Equivalence Principle Violations and Couplings of a Light Dilaton

Transcription

1 Equivalence Principle Violations and Couplings of a Light Dilaton Thibault Damour Institut des Hautes Études Scientifiques Second Microscope Colloquium, ONERA, Palaiseau January 2013 Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

2 (Einstein) Equivalence Principle (EP) Not a basic principle of physics A heuristic generalization of an experimental fact: hypothesis of equivalence (Einstein) very successful in building General Relativity (GR) Einstein s GR: η µν g µν (x) absolute, rigid spacetime elastic spacetime, dynamically influenced by matter BUT all the coupling constants of local (special relativistic) physics remain as absolute and rigid as in Special Relativity (SR): g a, Y, λ BEH, µ BEH non dynamical g a, Y, λ BEH, µ BEH Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

3 What determines the coupling constants? Very unsatisfactory to put them by hand: this is against the principle of reason nihil est sine ratione (Leibniz) The history of physics suggests that there are no absolute structures in physics Kaluza-Klein s idea: g 1 or α em 3 8 g 2 1 4π hc g 55 (x) higher-dimensional elastic spacetime Dynamical symmetry breaking: the vacuum state minimizes the energy V (φ) which dynamically determines φ µ λ m e Y e φ Y e µ λ Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

4 Varying Coupling Constants and EP Violations Then if any of the coupling constants of local physics (e.g., α em, m e /m p, m q /m p,...) is x-dependent = violation of equivalence principle (Dicke 1962) Notably violation of universality of free fall S mi = m i [α(x),...] g µν (x) dx µ dx ν Composition-dependent acceleration a i = g ln m i [α(x),...] = g ln m i α α... Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

5 General dilaton-like model of EP violations Assume general dependence of coupling constants on some dilaton field ϕ : α EM (ϕ), (m q /Λ QCD )(ϕ), (m e /Λ QCD )(ϕ),.... Then the dependence of m A upon fundamental coupling constants: m A = Λ QCD ^m A (α EM, m u m d,, Λ QCD Λ QCD m e Λ QCD a ϕ dependence of m A and a corresponding dilaton coupling to m A α A = ln m A(ϕ) ϕ Composition-dependent modification of Newtonian interaction V (r) = G m A m B (1 + α A α B e mϕr ) r In the following: inverse range of ϕ : m ϕ = 0. Weak EP violation ( ) a η AB = (α A α B ) α E a AB ) Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

6 General Dilaton Low-energy Couplings (Damour-Donoghue10) Organizing principle: keep track of all the possible ϕ couplings entering the effective action describing physics at the scale of nucleons. At this scale: heavy quarks (c, b, t; and, arguably, s) are integrated out. L eff = 1 4e 2 F µνf µν 1 4 F A µνf Aµν + i=e,u,d [i ψ i /D(A, g 3 A A )ψ i m i ψ i ψ i ] Five terms in L eff five possible (dimensionless) ϕ couplings: d e, d g, d me, d mu, d md [ L intϕ = ϕ + d e 4e 2 F µνf µν d gβ 3 F 2g µνf A Aµν ] (d mi + γ mi d g )m i ψ i ψ i. 3 i=e,u,d Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

7 Relation between dilaton couplings d a and the constants of Nature The five possible dilaton couplings d a = {d e, d g, d me, d mu, d md } are equivalent to: fine-structure constant α = e2 4π α(ϕ) = (1 + d e ϕ) α QCD energy scale Λ MeV Λ 3 (ϕ) = (1 + d g ϕ) Λ 3 electron mass m e m e (ϕ) = (1 + d me ϕ) m e light-quark masses at QCD scale m i (Λ 3 ) [m i (Λ 3 )](ϕ) = (1 + d mi ϕ) m i (Λ 3 ), i = u, d Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

8 Ratios of dimensional parameters As the Planck scale 1/κ = 1/ 4π G does not directly enter physics at the QCD scale (besides its possible impact on Λ 3 via Λ cut-off 1/κ?) : Mass of an atom: ( mu m A = Λ 3 M A, m d, m ) e, α Λ 3 Λ 3 Λ 3 where M A is a dimensionless function of four dimensionless quantities: ( mu k a = (k u, k d, k e, k α ), m d, m ) e, α Λ 3 Λ 3 Λ 3 Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

9 Composition-dependence of ϕ coupling to atom α A = ln[κm A(ϕ)] ϕ = a ln[κm A (k a )] k a k a ϕ where d g = ln Λ 3 ϕ α a = d g + ᾱ A is a universal (non EP-violating) contribution and ᾱ A = 1 M A M A ϕ = 1 M A [ a=u,d,e (d ma d g ) M A M A + d e ln k a ln α ]. Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

10 Analysis of scalar couplings to the binding energy of nuclei Need to relate the various contributions to the nuclear binding energy E bind = a v A + a s A 2/3 + a a (A 2Z ) 2 A + a c Z (Z 1) A 1/3 δ a p A 1/2 to the variability of light quark masses m u, m d, or ^m = m d +m u 2, δm = m d m u. Possible by combining Walecka-type analysis of nuclei binding (parametrized by scalar and vector coupling strengths G S, G V ) with recent work of Donoghue (2006) on the pion-mass dependence of G S and G V : A = (d ^m d g ) (120A 97A 2/3 )mπ 2 η S ᾱ bind m A m 2 π ^m η S ^m = η S m2 π m 2 π = 0.35 ± 0.10 Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

11 Implications for the Equivalence Principle α A = d g + ᾱ A ᾱ A = [ (d ^m d g )Q ^m + (d δm d g )Q δm + (d me d g )Q me + d e Q e ]A where the various dilaton charges Q ka are given by (with F A A m amu /m A 1) [ Q ^m = F A ] 2Z )2 4 Z (Z 1) 0.020(A A1/3 A , A 4/3 [ Q δm = F A A 2Z ], A [ Q me = F A Z ], A [ Q e = F A Z ] 1) + 7.7Z(Z A A 4/3 Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

12 Simplified Parametrization of EP Violations Under plausible approximations, only two dilaton charges dominate: Q ^m linked to average quark-mass sensitivity to nuclear binding, and Q α Q e linked to the fine-structure constant: α A dg + [ (d ^m d g )Q ^m + d eq e ] A Q Z (Z 1) ^m = A1/3 A 4/3 Q e 4 Z (Z 1) = A 4/3 Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

13 Approximate EP-violating dilaton charges Table : Approximate EP-violating dilaton charges for a sample of materials. These charges are averaged over the (isotopic or chemical, for SiO 2 ) composition. Material A Z Q ^m Q e Li Be Al Si SiO Ti Fe Cu Cs Pt Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

14 Composition-dependence of weak EP violations General possible (dilaton-like) phenomenology (Damour-Polyakov 94, Dent 08, Damour-Donoghue 10): A N + Z ( ) [ a c1 = a AB A + c Z 2 1/3 2 A + c A 2Z 4/3 3 A (A 2Z ) 2 ] + c 4 A 2 AB Plausible simplified (dilaton-like) phenomenology (Damour-Donoghue2010) ( ) [ a c1 a AB A + c Z 2 ] 1/3 2 A 4/3 AB Two dominant EP signals, linked to nuclear physics (variation of m q /Λ QCD ) and Coulomb effects (variation of α EM = e 2 / hc) Two material pairs suffice to constrain the two dominant EP parameters c 1, c 2 Dilaton-like models allow to a priori compare the sensitivity of various EP tests: e.g. the dilaton charge vector of the pair Rb 85, Rb 87 can be compared to that of Pt, Ti and is found to be 10 2 smaller. Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

15 Present Experimental Bounds Using the two current EP experiments that have reached the namely EötWash (Schlamminger et al. 2008) ( ) a = (α Be α Ti )α Earth = (0.3 ± 1.8) a Be Ti level, and Lunar Laser Ranging (Williams et al. 2004, 2009) ( ) a = (α Earth α Moon )α Sun = ( 1.0 ± 1.4) a Earth Moon one can get constraints on the two dilaton parameters Namely, at the 2σ level D ^m = d g (d ^m d g ), D e = d g d e. D ^m = ± , D e = ± Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

16 Comparing the Experimental Sensitivities of EP Experiments The simplified dilaton framework contains three independent parameters, d g (composition-independent) and d q d ^m d g, d e (composition-dependent). It is quite predictive and can be used as a guideline for comparing and/or planning EP experiments. Examples: Comparing composition-independent (Eddington s γ-parameter) and composition-dependent 1 γ 2d 2 g In dilaton models: also link EP and tests of (PN) gravity a a 10 2 d q d g 1 γ PPN 2 where d q ln(m q /Λ QCD )/ ϕ, d g ln(λ QCD /m Planck )/ ϕ and either d q d g or d q d g /40. In the worst case 1 γ PPN 10 4 a/a so that a/a γ PPN Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

17 Comparing the vectors of dilaton-charge differences (Q ^m, Q e) Pt Ti = (3.33, 2.04) 10 3 vs (Q ^m, Q δm, Q me Q e )87 Rb 85 Rb = ( 3.3, 3.4, 0.55, 9.2) also link between WEP and clock tests of EEP (e.g. grav. redshift) (see, e.g., TD gr-qc/ ). When comparing frequencies of atomic transitions A A at two different locations r 1, r 2 : where ν A A (r 1) ν A A (r 2) 1 + (1 + αaa α E)(U E (r 1 ) U E (r 2 )) α A A = ln E A A ϕ computable from coupling-constant dependence of E A A transition E A A m e e 4 g l m e m p e 4 F rel (Ze 2 ).. E.g. for hyperfine Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

18 Anthropic-type argument for EP violation (Damour-Donoghue2010) Independently of any specific theoretical model one might argue (along the anthropic approach to the vast multiverse of cosmological and/or string backgrounds) that: (i) the EP is not a fundamental symmetry principle of Nature (ii) the level η a/a of EP violation can be expected to vary, quasi-randomly, within some range of order unity over the full multiverse (iii) as there is probably a maximal level of EP-violation, say η 0, which is compatible with the development of life (and physicists), one should a priori expect to observe, in our local environment, an EP violation η of order η. Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

19 Conclusions (I) EP is intimately connected with some of the basic aspects of modern physics, and of the unification of gravity with particle physics. The historical tendency of physics to discard any absolute structures, as well as the generalized Kaluza-Klein aspects (moduli) of string theory a priori suggests there could exist EP violations. The recent observation of ρ vac mplanck 4 poses a challenge to physics which suggests that we are missing some key understanding of IR gravity. This might provide additional motivation for EP violation (either via some Nambu- Goldstone mode, or via anthropic arguments). Even within the majority view of the moduli stabilization issue, EP experiments are testing a key assumption of current string models. Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20

20 Conclusions (II) no firm prediction for level of EP violation, but some phenomenological models show that the violation could naturally be just below the currently tested level. In dilaton-like models, the composition-dependence of EP signals is (probably) dominated by two signals, depending on A 1/3 and Z 2 A 4/3. In such dilaton-like models, there exist correlated modifications of gravity ( a/a, γ PPN 1 0, α a 0, dα a /du 0,...) but EP tests stand out as our deepest probe of new physics, when compared to, e.g., solar-system (γ PPN ) or clock tests ( α a or dα a /du). Indeed, a a 10 2 d q d g 1 γ PPN 2 where d q ln(m q /Λ QCD )/ ϕ, d g ln(λ QCD /m Planck )/ ϕ and either d q d g or d q d g /40. In the worst case 1 γ PPN 10 4 a/a so that a/a γ PPN Thibault Damour (IHES) EP Violations and Light Dilaton ONERA, Palaiseau 29-30/01/ / 20