The ratio

## Abstract

We demonstrate that several anomalies seen in data from high energy physics experiments have their origin in quantum entanglement, and quantum information science more generally. A few examples are provided that help clarify this proposition. Our research clearly shows that there is a thermal behavior in particle kinematics from high energy collisions at both collider and fixed target experiments that can be attributed to quantum entanglement and entanglement entropy. And in those cases where no quantum entanglement is expected, the thermal component in the kinematics is absent, in agreement with our hypothesis. We show evidence that these phenomena are interaction independent, but process dependent, using results from proton-proton scattering at the Large Hadron Collider (LHC) and antineutrino-nucleus scattering at Fermilab. That is, this thermal behavior due to quantum entanglement is shown to exist in both the strong and electroweak interactions. However, the process itself must include quantum entanglement in the corresponding wave functions of interacting systems in order for there to be thermalization.

### Keywords

- Quantum Entanglement
- Entanglement Entropy
- High Energy Physics

## 1. Introduction

A complete understanding of multi-particle production dynamics continues to be a challenge for theory in high energy collisions. The full description of real-time dynamical evolution in a strongly coupled non-Abelian gauge theory can be notoriously difficult. The availability of large, diverse, and high quality accumulated proton-proton (

For example, the differential distribution of charged hadrons resulting from

It is interesting to consider the possibility that these two interactions of vastly differing collision or scattering energies are different manifestations of a single underlying fundamental process. There is growing interest in the link between quantum entanglement, entanglement entropy (EE), and high energy physics presently. Here, we describe a relationship between quantum entanglement in the nucleon wave functions associated with the hadron collisions at the LHC experiments and with the electroweak scattering in Fermilab experiments. There are several examples of these relationships in theoretical physics: Research on the dynamics of quantum entanglement and entanglement entropy in the regime of small Bjorken-

In [1, 2, 13], it is proposed that the thermal component is a result of entanglement between causally disconnected parts of the nucleon in the interaction. For this reason inelastic

If quantum entanglement and EE are responsible for the thermal behavior in charged hadron as well as Higgs boson production in

These topics are presented and discussed in this chapter. A brief description of the theory motivating this proposed link between quantum entanglement, entanglement entropy, and thermal behavior in

## 2. Entanglement entropy and thermal behavior in the strong interaction

We begin by considering the possibility that the observed thermalization in

Since a high-energy collision can be viewed as a rapid quench of the entangled partonic state [15], it is thus possible that the effective temperature inferred from the transverse momentum distributions of the secondaries in a collision can depend upon the momentum transfer, that is an ultraviolet cutoff on the quantum modes resolved by the collision. In analyzing the high-energy collisions with different characteristic momentum transfer

The presence of both a thermal and a hard scattering component in inclusive deep-inelastic scattering at HERA has been observed [20]. And the absence of this thermal component in processes characterized by a rapidity gap is also manifested in these studes. In diffractive events where there is a rapidity gap, the entire proton wave function is involved in the scattering process. In diffractive scattering, the proton remains fully intact in the central part of the collider detector where scattering takes place. There is no entanglement entropy due to different regions of the proton wave function being involved in the scattering in different ways. This observation points to a connection between this thermalization and quantum entanglement between different parts of the proton wave function. This link is described in the next section.

### 2.1 Entanglement and thermalization in high energy collisions - theory

A brief summary of these proposition is as follows. The hard process in

In this same figure, the spatial region

where

* single*sum in

Here

The density matrix formalism is now a better tool to use in the discussion. For a mixed state that is probed in region

where the symbol

In the case of a mixed state, the probabilities corresponding to the different states described above can be used to define the von Neumann entropy of the mixed state given by

It is the entanglement between regions

Studies of quantum entanglement and thermalization in atomic and condensed matter physics were shown to depend upon the quench properties, and that there is evidence for quantum propogation and information propagation [16, 21, 22, 23]. It is instructive to compare this with a quench induced by a high energy collision. The quench associated with the latter [17, 18] leads to the following interpretation. A quench produces a highly excited state of a Hamiltonian

As shown in [17, 18] for a rapid quench (such as the one that occurs in a high-energy collision) in a

where

The interpretation of the result (5) is the following [17, 18]. The quench leads to the production of entangled (quasi)particle pairs, since what used to be the ground state of the undisturbed Hamiltonian

For a quench induced by a high-energy collision, we sketch the resulting picture of thermalization from entanglement in Figure 2. Note that the hardest quasiparticle modes that propagate along the light cone thermalize first. For the softer particles that propagate in the interior of the light cone, it takes a longer time to thermalize, that is, to exhibit an extensive scaling of the entropy. The detection of particles is assumed to be performed within the interval of length

It is instructive to point out the difference in the mechanisms of thermalization expected at weak and strong coupling. At weak coupling, the “bottom-up” thermalization mechanism [28] also yields an effective temperature * hardest*modes resolved in the process. In the dual holographic description of conformal field theory, this process is described by the formation of trapped surface near the Minkowski boundary that then falls into the AdS bulk, corresponding to the spreading of thermalization from hard to soft modes [29, 30]. A similar picture emerges from the analysis of entanglement entropy in an expanding string [31], where the entropy has been found to have a thermal form with an effective temperature

### 2.2 Charged hadron transverse momentum distribution

The discussion presented in the previous sections provide motivation to compare with experimental results from inelastic collision events at high energies. It also gives the opportunity to explore the possible relation between effective temperature and the hard scale of the collision. Consider proton-proton collisions data recorded by the LHC ATLAS collaboration at

The normalized charged hadron transverse momentum distribution is shown in Figure 3. The thermal component is shown by the exponential, red dashed curve; we parameterize it as

where

where

The extracted value of the thermal temperature,

to the LHC 13 TeV collision energy; here

It’s interesting that the parameterizations (Eqs. (8) and (9)) imply that the effective thermal temperature

The fits to the charged hadron transverse momentum distribution in Figure 3 yields the hard scale temperature parameter

The integral of the area under the fit curves carries important information about entanglement in these and other in high energy physics processes. Defining the ratio

The calculation yields the value of

### 2.3 Diffractive events and di-muon pair transverse momentum distribution in proton-proton collisions

Diffractive proton-proton (

at

Figure 4 shows the transverse momentum distribution in the case of

### 2.4 Combined Higgs boson decays to γγ , ZZ∗ → 4l, and b b ¯

The Higgs boson differential transverse momentum cross section is undoubtedly adequately described by perturbation theory (see [34] for a review). An investigation is undertaken to determine whether the thermalization process due to entanglement is present in this system. The Higgs boson differential cross sections (differential in transverse momentum

In Figure 5 the transverse momentum distribution of the Higgs bosons is shown in the range from 5 GeV to 700 GeV for combined ATLAS and CMS data at 13 TeV

Interestingly, the ratio

### 2.5 Discussion: entanglement entropy in proton-proton collisions

The material presented in Section 2 provide evidence for an unconventional mechanism of apparent thermalization in high energy

The theory and the analyses of the data discussed in Section 2 appear to be consistent with the proposition that thermalization in these high energy collisions is induced by quantum entanglement. That the effective temperature determined from the data is proportional to the momentum transfer ^{1}

In diffractive events studied in Section 2, it is clearly seen that where studies of the coherent response of the entire proton in this scattering, there is no associated entanglement entropy [15], and that therefore there should be no thermal component to the transverse momentum distribution. The data confirms this prediction in diffractive Drell-Yan production analyzed in this section, as well as by the diffractive deep-inelastic scattering data shown in [20].

The findings presented here appear to support the proposition that a deep connection between quantum entanglement and thermalization in high-energy hadron collisions, and that this proposed link should be further investigated. Possibilities include the following as non-exhaustive examples. Combining measurements of the structure functions with the study of hadronic final states, especially in the target fragmentation region in deep inelastic scattering at the future Electron Ion Collider. Studies of the thermal component and the corresponding effective temperature in hard processes characterized by different momentum transfers in proton-proton, proton-nucleus and nucleus-nucleus collisions at RHIC and the LHC. Already, analysis of Pb–Pb HI collision data also points to a picture of thermalization as a result of quantum entanglement at high energies [39]. An investigation of the dependence of the apparent thermalization on rapidity – as depicted in Figure 2, suggesting that the thermal component and the corresponding effective temperature in hard processes characterized by different momentum transfer would be interesting. It suggests that thermalization is achieved faster if a measurement is performed in a smaller rapidity interval.

## 3. Entanglement entropy and thermal behavior in the electroweak interaction

The material and discussion in Section 2 supporting a picture of thermalization in hadronic physics due to quantum entanglement motivates an investigation of whether this same connection is manifested in weak interactions mediated by massive vector bosons. In this section that study, taken mainly from [5], is made using charged-current weak interaction processes such as

Similar to the partial probing of the nucleon wave function described in Section 2 the vector boson in this investigation probes only a part of the nucleon wave function, again denoted by the region

In this current analysis, we test the hypothesis, albeit disfavored by the conventional mechanism of thermalization, that the thermal feature found in the low-

### 3.1 Charged current weak interactions: analysis and results

We begin by considering neutral pion production in charged-current antineutrino interactions with a CH (hydrocarbon scintillator) target; see (Eq. (12)). This experimental data includes the total inclusive charged current weak interaction differential cross sections [39, 40] measurements at

The relativistic kinetic energy is related to the pion rest mass,

where

The normalized differential cross section that is used to describe the thermal behavior from the interaction is given by a very similar formula as in subSection 2.2 but here using

where

where

The CERN ROOT fitting program is used to fit these expressions to the MINERvA results. A total of five parameters are used in the fitting procedure:

The results of fitting the thermal and hard scattering components to the distribution in the analysis using data from the MINER

Final state interactions (FSI) are modeled using the GENIE Monte Carlo program [43] in the anayses described in [39, 40]. They show that the larger FSI effects on the data are at low pion momenta. These effects are small compared with the statistical and other systematic uncertainties from the analysis, and did not affect the fits and conclusions drawn in this present study.

Now consider the resulting momentum distribution when the process of antineutrino scattering is from the entire nucleus, and not from a partial region of the nucleon as described above. That is, when the antineutrino scatters from the nucleus coherently, as in

In this charged current weak interaction, there is no entanglement between different parts of a struck nucleon, and no thermal component to the momentum distribution of the single produced pion is expected. It is this description of the interaction that is supported by the coherent scattering data from the MINER

## 4. Conclusion

The results presented in this study support those given in [1, 2, 14, 46], namely that quantum entanglement in hadrons is what gives rise to the thermal behavior observed in hadronic collisions and, as the new results from charged-current neutrino scattering presented here suggest, that the thermalization process from entanglement, while process dependent, is interaction independent.

## Notes

- It is once again emphasized that this does not imply that the Higgs boson is produced thermally, but rather that its transverse momentum distribution is affected by thermal radiation due to entanglement.