Effects of long-lived strongly interacting particles on Big-Bang nucleosynthesis

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1 Effects of long-lived strongly interacting particles on Big-Bang nucleosynthesis This study is in progress! More precise results will be reported elsewhere. Motohiko Kusakabe Department of Astronomy, School of Science, University of Tokyo National Astronomical Observatory of Japan Research Fellow of the Japan Society for the Promotion of Science

2 SBBN prediction and observation 3 min. after the Big Bang Standard Big Bang nucleosynthesis: parameter : baryon-to-photon ratio h constraint on h by WMAP h=(6.27±0.17) (Dunkley et al. 2008) Kawano code (1992) Rates Smith et al. (1993) +Descouvemont et al. (2004) +Cyburt & Davids (arxiv: ) t n =881.9s (Mathews et al. 2005) Li problems! Metal-poor stars (Ryan et al. 2000) (Asplund et al. 2006)

3 Y X Ȳ Long-lived Heavy Colored Particles Kang et al. (2008) In the early universe, hypothetical colored particles annihilaterelic abundance n Y /s~10-15 (n Y /n b ~10-5 ) Temperature decreases When T<T c ~180MeV, heavy partons would get confined in hadrons X p Xs form bound statesdecay into lower energy state annilatefinal abundance n n Y b 2 3/ R TB m 1 GeV 180MeV TeV Goal Calculate the Big-bang nucleosynthesis with heavy exotic strongly interacting particles Derive a constraint on their abundance and lifetime Check if this case explain primordial elemental abundance 1/ 2

4 Model 1. Binding energies of nuclides and X system [Assumption] X is of spin 0, charge 0, mass m X >>1 GeV Nuclear potential 1)nucleon+X : well type reproducing binding energy of n+p system V 25.5MeV(for r 2.5fm) ( r N ) 0 (for 2.5fm r) 2)other nuclides: Woods-Saxon type (V 0 =50MeV, a=0.6fm, R=<r m2 > 1/2 ) We obtained binding energies from Schrödinger equation V N 2 2 V0 ( r) 1 exp ( r 2 V N ( r) R) / E ( r) (Gaussian expansion method, f. e. Hiyama et al. 2003) 0 a Only electric charge 0 case r X nuclide A Binding energies are of ~O(10MeV) X particles capture nuclides early

5 Binding energy nuclide r m RMS (fm) Reference E Bind (MeV) 1 n & 1 H --- NONE H ± [1] Martorell et al. (1995) H ± [2] Amroun et al. (1994) r RMS p He ± [2] r RMS p He 1.59 ± 0.04 [3] Tanihata et al. (1988) He 2.52 ± He radius [3] He 2.52 ± 0.03 [3] Li 2.35 ± Li radius [3] Li 2.35 ± 0.03 [3] Li 2.35 ± 0.03 [3] Li 2.38 ± 0.02 [3] Be 2.33 ± Be radius [3] Be 2.33 ± 0.02 [3] Be 2.33 ± Be radius [3] Be 2.38 ± 0.01 [3]

6 2. Nuclear reaction of X-bound nuclides-1 (only non-resonant reactions) We calculate reaction Q-values taking account of binding energies. Radiative X capture: (X,g) reaction A(n,g)B rate is adopted for A(X,g)A X rate p(x,g)p X and p X (p,g)pp X rates are calculated with a code RADCAP by Bertulani (2003) Radiative neutron capture: (n,g) reaction E1 hindered s n v~const.~<s n v> 10-3 times the rate for A(n,g)B is used for A X (n,g)b X rate n(x,g)n X reaction is neglected When the corresponding normal reaction rates are not available, rates for other reactions A (n,g)b are used b decay of A X : Standard b - decay rates for nuclides A are adopted and corrected for Q-values. As for 6 Be X (,e + n e ) 6 Li X rate, rate for b - decay of 6 He is used and corrected for the Q-value. Decay reactions are neglected when their Q-values are small.

7 2. Nuclear reaction of X-bound nuclides-2 (only non-resonant reactions) Reactions of charged particles: Rate sv t 3 t e S( E0' )cm s Az z E 0 =0.12(z 12 z 22 A) 1/3 T 9 2/3 MeV E 0 =E 0 +5T/6 t=3e 0 /T Nuclear chages (z 1, z 2 ), reduced mass (A A 1 A 2 /[A 1 +A 2 ]) are corrected. S-factor: S(E)=s(E)E exp(2pz 1 z 2 a/v) of standard reactions are used When the corresponding normal reaction rates are not available, rates for other reactions are used Reactions which comes to be of negative Q-values when X particles are attached: In order to use the purely nuclear component of standard nuclear reacion, only coulomb penetraion factors of input and exit channels are corrected.

8 2. Nuclear reaction of X-bound nuclides-3 (only non-resonant reactions) A X (n,p)b X reaction A(n,p)B rate is adopted for A X (n,p)b X rate When the corresponding normal reaction rates are not available, rates for other reactions A (n,p)b are used X-transfer: p X (n,p)n X 7 Be(n,p) 7 Li rate is substituted. n p n p X:massive & strong interaction X-transfer: p X (a,p) 4 He X 8 B(a,p) 11 C rate is substituted. a p a p X:massive & strong interaction

9 Nuclear reaction network 14 O X 15 O X 16 O X Up to X-bould O isotopes 12 N X 13 N X 14 N X 15 N X 10 C X 11 C X 12 C X 13 C X 14 C X 8 B X 9 B X 10 B X 11 B X 12 B X 6 Be X 7 Be X 8 Be X 9 Be X 10 Be X 5 Li X 6 Li X 7 Li X 8 Li X 3 He X 4 He X 5 He X 6 He X 1 H X 2 H X 3 H X Nuclear reactions b-decay 1 n X

10 Abundance Result Nuclear flow m x >>1GeV, n x =10-8 n b, t x = X-capture Temperature T 9 =T/(10 9 K)

11 Abundance Comparison only Negatively charged case Nuclear flow m x >>1GeV, n x =0.1n b, t x = dynamical calculation (Kusakabe et al. 2008) with precise rates (Kamimura et al. 2008) Strongly interacting particles have larger binding energies and larger cross sections for nucleon capturen bound states form earlier than in the case of only electromagnetically interacting particles. 5 Li X and 5 He X are stable against particle decays and heavier nuclides could be produced through those nuclides. Existence of exotic strongly interacting particle has large effect on nucleosynthesis Temperature T 9 =T/(10 9 K)

12 Parameter search Contours of observational constraints on primordial abundances Abundance Y X =n X /n b h= Li is produced more than observed in Metal Poor Stars lifetime t X

13 Summary I assume the existence of long-lived strongly interacting particle X 0 and calculated Big-bang nucleosynthesis including X 0 effects. X 0 particles get bound to normal nuclei at high temperature of K and X-bound nuclei are produced through 5 Li X and 5 He X. Long-lived strongly interacting particle X 0 has a larger effect on nucleosynthesis than only electrically interacting particle X -. (~10 5 times larger efficiency of 6 Li production) Considering X 0 decay, a constraint on abundance and lifetime is derived. (decay-triggered nucleosynthesis is not considered in this study) A parameter region exists where 6 Li abundance are consistent with the possible plateau level of MPHSs.

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