Measured proton electromagnetic structure deviates from theoretical predictions R. Li1 N. Sparveris1 H. Atac1 M.K. Jones2 M. Paolone3 Z. Akbar17 C. Ayerbe

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Measured proton electromagnetic structure deviates

from theoretical predictions

R. Li1, N. Sparveris1,**, H. Atac1, M.K. Jones2, M. Paolone3, Z. Akbar17, C. Ayerbe

Gayoso8, V. Berdnikov5, D.Biswas6,19, M. Boer1,19, A. Camsonne2, J. -P. Chen2, M.

Diefenthaler2, B. Duran 1, D. Dutta 7, D. Gaskell 2, O. Hansen 2, F. Hauenstein 9, N.

Heinrich 10, W. Henry 2, T. Horn 5, G.M. Huber 10, S. Jia 1, S. Joosten 11, A. Karki 7, S.J.D.

Kay 10, V. Kumar 10, X. Li 16, W.B. Li 8, A. H. Liyanage 6, S. Malace 2, P. Markowitz 4, M.

McCaughan 2, Z.-E. Meziani 11, H. Mkrtchyan 12, C. Morean 13, M. Muhoza 5, A. Narayan 14,

B. Pasquini 15,18, M. Rehfuss 1, B. Sawatzky 2, G.R. Smith 2, A. Smith 16, R. Trotta 5, C.

Yero 4, X. Zheng 17, and J. Zhou 16

List of afﬁliations*

ABSTRACT

The visible world is founded on the proton, the only composite building block of matter that is stable in nature. Consequently,

understanding the formation of matter relies on explaining the dynamics and the properties of the proton’s bound state. A

fundamental property of the proton involves the system’s response to an external electromagnetic (EM) ﬁeld. It is characterized

by the EM polarizabilities

that describe how easily the charge and magnetization distributions inside the system are distorted

by the EM ﬁeld. Moreover, the generalized polarizabilities

map out the resulting deformation of the densities in a proton subject

to an EM ﬁeld. They reveal essential information regarding the underlying system dynamics and provide a key for decoding the

proton structure in terms of the theory of the strong interaction that binds its elementary quark and gluon constituents together.

Of particular interest is a puzzle in the proton’s electric generalized polarizability that remains unresolved for two decades

Here we report measurements of the proton’s EM generalized polarizabilities at low four-momentum transfer squared. We

show evidence of an anomaly to the behaviour of the proton’s electric generalized polarizability that contradicts the predictions

of nuclear theory and we derive its signature in the spatial distribution of the induced polarization in the proton. The reported

measurements suggest the presence of a novel, not yet understood dynamical mechanism in the proton and present signiﬁcant

challenges to the nuclear theory.

Explaining how the nucleons - protons and neutrons -

emerge from the dynamics of their quark and gluon con-

stituents is a central goal of modern nuclear physics. The im-

portance of the question arises from the fact that the nucleons

account for 99% of the visible matter in the universe. More-

over, the proton holds a unique role of being nature’s only

stable composite building block. The dynamics of quarks

and gluons is governed by quantum chromodynamics (QCD),

the theory of the strong interaction. The application of pertur-

bation methods renders aspects of QCD calculable at large

energies and momenta - namely at high four-momentum

transfer squared (

) - and offers a reasonable understanding

of the nucleon structure at that scale. Nevertheless, in order

to explain the emergence of nucleon’s fundamental proper-

ties from the interactions of it’s constituents, the dynamics

of the system have to be understood at long distances (or low

), where the QCD coupling constant

αs

becomes large

and the application of perturbative QCD is not possible. The

challenge arises from the fact that QCD is a highly nonlinear

theory, since the gluons - the carriers of the strong force -

couple directly to other gluons. Here, theoretical calculations

can rely on lattice QCD

, a space-time discretization of the

theory based on the fundamental quark and gluon degrees

of freedom, starting from the original QCD Lagrangian. An

alternative path is offered by effective ﬁeld theories (EFTs),

such as the chiral effective ﬁeld theory

4–6

, which employ

hadronic degrees of freedom and is based on the approxi-

mate and spontaneously broken chiral symmetry of QCD.

Temple University, Philadelphia, PA 19122, USA.

Thomas Jefferson National Accelerator Facility, VA, USA.

New Mexico State University, Las

Cruces, NM 88003, USA.

Florida International University, University Park, Florida 33199, USA.

Catholic University of America , Washington, DC 20064.

Hampton University , Hampton, VA 23669.

Mississippi State University, Miss. State, MS 39762.

The College of William and Mary, Williamsburg, VA

23185.

Old Dominion University, Norfolk, VA 23529.

University of Regina, Regina, SK S4S 0A2, Canada.

Argonne National Laboratory, Lemont, IL

60439.

Artem Alikhanian National Laboratory, Yerevan, Armenia.

University of Tennessee, Knoxville, TN 37996.

Veer Kunwar Singh University,

Arrah, Bihar 802301, India.

University of Pavia, 27100 Pavia PV, Italy.

Duke University, Durham, NC 27708.

University of Virginia, Charlottesville,

VA, 22904.

INFN, 27100 Pavia (PV), Italy.

Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, USA.

∗∗

corresponding author:

sparveri@temple.edu

arXiv:2210.11461v1 [nucl-ex] 20 Oct 2022

Photon identification

Data

Simulation

(Missing Mass)2(GeV2)

-0.01 0 0.01 0.02

Counts x 10-3

0.5

1.5

120 140 160

s (nb/GeV/sr2)

qg*g (deg)

Polarizability measurement

Cross section with fitted

polarizability effect

Simul (π0)

electron

proton

photon

electron beam

Figure 1. Using virtual Compton scattering to measure the proton generalized polarizabilities

The experimental setup during the VCS (E12-15-001) experiment at Jefferson Lab. An electron beam impinges on a liquid

hydrogen (red sphere) target. The interaction is mediated through the exchange of a virtual photon (orange wavy line). The

scattered electron and recoil proton are detected with two magnetic spectrometers, in coincidence. The real photon (green wavy

line) that is produced in the reaction provides the electromagnetic perturbation and allows to measure the proton polarizabilities.

The (undetected) real photon is identiﬁed through the reconstruction of the reaction’s missing mass spectrum and allows the

selection of the VCS events. c) The cross section of the VCS reaction measures the proton generalized polarizabilities. The

dashed line denotes the Bethe Heitler+Born contributions to the cross section. The error bars correspond to the total uncertainty,

at the 1σor 68% conﬁdence level.

While steady progress has been made in recent years, we

have yet to achieve a good understanding of how the nu-

cleon properties emerge from the underlying dynamics of the

strong interaction. In order to accomplish this, the theoretical

calculations require experimental guidance and confronta-

tion with precise measurements of the system’s fundamental

properties.

For a composite system, like the proton, the polarizabili-

ties are fundamental structure constants, such as its size and

shape. Listed among the system’s primary properties in the

Particle Data Group (PDG)

, the two scalar polarizabilities

- the electric,

αE

, and the magnetic,

βM

- can be interpreted

as the response of the proton’s structure to the application of

an external electric or magnetic ﬁeld, respectively. They de-

scribe how easily the charge and magnetization distributions

inside the proton are distorted by the EM ﬁeld and provide

the net result on the system’s spatial distributions. In order

to measure the polarizabilities, one must generate an electric

(

) and a magnetic (

) ﬁeld. In the case of the proton, this

is provided by the photons in the Compton scattering pro-

cess. The two scalar polarizabilities appear as second order

terms in the expansion of the real Compton Scattering (RCS)

amplitude in the energy of the photon

H(2)

e f f =−4π(1

2αE~

E2+1

2βM~

H2).(1)

One can offer a simplistic description of the polarizabilities

through the resulting effect of an electromagnetic perturba-

tion applied to the nucleon constituents. An electric ﬁeld

moves positive and negative charges inside the proton in

opposite directions. The induced electric dipole moment

is proportional to the electric ﬁeld, and the proportionality

coefﬁcient is the electric polarizability which quantiﬁes the

stiffness of the proton. On the other hand, a magnetic ﬁeld

has a different effect on the quarks and on the pion cloud

within the nucleon, giving rise to two different contributions

in the magnetic polarizability, a paramagnetic and a diamag-

netic contribution, respectively. Compared to the atomic

polarizabilities, which are of the size of the atomic volume,

the proton electric polarizability

αE

is much smaller than

the volume scale of a nucleon

. The small magnitude under-

lines the stiffness of the proton, a direct consequence of the

2/13

strong binding of its constituents, and indicates the intrinsic

relativistic character of the system.

The generalization

of the two scalar polarizabilities in

four-momentum transfer space,

αE(Q2)

and

βM(Q2)

, is an

extension of the static electric and magnetic polarizabilities

obtained in RCS. They can be studied through measurements

of the virtual Compton scattering (VCS) process

2γ∗

→

The VCS is accessed experimentally through the ep

→

reaction. The deﬁnition of the reaction’s kinematical param-

eters is given in the Methods section. Here, the incident real

photon of the RCS process is replaced by a virtual photon.

The virtuality of the incident photon

(Q2)

sets the scale of

the observation and allows one to map out the spatial dis-

tribution of the polarization densities in the proton, while

the outgoing real photon provides the EM perturbation to

the system. The meaning of the generalized polarizabili-

ties (GPs) is analogous to that of the nucleon form factors.

Their Fourier transform will map out the spatial distribution

density of the polarization induced by an EM ﬁeld. They

probe the quark substructure of the nucleon and offer unique

insight to the underlying nucleon dynamics. The interest

on the GPs extends beyond the direct information that they

provide on the dynamics of the system. They frequently

enter as input parameters in various scientiﬁc problems. One

such example involves the hadronic two-photon exchange

corrections, which are needed for a precise extraction of the

proton charge radius from muonic Hydrogen spectroscopy

measurements7.

Bethe-Heitler Born VCS non-Born VCS

ee’

pp’

Figure 2. Feynman diagrams of photon

electroproduction

The mechanisms contributing to ep

→

. The small circles

represent the interaction vertex of a virtual photon with a

proton considered as a point-like particle, while the ellipse

denotes the non-Born VCS amplitude.

In this work, we report on measurements of the VCS

reaction at the Thomas Jefferson National Accelerator Fa-

cility (Jefferson Lab). The experiment accessed the region

=0.28 GeV

to 0.40 GeV

, where the two scalar GPs are

particularly sensitive to the nucleon dynamics, and aims to

address a long-standing puzzle in the proton’s electric GP.

A ﬁrst indication of an anomaly in this property, a local en-

hancement of the electric polarizability as a function of the

distance-scale in the system, was reported by a measurement

(later repeated by the same group) at

=0.33 GeV

28,9

al-

beit with a large experimental uncertainty. Nevertheless, this

anomaly has been questioned for many years. The theoreti-

cal calculations are unable to account for such a feature in

the

αE(Q2)

and instead predict a monotonic fall-off with

Recent experiments have attempted to explore further the

existence of such an effect with measurements that extend

around the kinematical regime of interest but have not suc-

ceeded to present any supporting evidence of such a puzzling

behavior in this fundamental property

10,11

. This has left

open a scenario that could involve issues in the experimental

measurement at

=0.33 GeV

28,9

as an explanation to this

problem. In lack of an independent experimental conﬁrma-

tion or of further evidence, the existence of this anomaly and

it’s dynamical origin remains an unresolved puzzle until this

day. In this work, we capitalize on the unique capabilities of

the experimental setup at Jefferson Lab along with a combi-

nation of new features in the experimental methodology to

conduct measurements of the scalar GPs with unprecedented

precision, targeting explicitly the kinematical regime that is

relevant to this conjectured anomaly. A ﬁrst advantage of

the experiment is that it exploits the sensitivity of the polar-

izabilities to the excited spectrum of the nucleon, that is e.g.

different compared to the nucleon elastic form factors that

describe only the ground state of the system. The measure-

ments were conducted in the nucleon resonance region. This

enables enhanced sensitivity to the polarizabilities compared

to previous experiments

8–11

that measured in the region of

the pion production threshold. This has been previously

exhibited e.g. in

12,13

. Furthermore, in this experiment the

methodology employed cross section measurements at az-

imuthally symmetric kinematics in the photon angle, namely

for

(φγ∗γ,π−φγ∗γ)

. The measurement of the azimuthal asym-

metry in the cross section enhances even further the sensi-

tivity in the extraction of the polarizabilities, and suppresses

part of the systematic uncertainties. Moreover, the ep

→

π0

reaction was measured, simultaneously with the ep

→

reaction. The pion electroproduction process is well under-

stood in this kinematic regime, and it’s measurement offers a

stringent, real-time normalization control to the measurement

of the ep

→

cross section. This offers a major enhance-

ment to the typical normalization studies that rely on elastic

scattering measurements, that we additionally also perform

in this experiment. Overall, a signiﬁcant improvement was

accomplished in the precision of the extracted generalized

polarizabilities compared to previous measurements.

The data were acquired in Hall C of Jefferson Lab during

the VCS (E12-15-001) experiment. Electrons with energies

of 4.56 GeV at a beam current up to 20

µA

were produced

by Jefferson Lab’s Continuous Electron Beam Accelerator

Facility (CEBAF) and were scattered from a 10 cm long

liquid-hydrogen target. The Super High Momentum Spec-

trometer (SHMS) and the High Momentum Spectrometer

3/13

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Figure1.UsingvirtualComptonscatteringtomeasuretheprotongeneralizedpolarizabilitiesa)TheexperimentalsetupduringtheVCS(E12-15-001)experimentatJeffersonLab.Anelectronbeamimpingesonaliquidhydrogen(redsphere)target.Theinteractionismediatedthroughtheexchangeofavirtualphoton(orangewavyline).Thescatteredele...

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Measured proton electromagnetic structure deviates from theoretical predictions R. Li1 N. Sparveris1 H. Atac1 M.K. Jones2 M. Paolone3 Z. Akbar17 C. Ayerbe

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