Axion-assisted electroweak baryogenesis

Transcription

1 Axion-assisted electroweak baryogenesis Nathaniel Craig IAS/Rutgers based on arxiv: w/ John March-Russell Cornell 09/22/10

2 Baryogenesis Measured baryon density η n B s One of the better-motivated BSM questions!

3 Baryogenesis Measured baryon density η n B s One of the better-motivated BSM questions! Sakharov criteria Violation of B number Violation of CP Departure from thermal equilibrium

4 Baryogenesis in EWPT? The Sakharov criteria are natural ingredients in the electroweak phase transition Violation of B number Violation of CP Departure from thermal equilibrium

5 Baryogenesis in EWPT? The Sakharov criteria are natural ingredients in the electroweak phase transition Violation of B number Large when EW symmetry is restored! Violation of CP Possible in MSSM or SM extensions? Departure from thermal equilibrium Certainly if EWPT is sufficiently strong

6 Baryogenesis in EWPT? The Sakharov criteria are natural ingredients in the electroweak phase transition Violation of B number Large when EW symmetry is restored! Violation of CP Possible in MSSM or SM extensions? Departure from thermal equilibrium Certainly if EWPT is sufficiently strong Certainly there are countless other mechanisms with these ingredients, but the EWPT is such a compellingly natural part of our cosmological history We ll focus on the source of CP violation

7 The question of CP violation A natural ingredient of the SM, but relation to baryogenesis is less clean... CP violation intrinsic to SM, but effects suppressed by Jarlskog invariant; effective CP violation in weak interactions is Can do it in MSSM with CP-violating soft masses; or by adding dimension-six operators by hand, but these are fairly tightly constrained by dl neutron/electron EDMs and CP-violating FCNC processes. ~ d L H d G ~ ~ d R! d R A little tension: want CP violation large during baryogenesis, but very small now? Wouldn t it be nice if we could somehow relax CP violation to satisfy current bounds?

8 Dynamical relaxation of CP violation We know of one such example: the strong CP angle in QCD with an axion! CP violation large in early universe, before axion relaxes. Axion relaxes starting around confinement; present value satisfies neutron EDM limits θ QCD < 10 9 Unsurprisingly, this is not a completely new idea...

9 The basic idea Induce an effective, CP-violating operator... L CP = g2 32π 2 W µν W µν Φ(T,H)

10 The basic idea Induce an effective, CP-violating operator... L CP = g2 32π 2 W µν W µν Φ(T,H)...related via anomaly equation to CS number: g 2 32π 2 W µν W µν = µ j µ CS

11 The basic idea Induce an effective, CP-violating operator... L CP = g2 32π 2 W µν W µν Φ(T,H)...related via anomaly equation to CS number: g 2 32π 2 W µν W µν = µ j µ CS A chemical potential for CS number! L CP = j 0 CS 0 Φ = n CS dφ/dt

12 The basic idea Induce an effective, CP-violating operator... L CP = g2 32π 2 W µν W µν Φ(T,H)...related via anomaly equation to CS number: g 2 32π 2 W µν W µν = µ j µ CS A chemical potential for CS number! L CP = j 0 CS 0 Φ = n CS dφ/dt Biases baryon number during EWPT: dn B dt = 1 T Γ aµ CS

13 The basic idea Induce an effective, CP-violating operator... L CP = g2 32π 2 W µν W µν Φ(T,H)...related via anomaly equation to CS number: g 2 32π 2 W µν W µν = µ j µ CS A chemical potential for CS number! L CP = j 0 CS 0 Φ = n CS dφ/dt Ultimate baryon asymmetry const α 5 wδφ

14 The idea in practice: QCD [Kuzmin, Shaposhnikov, Tkatchev 92] Integrate out quarks to generate an effective operator W µν G µν q 7α 3α m 4 q (G G)(W W ) G µν W µν

15 The idea in practice: QCD [Kuzmin, Shaposhnikov, Tkatchev 92] Integrate out quarks to generate an effective operator W µν G µν q 7α 3α m 4 q (G G)(W W ) G µν W µν Axion vev gives nonzero gluon condensate: α s 8π G G = m 2 a(t )f 2 a sin θ

16 The idea in practice: QCD [Kuzmin, Shaposhnikov, Tkatchev 92] Integrate out quarks to generate an effective operator W µν G µν q 7α 3α m 4 q (G G)(W W ) G µν W µν Axion vev gives nonzero gluon condensate: α s 8π G G = m 2 a(t )f 2 a sin θ This looks like a chemical potential for CS number, and δφ sin θ m 4 q f 2 a δm 2 a(t,v)

17 Quantitatively... Quantitative result depends on change in axion mass during EWPT... Axion mass in this regime only comes from instanton effects: δφ sin θ f 2 πm 2 π T 3 c Λ T c 9 This is terrible; need T c Λ for meaningful CP violation

18 Quantitatively... Quantitative result depends on change in axion mass during EWPT... Axion mass in this regime only comes from instanton effects: δφ sin θ f 2 πm 2 π T 3 c Λ T c 9 This is terrible; need T c Λ for meaningful CP violation...but instead have T c 100 GeV Λ 0.2 GeV

19 Quantitatively... Quantitative result depends on change in axion mass during EWPT... Axion mass in this regime only comes from instanton effects: δφ sin θ f 2 πm 2 π T 3 c Λ T c 9 This is terrible; need T c Λ for meaningful CP violation...but instead have T c 100 GeV Λ 0.2 GeV Strong CP won t work.

20 The next best thing? Try the silliest possible generalization: a confining sector with a higher confinement scale. What are the necessary ingredients? A confining gauge group with strong CP angle Some means of communicating to the SM Significant time-dependence during EWPT An axion for the new group May sound a bit hokey, but the results are appealing.

21 A simple (nonsupersymmetric) model SU(N) G gauge theory w/ bifundamental matter SU(N) G SU(2) L U(1) Y Q 2 Y Q Q 2 Y Q U 1 1/2+Y Q U 1 1/2 Y Q (anomaly-free; if you want unification, add colored multiplets to fill out 5 + 5) (I will assume colored multiplets are ~1 TeV and irrelevant to the IR phenomenology)

22 The theory I Start with vector masses and Higgs couplings: L G µ Q QQ µ U UU λh QU λ HQU + h.c. Spectrum has three dirac fermions w/ M = µ 1 Q 2 λv(t ) 1 λ v(t ) 2 µ U For µ Q = µ U = µ m Q (T )=µ, µ ± λλ 2 v(t )

23 The theory II Symmetries allow a theta term for the hidden gauge group L G α Gθ G 8π G µν G µν....and include a hidden group axion w/ usual coupling α G 8π a G f G G G

24 The theory II Symmetries allow a theta term for the hidden gauge group L G α Gθ G 8π G µν G µν....and include a hidden group axion w/ usual coupling α G 8π a G f G G G Hidden group confinement leads to axion mass, evolution of the axion vev Nonzero axion vev gives a hidden glue condensate α G 8π G G = m 2 a(t )f 2 G sin θ G

25 Effective theory below the scale m Q Integrate out the bifundamental matter: L eff α W α G 64π 2 1 m 4 Q W µν W µν G µν Gµν Axion vev leads to an effective operator g2 32π 2 W µν W µν 1 i m 4 Q,i (T )m2 a(t )f 2 G sin θ G.

26 Induced CP violation Effective operator serves as chemical potential for CS number L CP = g2 32π 2 W µν W µν Φ(T,H) L CP = j 0 CS 0 Φ = n CS dφ/dt

27 Induced CP violation Effective operator serves as chemical potential for CS number L CP = g2 32π 2 W µν W µν Φ(T,H) L CP = j 0 CS 0 Φ = n CS dφ/dt Leads to CP violating contribution to baryon asymmetry: δφ(t,h) δ i m 2 a(t ) m 4 Q,i (T ) fg 2 sin θ G Depends on change in quark, axion masses during EWPT

28 Estimating the asymmetry Clearly the result depends on the hierarchy of parameters: Confinement before EWSB, no light quarks 1. T c < Λ G <m Q 2. T c <m Q < Λ G 3. Λ G <T c <m Q Confinement before EWSB, light quarks Confinement after EWSB, no light quarks ( confinement after EWSB, light quarks is excluded by Tevatron)

29 First hierarchy: T c < Λ G <m Q Axion mass is parametrically m 2 af 2 G Λ 4 G. But the relevant confinement scale depends on quark masses: Λ G = Λ G,UV ΛG,UV m Q (b1,uv /b 1,IR 1)

30 First hierarchy: T c < Λ G <m Q Axion mass is parametrically m 2 af 2 G Λ 4 G. But the relevant confinement scale depends on quark masses: Λ G = Λ G,UV ΛG,UV m Q (b1,uv /b 1,IR 1) Ultimately this leads to δφ =sinθ G N λλ vδv µ 2 ΛG,UV µ (4 24/11N)

31 Second hierarchy: T c <m Q < Λ G Axion mass is parametrically m 2 af 2 G m Q Λ 3 G. Resulting asymmetry is simply δφ 10 sin θ G λλ vδv Λ3 G µ 5 (this will prove to be an uninteresting limit)

32 Third hierarchy: Λ G <T c <m Q In this case the axion still acquires mass from instantons! May estimate using dilute instanton gas approximation m 2 af 2 G Λ 4 G ΛG T 1 3 (11N 12)

33 Third hierarchy: Λ G <T c <m Q In this case the axion still acquires mass from instantons! May estimate using dilute instanton gas approximation ΛG 1 3 (11N 12) m 2 af 2 G Λ 4 G T Also incorporate dependence of Λ G on m Q λλ vδv ΛG,UV 2 ΛG,UV 11N 3 4. δφ 28 3 sin θ G µ 2 µ T

34 Cosmological evolution Another important effect to account for: cosmological evolution of the axion Axion vev begins to evolve when m a 3H Not sure what happens when oscillation begins; need to ensure that some CP violation remains by EWPT log 10 3 Hm a log 10 tt G Θ G Θ G, i

35 Cosmological evolution II A conservative limit: require that the axion vev not pass through zero before T c (this is often quite a bit after m a =3H)

36 Cosmological evolution II A conservative limit: require that the axion vev not pass through zero before T c (this is often quite a bit after m a =3H) These regimes are more interesting 1. T c < Λ G <m Q 2. T c <m Q < Λ G 3. Λ G <T c <m Q

37 Cosmological evolution III Also has implications for the size of f G f G = GeV Λ G 1 GeV f G = GeV Λ G 300 GeV

38 Cosmological evolution III Also has implications for the size of f G f G = GeV Λ G 1 GeV f G = GeV Λ G 300 GeV!!!!!

39 Cosmological evolution III Also has implications for the size of f G f G = GeV Λ G 1 GeV f G = GeV Λ G 300 GeV!!!!! Of course, we know that GUT-scale PQ scale requires the initial angle to be small in order to avoid DM overdensity; puts us in the anthropic axion range. In this case, requires θ G,i 0.01

40 Constraints How constrained is this scenario? Collider constraints on hidden sector PEWC constraints on bifundamental matter Cosmological constraints on the hidden sector Cosmological constraints on the hidden axion Leads to (mild) limits on µ, Λ G, θ i,f G that constrain new physics to lie near the weak scale, within LHC reach.

41 Collider constraints Hidden sector quarks: CDF Run II limits on uncolored fermions w/ Higgs coupling m Q 200 GeV (if colored, limit is m Q 250 GeV) Implies µ 300 GeV for 2 1 λv 100 GeV Λ G not strongly constrained (and too large in this scenario to be macroscopically quirky )

42 Precision electroweak constraints Contribution to S from, e.g., But these contributions decouple as Ngg 16π 2 λλ µµ m 4 Q 2 λv µ H HW µν B µν T 0.1 T S S

43 Cosmological constraints How safe is the new sector? Don t want to assume unusually low reheating!

44 Cosmological constraints How safe is the new sector? Don t want to assume unusually low reheating! Surprisingly safe! Scenario is basically a variation on quirk cosmology. Lightest quarks stable, but annihilate rapidly [Jacoby, Nussinov 07, Kang, Luty 08]

45 Cosmological constraints How safe is the new sector? Don t want to assume unusually low reheating! Surprisingly safe! Scenario is basically a variation on quirk cosmology. Lightest quarks stable, but annihilate rapidly [Jacoby, Nussinov 07, Kang, Luty 08] Glueballs decay rapidly into Higgs, EW bosons: τ m 4 Q 100 GeV s 300 GeV Λ G 7....so no problems with BBN

46 Cosmological constraints II What about the new axion? Limits on the axion familiar from QCD axion cosmology:

47 Cosmological constraints II What about the new axion? Limits on the axion familiar from QCD axion cosmology: Starts out as random field with vevs a G f G θ G,i Begins to oscillate when m a 3H

48 Cosmological constraints II What about the new axion? Limits on the axion familiar from QCD axion cosmology: Starts out as random field with vevs a G f G θ G,i Begins to oscillate when m a 3H Contributes to DM density Ω a h fg M P ΛG T i ag,i f G 2

49 Cosmological constraints II What about the new axion? Limits on the axion familiar from QCD axion cosmology: Starts out as random field with vevs a G f G θ G,i Begins to oscillate when m a 3H Contributes to DM density Ω a h fg M P ΛG T i ag,i f G 2 Abundance limit θ i =1 f G GeV θ i =0.01 f G GeV plausibly anthropic

50 Parameter space for AAEB If we fold all these constraints together, what do we get?

51 Parameter space for AAEB If we fold all these constraints together, what do we get? f G = GeV, θ i =1 N3; sin Θ G 1; f G GeV; T c 100 GeV; Λv100 GeV 700 µ(gev) Μ GeV G GeV Λ G (GeV)

52 Parameter space for AAEB If we fold all these constraints together, what do we get? f G = GeV, θ i =1 N3; sin Θ G 1; f G GeV; T c 100 GeV; Λv100 GeV f G = GeV, θ i =0.01 N3; sinθ G.01; f G GeV; T c 100 GeV; Λv100 GeV µ(gev) Μ GeV µ(gev) Μ GeV G GeV Λ G (GeV) G GeV Λ G (GeV)

53 Hidden sector physics at a TeV The various limits push us into an interesting space: both confinement scale and quark masses are below a TeV Λ G,µ too large axion relaxes too quickly Λ G too small insufficient CP violation µ too small collider limits GUT-scale anthropic axion most favored PEWC, hidden sector cosmology limits automatically satisfied in this region

54 Prospects for detection New physics within LHC reach; what would we expect to see? Hidden sector dynamics is classic pure-glue hidden valley

55 Prospects for detection New physics within LHC reach; what would we expect to see? Hidden sector dynamics is classic pure-glue hidden valley Hidden sector quarks produced via gauge bosons, Higgs

56 Prospects for detection New physics within LHC reach; what would we expect to see? Hidden sector dynamics is classic pure-glue hidden valley Hidden sector quarks produced via gauge bosons, Higgs Bound states decay rapidly to hidden sector glueballs

57 Prospects for detection New physics within LHC reach; what would we expect to see? Hidden sector dynamics is classic pure-glue hidden valley Hidden sector quarks produced via gauge bosons, Higgs Bound states decay rapidly to hidden sector glueballs Glueball decays are prompt and visible

58 Prospects for detection New physics within LHC reach; what would we expect to see? Hidden sector dynamics is classic pure-glue hidden valley Hidden sector quarks produced via gauge bosons, Higgs Bound states decay rapidly to hidden sector glueballs Glueball decays are prompt and visible Decays into electroweak bosons, Higgs

59 Prospects for detection New physics within LHC reach; what would we expect to see? Hidden sector dynamics is classic pure-glue hidden valley Hidden sector quarks produced via gauge bosons, Higgs Bound states decay rapidly to hidden sector glueballs Glueball decays are prompt and visible Decays into electroweak bosons, Higgs Final states rich in jets, leptons, photons

60 Prospects for detection II Dark matter in this scenario is some combination of hidden and visible sector axions Not ideal from the perspective of direct detection, but axion searches are sensitive to hidden sector axion

61 Prospects for detection II Dark matter in this scenario is some combination of hidden and visible sector axions Not ideal from the perspective of direct detection, but axion searches are sensitive to hidden sector axion No smoking gun, though weak-scale hidden valley would be suggestive (and no such hidden valley would falsify) Best indication would be hidden valley + parameters consistent with strong EWPT + no obvious signs of new CPV

62 A supersymmetric model The straightforward generalization: W G = µ Q QQ + µ U UU + λh u QU + λ H d QU Especially natural if µ Q,µ U come from the same physics that sets the SM µ term All the previous discussion goes through, with two additions: 1) Now you have an axino, possibly interesting? and...

63 A nice bonus 2) This conveniently solves the little hierarchy problem.

64 A nice bonus 2) This conveniently solves the little hierarchy problem. Radiative corrections from vector-like fourth generation lift the Higgs mass [Martin 09, Graham, Rajendran, Saraswat 09]

65 A nice bonus 2) This conveniently solves the little hierarchy problem. Radiative corrections from vector-like fourth generation lift the Higgs mass [Martin 09, Graham, Rajendran, Saraswat 09] But no reason this generation can t be charged under a new gauge group! Conveniently, the range of quark masses necessary for this to work coincides with the range over which AAEB is efficient

66 Conclusion A mechanism for producing large CP violation during baryogenesis, consistent with small CP violation in the present era. Requires confining gauge group, bifundamental quarks, and a hidden axion. Efficient CP violation during EWPT forces confinement scale and quark masses to within LHC reach Supersymmetric version is conveniently free of little hierarchy problems Signatures are essentially those of quirk or hidden valley scenarios, but...

67 Conclusion A mechanism for producing large CP violation during baryogenesis, consistent with small CP violation in the present era. Requires confining gauge group, bifundamental quarks, and a hidden axion. Efficient CP violation during EWPT forces confinement scale and quark masses to within LHC reach Supersymmetric version is conveniently free of little hierarchy problems Signatures are essentially those of quirk or hidden valley scenarios, but... From a model-builder s perspective, provides a reason for hidden valleys at the weak scale