Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks2013/inerttr1306253.pdf Äàòà èçìåíåíèÿ: Wed Jul 3 14:47:05 2013 Äàòà èíäåêñèðîâàíèÿ: Thu Feb 27 20:18:23 2014 Êîäèðîâêà: IBM-866

New options in Higgs-Dark physics: Strongly interacting dark matter; degeneracy of some intermediate state during co oling of the Universe
I. F. Ginzburg Sob olev Inst. of Mathematics, SB RAS and Novosibirsk State University Novosibirsk, Russia
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Inert Doublet Mo del. Brief review
SM with standard Higgs field S is supplemented by Higgs field D , having no interaction with matter fields and v.e.v. D = 0. G. Despande, L. Ma Phys.Rev. D18 (1978) 2574; many pap ers now. Some p oints rep eat I.F.G., K.A. Kanishev, M. Krawczyk, D. Sokolowska. Phys. Rev. D 82, 123533 (2010), hep-ph/1009.4593
S M + L + 1 (D D + D D ) - V . L = Lgf ²D ²D ²S ²S Y 2

Lagrangian:

M LSf : S U (2) ½ U (1) SM interaction of gauge b osons and fermions; g LY : Yukawa interaction of fermions with Higgs field S only.

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Z2 symmetric Higgs p otential (forbidding (S , D ) mixing), with all real i:
) 1( 2 2 ( ) + V = - m11(S S ) + m22 D D 2 ) ( 1 2 + ( )2 + ( )( )+ + 1(S S ) 2 DD 3 SS DD 2 ) 5 ( 2 + ( )2 + V . +4(S D )(D S ) + (S D ) 0 DS 2

We

fix 5 < 0. Potential is p ositive at large quasi-classical values for fields i and gives neutral DM if only (p ositivity) 1 > 0 , 2 > 0; R = (3 + 4 + 5)/ 12 > -1.


This p otential keeps D-parity D -D and S -parity S -S . The latter is violated by Yukawa interaction.
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Extrema of p otential
The extrema of the p otential define the values S,D of the fields S,D via equations: V / i|i=i = 0. For each extremum with S = 0
( )

0 vS with real vS > 0 ("neutral direction"). After this choice(the ) most ( ) 1 1 0 u general form extremum is S = , D = . vS vD 2 2 The vacuum with u = 0 is excluded for p otentials with 's, allowing the IDM with neutral DM particle. m2 m2 We use b elow abbreviations ²1 = 11 , ²2 = 22 . 1 2 we cho ose the z axis in the weak isospin space so that S =
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ï Complete set of extrema with their v.e.v.'s and energies Ea = Ea - V0. I. The electroweak symmetry preserving extremum E W s ï vD = 0, vS = 0, EE W s = 0. Electroweak symmetry violating extrema: I I. Inert extremum I1 , preserving D-parity: 2 vD = 0, vS = m2 /1, EI1 = -²2/8 ; 11 1 I I I. Inert-like extremum I2 , violating D-symmetry: 2 vS = 0, vD = m2 /2, EI2 = -²2/8 ; 2 22 IV. Mixed extremum M , violating D-symmetry: ²2 + ²2 - 2R²1²2 ²2 - R ²1 ²1 - R²2 2 2 2 ï , vD = ; EM = - 1 . vS = 2) 2) 2) 1(1 - R 2(1 - R 8(1 - R
2 If some of these va are negative, mixed extremum is absent.
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Assumption: our world is describ ed by I1 (inert This state can b e ground state with neutral DM particle if only m2 > 0 ; 4 + 5 < 0 ; 11 ²1 > ²2 at R > 1, R²1 > ²2 at |R| < 1. In this state we have (G‘, G í Goldstone mo des)
(

phase):

S =

, (v + h + iG)/ 2

G+

)

(

D = (D + iDA)/ 2

D+

)

.

Let Mh, MD , MA, M‘ M+ are masses of h, D, DA and D‘. 2 As in SM, Mh = 1v 2 with v = 246 GeV. For Mh = 125 GeV (LHC) it gives 1 = 0.25; 2 = (R² - ² )/2, M 2 = M 2 - v 2 , M 2 = M 2 - v 2 ( + )/2. MD 2 1 2 5 4 5 ‘ A D D Due to D-parity conservation, the lightest from these D-scalars can play a role of DM particle.
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Interactions of scalar h with the fermions and gauge b osons, just as their self-interactions, are the same as for Higgs b oson in the SM. D-scalars D, DA, D‘ don't couple to fermions directly. They couple to known particles via covariant derivative in kinetic term D²D D²D , that are D+D- , D+D-Z , D‘DW , D‘DAW , DDAZ . Dh interactions ] 2v § h + hh [ +D - + ( + ) (D D + D A D A ) + (D D - D A D A ) . 43 D 3 4 5 4 DD interactions ] [ 1 2 § (DD + DADA)(DD + DADA + 4D+D-) + D+D-D+D- . 8 Possible interactions of D and DA are identical. Their attribution as scalar and pseudoscalar is only subject of agreement. With our choice 5 < 0 b oson DA is heavier than D.
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Limitations for masses
1. Cosmology. Stability is provided by D-parity conservation. The rate of annihilation pro cesses DD W +W - together with DD h f ermions should b e low enough to keep mo dern abundance of D during life of Universe. It gives limitation MD < MW . More detail limitations dep end on DDh coupling value. Roughly we have MD < 60 GeV . (Another region MD > 1500 GeV, related to low density of DM particles in this case, is also discussed). 2. LEP limitations. The non-observation e+e- Z DD A DDZ and e+e- with either on-shell or off-shell W and Z MA > 100 GeV , M+ of pro cesses ( , Z ) D+D- DDW W gives 100 GeV .
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Possible discovery and measuring of masses
At ILC/CLIC (I.F.G. hep-ph/10105579;1211/2429) Pro cesses e+e- D+D- DDW +W - DD (q q )(q q ) ; DD (q q )( ) . ïï ï Study of energy distribution of diquark (dijet) and single lepton from W decay. The upp er end p oint in the dijet energy sp ectrum and singularities in the single lepton sp ectrum will give information, necessary to determine MD and M+. (The study of singularities in single lepton sp ectrum is new to ol, suggested in my pap er recently). Pro cess e+e- DD A DDZ allow to determine MA and MD via end p oints in the energy sp ectra of dilepton from decay of Z , but with lower accuracy.
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Effects in Higgs physics
1. Invisible decay of Higgs h DD with coupling 345 = 3 + 4 + 5, which can b e considered as free parameter of theory. It can b e measured in principle in Z H pro duction at LHC and (more precise) at ILC/CLIC. 2. Additional hD+D- contribution to two-photon width of Higgs which value is given by free parameter of theory 3 (with arbitrary value and sign). After measuring M+ and MD comparison of two-photon width and its invisible width allow to verify mo del completely.
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Possible strong interaction in Dark sector (NEW)
Interactions among D-particles are determined by parameter 2 which don't influence for standard Higgs sector at fixed MD . Therefore, the opp ortunity of large 2 cannot b e ruled. In this case we have strong interaction in dark sector. At the tree level it is repulsion (2 > 0). Therefore "light" DD, D+D-, DD +, etc. "molecules" don't app ear. However, one can exist resonances in the "D-matter", similar those discussed in many pap ers devoted to the strong interaction in Higgs sector.
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Inert-like phase I2

can b e ground state (vacuum) if

2 > 0 at any R 345 , m22 12 ²2 > ²1 at R > 1, R²2 > ²1 at |R| < 1. This state lo oks similar to the inert phase. Field D lo oks similar to Higgs field in SM. It splits into 3 Goldstone mo des + observable Higgs 2 b oson Dh with mass MD = 2v 2. Dh don't couple with fermions. h The S field is realized as physical fields SH , SA, S‘ with masses 2 = R²2 - ²1 , M 2 = M 2 - v 2 , M 2 = M 2 - v 2 4 + 5 . MS 1 5 SA SH S‘ SH H 2 2 They are couple to massless fermions. This state contains no candidates for DM particle.

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M (mixed phase)

is similar to that in 2HDM with Mo del

I for Yukawa interaction. Scalars h, H , A, H ‘ + 3 Goldstones mix comp onents of D and S . This extremum can b e minimum if only |R| = |345/ 12| < 1. Since symmetry D -D of entire Lagrangian (including Yukawa term), this extremum is degenerated in the sign of D , there are 2 mixed typ e states M‘, with D = vD and D = -vD - , -.

NEW-2013:

These vacua can b e distinguished by the SIGN of couplings of H to gauge b osons sin( - ) in the pro cesses like tï W W , etc. t The actual mixed phase consists of domains M+ and M-.
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Fate of Universe
At the finite temp erature the ground state of system is given by minimum of the Gibbs p otential ( ) ( ) ^ ^ -H /T /T r e-H /T . At high enough temp eratures in the VG = T r V e main approximation VG has the same form as V with the same i, and mass terms varying with temp erature m2 (T ) = m2 (0) - c2T 2 , 22 22 ~1 1, c2 = cH 2 + cS M ~2 2; c c 2 2 gt + gb 3g 2 + g 2 3i + 23 + 4 (i = 1, 2); cS M = ; cY = . cH i = 12 32 8 Here g and g are coupling constants of gauge EW interaction; the Yukawa couplings for t and b quarks are gt 1 and gb 0.03. Due to this variation of p otential, p osition and prop erties of ground state vary with temp erature.
2 1T ,
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Temp erature dep endence.

m2 (T ) = m2 (0) - c 11 11 c1 = cH 1 + cS M + cY


Thermal evolution of Universe
During co oling of the Universe mass terms in V were changed phase states were changed. Possible ways of evolution are shown here:
²
2

²

2

² M

2

I

P1 2 12 11 P2 ²
1

I

X

2 32

P3

I
²
1

2

53

M ²

P4 31 EWs

52 EWs 51

1

EWs 21

I

1

41

I

I

1

1

P5 54

.

R>1

1>R>0

0 > R > -1
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Evolution through mixed) phase (
Ray 32 m2 (T = 0) c2 0< < 22 . 2 (T = 0) c1 m11 . Starting from EWs state the Universe comes to the Inert-like phase I2 at TE W s,2 = ²2(0)/~2 (2-nd order phase transition (PT) with the c order parameter E W,2 2 vD ). (At some values of parameters more accurate calculation of the Gibbs p otential can transform this PT to the 1-st order PT). . The inert like phase I2 has no candidates for DM particles. The Universe co oled in this phase up to a temp erature T = T2,M = (²1(0) - R²2(0))/(~1 - R~2). c c

I

II

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I I I. At the temp erature T = T2,M the Universe comes to the mixed phase M with domains M+, M-. That is 2-nd order PT with order parameter 2,M S |²1 - R²2|, which is represented by mass MS H in the phase I2 and mass Mh in the mixed phases M‘. At the transition p oint these masses vanish. The height of domain wall is given by p osition of lowest saddle extremum b etween M+ and M-. Here ²2 > ²1, and lowest saddle extremum is inert-like I2 with (²2R - ²1)2 height of domain wall Eb = E I 2 - EM = . 2) 8(1 - R

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Near the PT I2 M (at T T2,M í small 2,M ) we have 2 (²2R - ²1) = A2(T 2 - T2,M ) with A2 > 0. At these temp eratures the system is highly non homogeneous, with the domains of I2 phase (obliged by fluctuation of temp erature and density), and phases M+ 4 and M- with height of wall b etween domains Eb 2,M . The distribution of these domains in the space is constantly changing. The characteristic correlation radius is 2 Rc(T ) 1/2,M 1/ |T 2 - T2,M |.

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With decreasing of temp erature the domains of I2 b ecome energetically unfavourable. The domains M+ and M- are hardened, since the height of walls b etween them increases. The correlation radius decreases, domains b ecome bubbles with surface tension s EbRc. The curved surface of this bubble is under pressure s/r, where r is the lo cal radius of curvature. This pressure leads to the absorption of small domains by larger. The lo cal velo city of motion of domain walls is c í sp eed of light. But the global merging pro cess is slow diffuse pro cess with character istic time (R/c) R/Rc, where R is characteristic radius of Universe inhomogeneity. This temp must b e compared with the temp of co oling of Universe.
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At the co oling of Universe b elow T = T2,1 = (²1(0) - ²2(0))/(c1 - c2), ~ ~ we come to the region ²1 > ²2, and the wall b etween domains M+ and (²1R - ²2)2 M- is given by inert extremum I1 with Eb = EI 1 - EM = . 8(1 - R2) With subsequent co oling the Universe passes to the inert phase I1 at the temp erature T = TM ,1 = (R²1(0) - ²2(0))/(R~1 - ~2). That is c c 2-nd order PT with order parameter 2 M ,1 D |R²1 - ²2| (T 2 - TM ,1), representing by mass MH in the mixed phases M‘ and mass of DM particle MD in the phase I1. At the transition p oint these masses vanish. The evolution of fluctuations (domains) near this transition in the mixed phase is similar to that discussed for the transition I2 M . It lo oks very probable, that after these transitions the Universe b ecome strongly inhomogeneous.
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IV. Below M I1 transition the system has fluctuations of typ e M+ and M-, obliged by fluctuations of temp erature and density. The previous history of fluctuations in the mixed phase can enhance size of these latest fluctuations. Dep ending on parameters of mo del, the temp erature of this transition TM ,1 can b e low enough. It can results inhomogeneities in the mo dern Universe. In this case these fluctuations can influence for history of baryogenesis. In this case our approximation can give only qualitative picture, lattice calculations can b e useful.

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The considered IDM can b e denoted as (1 + 1) IDM (1íDark, 1íStandard). More complex IDM with 2 "standard" Higgs field S 1, S 2 and one "dark" doublet D í (1 + 2) IDM can b e treated also (see e.g. B. Grzadkowski, O.M. Ogreid, P. Osland, A. Pukhov, M. Purmohammadi). Complete description of temp erature evolution of Universe in this mo del is absent to-day. Perhaps, the most interesting new physical phenomenon in the evolution of Universe in this case would b e intermediate stage with charged vacuum, without massless photons and electric charge conservation and with very strong winds after transition from this phase. The intermediate mixed phase similar to that describ ed ab ove with the same degeneracy and similar fluctuations takes place in such mo del as well.
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The end

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