Universal Nucleon Modification in SRC Pairs

• Universal modification of nucleons in SRC pairs is a phenomenon where nucleons in high-momentum correlated pairs exhibit consistent, structure-altering changes across nuclei, linking the EMC effect and SRC scaling.
• It relies on a convolution formalism of the nuclear spectral function, showing a universal scaling behavior that quantifies high-momentum nucleon contributions in various scattering experiments.
• Precision experiments and advanced nuclear theory demonstrate that both the SRC scaling factor and per-pair distortion function remain invariant across light to heavy nuclei, bridging nuclear structure and QCD dynamics.

Universal modification of nucleons in short-range correlated (SRC) pairs describes the phenomenon whereby nucleons participating in high-relative-momentum two-nucleon configurations acquire altered internal structure—at the level of partonic (quark/gluon) distributions—in a manner that is independent of the nuclear mass number, nuclear density, or isospin, once properly normalized. This concept provides the underlying dynamical bridge between the observed suppression of deep inelastic scattering (DIS) structure functions in nuclei (the EMC effect) and the abundance of SRC pairs quantified via inclusive electron scattering at $x>1$. The paradigm, supported by precision experiments and advanced nuclear theory, is that nucleons in SRC pairs are “universally” modified, with both the proportion of such pairs (“SRC scaling factor”) and the per-pair distortion function measurable and consistent across the nuclear chart.

1. Formalism: Spectral Function Tail and SRC Scaling

The starting point is the nuclear spectral function, $S_A(p,E)$, which encodes the probability of removing a nucleon of momentum $p$ and separation energy $E$ from a nucleus $A$. In the impulse approximation, the (inclusive) nuclear cross section is

$$\sigma_A(x,Q^2) \sim \int d^3p\,dE\, S_A(p,E)\, \sigma_N(x', Q^2, p^2)$$

with $x'$ the Bjorken scaling variable for the struck nucleon and $p^2$ its virtuality. For momenta $p$ well above the Fermi momentum $k_F$, the high-momentum tail of $S_A$ is dominated by SRC pairs and found to exhibit universal scaling: $$S_A(p, E) \simeq a_2(A)\, S_D(p, E) \quad (p > k_F)$$ where $S_D(p, E)$ is the deuteron spectral function and $a_2(A)$ is the measured SRC scaling factor: $$a_2(A) \equiv \frac{[\sigma_A(x>1.4, Q^2)/A]}{[\sigma_D(x>1.4, Q^2)/2]}$$ This universality underlies much of the phenomenology and quantifies the relative probability for SRC pairs in nucleus $A$ compared to the deuteron (Sargsian, 2012, Zhang et al., 24 Apr 2025, Hen et al., 2016, Ryckebusch et al., 2019).

2. Empirical Linear EMC–SRC Correlation

The EMC ratio, correcting for unequal proton/neutron numbers, is defined as

$$R_{\rm EMC}(x, Q^2) \equiv \frac{F_2^A(x, Q^2)/A}{F_2^D(x, Q^2)/2}$$

where $F_2^A$ is the nuclear per-nucleon DIS structure function. Across nuclei, the suppression (slope) in the region $0.3 \lesssim x \lesssim 0.7$ scales linearly with $a_2(A)$: $$S_{\rm EMC}(A) \equiv -\frac{dR_{\rm EMC}(x)}{dx}\bigg|_{0.3 < x < 0.7} \simeq C\, a_2(A)$$ with empirical $C\approx 0.09{-}0.10$ (Sargsian, 2012, Hen et al., 2016, Arrington, 2015). This linearity is robust from light ($A=3$) to heavy nuclei, tightly constraining any theoretical model of nuclear modification.

3. Virtuality-Driven Universal Modification

Nucleons in SRC pairs possess large negative virtuality, $\nu = p^2 - M^2$, a few $\times 10^2$ MeV$^2$, much greater than typical mean-field nucleons. The bound-nucleon structure function in the relevant $x$ region ($x \sim 0.5–0.8$) can be parameterized as

$$F_2^{\rm bound}(x, Q^2, p^2) = F_2^{\rm free}(x, Q^2)\left[1 + \delta(x)\, \frac{\nu}{M^2}\right]$$

The modification $$\Delta F_2^N(\nu; x, Q^2) = F_2^{\rm bound} - F_2^{\rm free}$$ is thus entirely controlled by the nucleon’s virtuality and the prefactor $\delta(x)$. The characteristic value $\langle \nu \rangle_{\rm SRC}/M^2 \sim 0.1–0.2$, and for $\delta(x)\sim 1–2$ yields per-nucleon structure suppression of order $10$–$30\%$ in the EMC region (Sargsian, 2012, Segarra et al., 2020).

An explicitly universal modification function $R(k^2, x)$ can be extracted by studying light nuclei ($d$, $^3$He) and is found to be independent of $A$, proton-neutron identity, or theoretical details of the nucleon motion treatment, provided sum rules are respected (Segarra et al., 2020, Segarra et al., 2019, Schmookler et al., 2020, Mirjalili et al., 8 Nov 2025). The convolution formalism demonstrates the dominance of SRC nucleons in driving the EMC effect, with mean-field contributions parametrically suppressed.

4. Mechanisms Behind Linearity and Predictive Power

The approximate linearity between $S_{\rm EMC}(A)$ and $a_2(A)$ arises from two complementary mechanisms (Sargsian, 2012):

1. Mean-field depletion: As $a_2(A)$ increases with $A$, less spectral strength remains in the mean-field component ($p<k_F$), diminishing the “unmodified” nucleon contribution near $x<1$ and suppressing $R_{\rm EMC}$.
2. Enhanced SRC modification: The increased fraction of high-momentum (SRC) nucleons with large virtuality leads to a proportionally greater fraction of scattering events from structurally modified nucleons, by the virtuality-dependent shift. The sum yields $S_{\rm EMC}\propto a_2(A)$.

This coherence is encapsulated in the phenomenological “two-component” convolution model (Arrington, 2015): $$F_2^A(x) = [1 - \alpha_2(A)]\, F_2^{N}(x) + \alpha_2(A)\, F_2^{\rm SRC}(x)$$ with $\alpha_2(A)=a_2(A)-1$, and $F_2^{\rm SRC}(x)$ carrying the same “universal modification” across all $A$.

5. Isospin Structure and Enhancement in Asymmetric Nuclei

Extensive exclusive scattering data reveal that SRC pairs are predominantly neutron–proton ($np$) pairs: $pn/pp \sim 20:1$ for $p>k_F$ in the relevant domain (Sargsian, 2012, Ryckebusch et al., 2014, Ryckebusch et al., 2019). In neutron-rich nuclei, the minority species (proton) is more likely to participate in an SRC pair. For $x>0.5$, as the proton structure function $F_2^p$ dominates over $F_2^n$, this “proton excess” in high-virtuality configurations translates to a measurable enhancement of the EMC effect in nuclei with $N > Z$. This isospin dependence leads to flavor-dependent nuclear PDFs, with clear implications for parity-violating DIS and neutrino scattering observables (Sargsian, 2012, Arrington, 2015, Mirjalili et al., 8 Nov 2025, Huang et al., 2021).

6. Experimental and Theoretical Signatures of Universality

Key observables and confirmations:

• The per-nucleon (e,e') cross-section ratio $\sigma_A/A$ to $\sigma_D/2$ shows a saturation (“$a_2(A)$ plateau”) in $1.4 < x < 1.75$ with only $\sim 20$–$30\%$ variation for $A>12$, demonstrating universality of SRC momentum distributions (Zhang et al., 24 Apr 2025, Schmookler et al., 2020).
• Direct extraction of the universal modification function $U(x)$ from simultaneous high-precision measurements of $R_{\rm EMC}(x)$ and $a_2(A)$ shows convergence of the extracted $U(x)$ for all nuclei, e.g.,

$$U(x) = \frac{3}{2 a_2(A)} \left[ \frac{F_2^A(x)}{A} - \frac{F_2^d(x)}{2} \right]$$

remains invariant from $A=4$ to $A=208$ (Schmookler et al., 2020, Segarra et al., 2020, Mirjalili et al., 8 Nov 2025).

• Tagged DIS and future semi-exclusive experiments are predicted to observe that $F_2^{\rm bound}/F_2^{\rm free}$ at fixed virtuality $\nu$ is independent of $A$, confirming the virtuality-universality hypothesis (Sargsian, 2012).

Tables: Universal Function Slope Extraction (from (Hen et al., 2019))

Nucleus	$dF_{\rm univ}/dx$	$\rho_{np}/\rho_{pp}(r < 1$ fm)	$\chi^2/{\rm dof}$
$^{12}$C	$-0.101 \pm 0.005$	$3.9 \pm 0.4$	$0.9$
$^{56}$Fe	$-0.099 \pm 0.006$	$4.2 \pm 0.5$	$1.1$
$^{208}$Pb	$-0.103 \pm 0.007$	$4.0 \pm 0.5$	$1.0$

Universality in Neutrino and Drell-Yan Scattering: Similar universal modification functions have been shown to collapse nuclear structure function ratios onto a single curve (after SRC scaling) for neutrino-nucleus DIS [$U_{F_3}(x)$, $U_{F_2}(x)$] and in pion-induced Drell-Yan processes, further confirming target-independence (Huang et al., 2021, Huang et al., 13 Jan 2025, Mirjalili et al., 8 Nov 2025).

7. Scope, Limitations, and Current Debates

By integrating high-precision cross-section and structure function data with operator-based and convolution-based nuclear theory, the case for universal modification of nucleons in SRC pairs is quantitatively robust and consistent with QCD-based expectations for short-range dynamics (Segarra et al., 2019, Hen et al., 2016, Wang et al., 2020). However, notable cautions remain:

• In light nuclei and at very high $A$, some analyses find the universal SRC-only picture underpredicts the full EMC effect, suggesting additional contributions from mean-field modifications, $\alpha$-clustering, or $3N$ (three-nucleon) SRC effects (Wang et al., 2022, Ma et al., 2023).
• The mean field may itself be weakly modified, or there could be a gradual break-down of strict universality, especially in extreme isospin or density regimes.
• The full dynamical QCD origin (e.g., via diquark–quark correlations or bag-model vacuum effects) of the universal function remains under active theoretical investigation, with proposals ranging from color-screening modifications to trace-anomaly–driven mass deficits (Wang et al., 2020, West, 2020).

Future precision measurements—tritium/tags (MARATHON, LAD/BAND), parity-violating DIS, high-$Q^2$ semi-exclusive knock-out, and Lattice QCD studies—will clarify the detailed role of SRCs in nuclear modification and determine the possible need for corrections beyond the existing universal phenomenology. The universal modification of nucleons in SRC pairs thus forms the quantitative and conceptual foundation for connecting high-density QCD physics with observed medium-induced nuclear structure function changes.