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Kyu Jung Bae AFFLECK-DINE LEPTOGENESIS WITH VARYING PQ SCALE Kyu Jung Bae, Center for Theoretical Physics of the Universe, based on JHEP 1702 (2017) 017 with H. Baer, K. Hamaguchi and K. Nakayama "Testing CP-Violation for Baryogenesis" @UMass-Amherst Mar. 29, 2018 INTRODUCTION • Baryogenesis via Leptogenesis - Due to (B-L)-conserving and (B+L)-violating process makes Lepton asymmetry Baryon asymmetry - Neutrino physics can show its footprints. • Affleck-Dine mechanism - scalar field dynamics in SUSY: CPV in SUSY breaking parameters - Along LHu direction: lepton number generation light neutrino mass required <10-9 eV; neutrinoless double beta decay • Varying PQ scale - PQ scale ~ Mp during leptogenesis but fa~109-12 GeV afterwards neutrino mass ~10-4 eV; suppress axion isocurvature INTRODUCTION • Dine-Fischler-Srednicki-Zhitnitsky model - SUSY DFSZ model provides strong CP solution, mu-term, also RHN mass - Dilution from saxion decay determines final lepton(baryon) asymmetry - suppress unwanted lepton number violation during saxion oscillation 14 [] = = [] = / = 1012 1012 -7 -6 10-5 -4 10-8 10-5 -4 10 10 10 10 10-3 10-3 GeV -8 GeV 10 10 1 -2 < < 10 T T 10-2 1011 1011 10-7 ] 10-1 ] 10-1 [ [ -6 10 GeV 10 < T m > 0.17 eV 1010 m > 0.17 eV 1010 m > 0.48 eV 8 m > 0.48 eV 8 fa N < 5 × 10 GeV fa NDW < 5 × 10 GeV DW 109 109 10. 102 103 104 105 102 103 104 105 [] [] FIG. 1: Contours of m⌫1 [eV] on the (µ, fa) plane to reproduce the observed baryon asymmetry. In the left (right) panel we have taken mσ =5µ (mσ = µ/5) while msoft = mφ = 10mσ (msoft = mφ = 50mσ). The light (dark) red shaded region corresponds to Tσ < 10 GeV (1 GeV) and the grey shaded region is excluded by the KamLAND-Zen experiment. The light-gray shaded region is constrained by Planck+BAO [34]. The light-purple shaded region indicates bound from SN1987A [35]. The blue shaded region corresponds to µ =(0.01 1)f 2/M . − a P region shows parameter space where the lightest neutrino mass is larger than the KamLAND-Zen bound [33]. We also show a bound from Planck+BAO constraint on the sum of neutrino masses, ( m⌫) < 0.17 eV [34]. The light-purple shaded region shows the bound from SN1987A [35]. The (light-)redP shaded region shows parameter space where the saxion decay temperature is smaller than 1 GeV (10 GeV). The blue shade indicates the region for which µ =(0.01 1)f 2/M .We − a P 6 consider fixed TR = 10 GeV since larger TR does not change or does suppress nB/s (see Eq. (28)). In the case where nB/s is suppressed, it requires a smaller neutrino mass that is less attractive. From the figure, it is clearly shown that neutrino mass is large for large µ and small fa while it becomes smaller for small µ and large fa. This feature stems from the saxion decay temperature. The saxion decay temperature is enhanced by the µ-term while suppressed by fa. It is also of great importance that small fa is good for obtaining a flatter direction during lepton number generation 10 as shown in Eq. (6). For µ & 1 TeV and fa . 10 GeV, our model predicts a rather large neutrino mass so that it is constrained by recent neutrinoless double beta decay (0⌫β) experiment. For this constraint, we take a conservative bound from KamLAND-Zen, m⌫ < 0.48 eV [33]. From the lower-right corner (µ 105 GeV, f 1010 GeV) to the upper-left corner (µ 102 GeV, f 1012 ⇠ a ⇠ ⇠ a ⇠ GeV), the resulting neutrino mass scans over 10 1 10 8 eV. − − − OUTLINE 1. Leptogenesis 2. AD mechanism along LHu direction 3. AD leptogenesis in DFSZ model with varying PQ scale 4. Summary OUTLINE 1. Leptogenesis 2. AD mechanism along LHu direction 3. AD leptogenesis in DFSZ model with varying PQ scale 4. Summary ber can be used to infer the ratio of the number density of baryons to photons in the Universe, a quantity that is measured independently from theprimordialnucleosynthesis of light elements. The WMAP results [4] are in agreement with the most recent nucle- osynthesis analysis of the primordial Deuterium abundance,buttherearediscrepancies with both the inferred 4He and 7Li values [5]. These latter values, however, may have an underestimated error [6]. Averaging the WMAP result only with that coming from the primordial abundance of Deuterium gives: nB −10 ηB =6.1 0.3 10 . (1) nγ ≡ ± × Why does this ratio have this value? In this review, we will principally try to address this last question which, as we shall see, is intimately related to the existence of a primordial matter-antimatter asymmetry. Nevertheless, we shall try, when germane, to connect our discussion with the broader issues of what constitutes dark energy and dark matter. There is good evidence that the Universe is mostly made up of matter, although it is possible that small amounts of antimatter exist [7]. However, antimatter certainly does not constitute one of the dominant components of the Universe’s energy density. Indeed, as Cohen, de Rujula, and Glashow [8] have compellingly argued, if there were to exist large areas of antimatter in the Universe they could only be atacosmicdistancescale from us. Thus, along with the question of why nB/nγ has the value given in Eq. (1), there is a parallel question of why the Universe is predominantly composed of baryons rather than antibaryons. In fact, these two questions are interrelated. If the Universe had been matter- antimatter symmetric at temperatures of O(1 GeV), as the Universe cools further and the inverse process 2γ B +B¯ becomes ineffective because of the Boltzmann factor, the → BARYONnumber density ASYMMETRY of baryons and antibaryons relative to photons would have been reduced ⌘B is determined both from light element productiondramatically in Big Bang as a result Nucleosynthesis of the annihilation (BBN) process B + B¯ 2γ.Astraightforward → and also from CMB measurements.Baryon Asymmetry Alternatively,calculation thisof isthe gives, sometimes Universe: in this case, expressed [9]: as the baryon-to-entropy ratio nB 10 cf) if universe were nB nB¯ −18 observed: 10− =(1.7) 10 . (2) s ' symmetric nγ nγ ≃ where s 7.04nγ in the present epoch. Thus, in a symmetric Universe the question is really why observationally n /n is so ' • Inflation dilutes all pre-existing particles. B γ Production of the baryon asymmetry of thelarge! Universe or BAU requires mechanisms which satisfy the three Sakharov criteria: 1. baryon number violation, 2. C and CP • We need a source ofIt B is asym. very diafterfficult inflation to imagine. processes at temperatures belowaGeVthatcould violation and 3. a departure from thermal equilibrium. Early proposals such as Planck enhance the ratio of the number density of baryons relative tothatofphotonsmuch scale or GUT scale baryogenesis seem no longer viable since the BAU would have been Sakharov’s conditions: 2 inflated away during the inflationary epoch of thebeyond Universe. the value Alternatively, this quantity most attains modern when baryon-antibaryon annihilation occurs. 2 proposals for developing the BAU take place afterAn the exception end of is the provided inflationary by some versions epoch, of at Affleck-Dine Baryogenesis [10] where a baryon excess • B violation or after the era of re-heating which occurs around the re-heat temperature T . In fact, R 4 the SM contains all the• ingredientsC & CP violation for successful electroweak baryogenesis since baryon (and lepton) number violating processes can take place at large rates at high temperature T>T 100 GeV via• departure sphaleron processes from thermal [43]. Unfortunately, equilibrium these first order phase weak ⇠ transition e↵ects require a Higgs mass . 50 GeV, and so has been excluded for many years. By invoking supersymmetry, then new possibilities emerge for electroweak baryogenesis. However, successful SUSY electroweak baryogenesis seems to require a Higgs mass mh . 113 GeV and a right-handed top-squark m 115 GeV [44]. These limits can be relaxed t˜R . to higher values so long as other sparticle/Higgs masses such as m 10 TeV. Such heavy A Higgs masses are not allowed if we stay true to our guidance from naturalness: after all, 2 2 2 Eq. 1.2 requires m / tan β . m /2. For heavy Higgs masses, then mA mHd and then Hd Z ⇠ from naturalness we find m 4 8 TeV (depending on tan β)[45]. A . − In Sec. 2, we survey several leptogenesis mechanisms as the most promising baryogen- esis mechanisms: 1. thermal leptogenesis [46, 47], 2. non-thermal leptogenesis via inflaton decay [49] 3. leptogenesis from oscillating sneutrino decay [50, 52] and 4. leptogenesis via an A✏eck-Dine condensate [53, 54, 50]. Each of these processes requires some range of re-heat temperature TR and gravitino mass m3/2, and indeed some of them run into conflict with the so-called cosmological gravitino problem [55]. In this case, gravitinos can be thermally produced in the early universe at a rate proportional to TR [56]. If TR is too high then too much dark matter arises from thermal gravitino production followed by cascade decays to the LSP. Also, even if dark matter abundance constraints are respected, if the gravitino is too long-lived, then it may decay after the onset of BBN thus destroying the successful BBN predictions of the light element abundances [57, 58, 59]. In the case of natural SUSY with mixed axion-higgsino dark matter, then similar con- straints arise from axino and saxion production: WIMPs or axions can be overproduced, or light element abundances can be destroyed by late decaying axinos and saxions.
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