DESY 12-054

New limits on hidden photons from past electron beam dumps

Sarah Andreas,∗ Carsten Niebuhr,† and Andreas Ringwald‡

Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Notkestrasse 85, Germany

Hidden sectors with light extra U(1) gauge bosons, so-called hidden photons, have recently at-tracted some attention because they are a common feature of physics beyond the Standard Modellike string theory and supersymmetry and additionally are phenomenologically of great interestregarding recent astrophysical observations. The hidden photon is already constrained by variouslaboratory experiments and presently searched for in running as well as upcoming experiments. Wesummarize the current status of limits on hidden photons from past electron beam dump exper-iments including two new limits from such experiments at the High Energy Accelerator ResearchOrganization in Japan (KEK) and the Laboratoire de l’accelerateur lineaire (LAL, Orsay) that haveso far not been considered. All our limits take into account the experimental acceptances obtainedfrom Monte Carlo simulations.

PACS numbers: 12.60.Cn, 14.70.Pw, 13.85.Rm

I. MOTIVATION

Light extra U(1) gauge bosons appear very naturallyin well-motivated extensions of the standard model (SM).Even if the paradigm of a highly symmetric high energytheory is to unify particles into representations of a large-rank local gauge group, the phenomenological fact thatat low energies these large gauge symmetries are seem-ingly broken possibly leaves us with the existence of manylower rank symmetries. In particular U(1)s are poten-tially most numerous since they are the lowest-rank lo-cal symmetries. Moreover, some of these U(1)s may behidden, because the SM particles are not charged underthem, and therefore escaped detection until now. Mostnotably, such hidden sectors often occur in supersymmet-ric extensions or superstring embeddings of the SM [1–5].

On general grounds, the dominant interaction of hid-den U(1) gauge bosons γ′ (hidden sector photons, shorthidden photons) with the SM at low energies genericallyappears already at the dimension four level through ki-netic mixing with the ordinary photon [6]. Correspond-ingly, the leading terms of the low energy effective La-grangian of the minimal hidden U(1) extension of theSM read,

Leff = LSM −1

4F ′µνF

′µν +m2γ′

2A′µA

′µ − χ

2F ′µνF

µν ,

where F ′µν is the field strength of the hidden gauge fieldA′µ, mγ′ the mass of the hidden photon, and Fµν the fieldstrength of the ordinary electromagnetic gauge field.

The hidden photon mass mγ′ and the kinetic mixingparameter χ have to be determined either theoretically,by specifying an ultraviolet completion of the theory, orphenomenologically, by comparing with observations. In

∗ sarah.andreas@desy.de† carsten.niebuhr@desy.de‡ andreas.ringwald@desy.de

this context, two very interesting mass regions have beenidentified recently:

i) mγ′ ∼ meV: Hidden photons in this mass rangemay explain the ∼ 2σ excess of dark radiation inthe universe [7], beyond the one from ordinary pho-tons and neutrinos, reported by recent global cos-mological analyses [8, 9]. This possibility can betested decisively in the next generation of light-shining-through-a-wall experiments [10].

ii) mγ′ ∼ GeV: Hidden photons in this mass rangemay explain the observed ∼ 3σ deviation of theanomalous magnetic moment of the muon [11] fromthe value expected in the SM [12]. Moreover, theymight explain possible terrestrial and cosmic raydark matter anomalies — notably the possible di-rect detection of dark matter by DAMA [13], Co-GeNT [14, 15] and CRESST [16, 17], in contrast toits nonobservation in CDMS [18] and XENON [19],and the observations of an excess in cosmic ray elec-trons and/or positrons observed by PAMELA [20]and Fermi [21] — if dark matter resides in the hid-den sector too and is charged under the hiddenU(1) [22–28]. This possibility can be tested seri-ously with new accelerator based experiments [29–31], especially with new beam dump and fixedtarget experiments exploiting high intensity elec-tron [32, 33] and proton beams [34, 35].

Motivated by this strong physics case, a number ofelectron beam dump and fixed target experiments tosearch for GeV scale hidden photons (dark forces) havebeen proposed or even taken first data [36–38]. In thiscontext it is very important to analyze also results frompast electron beam dump experiments in terms of hiddenphotons — a task which was accomplished quite exhaus-tively in Ref. [32]. However, in this paper two experi-ments have not been considered: i) a beam dump ex-periment searching for neutral penetrating particles ex-ploiting an electron linear accelerator at the High EnergyAccelerator Research Organization in Japan (KEK) [39]

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and ii) a beam dump experiment exploiting the OrsayLinac originally analyzed in terms of production and latedecay of scalars (Higgs) and pseudoscalars (axions) [40]1.In this paper, we derive the corresponding bounds onhidden photons, which exceed the bounds previously es-tablished by other electron beam dump experiments in acertain region of the parameter space.

II. γ′ IN ELECTRON BEAM DUMPS

In this section, we summarize the relevant formula(based on Ref. [32]) and computational steps necessaryto determine the expected signatures of a hidden photonγ′ in a beam dump experiment and to deduce the lim-its on its mass mγ′ and kinetic mixing χ set by differentexperiments.

A. γ′ production in bremsstrahlung

Hidden photons are generated in electron (or positron)collisions on a fixed target by a process analogous to or-dinary photon bremsstrahlung. For an incoming electronwith energy Ee the corresponding differential cross sec-tion in the range

me � mγ′ � Ee and xeθ2γ′ � 1 (1)

is given in Ref. [32] Eq. (A12) by

dσ

dxe d cos θγ′= 8α3χ2E2

exe ξ

√1−

m2γ′

E2e

(2)[1− xe +

x2e

2

U2+

(1− xe)2m4γ′

U4−

(1− xe)xem2γ′

U3

]

where xe = Eγ′/Ee is the fraction of the incoming elec-tron’s energy carried by the hidden photon, θγ′ is the labframe angle between emitted γ′ and incoming electronand Z and A are atomic number and mass number ofthe nucleus in the target. The effective flux of photons ξis given by

ξ(Ee,mγ′ , Z,A) =

∫ tmax

tmin

dtt− tmin

t2G2(t) , (3)

where tmin = (m2γ′/2Ee)

2, tmax = m2γ′ and the electric

form factor G2(t) defined in Ref. [32] consists of an elasticand an inelastic contribution both of which depend on theatomic number Z and mass A. The function U describes

1 In Ref. [41] it had already been suggested that the electronbeam dump experiment at Orsay could be used to constrain themore general U -boson for which another limit from proton beamdumps was obtained in Ref. [42].

the virtuality of the intermediate electron in initial-statebremsstrahlung and is given by

U(xe, Ee,mγ′ , θγ′) = E2e xe θ

2γ′ +m2

γ′1− xexe

+m2e xe .

(4)Integrating Eq. (2) over the emission angle θγ′ of thehidden photon from 0 to some maximum angle θmax setby the geometry of the experiment (for the experimentsunder consideration θmax < 0.5 rad) we obtain 2

dσ

dxe= 4α3χ2 ξ

√1−

m2γ′

E2e

1− xe +x2e

3

m2γ′

1−xexe

+m2exe

. (5)

B. Number of expected events behind a beamdump

For a beam dump experiment with an electron beamof energy E0 incident on a target (cf. Fig. 1) one has totake into account that the initial energy of the electronsin the beam becomes degraded as they pass through thetarget and interact with the material. This is describedby the energy distribution of the electrons after passingthrough a medium of t radiation length which accordingto Tsai [43] is roughly given by

Ie(E0, Ee, t) =1

E0

[ln(E0

Ee

)]bt−1

Γ(bt), (6)

where E0 is the initial monochromatic electron beam en-ergy at t = 0, Γ is the Gamma function and b = 4

3 . Thebremsstrahlung cross section from the previous subsec-tion which depends on the energy Ee of the electronstherefore has to be convoluted with this energy distribu-tion and integrated over the length Lsh of the target plusshield. Together with Eq. (6), the total number of hiddenphotons with an energy Eγ′ ≡ x0E0 that are produced inthe target via bremsstrahlung off the electron beam andthat decay at a distance z behind the front edge of thetarget is then given by

dN

dx0 dz= Ne

N0X0

A

∫ E0

Eγ′+me

dEe

∫ T

0

dt

[Ie(E0, Ee, t)

E0

Ee

dσ

dxe

∣∣∣∣xe=

Eγ′Ee

dP (z − X0

ρ t)

dz

], (7)

where Ne and E0 are the number and energy of the in-cident electrons, respectively, N0 ' 6 × 1023 mole−1 isAvogadro’s number, ρ [g/cm

3] and X0 [g/cm

2] are the

density and unit radiation length of the target material,

2 Note that this expression includes a factor 1/2 which has erro-neously been omitted in Ref. [32].

3

respectively, and T ≡ ρLsh/X0 is the length Lsh of targetplus shield in units of radiation length. The differentialcross section dσ/dxe discussed in Sec. II A is given inEq. (5). The differential decay probability dP/dz is de-fined as

dP (l)

dl=

1

lγ′e−l/lγ′ , (8)

where lγ′ is the decay length of the hidden photon lγ′ =

γτγ′ =Eγ′

mγ′1

Γγ′. For the mass range of interest, the total

decay width Γγ′ is given by

Γγ′ = Γγ′→e+e− + Γγ′→µ+µ− [1 +R(mγ′)] , (9)

where the second term is only present for mγ′ ≥ 2mµ,the partial decay width into leptons is given by [12]

Γγ′→l+l− =αχ2

3mγ′

(1 + 2

m2l

m2γ′

)√1− 4

m2l

m2γ′, (10)

and R(√s) is defined as the energy dependent ratio

σ(e+e−→hadrons,√s)

σ(e+e−→µ+µ−,√s)

taken from Ref. [44].

C. Special case: Thick target beam dumpexperiment

In the case of a thick target experiment, which we areinterested in, most of the hidden photon production takesplace within the first radiation length so that the t de-pendence in the γ′ decay probability can be neglectedand Eq. (7) simplifies to

dN

dx0 dz' Ne

N0X0

A

∫ E0

Eγ′+me

dEe

∫ T

0

dt

[Ie(E0, Ee, t)

E0

Ee

dσ

dxe

∣∣∣∣xe=

Eγ′Ee

dP (z)

dz

]. (11)

After carrying out the integration over z from Lsh toLtot ≡ Lsh + Ldec, where Lsh is the length of target plusshield and Ldec the length of the decay region, as sketchedin Fig. 1, this becomes

dN

dx0' Ne

N0X0

A

∫ E0

Eγ′+me

dEe

∫ T

0

dt

[Ie(E0, Ee, t)

E0

Ee

dσ

dxe

∣∣∣∣xe=

Eγ′Ee

e−Lsh/lγ′(

1− e−Ldec/lγ′)]

.

(12)

The total number of events behind the dump resulting

Lsh Ldec

target

shield

detector

Ltot

E0

e−γ ′

Eγ′

e−

e+

FIG. 1. Sketch of the setup of an electron beam dump exper-iment illustrating the definitions of the lengths Lsh, Ldec andLtot used in the text. An incoming electron beam of energy E0

hits the target and produces in bremsstrahlung a hidden pho-ton γ′ with energy Eγ′ that decays behind the shield e.g. intoe+e− which can then be observed in the detector.

from the decay of the hidden photon is then given by

N ' NeN0X0

A

∫ E0−me

mγ′

dEγ′

∫ E0

Eγ′+me

dEe

∫ T

0

dt[Ie(E0, Ee, t)

1

Ee

dσ

dxe

∣∣∣∣xe=

Eγ′Ee

e−Lsh/lγ′(

1− e−Ldec/lγ′)]

BRdetect . (13)

where BRdetect is the branching ratio into those decayproducts that the detector is sensitive to, i.e. electronsor muons or both.

D. Acceptance of different experiments

Up to now we have not taken into account that de-pending on the angle under which the final decay prod-ucts are emitted and the geometry of the detector, not allevents computed according to Eq. (13) are actually seenby the detector. With the use of MadGraph [45, 46]we generated for the different experiments (see Table I)Monte Carlo simulations of the hidden photon’s produc-tion in bremsstrahlung followed by its decay into e+e−.Comparing the thereby obtained decay angles with thegeometrical setup of the experiment an acceptance spe-cific for each experiment can be determined. Repeatingthis procedure for every experiment along the rough ex-clusion contour obtained using Eq. (13) we can rescalethe limit with the proper acceptance to get the final ex-clusion region. In the cases where the acceptances havebeen given in the experiment’s paper, we compared andfound them in reasonable agreement with the results ofour Monte Carlo simulations.

4

Experiment targetE0 Nel Lsh Ldec

Nobs N95%up[GeV] electrons Coulomb [m] [m]

E141 [47] W 9 2×1015 0.32 mC 0.12 35 1126+1312−1126 3419

E137 [48] Al 20 1.87×1020 30 C 179 204 0 3

E774 [49] W 275 5.2×109 0.83 nC 0.3 2 0+9−0 18

KEK [39] W 2.5 1.69×1017 27 mC 2.4 2.2 0 3

Orsay [40] W 1.6 2×1016 3.2 mC 1 2 0 3

TABLE I. Overview of the different beam dump experiments analyzed in this work and their specifications. The number ofobserved events Nobs have directly been extracted from the experiment’s papers and differ in the case of E141 and E137 slightlyfrom the estimates used in Ref. [32] as do the corresponding 95% C.L. values.

III. ELECTRON BEAM DUMP EXPERIMENTS

An overview of the different electron beam dump ex-periments and their properties is shown in Table I. InRef. [32], the limits set by the E141 and E137 experimentsat the Stanford Linear Accelerator Center (SLAC) as wellas the Fermilab E774 experiment have already been an-alyzed. In the present paper, we extend their analysisby two experiments that so far have not been consid-ered: one electron beam dump experiment at KEK inJapan [39] and one at the Orsay Linac in France [40].In addition, our analysis includes the experimental ac-ceptances obtained from Monte Carlo simulations withMadGraph in the determination of the limits for all ex-periments, as described in Sec. II D.

For the SLAC E141 experiment [47], we extract fromFig. 1c for x ≥ 0.7 a total of 1126±1312 events, whichcorresponds to a 95% C.L. upper limit of N95%up = 3419events. The appropriate exclusion contour shown inFig. 2 takes into account the acceptance from Mad-Graph.

As the SLAC E137 experiment reported in Ref. [48]that no candidate events were observed in their searchfor axionlike particles, the 95% C.L. upper limit is givenby N95%up = 3 events. Together with the acceptance wethen find the exclusion contour presented in Fig. 2.

For the Fermilab E774 experiment we find a totalof zero events with excess multiplicity 2 from Fig. 4cin Ref. [49]. Resulting from a substraction of the back-ground from the original spectrum, the statistical errorof√

89 is dominated by the total number of events inFig. 4b. The acceptance corrected 95% C.L. upper limitof N95%up = 18 events leads to the exclusion contour inFig. 2.

In the electron beam dump experiment at KEK [39]no signal was observed in their search for axionlike par-ticles. The corresponding 95% C.L. upper limit N95%up

of 3 events together with the acceptance leads for hiddenphotons to the exclusion contour presented in Fig. 2.

The electron beam dump experiment in Orsay [40]also found no positive signal when looking for light Higgsbosons. This translates to a 95% C.L. upper limit N95%up

of 3 events on hidden photons. Considering the experi-ment’s acceptance we find the exclusion contour shownin Fig. 2.

E774

E141

Orsay

KEKE137

10-2 10-1

10-7

10-6

10-5

10-4

10-3

10-2

mΓ' @GeVD

Χ

FIG. 2. Limits on the hidden photon mass mγ′ and kineticmixing χ from different electron beam dump experiments. Inaddition to the limits from E141 (magenta dotted line), E137(red dashed line) and E774 (orange long-dashed line) pre-sented already in Ref. [32], the regions labeled KEK (greendash-dotted line) and Orsay (blue solid line) have been ex-cluded in the present work.

5

IV. DISCUSSION

As presented in Fig. 2, the experiments at KEK and inOrsay were found to exclude a similar region of the pa-rameter space which so far has not been constrained byany other electron beam dump experiment. Our limitsfrom the previously analyzed experiments at SLAC andFermilab are comparable to those derived in Ref. [32]but are generally slightly weaker because of the factor1/2 discrepancy in Eq. (5), the fact that our Monte Carlosimulations yield somewhat different experimental accep-tances and due to a little different numbers of eventsN95%up used for our 95% C.L. contours.

Besides the limits from electron beam dump experi-ments discussed in this article, there are various otherconstraints on the hidden photon mass and kinetic mix-ing which we briefly summarize in the following. Theircomparison to the electron beam dump experiments fromFig. 2 is shown in Fig. 3.

E774

E141

Orsay

KEK

E137

Ν-Cal I

CHARM

NOMAD& PS191

aΜae

K®ΜΝΓ¢KLOE

APEX A1

SM PM

e+e-®ΓΜ+ Μ-

10-2 10-1 1 10 102

10-7

10-6

10-5

10-4

10-3

10-2

10-1

mΓ' @GeVD

Χ

FIG. 3. Collection of all current limits on hidden photons:from the electron beam dump experiments of the presentwork (colored lines, cf. Fig. 2, all other limits as gray lines),Standard Model precision measurements, muon and electronanomalous magnetic moment, a reinterpretation of the BaBarsearch e+e− → γµ+µ− for pseudoscalars, the electron fixedtarget experiments A1 and APEX, the ν-Cal I experimentat the Serpukhov proton beam dump, the KLOE experiment,the neutrino experiments NOMAD, PS191 and CHARM, andfrom the Kaon decay K → µνγ′, cf. text for details.

In Ref. [50], SM precision measurements were foundto exclude large values of hidden photon mass and ki-netic mixing as indicated in Fig. 3 by the label “SMPM”. Furthermore, as presented in Ref. [12] the muonand electron anomalous magnetic moment receiving aone-loop contribution from the hidden photon place ad-ditional constraints labeled “aµ” and “ae” respectively;the latter was updated [51, 52] while this work has beencompleted. The reinterpretation of the BaBar search fora pseudoscalar around the Υ(3S) resonance [53] in theprocess e+e− → γµ+µ− was used in Ref. [31, 36, 50, 54]to derive a limit on hidden photons. The two fixed tar-get experiments A1 at MAMI in Mainz [37] and APEXat JLab [38] both searching for hidden photons behinda thin target from bremsstrahlung off an electron beamstarted recently and were already able to set first newlimits. Reanalyzing proton beam dump data from theν-Cal I experiment at the U70 accelerator at IHEP Ser-pukhov a region overlapping with the one of KEK andOrsay has been excluded in Ref. [55]. The KLOE-2 ex-periment [56] at the Frascati DAφNE φ-factory uses e+e−

collisions to place further constraints. Very recently theproduction of hidden photons in the radiative decaysof neutral pseudoscalar mesons, generated by a protonbeam in neutrino experiments at CERN, has been con-strained with NOMAD and PS191 [57] in the decay ofπ0 and CHARM [58] in the one of η and η′. While thiswork was completed a new limit from the Kaon decayK → µνγ′ was derived [59] which would have improvedthe previous ae bound but is not competitive with theupdated one.

An up-to-date overview of all current constraints onthe mass mγ′ and kinetic mixing χ of the hidden photonfrom various searches including the electron beam dumpexperiments presented in this work is shown in Fig. 3.Despite the large number of constraints a broad regionof the parameter space remains open and is partly goingto be tested in currently already running [36–38] andplanned future experiments [33, 60, 61], see Ref. [62] foran overview.

ACKNOWLEDGMENTS

We would like to thank Yuri Soloviev for pointing outRef. [39] and Jonathan Jacobsohn for discussions at anearly stage of this work. We are also grateful that Rou-ven Essig, Philip Schuster and Natalia Toro provided uswith their MadGraph code for hidden photons whichallowed us to simulate the acceptances of the differentbeam dump experiments. Special thanks to Rouven Es-sig for helpful discussions regarding the factor 1/2 dis-crepancy in the cross section.

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