The fifth force and constraints

on its constants

V. M. MOSTEPANENKO

Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences

V. M. MOSTEPANENKOV. M. MOSTEPANENKO

CONTENT

1. 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

1. INTRODUCTION

Yukawa-type corrections to Newton’s law:

Power-type corrections to Newton’s law:

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.

2) Extra-dimensional theories with low-energy compactification scale

Arkani-Hamed, Dimopoulos, Dvali, Phys. Rev. D, 1999

cm

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

2. CONSTRAINTS ON CONSTANTS OF POWER-TYPE POTENTIALS

The Yukawa-type force between two macrobodies

3. CONSTRAINTS ON CONSTANTS OF YUKAWA-TYPE POTENTIALS

Gundlach et al., Space Sci. Rev., 2009

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.

3.1 Experiments of Eotvos-type

Adelberger et al., Progr. Part. Nucl. Phys., 2009

A) LAGEOS --- 2003 (Laser Geodynamic Satellite)

В) LLR--- Lunar Laser Ranging, 2004.

3.2 Experiments of Cavendish-type

Lucchesi, Peron, Phys. Rev. Lett., 2010)

Haranas, Ragos, Astrophys. Space Sci., 2011)

(Laser Geodynamic Satellites:

(Gravity Recovery and Climate Experiment:

Adelberger et al., Progr. Part. Nucl. Phys., 2009

Eot-Wash ---2004

Irvine --- 2007

Wuhan --- 1980

Colorado --- 1985

Stanford --- 2003

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

Measured quantities are the Casimir force or its gradient:

Obtaining constraints on Yukawa forces:

3.3 Measurements of the Casimir force

The strongest constraints onconstants of Yukawa-type corrections to 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 experimentof 1997 (grey line) and from thetorsion balance experiment 2009(black line).

Constraints on constants of Yukawa-type interaction

which are obtained from the experiments performedby means of a micromechanical torsional oscillator with acorrugated Si plate (pink line) and with a flat Au-coated plate (greenline), from the Casimir-lessexperiment (blue line), and from the experiments using a torsion pendulum (grey and black lines).

Bezerra, Klimchitskaya, Mostepanenko, Romero, Phys. Rev. D, 2011

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

Banishev, Klimchitskaya, Mostepanenko, Mohideen, Phys. Rev. B, 2012; Phys. Rev. B, 2013; Phys. Rev. Lett., 2013Klimchitskaya, Mohideen, Mostepanenko, Phys. Rev. D, 2012; Phys. Rev. D, 2013

Constraints obtained frommeasurements of the Casimirforce gradient using the dynamicAFM with theAu-Au (solid line),Au-Ni (dashed line) andNi-Ni (dotted line) sphere and plate.

Constraints are obtained frommeasuring:

the Casimir force betweencorrugated surfaces of a sphere and a plate (solid line),lateral Casimir force (dashed line 1) and effective Casimir pressure between Au-coated test bodies (dashed line 2).

Banishev, Wagner, Emig, Zandi, Mohideen, Phys. Rev. Lett., 2013Klimchitskaya, Mohideen, Mostepanenko, Phys. Rev. D, 2013

Antoniadis et al., Compt. Rend. Phys., 2011Karshenboim, Phys. Rev. D, 2010; Phys. Rev. Lett., 2010

3.4 Atomic and neutron physics

The best constraints on the Yukawa-type potentialswith the interaction range

Antoniadis et al., Compt. Rend. Phys., 2011

Constraints on constantsof Yukawa-type interactionsare obtained from:

- gravitational experiments(lines 1, 2 );- measurements of the Casimirforce (lines 3, 4, 12, 13, 14);- neutron physics(lines 5, 6, 7);- exotic atoms(line 8);- search for solar bosons oflow mass (line 15).

Lines 9, 10, 11 --- expected strengthening of constraints from differentexperiments with neutrons.

4. CONSTRAINTS ON CONSTANTS OF SPIN-DEPENDENT POTENTIALS

Dobrescu, Mocioiu, JHEP, 2006

Exchange by an axion between a polarized and an unpolarized fermions:

Exchange by a vector boson between two polarized fermions:

Antoniadis et al., Compt. Rend. Phys., 2011

Constraints on constants ofspin-dependent Yukawa-typecorrections to Newton's law are obtained when investigating the following interactions:

-polarized electron beam near anunpolarized torsion pendulum(line 1);- rotation of a magnetized metal plate near 3 unpolarized testmasses (line 2);- magnetization of a paramagneticsalt under the rotation of a nonmagnetic copper body aroundit (line 3).

The globe as a soarce of polarized electrons

Hunter, Gordon, Peck, Ang, Lin, Science, 2013

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.