Search by the SENSEI Experiment for Millicharged Particles Produced in the NuMI Beam

Search by the SENSEI Experiment for Millicharged

Particles Produced in the NuMI Beam

Liron Barak,

Itay M. Bloch,

2,3

Ana M. Botti,

Mariano Cababie,

5,4

Gustavo Cancelo,

Brenda A. Cervantes-Vergara,

Luke Chaplinsky,

6,7,8

Michael Crisler,

Alex Drlica-Wagner,

4,9,10

Rouven Essig,

Juan Estrada,

Erez Etzion,

Guillermo Fernandez Moroni,

Stephen E. Holland,

Yaron Korn,

Ian Lawson,

Steffon Luoma,

Sravan Munagavalasa,

9,13,7,8

Aviv Orly,

Santiago E. Perez ,

5,4,*

Dario Rodrigues,

5,14

Nathan A. Saffold,

Silvia Scorza,

Aman Singal,

7,8

Miguel Sofo Haro,

4,16

Leandro Stefanazzi,

Kelly Stifter,

Javier Tiffenberg,

Sho Uemura,

Tomer Volansky,

Tien-Tien Yu,

(SENSEI Collaboration)

Roni Harnik,

†

Zhen Liu,

18,

†

and Ryan Plestid

19,

†

School of Physics and Astronomy,

Tel-Aviv University

, Tel-Aviv 69978, Israel

Berkeley Center for Theoretical Physics,

University of California

, Berkeley, California 94720, USA

Theoretical Physics Group,

Lawrence Berkeley National Laboratory

, Berkeley, California 94720, USA

Fermi National Accelerator Laboratory

, P.O. Box 500, Batavia, Illinois 60510, USA

Universidad de Buenos Aires

, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina

University of Massachusetts

, Amherst Center for Fundamental Interactions and Department of Physics,

Amherst, Massachusetts 01003, USA

C.N. Yang Institute for Theoretical Physics,

Stony Brook University

, Stony Brook, New York 11794, USA

Department of Physics and Astronomy,

Stony Brook University

, Stony Brook, New York 11794, USA

Kavli Institute for Cosmological Physics,

University of Chicago

, Chicago, Illinois 60637, USA

Department of Astronomy and Astrophysics,

University of Chicago

, Chicago, Illinois 60637, USA

Lawrence Berkeley National Laboratory

, One Cyclotron Road, Berkeley, California 94720, USA

SNOLAB

, Lively, ON P3Y 1N2, Ontario, Canada

The Enrico Fermi Institute,

The University of Chicago

, Chicago, Illinois 60637, USA

CONICET - Universidad de Buenos Aires,

Instituto de Física de Buenos Aires (IFIBA)

, Buenos Aires, Argentina

Universit ́

e Grenoble Alpes

, CNRS, Grenoble INP, LPSC-IN2P3, Grenoble 38000, France

Centro Atómico Bariloche

, CNEA/CONICET/IB, Bariloche, Argentina

Department of Physics and Institute for Fundamental Science,

University of Oregon

, Eugene, Oregon 97403, USA

School of Physics and Astronomy,

University of Minnesota

, Minneapolis, Minnesota 55455, USA

Walter Burke Institute for Theoretical Physics,

California Institute of Technology

, Pasadena, California 91125, USA

(Received 26 May 2023; revised 19 September 2023; accepted 28 June 2024; published 13 August 2024)

Millicharged particles appear in several extensions of the standard model, but have not yet been detected.

These hypothetical particles could be produced by an intense proton beam striking a fixed target. We use

data collected in 2020 by the SENSEI experiment in the MINOS cavern at the Fermi National Accelerator

Laboratory to search for ultrarelativistic millicharged particles produced in collisions of protons in the

NuMI beam with a fixed graphite target. The absence of any ionization events with 3 to 6 electrons in the

SENSEI data allow us to place world-leading constraints on millicharged particles for masses between 30

to 380 MeV. This work also demonstrates the potential of utilizing low-threshold detectors to investigate

new particles in beam-dump experiments, and motivates a future experiment designed specifically for this

purpose.

DOI:

10.1103/PhysRevLett.133.071801

Status of millicharged particle searches

—

Fractionally

charged particles are a well-known feature of the standard

model (SM): quarks and antiquarks have an electric charge

that of the electron. However, there is no

particle in the SM with a charge number less than

Millicharged particle (mCP) models are extensions of the

SM where a new particle is introduced with a very small

Contact author: santiep.137@gmail.com

†

Collaborated with SENSEI on this Letter.

Published by the American Physical Society under the terms of

the

Creative Commons Attribution 4.0 International

license.

Further distribution of this work must maintain attribution to

the author(s) and the published article

’

s title, journal citation,

and DOI. Funded by SCOAP

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133(7)

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Published by the American Physical Society

electric charge. This can be achieved by adding a U(1)

symmetric Lagrangian term charged under the standard

model hypercharge,

L

mCP

∂

−

mCP

;

where

is the particle,

is the SM electroweak vector

boson and

is the millicharge. These mCPs can also

appear, for example, in models where a dark photon has a

small kinetic mixing with the SM photon, resulting in a

very small charge for the dark sector particles, in which

case a different vector boson

has to be considered

[1]

mCPs have also been suggested as dark matter (DM)

candidates

[2]

, and extensions of the SM with mCPs have

been considered to describe several experimental results

–

. For these reasons, mCPs in the MeV to GeV mass

range are interesting targets for experiments.

mCPs could be produced in high energy collisions at

particle accelerators. Some recent accelerator experiments

which looked for, or had searches recast for, mCPs include

milliQ

[9]

, milliQan

[10,11]

, LSND

[12,13]

, MiniBooNE

[12,14]

, and ArgoNeuT

[15,16]

. Future experiments with

sensitivity to mCPs have been proposed at accelerator

facilities

[17

–

20]

mCPs could also be produced from cosmic rays in the

Earth

’

s upper atmosphere

[21]

. In this case, high-energy

SM particles (mainly protons) reach the atmosphere and

produce showers of secondary particles. mCPs produced in

these collisions could reach detectors on the Earth

’

s surface

and also underground

[21

–

23]

. This flux of mCPs could be

enhanced by several orders of magnitude due to the

trapping of charged particles in the galactic magnetic field

[24]

. A flux of mCPs at detectors could also be generated

from cosmic-ray upscattering of a millicharged component

of DM

[24]

In this Letter, we present the results of a mCP search

utilizing data from the SENSEI detector. These results give

new constraints on the mass and millicharge parameter

space for particles with MeV to GeV masses.

Skipper-CCDs as a mCP probe

—

Charge-coupled devi-

ces (CCDs) are pixelated silicon sensors commonly used in

astronomical applications. Recently, CCDs have demon-

strated their utility in particle physics experiments, and

large arrays of thick, fully depleted CCDs have been

successfully deployed in a low-background environment

to search for ionization signals from particle DM

[25]

However, conventional scientific CCDs are limited by the

readout noise on the measured charge in each pixel, which

is typically

∼

−

(rms). The Skipper-CCD substantially

reduces this noise by taking multiple, nondestructive

samples of the charge in each pixel. The concept was

initially proposed in the 1990s

[26,27]

, but the performance

as a single-electron counting device was only recently

demonstrated

[28]

. Skipper CCDs have enabled a new

generation of low-mass DM searches

[29

–

33]

and coherent

elastic neutrino-nucleus scattering (CE

NS) experiments

[34]

. Future experiments are planned using this technology

[35]

. The single-electron threshold capability of Skipper-

CCDs makes them an ideal tool to search for mCPs with

sensitivities not accessible to other technologies.

The SENSEI

[32]

Collaboration performed a search in

2020 for low-mass DM using a

∼

g Skipper-CCD. The

sensor used was designed by the Lawrence Berkeley

National Laboratory (LBNL), and fabricated at Teledyne/

DALSA using high-resistivity (

-cm) silicon

wafers with a thickness of

675

m. With a total exposure

of 24 days at a shallow underground laboratory at Fermi

National Accelerator Laboratory (FNAL) (107 m deep),

SENSEI demonstrated the lowest rates of events containing

one and two electrons in silicon detectors. Using these

results, SENSEI achieved world-leading sensitivity for a

wide range of sub-GeV DM masses interacting via electron

recoils. Here, the results from the SENSEI DM search are

used to establish a new limit on the mCP millicharge and

mass parameter space. To extend the sensitivity of the

search, the published analysis procedure that was applied to

the

–

−

channels is also applied to

–

−

. For each

channel, we calculated the effective efficiency, defined as

the fraction of pixels that pass all cuts corrected by

exposure and combined with a geometric efficiency for

the channels with more than

−

. This geometric efficiency

accounts for mCP events with more than

−

to be spread

out more than one pixel due to charge diffusion. For each

new channel, we report the number of observed events.

These results are shown in Table

, including the detection

efficiency and the total effective exposure for all channels

considered. It is worth noting that no events with signals

from 3 to 6 electron events were observed.

The SENSEI detector at Fermilab is located in the

MINOS underground hall. This location was selected

because it provides sufficient shielding from cosmic rays

that bombard Earth

’

s surface, and has been used in the past

to test sensitive particle detector technology. The detector is

located 1 km away from the target of the neutrino beamline

(Fig.

). Given that the SENSEI experiment was designed

to search for DM from astrophysical sources, it is not

surprising that it is not perfectly aligned with the neutrino

beamline. As will be described in the following sections,

TABLE I. Performance of the SENSEI experiment for events

containing

–

−

. The efficiency here includes the effect of all

selection cuts on the data (see Ref.

[32]

for details). The bottom

two rows, respectively, list the efficiency-corrected exposure, and

the number of observed events after cuts. Compared to the results

reported in

[32]

, we add here the

−

and

−

channels.

−

Effective Efficiency 0.069 0.105 0.325 0.327 0.331 0.338

Exposure [g-day]

1.38 2.09 9.03 9.10 9.23 9.39

Observed Events 1311.7 5

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the alignment and orientation of the silicon detector is not

relevant because the mCPs of interest have a low proba-

bility of interaction and because the whole detector is

contained in the solid angle subtended by mCPs generated

from the beam.

mCP production in the neutrino beamline and

acceptance by the SENSEI detector

—

In a wide range of

neutrino experiments, accelerator-based neutrino beams are

sourced by a high-intensity proton beam colliding with a

fixed target. If mCPs exist, they may be produced collin-

early with the neutrino beam in photon-mediated decays of

scalar mesons, vector mesons, and direct Drell-Yan proc-

esses resulting from each collision (Fig.

). The NuMI

beamline provides 120 GeV protons which strike a fixed

graphite target. Following Ref.

[36]

, where mCP produc-

tion is calculated using

ythia8

, we show in Fig.

the flux of

mCPs created in the neutrino beamline for each decay

product, integrated over the entire energy range that would

reach the SENSEI detector. As the mass of the mCP

increases, decays into millicharged pairs become kinemat-

ically inaccessible, and the flux reaching the detector is

greatly reduced. Note that we conservatively only include

the leading productions of mCPs from meson decays at the

target location, there are additional contributions to the

mCP fluxes from other primary production modes

[37]

secondary productions

[38]

and productions at the absorber

location

[39,40]

. However, the proper modeling of all these

effects involves highly nontrivial progress in strong dynam-

ics, which is beyond the scope of this current work. Further

inclusion of these contributions will increase the mCP flux

and improve sensitivity. The number of protons on target

(POT) used for this calculation was taken from beam

operation data at Fermilab during the SENSEI data-taking

period from February 25, 2020 to March 19, 2020 and

amounted to

during the entire experiment,

these data were used to compute the predicted mCP flux

reaching the detector as a function of

and

Of the 1 km between the NuMI target and the SENSEI

detector, approximately 500 m is dirt, which the mCPs

must traverse before reaching the detector. As is discussed

in Ref.

[36]

, this leads to two effects that must be

considered: energy losses to the material and angular

deflections caused by the interactions. To treat these two

effects, it is important to distinguish between two types of

interactions between mCPs and matter: soft collisions,

which dominate the number of low energy scatters expe-

rienced by the particle, and the rare hard collisions, which

dominate energy losses. Soft collisions will be discussed in

detail in the following sections. Because of the energy

(

∼

GeV) of the mCPs produced by the beam and the

probability of interaction given by the Bethe-Fano formula

for high energy recoils, it is expected that the particles

would lose only about an order of

∼

MeV of energy, which

would not alter the energy spectrum of the mCPs nor the

number of particles reaching the detector by a significant

amount. The angular deflection is also small enough to be

negligible for our analysis. For mCPs deflected due to soft

collisions with nuclei, the maximum possible scattering is

of order

[36]

. mCPs produced by protons in the neutrino

beamline would be highly boosted, and given that the

FIG. 1. Location of the SENSEI tent inside Fermilab

’

s MINOS

underground hall. The red star indicates the detector

’

s position

and the orange the clean tent that houses the experiment.

FIG. 2. Schematic of millicharged particle production in the

neutrino beamline via a meson decay and a virtual photon; figure

modified from

[41]

FIG. 3. Number of mCPs accepted by the SENSEI@MINOS

detector (

cm ×

cm) placed 1 km away from the target

integrated over all mCP energies for each production channel.

This flux was calculated assuming

−

. Adapted from

[36]

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SENSEI detector has a relatively small area of

, they will have a spatially uniform flux

over the entire detector.

Interaction of mCPs with silicon

—

The theory of electro-

magnetic excitations from passing pointlike charged par-

ticles has a long history dating back to early work by Bethe,

Fermi, and Landau, among others

[42

–

46]

, and references

therein. Much of the modern literature focuses on the

energy loss per unit length, or d

, which is typically

dominated by ionization (for muons or nonrelativistic

electrons) or bremsstrahlung (for relativistic electrons).

This is the relevant quantity when describing the statistical

properties of energy loss by particles with

“

large

”

electric

charges. For our current purposes, we are interested in the

limit in which only countably few interactions take place.

One must therefore consider instead the process that

produces the largest

event rate

that is available with the

SENSEI data. Crucially, this is distinct from the dominant

energy loss mechanism. As we outline below, this neces-

sitates a proper treatment of collective modes, and in

particular silicon

’

s bulk plasmon excitation.

A more detailed discussion of phenomenological appli-

cations for the low-threshold detection of highly relativistic

particles with silicon detectors will appear elsewhere

[47]

and we provide here only the salient features.

An appropriate theory of energy losses for a passing

relativistic charged particle was first provided by Fermi

[43]

. This theory treats the passing mCP as a classical

source of electromagnetic fields and incorporates the

relevant bulk material properties via a complex dielectric

function. The formalism is exact in the eikonal limit,

defined by

≪

, where

is the four-momentum

transfer to the target,

is the mCP four-momentum,

and

“

≪

”

is used component by component, and where the

particle can be approximated by a straight-line trajectory

(see, e.g., Sec. 13.6 of

[48]

). The effective interaction cross

section between mCPs and silicon is given by

[43]

[cf.,

Eq. (15) of

[46]

]

αε

∞

−

;

where

is the mCP

’

s charge,

the fine structure constant,

p=E

the velocity of the mCP,

¼ð

;

k

the

number of electrons per unit volume, and

¼j

k

in the

integration above. Relativistic effects related to, e.g., the

field contraction of a highly boosted particle are treated

exactly, and we have retained both transverse and longi-

tudinal components of the field. Nonrelativistic treatments

typically drop the transverse contribution and retain only

the term proportional to the energy loss function (ELF),

−

, where

is the dielectric function of the

material. The bulk plasmon excitation of silicon manifests

itself as a zero in the real part of the dielectric function.

We used density functional theory calculations of the

dielectric function for silicon. We take these from the

DarkELF repository

[49]

which makes use of tabulated

GPAW calculations

[50]

. The tabulated GPAW dielectric

functions from the DarkELF repository were compared

directly against publicly available electron energy loss

spectroscopy data and show excellent agreement. This

serves as a direct validation of the microscopic calculations,

and therefore supplies a robust first-principles prediction of

the energy loss spectrum in silicon. As alluded to above, the

most important feature in the silicon dielectric function is

the bulk plasmon

[51,52]

. This is easily understood, since

the response of the system is resonantly enhanced, and

provides electronic excitations above the SENSEI threshold

in a region where no background events are observed.

Unlike in DM direct detection, where plasmons have

received substantial attention

[53

–

56]

, the kinematics of

boosted particles from accelerator beams are such that the

plasmon is easily accessible

[57,58]

. Setting

Eq.

(2)

, we can write

int

as the interaction cross section

defined via,

int

∞

mCP detection with SENSEI

—

Once the mCP interacts

with the detector, the likelihood of an electron recoil

ionizing

–

−

in the detector, which corresponds to

(

∼

–

eV) energy depositions, is determined by the

model outlined in

[59]

. In order to include this effect that

directly impacts energy reconstruction, the cross section

calculated via Eq.

(3)

must be convolved with the prob-

ability of producing electron-hole pairs for each individual

channel yielding the detection cross section

det

We calculate the expected number of events at our

detector as

Þ¼

hits

≥

;

where

is the detector area,

is the flux of

millicharged particles,

is the total exposure and

hits

≥

Þ¼

−

;

is the probability of interaction set by the mean free path

¼ð

det

−

, which depends on the particle millicharge

and the electron number density

. As a reference value,

for

−

hits

≥

Þ¼

−

so a sizable

flux of mCPs is needed to obtain a signal capable of

excluding this region of the parameter space.

When

is small,

hits

≥

≈

. Substituting this

probability in Eq.

(4)

makes it clear that the number of

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expected events depends solely on the detector volume, and

that no geometric effects need to be considered.

Additionally in this regime the probability of interaction

scales with

. For a general discussion involving geometric

effects, see Ref.

[60]

In addition, since the bulk of the flux from an accelerator

source is highly boosted, to a very good approximation,

Eq.

(4)

can be reduced to

Þ¼

fast

det

;

where

fast

is defined as the total flux of mCPs with

boosts larger than

(as shown in Fig.

), and

is the

number of electrons in the SENSEI detector. The reduced

form of Eq.

(6)

underscores the fact that the limits set by

SENSEI are primarily sensitive to the integrated flux of

mCPs, and are insensitive to the detailed shape of the

spectrum.

In Fig.

, we show the 95% C.L. constraints on the mCP

parameter space from the published SENSEI data, which is

reproduced in Table

, and compare these constraints with

the existing bounds from other experiments. This limit was

calculated for each electron channel independently, taking

into account their different backgrounds and then combined

using a frequentist approach based on the likelihood ratio as

[32]

. We see that we improve on previous bounds by as

much as a factor of 2 in the mass range 100 to 210 MeV.

Below 10 MeV, the BBN

eff

constraints are domi-

nant

[61]

Regarding systematic uncertainties, a Monte Carlo sim-

ulation was performed for each parameter assuming

Gaussian uncertainties. The limit was recalculated for each

sample and the error on limit taken as the total deviation

between the results. The combined error from all the

parameters was obtained by adding in quadrature the errors

on limit. The mCP flux calculation follows

[15,16]

, the

event generator was calibrated using the pion flux from

other experiments in the neutrino beamline, for uncertain-

ties on the meson fluxes from hadron production we choose

22% to show the impact on our limit as in

[65]

Furthermore, as mentioned above we are only taking the

leading production channels for mCPs and do not consider

secondary mesons from the absorber which increase the

mCP flux. For

int

, Eq.

(3)

, following

[47]

we take the

difference between the

“

Mermin

”

and

“

GPAW

”

DarkELF

curves as a proxy for the systematic uncertainty which

yields a 5% value for the energy bins of interest. As

mentioned in

[59,66]

uncertainty on energy reconstruction

is well below 10%, this number is used as a very

conservative upper bound on our uncertainty. To account

for this effect, we shift the electron-hole pair creation

probabilities

[59]

to lower recoil energies by sampling a

one sided Gaussian distribution, meaning more energy

would be needed to excite an electron-hole pair.

Luminosity in the NuMi beam is directly measured yield-

ing a systematic uncertainty of 1%, following

[67]

we take

2% to take into account other beam related parameters such

as position and width. The impact on the limit by each of

these systematics can be seen in Table

where we find that

the total uncertainty of 7% falls between the width of the

line in Fig.

Conclusion

—

In this work, we set new constraints on

millicharged particles using data from the SENSEI 2020

run

[32]

and extending this search to the

−

and

−

channels. The very low background and low detection

threshold of the Skipper-CCD installed in the MINOS

cavern at Fermilab enables a very sensitive search for these

proposed particles. By utilizing a validated GPAW calcu-

lation against publicly available electron energy loss

spectroscopy data, the interaction cross section between

mCPs and silicon at low energies was computed. The bulk

plasmon effects play a critical role in this interaction due to

the fact that the particles coming from the neutrino beam-

line can easily access the plasmon energies and excite

electrons well above the SENSEI threshold. This result

provides the most stringent limits to date in the mass range

FIG. 4. Cyan line or region shows the 95% C.L. limit on mCPs

from the SENSEI data collected in the MINOS cavern in 2020.

Gray line or region shows constraints from other experiments

[9,12,62

–

64]

TABLE II. Systematic uncertainties for each parameter. The

corresponding error on the limit by each parameter was calculated

via Monte Carlo simulation. The leading uncertainty comes from

meson production in the neutrino beamline. The total systematic

uncertainty on the limit placed by SENSEI is around 7% which

falls between the width of the cyan line in Fig.

Source

Uncertainty [%]

Error on limit [%]

mCP flux

int

CCI

≪

POT

0.5

Total:

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from 30 to 380 MeV, and establishes Skipper-CCDs as a

very promising technology to probe new parameter space

for millicharged particles in future experiments.

Acknowledgments

—

We are grateful for the support of the

Heising-Simons Foundation under Grant No. 79921. This

work was supported by Fermilab under U.S. Department of

Energy (DOE) Contract No. DE-AC02-07CH11359. The

CCD development work was supported in part by the

Director, Office of Science, of the DOE under No. DE-

AC02-05CH11231. R. E. acknowledges support from DOE

Grant DE-SC0009854 and Simons Investigator in Physics

Award 623940. The work of T. V. and E. E. is supported by

the I-CORE Program of the Planning Budgeting

Committee and the Israel Science Foundation (Grant

No. 1937/12). T. V. is further supported by the European

Research Council (ERC) under the EU Horizon 2020

Programme (ERC- CoG-2015 -Proposal No. 682676

LDMThExp), and a grant from The Ambrose Monell

Foundation, given by the Institute for Advanced Study.

The work of S. U. is supported in part by the Zuckerman

STEM Leadership Program. I. B. is grateful for the support

of the Alexander Zaks Scholarship, The Buchmann

Scholarship, and the Azrieli Foundation. R. P. is funded

by the Neutrino Theory Network Program Grant under

Grant No. DEAC02-07CHI11359 and the U.S. DOE under

Award No. DE-SC0020250. R. P. is also supported in part

by the U.S. Department of Energy, Office of Science,

Office of High Energy Physics, under Award No. DE-

SC0011632 and by the Walter Burke Institute for

Theoretical Physics. I. L. and S. L. are supported by the

Canada Foundation for Innovation through the Major

Science Initiatives Fund and the Province of Ontario

Ministry of Colleges and Universities. The work of Z. L.

was supported in part by the DOE Grants No. DE-

SC0022345 and No. DE-SC0011842. This manuscript

has been authored by Fermi Research Alliance, LLC under

Contract No. DE-AC02-07CH11359 with the U.S.

Department of Energy, Office of Science, Office of High

Energy Physics. The U.S. Government retains and the

publisher, by accepting the article for publication, acknowl-

edges that the U.S. Government retains a nonexclusive,

paid-up, irrevocable, world-wide license to publish or

reproduce the published form of this manuscript, or allow

others to do so, for U.S. Government purposes.

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