Papers – Prof. Schmidt's personal page

22/05/2025

First measurement of sub-threshold J/ψ production from nuclei published in Physical Review Letters

My latest paper, working with a team of collaborators from MIT, Duke, Mississippi State, Tel Aviv University and others, was published as an editor’s suggestion in Physical Review Letters, and has been profiled by Jefferson Lab and by Physics Magazine. It presents the first measurement of sub-threshold photo-production of the J/ψ meson from protons bound inside nuclei. The J/ψ meson is an unstable particle formed from a charm quark bound to an anti-charm quark, and has a mass about three times that of the proton. It quickly decays, and often results in a high energy electron and positron. It takes quite a bit of energy to make J/ψ mesons, and it is just barely in reach in collisions at Jefferson Lab on stationary proton targets, i.e., the accelerator exceeds the energy threshold for the reaction. When using a nucleus as a target, J/ψ mesons can be produced even with energy beneath that threshold. This is because protons inside nuclei are moving! Their own kinetic energy within the nucleus can contribute to the reaction, and be turned into mass.

Fig. 1 from our paper, showing how the J/ψ meson can be identified as a peak in the spectrum of masses inferred from the detected electron and positron.

Why study the J/ψ? Since it’s constituent quarks are so heavy, the primary mechanism for making one in is through a reaction called gluon exchange. The gluon is the fundamental particle that mediates the strong nuclear force. The angular distribution of J/ψ mesons turns out to be related to the spatial distribution of the gluon field within the proton.

The story gets even more interesting when looking at protons bound inside nuclei. Nuclear physicists have already known for over four decades that the motion of quarks inside bound protons is distorted compared to quarks in free protons, an observation called the “EMC Effect.” We don’t know if that distortion also happens for gluons. While our measurement isn’t conclusive, there are some suggestive hints. My collaborators and I have already proposed a longer follow up experiment to Jefferson Lab to this year’s Program Advisory Committee.

Data for this paper were collected in a 2021 experiment at Jefferson Lab’s Experimental Hall D, using the GlueX spectrometer, pictured above.

16/03/2021

“Extracting the number of short-range correlated nucleon pairs from inclusive electron scattering data” published in Physical Review C

Graph showing kinematic envelopes of quasi-elastic scattering from deuterium and carbon — The kinematic envelope relating Bjorken-x and minimum nucleon momentum is subtly different for deuterium and carbon, depending on both nucleon motion and residual excitation energy.

Comparisons of inclusive quasi-elastic cross sections in “x_B>1 kinematics” have long been interpreted as a measure of the relative number of high-momentum nucleons in different nuclei. This interpretation relies on a the effect of a kinematic envelope relating the inclusive scattering parameter Bjorken-x, x_B, and the minimum nucleon momentum. In our latest paper, “Extracting the number of short-range correlated nucleon pairs from inclusive electron scattering data,” we argue that the picture is a bit more subtle.

In quasi-elastic scattering (in which the electron ejects an intact proton or neutron from the nucleus) not all combinations of x_B and nucleon momentum legally conserve energy and momentum. In order to satisfy this conservation, scattering at high x_B can only happen from a nucleon with high momentum. There is an envelope (shown in the figure above), above which the reaction can proceed, below which it is forbidden.

To determine the number of high-momentum nucleons in a nucleus, say carbon, one could compare the high-x_B inclusive cross section in electron-carbon scattering to the same quantity in electron-deuterium scattering. By requiring high-x_B, one is directly probing high-momentum nucleons. The ratio of cross sections can be interpreted as a ratio of the number of high-momentum nucleons in the nucleus.

However, we point out that nuclear effects, such as the way the high-momentum of the nucleon is balanced, as well as the residual excitation energy of the nuclear remnant after the scattering interaction can change the kinematic envelope. We argue that such effects can distort any extraction.

We follow this up with calculations, built around the tool called “Generalized Contact Formalism” that show the wide-range of combinations of nuclear parameters that are consistent with the data from previous scattering experiments.

This paper was a result of the hard work of several collaborators: Hebrew University (Jerusalem) graduate student Ronan Weiss, as well as MIT graduate students Andrew Denniston (pictured below) and Jackson Pybus.

21/04/202021/04/2020

New Generalized Contact Formalism result published Physics Letters B

Generalized contact formalism matches data for the relative abundances of proton-neutron and proton-proton correlations in Helium-4.

Our group has a new result using the Generalized Contact Formalism, which has proved so successful in describing short-range correlations between nucleons. MIT graduate student Jackson Pybus, performed calculations corresponding to a measurement made in 2011 in Hall A of Jefferson Lab of the triple-coincidence (e,e’pN) reaction on a helium-4 target. The GCF calculations match the experimental measurements without any free parameters, and further confirm the acceptance corrections made in the original analysis. This is one more example of GCF proving effective at describing the electron-induced knock-out of correlated nucleons, following previous results in PRL and in Nature on carbon.

MIT graduate student Jackson Pybus, lead author of this work

I’ve been fortunate to work with Jackson on a number of projects starting when I was a postdoc at MIT, and I’m thrilled that we’ve continued to collaborate since I’ve come to GW.

21/04/202021/04/2020

Phenomenological approach to two-photon exchange published in Journal of Physics G

In a new paper in Journal of Physics G, I argue that three recent experiments measuring the positron-proton to electron-proton elastic cross section ratio can make no definitive statements about proton form factor discrepancy because even the size of the discrepancy is not well-constrained. It is widely believed that the discrepancy between polarized and unpolarized measurements of the proton’s form factors is caused by the effects of two-photon exchange (TPE). Three recent experiments—one at the VEPP-3 Storage Ring in Novosibirsk, one using the CLAS detector at Jefferson Lab, and finally the OLYMPUS Experiment at DESY in Hamburg—looked for two-photon exchange by looking for any difference between the positron-proton and electron-proton cross sections. The measurements found only modest differences, and the results have been variously interpreted as supporting or contradicting the TPE hypothesis. Using a phenomenological approach, I estimate the e+p/e–p ratio one would need to resolve the discrepancy, as well as, for the first time, an estimate of the uncertainty. I find wide variation depending on what one assumes about unpolarized form factor measurements. The TPE hypothesis is neither confirmed nor denied, and future measurements at higher momentum transfer are needed.

The OLYMPUS experiment saw only slight differences between the e+p and e-p cross sections, but this is perfectly consistent with the small discrepancy at the accessible momentum transfer.

06/03/2020

New paper in PRL on the quark structure of neutrons

Tyler and I, along with our collaborators at MIT, Old Dominion, Penn State, Tel Aviv, and Jefferson Lab have just published an article in Physical Review Letters on the quark structure of free neutrons. Whereas free protons are easy to study (using my favorite technique, electron scattering!), neutrons decay with a lifetime of about 15 minutes, and can’t be practically made into a target. Instead, we learn about the neutron by scattering from nuclei, like deuterium or helium, and try to account for any effects that come from nuclear binding. One problematic effect is that the nuclear environment seems to change the structure of protons and neutrons, which we’ve given the name “The EMC Effect.”

In this work, first-authored by MIT graduate student Efrain Segarra, we looked at electron-scattering data from lots of different nuclei, including heavy nuclei, where the EMC Effect is large. Then, using the model developed in one of our recent papers, in which the EMC Effect stems only from short-range correlated proton-neutron pairs, we inferred what the free neutron structure must be to explain the data. This has consequences for the results of the MARATHON Experiment, which will hopefully be published soon.

If short-range correlations are responsible for the EMC Effect, then heavy nuclei would indicate a larger F2n/F2p ratio at large x.

Our paper is a quick read, and I hope you enjoy it.

26/02/2020

“Probing the core of the strong nuclear interaction” published in Nature

My latest research article, “Probing the core of the strong nuclear interaction” has been published in the February 26th issue of the journal, Nature. The article describes a study of the force between protons and neutrons (collectively called “nucleons”) at very short distance scales, that is, less than a femtometer or 10^-15 m. Nuclear forces have traditionally been studied by shooting one accelerated nucleon at another, and looking at the distributions of scattering angles as a function of momentum. To study forces at shorter distance scales, one needs to shoot nucleons with higher and higher momenta. At very short-distance scales, this technique becomes unwieldy, not because we can’t build particle accelerators of sufficient size, but because the collisions start producing copious amounts of other particles, complicating the interpretation in terms of nuclear forces. In this paper, my collaborators and I show how a new approach can work. Nucleons inside the nucleus are constantly moving around, and at any given moment, some will find themselves a very short-distance away from a partner nucleon. By using high-energy electron scattering, we can knock this “short-range correlated pair” out of the nucleus and study it. In doing so, we found clear evidence of a transition to a “repulsive core” at extremely short distances! This can have big implications for the structure of the cores of neutron stars, in which neutrons are packed at even higher density than inside a nucleus.

Figure 2 from the paper — Fig. 2 from the paper shows how the data support a transition from a primarily tensor force at low relative momentum to a hard isospin-independent repulsive core at high relative momentum.

If you’re interested to learn more, I invite you to read the excellent “News and Views” companion piece by Prof. Alexandra Gade of Michigan State.

05/09/201905/09/2019

Published in Phys. Lett. B: “Comparing proton momentum distributions in A = 2 and 3 nuclei via 2H, 3H, and 3He (e,e’p) measurements”

The Journal “Physics Letters B” has just published our paper measuring (e,e’p) cross section ratios in deuterium, tritium, and Helium-3 using the Jefferson Lab Hall A high resolution spectrometers. This experiment was part of the “Tritium Run Group” at Jefferson Lab, a once in a generation opportunity to perform electron-scattering experiments on the radioactive isotope of hydrogen with one proton and two neutrons. Tritium decays with a half life of about 12 years, which means it hangs around long enough to perform experiments, but it’s decay (via beta decay) means that it is constantly giving off radiation and is a significant safety hazard. It’s pretty rare that a National Lab will go through the rigorous steps to make a safe tritium target, and it was fantastic opportunity to do some very interesting science. The cool thing about tritium is that it’s isospin partner Helium-3 (stable with two protons and one neutron) can be studied together to disentangle the behavior of protons and neutrons in asymmetric nuclei.

We found that while most models for nucleon momentum distributions can explain the measured He3/H3 proton momentum distribution ratio up to about 250 MeV/c, at higher momentum there are still some significant unknown effects.

This paper was largely the work of MIT graduate student, Reynier Cruz-Torres, for whom this will be a big part of his thesis. This was the first experiment I got to run with Rey, and he did an amazing job coordinating the experiment’s run plan and working some very late nights trying to analyze the data as it was coming in.