1. Time Dependent Quark Masses and Big Bang Nucleosynthesis Myung-Ki Cheoun, G. Mathews, T. Kajino, M. Kusagabe Soongsil University, Korea Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

2. Contents 1. Introduction and motivation - BBN and 7 Li problem - Motivation (the variation of α) - The coupling constants and the masses of particles in standard model 2. Hadron Mass Variations by quark mass change - Linear sigma model - Chiral perturbation theory… 3.Binding Energy Variations of Light Nuclei 4.Relevant Nuclear Reactions 5.Results 6.Summary Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

3. 1.Introduction and motivation Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

4. Motivation 2 History of the Universe and BBN Nucleosynthesis 97 % of the elements (Hydrogen and Helium) are produced at the BBN !! More stringent tests of physics are possible !! Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

5. BBN chain and Li problem η = 6.23 × 10−10 deduced from the WMAP 7 year data, Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

6. Motivation – Why the variation of couplings at BBN ? - The production of light nuclei in BBN at early Universe The binding energy of light nuclei - NN interaction, three body force and so on Variation of Hadron masses by the quark mass variation – NN interactions Variations of quark masses and α s (or Λ QCD ) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

7. 2. Hadron and Light Nuclei Masses Variations by the quark mass variations Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

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9. 3. Relevant Reaction Rates Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

10. PHYSICAL REVIEW D 69, 063506,2004 Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

11. 1. Radiative Capture or Photo-Disintegration : (n A -> A+1 g) and ( g A+1 -> A n) reactions E E_g = E + Q Q Triplet and Singlet in spin Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

12. 2. Charge Exchange Reactions : (a A -> A+1 b) and ( b A+1 -> A a) reactions E E’ = E + Q Q Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

13. 3. Charge Exchange Resonant Reactions : (a A -> A+1 b) and ( b A+1 -> A a) reactions Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

14. 4. Roles of Resonances in entrance and exit channels Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

15. 5. Results Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

16. 5. Nuclear Abundances from BBN (K_Li5, K_He5)^* = (-1.54,-1.44) = (-3.35,-3.19) = (-2.29,-2.21) = (-3.131,-2.867) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24 SBBN

17. 6. Summaries Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

18. 1. Abundances of light nuclei in Early Universe may give a stringent test for new physics. 2. There are Li problems in BBN : We hope to solve this problem with the variations of QCD coupling constants, α s or Λ QCD, and quark mass. 3.In this work, we first calculate meson mass variations by the quark mass variation in QCD inspired models. 4. Next work is the calculation for the change of binding energies of light nuclei by the hadron mass variation. 5.We need to check the other models (Lattice QCD, QCD sum rule and so on) and also consider the possibility of the other values. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

19. 5.We consider the effects of resonance variations of exit channels as well as the variations of the Q values in the nuclear reactions at BBN stage. 6.Previous results for the quark mass variations might be reduced to more conservative value, no change of the quark mass at the BBN stage. 7.More updated results of the abundances of the light elements are exploited for more stringent test. 8.Linear variation of He4 and D with the quark mass variation indicates that more fundamental approach, chiral perturbation theory, for the relevant reactions rate can be used to investigate the quark mass variations at the BBN stage. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

20. Thanks for your attention ! 감사합니다. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

21. History of Universe and BBN Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

22. Motivation I PRL 87:091301 (2001) - At early Universe, QED coupling “α“ might be different from a present value. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

23. Motivation II – GUT and standard model Theory of everything (String?) GUT - α GUT Gravity - G QCD –α S (g 2 3 /4π) Electro-Weak (Weinberg- Salam) Model – g1, g2 Higgs mechanism Electromagnetic and Weak interaction Standard Model in particle physics Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

24. Motivation III – Weinberg Salam theory WS model SU(2) X U(1) : g1 (SU(2)), g2 (U(1)) : massless gauge theory SSB (Higgs mechanism) EM : e = g1 cos θw = g2 sin θw Weak : The masses of quarks and leptons : The boson masses in the model : The Weinberg angle : Thus, the variation of e or αmeans the variation of all couplings and bosons in the model. We can also consider the possibility for the variation of VEV of Higgs, v.  all masses of quarks and leptons will be changed. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

25. Motivation IV – Quantum Chromodynamics QCD SU(3) color 1. In chiral limit, QCD has the chiral symmetry, SU(3) L X SU(3) R X U(1) V 2. Quark degrees of freedom : confinement problem 3. The coupling constant α s = g 3 / 4π and QCD cutoff Λ QCD Symmetry breaking (???) 1. Hadronic degrees of freedom (baryons and mesons) 2. Low energy ( u, d, s-quarks : SU(3) ) : baryon octet and pseudo-Goldstone bosons (8 : π, K, η) Effective models for strong interaction with hadronic degrees of freedom We can lead the possibility for the variation of g3 from GUT, because g1, g2 and g3 may be came from g GUT. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

26. Motivation V – QCD and hadron masses The energy-momentum tensor of QCD and hadron masses Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

27. QCD and hadron fields 1.Lattice QCD : this can numerically calculate the hadron masses from QCD directly. 2.QCD based models : QCD sum rule 3.Phenomenological models with quarks i) Bag models (MIT, Dressed, Chiral …….) ii) Solition models (meson, meson+quark) 4. Chirally motivated effective models i) Linear Sigma model (scalar and pseudoscalar mesons) ii) Chiral perturbation theory (psedoscalar mesons) iii) NJL type models (quarks) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

28. QCD and effective models Quantum Chromodynamics (QCD ) 1. Quarks and gluon degrees of freedom : Those cannot be observed in experiment. 2. Non-perturbative property : The hadrons cannot be generated from QCD.(confinement problem) Effective models with hadrons 1. Baryons and mesons degrees of freedom : Those can be observed in experiment. 2.Imitate the properties of QCD with hadrons : chiral symmetry and Spontaneous symmetry breaking Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

29. Chiral perturbation theory χPT : The general formular with 8 Goldstone bosons (SU(3)) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

30. The masses of Goldstone bosons at O(p4) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

31. The masses of Goldstone bosons in χPT 1. The obtained masses of Goldston bosons in χPT at O(p 4 ). Using Bm and Bms as free parameter, we fit both values to reproduce pion and kaon masses, (Pion = 134.97 MeV, Kaon = 495.66 MeV). 2. The obtained mass of eta meson is Eta = 546.57 MeV. 3. We can choose some variations for these mass formula. For instance, m, ms, or m/ms and so on. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

32. SU(3) x SU(3) Linear Sigma Model QCD has the chiral symmetry SU(3) L X SU(3) R X U(1) V when we ignore quark masses of (u, d, s)-quarks 1.Nonet of scalar and pseudoscalar mesons : 9 scalar (a0, κ, σ, f0) and 9 Peudoscalar (π, K, η, η’)mesons 2. Explicit SU(3) symmetry breaking (final term) and U(1) A symmetry breaking (determinant term) 3. Spontaneous symmetry breaking (All meson masses are generated.) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

33. SSB and the masses of mesons The masses of scalar and pseudoscalar mesons : The coupling constants : Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

34. The variation of quark mass ratio Quark fields (u, d, s) + Linear sigma model The masses of u, d, s quarks in this model : We simply choose the parameter,, assuming that the ratio of vacuum expectation values might be varied. In order to fix one, we choose pion decay constant keeps 92.4 MeV. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

35. The masses of mesons in LSM Binding energy can be calculated with NN potential with boson exchange model. So, with this values, we can study the variation of binding energy of light nuclei. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

36. N-N interaction NN interaction g g N N where V N N depends on the mass of meson and coupling constants. In this work, we focus on the meson masses. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

37. N-N interaction and the binding energy of light nuclei N-N interaction is described with mesons. The binding energies of light nuclei can be derived from NN interaction. (but need three body force or etc) Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

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40. 5. He3 and T Radiative Capture Reactions Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

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43. Summary I for motivation Standard model 1. Coupling constants of SM – g1, g2, g3 - α, G F, α s (Λ QCD ) 2. The masses of quarks(WS) - m q ∝ v (v is the vacuum expectation value of Higgs fields) GUT : g GUT All things (couplings or quark masses) may be changed as the Universe cools down. So, to make the problem simple, we first need to find the largest effect or the observable quantities. : a simplest thing – assumes that Λ QCD does not vary. - We can find the relation between quark masses and hadrons. Asian Pacific Few Body 2011, Seoul, Korea 2016-01-24

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