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The Scalar Hexaquark $ Uuddss $: a Candidate to Dark Matter?

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The Scalar Hexaquark $ Uuddss $: a Candidate to Dark Matter? The Scalar Hexaquark uuddss: a Candidate to Dark Matter? K. Azizi,1,2, ∗ S. S. Agaev,3 and H. Sundu4 1Department of Physics, University of Tehran, North Karegar Ave., Tehran 14395-547, Iran 2Department of Physics, Doˇgu¸sUniversity, Acibadem-Kadik¨oy, 34722 Istanbul, Turkey 3Institute for Physical Problems, Baku State University, Az–1148 Baku, Azerbaijan 4Department of Physics, Kocaeli University, 41380 Izmit, Turkey It is conventionally argued that Dark Matter (DM) has a non-baryonic nature, but if we assume that DM was frozen out before primordial nucleosynthesis and could not significantly impact pri- mordial abundances this argument may be evaded. Then a hypothetical SU(3) flavor-singlet, highly symmetric, deeply bound neutral scalar hexaquark S = uuddss, which due to its features has escaped from experimental detection so far, may be considered as a candidate for a baryonic DM. In the present work we calculate the mass and coupling constant of the scalar six-quark particle S by means +40 of the QCD sum rule method. Our predictions for its mass are mS = 1180−26 MeV (ms = 95 MeV) e +42 and mS = 1239−28 MeV (ms = 128 MeV). Although these values of mass would produce thermally the cosmological DM abundance, existence of this state may contradict to stability of the oxygen nuclei, which requires further thorough analysis. Introduction: From first days of the quark-parton for analysis, Jaffe predicted existence of a H-dibaryon, model and Quantum Chromodynamics (QCD), hadrons i.e., of flavor-singlet and neutral six-quark uuddss bound with unusual quantum numbers and/or multiquark con- state with isospin-spin-parities I(J P ) = 0(0+). This tents attracted interest of physicists. The conventional double-strange six-quark structure with mass 2150 MeV hadrons have quark-antiquark or three-quark composi- lies 80 MeV below the 2mΛ = 2230 MeV threshold and tions. Their masses and quantum parameters J PC are is stable against strong decays. It can decay through in accord with predictions of this scheme and can be cal- weak interactions, which means that mean lifetime of H- culated using standard methods of particle physics. Un- dibaryon, τ 10−10s, is considerably longer than that usual or exotic hadrons is expected to be built of four of conventional≈ mesons. The H-dibaryon with the mass and more valence quarks or contain valence gluons. A obeying this limit is loosely-bound state, a subject to main reason triggered intensive investigations of four- weak transformations. quark states was a mass hierarchy inside the lowest scalar The original work [7] was followed by numerous theo- multiplet, which found its explanation in the context of retical investigations, in which various models and meth- the four-quark model suggested by R. Jaffe [1]. Start- ods of particle physics were used to calculate the H- ing from 2003, i.e. from first observation of the exotic dibaryon’s mass [8–16]. As usual, results of these studies meson X(3872) theoretical and experimental investiga- are controversial: thus, calculations in the framework of tions of tetra and pentaquarks became one of the in- the corrected MIT bag model led to mH = 2240 MeV teresting and rapidly growing branches of high energy which is just above the 2mΛ threshold [8], whereas in physics. Now, valuable experimental information col- a chiral model the authors [9] found mH = 1130 MeV. lected during past years, as well as theoretical progress To analyze Λ Λ interaction and estimate ΛΛ binding achieved to date, form two essential components of the energy other quark− models were invoked as well [10, 12– exotic hadrons physics [2–6]. 14]. The H-dibaryon’s mass extracted from the QCD Another interesting result about multiquark hadrons two-point sum rules is consistent with the original result with far-reaching consequences was obtained also by of Jaffe [15, 16]. In fact, mH from Ref. [15] varies in arXiv:1904.09913v5 [hep-ph] 26 Jun 2020 R. Jaffe [7]. He considered six-quark (dibaryon) states limits 2.0 2.4 GeV and within an accuracy of the sum − built of only light u, d, and s quarks that belong to fla- rule method 20% agrees with the result of the quark- ∼ vor group SUf (3). By combining the color and spin of bag model. Calculations in Ref. [16] also confirmed ex- quarks and forming SUcs(6) ”colorspin” group, Jaffe an- istence of a bound state lying 40 MeV below the 2mΛ alyzed its representations and found that dibaryons only threshold. The lattice simulations performed in Ref. [17] from the singlet and octet representations of SUf (3) may led to conclusion that mH was below the 2mN threshold be light enough to be bound or resonant. Among six- 1880 MeV. In this paper the authors took into account quark states from these two representations SUf (3) sin- the stability conditions of the nucleus and extracted glet particles have zero spins. At the same time, all of mH 1850 MeV. The later lattice studies confirmed ≈ singlet and octet dibaryons are strange particles, there- existence of a bound-state H-dibaryon, and predicted its fore structures containing merely u and d quarks cannot binding energy 74.6 MeV [18] and (19 10) MeV [19], ≈ ± be bound and stable. Using the MIT quark-bag model respectively. In the context of the holographic QCD H- dibaryon was explored in Ref. [20], in which its mass was estimated about mH =1.7 GeV. The hexaquark S (except for original papers, hereafter ∗Corresponding author we use a hexaquark instead of a six-quark state, and de- 2 note it by S) was searched for by KTeV, Belle, and BaBar turbative methods to explore hadrons. As starting point, collaborations in exclusive S Λpπ− and inclusive the method uses the correlation function Υ(1S) and Υ(2S) decays, in processes→ Υ(2S, 3S) SΛΛ → [21–24]. All these experiments could not find evidence for Π(p)= i d4xeipx 0 J(x)J †(0) 0 , (1) the hexaquark S near the threshold 2mΛ and were able Z h |T { }| i only to impose limits on its mass m the latest being S and extract from its analysis sum rules to compute spec- m < 2.05 GeV. S troscopic parameters of the hexaquark. The main ingre- Recent activities around the S is inspired by renewed dient of this analysis is the interpolating current J(x) suggestions to consider it as a possible candidate to which we choose it in the following form dark matter [25–29]. In accordance with this scenario if m 2(m + m ) = 1877.6 MeV the hexaquark is ab- a b S p e J(x) = ǫabc uT (x)Cγ d(x) uT (x)Cγ s(x) solutely≤ stable, because all possible decay channels of a 5 5 T c free S is kinematically forbidden. For the mS obeying the d (x)Cγ s(x) , (2) × 5 inequality mS <mΛ + mp + me = 2054.5 MeV the hex- T ′ a amn T ′ aquark decays through a double-weak interaction, but where [q Cγ5q ] = ǫ [qmCγ5qn] and a, b, c, m, n even in this case its lifetime could be comparable with are color indices with C being the charge-conjugation the age of the Universe. The lower bound of mS is deter- operator. mined by a stability of ordinary nuclei, which are stable if As is seen, the hexaquark is composed of the scalar di- T ′ a mS >mp+mn+me 2E, where 2E is a binding energy of quarks [q Cγ q ] in the color antitriplet and flavor an- − 5 p + n. Then, for masses 1860 <mS < 1880 MeV, which tisymmetric states. These diquarks are most attractive assures a stability of the hexaquark and conventional nu- ones [34], and six-quark mesons composed of them should clei, the S can explain both the relic abundance of the be lighter and more stable than bound states of other DM in the Universe and observed DM to ordinary mat- two-quarks. Mathematical manipulations to derive sum ter ratio with less than 15% uncertainty [29]. But even rules for the mass and coupling of the hexaquark are car- S with the mass in the range 1.3 . mS . 2mp and with ried out in accordance with standard prescriptions of the radius (1/6 1/4)rp, where rp 0.86 fm is the a proton method. Thus, first we express the correlation function − ≈ radius, is consistent with the stability of nuclei, with Λ Π(p) in terms of the hexaquark’s mass mS and coupling decays in double-strange hypernuclei and experimental fS, as well as its matrix element limits on existence of exotic isotopes of helium and other nuclei [25]. There are, however, objections to this picture 0 J S = mSfS. (3) connected with a production process of hexaquarks in the h | | i early-universe [30], or with observed supernova explosion Separating from each another the ground-state term and [31]. contributions due to higher resonances and continuum Phys The hexaquark S as a candidate to DM was recently states for Π (p) we get analyzed in Ref. [32] as well. In this work the mass 0 J S(p) S(p) J † 0 of S was evaluated by modeling it as a bound state of ΠPhys(p)= h | | ih | | i + . (4) scalar diquarks. Using the effective Hamiltonian to de- m2 p2 ··· S − scribe dominant spin-spin interactions in diquarks [4], the authors expressed mS in terms of constituent di- The expression of the matrix element (3) allows us to Phys quark masses mij and chomomagnetic couplings kij . The rewrite Π (p) in the form masses of diquarks and chomomagnetic couplings may 2 2 be extracted from analysis of baryon spectroscopy.
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