Flaxion. a minimal extension to solve puzzles in the standard EW 2018, Mar. 13, 2018

Transcription

1 Flaxion a minimal extension to solve puzzles in the standard model Koichi Hamaguchi (University of EW 2018, Mar. 13, 2018 Based on Y. Ema, KH, T. Moroi, K. Nakayama, arxiv: [JHEP 1701 (2017) 096], Y. Ema, D. Hagihara, KH, T. Moroi, K. Nakayama, arxiv:

2 Summary: U(1) FN = U(1) PQ 2

3 Summary: We proposed a new model (scenario) that explains the hierarchical flavor structure of quarks/leptons, Mass kev MeV GeV TeV e u c d s b μ τ t Why? and solves the strong CP problem, L = s 8 F a µ ef aµ, = + arg det m q from neutron EDM Why? and includes DM, Leptogenesis, and Inflation. 3

4 Q: What s the origin of the quark and lepton mass hierarchy and mixings?? cf. Talks by R. Alonso J. Fuentes-Martín on Sunday. Mass kev MeV GeV TeV v 1,2,3 e u c d s b μ τ t ŷ u ij Q i Hu Rj Yukawa large hierarchy quark mixing neutrino mixing 4

5 A simple possibility: a spontaneously broken global U(1) symmetry. [Froggatt-Nielsen, 79] ŷ u ij Q i Hu Rj up-type quark Yukawa couplings in the Standard Model 5

6 A simple possibility: a spontaneously broken global U(1) symmetry. [Froggatt-Nielsen, 79] ŷ u ij Q i Hu Rj Q i u Rj H U(1) charge q Qi q uj 0 +1 y u ij M qqi New complex scalar: Flavon q uj Qi Hu Rj up-type quark Yukawa couplings in the Standard Model cutoff scale 5

7 A simple possibility: a spontaneously broken global U(1) symmetry. [Froggatt-Nielsen, 79] ŷ u ij Q i Hu Rj Q i u Rj H U(1) charge q Qi q uj 0 +1 y u ij M qqi New complex scalar: Flavon q uj Qi Hu Rj After U(1) breaking by <φ> 0, m u ij = yij u q Q i q uj hhi O(1) h i where M < 1 }Mass hierarchy and mixings Example: q Q = {3, 2, 0},q u = { 5, 1, 0} 0 1! m A 5 1 up charm top 6

8 A simple possibility: a spontaneously broken global U(1) symmetry. [Froggatt-Nielsen, 79] Our setup: where L = y d ij + y l ij yn M M n d ij n l ij M n N Q i Hd Rj + y u ij L i Hl Rj + y i MN c R N R h i M ' n u ij = q Q i q uj, >< n d ij = q Q i q dj, n l ij = q L i q lj, n i >: = q L i q N n N = q N q N. M M n u ij n i +h.c. Q i e HuRj L i e HNR We also introduce 2 or 3 right-handed neutrinos. 7

9 A simple possibility: a spontaneously broken global U(1) symmetry. [Froggatt-Nielsen, 79] Then, Quark mass hierarchy as well as CKM angles are naturally explained as e.g., diag(m u ) ( 8, 3, 1)hHi, u,c,t 8 >< q Q = {3, 2, 0}, q u = { 5, 1, 0}, >: q d = { 4, 3, 3}! >< m u ij m >: d ij C A hhi, C A hhi, 4 3 3! >< diag(m d ) ( 7, 5, 3 )hhi, V CKM >: C A d,s,b 8

10 A simple possibility: a spontaneously broken global U(1) symmetry. [Froggatt-Nielsen, 79] Then, Quark mass hierarchy as well as CKM angles are naturally explained as e.g., diag(m u ) ( 8, 3, 1)hHi, u,c,t 8 >< q Q = {3, 2, 0}, q u = { 5, 1, 0}, >: q d = { 4, 3, 3}! >< m u ij m >: d ij C A hhi, C A hhi, 4 3 3! >< diag(m d ) ( 7, 5, 3 )hhi, V CKM >: Lepton masses and MNS angles are also explained as 8 >< q L = {1, 0, 0}, q e = { 8, 5, 3}, >: q N = {q N1,q N2, (q N3 )}! 8 >< mìj m >: ij q N -dependence cancels C A hhi, B 1 1A hhi2 M, 1 1 because of the seesaw formula.! C A diag(m e ) ( 9, 5, 3 )hhi, >< diag(m ) ( 2, 1, 1) hhi2 M, V MNS >: B 1 1A 1 1 d,s,b e,μ,τ large 2-3 mixing [cf. Sato-Yanagida, 98, Ramond, 98] 8

11 Standard Model Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. 9

12 Quark and lepton mass hierarchy and mixings. Standard Model + one complex scalar with U(1) F = p 1 (' + ia) : flavon 2 Neutrino masses and mixings. seesaw + 2 (or 3) right-handed neutrinos. 9

13 Our setup: L = y d ij + y l ij yn M M n d ij n l ij M n N Q i Hd Rj + y u ij L i Hl Rj + y i MN c R N R can explain the quark and lepton mass hierarchy and mixings. M M n u ij n i +h.c. Q i e HuRj L i e HNR OK, but What s new? Froggatt-Nielsen paper was in

14 Our setup: L = yd ij + y l ij yn M M n d ij n l ij M n N Q i Hd Rj + y u ij L i Hl Rj + y i MN c R N R POINT: The global, spontaneously broken U(1) flavor symmetry is anomalous under SU(3) C, which means the Peccei-Quinn mechanism (to solve the strong CP problem) is automatically included: U(1) F = U(1) PQ!! Flaxion M M n u ij n i +h.c. Q i e HuRj L i e HNR * As far as we know, this simple realization has not been studied explicitly before. cf. related earlier works, Wilczek, 82, Geng-Ng, 89, Berezhiani-Khlopov, 91, Babu-Barr, 92, Albrecht et.al., 10, Fong-Nardi, 13, Ahn, 14, 16, Celis et.al., 14,.. 11

15 12

16 Flaxion = 1 p 2 (' + ia) flavon axion 13

17 Flaxion = 1 p 2 (' + ia) flavon axion (1) Strong CP problem is solved by the PQ mechanism. [Peccei-Quinn, 77] L = g2 s a 32 2 G a µ G f eaµ where f a = a p 2h i N DW, N DW = X i (2q Qi q ui q di ) a (In the example before, N DW = 26.) = 0 a 13

18 Flaxion = 1 p 2 (' + ia) flavon axion (1) Strong CP problem is solved by the PQ mechanism. (2) The axion can be the dark matter. a h 2 = i 1.19 f a GeV [Turner, 86] 14

19 Flaxion = 1 p 2 (' + ia) flavon axion (1) Strong CP problem is solved by the PQ mechanism. (2) The axion can be the dark matter. Any new prediction? 15

20 Flaxion = 1 p 2 (' + ia) flavon axion (1) Strong CP problem is solved by the PQ mechanism. (2) The axion can be the dark matter. Any new prediction? Yes! (3) Characteristic flavor-changing signals are predicted. [cf. Wilczek, 82] 15

21 (3) Characteristic flavor-changing signals. L = y d ij + y l ij L = yn M M X f=u,d,l n d ij n l ij M " n N m f ij Q i Hd Rj + y u ij L i Hl Rj + y i MN c R N R 1+ h p 2hHi # + mf ij nf ij (s + ia) p f Li f Rj +h.c. 2h i They are not simultaneously diagonalized. -> flavor changing processes. The most stringent bound comes from K + -> π + a. M M n u ij n i +h.c. Q i e HuRj L i e HNR Br(K +! + a) ' GeV f a! f a & GeV 2 26 N DW 2 (apple d AH ) 12 m s m d {z } O(1) 2 < [BNL-E787, E949] CERN NA62 experiment can improve the sensitivity!! 16

22 Flaxion Scenario Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. Strong CP problem. Dark Matter. 17

23 Flaxion Scenario Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. axion Strong CP problem. Dark Matter. 17

24 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. axion characteristic signal: K π a Strong CP problem. Dark Matter. 17

25 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. axion What about the real part? characteristic signal: K π a Strong CP problem. Dark Matter. 18

26 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. inflaton axion characteristic signal: K π a Strong CP problem. Dark Matter. Inflation! 19

27 Flaxion Inflation: L 2 (1 2 / 2 ) 2 2 v 2 2 v < < p 2v canonical field e' : ' p 2 tanh e' p 2 20

28 Flaxion Inflation: L 2 (1 2 / 2 ) 2 2 v 2 2 Curvature fluctuation: v < < p 2v canonical field e' : ' p 2 tanh e' p 2 P = 2.2 x 10-9 [Planck, 15] is reproduced for. 1 and & GeV, which is consistent with the scale for flaxion DM. (n s, r) is in the Planck best-fit region. The U(1) symmetry is never restored -> No Domain wall. fluctuation 2 n is suppressed. s ' 1, r ' 4 2 N Reheating e N 2. temperature e M is high P enough for. 21

29 Flaxion Inflation: L 2 (1 2 / 2 ) 2 2 v 2 2 Curvature fluctuation: v < < p 2v canonical field e' : ' p 2 tanh e' p 2 P = 2.2 x 10-9 [Planck, 15] is reproduced for. 1 and & GeV, which is consistent with the scale for flaxion DM. (n s, r) is in the Planck best-fit region. The U(1) symmetry is never restored -> No Domain wall. Isocurvature fluctuation is suppressed. Reheating temperature is high enough for Leptgenesis. (T R GeV) ("strong washout ) 22

30 Flaxion Inflation: L 2 (1 2 / 2 ) 2 2 v 2 2 Curvature fluctuation: v < < p 2v canonical field e' : ' p 2 tanh e' p 2 P = 2.2 x 10-9 [Planck, 15] is reproduced for. 1 and & GeV, which is consistent with the scale for flaxion DM. (n s, r) is in the Planck best-fit region. The U(1) symmetry is never restored -> No Domain wall. Isocurvature fluctuation is suppressed. See Backup slides for details. Reheating temperature is high enough for Leptgenesis. (T R GeV) ("strong washout ) 22

31 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. inflaton axion characteristic signal: K π a Strong CP problem. Dark Matter. Inflation. 23

32 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. inflaton axion characteristic signal: K π a Strong CP problem. Dark Matter. P & (n s, r) in the Planck best-fit region Inflation. 23

33 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. inflaton axion characteristic signal: K π a Strong CP problem. Dark Matter. solves DW and isocurvature problems P & (n s, r) in the Planck best-fit region Inflation. 23

34 Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Leptogenesis Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. inflaton axion characteristic signal: K π a Strong CP problem. Dark Matter. solves DW and isocurvature problems Baryon asymmetry of the Universe. High enough reheating P & (n s, r) in the Planck best-fit region Inflation. 24

35 Summary Quark and lepton mass hierarchy and mixings. Neutrino masses and mixings. seesaw Leptogenesis Flaxion Scenario Standard Model + one complex scalar with U(1) F = U(1) PQ flavon = 1 p 2 (' + ia) + 2 (or 3) right-handed neutrinos. inflaton axion characteristic signal: K π a Strong CP problem. Dark Matter. solves DW and isocurvature problems Baryon asymmetry of the Universe. High enough reheating P & (n s, r) in the Planck best-fit region Inflation. 25

36 Backup 26

37 Summary Flaxion Scenario 2 L = (1 2 / 2 ) 2 2 v 2 2 n d + yij d ij Q M i Hd Rj + yij u M n l + yij l ij L i Hl Rj + yi M M + 1 n N 2 yn MNR c M N R +h.c. n u ij n i Q i e HuRj L i e HNR 27

38 Summary scale Flaxion Scenario GeV 0.2 M q N1 =1 q Leptogenesis N1 = v 1 inflation 10 6 p 2 N DW 0.1 f a i 1 axion DM i 10 3 K π a [BNL-E787, 949] CERN-NA62 28

39 Supersymmetric flaxion? Cosmology becomes nontrivial; gravitino, sflaxion, SUSY flavor/cp, R-parity violation, Inflation model, Y. Ema, D. Hagihara, KH, T. Moroi, K. Nakayama, arxiv:

40 Other constraints? apple f H ij apple f AH ij = 1 2 V f bq Q V f U f bq f U f ij (mf j + mf i ), = 1 2 V f bq Q V f + U f bq f U f ij (mf j m f i ). K + π + a μ e a γ SN1987A cooling of the white dwarf stars. (g aee ) 30

41 [arxiv: ] The NA62 experiment at CERN: status and perspectives NA62 Collaboration 31

42 B + K + a?? [arxiv: ] Phys.Rev. D95 (2017) The Axiflavon L. Calibbi, F. Goertz, D. Redigolo, R. Ziegler, J. Zupan ' } GeV f a 32

43 Flaxion Dark Matter: a a Case 1: U(1) is broken after inflation. -> Domain Wall! In the flaxion scenario, typically N DW 1, and this possibility is excluded. Case 2: U(1) was already broken during inflation. Quantum fluctuation during inflation leads to DM isocurvature perturbation, which is severely constrained [Planck, 15]. -> Strong bound on inflation scale. a H inf H inf GeV 1 i GeV. f a 33

44 Flaxion Dark Matter: a a Case 1: U(1) is broken after inflation. -> Domain Wall! In the flaxion scenario, typically N DW 1, and this possibility is excluded. Case 2: U(1) was already broken during inflation. Quantum fluctuation during inflation leads to DM isocurvature perturbation, which is severely constrained [Planck, 15]. No problem in ``flaxion-inflation scenario! -> Strong bound on inflation scale. a H inf H inf GeV 1 i GeV. f a 34

45 Flaxion Inflation: L 2 (1 2 / 2 ) 2 2 v 2 2 The U(1) symmetry is never restored v < < p 2v canonical field e' : ' p 2 tanh e' p 2 -> No Domain wall. 35

46 Flaxion Inflation: L 2 (1 2 / 2 ) 2 2 v 2 2 The U(1) symmetry is never restored v < < p 2v canonical field e' : ' p 2 tanh e' p 2 -> No Domain wall. Isocurvature fluctuation is suppressed. a inf H inf 36

47 Flaxion Inflation: Reheating and Leptogenesis Inflaton partial decay rate into RHNs, Reheating is completed almost instantaneously.. Reheating temperature T R GeV. 37

48 Flaxion Inflation: Reheating and Leptogenesis and thermal leptogenesis [Fukugita-Yanagida, 86] can work successfully for m N1 O(10 12 ) GeV! In more details, Final baryon asymmetry: Asymmetry parameter: Effective neutrino mass: -> Efficiency factor (strong washout region) Altogether, observed asymmetry n B /s 0.9 x can be obtained for m N1 O(10 12 ) GeV, corresponding to 38

49 Proton decay? > In the case of example charge assignments, the most dangerous one is the last one. With O(1) coefficients, M > 5 x GeV is sufficient to suppress it. 39