Lattice QCD Input to Axion Cosmology

Transcription

1 Colgate-Palmolive Lattice QCD Input to Axion Cosmology Evan Berkowitz Lawrence Livermore National Laboratory INT-15-3 Intersections of BSM Phenomenology and QCD for New Physics Searches Institute for Nuclear Theory Tuesday, October 13th, 2015 PRD / arxiv: E. Berkowitz, M. Buchoff, E. Rinaldi. LLNL-PRES This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA

2 Outline Introduction Whence axions? What is the over-closure bound? Inputs to the over-closure bound from lattice QCD Outlook 2

3 Big Idea Axions were originally proposed to deal with the Strong CP Problem, also form a plausible DM candidate. Calculating the axion energy density requires nonperturbative QCD input. Being sought in ADMX (LLNL, UW) & CAST (CERN), and (soon) IAXO with large discovery potential in the next few years. Β The Economist, 19 Dec 2006 CDM Requiring Ωa ΩCDM yields a lower bound on the axion mass today. Λ Preskill, Wise & Wilczek, Phys Lett B 120 (1983) Ωtot = 1.000(7) PDG 2014 via P.A.R. Ade, et al., (Planck Collab XVI), arxiv: v1. 3

4 QCD Theta Term QCD has a parameter, θ. L QCD µ F µ F Controls QCD CP violation. Topological. θ can take any value in (-π,π]. Q = CP Violating Z d 4 x µ F µ F 2 Z e is / e iq Neutron EDM e cm Baker et al., PRL 97, (2006) / hep-ex/ θ Strong CP Problem: Why is θ so small? 4

5 (Some) Resolutions of the Strong CP Problem Just declare CP to be good in the strong sector Why in the strong and not in the weak? mu = 0 mu 0 q i /D me i 0 5 q t Hooft PRL 37 8 (1976) Jackiw & Rebbi, PRL (1976) Callan, Dashen & Gross PLB (1976) Kaplan & Manohar PRL (1986) Gasser & Leutwyler PhysRept (1982) Additional Peccei-Quinn symmetry & axions Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791 Fine tuning problem can be reintroduced via high-dimensional (11 + ) operators at Planck scale. Holman et al. arxiv:hep-ph/ Cheung arxiv: Colangelo et al. (FLAG) arxiv:

6 Axions Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791 Couple to topological charge L QCD µ F µ F Otherwise have shift symmetry. Amenable to effective theory treatment PQ symmetry can break before or after inflation. 6

7 Axions Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791 Couple to topological charge L axions = 1 2 (@ µa) 2 + a 1 + f a 32 2 µ F µ F Otherwise have shift symmetry. Amenable to effective theory treatment PQ symmetry can break before or after inflation. a! a + V e cos + hai f a m 2 af 2 a 2 =0 6

8 Axions Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791 Couple to topological charge L axions = 1 2 (@ µa) 2 + a 1 + f a 32 2 µ F µ F Otherwise have shift symmetry. a! a + Amenable to effective theory treatment V e cos + hai f a m 2 af 2 a = PQ symmetry can break before or after inflation. 6

9 Axions Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791 Couple to topological charge L axions = 1 2 (@ µa) 2 + a 1 + f a 32 2 µ F µ F Otherwise have shift symmetry. a! a + Amenable to effective theory treatment V e cos + hai f a PQ symmetry can break before or after inflation. m 2 af 2 a = Axion mass QCD Topological Susceptibility 6

10 Current Axion Constraints Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Non RF-cavity Techniques Axion Coupling g a (GeV -1 ) Too Much Dark Matter ADMX Published Limits 2016 White Dwarf and Supernova Bounds "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter Axion Mass (µev) Courtesy GP Carosi, ADMX 7

11 Current Axion Constraints Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Axion Coupling g a (GeV -1 ) Too Much Dark Matter ADMX Published Limits Over-closure constraint on axion mass Non RF-cavity Techniques White Dwarf and Supernova Bounds "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter Axion Mass (µev) Courtesy GP Carosi, ADMX 7

12 The Over-Closure Bound High temperature arguments imply χ vanishes as T 8

13 The Over-Closure Bound High temperature arguments imply χ vanishes as T Universe cools as it expands 8

14 The Over-Closure Bound High temperature arguments imply χ vanishes as T Universe cools as it expands Axion number fixed when 3H ~ ma T1 5.5 Tc H: Hubble constant 8

15 The Over-Closure Bound Axion number fixed when 3H ~ ma T1 5.5 Tc 3H(T 1 ) m a (T 1 ) 9H 2 (T 1 )f 2 a (T 1 ) T 1 = T 1 (f a, (T )) 9

16 The Over-Closure Bound Axion number fixed when 3H ~ ma T1 5.5 Tc 3H(T 1 ) m a (T 1 ) 9H 2 (T 1 )f 2 a (T 1 ) T 1 = T 1 (f a, (T )) Axions continue to get heavier after production stops! (t) 6= a(t1 ) a(t) 3 (t 1 ) 9

17 The Over-Closure Bound Axion number fixed when 3H ~ ma T1 5.5 Tc 3H(T 1 ) m a (T 1 ) 9H 2 (T 1 )f 2 a (T 1 ) T 1 = T 1 (f a, (T )) Axions continue to get heavier after production stops! (t)r 3 m a (t) = # axions in a fixed comoving volume 9

18 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 10

19 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 χpt f 2 am 2 a(t )= m u m d (m u + m d ) 2 f 2 m 2 10

20 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 3H ~ ma χpt Cosmology Strong Dynamics 10

21 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 3H ~ ma χpt Cosmology Initial conditions Strong Dynamics 10

22 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 3H ~ ma χpt Cosmology Initial conditions Strong Dynamics = 2 Late PQ breaking: constraints on ma, fa Early PQ breaking: constraints depend on θ1 10

23 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume q R(T1 ) 3 (T )= (T ) (T 1 ) R(T ) If T1 goes down, ρ(τγ) goes up... 9H 2 (T 1 )f 2 a (T 1 ) T1 goes down as fa goes up. If fa goes up, ρ(τγ) goes up... m 2 af 2 a = Small ma are excluded by observed dark matter abundances! 11

24 Prior Over-Closure Bound c < CDM =0.12 ma(t) is provided by models. fa (2.8 ± 2) GeV ma 21 ± 2 μev ( ± uncontrolled systematic) Wantz & Shellard, arxiv:

25 a apple CDM Current Axion Constraints Wantz & Shellard, arxiv: Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Non RF-cavity Techniques Axion Coupling g a (GeV -1 ) Too Much Dark Matter ADMX Published Limits 2016 White Dwarf and Supernova Bounds "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter Axion Mass (µev) Courtesy GP Carosi, ADMX 13

26 a apple CDM Current Axion Constraints Wantz & Shellard, arxiv: Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Axion Coupling g a (GeV -1 ) Too Much Dark Matter Wantz & Shellard IILM ADMX Published Limits Non RF-cavity Techniques White Dwarf and Supernova Bounds systematic uncertainty? Axion Mass (µev) "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter Courtesy GP Carosi, ADMX 13

27 a apple CDM Current Axion Constraints Wantz & Shellard, arxiv: Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Axion Coupling g a (GeV -1 ) Too Much Dark Matter Wantz & Shellard IILM ADMX Published Limits Non RF-cavity Techniques White Dwarf and Supernova Bounds systematic uncertainty? "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter 2017 Reliance on models is unnecessary: we can calculate χ from lattice QCD! Axion Mass (µev) Courtesy GP Carosi, ADMX 13

28 CAVEAT We study pure Yang-Mills, and not yet full QCD. Dramatically more efficient algorithms enable huge statistics and volumes, shorter autocorrelation times. Tc is ~284 MeV, compared to 154 MeV in QCD. High temperature tends to suppress quark loops. What counts as high temperature? Unclear if this holds true for topological observables. But: for getting a lower bound on ma it's not so bad! 14

29 Overview of Lattice Ensembles & Measurements Berkowitz, Buchoff, and Rinaldi, arxiv: SU(3) YM with Wilson plaquette action T between 1.2 and 2.5 Nσ between 48 and 144 (larger at higher T) Nτ either 6 or 8 Between and measurements Combined hot & cold starts Cut of 2000 cfg.s for thermalization 10 compound sweeps of 1 heatbath step and 8 over-relaxation steps Q R Q Z Q a Q f Q OV Q WF 1 X 32 2 x µ raw measurement naïve rounding artifact corrected globally fit µ Lucini & Teper, hep-lat/ del Debbio et al., hep-th/ overlap Wilson Flow 15

30 Overview of Lattice Ensembles & Measurements Berkowitz, Buchoff, and Rinaldi, arxiv: SU(3) YM with Wilson plaquette action T between 1.2 and 2.5 Q R 1 X 32 2 x µ raw measurement µ Nσ between 48 and 144 (larger at higher T) Nτ either 6 or 8 Between and measurements Combined hot & cold starts Cut of 2000 cfg.s for thermalization 10 compound sweeps of 1 heatbath step and 8 over-relaxation steps Q Z Q a Q f naïve rounding artifact corrected Lucini & Teper, hep-lat/ globally fit del Debbio et al., hep-th/ Essentially no discretization or finite volume corrections 15

31 Overview of Lattice Ensembles & Measurements Berkowitz, Buchoff, and Rinaldi, arxiv: SU(3) YM with Wilson plaquette action T between 1.2 and 2.5 Nσ between 48 and 144 (larger at higher T) Nτ either 6 or 8 Between and measurements Combined hot & cold starts Cut of 2000 cfg.s for thermalization 10 compound sweeps of 1 heatbath step and 8 over-relaxation steps Q R Q Z Q a Q f raw measurement naïve rounding artifact corrected Lucini & Teper, hep-lat/01 globally fit del Debbio et al., hep-th/ 15

32 Best Lattice Results Berkowitz, Buchoff, and Rinaldi, arxiv: Pure glue measurements show χ vanishes as T Measurement N Measurement N /4 /Tc Gattringer et al., arxiv:hep-lat/ up to T/Tc ~ 1.3 T/T c 16

33 DIGM Best Fit & Extrapolation Berkowitz, Buchoff, and Rinaldi, arxiv: Pure glue measurements show χ vanishes as T Measurement N T 4 c = C (T/T c ) n 96 1/4 /Tc Best Fit n T/T c C C n Best Fit Covariance Matrix C n

34 Axion Production Ceases Berkowitz, Buchoff, and Rinaldi, arxiv: Axions production stops when 3H ~ ma T1 5.5 Tc from models H = m a DIGM fit 9H 2 f 2 a /T 4 c,f a =10 10 GeV 9H 2 f 2 a /T 4 c,f a =10 11 GeV fa [GeV] H 2 f a 2 /T c 4,f a =10 12 GeV /Tc T/T c 18

35 Axion Production Ceases Berkowitz, Buchoff, and Rinaldi, arxiv: Axions production stops when 3H ~ ma T1 5.5 Tc from models H 2 f 2 a = m 2 af 2 a = DIGM fit 9H 2 f 2 a /T 4 c,f a =10 10 GeV 9H 2 f 2 a /T 4 c,f a =10 11 GeV fa [GeV] H 2 f a 2 /T c 4,f a =10 12 GeV /Tc T/T c H 2 = m 2 P g R (T ) T 4 18

36 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 3H ~ ma χpt Cosmology Initial conditions Strong Dynamics 19

37 Axion Density (t)r 3 m a (t) = # axions in a fixed comoving volume Cosmological EOM: (T 1 )= m 2 af 2 a = (T 1 ) (T )= q (T ) (T 1 ) R(T1 ) R(T ) 3 3H ~ ma χpt Cosmology Initial conditions Lattice! 19

38 a apple CDM The Over-Closure Bound As It Stands Today Berkowitz, Buchoff, and Rinaldi, arxiv: Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Axion Coupling g a (GeV -1 ) Too Much Dark Matter Wantz & Shellard IILM ADMX Published Limits Non RF-cavity Techniques White Dwarf and Supernova Bounds Axion Mass (µev) "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter Courtesy GP Carosi, ADMX 20

39 a apple CDM The Over-Closure Bound As It Stands Today Berkowitz, Buchoff, and Rinaldi, arxiv: Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Axion Coupling g a (GeV -1 ) Too Much Dark Matter Lattice SU(3) Pure Glue Late PQ Breaking ADMX Published Limits Non RF-cavity Techniques White Dwarf and Supernova Bounds Axion Mass (µev) "Hadronic" Coupling Minimum Coupling Axion Cold Dark Matter Warm Dark Matter fa < (4.10±0.04) GeV ma > (14.6±0.1) μev Courtesy GP Carosi, ADMX 20

40 a apple CDM The Over-Closure Bound As It Stands Today Berkowitz, Buchoff, and Rinaldi, arxiv: Gen 2 ADMX Projected Sensitivity Cavity Frequency (GHz) Axion Coupling g a (GeV -1 ) Too Much Dark Matter Lattice SU(3) Pure Glue Late PQ Breaking ADMX Published Limits Non RF-cavity Techniques axions < 100% of DM White Dwarf and Supernova Bounds Axion Mass (µev) "Hadronic" Coupling smaller χ Minimum Coupling Axion Cold Dark Matter Warm Dark Matter fa < (4.10±0.04) GeV ma > (14.6±0.1) μev Courtesy GP Carosi, ADMX 20

41 Conclusions & Outlook PQ symmetry: cleans up the Strong CP problem provides a plausible, largely unconstrained DM candidate: the axion. The Economist, 19 Dec 2006 Axion searches will search large swaths of interesting parameter space soon. Power law (DIGM-inspired) fits outstandingly to pure glue at high temperature. Lattice QCD can provide important nonperturbative input for calculating Ωa 21

42 Future Steps Measure higher moments? May be able to get χ4, χ6. T=0: Cé, Consonni, Engle & Giusti, arxiv: Incorporate quarks Move to Wilson Flow definition Move to anisotropic lattices to alleviate finite-volume effects at high T. Fixed topology methods / open boundary conditions at high T. Aoki et al., arxiv: v2 Lüscher & Schæfer, arxiv: Finite θ: Imaginary-θ has no sign problem Real, finite θ may be amenable to Langevin methods 22

43 Backup Slides 23

44 Finite Volume Effects Berkowitz, Buchoff, and Rinaldi, arxiv: Measurement N /4 /Tc T/T c 24

45 Discretization Effects Berkowitz, Buchoff, and Rinaldi (arxiv: ), Kitano & Yamada (arxiv: ) 0.4 Measurement N /4 /Tc T/T c 25

46 Pure glue measurements show χ vanishes as T Comparisons Measurement ( ) 12 = 16 / = 18 / = 20 N ( = + + = ) 64 1/4 /Tc / 80 ( = = = ) = = T/T c 26

47 Pure glue measurements show χ vanishes as T Comparisons = = 1/4 /Tc 0.4 Measurement N ( ) 12 = / ( = = = ) T/T c 27

48 The Misalignment Mechanism At high temperature, the axion potential is flat. At T ~ 1 GeV, potential develops and axion mass begins to grow. Axion begins to oscillate when Compton λ fits inside the universe 3H ~ ma 28