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Proton Radius Puzzle and Large Extra Dimensions Wei-Tou Ni (倪維斗) National Tsing Hua University

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Proton Radius Puzzle and Large Extra Dimensions Wei-Tou Ni (倪維斗) National Tsing Hua University School & Symposium on Precision Measurement and Gravity Experiment, Taipei, 1/24-2/2/1983 Proton radius puzzle and large extra dimensions Wei-Tou Ni (倪維斗) National Tsing Hua University Based on (i) arXiv:1303.4885, Proton radius puzzle and large extra dimension, Li-Bang Wang, W-T Ni (ii) Atomic transition frequencies and extra dimensions Talk given by Li-Bang Wang (王立邦) in Workshop on the Microscopic Origin of Gravity & related topics, NCTS, Hsinchu, 1/26-27/2013 Atomic transitions frequencies and extra dimensions, talk given by Li-Bang Wang Cosmic Bubbles, Spacetime Foams Primordial Black Holes, Worm Holes, White Holes, Primordial Soup & Transmutation of Dimensions in the Planckian World Introduction “Frequency”: the physics quantity that can be measured very precisely Magnetic moment of electron, ge (exp) = 2.0023193043617(15) Rydberg constant = 109,737.31568639(91) −27 EDM of electron |de| < 1.05×10 e·cm The best atomic clock f/f = 8×10-18 [1] G. Gabrielse et al., Phys. Rev Lett. 97, 30802 (2006) [2] Th. Udem et al., Phys. Rev. Lett. 79, 2646 (1997) [3] JJ Hudson et al., Nature 473, 493 (2011) [4] CW Chou et al., Phys. Rev. Lett. 104, 070802 (2010) G measurements Fixler et al., Science 315, 74-77 (2007) Atom Torsion Free fall with interferometer balance laser tracking G = 6.673 84(80) x 10-11 G/G ~ 100 ppm Outline Gravity problem Extra dimension and ADD model Precision atomic measurement Recent examples Proton Radius Puzzle Other possible tests Conclusion What’s wrong with Gravity? In Planck scale: F. Wilczek, Physics Today Oct. (1991) c 1 M 1019GeV pl G G Gm m m m F 1 2 1 2 Gravity 2 2 2 r M pl r Explanations? Not force at all! E. P. Verlinde, JHEP 1104, 029 (2011) Modified Gravity or MOND Modify Newton’s Law Gravity only tested ~100 m, (U. W.) Rotation curve in galaxies Cosmology argument Dark matter vs Modified gravity Numerical Coincidence or not??? 푎0 ≈ 푐퐻0/2휋 MOND phenomenology This acceleration scale appears in various seemingly unrelated galactic scaling relations, mostly unpredicted by the ΛCDM model The value of −10 −2 this scale is 푎0 ≃ 10 m s , which yields in natural units, 푎 0 ∼ 퐻0 (or 푎0 ≈ 푐퐻0/2휋). It is perhaps even more meaningful 2 to note that: 푎0 ∼ Λ MOND: Observational Phenomenology and Relativistic Extensions Famaey & McGaugh lrr 2012 Modified Gravity Modify Newton’s Law Gravity only tested ~100 m, (U. W.) Rotation curve in galaxies Cosmology argument Dark matter vs Modified gravity General relativity 1915 MOND Modified Newtonian Dynamics M Milgrom, ApJ 270, 365 (1983) When a << a0 GM a (a0aN ), where a N 2 r No dark matter needed Of minor interests as compared with dark matter in the physics community ADD Model with LED Larger extra dimensions (LED) Arkani-Hamed, Dimopoulos, Dvali (ADD model) Phys. Lett B 429, 263 (1998) Real world with everyday physics Graviton propagates Very small extra Dimensions ~ Rn ADD Model (4 + n) dimensions within Rn Rn too small to be observed directly m1 m2 1 V (r) n2 n1 , (r Rn ) M pl(4n) r m1 m2 1 V (r) n2 n , (r Rn ) M pl(4n) Rn r 2 n2 n M pl M pl(4n) Rn 12 M pl(4n) ~ MEW ~ TeV, R1 310 m, R2 0.3mm ruled out Atomic probe Atomic scale ~ 10-10 m Nuclear scale ~ 10-15 m LED effect small precise comparison Best testing ground transition frequencies Requirement: Atomic theory for electronic structures Nuclear effect: nuclear size, nuclear moments, form factors, polarizibility, meson exchange current, weak interaction, etc… QED effect, Lamb shift 2008 Hydrogen 1 13.6eV En 2mc 2 2 2 non-relativistic 2n n 4 2 1 2n 3 relativistic correction mc 2 4n (l 1/ 2) 2 1 2n 3 4 2 spin-orbit interaction mc 2 4n ( j 1/ 2) 2 (LS, fine structure) 5 2 1 1 QED effect (Lamb shift) mc 3 k(n,l) 4n ( j 1/ 2)(l 1/ 2) m 4 nuclear magnetic moment 4mc 2 p f ( f 1) 3 / 2 2 m p 3n (hyperfine structure) 2 2 nuclear size effect Ze2 (0) r 2 3 proton E=EBohr+Erel+ELS+EDarwin+EHF+EQED+Enuclear The Lamb Shift p LS QED e+ e- 1 2 P3/2 - p e- e 2 S1/2 2 P1/2 p e- 2 p 1 S1/2 e- p e- Willis Eugene Lamb 3 Nobel Prize in Physics 1955 1947 by Lamb ~1060 MHz "for his discoveries concerning the p fine structure of the hydrogen Now exp: 1057.845(3) MHz e- Now th: 1057.833(4) MHz spectrum" Eides et al.,Theory of light hydrogenlike atoms, e- gun Physics Reports, 342, 63-261 (2001). Microwave region H 2 Detector source Energy shift due to LED e- Electron mass renormalization p Energy shift for bound electron p A I e- A 2 max e E 2 E ln d 3 x 2V (x) A 12 2 m 2c3 E E A 0 e I A AVG rcutoff • H.A. Bethe,The electromagnetic shift of energy levels, Phys. Rev. 72, 339 (1947). • J.J. Sakurai, Advanced quantum mechanics, p70. Next step put V(x) = V(gravity with ADD) Integration outside proton, rcut-off ~ 0.88 fm Numerical results Energy shift due to modified gravity (in eV) state n = 3 n = 4 n = 5 n = 6 -29 -24 -20 -15 1s 1.310 B3 1.010 B4 7.410 B5 5.110 B6 Hydrogen -30 -25 -21 -16 2s 1.710 B3 1.310 B4 9.310 B5 6.410 B6 -24 -17 -9 -2 1s 6.810 B3 8.010 B4 1.010 B5 1.110 B6 Muonium -24 -17 -10 -3 2s 0.910 B3 1.010 B4 1.310 B5 1.410 B6 Z.-G. Li, W.-T. Ni and A. Pulido-Paton, Chin. Phys. B 17, 70 (2008) n Bn = (Rn/0.529 Å ) , Rn : size of LED Comparison Eexp – Eth(no gravity) = E(LED) Eth = EBohr+Erel+ELS+EDarwin+EHF+EQED+Enuclear For hydrogen atom EQED = Lamb shift 2 = 8171.657 + 1.56rp MHz for H 1s state 2 = 1057.685 + 0.199rp MHz for H 2s state Enuclear = Esize + Epolarizibility + EZemach + Eweak desired small, th + exp Electron scattering Electron beam on nucleus detector 2 2 2 d Z c electron beam ( ) Rutherford d 4E 2 sin 4 2 Target Nuclei with finite size: d d 2 2 2 ( ) ( ) * cos * GE(q ) d exp d Rutherford 2 2 2 2 dGE(q ) r 6 2 dq2 q 0 Note: not the shape to fit, but the slope at q2=0 Discrepancy 0.862(12) fm, original electron scattering result G.G. Simon et.al. Nucl. Phys. A 333, 381 (1980) 0.895(18) fm, re-analysis of world data I. Sick, Phys. Lett. B 576, 62-67 (2003) 0.879(8) fm, new experiment by GSI J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010) 0.883(14) fm, hydrogen spectroscopy, ENS Paris C. Schwob et al., Phys. Rev. Lett. 82, 4960 (1999). K. Melnikov and T. van Ritbergen, Phys. Rev. Lett. 84, 1673(2000). 0.890(14) fm, hydrogen spectroscopy, MPI Garching T. Udem et al. Phys. Rev. Lett. 79, 2646, (1997). 0.8775(51) fm, CODATA Nuclear size effect E E r r p p s s a) point nucleus b) finite size nucleus V ~ -1/r transition from s to p state → decrease transition frequency 2 2 Frequency shift [(0)] < rp > Optical frequency measurement Frequency chain Optical atomic clock Frequency comb: pioneering work by T.W. Hänsch and J. Hall made frequency measurement possible Frequency Comb basics n= n r + offset r : 50MHz ~ 1GHz r: Determined by cavity length offset: measured by f-2f technique Picture from Th. Udem, R. Holzwarth, T.W. Hänsch, Nature 416, 233, 2002 Discrepancy 0.862(12) fm, original electron scattering result G.G. Simon et.al. Nucl. Phys. A 333, 381 (1980) 0.895(18) fm, re-analysis of world data I. Sick, Phys. Lett. B 576, 62-67 (2003) 0.879(8) fm, new experiment by GSI J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010) 0.883(14) fm, hydrogen spectroscopy, ENS Paris C. Schwob et al., Phys. Rev. Lett. 82, 4960 (1999). K. Melnikov and T. van Ritbergen, Phys. Rev. Lett. 84, 1673(2000). 0.890(14) fm, hydrogen spectroscopy, MPI T. Udem et al. Phys. Rev. Lett. 79, 2646, (1997). 0.8775(51) fm, CODATA Muonic hydrogen m/me ~ 200 4 2 a 0 Bohr radius 0 m e2 4e e me Energy level En proton - 2 2 2(4 0) n Wave function 3/ 2 r / a0 r ~ a0 e Energy shift due to nuclear size~ 2 2 muon decay e 0 r 2 Sensitivity ~ (m/me) Proton size puzzle rp = 0.84184(67) fm R. Pohl et al, Nature 466, 213–216, 2010 rp = 0.84087(39) fm A. Antognini et al, Science 339, 417–420, 2013 Comparison Eexp – Eth(no gravity) = E(LED) Eth = EBohr+Erel+ELS+EDarwin+EHF+EQED+Enuclear For hydrogen atom EQED = Lamb shift 2 = 8171.657 + 1.56rp MHz for H 1s state 2 = 1057.685 + 0.199rp MHz for H 2s state Enuclear = Esize + Epolarizibility + EZemach + Eweak desired small, th + exp Hydrogen 2S-2P 280 200 n = 3 260 n = 4 m) ( 180 3 (nm) 240 4 160 220 140 200 X 120 180 100 160 Upper limit for R X Upper limit for R 140 0.84 0.85 0.86 0.87 0.88 0.89 0.84 0.85 0.86 0.87 0.88 0.89 Proton radius (fm) Proton radius (fm) X: result from Z.G.
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