COSMIC RAYS AND TESTS OF FUNDAMENTAL PRINCIPLES

Luis Gonzalez-MestresLAPP, CNRS-IN2P3 – Université de Savoie

France

The relativity principleHenri Poincaré, 1895

”A propos de la théorie de M.Larmor”L’Eclairage électrique, Vol. 5, 5.

”Absolute motion of matter, or, to be more precise, the relative motion of weighable matter and ether, cannot be disclosed. All that can be done is to reveal the motion of weighable matter with respect to weighable matter”.

Possible Lorentz symmetry breakingAlbert Einstein, 1921

Geometry and Experiment (English, 1922)"It is true that this proposed physical interpretation of geometry breaks down when applied immediately to spaces of sub-molecular order of magnitude. But nevertheless, even in questions as to the constitution of elementary particles, it retains part of its importance. For even when it is a question of describing the electrical elementary particles constituting matter, the attempt may still be made to ascribe physical importance to those

ideas of fields which have been physically defined for the purpose of describing the geometrical behaviour of bodies which are large as compared with the molecule. Success alone can decide as to the justification of such an attempt, which postulates physical reality for the fundamental principles of Riemann's geometry outside of the domain of their physical definitions. It might possibly turn out that this extrapolation has no better warrant than the extrapolation of the idea of temperature to parts of a body of molecular order of magnitude”

Source : MacTutor History of Mathematics Archive

More than 20 ordres of magnitude…… between molecular distance scales and those associated to the wavelengts of the highest- energy cosmic rays observed. And no well-established violation of relativity !

What to do ?Follow Einstein’s reasoning : Try to apply, try to break, make measurements… and see what happens => Cosmic-ray experiments

Other fundamental principles to test

• Quantum mechanics – Standard uncertainty principe, …• Energy and momentum conservation

as a consequence of space-time translation invariance• (At least) four effective space-time

dimensions• (CPT, Lagrange-Hamilton, vacuum…)

Models of Lorentz symmery violation (LSV) that can be tested by UHCR. Example, QDRK :

(Quadratically deformed relativistic kinematics) E = (2π)⁻¹ h c a⁻¹ e (k a)

e² (k a) (k a)² − ≃ α (k a)⁴ + (2 a)² h⁻² m² c²k = wave vector, a = fundamental length

Expansion for ka << 1, α (ka)⁴ generates LSV New physics when α (ka)⁴ becomes of the same

order as the mass term (2 a)² h⁻² m² c²Needs an absolute (vacuum) rest frame (VRF)

Otherwise : no observable effect for UHECR (go to the center of mass frame, corrections to SR are too small)

Example of new physics : Possible suppression of the GZK cutoff, but there is more…

=> transition region E ≈ E (trans) where :α (k a)⁴ ≈ (2 a)² h⁻² m² c²

Above E (trans) kinematical balances are modified => the GZK cutoff would disappear because of the new cost in energy to split p with the term − p c (k a)²/2 in the dispersion relation. BUT QUESTIONS : What is the right value of α for each particle ? What is the « fundamental » value of α for standard matter ? => take protons and/or nuclei, or quarks and gluons ? Estimate the difference.

Is the fundamental scale the Planck scale ?

See CRIS 2008 ProceedingsPresent data do not necessarily exclude « maximal » LSV

with α ≈ 0.1 – 1 for quarks and gluons, a = Planck length => UHECR composition and sources ?

Gonzalez-Mestres, 1997 : « For α a² > 10⁻⁷² cm² , and assuming a universal value of α, the

GZK cutoff is suppressed for the particles under consideration and ultra-high energy cosmic rays (e.g. protons) produced anywhere in the presently observable Universe can reach the earth without losing their energy in collisions with the cosmic microwave background radiation » (α > 10⁻⁶ if a = Planck length)

It was actually assumed that the highest-energy cosmic rays are protons => If so, this is the upper bound on α (proton) from the possible existence of the GZK cutoff => For large systems , α proportional to M⁻² in order to get a consistent QDRK => Extra M⁻² when comparing with M² /p .

Gonzalez-Mestres, 1997 : If particle 1 has a positive value of α larger than that of particle 2, particle 2 can decay into particle 1 + (…) at high enough energy ( p -> p + γ ). But : i) often dynamically difficult ; ii) time dilation => In general, very slow process => f.i. can the decays p -> p + γ , N -> N + γ replace the GZK cutoff for protons and nuclei ?

=> Possible suppression of photons by γ -> e+ e⁻ ?

Gonzalez-Mestres, 1997 and 2000 : suppression of synchrotron radiation in UHE cosmic accelerators.

=> New experimental tests of LSV, bounds… ?

Pierre Auger Collaboration, February 2010 :“… a suppression of the flux with respect to a power lawextrapolation is found , which is compatible with the predicted Greisen-Zatsepin-Kuz’min (GZK) effect, but couldalso be related to the maximum energy that can be reached at the sources.”

Suppression of synchrotron radiation by LSV(Gonzalez-Mestres, 2000, arXiv:astro-ph/0011182 , on LSV and acceleration in relativistic schocks) => Extra check ?LSV at energies above E (trans) : the emission of synchrotron radiation by a UHE particle (e.g. proton) becomes more and more difficult, as the negative deformation energy increases

Pierre Auger Collaboration, September 2010 :[arXiv:1009.1855 ] Measurements by the Pierre Auger Observatory of the depth shower maximum and its fluctuations indicate a trend toward heavy nuclei with increasing energy. Although the measurements available now are only up to about 55 EeV, the trend suggests that primary CRs are likely to be dominated by heavy nuclei at higher energies. This interpretation of the shower depths is not certain, however. It relies on shower simulations that use hadronic interaction models to extrapolate particle interaction properties two orders of magnitude in center-of-mass energy beyond the regime where they have been tested experimentally. A knowledge of CR composition is important for deciding which of several source scenarios is more likely. The trajectories of highly charged nuclei are expected toundergo large deflections due to the Galaxy’s magnetic fields. While a correlation of arrival directions with nearby matter on small angular scales is plausible for protons above 55 EeV, it is puzzling if the CRs are heavy nuclei.Definitive conclusions must await additional data. The correlation of recent data with objects in the VCV catalog is not as strong as that observed in 2007. If the evidence for anisotropy is substantiated by future data, then it should also become possible to discriminate between different astrophysical scenarios (…)

More involved scenariosD-Foam models, space-time foam model based on recoiling D-branes, where Lorentz symmetry is violated for photon propagation and reactions not involving incident charged particles, but not for charged particle propagation and interactions => LDRK (linearly deformed relativistic kinematics E pc − ≃ α’ p²/MPlanck ) for photons.

J.Ellis, N.E. Mavromatos, D.V. Nanopoulos, arXiv:1004.4167L. Maccione, S. Liberati, G. Sigl, arXiv:1003.5468v1 and v2According to J. Ellis et al. “particle interactions conserve Lorentz-invariantly” energy and momentum “in a leading approximation”. All formulae are given at a first-order approximation => What happens at “non-leading” orders, which contain in particular the quadratic deformations ?

LDRK and phenomenology

My 1997 papers discarded LDRK for phenomenological reasons : it naturally leads to too strong effects. Even for a more sophisticated string model considered by Ellis et al. where linear LSV is strongly restricted, Maccione et al. find that “this model would predict too many photons in the ultra-high energy cosmic ray flux to be consistent with observations” in spite of the fact that “only purely neutral particles, such as photons or Majorana neutrinos, posses LV modified dispersion relations”. The last paper by Ellis et al. is supposed to avoid the recent criticism addressed by Maccione et al. using AUGER data ( arXiv:0712:1147 ).

BUT WHAT CAN BE THE FUNDAMENTAL PHYSICS BEHIND STRINGS ?

STRINGS, 40 YEARS AGOString theory has its origins in the DUAL RESONANCE MODEL introduced by Gabriele Veneziano in 1968 using the Euler beta fonction for a four-point amplitude. The model was generalized to an N-point amplitude by Ziro Koba and Holger Bech Nielsen. Dual models of strong interactions were described by Yoichiro Nambu, H.B. Nielsen and Leonard Susskind in terms of strings (infinite number of simple harmonic oscillators describing the motion of an extended one-dimensional string). In 1970, H.B. Nielsen and Poul Olesen, and Bunji Sakita and Miguel Angel Virasoro obtained the dual amplitudes as an approximation to the sum of a large number of planar “fishnet” Feynman diagrams.

=> Natural link strings <-> underlying constituent structure

Why not a constituent structure behind string theories ? =>SUPERBRADYONS

Vacuum = material medium, « elementary » particles = excitations of this medium, Lorentz symmetry could beof dynamical origin. Solid state book, simplest dispersion relation for phonons in a lattice is of the QDRK type :

e (k a) = 2 sin (ka/2) with c (sound) instead of c (light) => Assume the real fundamental matter has a critical speed in vacuum : c (fundamental matter) >> c (light) , just as c (light) >> c (sound) , but not tachyonic : E > 0, m > 0, standard Lorentz symmetry replaced by another symmetry

=> SUPERBRADYON HYPOTHESIS <= Einstein, 1921 ?

Abdus Salam, 1979 Nobel lecture

”Einstein knew that nature was not economical of structures: only of principles of fundamental applicability. The question we must ask ourselves is this: have we yet discovered such principles in our quest for elementarity, to justify having fields with such large numbers of components as elementary ?Recall that quarks carry at least three charges (colour, flavour and a family number). Should one not, by now, entertain the notions of quarks (and possibly of leptons) as being composites of some more basic entities (PRE-QUARKS or PREONS), which each carry but one basic charge ? “

Source : Nobel Foundation site

QUESTIONS ON POSSIBLE PREON MODELS AND THEORIES

- Should preons have the same critical speed in vacuum as

conventional particles ? -> Not the case for γ and phonons. Speed of light >> speed of sound.

- Should standard « elementary » particles be made of two or three preons, just as mesons and baryons are made of two or

three quarks /antiquarks ? -> Not the case for phonons, solitons… in condensed matter physics.

Some basic ingredients of the present standard model of particle physics came from condensed matter physics : spontaneous symmetry breaking, Higgs mechanism (from superfluidity, superconductivity…) .

MAYBE ONE NEEDS A PREON APPROACH DIFFERENT FROM THOSE CONSIDERED THREE DECADES AGO =>

SUPERBRADYONS ? (Gonzalez-Mestres, 1995)cs >> c

Es = cs (ps2 + ms

2 cs2) −1/2 (if new Lorentz symmetry)

ps = ms vs (1 − vs2 cs

−2 )−1/2

« Cherenkov radiation » in vacuum for vs > c => spontaneous emission of « conventional » particles.

Needs compatibility with low-energy bounds on LSV. Must preserve conventional relativity in the ”low- energy limit “.=> Ultra-high energy phenomenon. But superbradyonic remnants may exist in the present universe and play a

cosmological role => Dark matter, dark energy ?

SUPERBRADYONS IN OUR UNIVERSE ?

If superbradyons obey a new Lorentz symmetry with

critical speed cs (fundamental matter) >> c (light)

”relativistic“ superbradyons will have energies >> ps c and

can in principle be able to spontaneously emit ”standard“ particles => Such processes cease to be allowed when the

superbradyon speed becomes close to c (light).

=> A cosmological sea of superbradyons traveling at speed c (light) ? => Or slower superbradyons ?

What about superbradyons in the physical vacuum ?How does the vacuum behave at very low distances ?

« [at ICHEP 2010] Landsberg (…) is presenting an ambitious new theory in which the number of dimensions in the Universe increases as itgrows in size. He and his colleagues propose that the Universe began with just one spatial dimension and one time dimension. “Think of the Universe as a one-dimensional thread that gradually wove itself into a two-dimensional tapestry as it grew, and then wrapped itself up further to create three dimensions”, he says. (…) Evidence of vanishing dimensions may already have been spotted in the shower of particles created by cosmic rays entering our atmosphere (…) [in] cosmic-ray

data collected 15 years ago in the Pamir mountains in central Asia. » See also the transparencies by Greg Landsberg at the ICHEP 2010 site.

Nature, 466, 426 (2010)« Collider gets yet more exotic 'to-do' list »

Zeeya Merali

ORIGINAL PAPER :arXiv:1003.5914

Vanishing Dimensions and Planar Events at the LHC Luis Anchordoqui, De Chang Dai, Malcolm Fairbairn, Greg Landsberg,

Dejan StojkovicWe propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate scales the space is three-dimensional; and at large scales, the space is effectively higher dimensional. This setup allows for some fundamental problems in cosmology, gravity, and particle physics to be attacked from a new perspective. The proposed framework, among the other things, offers a new approach to the cosmological constant problem and results in striking collider phenomenology.

The need of new physics for Pamir data is not obvious, and LSV can in principle yield other ways to solve problems related to renormalization. Furthermore, does one need, in LSV models, such a drastic dimensional suppression to get alignement phenomena ay very high energy ?

A threshold at the 1016 eV energy scale would be equivalent to a threshold at the 10-20 cm distance scale. => Perhaps vacuum can then react to the collision between the cosmic ray and the atmospheric target, by capturing a comparatively small amount of energy equivalent to a fraction of the target energy, and release this energy in the form of superbradyonic matter and waves (ΔE >> Δp c ).

The approach by Anchordoqui et al. explicitly breaks Lorentz symmetry => requires a VRF

By capturing a fraction of the target energy, but not its conventional equivalent in momentum, the vacuum generates a suppression of the available energy for the transverse momenta of the high-energy particles produced in the collision of the cosmic ray with the atmosphere.(Gonzalez-Mestres, arXiv:1009.1853 )

A few rough numbers : ΔE and superbradyon rest energy in

the GeV range, cs ~ 106 c and vs ~ c would imply :

superbradyon mass ~ meV c−2

superbradyon momentum ~ meV c−1

superbradyon kinetic energy ~ meV

=> not detectable, as expected to interact very weakly

DARK MATTER SUPERBRADYONS AS A POSITRON SOURCE ?

PAMELA Collaboration, Nature 458, 607 (2 April 2009) : An anomalous positron abundance in cosmic rays with energies 1.5–100 GeV

(…) Previous statistically limited measurements of the ratio of positron and electron fluxes have been interpreted as evidence for a primary source for the positrons, as has an increase in the total electron+positron flux at energies between 300 and 600 GeV. Here we report a measurement of the positron fraction in the energy range 1.5–100 GeV. We find that the positron fraction increases sharply over much of that range, in a way that appears to be completely inconsistent with secondary sources. We therefore conclude that a primary source, be it an astrophysical object or dark matter annihilation, is necessary.

« Non-relativistic » remnant superbradyons with v close to c ?

E m c≃ s2 + m v2/2

p m v ≃Ekin m v≃ 2/2

To explain (or contribute to) the positron flux (Gonzalez-Mestres, arXiv:0905.4146):

- Decays or annihilations into « conventional » particles => use the whole superbradyon energy, including rest energy - « Cherenkov » decays emitting « conventional » Particles => use only a fraction of the superbradyon kinetic energy

Equivalent superbradyonic rest energies

Decays and annihilations spending the superbradyon rest energy : if cs ~ 106 c and m cs

2 ~ 1 TeV , v ~ c =>

superbradyon mass ~ eV c−2

superbradyon momentum ~ eV c−1

superbradyon kinetic energy ~ eV

« Cherenkov » decays using only a fraction of the superbradyon kinetic energy : m c2

~ 1 TeV =>

m cs2 ~ 1024 eV =>

REAL SUPERHEAVY OBJECT

The basic question being : is there « something » beyond Planck scale, and can we experimentally find some track of such a « beyond » ? Standard relativity is not the only fundamental principle concerned => Quantum mechanics can be « deformed » in a similar way.CODATA value of h : 6.62606896 x 10−34 J s with a 5.0 x 10−8 standard accuracy and based on low-energy measurements (P.J. Morr, B.N. Taylor and D.B. Newell, Rev. Mod. Phys. 80, 633, 2008) => what happens at ultra-high energies ?

SUPERBRADYONS AND QDRK ARE JUST A TOOL

There has already been important work on possible departures from standard quantum mechanics : f.i. Julius Wess, q-Deformed Heisenberg Algebras, arXiv:math-ph/9910013 (see also the references given in Gonzalez-Mestres, arXiv:0908.4070 ).

Develop the equivalent of QDRK for quantum mechanics ? => New commutation relations, where the effect of the modification increases with energy=> can lead, for instance, to unexpected intrinsic uncertainties (direction, momenta, energy…)More basically, for instance : can hamiltonian and lagrangian formalisms describe the behaviour of vacuum at ultra-short distance scales ?

A very small failure of energy and momentum conservation at ultra-high energies can fake the Greisen – Zatsepin – Kuzmin cutoff. And what is the vacuum doing at such ultra-short wavelengths ?

Would superbradyons and similar objects obey quantum mechanics ? Or is quantum mechanics a « composite » phenomenon ?And many other similar questions…

TO CONCLUDE :

Cosmic-ray experiments have extraordinary and unprecedented discovery potentialities