In an extention of the Standard Model by three relatively light right-handed
neutrinos (the nuMSM model) the role of the dark matter particle is played by
the lightest sterile neutrino. We demonstrate that the observations of the
extragalactic X-ray background allow to put a strong upper bound on the mass of
the lightest active neutrino and predict the absolute values of the mass of the
two heavier active neutrinos in the nuMSM, provided that the mass of the dark
matter sterile neutrino is larger than 1.8 keV.Comment: 6 pages. revtex

A. Boyarsky

A. D. Dolgov

A. Kusenko

A. Neronov

A. Strumia

D. N. C. Lin

E. K. Akhmedov

K. Abazajian

M. Shaposhnikov

O. Ruchayskiy

P. B. Pal

P. Minkowski

S. Dodelson

S. H. Hansen

S. Tremaine

T. Asaka

V. D. Barger

X. Shi

English

arXiv

Crossref

Masses of active neutrinos in the νMSM from x-ray astronomy

In an extension of the Standard Model by three relatively light right-handed neutrinos (the νMSM model) the role of the dark matter particle is played by the lightest sterile neutrino. We demonstrate that the observations of the extragalactic x-ray background allow us to put a strong upper bound on the mass of the lightest active neutrino and predict the absolute values of the mass of the two heavier active neutrinos in the νMSM provided that the mass of the dark matter sterile neutrino is larger than 1.8 keV. © Pleiades Publishing, Inc. 2006.LPP

Boyarsky, Alexey

Neronov, A.

Ruchayskiy, O.

Shaposhnikov, M.

Infoscience - École polytechnique fédérale de Lausanne

arXiv:hep-ph/0601098v1  12 Jan 2006CERN-PH-TH/2006-006The masses of active neutrinos in the νMSM from X-rayastronomyA. Boyarsky,1 A. Neronov,2 O. Ruchayskiy,3 and M. Shaposhnikov41CERN, Theory department, Ch-1211 Geneve 23, Switzerland2 INTEGRAL Science Data Center,Chemin d’E´cogia 16, 1290 Versoix,Switzerland and Geneva Observatory,51 ch. des Maillettes, CH-1290 Sauverny, Switzerland3Institut des Hautes E´tudes Scientifiques, Bures-sur-Yvette, F-91440, France4E´cole Polytechnique Fe´de´rale de Lausanne,Institute of Theoretical Physics, FSB/ITP/LPPC,BSP 720, CH-1015, Lausanne, Switzerland(Dated: February 7, 2008)AbstractIn an extention of the Standard Model by three relatively light right-handed neutrinos (theνMSM model) the role of the dark matter particle is played by the lightest sterile neutrino. Wedemonstrate that the observations of the extragalactic X-ray background allow to put a strongupper bound on the mass of the lightest active neutrino and predict the absolute values of themass of the two heavier active neutrinos in the νMSM, provided that the mass of the dark mattersterile neutrino is larger than 1.8 keV.PACS numbers: 14.60.Pq, 98.80.Cq, 95.35.+d1Recently a simple extention of the Minimal Standard Model (MSM) by three relativelylight (with the Majorana masses smaller than the electroweak scale) right-handed neutri-nos was suggested [1, 2]. The model (dubbed νMSM ) allows simultaneous explanation ofneutrino oscillations and baryon asymmetry of the universe and proposes the candidate forthe dark matter – the lightest long-lived sterile neutrino. Unlike traditional see-saw mech-anism [3], the tiny values of the active neutrino masses in this model are related to thesmall Yukawa coupling constants between sterile neutrinos and left-handed leptonic dou-blets. Small Yukawas are essential for the explanation of dark matter: the lightest sterileneutrino with the mass of a few keV can be sufficiently long-lived [4, 5]. In addition tothis, small Yukawa couplings are crucial for baryogenesis in the νMSM, leading to coherencein the oscillations of sterile neutrinos [2, 6]. Moreover, they are required by some models,explaining pulsar kick velocities [7].The Lagrangian of the νMSM has the following form:LνMSM = LMSM + iN¯I /∂NI −(L¯αMDαINI +12MIN¯cINI + h.c.). (1)In Eq. (1) we fixed the basis in which the sterile neutrino Majorana mass matrix MI isdiagonal (fields NI denote right-handed neutrinos, I = 1, 2, 3), whereas the Dirac massmatrix providing the mixing between left-handed Lα and right-handed neutrinos is MDαI ≡FαI〈Φ〉 where α = {e, µ, τ} is the active neutrino flavor, FαI is a set of Yukawa couplings,and 〈Φ〉 ≃ 174 GeV is the Higgs vacuum expectation value. The sterile neutrino with I = 1is supposed to be the lightest one.It was pointed out in [1] that a prediction of the absolute values of the masses of activeneutrinos can be made, provided that the only source of the sterile neutrino production in theearly universe is their mixing with active neutrinos. Assuming that the initial concentration(say, at temperatures greater than 1 GeV) of sterile neutrinos were zero, one can estimate [4,5, 8] the sterile neutrino abundance Ωs and identify it with that of the dark matter ΩDM .The abundance is proportional to the square of the Dirac mass and depends only weakly onthe sterile neutrino Majorana mass in the keV region [4, 5, 8]. With the use of these resultsthe constraint on the parameters of the νMSM can be written as [1]:∑α=e,µ,τ|MDα1|2 = m20, (2)where m20= O(0.1eV)2 with an uncertainty of, say, factor of a few, coming from the poor2knowledge of the dynamics of the hadronic plasma at the temperature of the sterile neutrinoproduction. The restrictions from the observations of the cosmic microwave background andthe matter power spectrum inferred from Lyman-α forest data [9, 10] gives a constraint (seealso [11] for a most recent study):M1 > 2 keV . (3)Similarly to Eq. (2) this constraint assumes that the sterile neutrino was produced inactive-sterile neutrino oscillations and plays a role of so-called warm dark matter (WDM).A weaker, but an assumption-free lower bound on the mass of the lightest sterile neutrinoM1 & 0.5 keV (4)comes from the application of Tremaine-Gunn arguments [12] to the dwarf spheroidal galax-ies [13]. Now, since M1 from (3,4) is much larger than m0, the see-saw formula [3] for activeneutrino massesMν = −(MD)TM−1I MD (5)is valid. The analysis of Eq. (5) reveals [1] that the constraint (2) together with (3) leadsto an upper bound on the lightest neutrino mass, mν < m20/M1 ≃ O(10−5) eV. Now, sincethis bound is much smaller than√∆m2sol≃ 10−2 eV, where ∆m2solis the solar mass squaredifference, the masses of other two active neutrinos should be given bym2 =√∆m2sol, m3 =√∆m2atm (6)or bym1 ≈ m2 =√∆m2atm, m21−m22= ∆m2sol, (7)if the hierarchy is inverted1. In numbers [14],∆m2sol= (7.2− 8.9) · 10−5 eV2, ∆m2atm= (1.7− 3.3) · 10−3 eV2 . (8)The errors correspond to 99% confidence level range of 2.58σ. Clearly, the predictions (6,7)remain in force provided the mass of the lightest neutrino is smaller than the error bar inthe solar neutrino mass difference, namely for (99% C.L.)mν < 3 · 10−3eV . (9)1 The same conclusion is true if the bound (4) is taken.3In fact, the results (2) and (3) are not universal and do depend on the details of universeevolution above the temperature of Big Bang Nucleosynthesis (BBN). In particular, they aresensible to the universe content at the time of sterile neutrino production and on particlephysics well beyond the electroweak scale. For example, a substantial lepton asymmetrymay lead to enhancement of the production of the sterile neutrinos [15]. If the reheatingtemperature of the universe is just above the nucleosynthesis scale [16] the considerationleading to Eq. (2) is not applicable at all. If the sterile neutrino has large enough couplingto inflaton it will be created right after inflation rather than at small temperatures. Thereheating of the universe between the moment of the sterile neutrino production and nucle-osynthesis due to late phase transitions or due to hypothetical heavy particle decays woulddilute the concentration of the sterile neutrinos and decrease their momentum, leading tosmaller free streaming lengths at the onset of structure formation.In this note we consider the question whether a robust prediction (which does not dependon the uncertainties discussed above) can be made for active neutrino masses in the νMSMprovided all 100 % of the dark matter in the universe is associated with sterile neutrino.Our analysis is based on the astrophysical constraint coming from the analysis of theX-ray background derived in [17] (for earlier works see [5, 18]). In the νMSM the lighteststerile neutrino can decay into active neutrino and photon with the width given by a trivialgeneralization of Pal and Wolfenstein formula [19, 20]:Γγ =9αem G2F M31256 pi4∑α=e,µ,τ|MDα1|2 . (10)The increase of the Dirac neutrino mass |MDα1|2 (notice that exactly the same combinationappears in Eq. (2)) would lead to the increase of the X-ray flux from the sterile neutrinodark matter. Clearly, the astrophysical constraints on this flux would lead to the limit onm0, and, therefore to the prediction of active neutrino masses if m0 happens to be smallenough.The corresponding bound on m0 can be found from ref. [17]. As we have shown in thispaper, a non-observation of a peculiar feature in the X-ray background associated with thedecays of dark matter sterile neutrino implies that2Ωs sin2(2θ) < 3× 10−5(M1keV)−5, (11)2 Sterile neutrino mass M1 was denoted by ms in [17], mixing angle θ is defined via tan 2θ ≡ 2m0/M1.4where Ωs is the dark matter abundance. This equation describes an empirical fit to thecorresponding exclusion region coming from the analysis of the HEAO-1 and XMM missionsand is valid at M1 > 1 keV (see [17] and references therein). In the limit m0 ≪ M1, onegets an upper bound on the lightest active neutrino mass mν < m20/M1. Combined withEq. (11), this can be recast into the constraint on mν :mν < 3.4× 10−2(0.22Ωs)(keVM1)4eV . (12)The weakest limit on the mass of the lightest active neutrino comes from the region ofsmaller sterile neutrino masses. One can see that for Ωs = 0.22 andM1 > 1.8 keV (13)the condition (9) is satisfied. In other words, the prediction of active neutrino masses (6,7),made in [1] is robust if the mass of dark matter sterile neutrino is large enough.In conclusion, we have demonstrated that in the νMSM the astronomical observationsof the X-ray background allow to put severe constraints on the mass of the lightest sterileneutrino and to make a prediction of the masses of other active neutrinos, independently onassumptions on the evolution of the early universe above the BBN temperatures, providedthe mass of dark matter neutrino is larger than 1.8 keV. For smaller masses M1, admittedby the constraint (4), the predictions (6,7) are not in general valid.The authors thank A. Kusenko for discussion. This work was supported in part by theSwiss Science Foundation and by European Research Training Network contract 005104”ForcesUniverse”.[1] T. Asaka, S. Blanchet and M. Shaposhnikov, Phys. Lett. B 631 (2005) 151[arXiv:hep-ph/0503065].[2] T. Asaka and M. Shaposhnikov, Phys. Lett. B 620, 17 (2005) [arXiv:hep-ph/0505013].[3] P. Minkowski, Phys. Lett. B 67 (1977) 421; T. Yanagida, in Proc. of the Workshop on theUnified Theory and the Baryon Number in the Universe, Tsukuba, Japan, Feb. 13-14, 1979,p. 95, eds. O. Sawada and S. Sugamoto, (KEK Report KEK-79-18, 1979, Tsukuba); Progr.Theor. Phys. 64 (1980) 1103 ; M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, eds.P. van Niewenhuizen and D. Z. Freedman (North Holland, Amsterdam 1980); P. Ramond, in5Talk given at the Sanibel Symposium, Palm Coast, Fla., Feb. 25-Mar. 2, 1979, preprint CALT-68-709 (retroprinted as hep-ph/9809459); S. L. Glashow, in Proc. of the Carge´se SummerInstitute on Quarks and Leptons, Carge´se, July 9-29, 1979, eds. M. Le´vy et. al, , (Plenum,1980, New York), p707; R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44 (1980) 912.[4] S. Dodelson and L. M. Widrow, Phys. Rev. Lett. 72 (1994) 17 [arXiv:hep-ph/9303287].[5] A. D. Dolgov and S. H. Hansen, Astropart. Phys. 16 (2002) 339 [arXiv:hep-ph/0009083].[6] E. K. Akhmedov, V. A. Rubakov and A. Y. Smirnov, Phys. Rev. Lett. 81 (1998) 1359[arXiv:hep-ph/9803255].[7] A. Kusenko and G. Segre, Phys. Lett. B 396 (1997) 197 [arXiv:hep-ph/9701311].[8] K. Abazajian, G. M. Fuller and M. Patel, Phys. Rev. D 64 (2001) 023501[arXiv:astro-ph/0101524].[9] S. H. Hansen, J. Lesgourgues, S. Pastor and J. Silk, Mon. Not. Roy. Astron. Soc. 333 (2002)544 [arXiv:astro-ph/0106108].[10] M. Viel, J. Lesgourgues, M. G. Haehnelt, S. Matarrese and A. Riotto, Phys. Rev. D 71 (2005)063534 [arXiv:astro-ph/0501562].[11] K. Abazajian, arXiv:astro-ph/0512631.[12] S. Tremaine and J. E. Gunn, Phys. Rev. Lett. 42, 407 (1979).[13] D. N. C. Lin and S. M. Faber, Astrophys. J. 266 (1983) L21.[14] A. Strumia and F. Vissani, Nucl. Phys. B 726 (2005) 294 [arXiv:hep-ph/0503246].[15] X. d. Shi and G. M. Fuller, Phys. Rev. Lett. 82, 2832 (1999) [arXiv:astro-ph/9810076].[16] G. Gelmini, S. Palomares-Ruiz and S. Pascoli, Phys. Rev. Lett. 93, 081302 (2004)[arXiv:astro-ph/0403323].[17] A. Boyarsky, A. Neronov, O. Ruchayskiy and M. Shaposhnikov, astro-ph/0512509.[18] K. Abazajian, G. M. Fuller and W. H. Tucker, Astrophys. J. 562 (2001) 593[arXiv:astro-ph/0106002].[19] P. B. Pal and L. Wolfenstein, Phys. Rev. D 25, 766 (1982).[20] V. D. Barger, R. J. N. Phillips and S. Sarkar, Phys. Lett. B 352, 365 (1995) [Erratum-ibid.B 356, 617 (1995)] [arXiv:hep-ph/9503295].6

The masses of active neutrinos in the nuMSM from X-ray astronomy

In an extention of the Standard Model by three relatively light right-handed neutrinos (the nuMSM model) the role of the dark matter particle is played by the lightest sterile neutrino. We demonstrate that the observations of the extragalactic X-ray background allow to put a strong upper bound on the mass of the lightest active neutrino and predict the absolute values of the mass of the two heavier active neutrinos in the nuMSM, provided that the mass of the dark matter sterile neutrino is larger than 1.8 keV.In an extention of the Standard Model by three relatively light right-handed neutrinos (the nuMSM model) the role of the dark matter particle is played by the lightest sterile neutrino. We demonstrate that the observations of the extragalactic X-ray background allow to put a strong upper bound on the mass of the lightest active neutrino and predict the absolute values of the mass of the two heavier active neutrinos in the nuMSM, provided that the mass of the dark matter sterile neutrino is larger than 1.8 keV

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The masses of active neutrinos in the $\nu$MSM from X-ray astronomy

The masses of active neutrinos in the nuMSM from X-ray astronomy

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