Blejske delavnice iz fizike Bled Workshops in Physics ISSN 1580-4992 Letnik 16, St. 2 vOL. 16, nO. 2 Proceedings to the 18th Workshop What Comes Beyond the Standard Models Bled, July 11-19, 2015 Edited by Norma Susana Mankoc Borstnik Holger Bech Nielsen Dragan Lukman dmfa - zaloZniStvo Ljubljana, december 2015 The 18th Workshop What Comes Beyond the Standard Models, 11.- 19. July 2015, Bled was organized by Society of Mathematicians, Physicists and Astronomers of Slovenia and sponsored by Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana Society of Mathematicians, Physicists and Astronomers of Slovenia Beyond Semiconductor (Matjaži Breskvar) Scientific Committee John Ellis, CERN David Gross, KITP Roman Jackiw, MIT Organizing Committee Norma Susana Mankoč Borštnik Holger Bech Nielsen Maxim Yu. Khlopov The Members of the Organizing Committee of the International Workshop "What Comes Beyond the Standard Models", Bled, Slovenia, state that the articles published in the Proceedings to the 18th Workshop "What Comes Beyond the Standard Models", Bled, Slovenia are refereed at the Workshop in intense in-depth discussions. Workshops organized at Bled > What Comes Beyond the Standard Models (June 29-July 9,1998), Vol. 0 (1999) No. 1 (July 22-31,1999) (july 17-31, 2000) (july 16-28, 2001), Vol. 2 (2001) No. 2 (july 14-25, 2002), Vol. 3 (2002) No. 4 (july 18-28, 2003) Vol. 4 (2003) Nos. 2-3 (july 19-31, 2004), Vol. 5 (2004) No. 2 (july 19-29, 2005), Vol. 6 (2005) No. 2 (September 16-26, 2006), Vol. 7 (2006) No. 2 (july 17-27, 2007), Vol. 8 (2007) No. 2 (july 15-25, 2008), Vol. 9 (2008) No. 2 (july 14-24, 2009), Vol. 10 (2009) No. 2 (july 12-22, 2010), Vol. 11 (2010) No. 2 (july 11-21, 2011), Vol. 12 (2011) No. 2 (july 9-19, 2012), Vol. 13 (2012) No. 2 (july 14-21, 2013), Vol. 14 (2013) No. 2 (july 20-28, 2014), Vol. 15 (2014) No. 2 (july 11-19, 2015), Vol. 16 (2015) No. 2 > Hadrons as Solitons (july 6-17,1999) > Few-Quark Problems (july 8-15, 2000), Vol. 1 (2000) No. 1 > Selected Few-Body Problems in Hadronic and Atomic Physics (july 7-14, 2001), Vol. 2 (2001) No. 1 > Quarks and Hadrons (july 6-13, 2002), Vol. 3 (2002) No. 3 > Effective Quark-Quark Interaction (july 7-14, 2003), Vol. 4 (2003) No. 1 > Quark Dynamics (july 12-19, 2004), Vol. 5 (2004) No. 1 > Exciting Hadrons (july 11-18, 2005), Vol. 6 (2005) No. 1 > Progress in Quark Models (july 10-17, 2006), Vol. 7 (2006) No. 1 > Hadron Structure and Lattice QCD (july 9-16, 2007), Vol. 8 (2007) No. 1 > Few-Quark States and the Continuum (September 15-22, 2008), Vol. 9 (2008) No. 1 > Problems in Multi-Quark States (june 29-july 6, 2009), Vol. 10 (2009) No. 1 > Dressing Hadrons (july 4-11, 2010), Vol. 11 (2010) No. 1 > Understanding hadronic spectra (july 3-10, 2011), Vol. 12 (2011) No. 1 > Hadronic Resonances (july 1-8, 2012), Vol. 13 (2012) No. 1 > Looking into Hadrons (july 7-14, 2013), Vol. 14 (2013) No. 1 > Quark Masses and Hadron Spectra (july 6-13, 2014), Vol. 15 (2014) No. 1 > Exploring Hadron Resonances (july 5-11, 2015), Vol. 16 (2015) No. 1 > o Statistical Mechanics of Complex Systems (August 27-September 2, 2000) o Studies of Elementary Steps of Radical Reactions in Atmospheric Chemistry (August 25-28, 2001) Contents Preface in English and Slovenian Language............................VII Talk Section........................................................ 1 1 Aspects of String Phenomenology in Particle Physics and Cosmology I. Antoniadis........................................................ 1 2 Results on DAMA/LIBRA-Phase1 and Perspectives of the Phase2 R. Bernabei etal...................................................... 13 3 Pure Contact Term Correlators in CFT L. Bonora and B.L. de Souza........................................... 22 4 Novel Perspectives from Light-Front QCD, Super-Conformal Algebra, and Light-Front Holography S.J. Brodsky......................................................... 35 5 Charged Fermion Masses and Mixing from a SU(3) Family Symmetry Model A. Hernandez-Galeana............................................... 47 6 Gravitational Effects for Dirac Particles U.D. Jentschura and J.H. Noble........................................ 63 7 10 Years of Dark Atoms of Composite Dark Matter M.Yu. Khlopov...................................................... 71 8 Describing 2-TeV Scale WLWL Resonances with Unitarized Effective Theory F.J. Llanes-Estrada, A. Dobado and R.L. Delgado......................... 78 9 The Spin-Charge-Family Theory Offers the Explanation for all the Assumptions of the Standard Model, for the Dark Matter, for the Matter/Antimatter Asymmetry, Making Several Predictions. N.S. Mankoc Borstnik................................................ 87 10 Fermionization in an Arbitrary Number of Dimensions N.S. Mankoc Borstnik and H.B.F. Nielsen...............................111 VI Contents 11 Unified Description of Quarks and Leptons in a Multi-spinor Field Formalism I.S. Sogami..........................................................129 Discussion Section..................................................141 12 A Democratic Suggestion A. Kleppe...........................................................143 13 Discussion Section on LHC Data F.J. Llanes-Estrada...................................................152 14 Vector and Scalar Gauge Fields with Respect to d = (3 +1 ) in Kaluza-Klein Theories and in the Spin-charge-family theory D. Lukman and N.S. Mankoc Borštnik..................................158 15 Degrees of Freedom of Massless Boson and Fermion Fields in Any Even Dimension N.S. Mankoc Borštnik and H.B.F. Nielsen...............................165 Virtual Institute of Astroparticle Physics Presentation...................175 16 Virtual Institute of Astroparticle Physics and Discussions at XVIII Bled Workshop M.Yu. Khlopov......................................................177 Preface The series of workshops on "What Comes Beyond the Standard Models?" started in 1998 with the idea of Norma and Holger for organizing a real workshop, in which participants would spend most of the time in discussions, confronting different approaches and ideas. It is the eighteenth workshop which took place this year in the picturesque town of Bled by the lake of the same name, surrounded by beautiful mountains and offering pleasant walks and mountaineering. In our very open minded, friendly, cooperative, long, tough and demanding discussions several physicists and even some mathematicians have contributed. Most of topics presented and discussed in our Bled workshops concern the proposals how to explain physics beyond the so far accepted and experimentally confirmed both standard models - in elementary particle physics and cosmology. Although most of participants are theoretical physicists, many of them with their own suggestions how to make the next step beyond the accepted models and theories, experts from experimental laboratories were very appreciated, helping a lot to understand what do measurements really tell and which kinds of predictions can best be tested. The (long) presentations (with breaks and continuations over several days), followed by very detailed discussions, have been extremely useful, at least for the organizers. We hope and believe, however, that this is the case also for most of participants, including students. Many a time, namely, talks turned into very pedagogical presentations in order to clarify the assumptions and the detailed steps, analysing the ideas, statements, proofs of statements and possible predictions, confronting participants' proposals with the proposals in the literature or with proposals of the other participants, so that all possible weak points of the proposals showed up very clearly. The ideas therefore seem to develop in these years considerably faster than they would without our workshops. In the eighteen years of our workshops the organizers, together with the participants, are trying to answer several open questions of the elementary particle physics and cosmology. Experiments have made large steps in this time. Among the most notable and might be also among the most important ones was two years ago the LHC confirmation that the scalar field, the higgs is like other fermionic and bosonic fields - just a field. And yet it is a very unusual field: A boson with the fractional weak and hyper charges, resembling fermion charges. Do we have the explanation for that? Can we explain the origin of families and Yukawa couplings? Can we understand and explain all the assumptions of the standard model? That is, can we explain the appearance of the charges of the family members, quarks and leptons, the left handed members distinguishing in charges from the right handed ones? Can we understand the appearance of the vector and scalar gauge fields of these charges? How many are they? Can we understand the origin of the matter-antimatter asymmetry, of the dark matter? The behaviour of the nature, that is the evolution of our universe and the dynamics of it can be understood on all levels — from the elementary fermionic and bosonic particles (fields) and their mutual interactions to matter of all kinds, forming galaxies, clusters of galaxies and our universe — only if we have the theory behind, which explains the observed phenomena and predicts new phenomena. It is hard to distinguish among theories, which all explain the same observed phenomena, unless one of them is more predictive, better mathematically supported, offering more detailed predictions for the future observations. Should we design theories and models in steps, each one more or less adapted for explaining a new experimental observation, in particular if such models can help to explain a small next step? Or can we suggest the theory which answers many open questions at the same time? Can it happen that at the LHC no new fields - scalars, vectors or fermions - will be observed, so that there will be no sign which will help to make a trustable step beyond the standard model? This can hardly happen. The (so far) observed three families, (only) one scalar field and several Yukawa couplings call for explanation for the origin of families and of the higgs, suggesting that there are several scalar fields, which manifest as the higgs and the Yukawa couplings. If trusting the spin-charge-family theory, presented in this workshop in details, there exists the fourth family, coupled to the observed three families, and several scalar fields, all with the weak and the hyper charges of the higgs, carrying additional quantum numbers — either the family ones or the family members ones — which explain the origin of Yukawa couplings. This theory, which offers the explanation for all the assumptions of the standard model — for the appearance of charges of the family members, for families, for all the properties of fermions and of the vector gauge fields, explaining why there are scalar fields with the weak and the hyper charge of the standard model higgs — offers also the explanation for the appearance of the matter/anti-matter asymmetry in the universe by predicting that there are scalars, which are colour triplets, causing transitions between anti-leptons into quarks and anti-quarks into quarks and back. In the presence of the scalar condensate of the two right handed neutrinos, which breaks the CP symmetry, might in the expanding universe in thermal inequilibrium take care of the matter/anti-matter asymmetry. Predicting two groups of four families of quarks and leptons the theory might explain also the appearance of the dark matter. The fermionization/bosonization theory, showing that at least for free massless particles it is possible to construct a boson theory, which is equivalent (in terms of momenta and energy) to a fermion theory, might help to understand whether the spin-charge-family theory, doing so well in explaining the assumptions of the standard model, is the acceptable next step beyond the standard model, and what might be beyond the spin-charge-family theory. The models, like a model of supersymmetry in the presence of a very small cosmological constant, which is able to manifest at the low energy regime the observed data, might help to understand how has the nature proceeded in the expanding universe. In particular since the model shows correspondence with string and other models. The conformal field theory action and its correspondence to the Chern-Simons action, discussed in this workshop, is manifesting the use of mathematical approaches while making the correspondence among approaches, in order to better understand "thoughts" of the nature. The mathematical proofs are essential for all the theories. The proof is discussed and presented, showing the equivalence between the vielbeins and the spin connection fields in the Kaluza-Klein theories when representing the vector (and the scalar) gauge fields in d = 3 + 1. The studies of the origin of families, which might explain, why the nature manifests in the low energy regime the families of quarks and leptons with the observed properties, go in this workshop in several attempts: Besides with the spin-charge-family theory, which is able to explain the properties of families of quarks and leptons, also by using a triple tensor products of the Dirac spinors, the representations of which can be identified with the three observed families of quarks and leptons and one more family, offering the explanation for the existence of the dark matter. It is also the attempt, presented in this workshop, which demonstrates, how close to the democratic matrix can the mass matrices of quarks and leptons be parametrized while still manifesting the quarks mixing matrices. There is the attempt, presented in this workshop, to extend the standard model with new fermion and boson fields to explain mass matrices of quarks and leptons and correspondingly their masses and mixing matrices. There is also the possibility, that the dark matter might consist of the —2 electro-magnetically charged particles, bound by the ordinary Coulomb interaction with primordial helium in OHe. The author discussed the solved and not yet solved problems of this model. The last progress in experiments, manifesting that the measured annual modulation, can hardly be something else but the interaction of the dark matter from our galaxy with the scintillators in DAMA/NaI and DAMA/LIBRA experiments is reported. There were works on many body problems on hadron physics, interesting for high energy physics as well. It is happening many times in physics, that experiences from one field of physics can successfully be used also on other fields, provided that the symmetry of the systems is comparable. It is suggested to use the experiences with the effective action, developed for studying hadron resonances, to calculate the scattering of two higgses or two heavy bosons in the energy region of 1-3 TeV. It is claimed and represented that the light-front is providing a physical, frame independent formalism, offering a new inside into the hadronic mass scale, hadronic spectrum and the running coupling constants in nonperturbative domain. It is demonstrated that the theory of Dirac particles in curved space-times caused by several central potential confirms the weak equivalence principle in deep gravitational potentials. As every year also this year there has been not enough time to mature the very discerning and innovative discussions, for which we have spent a lot of time, into the written contributions. Since the time to prepare the proceedings is indeed very short, three months if vacations included, authors did not have a time to polish their contributions carefully enough. Bled Workshops owe their success to participants who have at Bled in the heart of Slovene Julian Alps enabled friendly and active sharing of information and ideas, yet their success was boosted by videoconferences. Questions and answers as well as lectures enabled by M.Yu. Khlopov via Virtual Institute of Astroparticle Physics (viavca.in2p3.fr/site.html) of APC have in ample discussions helped to resolve many dilemmas. The reader can find the records of all the talks delivered by cosmovia since Bled 2009 on viavca.in2p3.fr/site.html in Previous - Conferences. The six talks delivered by: L. Bonora (Regularization of conformal correlators), R. Cerulli (Particle Dark Matter direct detection), N.S. Mankoc Borštnik (How many answers of the open questions of the Standard Model can the Spin-Charge-Family theory offer?), S. Brodsky (New perspectives for hadron physics and the cosmological constant problem), M. Yu. Khlopov (Composite dark matter) and H.B.F. Nielsen (Fermion-ization in an Arbitrary Number of Dimensions), can be accessed directly at http://viavca.in2p3.fr/what_comes_beyond_the_standard_models_xvm.html Most of the talks can be found on the workshop homepage http://bsm.fmf.uni-lj.si/. Let us conclude this preface by thanking cordially and warmly to all the participants, present personally or through the teleconferences at the Bled workshop, for their excellent presentations and in particular for really fruitful discussions and the good and friendly working atmosphere. The workshops take place in the house gifted to the Society of Mathematicians, Physicists and Astronomers of Slovenia by the Slovenian mathematician Josip Plemelj, well known to the participants by his work in complex algebra. Norma Mankoc Borštnik, Holger Bech Nielsen, Maxim Y. Khlopov, (the Organizing comittee) Norma Mankoč Borštnik, Holger Bech Nielsen, Dragan Lukman, (the Editors) Ljubljana, December 2015 1 Predgovor (Preface in Slovenian Language) Serija delavnic "Kako preseči oba standardna modela, kozmološkega in elek-trosibkega" ("What Comes Beyond the Standard Models?") se je zacela leta 1998 z idejo Norme in Holgerja, da bi organizirali delavnice, v katerih bi udelezenci v izcrpnih diskusijah kriticno soocili razlicne ideje in teorije. Letos smo imeli osemnajsto delavnico na Bledu ob slikovitem jezeru, kjer prijetni sprehodi in pohodi na cšudovite gore, ki kipijo nad mestom, ponujajo prilozšnosti in vzpodbudo za diskusije. K našim zelo odprtim, prijateljskim, dolgim in zahtevnim diskusijam, polnim iskrivega sodelovanja, je prispevalo veliko fizikov in celo nekaj matematikov. Vecina predlogov teorij in modelov, predstavljenih in diskutiranih na naših Blejskih delavnicah, isce odgovore na vprašanja, ki jih v fizikalni skupnosti sprejeta in s sštevilnimi poskusi potrjena standardni model osnovnih fermionskih in bo-zonskih polj ter kozmoloski standardni model pušcata odprta. Ceprav je vecina udelezencev teoreticnih fizikov, mnogi z lastnimi idejami kako narediti naslednji korak onkraj sprejetih modelov in teorij, so še posebej dobrodošli predstavniki eksperimentalnih laboratorijev, ki nam pomagajo v odprtih diskusijah razjasniti resnicno sporocilo meritev in kaksne napovedi so potrebne, da jih lahko s poskusi dovoljzanesljivo preverijo. Organizatorji moramo priznati, da smo se na blejskih delavnicah v (dolgih) predstavitvah (z odmori in nadaljevanji cez vec dni), ki so jim sledile zelo podrobne diskusije, naucili veliko, morda vec kot vecina udelezencev. Upamo in verjamemo, da so veliko odnesli tudi študentje in vecina udelezencev. Velikokrat so se predavanja spremenila v zelo pedagoške predstavitve, ki so pojasnile predpostavke in podrobne korake, soocšile predstavljene predloge s predlogi v literaturi ali s predlogi ostalih udelezencev ter jasno pokazale, kje utegnejo ticati šibke tocke predlogov. Zdi se, da so se ideje v teh letih razvijale bistveno hitreje, zahvaljujoc prav tem delavnicam. V teh osemnajstih letih delavnic smo organizatorji skupaj z udelezenci poskusili odgovoriti na marsikatero odprto vprasanje v fiziki osnovnih delcev in kozmologiji. Na vsakoletnem napovedniku naše delavnice objavimo zbirko odprtih vprašanj, na katera bi udeleženci utegnili predlagati resitve. V osememnajstih letih so eksperimenti napravili velike korake. Med najpomembnejšimi dosezki je potrditev LHC, da je skalarno pole, Higgsov delec, prav tako polje kot ostala fermionska in bo-zonska polja. In vendar je to skalarno polje zelo nenavadno polje: Je bozon s polovicnim šibkim in hiper nabojem, kot priticeta fermionom. Ali to razumemo? Ali lahko pojasnimo izvor druzin in Yukawinih sklopitev? Znamo pojasniti nes-imetrijo med snovjo in antisnovjo v vesolju? Znamo razloziti privzetke standardnega modela? Dinamiko vesolja na vseh nivojih, od osnovnih delcev do snovi, lahko razumemo samo, ce ponudimo teorijo, ki opaZanja razloZi in napove nova spoznanja. Je prava pot pri postavljanju teorijta, da prilagodimo teorijo eksperimentalnim spoznanjem po korakih in s tem omogočimo napovedi za naslednje majhne korake? Ali pa ponudimo teorijo, ki odgovori na mnoga (morda vsa) doslejodprta vprasanja? Naravne zakone, to je razvojnasega vesolja in njegovo dinamiko, lahko razumemo na vseh nivojih — od elementarnih fermionskih in bozonskih delcev (polj) in njihovih vzajemnih interakcij s snovjo vseh vrst, ki tvori galaksije, gruče galaksij in nase vesolje — le, ce imamo teorijo, ki pojasni opažene pojave in napove nove. Med teorijami, ki pojasnjujejo iste pojave, je tezko locevati, razen, ce je kakšna bolj elegantna, preprosteša, ima boljse matematicne temelje in daje bolj natancne napovedi za prihodnja opazovanja. Kaj pa, ce na LHC ne bodo izmerili nobenega novega polja, ne skalarnega, ne vektorskega, ne fermionskega in ne bo ponudil eksperiment nobenega napotka, kako napraviti naslednji korak od standardnega modela? Menimo, daje to malo verjetno. Dosedajopazene (tri) druzine, (samo) eno skalarno polje in vec Yukawinih sklopitev klice po razlagi izvora druzin in higgsa in namiguje, da je skalarnih polj vec in da se kanejo kot higgs in Yukawine sklo-pitve. Ce ima prav teorija spina, naboja in družin, ki je bila podrobno predstavljena na tej delavnici, potem obstaja cetrta druzina, ki je sklopljena z ze opaženimi. Je tudi vec skalarnih polj, vsa s šibkim in hiper nabojem kot ga ima higgs, in še z dodatnimi kvantnimi števili — s kvantnimi stevili druzin in njihovih clanov — ki pojasnijo izvor Yukawinih sklopitev. Ta teorija ponudi razlago za vse privzetke standardnega modela — pojasni izvor nabojev clanov druzin, izvor druzin in družinskih kvantnih sštevil, pojasni lastosti fermionov in vektorskih umeritvenih polj, pojasni, zakaj nosijo skalarna polja sšibki in hiper naboj higgsa — in ponudi tudi razlago za pojav asimetrije med snovjo in antisnovjo opazeno v vesolju, sajnapove obstojskalarjev, barvnih tripletov, ki sprozšijo prehod antileptonov v kvarke in antikvarkov v kvarke ter obratne procese. Skalarni kondenzat dveh desnorocnih nevtrinov, ki zlomi CP simetrijo, lahko povzroci asimetrijo snovi in antisnovi v vesolju, ki se razsirja in je v toplotnem neravnovesju. Ker napove dve skupini po štiri druzine kvarkov in leptonov, lahko morda pojasni pojav temne snovi. Teorija fermionizacije/bozonizacije, ki pokaze, da ja vsajza proste brezmasne delce mozšno konstruirati bozonsko teorijo, ki je ekvivalentna (vsaj kar se ticše gibalne kolicšine in energije) fermionski teoriji, morda lahko pomaga razumeti, ali je teorija spinov-nabojev-družin, ki je tako uspesna pri razlagi predpostavk standardnega modela, sprejemljiv naslednji korak onkraj standardnega modela in kaj je morda onkraj te teorije. Modeli, kot je model supersimetrije v prisotnosti zelo majhne kozmolosške konstante, ki lahko v obmocšju nizkih energij ponudi ujemanje napovedi modela z meritvami, lahko pomagajo razumeti, kako se narava razvija v razsširjajocšem se vesolju, zlasti ce model pokaze povezavo s strunami in ostalimi modeli. Akcija konformne teorije polja in njena povezava z akcijo Cherna in Simonsa, predstavljena na delavnici, je demonstracija uporabe razlicnih matematicnih pristopov ter povezav med njimi, ki mnogo prispevajo k boljsšemu razumevanju narave. Matematični dokaz, prikazan na delavnici, pokaže ekvivalentnost predstavitve umeritvenih vektorskih (in skalarnih) polj v d = 3 + 1 med vektorskimi svežnji in polji spinskih povezav v teorijah Kaluze-Kleinovega tipa v poljubno razsežnih prostorih. Raziskave izvora druzin, ki naj pojasnijo, zakaj se v naravi pojavijo pri nizkih energijah druzine kvarkov in leptonov z opaženimi lastnostmi, se na tejdelavnici lotimo na več načinov: poleg teorije spinov-nabojev-družin, ki lahko pojasni lastnosti kvarkov in leptonov, se s pristopom s trojnim tenzorskim produktom Diracovih spinorjev, katerega upodobitve lahko identificiramo s tremi poznanimi druzinami kvarkov in leptonov ter s še eno družino, ki pojasni temno snov. Na tej delavnici je prikazan uspešen poskus takšne parametrizacije kvarkovskih masnih matrik, ki so zelo blizu demokraticnima, tako da produkt unitarnih transformacijteh matrik pojasni izmerjene lastnosti mešalne matrike kvarkov. V zborniku je predstavljen poskus razsiritve standardnega modela z novimi fermionskimi in bozonskimi polji z družinskimi kvantnimi števili simetrije SU(3), kar lahko pojasni masne matrike kvarkov in leptonov, njihove mase in mesalne matrike. Obravnavamo tudi možnost, da temno snov sestavljajo delci z elektromagnetnim nabojem -2, ki jih obicajna Coulombska interakcija veze s prvotnim helijem v OHe. Avtor obravnava resene in odprte probleme v tem modelu. Porocilo o vseh dosedaj narejenih meritvah na eksperimentu DAMA/NaI in DAMA/LIBRA, ki kanejo izrazito letno modulacijo, skoraj ne dopušca dvoma, da gre za interakcijo temne snovi nase galaksije s scintilatorji DAMA/NaI in DAMA/LIBRA. Zanimivo je tudi delo, ki prenasa izkusnje iskanja resitev sistemov mnogih teles v fiziki hadronov, na fiziko visokih energij. Kot se zgodi mnogokrat v fiziki, lahko tudi tu izkušnje iz enega podrocja fizike prenesemo na drugo podrocje, kadar so simetrije sistemov primerljive. Avtorji predlagajo uporabo efektivne akcije, razvito za sštudij hadronskih resonanc, za sštudij sipanja dveh higgsov ali dveh tezških bozonov v energijskem obmocju 1-3 TeV. Avtor uporabe koordinatnega sistema na svetlobnem stozšcu (light front) in z od opazovalnega sistema neodvisnim formalizmom ponudi nov vpogled v masno skalo hadronov, spekter hadronov in spremenljivo sklopitveno konstanto v neper-turbacijskem obmocju kromodinamike. Iskanje rešitev Diracovih delcev v ukrivljenih prostor-casih, ki jih povzrocijo razlicšni potencali, ovrzše domnevo, da v v globokih gravitacijskih potencialih nacelo sibke ekvivalencene velja. Kot vsako leto nam tudi letos ni uspelo predstaviti v zborniku kar nekajzelo obetavnih diskusij, ki so tekle na delavnici. Premalo je bilo ca do zakljucka redakcije. Cetudi so k uspehu „Blejskih delavnic" najvec prispevali udeleženci, ki so na Bledu omogocili prijateljsko in aktivno izmenjavo mnenj v osrcju slovenskih Julijcev, so k uspehu prispevale tudi videokonference, ki so povezale delavnice z laboratoriji po svetu. Vprasanja in odgovori ter tudi predavanja, ki jih je v zadnjih letih omogocil M.Yu. Khlopov preko Virtual Institute of Astroparticle Physics (viavca.in2p3.fr/site.html, APC, Pariz), so v izcrpnih diskusijah pomagali razcistiti marsikatero dilemo. Bralec najde zapise vseh predavanj, objavljenih preko "cosmovia" od leta 2009, na viavca.in2p3.fr/site.html v povezavi Previous - Conferences. Sest letošnjih predavanj, L. Bonora (Regularization of conformal correlators), R. Cerulli (Particle Dark Matter direct detection), N.S. Mankoc Borstnik (How many answers of the open questions of the Standard Model can the Spin-Charge-Family theory offer?), S. Brodsky (New perspectives for hadron physics and the cosmological constant problem), M. Yu. Khlopov (Composite dark matter) in H.B.F. Nielsen (Fermioniza-tion in an Arbitrary Number of Dimensions), je dostopnih na http://viavca.in2p3.fr/what_comes_beyond_the_standard_models_xviii.html Vecino predavanjnajde bralec na spletni strani delavnice na http://bsm.fmf.uni-lj.si/. Naj zakljucšimo ta predgovor s prisrcšno in toplo zahvalo vsem udelezšencem, prisotnim na Bledu osebno ali preko videokonferenc, za njihova predavanja in se posebno za zelo plodne diskusije in odlično vzdusje. Delavnica poteka v hiši, ki jo je Društvu matematikov, fizikov in astronomov Slovenije zapustil v last slovenski matematik Josip Plemelj, udelezencem delavnic, ki prihajajo iz razlicnih koncev sveta, dobro poznan po svojem delu v kompleksni algebri. Norma Mankoč Borštnik, Holger Bech Nielsen, Maxim Y. Khlopov, (Organizacijski odbor) Norma Mankoč Borštnik, Holger Bech Nielsen, Dragan Lukman, (uredniki) Ljubljana, grudna (decembra) 2015 Talk Section All talk contributions are arranged alphabetically with respect to the authors' names. Bled Workshops in Physics Vol. 16, No. 2 A Proceedings to the 1 8th Workshop What Comes Beyond ... (p. 1) Bled, Slovenia, July 11-19, 2015 1 Aspects of String Phenomenology in Particle Physics and Cosmology I. Antoniadis * LPTHE, UMR CNRS 7589 Sorbonne Universites, UPMC Paris 6, 75005 Paris, France and Albert Einstein Center, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, 3012 Bern, Switzerland Abstract. We describe the phenomenology of a model of supersymmetry breaking in the presence of a tiny (tunable) positive cosmological constant. It utilises a single chiral multiplet with a gauged shift symmetry, that can be identified with the string dilaton (or an appropriate compactification modulus). The model is coupled to the MSSM, leading to calculable soft supersymmetry breaking masses and a distinct low energy phenomenology that allows to differentiate it from other models of supersymmetry breaking and mediation mechanisms. Povzetek. Avtor obravnava lastnosti modela za zlom supersimetrije, ko majhno pozitivno kozmolosko konstanto prilagaja fenomenoloskim lastnostim. Obravnava primer kiralnega multipleta, ko postane umeritvena simetrija dilatacijska simetrija strune (uporabiti pa je mogoce tudi kak drug model kompaktifikacije). Model poveže s standardnim modelom z minimalno supersimetrijo, kar omogoči izračun mas pri mehki zlomitvi supersimetrije. Model uspesno opise fenomenoloske lastnosti polj, kar ga loci od ostalih modelov za zlomitev supersimetrije. 1.1 Introduction If String Theory is a fundamental theory of Nature and not just a tool for studying systems with strongly coupled dynamics, it should be able to describe at the same time particle physics and cosmology, which are phenomena that involve very different scales from the microscopic four-dimensional (4d) quantum gravity length of 10-33 cm to large macroscopic distances of the size of the observable Universe -1028 cm spanned a region of about 60 orders of magnitude. In particular, besides the 4d Planck mass, there are three very different scales with very different physics corresponding to the electroweak, dark energy and inflation. These scales might be related via the scale of the underlying fundamental theory, such as string theory, or they might be independent in the sense that their origin could be based on different and independent dynamics. An example of the former constrained and more predictive possibility is provided by TeV strings with a fundamental scale at low energies due for instance to large extra dimensions transverse to a * E-mail: ignatios.antoniadis@polytechnique.edu 2 I. Antoniadis four-dimensional braneworld forming our Universe [1]. In this case, the 4d Planck mass is emergent from the fundamental string scale and inflation should also happen around the same scale [2]. Here, we will adopt the second more conservative approach, assuming that all three scales have an independent dynamical origin. Moreover, we will assume the presence of low energy supersymmetry that allows for an elegant solution of the mass hierarchy problem, a unification of fundamental forces as indicated by low energy data and a natural dark matter candidate due to an unbroken R-parity. The assumption of independent scales implies that supersymmetry breaking should be realized in a metastable de Sitter vacuum with an infinitesimally small (tunable) cosmological constant independent of the supersymmetry breaking scale that should be in the TeV region. In a recent work [3], we studied a simple N = 1 supergravity model having this property and motivated by string theory. Besides the gravity multiplet, the minimal field content consists of a chiral multiplet with a shift symmetry promoted to a gauged R-symmetry using a vector multiplet. In the string theory context, the chiral multiplet can be identified with the string dilaton (or an appropriate compactification modulus) and the shift symmetry associated to the gauge invariance of a two-index antisymmetric tensor that can be dualized to a (pseudo)scalar. The shift symmetry fixes the form of the superpotential and the gauging allows for the presence of a Fayet-Iliopoulos (FI) term, leading to a supergravity action with two independent parameters that can be tuned so that the scalar potential possesses a metastable de Sitter minimum with a tiny vacuum energy (essentially the relative strength between the F- and D-term contributions). A third parameter fixes the Vacuum Expectation Value (VEV) of the string dilaton at the desired (phenomenologically) weak coupling regime. An important consistency constraint of our model is anomaly cancellation which has been studied in [5] and implies the existence of additional charged fields under the gauged R-symmetry. In a more recent work [6], we analyzed a small variation of this model which is manifestly anomaly free without additional charged fields and allows to couple in a straight forward way a visible sector containing the minimal supersymmetric extension of the Standard Model (MSSM) and studied the mediation of super-symmetry breaking and its phenomenological consequences. It turns out that an additional 'hidden sector' field z is needed to be added for the matter soft scalar masses to be non-tachyonic; although this field participates in the supersymmetry breaking and is similar to the so-called Polonyi field, it does not modify the main properties of the metastable de Sitter (dS) vacuum. All soft scalar masses, as well as trilinear A-terms, are generated at the tree level and are universal under the assumption that matter kinetic terms are independent of the 'Polonyi' field, since matter fields are neutral under the shift symmetry and supersymmetry breaking is driven by a combination of the U(1) D-term and the dilaton and z-field F-term. Alternatively, a way to avoid the tachyonic scalar masses without adding the extra field z is to modify the matter kinetic terms by a dilaton dependent factor. A main difference of the second analysis from the first work is that we use a field representation in which the gauged shift symmetry corresponds to an ordinary U(1) and not an R-symmetry. The two representations differ by a Kahler 1 Aspects of String Phenomenology in Particle Physics and Cosmology 3 transformation that leaves the classical supergravity action invariant. However, at the quantum level, there is a Green-Schwarz term generated that amounts an extra dilaton dependent contribution to the gauge kinetic terms needed to cancel the anomalies of the R-symmetry. This creates an apparent puzzle with the gaugino masses that vanish in the first representation but not in the latter. The resolution to the puzzle is based to the so called anomaly mediation contributions [7,8] that explain precisely the above apparent discrepancy. It turns out that gaugino masses are generated at the quantum level and are thus suppressed compared to the scalar masses (and A-terms). 1.2 Conventions Throughout this paper we use the conventions of [9]. A supergravity theory is specified (up to Chern-Simons terms) by a Kahler potential K, a superpotential W, and the gauge kinetic functions fAB (z). The chiral multiplets za,xa are enumerated by the index a and the indices A, B indicate the different gauge groups. Classically, a supergravity theory is invariant under Kahler tranformations, viz. K(z,z) —» K(z,z) + J(z) + J(z), W(z) —> e-l<2j(z)W(z), (1.1) where k is the inverse of the reduced Planck mass, mp = k-1 = 2.4 x 1015 TeV. The gauge transformations of chiral multiplet scalars are given by holomorphic Killing vectors, i.e. Sza = eAkA(z), where eA is the gauge parameter of the gauge group A. The Kahler potential and superpotential need not be invariant under this gauge transformation, but can change by a Kahler transformation SK = eA Mz)+ ta(z)] , (1.2) provided that the gauge transformation of the superpotential satisfies SW = -eA K2rA (z) W. One then has from SW = WaSza WakA = -K2rAW, (1.3) where Wa = 9aW and a labels the chiral multiplets. The supergravity theory can then be described by a gauge invariant function g = k2 K + log(K6WW). (1.4) The scalar potential is given by V = vf +vd VF = eK2'c (-3k2ww + VaWgaPVpW) vd = 2 (Ref)-1 AB PaPb, (1.5) where W appears with its Kahler covariant derivative VaW = 9aW(z) + k2(9«K)W (z). (1.6) 4 I. Antoniadis The moment maps PA are given by Pa = i(k£3aK - ta). (1.7) In this paper we will be concerned with theories having a gauged R-symmetry, for which rA (z) is given by an imaginary constant rA (z) = iK-2£,. In this case, k-2£ is a Fayet-Iliopoulos [10] constant parameter. 1.3 The model The starting point is a chiral multiplet S and a vector multiplet associated with a shift symmetry of the scalar component s of the chiral multiplet S 6s = -ic9, (1.8) and a string-inspired Kahler potential of the form —p log(s + s). The most general superpotential is either a constant W = K-3a or an exponential superpotential W = K-3aebs (where a and b are constants). A constant superpotential is (obviously) invariant under the shift symmetry, while an exponential superpotential transforms as W —» We-lbc0, as in eq. (1.3). In this case the shift symmetry becomes a gauged R-symmetry and the scalar potential contains a Fayet-Iliopoulos term. Note however that by performing a Kahler transformation (1.1) with J = K-2bs, the model can be recast into a constant superpotential at the cost of introducing a linear term in the Kahler potential 6K = b(s + s). Even though in this representation, the shift symmetry is not an R-symmetry, we will still refer to it as U(1 )R. The most general gauge kinetic function has a constant term and a term linear in s, f(s) = 6 + (3s. To summarise,1 K(s, s) = —p log(s + s) + b(s + s), W (s) = a, f(s)= 6 + (s, (1.9) where we have set the mass units k = 1. The constants a and b together with the constant c in eq. (1.8) can be tuned to allow for an infinitesimally small cos-mological constant and a TeV gravitino mass. For b > 0, there always exists a supersymmetric AdS (anti-de Sitter) vacuum at (s + s) = b/p, while for b = 0 (and p < 3) there is an AdS vacuum with broken supersymmetry. We therefore focus on b < 0. In the context of string theory, S can be identified with a compact-ification modulus or the universal dilaton and (for negative b) the exponential superpotential may be generated by non-perturbative effects. 1 In superfields the shift symmetry (1.8) is given by 6S = —icA, where A is the superfield generalization of the gauge parameter. The gauge invariant Kahler potential is then given by K(S, S) = —pK-2 log(S + S + cVR) + K-2b(S + S + cVR), where VR is the gauge superfield of the shift symmetry. 1 Aspects of String Phenomenology in Particle Physics and Cosmology 5 The scalar potential is given by: V = Vf + VD Vf = a2eblp-2 j 1 (pi - b)2 - 3l2J I = 1/(s + s) Vd = c2 p+251 (Pl - b)2 (L10) In the case where S is the string dilaton, VD can be identified as the contribution of a magnetized D-brane, while VF for b = 0 and p = 2 coincides with the tree-level dilaton potential obtained by considering string theory away its critical dimension [11]. For p > 3 the scalar potential V is positive and monotonically decreasing, while for p < 3, its F-term part VF is unbounded from below when s + s —} 0. On the other hand, the D-term part of the scalar potential VD is positive and diverges when s + s —» 0 and for various values for the parameters an (infinitesimally small) positive (local) minimum of the potential can be found. If we restrict ourselves to integer p, tunability of the vacuum energy restricts p = 2 or p = 1 when f(s) = s, or p = 1 when the gauge kinetic function is constant. For p = 2 and f(s) = s, the minimization of V yields: b/l = a « -0.183268 , p = 2 (1.11) a2 A —2 = A2(a) + B2(a)-A2 « -50.6602 + O(A), (1.12) bc2 b3c2 where A is the value of V at the minimum (i.e. the cosmological constant), — is the negative root of the polynomial -x5 + 7x4 - 10x3 - 22x2 + 40x + 8 compatible with (1.12) for A = 0 and A2(a), B2(a) are given by A2(a)= 2e-a -4 + 4 ^- f ; B2M = (1.13) 3 - 4 2 - 2 2 - 4 -2 It follows that by carefully tuning a and c, A can be made positive and arbitrarily small independently of the supersymmetry breaking scale. A plot of the scalar potential for certain values of the parameters is shown in figure 1.1. At the minimum of the scalar potential, for nonzero a and b < 0, supersym-metry is broken by expectation values of both an F and D-term. Indeed the F-term and D-term contributions to the scalar potential are 2 vfU_f = 2aW(1 - >°, b3C2 ( 2 — VdIs+5_a = - 1 - - >0. (1.14) S+S_ b - V — The gravitino mass term is given by n2b2 (ma/2)2 = eG = —r ea. (1.15) Due to the Stueckelberg coupling, the imaginary part of s (the axion) gets eaten by the gauge field, which acquires a mass. On the other hand, the Goldstino, which is 6 I. Antoniadis V Fig. 1.1. A plot of the scalar potential for p = 2, b = —1, 5 = 0, | = 1 and a given by equation (1.12) for c = 1 (black curve) and c = 0.7 (red curve). a linear combination of the fermion of the chiral multiplet x and the gaugino A gets eaten by the gravitino. As a result, the physical spectrum of the theory consists (besides the graviton) of a massive scalar, namely the dilaton, a Majorana fermion, a massive gauge field and a massive gravitino. All the masses are of the same order of magnitude as the gravitino mass, proportional to the same constant a (or c related by eq. (1.12) where b is fixed by eq. (1.11)), which is a free parameter of the model. Thus, they vanish in the same way in the supersymmetric limit a —» 0. The local dS minimum is metastable since it can tunnel to the supersymmetric ground state at infinity in the s-field space (zero coupling). It turns out however that it is extremely long lived for realistic perturbative values of the gauge coupling 1 ~ 0.02 and TeV gravitino mass and, thus, practically stable; its decay rate is [5]: 1.4 Coupling a visible sector The guideline to construct a realistic model keeping the properties of the toy model described above is to assume that matter fields are invariant under the shift symmetry (1.8) and do not participate in the supersymmetry breaking. In the simplest case of a canonical Kahler potential, MSSM-like fields ^ can then be added as: where WMssm(^) is the usual MSSM superpotential. The squared soft scalar masses of such a model can be shown to be positive and close to the square of r - e-B with B« 10300 . (1.16) k = — k 2 log(s + s) + K 2b(s + (( W = K-3a + Wmssm, (1.17) 1 Aspects of String Phenomenology in Particle Physics and Cosmology 7 SL = (1.18) the gravitino mass (TeV2). On the other hand, for a gauge kinetic function with a linear term in s, (3 = 0 in eq. (1.9), the Lagrangian is not invariant under the shift symmetry ,Pc T and its variation should be canceled. As explained in Ref. [5], in the 'frame' with an exponential superpotential the R-charges of the fermions in the model can give an anomalous contribution to the Lagrangian. In this case the 'Green-Schwarz' term ImsFF can cancel quantum anomalies. However as shown in [5], with the minimal MSSM spectrum, the presence of this term requires the existence of additional fields in the theory charged under the shift symmetry. Instead, to avoid the discussion of anomalies, we focus on models with a constant gauge kinetic function. In this case the only (integer) possibility2 is p = 1. The scalar potential is given by (1.10) with ( = 0, 6 = p = 1. The minimization yields to equations similar to (1.11), (1.12) and (1.13) with a different value of a and functions Ai and Bi given by: b(s + s) = a « -0.233153 bc2 A = A1 (a) + B1 (a)^- « -0.359291 + O(A) (1.19) a2 a2- Ai(a)= 2eaa3 - (a -^ , Bi(a)= (a - 1)2 ' 11 J (a - 1)2 ' where a is the negative root of —3+(a-1 )2(2-a2/2) = 0 close to -0.23, compatible with the second constraint for A = 0. However, this model suffers from tachyonic soft masses when it is coupled to the MSSM, as in (1.17). To circumvent this problem, one can add an extra hidden sector field which contributes to (F-term) supersymmetry breaking. Alternatively, the problem of tachyonic soft masses can also be solved if one allows for a non-canonical Kahler potential in the visible sector, which gives an additional contribution to the masses through the D-term. Let us discuss first the addition of an extra hidden sector field z (similar to the so-called Polonyi field [12]). The Kahler potential, superpotential and gauge kinetic function are given by K = -K-2 log(s + s) + K-2b(s + s) + zz + pp , W = K-3a(1 + YKz)+ Wmssm(p) , f(s) = 1 , fA = 1/gA, (1.20) where A labels the Standard Model gauge group factors and y is an additional constant parameter. The existence of a tunable dS vacuum with supersymmetry 2 If f(s) is constant, the leading contribution to Vd when s + s —> 0 is proportional to 1/(s + s)2, while the leading contribution to VF is proportional to 1/(s + s)p. It follows that p < 2; if p >2, the potential is unbounded from below, while if p = 2, the potential is either positive and monotonically decreasing or unbounded from below when s + s —> 0 depending on the values of the parameters. 8 I. Antoniadis breaking and non-tachyonic scalar masses implies that y must be in a narrow region: 0.5