We study the experimental constraints on theories, where the equivalence
principle is violated by dilaton-exchange contributions to the usual
graviton-exchange gravity. We point out that in this case it is not possible to
have any CPT violation and hence there is no constraint from the CPT violating
measurements in the $K-$system. The most stringent bound is obtained from the
$K_L - K_S$ mass difference. In contrast, neither neutrino oscillation
experiments nor neutrinoless double beta decay imply significant constraints.Comment: 7 page

Baudis

H. Päs

H.V. Klapdor-Kleingrothaus

Halprin

Horvat

Klapdor-Kleingrothaus

Muto

U. Sarkar

Physics Letters B

English

arXiv

Crossref

Confronting dilaton-exchange gravity with experiments

We study the experimental constraints on theories, where the equivalence principle is violated by dilaton-exchange contributions to the usual graviton-exchange gravity. We point out that in this case it is not possible to have any CPT violation and hence there is no constraint from the CPT violating measurements in the K-system. The most stringent bound is obtained from the KL-KS mass difference. In contrast, neither neutrino oscillation experiments nor neutrinoless double beta decay imply significant constraints

Klapdor-Kleingrothaus, H. V.

Päs, H.

Sarkar, U.

Publications of the IAS Fellows

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hep-ph/0004122
Confronting Dilaton-exchange gravity with experiments
H.V. Klapdor–Kleingrothaus1, H. Pa¨s1 and U. Sarkar2
1 Max–Planck–Institut fu¨r Kernphysik, P.O. Box 103980, D–69029 Heidelberg, Germany
2 Physical Research Laboratory, Ahmedabad 380 009, India
Abstract
We study the experimental constraints on theories, where the equivalence principle is violated
by dilaton-exchange contributions to the usual graviton-exchange gravity. We point out that in
this case it is not possible to have any CPT violation and hence there is no constraint from the
CPT violating measurements in the K−system. The most stringent bound is obtained from the
KL−KS mass difference. In contrast, neither neutrino oscillation experiments nor neutrinoless
double beta decay imply significant constraints.
At present we have no indication for the the violation of gravitational laws. But some theories
like string theory suggest deviations from the usual graviton-exchange theories of gravity. Thus it
becomes neccessary to find out the extent of applicability of the general theory of relativity. Several
experiments were performed to test the equivalence principle [1] for ordinary matter and to test
local Lorentz invariance [2, 3]. Attempts were also made to test these laws in the neutrino sector
[4, 5, 6], but these works included only tensorial interactions. In the K-system both tensorial and
vectorial interactions were studied by many authors [7].
Recently it has been suggested [8] that string theory may lead to a different kind of violation
of the equivalence principle (VEP) via interactions of the dilaton field, which gives an additional
contribution to the usual graviton exchange gravity. The resulting theory is of scalar-tensor type
(in contrast to purely tensorial VEP discussed previously) with the two particle static gravitational
energy
V (r) = −GNmAmB(1 + αAαB)/r, (1)
where GN is Newton’s gravitational constant and αj are the couplings of the dilaton field φ to the
matter field of type j, ψj. This additional contribution may result from a gravitational interaction
L = mjαjψjψjφ. (2)
The distinct feature of this new contribution are specific couplings of the dilaton field to different
matter fields, which violates the equivalence principle. It has been discussed recently whether this
feature can be tested in neutrino oscillation experiments [9, 10].
Unlike the violation of the equivalence principle through tensorial interactions, in the dilaton-
exchange gravity the gravitational basis is always the same as the mass basis, since the additional
term due to dilaton exchange is directly proportional to the mass. For this reason, a dilaton-
exchange gravity cannot explain the neutrino mixing phenomenon by itself – the discussion in ref
[9] seems to overlook this point. However, it is possible that a mass difference between degenerate
neutrinos is implied, what has been considered in [9]. In this article we discuss constraints on
this additional contribution from the KL−KS mass difference, the non-observation of neutrinoless
double beta decay as well as neutrino oscillation experiments.
In a linearized classical theory one may replace the effective mass of a fermion by
m∗i = mi −miαiφc (3)
where φc is the classical value of the dilaton field and is proportional to the Newtonian potential
φN ,
φc = αextφN .
2
The first term results from the usual graviton-exchange gravity, while the second term is the new
contribution coming from the dilaton-exchange gravity.
To get the interaction of the usual neutrinos of different flavour, we can rotate the effective
hamiltonian in the mass and the gravitational bases through the same unitary rotations
Hw = U(Hm +Hg)U
−1. (4)
In presence of the dilaton-exchange gravity, the effective hamiltonian in the mass basis is
Hm +Hg = pI +
1
2p
(
m1 − α1m1φc 0
0 m2 − α2m2φc
)2
. (5)
Here p denotes the momentum, I represents an unit matrix, and for any quantity X we define
δX = (X1 −X2) and X¯ = (X1 +X2)/2.
Assuming there is no CP violation, the effective hamiltonian becomes real and symmetric and
we can parametrize the mixing matrix by
U =
(
cos θ sin θ
− sin θ cos θ
)
(6)
where θ is the mixing angle. Then the effective hamiltonian in the weak basis becomes
Hw = pI +
1
2p
(
M+ M12
M12 M−
)2
(7)
with
M± = m¯+
1
2
(α1m1 + α2m2)φc ± 1
2
[δm + (α1m1 − α2m2)φc] cos 2θ
M12 = −1
2
[δm + (α1m1 − α2m2)φc] cos 2θ. (8)
The mass squared difference between the physical masses is given by
∆m∗2 = ∆m2 − 2φc(α2m22 − α1m21) + φ2c(α22m22 − α21m21), (9)
while the mass difference is given by
m∗2 −m∗1 = δm + (α2m2 − α1m1)φc. (10)
We shall now use the above formalism to analyse the constraints on dilaton-induced gravity from
the KL−KS mass difference, neutrinoless double beta decay and neutrino oscillation experiments.
For the K−system, the physical states are the KL and KS states, while the weak states are the K◦
and K◦ states. Thus the KL −KS mass difference can be read off from equation [10],
m∗L −m∗S = (mL −mS)−mLφc(αL −
mS
mL
αS). (11)
3
The experimental value m∗L−m∗S is dominated by the mass difference mL−mS . Thus no significant
cancellations are expected and a conservative bound for the contribution from dilaton exchange is
|mLφc(αL − mS
mL
αS)| < m∗L −m∗S .
Using also mS ≃ mL this implies a bound on the dilaton-induced gravity coupling of
δα <
1
φc
(
mL −mS
mL
)
expt
=
7× 10−15
φc
, (12)
where we used mL−mSmL ∼ 7× 10−15 [11]. While the bound depends on the absolute value of φc, we
can obtain a rough estimate by considering the value of the Newtonian gravitational potential to
be due to the great attractor, which is about 3 × 10−5 and αext ∼ 0.03, so that φc ∼ 10−6. Then
the bound becomes δα < 7× 10−9.
Unlike for the tensorial interactions, in this case the measurement of the CPT violating param-
eter, the mass difference of K◦ and K◦, does not yield any constraint. This can be understood by
considering the mass difference, which can be read off from equation (8) to be
M+ −M− = δm cos 2θ + φc cos 2θ(α2m2 − α1m1). (13)
Here the first contribution is the usual mass contribution and the second contribution is the one
coming from dilaton exchange. Since there is no CPT violation in the usual gravity, we have
cos 2θ = 0. This implies that there is no contribution coming from the dilaton exchange gravity.
We now turn over to discuss the constraints coming from the neutrino sector. The decay rate
for neutrinoless double beta decay is given by,
[T 0νββ
1/2 ]
−1 =
M2+
m2e
G01|ME|2, (14)
where ME denotes the nuclear matrix element ME =MF −MGT , (for numerical values see [12]),
G01 corresponds to the phase space factor defined in [13] and me is the electron mass. In contrast
to the tensorial VEP [6] for dilaton exchange gravity the observable has no explicit momentum
dependence. The contribution of the dilaton exchange to the observable for neutrinoless double
beta decay is given by
M+dil =
1
2
m2φc[(
m1
m2
α1 + α2) + (
m1
m2
α1 − α2) cos 2θ]. (15)
Since no momenta enter the observable, the decay rate is suppressed considerably (see also the
discussion in [14], which critizizes the treatment in [15]).
4
The dominant contribution to the neutrino oscillations comes through the change in the mass
squared difference, given by
< ∆m2 >dil= −2φcm22(α2 −
m22
m21
α1). (16)
In the almost degenerate case the bounds from the two experiments can be compared if we assume
that there is no mean deviation of usual gravity (α1 + α2) = 0, which is assumed in most cases.
An alternative natural choice is to assume that the masses of the neutrinos are hierarchical to
explain the atmospheric and solar neutrino problems. In the case of hierarchical neutrino masses,
m2 ≫ m1, α1 drops out from both expressions and without any further assumption all experiments
can be compared in terms of the single unknown parameter α2. In this case it is even more difficult
to obtain any bound from neutrino experiments since for neutrino masses mi only upper bounds
exist.
If we consider according to ref. [9] the upper bound of αext ∼
√
10−3 as its absolute value,
and the dominant contribution to the local gravitational potential to be due to the great attractor,
which is about φN = 3 · 10−5, we can estimate the bounds on the dilaton couplings. Although this
bound cannot be taken seriously, this allows us to compare our result with earlier results. Only in
the almost degenerate case (m1 ∼ m2 ∼ m), assuming m = 2.5 eV (as an upper bound obtained
from tritium beta decay experiments [16]) and only for the case the vacuum oscillation solution of
the solar neutrino problem will turn out to be realized in nature, the experimental ∆m∗2 may be
large enough to imply a significant bound (see however the discussion of medium effects in [10]).
The search for neutrinoless double beta decay [17], implying M+dil < 0.3 eV suffers from an even
more severe suppression, since the bound for M+ is less stringent than the one for ∆m
∗2.
In summary, we point out that the dilaton exchange gravity cannot be constrained substantially
in the neutrino sector, while the bound coming from the KL − KS mass difference is significant,
modulo the uncertainty of classical background potential. Unlike the new tensorial or vectorial grav-
itational interactions, this scalar interaction cannot introduce any CPT violation in the K−system.
References
[1] V.W. Hughes, H.G. Robinson, and V. Beltran-Lopez, Phys. Rev. Lett. 4 (1960) 342; R.W.P.
Drever, Philos. Mag. 6 (1961) 683; D. Newman, G.W. Ford, A. Rich and E. Sweetman, Phys.
Rev. Lett. 40 (1978) 1355; A. Brillet and J.L. Hall, Phys. Rev. Lett. 42 (1979) 549; J.D.
Prestage, J.J. Bollinger, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 54 (1985) 2387;
5
S.K. Lamoureaux, J.P. Jacobs, B.R. Heckel, R.J. Raab, and E.N. Fortson, Phys. Rev. Lett.
57 (1986) 3125.
[2] C. M. Will, Theory and Experiment in Gravitational Physics, 2nd edition (Cambridge Univer-
sity Press, Cambridge, 1992).
[3] M.P. Haugan and C.M. Will, Phys. Today 40 (1987) 60; E. Fishbach, M.P. Haugan, D. Tadic
and H.Y. Cheng, Phys. Rev. D 32 (1985) 154; G.L. Greene, M.S. Dewey, E.G. Kessler,Jr.,
and E. Fishbach, Phys. Rev. D44 (1991) 2216.
[4] M. Gasperini, Phys. Rev. Lett. 62 (1989) 1945; Phys. Rev. D38, 2635 (1988); ibid. D39
(1989) 3606; A. Halprin and C.N. Leung, Phys. Rev. Lett. 67 (1991) 1833; Nucl. Phys. B28A
(Proc. Supp.) (1992) 139; M. N. Butler et al., Phys. Rev. D47 (1993) 2615; J. N. Bahcall, P.
I. Krastev, and C. N. Leung, Phys. Rev. D52 (1995) 1770; R.B. Mann and U. Sarkar, Phys.
Rev. Lett 76 (1996) 865; J.R. Mureika and R. B. Mann, Phys. Rev. D 54 (1996) 2761.
[5] S. Coleman and S.L. Glashow, Phys. Lett. B 405 (1997) 249; S.L. Glashow, A. Halprin, P.I.
Krastev, C.N. Leung, and J. Panteleone, Phys. Rev. D 56 (1977) 2433; G.L. Fogli, E. Lisi, A.
Marrone and G. Scioscia, Phys. Rev. D60 (1999) 053006.
[6] H.V. Klapdor-Kleingrothaus, H. Pa¨s and U. Sarkar, Eur. Phys. Jour. A 5 (1999) 3.
[7] M.L. Good, Phys. Rev. 121 (1961) 311; O. Nachtmann, Acta Physica Austriaca, Supp. VI
Particle Physics ed. P. Urban, (1969) p. 485; I.R.Kenyon, Phys. Lett. B 237 (1990) 274;
R.J. Hughes, Phys. Rev. D 46 (1992) R2283; S.H. Aronson, G.J. Bock, H.-Y. Cheng and E.
Fishbach, Phys. Rev. Lett. 48 (1982) 1306; Phys. Rev. D 28 (1993) 495; T. Hambye, R.B.
Mann and U. Sarkar, Phys. Lett. B 421 (1998) 105; Phys. Rev. D 58 (1998) 025003; A.
Kostelecky, hep-ph/9912456 and references therein.
[8] T. Damour, A.M. Polyakov, Gen. Rel. Grav. 26 (1994) 1171; Nucl. Phys. B 423 (1994) 532
[9] A. Halprin, C. Leung, Phys. Lett. B 416 (1998) 361
[10] R. Horvat, Phys. Rev. D 58 (1998) 125020
[11] Review of Particle Properties, C. Caso et al, The European Physical Journal C3 (1998) 1
[12] K. Muto, E. Bender, H.V. Klapdor, Z. Phys. A 334 (1989) 187
[13] M. Doi, T. Kotani, E. Takasugi, Progr. Theor. Phys. Suppl. 83 (1985) 1.
6
[14] H. V. Klapdor–Kleingrothaus, H. Pa¨s, U. Sarkar, Phys.Lett. B478 (2000) 269-274
[15] A. Halprin, R. R. Volkas, Phys.Lett. B459 (1999) 183-185
[16] V. Lobashev et al., Phys. Lett. B 460 (1999) 227; Ch. Weinheimer et al., Phys. Lett. B 460
(1999) 219
[17] L. Baudis et al. (Heidelberg–Moscow Collab.), Phys. Rev. Lett. 83 (1999) 41
7


Indian Academy of Sciences

ar
X
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:h
ep
-p
h/
00
04
12
2v
2 
 1
6 
A
ug
 2
00
0
hep-ph/0004122
Confronting Dilaton-exchange gravity with experiments
H.V. Klapdor–Kleingrothaus1, H. Päs1 and U. Sarkar2
1 Max–Planck–Institut für Kernphysik, P.O. Box 103980, D–69029 Heidelberg, Germany
2 Physical Research Laboratory, Ahmedabad 380 009, India
Abstract
We study the experimental constraints on theories, where the equivalence principle is violated
by dilaton-exchange contributions to the usual graviton-exchange gravity. We point out that in
this case it is not possible to have any CPT violation and hence there is no constraint from the
CPT violating measurements in the K−system. The most stringent bound is obtained from the
KL −KS mass difference. In contrast, neither neutrino oscillation experiments nor neutrinoless
double beta decay imply significant constraints.
At present we have no indication for the the violation of gravitational laws. But some theories
like string theory suggest deviations from the usual graviton-exchange theories of gravity. Thus it
becomes neccessary to find out the extent of applicability of the general theory of relativity. Several
experiments were performed to test the equivalence principle [1] for ordinary matter and to test
local Lorentz invariance [2, 3]. Attempts were also made to test these laws in the neutrino sector
[4, 5, 6], but these works included only tensorial interactions. In the K-system both tensorial and
vectorial interactions were studied by many authors [7].
Recently it has been suggested [8] that string theory may lead to a different kind of violation
of the equivalence principle (VEP) via interactions of the dilaton field, which gives an additional
contribution to the usual graviton exchange gravity. The resulting theory is of scalar-tensor type
(in contrast to purely tensorial VEP discussed previously) with the two particle static gravitational
energy
V (r) = −GNmAmB(1 + αAαB)/r, (1)
where GN is Newton’s gravitational constant and αj are the couplings of the dilaton field φ to the
matter field of type j, ψj. This additional contribution may result from a gravitational interaction
L = mjαjψjψjφ. (2)
The distinct feature of this new contribution are specific couplings of the dilaton field to different
matter fields, which violates the equivalence principle. It has been discussed recently whether this
feature can be tested in neutrino oscillation experiments [9, 10].
Unlike the violation of the equivalence principle through tensorial interactions, in the dilaton-
exchange gravity the gravitational basis is always the same as the mass basis, since the additional
term due to dilaton exchange is directly proportional to the mass. For this reason, a dilaton-
exchange gravity cannot explain the neutrino mixing phenomenon by itself – the discussion in ref
[9] seems to overlook this point. However, it is possible that a mass difference between degenerate
neutrinos is implied, what has been considered in [9]. In this article we discuss constraints on
this additional contribution from the KL −KS mass difference, the non-observation of neutrinoless
double beta decay as well as neutrino oscillation experiments.
In a linearized classical theory one may replace the effective mass of a fermion by
m∗i = mi −miαiφc (3)
where φc is the classical value of the dilaton field and is proportional to the Newtonian potential
φN ,
φc = αextφN .
2
The first term results from the usual graviton-exchange gravity, while the second term is the new
contribution coming from the dilaton-exchange gravity.
To get the interaction of the usual neutrinos of different flavour, we can rotate the effective
hamiltonian in the mass and the gravitational bases through the same unitary rotations
Hw = U(Hm +Hg)U
−1. (4)
In presence of the dilaton-exchange gravity, the effective hamiltonian in the mass basis is
Hm +Hg = pI +
1
2p
(
m1 − α1m1φc 0
0 m2 − α2m2φc
)2
. (5)
Here p denotes the momentum, I represents an unit matrix, and for any quantity X we define
δX = (X1 −X2) and X̄ = (X1 +X2)/2.
Assuming there is no CP violation, the effective hamiltonian becomes real and symmetric and
we can parametrize the mixing matrix by
U =
(
cos θ sin θ
− sin θ cos θ
)
(6)
where θ is the mixing angle. Then the effective hamiltonian in the weak basis becomes
Hw = pI +
1
2p
(
M+ M12
M12 M−
)2
(7)
with
M± = m̄+
1
2
(α1m1 + α2m2)φc ±
1
2
[δm + (α1m1 − α2m2)φc] cos 2θ
M12 = −
1
2
[δm + (α1m1 − α2m2)φc] cos 2θ. (8)
The mass squared difference between the physical masses is given by
∆m∗2 = ∆m2 − 2φc(α2m22 − α1m21) + φ2c(α22m22 − α21m21), (9)
while the mass difference is given by
m∗2 −m∗1 = δm + (α2m2 − α1m1)φc. (10)
We shall now use the above formalism to analyse the constraints on dilaton-induced gravity from
the KL −KS mass difference, neutrinoless double beta decay and neutrino oscillation experiments.
For the K−system, the physical states are the KL and KS states, while the weak states are the K◦
and K◦ states. Thus the KL −KS mass difference can be read off from equation [10],
m∗L −m∗S = (mL −mS) −mLφc(αL −
mS
mL
αS). (11)
3
The experimental value m∗L−m∗S is dominated by the mass difference mL−mS . Thus no significant
cancellations are expected and a conservative bound for the contribution from dilaton exchange is
|mLφc(αL −
mS
mL
αS)| < m∗L −m∗S .
Using also mS ≃ mL this implies a bound on the dilaton-induced gravity coupling of
δα <
1
φc
(
mL −mS
mL
)
expt
=
7 × 10−15
φc
, (12)
where we used mL−mSmL ∼ 7× 10
−15 [11]. While the bound depends on the absolute value of φc, we
can obtain a rough estimate by considering the value of the Newtonian gravitational potential to
be due to the great attractor, which is about 3 × 10−5 and αext ∼ 0.03, so that φc ∼ 10−6. Then
the bound becomes δα < 7 × 10−9.
Unlike for the tensorial interactions, in this case the measurement of the CPT violating param-
eter, the mass difference of K◦ and K◦, does not yield any constraint. This can be understood by
considering the mass difference, which can be read off from equation (8) to be
M+ −M− = δm cos 2θ + φc cos 2θ(α2m2 − α1m1). (13)
Here the first contribution is the usual mass contribution and the second contribution is the one
coming from dilaton exchange. Since there is no CPT violation in the usual gravity, we have
cos 2θ = 0. This implies that there is no contribution coming from the dilaton exchange gravity.
We now turn over to discuss the constraints coming from the neutrino sector. The decay rate
for neutrinoless double beta decay is given by,
[T 0νββ
1/2 ]
−1 =
M2+
m2e
G01|ME|2, (14)
where ME denotes the nuclear matrix element ME = MF −MGT , (for numerical values see [12]),
G01 corresponds to the phase space factor defined in [13] and me is the electron mass. In contrast
to the tensorial VEP [6] for dilaton exchange gravity the observable has no explicit momentum
dependence. The contribution of the dilaton exchange to the observable for neutrinoless double
beta decay is given by
M+dil =
1
2
m2φc[(
m1
m2
α1 + α2) + (
m1
m2
α1 − α2) cos 2θ]. (15)
Since no momenta enter the observable, the decay rate is suppressed considerably (see also the
discussion in [14], which critizizes the treatment in [15]).
4
The dominant contribution to the neutrino oscillations comes through the change in the mass
squared difference, given by
< ∆m2 >dil= −2φcm22(α2 −
m22
m21
α1). (16)
In the almost degenerate case the bounds from the two experiments can be compared if we assume
that there is no mean deviation of usual gravity (α1 + α2) = 0, which is assumed in most cases.
An alternative natural choice is to assume that the masses of the neutrinos are hierarchical to
explain the atmospheric and solar neutrino problems. In the case of hierarchical neutrino masses,
m2 ≫ m1, α1 drops out from both expressions and without any further assumption all experiments
can be compared in terms of the single unknown parameter α2. In this case it is even more difficult
to obtain any bound from neutrino experiments since for neutrino masses mi only upper bounds
exist.
If we consider according to ref. [9] the upper bound of αext ∼
√
10−3 as its absolute value,
and the dominant contribution to the local gravitational potential to be due to the great attractor,
which is about φN = 3 · 10−5, we can estimate the bounds on the dilaton couplings. Although this
bound cannot be taken seriously, this allows us to compare our result with earlier results. Only in
the almost degenerate case (m1 ∼ m2 ∼ m), assuming m = 2.5 eV (as an upper bound obtained
from tritium beta decay experiments [16]) and only for the case the vacuum oscillation solution of
the solar neutrino problem will turn out to be realized in nature, the experimental ∆m∗2 may be
large enough to imply a significant bound (see however the discussion of medium effects in [10]).
The search for neutrinoless double beta decay [17], implying M+dil < 0.3 eV suffers from an even
more severe suppression, since the bound for M+ is less stringent than the one for ∆m
∗2.
In summary, we point out that the dilaton exchange gravity cannot be constrained substantially
in the neutrino sector, while the bound coming from the KL − KS mass difference is significant,
modulo the uncertainty of classical background potential. Unlike the new tensorial or vectorial grav-
itational interactions, this scalar interaction cannot introduce any CPT violation in the K−system.
References
[1] V.W. Hughes, H.G. Robinson, and V. Beltran-Lopez, Phys. Rev. Lett. 4 (1960) 342; R.W.P.
Drever, Philos. Mag. 6 (1961) 683; D. Newman, G.W. Ford, A. Rich and E. Sweetman, Phys.
Rev. Lett. 40 (1978) 1355; A. Brillet and J.L. Hall, Phys. Rev. Lett. 42 (1979) 549; J.D.
Prestage, J.J. Bollinger, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 54 (1985) 2387;
5
S.K. Lamoureaux, J.P. Jacobs, B.R. Heckel, R.J. Raab, and E.N. Fortson, Phys. Rev. Lett.
57 (1986) 3125.
[2] C. M. Will, Theory and Experiment in Gravitational Physics, 2nd edition (Cambridge Univer-
sity Press, Cambridge, 1992).
[3] M.P. Haugan and C.M. Will, Phys. Today 40 (1987) 60; E. Fishbach, M.P. Haugan, D. Tadic
and H.Y. Cheng, Phys. Rev. D 32 (1985) 154; G.L. Greene, M.S. Dewey, E.G. Kessler,Jr.,
and E. Fishbach, Phys. Rev. D44 (1991) 2216.
[4] M. Gasperini, Phys. Rev. Lett. 62 (1989) 1945; Phys. Rev. D38, 2635 (1988); ibid. D39
(1989) 3606; A. Halprin and C.N. Leung, Phys. Rev. Lett. 67 (1991) 1833; Nucl. Phys. B28A
(Proc. Supp.) (1992) 139; M. N. Butler et al., Phys. Rev. D47 (1993) 2615; J. N. Bahcall, P.
I. Krastev, and C. N. Leung, Phys. Rev. D52 (1995) 1770; R.B. Mann and U. Sarkar, Phys.
Rev. Lett 76 (1996) 865; J.R. Mureika and R. B. Mann, Phys. Rev. D 54 (1996) 2761.
[5] S. Coleman and S.L. Glashow, Phys. Lett. B 405 (1997) 249; S.L. Glashow, A. Halprin, P.I.
Krastev, C.N. Leung, and J. Panteleone, Phys. Rev. D 56 (1977) 2433; G.L. Fogli, E. Lisi, A.
Marrone and G. Scioscia, Phys. Rev. D60 (1999) 053006.
[6] H.V. Klapdor-Kleingrothaus, H. Päs and U. Sarkar, Eur. Phys. Jour. A 5 (1999) 3.
[7] M.L. Good, Phys. Rev. 121 (1961) 311; O. Nachtmann, Acta Physica Austriaca, Supp. VI
Particle Physics ed. P. Urban, (1969) p. 485; I.R.Kenyon, Phys. Lett. B 237 (1990) 274;
R.J. Hughes, Phys. Rev. D 46 (1992) R2283; S.H. Aronson, G.J. Bock, H.-Y. Cheng and E.
Fishbach, Phys. Rev. Lett. 48 (1982) 1306; Phys. Rev. D 28 (1993) 495; T. Hambye, R.B.
Mann and U. Sarkar, Phys. Lett. B 421 (1998) 105; Phys. Rev. D 58 (1998) 025003; A.
Kostelecky, hep-ph/9912456 and references therein.
[8] T. Damour, A.M. Polyakov, Gen. Rel. Grav. 26 (1994) 1171; Nucl. Phys. B 423 (1994) 532
[9] A. Halprin, C. Leung, Phys. Lett. B 416 (1998) 361
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Confronting Dilaton-exchange gravity with experiments

Confronting Dilaton-exchange gravity with experiments

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