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Dark Matter from vector-like Technicolor. Part II.


Vitaly Beylin 1 and Maxim Bezuglov , Vladimir Kuksa Institute of Physics, Southern Federal University, Stachki 194, 344090 Rostov-on-Don, Russia Department of Physics, Southern Federal University, Zorge 5, 344090 Rostov-on-Don, Russia

Model of vector-like Technicolor with two Techni-quark generations and zero hypercharge contains a number of diquark states (bound states of Techni-quarks). We consider a triplet of scalar Techni-baryons - B-baryons (diquarks) as possible carriers of the Dark Matter. As it follows from direct calculations of mass splitting between components of the triplet, its neutral component is the lightest. Due to smallness of the splitting all possible coannihilation processes of this Technicolor Dark Matter were taken into account in analysis of the Dark Matter relic abundance formation. The scenario predicts value of B-baryons mass 1 TeV and gives strong relation between some model parameters which can be interesting for the LHC.

1 Introduction
The vector-like Technicolor model based upon SU(2) confined gauge symmetry was previously studied in articles [1, 2], some important details were discussed also in the [3] and in the report of V. Beylin at this Workshop. Namely, the model contains doublet of Techni (T)-quarks ~ Q= U D , (1)

having hypercharge YQ = 0. There arise heavy composite diquark scalar states possessing an additional ~ conserved quantum Techni-baryon number TB B+ = U U , B- = D D, B0 = U D, TB = +1 B = U U , B = D D, B = U D, TB = -1
+ -
0

~

+

1 ~ ~ = U D, 0 = (U U - D D ), - = U D, TB = 0. 2

The model considered operates with vector-like interaction of Dirac type T-fields, all needed parts of the Lagrangian can be extracted from references above. Preliminary, we estimate B-baryon masses as 1 - 2 TeV. However, it is necessary to calculate mass splitting in the B-triplet to reach the conclusion that the lightest triplet component can be the Dark Matter (DM) particle. Besides, a smallness of the mixing between (standard) Higgs boson (here we do not introduce a composite scalar state that is insufficient for ~ the case) and -meson (an analog of low-energy - meson) is used to provide an agreement with measured characteristics of the SM Higgs boson with Mh 125 GeV. Remind that T-mesons, T-baryons and other bound states of T-fermions are introduced in the framework of Techni-sigma model in an analogy with low-energy hadron physics.
1

vitbeylin@gmail.com

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XXIInd International Workshop "High-Energy Physics and Quantum Field Theory", June 24 ­ July 1, 2015, Samara, Russia

2 T-baryon mass splitting
The mass splitting between charged and neutral components of the T-baryon triplet occurs due to loop contributions (corresponding diagrams are shown in Fig.1). Non-zero mass splitting follows from electroweak interaction only, because of all Techni-strong exchanges cancel each other.

Figure 1: T-baryon triplet mass splitting one-loop diagrams Due to EW character of interaction, exact formula for T-baryon mass splitting involves known masses and couplings from the Standard Model (SM), so T-baryon mass ( MB )remains the only free parameter. For the mass splitting we get:

MB =

22 g2 MW 16 2 M

ln
B

M2 Z 2 MW

- 2 ln(µ Z ) + 2 ln(µW ) Z W + arc t g + arc t g
µZ 2 Z (2)

4 3 - Z arc t g µZ 4 3 - W arc t g µW

2 - µZ 2 µZ Z

2 - µW 2 µW W

µW 2 W

2 where µV = MV / M2 , V = 1 - µV /4 and GF is Fermi constant. We found that MB depends on B MB very weakly (see Fig.2), so we use the value MB 160 MeV in a very wide interval of MB masses. Importantly, MB MB .

3 Cosmological evolution
Cosmological evolution of T-baryon (as the DM) density in the early Universe is determined by annihilation processes. Annihilation of T-baryons can take place in two phases: high-symmetry and low-symmetry phase, in other words, before or after the EW phase transition epoch. Here we consider T-baryon abundance formation mainly in the low-symmetry phase. This means that the T-baryon mass must be less than 2 TeV, B so freeze-out temperature, T f M0 less than the EW phase transition temperature TEW 100 - 200 GeV. 2 To calculate T-baryon abundance we use following relation from Ref. [4]:

TB

0.2
2

D (v) anM n ( v)to t

(3)


XXIInd International Workshop "High-Energy Physics and Quantum Field Theory", June 24 ­ July 1, 2015, Samara, Russia

Figure 2: T-baryon triplet mass splitting as function of M

B

(v)

DM ann

2.0 â 10

-9

G eV

-2

(4)

To estimate some parameters of the model, we compare calculated relative density of the model DM with experimental data of WMAP nine-year mission [5] C D M h2 = 0.1138 ± 0.0045. In an analogy with conventional baryons, it can be T-Baryon asymmetry which is crucial for the scalar T-baryon Dark Matter amount (it is essential in the case of large T-baryon-scalar couplings). So, the T-baryon asymmetry can completely determine the amount of such DM in the present Universe in the case of too fast annihilation rates. Because of relatively small mass splitting, charged T-baryons have a large lifetime, (4 - 5) ns; this value is comparable with the time of the low-symmetry phase start. This means that the charged T-baryons do participate in the formation of the DM relic abundance. Therefore, processes of all B-triplet components coannihilation should be taken into account. We perform this procedure with the known approach from Ref. [6], for example, and it uses following equations:

e

ff

=


ij ef f

N

i

gi g j j2 ge f f

(1 + i )

3/2

(1 + j )
ex p

3/2

ex p
i

- M B ( i + j ) T
, i = Mi - M MB
B

g

=


i =1

N

gi ( 1 + i )

3/2

- MB T

(5)

Making use of this equation we will assume that the initial density of all components of the T-baryon triplet is essentially the same. All types of annihilation and coannihilation processes are listed in Table 1. (see also Fig.3). Totally there are 52 processes, 25 of them are different and united into groups. Cross sections for these processes has been calculated analytically in the leading approximation: s 4 M DM consideration. 3
2 B

1+

v2 4

, v 1 which corresponds to Cold


XXIInd International Workshop "High-Energy Physics and Quantum Field Theory", June 24 ­ July 1, 2015, Samara, Russia

Table 1: List of B-baryons (co)annihilation channels Initial states + - B+ B ( B- B ) + - B+ B ( B- B ) 0 B ± B ( B0 B 0 0 B± B ( B B 0 B0 B 0 B0 B ± B B Final states W W - , , Z Z , Z , f f ~~ ~ ~ ~ ~~ + - , 0 0 , h h, , h ± , ZW ± , l , l , u d, d u W l l ~~ 0 ±
+

W + W - , Z Z, f f ~ ~ ~~ ~~ ~ - , 0 0 , h h, , h W , ~~ W
+

Types of final particles EW fields TC fields EW fields TC fields EW fields TC fields EW and TC fields

Figure 3: Types of coannihilation diagrams In general, this cross section depends on a large number of parameters: particle masses and scalar selfcoupling constants. In numerical analysis we consider for simplicity simple vector-like Technicolor scenario in the near-conformal regime setting all scalar self-couplings approximately equal each other (basic conclusions are unaltered in this case). g

B ,i

=g

TC

=

M

~ Q

u

, MQ ~

M 2

B

(6)

So, in this simplified scenario we have only three independent fr parameters: MB , m , m . Here, ee ~ ~ ~ instead of M we use following linear combination: m = M - 3m ; it relates Higgs and T- mixing ~ ~ ~ ~ behavior with this combination: S 0 corresponds to m 0. ~

4 T-baryon DM relic abundance
To calculate relic density of the Technicolor DM it is necessary to get T-baryon kinetic (co)annihilation cross section, namely, we consider annihilation of charged T-baryons with its antiparticles in different channels (see Fig.4). 4


XXIInd International Workshop "High-Energy Physics and Quantum Field Theory", June 24 ­ July 1, 2015, Samara, Russia

Figure 4: Cross-sections of coannihilation in various channels From this qualitative analysis we conclude that T-baryon (co)annihilation cross sections in the scalar (pseu~ doscalar) and spinor channels vanish in the limit of small h - mixing. So, in the limit relic DM density is determined only by T-baryons annihilation to the SM vector bosons. Now, with kinetic cross sections in hand we can calculate the model DM relic density as it was mentioned before. First, we show that the processes of coannihilation play an important role in the DM formation. We demonstrate here the ratio of relic abundances calculated with and without account of coannihilation processes as a function of different parameters. Obviously, inclusion of the coannihilation is reasonable both from qualitative and quantitative viewpoint: it changes kinetic cross section value substantially, see Fig.5.

Figure 5: Ratio of relic abundances calculated with and without account of coannihilation Then, we present in Fig.6 relic abundance of T-baryon DM depending on various theoretical parameters, experimental value of the DM relic density marked with the horizontal bar. From the analysis it follows that the most important parameters for the relic density are MB and m , and dependence on T-pion mass ~ is relatively weak. As to other parameters values, we identify a lower limit of the T-baryon mass as MB 1.0 TeV and upper 5


XXIInd International Workshop "High-Energy Physics and Quantum Field Theory", June 24 ­ July 1, 2015, Samara, Russia

Figure 6: T-baryon relic abundance as a function of MB and m , m is a free parameter ~ ~ limit for |m | 1.5 GeV. Note, in principle mass of T-pions can be considered as large - up to 1 TeV, ~ however it corresponds to small m 0.01 GeV and m 600 G eV . Let's remind also that we consider ~ ~ the Dark Matter consisting of T-baryons only, and do not analyze hypothesis of the DM asymmetry.

5 Summary and conclusions
T-baryon sector from the Technicolor model with vector-like interaction has been considered, it is suggested that the lightest component of the T-baryon triplet is the cold DM specimen. It was found from direct calculations that mass splitting in the T-baryon triplet is very small, MB 0.16GeV MB , so we must take into account coannihilation processes. All needed cross sections was calculated analytically in the leading approximation. Quantitative analysis results in conclusion that symmetric T-baryon DM formation in the low-symmetry phase is possible only under specific parameter values: MB = 1 - 1.2 TeV and |m | ~ 1 GeV . This value of m is in agreement with the smallness of Higgs and T-sigma mixing following from ~ previos studies [1]. Also, this implies that there is strong relation between T-sigma and T-pion masses u M - 3m 0. So, from astrophysical data on the DM relic abundance there are follow (under the DM ~ ~ carriers and structure of interactions assumptions ) estimates of the model parameters. Prediction for MB and relation between m and m can be useful for future LHC experiments. Note, interesting question ~ ~ on the T-pion stability and possibility for the DM to be multicomponent including stable T-pions will be discussed in the next paper.

References
[1] R. Pasechnik, V. Beylin, V. Kuksa, G. Vereshkov, Phys. Rev. D 88, 075009 (2013). [2] R. Pasechnik, V. Beylin, V. Kuksa, G. Vereshkov, arXiv:1407.2392 (2014). [3] V. Beylin, V. Kuksa, G. Vereshkov, R. Pasechnik, Part. and Nucl. Lett. 13, 1 (2016). [4] G. Steigman, B. Dasgupta and J. F. Beacom, Phys. Rev. D 86, 023506 (2012). [5] G. Hinshaw et al. [WMAP Coll.], Astrophys. J. Suppl. 208, 19 (2013). 6


XXIInd International Workshop "High-Energy Physics and Quantum Field Theory", June 24 ­ July 1, 2015, Samara, Russia

[6] K. Griest, D. Seckel, Phys. Rev. D 43, 3191 (1991).

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