A model of heavy QCD axion

Transcription

1 A model of heavy QCD axion Masahiro Ibe (ICRR, Kavli-IPMU) Beyond the Standard Model in Okinawa /3/7 with H. Fukuda (IPMU), K. Harigaya(UC Berkeley), T.T.Yanagida (IPMU) Phy.Rev.D92(2015),1, with CW Chiang (NCU) H. Fukuda (IPMU), T.T.Yanagida (IPMU) arxiv :

2 Strong CP problem Experimentally, QCD is known to preserve CP symmetry very well. Hadron spectrum respects CP symmetry very well. CP violating transitions in the SM are caused by CP violation in the weak interaction (i.e. by the CKM phase). Picture from :

3 Strong CP problem This feature is not automatically guaranteed in QCD. QCD has its own CP-violating parameter : θ θ - term violates the P and CP symmetries The θ - term is highly constrained experimentally! n π d n /e ~ θ γ n [ 79 Crewther ] Null observation of the neutron EDM : d n /e < 2.9 x 90%CL [hep-ex/ ] θ < Why so small? = Strong CP Problem

4 Peccei-Quinn Mechanism [ 77 Peccei, Quinn ] Two Higgs doublet Model (H u, H d ) U(1) Peccei-Quinn symmetry (anomaly of SU(3) c ) H u,d e iα H u,d u R e -iα u R d R e -iα d R By the Peccei-Quinn rotation, θ can be shifted away! so that the θ is unphysical! θ θ = θ - 2N g α (N g =3)

5 Weinberg-Wilczek Axion [ 78 Weinberg, 78 Wilczek ] U(1) PQ is spontaneously broken at the EWSB axion Axion is massive due to the SU(3) c anomalous breaking ~ 100 kev In terms of the axion, the PQ mechanism can be interpreted as a dynamical tuning of the θ angle. θ eff = 0 a

6 Weinberg-Wilczek Axion f a is constrained by meson decay into axion. K ± π 0 x a Br( K± π ± + a (invisible) ) = O( f π 2 / f a 2 ) x Br( K± π ± + π 0 ) < 5 x [E787 hep-ex/ ] π ± f a > O(1)TeV [Axion decays into two photon but the lifetime is so long for m a ~ 100 kev. ] Original PQ-mechanism has been excluded!

7 Invisible Axion : f a >> v EW [ 80 Zhitnitsky, 81 Dine, Fischler, Sredniki ] ZDFS axion : Two Higgs doublet Model (H u, H d ) and a Singlet S U(1) Peccei-Quinn symmetry H u,d e iα H u,d S e i2α S u R e -iα u R d R e -iα d R U(1) PQ is spontaneously broken by <S> = v s >> v The axion evades constraints from the meson decay rates!

8 Invisible Axion : f a >> v EW [ 79 Kim, 80 Shifman, Vainshtein, Zakharov ] KSVZ axion : SM matter field are not U(1) PQ neutral. Singlet S Extra colored fermions q L, q R U(1) Peccei-Quinn symmetry ( SU(3) c anomaly ) S e iα S q L,R e -iα/2 q L,R U(1) PQ is spontaneously broken by <S> = v s >> v The axion evades constraints from the meson decay rates!

9 Invisible Axion : f a >> v EW Invisible axion is very light : axion is subject to constraints not only from the meson decays but also from astrophysics! Resultant constraint on the decay constant is f a > 10 9 GeV The axion is invisible in collider experiments

10 Invisible Axion : f a >> v EW A drawback of invisible axion models If the physics at the Planck scale breaks PQ symmetry we would have which distorts the axion potential. As a result the effective θ eff -parameter becomes non-vanishing! If we require θ eff <<10-11, we forbid m < 10 for f a > 10 9 GeV. We need some (discrete) symmetries for high quality U(1) PQ. [Or an effective large f a in aligned axion model (as explained by Takahashi san) ]

11 Visible Axion : m a >> m a PQWW Why is the axion so light? U(1) PQ is explicitly broken only by the QCD anomaly. We can make the axion HEAVY by adding other U(1) PQ breaking terms. However, such additional breaking leads to a too large θ eff! QCD anomaly Additional breaking θ eff = 0 θ eff = O(1) a Is there any way to make axion heavy while keeping θ eff = 0?

12 Visible Axion : m a >> m a PQWW Use QCD in a mirror copied Standard Model! [ 97 Rubakov] SM SM Z 2 exchange symmetry By the Z 2 exchange symmetry, gauge couplings, etc are equal in these two sectors at high energy scale. In particular θ SM = θ SM. If the axion couples to both two sectors, axion settles at θ eff = θ eff = 0!

13 Visible Axion : m a >> m a PQWW Use QCD in a mirror copied Standard Model! [ 97 Rubakov] SM SM spontaneous Z 2 breaking! If Z 2 is spontaneously broken at intermediate scale, the mass scales in the SM can be larger! [ Similar mechanism used in Volkas s talk. ] m aqcd >>m aqcd while the axion still settles at θ eff = θ eff = 0! We can make the axion heavy while not spoiling the PQ-mechanism! [ 01 Berechiani, Gianfagna, Giannotti, 14 Hook, 16 Albaid, Dine, Draper]

14 Visible Axion : m a >> m a PQWW How can we construct concrete models? Experimental constraints? Astrophysical constraints? Cosmological constraints? How low f a can we take?

15 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] KSVZ axion model with a copied SM sector Singlet S (common) Extra quarks q L ( ), q R ( ) in the SM ( ). U(1) Peccei-Quinn symmetry (SU(3) c and SU(3) c anomaly) S e i2α S q R e -iα q R q R e -iα q R U(1) PQ is spontaneously broken by <S> = v s Axion mass is dominated by the contributions of the copied sector anomaly! m a ' p z 0 1+z 0 f 0m 0 f a For example, m a =O(100)MeV is possible for v EW = 10 3 x v EW, Λ QCD = 10 3 x Λ QCD, f a = 10 3 GeV.

16 Axion properties Basic properties of the axion [Fukuda, Harigaya, Yanagida and MI arxiv: ] Axion mass is dominated by the QCD anomaly effect m a ' p z 0 1+z 0 f 0m 0 f a Axion coupling below the scale of <S> L e ' a f a + e (G G + G 0 G0 )+ 6Q2 Y 32 2 a f a (Y Ỹ + Y 0 Ỹ 0 ), No direct coupling to the leptons and quarks at high energy Axion main decay modes: For m a < 3 m π : a 2 γ, 2 γ (10-7 s for m a =100MeV, f a =TeV) For m a > 3 m π : a hadronic, 2 γ, 2 γ (will be discussed later) For m a >> 3 m π : a jets KFVZ axion has no decay modes in leptons at tree level!

17 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] Summary of experimental/astrophysical Constraints. 9 8 K ± π ± + a (invisible) K ± π 0 x a 7 SN Log a êgev D HB Beam Dump Purple shaded region : π ± Br( K ± π ± + a (invisible) ) > 5 x (E787 [hep-ex/ ]) 3 K ± Æ p ± +a M q >800GeV Hg=1L Log a êgev D [Weaker than the DFSZ type model due to the lack of direct coupling to heavy quarks and leptons! e.g. No constraints from B K + a( ll) ] Beam Dump (CHARM Experiment) Cu proton beam-dump (CERN-SPS:400GeV) axion 445m photon pair 35m Decay Tunnel Axion production rate ~ pion production rate x ( f π / f a ) 2 Red shaded region : #[Axion decay in distance from 445m to 480m from the beam target] > 3 [ 82 CHARM]

18 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] Summary of experimental/astrophysical Constraints. Log a êgev D HB SN K ± Æ p ± +a Beam Dump M q >800GeV Hg=1L Log a êgev D Constraint from Horizontal Branch The axion enhances the energy loss rate of the stars in Horizontal Branch of globular clusters via the Primakoff conversion γ He 2+ He 2+ Blue shaded region: E loss > 10 g -1 erg s -1 ( T HB core ~ 10 kev ) [arxiv: ] a Supernovae Constraint (1987a) a N N π N N Green Shaded region: E loss by axion < E loss by neutrino [arxiv: ] ( T SN ~ 30MeV, mean free path > 10km )

19 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] Summary of experimental/astrophysical Constraints SN Constraints on Extra Quarks We assume small mixing of them with the SM quarks Log a êgev D 6 5 HB L = i q L dri + 0 iq 0 L d 0 Ri +h.c., Leading to a small coupling to the SM 4 Beam Dump 3 K ± Æ p ± +a M q >800GeV Hg=1L Log a êgev D The extra quarks decay into H + b, Z + b, W + t (1:1:2 for SU(2) singlet ) LHC constraint : m extra quark > 800GeV (8TeV, 19.7fb -1 ) [CMS : arxiv: ] leading to f a = 2 m extra quark /g > 1120GeV /g

20 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] Constraints from Cosmology In the minimal model, γ in the copied sector is massless. For f a = O(1)TeV, γ is in thermal equilibrium for T > m a. γ γ a γ γ If, m a < T QCD, γ decouples below T QCD. γ contributes to N eff by 8/7. N eff (SM) = 3.05 N eff = 3.15±0.23 (68%CL PLANCK 2015) For m a >> T QCD, γ decouples above T QCD. γ contribution to N eff is diluted by QCD phase transition. ΔN eff (γ ) = 8/7 x ( g(t QCD )/ g(m a ) ) 4/3 < 0.2 ( See also a talk by Okui)

21 Axion properties Constraints from Cosmology What is the fate of ν? [Fukuda, Harigaya, Yanagida and MI arxiv: ] In the Standard Model sector, we assume the seesaw mechanism as the origin of the neutrino mass. Seesaw mechanism is also good to explain the Baryon asymmetry via Leptogenesis. In the mirror sector, the neutrino masses get enhanced as the v EW >> v EW (say v EW ~10 3 x v EW ) m 0 = v2 EW 0 v 2 EW m 0 For m ν > O(100)keV, the ν density exceeds the observed dark matter density!

22 Axion properties Constraints from Cosmology What is the fate of ν? [Fukuda, Harigaya, Yanagida and MI arxiv: ] In the Standard Model sector, we assume the seesaw mechanism as the origin of the neutrino mass. Seesaw mechanism is also good to explain the Baryon asymmetry via Leptogenesis. We ``turn off the seesaw mechanism (by a trick of Z 2 breaking ): m ν = y ν v EW In this case, ν becomes heavy and they decay into π ν π + e and hence, no contribution to the dark matter density! [ Or, if the lightest ν is very light, then the lightest ν can be also light enough. ]

23 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] Constraints from Cosmology Charged π s are stable (due to the lack of the lighter neutral fermion!) The pion annihilates into two dark photons and the resultant abundance is 0h m GeV The model is consistent as long as m π ~ 100GeV. Protons and neutrons are also stable. We have turned off the seesaw mechanism = no baryon asymmetry in the mirror sector! N 0h m N 0 TeV Again, the number density can be small enough. [It is possible to make them dark matter as in the talk by Foot?] 2

24 Axion properties [Fukuda, Harigaya, Yanagida and MI arxiv: ] Axion mass is dominated by the copied sector contributions. e.g) m a =O(100)MeV - O(1)GeV is possible for v EW = 10 3 x v EW, Λ QCD = 10 3 x Λ QCD, f a = 10 3 GeV. A heavy axion with m a > O(100)MeV evades constraints from (1) collider experiments (2) astrophysics (3) cosmology even for f a = O(1)TeV! [ It is safe to switch off the seesaw mechanism in the copied sector. ] The heavy is durable to explicit PQ-symmetry breaking by Planck suppressed operators e.g.) The effects of dimension 5 PQ-breaking operator leads to 3 e fa 1GeV apple 10 3 GeV m a which is consistent with current upper limit on θ eff. ' 2

25 Visible? Due to a rather small f a, direct productions at collider experiments are possible. (mainly decaying to γs or hadrons ) Fixed target experiments such as the SHIP experiment? KSVZ type model is accompanied by new extra quarks in the TeV range. m extra quark = 700GeV x ( f a / 1TeV ) The axion is accompanied by a scalar boson S with a mass of O(f a ). Can we identify the scalar boson S with the 750GeV diphoton resonance?

26 Diphoton Resonance [ Cheng-Wei, Fukuda, Yanagida and MI arxiv: ] Interactions of the scalar boson with a mass 750GeV. L = µ a@ µ a + s f a 8 = p 1 (f a + s)e ia/f a 2 g p 2MD f (t D ) sg µ G µ The scalar boson also couples to photons. g g γ { γ S(750GeV) a a ( Volk s Model) ( Dominant! ) [ Similar to the Takahashi san s idea. ]

27 Diphoton Resonance [ Cheng-Wei, Fukuda, Yanagida and MI arxiv: ] a is boosted so if it decays into 2γ, s 2a mimics the diphoton! (See also talks by Tobioka, Hamaguchi and Strumia) Production cross section (leading order) 2 f(xd ) 1TeV (g + g! s) ' 11 fb 2/3 f a 2 Branching ratio of the axion for m a < 3 m π (decays outside of detectors) for m a >> GeV Can the axion have BR(a 2γ) = O(1) with a short enough lifetime?

28 Diphoton Resonance [ Cheng-Wei, Fukuda, Yanagida and MI arxiv: ] Axion decay for 3 m π < m a < GeV In this mass range, the axion couples to SM though the mixings to η and η in the SM (since the model is KSVZ type.) L = 1 µa@ µ a + 1 µ µ µ µ m2 a a m ' 2 m p 6 f 2 0 a f a m 2 8 ' 1 (m u + m d +4m s ) 3 (m u + m d ) p m 2 2 ' p 2 3 (m u + m d 2m s ) m 2 (m u + m d ) We can estimate the axion decay amplitudes from the decay widths of η and η.

29 Diphoton Resonance [ Cheng-Wei, Fukuda, Yanagida and MI arxiv: ] Mixing angles ah, ah' Mixing angles are enhanced for either m a ~ m η or m a ~m η m a êmev G êev γγ 3π Decay widths ργ 2π+η m a êmev Two photon mode comes from the anomalous coupling of η and η. For m a ~ 650MeV, γγ mode is vanishing due to the η η mixing.

30 Diphoton Resonance [ Cheng-Wei, Fukuda, Yanagida and MI arxiv: ] Æ ggd Branching Ratio into photons Branching ratio into 2γ is sizable! [Green band denotes the O(1) ambiguities of the 3π and 2π+η modes.] g c t ê cm 0.02 f a =1TeV m a êmev Boosted decay length of a 0.01 f a =1TeV m a êmev Boosted axion decays before the EM calorimeters ( γcτ = O(10)cm ). [Green band denotes the O(1) ambiguities of the 3π and 2π+η modes.]

31 Required decay constant [ Γ(a 3π, 2π+η) x 1/3 (orange), x1 (blue), x3 (green) ] f a êtev m a êmev The diphoton excess can be explained for f a = 1TeV! g g S Aparicio-Azatov-Hardy-Romanino, Ellwanger-Hugonie, Knapen, Melia-Papucci-Zurek, Agrawal-Fan-Heidenreich-Reece-Strassler, Chala-Duerr-Kahlhoefer-Schmidt-Hoberg, Dasgupta-Kopp-Schwaller Acceptance, angular distribution of the signal require more careful study. Once, Z+γ mode is observed, this model can be easily excluded. a a For f a = O(1)TeV, we can introduce multiple extra colored particles without causing the domain wall problem. In this case, f a is replaced with f a /N quark, and hence, extra quarks mass can be O(1)TeV even for f a /N quark = O(100)GeV.

32 Summary KSVZ axion model with a mirror world can be a good model of heavy axion. A heavy axion with m a > O(100)MeV evades constraints from (1) collider experiments (2) astrophysics (3) cosmology even for f a = O(1)TeV! [ It is safe to switch off the seesaw mechanism in the copied sector. ] The heavy is durable to explicit PQ-symmetry breaking by Planck suppressed operators Small decay constant allow us to look for the axion in future experiments by LHC and future fixed-target experiments. 750GeV diphoton resonance can be identified with the scalar boson in the KSVZ type model for f a ~ 1TeV.