Stable Superstring Relics and UHECR Claudio Corianò Dipartimento di Fisica Universita di Lecce, INFN Sezione di Lecce Alessandro Cafarella (DdF and INFN Lecce) Alon Faraggi (Oxford) IFAE Lecce, Aprile 2003
Superstring Theory predicts the existence of relics, metastable particles, whose average lifetime is larger than the age of the universe and which could, in principle, be good dark matter candidates. At the same time, these states be responsible for the Ultra High Energy Cosmic Rays (UHECR) events which will be searched for by various experimental collaborations around the world in the near future. I describe a possible path we can take in order to link theoretical predictions with the observations, although a lot of phenomenological work still remains to be done in order to see whether the path that we suggest is a good one. Other suggestions, however, may emerge along the way
How do we Test Theories? This turns out to be the single and most difficult issue we will be facing in this and in the next decade. Strings are with no doubt the richest theoretical constructs of the last decades, but we have no experimental signal pointing toward a validation or falsification of the theory. Not a single new result has come out yet from collider experiments, and we seriously hope that we will be taken by surprise once the LHC is in full operation. Large QCD backgrounds: many years of data analysis are ahead of us before some claims can be made on new physics, possible new signals, etc
In the meanwhile Particle Astrophysics, in particular cosmic rays astrophysics, may not be able to reach the level of accuracy that we expect from other types of experiments, such as collider experiments. But the technology is rapidly changing and we may hope for serious improvements within a decade or less. Tools of analysis Theoretical methods and tools of analysis which are common in collider phenomenology are not immediately applicable to astroparticle physics, since the physical scales entering in the dynamics, for instance in the UHECR dynamics, are substantially different, in practice much much larger.
The attempt we want to make is to connect standard research in Collider Phenomenology to Cosmic Rays Astrophysics. We will be lead, in the course of these analysis, to the notion of Supersymmetric Parton Model as a basic tool for the investigation of UHECR collisions and underline what needs to be done in order to improve the parton model picture for cosmic rays applications. Our motivations are, of course, string inspired, but remain true Since they are of general applicability to very high energy Collisions. We rely on the use of the renormalization group in the Analysis (preliminary) of the structure of the the fragmenation region is UHECR collisions.
Mean Free Path of protons decreses rapidly @ 3 x 10^20 ev Even smaller MFP for nuclei 1962 John Linsey and Coll. Discovered the first cosmic ray with an Energy of about 10^20 ev in the Volcano Ranch array in New Mexico 1991 The Fly s eye cosmic ray research group in the USA observed A cosmic ray event with an energy of 3 x 10^20 ev. Events with energy of 10^20 ev have been reported in the Previous 30 years, but this was the most energetic
Experimental Motivations Cosmic Ray Particles with energies in excess of 4 x 10^11 GeV have been detected HAVERAH PARK AGASA FLYE s EYE 1966 After Penzias and Wilson s discover that low energy microwave Photons permeate the universe, Greisen, Zatsepin and Kuzmin Pointed out that cosmic rays would interact with the CBR. The interaction would reduce their energy so that particles Traveling inter galactic spaces would not have an energy greater than Than 5 x 10^19 ev (GZK cutoff)
1994 The Agasa group in Japan and the Yakutsk group in Russia Each reported an event with an energy of 2 x 10^20 ev. The Fly s Eye event and these events are higher in energy Than any seen before... Who ordered them? Fermi s mechanism (1954) based on acceleration of charged cosmic rays (schok waves) predicts N(E) =E^(-x), x=2.3, 2.5
Electric Fields accelerate the particles. Magnetic Fields deflect them and diffuse them. Some particles are trapped in the wavefront of the schock wave Which can be of astronomic size, long enough in order for the particles to acquire gigantic energies. Particles can escape the schock wave and can back feed the plasma. Wonderful Physics is involved in the formation of UHECR, nonlinear effects in Schock wave accelerations, HEP beyond the Standard Model, Which make the field a truly interesting laboratory.
The Pierre Auger project will construct two 3000 Km^2 grids of detectors spaced at 1.5 Km intervals. one array in the Northern Hemisphere and a second in the Southern Hemisphere
A cascade develops in the atmosphere With increasing multiplicities of the secondary as Energy is spread through the secondary. The process is characterized by very large multiplicity with increasing energies
The integrated flux is well described by a local power law over a large energy range K E ( E) x N = 1 GeV < E <10 11 GeV For a given spectral index x. Only at low energies are the primaries detected directly φ φ ( E = 100GeV ) 1particle / km / sec ( 11 ) 2 E = 10 GeV 1particle / km / century Flux changes dramatically over the entire energy range 2
Up to 1 Tev good discrimination of the various components Through direct detection protons 87% helium 12% nuclei 1% Differences between species understood in terms of Source production and propagation Relative abundances modified by the interstellar medium
Spectral Index The Knee: X~2.5 for E~(10^3-10^4) GeV (flattening) X~3.08 for E~(10^7 10^11) GeV (steeping) Steeps fairly dramatically above this range. Various effects may be responsible for this behaviour 1) Diffusion of cosmic rays from galaxy due To larger than galaxy gyromagnetic radii 2) Anomalous diffusion due to fractional Brownian motion ( Markov process with memory kernel, linked to fractal distribution of intergalactic matter) Proton dominated The Ankle: X~ 3.16, E<10^11 GeV (steeping) X~2.78 E>10^11 GeV (flattening)
Superstring Relics For concreteness we study these questions in the context of realistic free fermionic heterotic string models. Heterotic string allows for embeddings of the Standard Model in SO(10) mutiplets. Type I U(n) as generic structure Heterotic Models exotic matter states due to breaking of the Non Abelian unifying gauge symmetry G by Wilson lines.
Wilson line breaking mechanism Stable massless states with fractional electric charge in the massless spectrum. They must be diluted away or be extremely massive. Standard charges under the SM + fractional charge under a different subgroup of the unifying G. G SO(10) U(1)z SO(10) U(1)z U(1)y Wilsonian matter heavy stable if the U(1)z, symmetry is left unbroken down to low energies long lived.
Free fermion formulation { 1, S, b1, b2, b3 } G=SO(10) x SO(6) 3 x E8 Twisted sector NS 48gen Z2xZ2 N=1 orbifold compattification gravity gauge multiplet 6 multiplets in 10 of SO(10) several singlets of SO(10) transforming under SO(6) E 8 is unbroken hidden matter does not arise No candidates for UHECR
NAHE + basis vectors (Wilson lines) from 48 generations 3 generation + gauge symmetry breaking SU(3) x U(1) B-L x SU(L) L x SU(L) R SU(5)xU(1) SO(6)xSO(4) SU(B) x SU(L) x U(1) B-L x U(1)T 3R E8 broken Exotic matter:related to the subgroup which is left unbroken. GS0 projection + boundary condictions for the basis vectors.
Superstring Standard like-models generalized GSO projection SU(3) c x U(1) c x SU(L) L x U(1) L x U(1) 3 x U(1) n U(1) em = T 3L + U(1) y SU(L) L U(1) Y = 1 / 3 U(1) c + ½ U(1) L U(1) Z =U(1) c U(1) L
Steps in the formation of the UHECRs 1. A relic decays and generates a given initial distribution of primaries 2. Primaries propagate and mostly proton survive 3. Primaries collide with the athmosphere generating showers 4. Showers are detected 5. Shapes of the showers can be reconstructed (fluorescence) 6. Multiplicities measured Theoretical suggestion: Inlcude in the analysis of the first impact of the primary the possibility of having new physics. 1) By modifying the fragmentation region and distribution of the first fragments 2) As a second step refine the entire first stages of the shower formation
Supersymmetry and the parton model At high energy and Momentum transefs we restart to a parton model description of the Strong interactions. S ~ 400 Tev in UHECR much above any current factorization scale Light-cone dominance parton distribution factorization theorems: σ pp =Int( dx 1, dx 2 f(x 1,Q 2,µ 2 ) f (x 2,Q 2,µ 2 ) σ^ij (x 1,x 2,..)) p->i p->j With parton distribution evolving according to Renorm.Group Eqs. There are total diffractive contributions to the total cross section (dominance from vacuum channel) => We claim that this could be the first occasion the apply a susy version of the BFKL
Let s focus on the longe transverse momentum contributions. 1.At high energy and momentum transfers for large collision/factorization scales we add (+) in supersymmetry. 1a.Supersymmetry affecting the initial state. 1b.Supersymmetry affecting the final state. 2.Include supersymmetry in the evolution of the regular and of the supersymmetric parton distributions.
Backward evolution: mixing of anomalous dimensions
SQCD Supersymmetric QCD is a theory characterized by quarks, gluons, scalar quarks and gluinos. It is the natural generalization of QCD to include new physical states.. The gluino is a Majorana fermion. Perturbative computations can be performed in systematic fashion. (flipping rules) as specified below.. Mixing between squarks is neglected.
Squark-quark-gluino interaction Majorana
Flipping rules: separate fermion flow from fermion number
Unitarity view of parton distributions Optical Theorem (quark case)
Supersymmetrization introduces new ladders and new light-cone correlators
Evolution
Short overview: LO and NLO QCD evolution Initial State scaling violations QCD kernels
Non singlet singlet After squark decoupling Non singlet singlet
Solution built by sewing the various regions Recursion relations
Allow beta-function changes Ordinary anomalous Dimensions are now Embedded into larger Matrices. PDF are generated Radiatively from vanishing Bc s and now include Supersymmetric pdf s as well
Susy kernels Distinguish the case of quark-squark-gluon-gluino coupling from the case of quark-gluon-gluino coupling
Antoniadis, Kounnas and Lacaze Kounnas and Ross
Distributions of supersymmetric partners are generated radiatively. Coupled systems of over 100 equations to be solved for a complete flavour decomposition Parametric dependence on the scales chosen to describe the evolution Gluino density: Dynamically generated at small-x from the RG evolution C. C.
CC
Sum Rules can however give information on the distribution of momenta among the incoming partons (Kounnas and Ross; Ellis et al.) A more general analysis needs to be performed to include the intermediate Thresholds (C C)
First and second moment sum rules in a general setting (coupled squarks and gluinos) C.C.
QCD asymptotics New asymptotics now depend on the scale at which we couple the superpartners
Momentum distributions among the Superpartners: an example CC
Susy Fragmentation functions Alon Faraggi, C.C.
D(x,Q) fragmentation functions
Match the various regions as for susy pdf s. Perform complete flavour decompositions
Radiatively generated fragmentation functions initials
Various fragmentation functions Parametric dependence
The rearrangement of the spectrum is at a few percent level (peaks shifted toward smaller-x values) (Qf= 15 TeV)
R= total fragmentation of quarks into protons as a function of the initial fragmenting scale Q. This plot requires a solution of a complex set of about 100 fragmenting equations and very high numerical accuracy (rad. gen). The spectrum is rearranged at a few percent level if susy is included AF, CC
The spectrum is indeed readjusted. Effects of fragmenatation of superpartners startes appearing At scales of several Tev s. Sum Rules in the fragmentation region can also be analized to obtain a clear picture of how the spectrum is affected.
How are we going to interface these results with the Experiments? What do the experimentalists see? What does the detector (in the experimetalists s mind) see? 1) The experimentalists run complex Monte Carlos to analize the multiplicites. 2) The results of the simulations are fed into a detector simulation 3) Measurement and simulations are compared Let s first see what Monte Carlo has to say
1 Distribution in rapidity of multiplicities For various final detected particles 2 3 1 : photons 2 : e - 3 : ν µ A. Cafarella, C.C.
1 2 3 1 : photons 2 : e - 3 : ν µ
1 2 3 1 : photons 2 : e - 3 : ν µ
E=100 000 TeV
INFN-LECCE Computer Farm
Cosmic Ray experiments may give some hints of new physiscs although the pattern to follow seems to be rather complex. Beside determining the origin of these rays (correlation Uncorrelation with the galactic plane, point-like origin etc) They can possibly be used to look to search for new fundamental physics. Supersymmetry, at parton level, predicts small (4-5%) readjustments of the decay spectra in the fragmentation Region. Initial state scaling violations can also be introduced In a more complete analysis of the p-p collisions in the Athmosphere. We have quantified them: few percent level. What about diffraction, angular ordering of the susy cascade etc? However, the possibility of detecting new physics directly From the structure of the shower seems to be quite remote.