Unparticle effects on cosmic ray photon and $e^pm$

arXiv:0907.1996v3 [astro-ph.HE] 14 Sep 2009 Unparticle Physics on Cosmic Ray Photon and e± Shao-Xia Chen1 School of Space Science and Physics, Shandong University at Weihai, Weihai, Shandong 264209, China Rong Hu2 School of Mechanical Engineering, Beijing Technology and Business University, Beijing 100048, China Abstract We study the effects of unparticle physics on the cosmic ray photon and e±, including on the pair production (PP) and elastic scattering (ES) of cosmic ray photon offvarious background radiations, and on the inverse Compton scattering of cosmic ray e± with cosmic radiations. We compute the spin-averaged amplitudes squared of three processes and find that the advent of unparticle will never significantly change the interactions of cosmic ray photon and e± with various background radiations, although the available papers show that ES which occurs in the tree-level through unparticle exchanges will easily surpass PP in the approximate parameter regions. PACS numbers: 12.60.−i, 14.80.−j, 95.85.Ry, 13.85.Tp, 98.70.Sa 1 Introduction In convention, it is convinced that the dominant energy loss is PP instead of ES in the Standard Model (SM) for the cosmic ray photon with energy above the PP threshold Eth [1] Eth = m2 e/ǫ ≃2.6 × 1011eV ×  ǫ eV −1 , (1) where ǫ is the energy of a background photon. However recent research [2, 3, 4] on diphoton interaction reveals that the cross section of unparticle exchange can easily surpass the SM one at high enough energy because unparticle exchanges are also at the tree-level through all s-, t-, and u-channels. It is natural to explore the consequence of unparticle physics on the cosmic ray photon, especially on whether the appearance of unparticle will lead to its dominant energy loss process to change from PP to ES, which will cause nontrivial observational signals in the spectrum of cosmic ray photon. In the meanwhile, very recently the Pamela collaboration announced their first measurements on the cosmic ray (CR) positron fraction [5] in the energy range 1.5 −100GeV. The positron fraction of Pamela data shows a prominent excess to the background estimation [6, 7] of the conventional CR propagation model in the region ∼10−100GeV. This result is consistent with previous measurements by, e.g., HEAT [8] and AMS [9]. On the other hand, the electron spectrum up to several TeV measured 1ruxanna@sdu.edu.cn 2hur@ihep.ac.cn 1 by ATIC collaboration also displays an obvious excess in the region around 300 ∼800GeV [10], which confirms the measurements of the electron spectrum by PPB-BETS [11], H.E.S.S. [12, 13], and most recently by Fermi [14]. The mismatch between theory and observations stimulates a lot of interest on the cosmic ray e±, and we will reexamine the propagation of cosmic ray e± in the framework of unparticle physics. On particular, we address the dominant loss process for cosmic ray e±, inverse Compton scattering, to study the impact of unparticle stuffon e± and further on the observational excess. The paper is organized as follows. In the next section, we overview the basic property of unparticle physics, including the odd propagator and phase space of unparticle stuffwith different Lorentz structures. In Sec.3, we derive the scattering amplitudes for the involved processes, that is, the PP and ES for the photon and the Compton scattering for e±. In Sec.4, we apply the results in the previous section to the cosmic ray physics and analyze the specific cases to draw definite results to the propagation of cosmic ray photon and e±. In the final section, we present some comments on this manuscript. 2 Basic property of Unparticle stuff Two years ago, Georgi [15] proposed the existence of unparticle, which is a scale invariant sector with a non-trivial infrared fixed-point. He assumed that the very high energy theory contains both the SM fields and the fields of a theory with a nontrivial infrared fixed point, which we will call BZ (for Banks-Zaks [16]) fields. The two sectors interact through the exchange of particles with a large mass scale MU. Below the scale MU, there are nonrenormalizable couplings involving both SM fields and BZ fields suppressed by powers of MU. These have the generic form 1 M k U OsmOBZ (2) where Osm is an operator with mass dimension dsm built out of SM fields and OBZ is an operator with mass dimension dBZ built out of BZ fields. The renormalizable couplings of the BZ fields then cause dimensional transmutation as scale-invariance in the BZ sector emerges at an energy scale ΛU. In the effective theory below the scale ΛU the BZ operators match onto unparticle operators, and the interactions of (2) match onto interactions of the form CUΛdBZ−dU U M k U OsmOU , (3) where dU is the scale dimension of the unparticle operator OU and the constant CU is a coefficient function. It was also pointed out [15] that an unparticle stuffwith scale dimension dU looks like a non- integral number dU of invisible particles. In the same Letter [15], Georgi derived the peculiar pha

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