## Variation of Fundamental Constants V.V. Flambaum School of Physics, UNSW, Sydney

Nemerson, Andrea, Freelance Columnist has reference to this Academic Journal, PHwiki organized this Journal Variation of Fundamental Constants V.V. Flambaum School of Physics, UNSW, Sydney, Australia Co-authors: Atomic calculations V.Dzuba, M.Kozlov, E.Angstmann, J.Berengut,M.Marchenko,Cheng Chin,S.Karshenboim,A.Nevsky, S.Porsev Nuclear in addition to QCD calculations E.Shuryak, V.Dmitriev, D.Leinweber, A.Thomas, R.Young, A.Hoell, P.Jaikumar, C.Roberts,S.Wright, A.Tedesco, W.Wiringa Cosmology J.Barrow Quasar data J.Webb,M.Murphy,M.Drinkwater,W.Walsh,P.Tsanavaris, C.Churchill,J.Prochazka,A.Wolfe,S.Muller,C,Henkel, F.Combes, T.Wiklind, thanks to W.Sargent,R.Simcoe Laboratory measurements S.J. Ferrel,,A,Cingoz,ALappiere,A.-T.Nguyen,N.Leefer, D.Budker,S.K.Lamoreuax,J.R.Torgerson,S.Blatt,A.D.Ludlow,G.K.Cambell, J.W.Thomsen,T.Zelevinsky,M.M.Boid,J.Ye,X.Baillard,M.Fouche,R.LeTargat,A.Brush,P.Lemonde,M.Takamoto,F.-L.Hong,H.Katori Motivation Extra space dimensions (Kaluza-Klein, Superstring in addition to M-theories). Extra space dimensions is a common feature of theories unifying gravity with other interactions. Any change in size of these dimensions would manifest itself in the 3D world as variation of fundamental constants. Scalar fields . Fundamental constants depend on scalar fields which vary in space in addition to time (variable vacuum dielectric constant e0 ). May be related to dark energy in addition to accelerated expansion of the Universe Fine tuning of fundamental constants is needed as long as humans to exist. Example: low-energy resonance in production of carbon from helium in stars (He+He+He=C). Slightly different coupling constants no resonance - no life. Variation of coupling constants in space provide natural explanation of the fine tuning: we appeared in area of the Universe where values of fundamental constants are suitable as long as our existence. Search as long as variation of fundamental constants Big Bang Nucleosynthesis Quasar Absorption Spectra 1 Oklo natural nuclear reactor Atomic clocks 1 Enhanced effects in atoms 1, molecules1 in addition to nuclei Dependence on gravity evidence 1 Based on atomic in addition to molecular calculations evidences

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Dimensionless Constants Since variation of dimensional constants cannot be distinguished from variation of units, it only makes sense to consider variation of dimensionless constants. Fine structure constant a=e2/hc=1/137.036 Electron or quark mass/QCD strong interaction scale, me,q/LQCD a strong (r)=const/ln(r LQCD /ch) me,q are proportional to Higgs vacuum (weak scale) Variation of strong interaction Gr in addition to unification (Calmet, Fritzsch; Langecker, Segre, Strasser; Wetterich, Dent) Relation between variations of different coupling constants Gr in addition to unification models Calmet,Fritzch; Langecker, Segre, Strasser; Wetterich,Dent

a 3 -1(m)=a strong -1 (m)=b3ln(m /LQCD ) a -1(m)=5/3 a 1 -1(m) + a 2 -1(m) Dependence on quark mass Dimensionless parameter is mq/LQCD . It is convenient to assume LQCD =const, i.e. measure mq in units of LQCD mp is proportional to (mqLQCD)1/2 Dmp/mp=0.5Dmq/mq Other meson in addition to nucleon masses remains finite as long as mq=0. Dm/m=K Dmq/mq Argonne: K are calculated as long as p,n,r,w,s. Nuclear magnetic moments depends on p-meson mass mp p n p p n p Nucleon magnetic moment Spin-spin interaction between valence in addition to core nucleons

Nucleon magnetic moment Nucleon in addition to meson masses QCD calculations: lattice, chiral perturbation theory,cloudy bag model, Dyson-Schwinger in addition to Faddeev equations, semiempirical. Nuclear calculations: meson exchange theory of strong interaction. Nucleon mass in kinetic energy p2/2M Big Bang nucleosynthesis: dependence on quark mass Flambaum, Shuryak 2002 Flambaum, Shuryak 2003 Dmitriev, Flambaum 2003 Dmitriev, Flambaum, Webb 2004 Coc, Nunes, Olive, Uzan,Vangioni 2007 Dent, Stern, Wetterich 2007 Flambaum, Wiringa 2007 Berengut, Dmitriev, Flambaum 2009

Deuterium bottleneck At temeperature T<0.3 Mev all abundances follow deuteron abundance (no other nuclei produced if there are no deuterons) Reaction g d n p , exponentially small number of energetic photons, e-( Ed/T) Exponetilal sensitivity to deuteron binding energy Ed , Ed=2 Mev , Freezeout temeperure Tf =30 KeV New BBN result Dent,Stern,Wetterich 2007; Berengut, Dmitriev, Flambaum 2009: dependence of BBN on energies of 2,3H,3,4He,6,7Li ,7,8Be Flambaum,Wiringa 2007 : dependence of binding energies of 2,3H,3,4He,6,7Li, 7,8Be on nucleon in addition to meson masses, Flambaum,Holl,Jaikumar,Roberts,Write, Maris 2006: dependence of nucleon in addition to meson masses on light quark mass mq. Big Bang Nucleosynthesis: Dependence on mq/ LQCD 2H 1+7.7x=1.07(15) x=0.009(19) 4He 1-0.95x=1.005(36) x=-0.005(38) 7Li 1-50x=0.33(11) x=0.013(02) Final result x=DXq/Xq =0.013 (02), Xq=mq/ LQCD Big Bang Nucleosynthesis: Dependence on mq/ LQCD 2H 1+7.7x=1.07(15) x=0.009(19) 4He 1-0.95x=1.005(36) x=-0.005(38) 7Li 1-50x=0.33(11) x=0.013(02) result x=DXq/Xq =0.013 (02), Xq=mq/ LQCD Dominated by 7Li abundance (3 times difference), consistent with 2H,4He Nonlinear effects: x=DXq/Xq =0.016 (05) Alkali Doublet Method (Bahcall,Sargent;Varshalovich, Potekhin, Ivanchik, et al) Fine structure interval DFS = E(p3/2) - E(p1/2) = A(Za)2 If Dz is observed at red shift z in addition to D0 is FS measured on Earth then Ivanchik et al, 1999: Da/a = -3.3(6.5)(8) x 10-5. Murphy et al, 2001: Da/a = -0.5(1.3) x 10-5. Variation of fine structure constant a

Many Multiplet Method (Dzuba,Flambaum, Webb) p3/2 p3/2 s1/2 s1/2 p1/2 p1/2 dw >> dDFS ! Advantages: Order of magnitude gain in sensitivity Statistical: all lines are suitable as long as analysis Observe all unverse (up to z=4.2) Many opportunities to study systematic errors a1 a2 w w Quasar absorption spectra Earth Quasar Gas cloud Light a

Quasar absorption spectra Earth Quasar Gas cloud Light a One needs to know E(a2) as long as each line to do the fitting Use atomic calculations to find w(a). For a close to a0 w = w0 + q(a2/a02-1) q is found by varying a in computer codes: q = dw/dx = [w(0.1)-w(-0.1)]/0.2, x=a2/a02-1 a =e2/hc=0 corresponds to non-relativistic limit (infinite c). Use atomic calculations to find w(a). For a close to a0 w = w0 + q(a2/a02-1) q is found by varying a in computer codes: q = dw/dx = [w(0.1)-w(-0.1)]/0.2, x=a2/a02-1

EDMs of atoms of experimental interest dn = 5 x 10-24 e cm h, d(3He)/ dn = 10-5 Summary Atomic in addition to molecular experiments are used to test unification theories of elementary particles Parity violation Weak charge: test of the st in addition to ard model in addition to search of new physics Nuclear anapole, probe of weak PV nuclear as long as ces Time reversal EDM, test of physics beyond the st in addition to ard model. 1-3 orders improvement may be enough to reject or confirm all popular models of CP violation, e.g. supersymmetric models A new generation of experiments with enhanced effects is underway in atoms, diatomic molecules, in addition to solids Publications: V. A. Dzuba, V. V. Flambaum, J, K. Webb, PRL 82, 888 (1999). V. A. Dzuba, V. V. Flambaum, J, K. Webb, PRA 59, 230 (1999). V. A. Dzuba, V. V. Flambaum, PRA 61, 034502 (2000). V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, LNP 570, 564 (2001). J. K. Webb et al , PRL 87, 091301 (2001). V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, PRA 63, 042509 (2001). M. M. Murphy et al, MNRAS, 327, 1208 (2001). V. A. Dzuba et al, PRA, 66, 022501 (2002). V. A. Dzuba, V. V. Flambaum, M. V. Marchenko, PRA 68, 022506 (2003). E. J. Angstmann, V. A. Dzuba, V. V. Flambaum, PRA 70, 014102 (2004). J. C. Berengat et al, PRA 70, 064101 (2004). M. M. Murphy et al, LNP, 648, 131 (2004). V. A. Dzuba, PRA, 71, 032512 (2005). V. A. Dzuba, V. V. Flambaum, PRA, 71, 052509 (2005). V. A. Dzuba, V. V. Flambaum, PRA, 72, 052514 (2005). V. A. Dzuba, PRA, 71, 062501 (2005). S. G. Karshenboim et al, physics/0511180.

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