The fifth force and constraints on its cons tants V. M. MOSTEPANENKO

1. The fifth force and constraints on its constantsV. M. MOSTEPANENKO V. M. MOSTEPANENKO V. M. MOSTEPANENKO Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences

2. CONTENT Introduction 2. Constraints on constants of power-type potentials 3. Constraints on constants of Yukawa-type potentials 3.1 Experiments of Eotvos-type 3.2 Experiments of Cavendish-type 3.3 Measurements of the Casimir force 3.4 Atomic and neutron physics 4. Constraints on constants of spin-dependent potentials 5. Conclusions and discussion

3. 1. INTRODUCTION Yukawa-type corrections to Newton’s law: Power-type corrections to Newton’s law:

4. Yukawa-type potentials originate from: 1) Exchange of light elementary particles, such as: --- scalar axion; --- graviphoton; --- dilaton; --- goldstino; --- moduli. These particles may contribute to the dark matter.

5. 2) Extra-dimensional theories with low-energy compactification scale cm Arkani-Hamed, Dimopoulos, Dvali, Phys. Rev. D, 1999

6. Power-type potentials originate from: 1) Exchange of massless elementary particles such as arion 2) Extra-dimensional models with noncompact but warped extra dimensions Randall and Sundrum, Phys. Rev. Lett., 1999

7. 2. CONSTRAINTS ON CONSTANTS OF POWER-TYPE POTENTIALS

8. 3. CONSTRAINTS ON CONSTANTS OF YUKAWA-TYPE POTENTIALS The Yukawa-type force between two macrobodies

9. 3.1 Experiments of Eotvos-type А) torsion pendulum: PU64 --- Принстон, 1964; MSU72 --- МГУ, 1971, 1972; EW94 --- Вашингтон 1994; EW99 --- Вашингтон, 1999; EW08 --- Вашингтон, 2008; В) LLR04 --- Lunar Laser Ranging, 2004. Gundlach et al., Space Sci. Rev., 2009

10. 3.2 Experiments of Cavendish-type A) LAGEOS --- 2003 (Laser Geodynamic Satellite)‏ В) LLR--- Lunar Laser Ranging, 2004. Adelberger et al., Progr. Part. Nucl. Phys., 2009

11. (Laser Geodynamic Satellites: Lucchesi, Peron, Phys. Rev. Lett., 2010)‏ (Gravity Recovery and Climate Experiment: Haranas, Ragos, Astrophys. Space Sci., 2011)‏

12. Eot-Wash ---2004 Irvine --- 2007 Wuhan --- 1980 Colorado --- 1985 Stanford --- 2003 Adelberger et al., Progr. Part. Nucl. Phys., 2009

13. Yang et al., Phys. Rev. Lett., 2012

14. 3.3 Measurements of the Casimir force Measured quantities are the Casimir force or its gradient: Obtaining constraints on Yukawa forces:

15. The strongest constraints on constants of Yukawa-type correctionsto Newton's gravitational law obtained from measurement of the Casimir force using an atomic force microscope (red line), from measurement of the Casimir pressure by means of micromachined oscillator (green line), from the Casimir-less experiment (blue line), from the torsion pendulum experiment of 1997 (grey line) and from the torsion balance experiment 2009 (black line).

16. Constraints on constants of Yukawa-type interaction which are obtained from the experiments performed by means of a micromechanical torsional oscillator with a corrugated Si plate (pink line) and with a flat Au-coated plate (green line), from the Casimir-less experiment (blue line), and from the experiments using a torsion pendulum (grey and black lines). Bezerra, Klimchitskaya, Mostepanenko, Romero, Phys. Rev. D, 2011

17. Constraints on constants of Yukawa-type interaction from measurements of the lateral Casimir force between corrugated surfaces (red line), from measurements of the normal Casimir force by means of an atomic force microscope (red dashed line), and a micromachined oscillator (green line). Bezerra, Klimchitskaya, Mostepanenko, Romero, Phys. Rev. D, 2010

18. Constraints obtained from measurements of the Casimir force gradient using the dynamic AFM with the Au-Au (solid line), Au-Ni (dashed line) and Ni-Ni (dotted line) sphere and plate. Banishev, Klimchitskaya, Mostepanenko, Mohideen, Phys. Rev. B, 2012; Phys. Rev. B, 2013; Phys. Rev. Lett., 2013 Klimchitskaya, Mohideen, Mostepanenko, Phys. Rev. D, 2012; Phys. Rev. D, 2013

19. Constraints are obtained from measuring: the Casimir force between corrugated surfaces of a sphere and a plate (solid line), lateral Casimir force (dashed line 1) and effective Casimir pressurebetween Au-coated test bodies (dashed line 2). Banishev, Wagner, Emig, Zandi, Mohideen, Phys. Rev. Lett., 2013 Klimchitskaya, Mohideen, Mostepanenko, Phys. Rev. D, 2013

20. 3.4 Atomic and neutron physics The best constraints on the Yukawa-type potentials with the interaction range Antoniadis et al., Compt. Rend. Phys., 2011 Karshenboim, Phys. Rev. D, 2010; Phys. Rev. Lett., 2010

21. Constraints on constants of Yukawa-type interactions are obtained from: - gravitational experiments (lines 1, 2 ); - measurements of the Casimir force (lines 3, 4, 12, 13, 14); - neutron physics (lines 5, 6, 7); - exotic atoms (line 8); - search for solar bosons of low mass (line 15). Lines 9, 10, 11 --- expected strengthening of constraints from different experiments with neutrons. Antoniadis et al., Compt. Rend. Phys., 2011

22. 4. CONSTRAINTS ON CONSTANTS OF SPIN-DEPENDENT POTENTIALS Exchange by an axion between a polarized and an unpolarized fermions: Exchange by a vector boson between two polarized fermions: Dobrescu, Mocioiu, JHEP, 2006

23. Constraints on constants of spin-dependent Yukawa-type corrections to Newton's law are obtained when investigating the following interactions: -polarized electron beam near an unpolarized torsion pendulum (line 1); - rotation of a magnetized metal plate near 3 unpolarized test masses (line 2); - magnetization of a paramagnetic salt under the rotation of a nonmagnetic copper body around it (line 3). Antoniadis et al., Compt. Rend. Phys., 2011

24. The globe as a soarce of polarized electrons Hunter, Gordon, Peck, Ang, Lin, Science, 2013

25. 5. CONCLUSIONS 1. The Newton law of gravitation is still not verified experimentally with sufficient precision at short separations, where both the Yukawa- and power-type corrections to it are allowed which exceed Newtonian gravity by many orders of magnitude. 2. Many different phenomena in the fields of gravitation, Casimir effect, neutron physics and atomic spectroscopy give the possibility to obtain the stronger constraints. 3. Experiments on measuring the Casimir force lead to stronger constraints on the Yukawa-type corrections to Newton's law in the interaction range below a few micrometers where the gravitational experiments do not work. 4. From precise measurements of the lateral Casimir force the previously known constraints were strengthened up to a factor of twenty four millions. 5. In near future further strengthening of constraints on both spin-independent and spin-dependent corrections is expected.