratta, G., Strauss, N., Strigin, S., Sturani, R., Stuver, A., Summerscales, T., Sun, L., Sutton, P., Swinkels, B., Szczepańczyk, M., Tacca, M., Talukder, D., Tanner, D., Tápai, M., Tarabrin, S., Taracchini, A., Taylor, R., Theeg, T., Thirugnanasambandam, M., Thomas, E., Thomas, M., Thomas, P., Thorne, K., Thorne, K., Thrane, E., Tiwari, S., Tiwari, V., Tokmakov, K., Tomlinson, C., Tonelli, M., Torres, C., Torrie, C., Töyrä, D., Travasso, F., Traylor, G., Trifirò, D., Tringali, M., Trozzo, L., Tse, M., Turconi, M., Tuyenbayev, D., Ugolini, D., Unnikrishnan, C., Urban, A., Usman, S., Vahlbruch, H., Vajente, G., Valdes, G., Vallisneri, M., van Bakel, N., van Beuzekom, M., van den Brand, J., Van Den Broeck, C., Vander-Hyde, D., van der Schaaf, L., van Heijningen, J., van Veggel, A., Vardaro, M., Vass, S., Vasúth, M., Vaulin, R., Vecchio, A., Vedovato, G., Veitch, J., Veitch, P., Venkateswara, K., Verkindt, D., Vetrano, F., Viceré, A., Vinciguerra, S., Vine, D., Vinet, J., Vitale, S., Vo, T., Vocca, H., Vorvick, C., Voss, D., Vousden, W., Vyatchanin, S., Wade, A., Wade, L., Wade, M., Waldman, S., Walker, M., Wallace, L., Walsh, S., Wang, G., Wang, H., Wang, M., Wang, X., Wang, Y., Ward, H., Ward, R., Warner, J., Was, M., Weaver, B., Wei, L., Weinert, M., Weinstein, A., Weiss, R., Welborn, T., Wen, L., Weßels, P., Westphal, T., Wette, K., Whelan, J., Whitcomb, S., White, D., Whiting, B., Wiesner, K., Wilkinson, C., Willems, P., Williams, L., Williams, R., Williamson, A., Willis, J., Willke, B., Wimmer, M., Winkelmann, L., Winkler, W., Wipf, C., Wiseman, A., Wittel, H., Woan, G., Worden, J., Wright, J., Wu, G., Yablon, J., Yakushin, I., Yam, W., Yamamoto, H., Yancey, C., Yap, M., Yu, H., Yvert, M., Zadrożny, A., Zangrando, L., Zanolin, M., Zendri, J., Zevin, M., Zhang, F., Zhang, L., Zhang, M., Zhang, Y., Zhao, C., Zhou, M., Zhou, Z., Zhu, X., Zucker, M., Zuraw, S., Zweizig, J., & , . (2016). Observation of Gravitational Waves from a Binary Black Hole Merger Physical Review Letters, 116 (6) DOI: 10.1103/PhysRevLett.116.061102

Filed under: Astronomy, Astrophysics, General Relativity, Physics Tagged: Black holes, Gravitational waves, LIGO ]]>

Now, back to sane QCD.

Happy new year!

Filed under: Applied Mathematics, Mathematical Physics, Quantum mechanics, Scientific Publishing Tagged: Foundations of quantum mechanics, Noncommutative geometry, Quantum mechanics, Stochastic processes, Unpublished ]]>

Quantum gravity appears today as the Holy Grail of physics. This is so far detached from any possible experimental result but with a lot of attentions from truly remarkable people anyway. In some sense, if a physicist would like to know in her lifetime if her speculations are worth a Nobel prize, better to work elsewhere. Anyhow, we are curious people and we would like to know how does the machinery of space-time work this because to have an engineering of space-time would make do to our civilization a significant leap beyond.

A fine recount of the current theoretical proposals has been rapidly presented by Ethan Siegel in his blog. It is interesting to notice that the two most prominent proposals, string theory and loop quantum gravity, share the same difficulty: They are not able to recover the low-energy limit. For string theory this is a severe drawback as here people ask for a fully unified theory of all the interactions. Loop quantum gravity is more limited in scope and so, one can think to fix the problem in a near future. But of all the proposals Siegel is considering, he is missing the most promising one: Non-commutative geometry. This mathematical idea is due to Alain Connes and earned him a Fields medal. So far, this is the only mathematical framework from which one can rederive the full Standard Model with all its particle content properly coupled to the Einstein’s general relativity. This formulation works with a classical gravitational field and so, one can possibly ask where quantized gravity could come out. Indeed, quite recently, Connes, Chamseddine and Mukhanov (see here and here), were able to show that, in the context of non-commutative geometry, a Riemannian manifold results quantized in unitary volumes of two kind of spheres. The reason why there are two kind of unitary volumes is due to the need to have a charge conjugation operator and this implies that these volumes yield the units in the spectrum. This provides the foundations for a future quantum gravity that is fully consistent from the start: The reason is that non-commutative geometry generates renormalizable theories!

The reason for my interest in non-commutative geometry arises exactly from this. Two years ago, I, Alfonso Farina and Matteo Sedehi obtained a publication about the possibility that a complex stochastic process is at the foundations of quantum mechanics (see here and here). We described such a process like the square root of a Brownian motion and so, a Bernoulli process appeared producing the factor 1 or i depending on the sign of the steps of the Brownian motion. This seemed to generate some deep understanding about space-time. Indeed, the work by Connes, Chamseddine and Mukhanov has that understanding and what appeared like a square root process of a Brownian motion today is just the motion of a particle on a non-commutative manifold. Here one has simply a combination of a Clifford algebra, that of Dirac’s matrices, a Wiener process and the Bernoulli process representing the scattering between these randomly distributed quantized volumes. Quantum mechanics is so fundamental that its derivation from a geometrical structure with added some mathematics from stochastic processes makes a case for non-commutative geometry as a serious proposal for quantum gravity.

I hope to give an account of this deep connection in a near future. This appears a rather exciting new avenue to pursue.

Ali H. Chamseddine, Alain Connes, & Viatcheslav Mukhanov (2014). Quanta of Geometry: Noncommutative Aspects Phys. Rev. Lett. 114 (2015) 9, 091302 arXiv: 1409.2471v4

Ali H. Chamseddine, Alain Connes, & Viatcheslav Mukhanov (2014). Geometry and the Quantum: Basics JHEP 12 (2014) 098 arXiv: 1411.0977v1

Farina, A., Frasca, M., & Sedehi, M. (2013). Solving Schrödinger equation via Tartaglia/Pascal triangle: a possible link between stochastic processing and quantum mechanics Signal, Image and Video Processing, 8 (1), 27-37 DOI: 10.1007/s11760-013-0473-y

Filed under: Applied Mathematics, Mathematical Physics, Particle Physics, Physics, Quantum gravity, Quantum mechanics Tagged: Alain Connes, Noncommutative geometry, Quantum gravity, Square root of a stochastic process, Stochastic processes, Volume quantization ]]>

Two days ago, CERN presented their new results at 13 TeV to the World. Of course, collected data so far are not enough for conclusive results but the these are exciting anyway. The reason is that both the collaborations, CMS and ATLAS, see a bump at around 750 GeV in the decay. Summing up the results of the two collaborations, they are around without look elsewhere effect, not yet a discovery but, probably, at the summer conferences they will have something more conclusive to say. This could be an unlucky fluctuation but this situation remember us the story of the discovery of the Higgs boson more than three years ago. The question if this is beyond Standard Model physics is what I will try to answer in these few lines.

Firstly, if this particle is real, it decays with two photons exactly as the Higgs boson. Secondly, with a final state like this it can have only spin 0 or 2. We will be conservative and assume that this is not a graviton. Rather, it is a sibling of the Higgs particle. Besides, it was not observed in run I but is not inconsistent with data from there. It appears like the increased luminosity favored its appearance. We want to be more conservative and we take for granted just the Lagrangian of the Standard Model. So, what is this beast?

My answer is that this could be an excited state of the Higgs boson that, having a production rate lower than its ground state seen at run I, needed more luminosity to be observed. You do not need to change the Lagrangian of the Standard Model for this and it is not BSM physics yet. You do not even need a technicolor theory to describe it. The reason is that the Higgs part of the Standard Model can be treated mathematically yielding exact solutions. The quantum field theory can be exactly solved and the spectrum of the theory says exactly what I stated above (see here, and here). The Higgs model *per se* is exactly solvable. So, Jester’s idea to add another scalar field to the Lagrangian model is useless, it is all just inside and you will get a two photon final state as well.

Of course, it is too early to draw a final conclusion and a wealth of papers with a prompt explanation flooded arxiv in these two days. With the restart of LHC on spring and the collecting of more data, things will be clearer than now. For the moment, this hint is enough to keep us excited for the next few months.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model arxiv arXiv: 1504.02299v2

Marco Frasca (2015). Quantum Yang-Mills field theory arxiv arXiv: 1509.05292v1

Filed under: Mathematical Physics, Particle Physics Tagged: ATLAS, CERN, CMS, Higgs particle, LHC ]]>

There has been a lot of rumor on measurements performed by Eagleworks labs at NASA this spring. After that, NASA imposed a veto on whatever information should coming out about the work of this group until peer-reviewed work should have appeared. Most of the problems come out from the question of the EmDrive. This is a presumed thruster obtained by pumping radio-frequency into a cavity shaped as a closed frustum. This device has been largely dismissed by the physicists’ community due to a blatant violation of conservation of momentum. Such an object should stand still aside from known physical effects as Lorentz force or thermal thrust arising from heating of the cavity in the air. The claimed effect is really tiny standing on measurements that has been done since now and so, mundane explanations remain the most credited. Notwithstanding this, people at NASA have kept on working. This is testified by the recent posts by Paul March at Nasaspaceflight forum. Paul march is a member of the NASA group working on new propulsion technologies and what he is claiming is really striking. I report this here

where he claims that, notwithstanding all the precautions, they keep on seeing a thrust. They know perfectly that, for Maxwell theory, no thrust should be observed as stated by the following post

So, they see a thrust, after having removed all mundane effects, and the possible explanation for it is not classical electromagnetism as all said from the start. In particular, it is cited by the questioner the link to Greg Egan’s post explaining why there cannot be any thrust by known electromagnetism with this geometry (see Greg Egan’s post). I think that they will make their results known once the peer-review process will be concluded. I would like to remember that other NASA labs asked to concur to confirm their measurements.

This group also performed interference experiments on this cavity and observed an effect. If all this will be confirmed it will represent a breakthrough, not only from the technological side let me say, as a new physical effect will be proved at work with general relativity now to be experimentally managed on a tabletop device. Note that general relativity is always at work in this situation with a large density of electromagnetic energy as I also discussed here. It should be said that this has nothing to do with warp drive as conceived in Alcubierre metric and similar.

We hope to hear very soon from this group with more official channels. Surely, their results will provide a wealth of new avenues to pursue for research and technology.

Marco Frasca (2015). Einstein-Maxwell equations for asymmetric resonant cavities arXiv arXiv: 1505.06917v1

Filed under: Astronautics, General Relativity, Physics Tagged: Astrodynamics, Eagleworks Labs, EmDrive, NASA ]]>

LHCP 2015 is going on at St. Peterburg and new results were presented by the two main collaborations at CERN. CMS and ATLAS combined the results from run 1 and improved the quality of the measured data of the Higgs particle discovered on 2012. CERN press release is here. I show you the main picture about the couplings between the Higgs field and the other particles in the Standard Model widely exposed in all the social networks

What makes this plot so striking is the very precise agreement with the Standard Model. Anyhow, the ellipses are somewhat large yet to grant new physics creeping in at run 2. My view is that the couplings, determining the masses of the particles in the Standard Model, are less sensible to new physics than the strength of the signal at various decays. Also this plot is available (hat tip to Adam Falkowski)

In this plot you can see that the Standard Model, represented by a star, is somewhat at the border of the areas of the ZZ and WW decays and that of the WW decay is making smaller. This does not imply that in the future deviations from the Standard Model will be seen here but leave the impression that this could happen in run 2 with the increasing precision expected for these measurements.

The strengths are so interesting because the Higgs sector of the Standard Model can be solved exactly with the propagator providing the values of them (see here). These generally disagree from those obtained by standard perturbation theory even if by a small extent. Besides, Higgs particle should have internal degrees of freedom living also in higher excited states. All of this to be seen at run 2 as the production rate of these states appears to be smaller as higher is their mass.

Run 2 is currently ongoing even if the expected luminosity will not be reached for this year. For sure, the next year summer conferences could provide a wealth of shocking new results. Hints are already seen by both the main collaborations and LHCb. Something new is just behind the corner.

Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model arxiv arXiv: 1504.02299v1

Filed under: Mathematical Physics, Particle Physics, Physics Tagged: ATLAS, CERN, CMS, Higgs particle, LHCb ]]>