Some aspects of the phenomenology of canonical noncommutative spacetimes

a r X i v :h

e

p -t h /0401136v 1 20 J a n 2004Some aspects of the phenomenology of canonical noncommutative spacetimes ?

Luisa Doplicher

Dipart.Fisica,Univ.Roma “La Sapienza”,P.le Moro 2,

00185Roma,Italy ?

I describe some phenomenological contexts in which it is possible to investigate e?ects induced

by (string-motivated)canonical noncommutative spacetime.Due to the peculiar structure of the

theory the usual criteria adopted for the choice of experimental contexts in which to test a theory

may not be applicable here;care is required in taking into account the e?ects of IR/UV mixing.

This invites one to consider contexts involving particles of relatively high energies,like high-energy

cosmic rays and certain high-energy gamma rays observed from distant astrophysical sources.

Canonical noncommutative spacetime is characterized by coordinate noncommutativity of the form:

[x μ,x ν]=iθμν.(1)An increase of interest in this type of noncommutativity has been recently motivated by the observation that it may be relevant to the description of some aspects of string theories formulated in presence of a background B ?eld.Since they re?ect the properties of a background the θμνparameters cannot be observer independent;thus,as a normal background ?eld would,they break [1,2,3,4]some spacetime symmetries of the theory.This symmetry loss causes one-loop E (p )dispersion relations to be deformed.Dispersion relation deformations in (non supersymmetric)U (1)theory turn out to be as follows.For photons the modi?cation to the self-energy is proportional to [3](pθ)μ(pθ)ν(pθ)2;(3)where C is a constant.This dispersion relation deformation is polarization dependent,in the sense that only photons with polarization vector parallel to the direction of the vector (pθ)μare a?ected by the modi?cation.For neutral scalars the modi?cation to the self-energy is proportional to (pθ)?2and thus the dispersion relation is modi?ed in this way:p 20=m 2+ p 2+C ′

?

This work is based on Refs.[1]and [2],to which I refer the reader for all details.?Electronic address:doplicher@roma1.infn.it 1For simplicity I am assuming that the matrix θμνcan be described in terms of a single characteristic scale θ.

2 The deformation(3)of the photon dispersion relation brings about a deformation of the propagation of light;the speed of light acquires a dependence upon wavelength.A good opportunity to test this e?ect is provided by Blazars [6,7],which indeed have been observed[8]at and above the TeV scale.For some choices of the cuto?Λthe analysis of recently-observed Blazars allows[1]to set limits onθin the neighborhood ofθ 10?40cm2The surprising fact that limit takes the form of an upper bound re?ects some features of the IR/UV mixing.In fact,the observations only allow to determine that one of two options is realized:either the cuto?estimate is incorrect or a suitable upper bound onθmust be inforced.The mentioned polarization dependence of the e?ect implies that,for unpolarized sources, only a fraction of the?ux can be used for the analysis.

In the context of observations of cosmic rays an opportunity for canonical noncommutativity to enter the analysis originates from(4),which suggests a modi?cation of the dispersion relation for pions.This would a?ect the threshold energy requirements for photopion production,

p+γ=p+π,(5) which is known to be relevant for the analysis of the interactions between high-energy cosmic rays and CMB(cosmic microwave background)photons.The usual special relativistic analysis of photopion production leads to the prediction that the?ux of cosmic rays with energies above a cuto?energy of1019eV should be strongly suppressed.The value of this cuto?energy can be signi?cantly higher[1]if one takes into account the modi?ed dispersion relation(4)for the pion,while keeping unmodi?ed the law of energy-momentum conservation and the dispersion relations for the proton and the CMB photon.Support for an unmodi?ed law of energy-momentum conservation is found[2,9]in the analysis of?eld theories in canonical noncommutative spacetime2,the assumption of unmodi?ed proton dispersion relation is justi?ed by some general properties[11]of charged spin-1/2high-energy particles in canonical noncommutativity, and we assumed[1]an unmodi?ed dispersion relation for CMB photons because of their very low typical energies (likely below the mentioned low-energy cuto?of validity of our framework)and the strong experimental basis for an unmodi?ed dispersion relation for low-energy photons.Forthcoming cosmic-ray observatories could be sensitive to the e?ects of canonical noncommutativity ifθtakes a value which is roughly in the neighborhood[1]of10?38cm2.

[1]G.Amelino-Camelia,L.Doplicher,S.Nam and Y.S.Seo,Phys.Rev.D67(2003)085008,hep-th/0109191.

[2]G.Amelino-Camelia,M.Arzano and L.Doplicher,hep-th/0205047.

[3]A.Matusis,L.Susskind and N.Toumbas,JHEP0012(2000)002,hep-th/0002075.

[4]C.E.Carlson,C.D.Carone and R.F.Lebed,Phys.Lett.B549:337-343,2002,hep-ph/0209077.

[5]S.Minwalla,M.Van Raamsdonk and N.Seiberg,JHEP0002(2000)020,hep-th/9912072.

[6]G.Amelino-Camelia,J.Ellis,N.E.Mavromatos,D.V.Nanopoulos and S.Sarkar,Nature393(1998)763,astro-ph/9712103;

G.Amelino-Camelia and T.Piran,Phys.Rev.D64(2001)036005,astro-ph/0008107.

[7]R.J.Protheroe and H.Meyer,Phys.Lett.B493(2000)1,astro-ph/0005349.

[8]S.D.Biller et al,Phys.Rev.Lett.83(1999)2108.

[9]N.R.Douglas and N.A.Nekrasov,Rev.Mod.Phys.73(2001)977.

[10]G.Amelino-Camelia,Int.J.Mod.Phys.D11(2002)35,gr-qc/0012051;Phys.Lett.B510(2001)255,hep-th/0012238.

[11]L.Alvarez-Gaume and J.L.F.Barbon,Int.J.Mod.Phys.A16:1123-1146,2001,hep-th/0006209.