The Quantum Focusing Conjecture (QFC) lies at the foundation of holography and semiclassical gravity. The QFC implies the Bousso bound and the Quantum Null Energy Condition (QNEC). The QFC also ensures the consistency of the quantum extremal surface prescription and bulk reconstruction in AdS/CFT.

United States

Raphael Bousso

Elisa Tabor

Discrete Max-Focusing

<p>Renormalization group evolution equations describing the scale dependence of quantities in quantum chromodynamics play a central role in the interpretation of experimental data. Arguably the most important evolution equations for collider physics applications are the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations, which describe the evolution of a quark or gluon fragmenting into hadrons, with only a <i>single</i> hadron identified at a time. In recent years, the study of the correlations of energy flow within jets has come to play a central role at collider experiments, necessitating an understanding of correlations, going beyond the standard DGLAP paradigm. In this paper we derive a general renormalization group equation describing the collinear dynamics that account for correlations in the fragmentation. We compute the kernel of this evolution equation at next-to-leading order, where it involves the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo stretchy="false">→</mo><mn>3</mn></mrow></math> splitting functions, and develop techniques to solve it numerically. We show that our equation encompasses all previously known collinear evolution equations, namely DGLAP and the evolution of multihadron fragmentation functions. As an application of our results, we consider the phenomenologically relevant example of energy flow on charged particles, computing the energy fraction in charged particles in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo></math> hadrons at next-to-next-to-leading order. Our results are an important step toward improving the understanding of the collinear dynamics of jets, with broad applications in jet substructure, ranging from the study of multihadron correlations, to the description of inclusive (sub)jet production, and the advancement of modern parton showers.</p>

China

Hao Chen

Netherlands

Max Jaarsma

Yibei Li

Ian Moult

Wouter J. Waalewijn

Hua Xing Zhu

Collinear parton dynamics beyond Dokshitzer-Gribov-Lipatov-Altarelli-Parisi framework

In view of the increasing precision of theoretical calculations and experimental measurements, power corrections to transverse-momentum-dependent observables are highly important. We study the next-to-leading power corrections for transverse momentum measurements in e + e  −  → 2 jets. We obtain a factorized expression for the cross section, which involve twist-2 and twist-3 operators, and identify the new jet functions that appear in it. We calculate these jet functions at order α  s  for a family of recoil-free schemes, and provide the corresponding anomalous dimensions at leading order. Additionally, we show that the (endpoint) divergences that typically arise in sub-leading-power factorization can be subtracted and cancel for our case. By working with jets, everything is perturbatively calculable and there are substantial simplifications compared to the general next-to-leading power framework. Importantly, our analysis with jets can be extended to semi-inclusive deep-inelastic scattering, with the future Electron-Ion Collider as key application.

Spain

Rafael Castillo

Ignazio Scimemi

Wouter Waalewijn

Transverse momentum measurements with jets at next-to-leading power

Energy correlators measured inside high-energy jets at hadron colliders have recently been demonstrated to provide a new window into both perturbative and non-perturbative Quantum Chromodynamics. A number of the most interesting features of these correlators, namely their universal scaling behavior and the ability to image the confinement transition, require precise angular resolution, necessitating the use of tracking information in experimental measurements. Theoretically, tracking information can be incorporated into the energy correlators using track functions, which are non-perturbative functions describing the fragmentation of quarks and gluons into charged hadrons. In this paper, we apply our recently developed track function formalism to energy correlators, and study in detail the interplay of track functions with perturbative resummation and non-perturbative power corrections. We provide resummed results for the energy correlators at collinear next-to-leading-logarithmic accuracy and compare with parton shower Monte Carlo simulations. For the two-point correlator the use of tracking has a minimal effect throughout the entire distribution, but it has a significant effect for higher point correlators. Our results are crucial for the theoretical interpretation of recent experimental measurements of the energy-energy correlators.

Hua Zhu

Energy correlators on tracks: resummation and non-perturbative effects

In double parton scattering (DPS), two partonic collisions take place between one pair of colliding hadrons. The effect of DPS can be significant for precision measurements due to the additional radiation from secondary partonic collisions, and especially for specific processes such as same-sign WW production. Its effect is usually included through Monte Carlo parton showers. In a factorization approach to DPS, the initial state is described by double parton distributions (DPDs). These are currently poorly constrained by experiment, but provide a view on interesting correlations between partons in the hadron. Here we show that the Large Momentum Effective Theory approach can be applied to DPDs. Specifically, we present a general matching relation between DPDs and lattice-calculable quasi-DPDs for general flavor, spin and color structures. We furthermore calculate the one-loop matching coefficients for the quark-quark DPDs, verifying that the infrared logarithms and divergences cancel in the matching. While we restrict to the flavor-non-singlet case, we do take color and spin correlations into account. Interestingly, quasi-DPDs combines nontrivial features from both the collinear and transverse momentum dependent quasi-parton distribution functions. This represents a first step in extending the quasi-PDF approach to DPDs, opening up a new way to constrain these distributions using lattice QCD.

United Kingdom

Rudi Rahn

Towards double parton distributions from first principles using Large Momentum Effective Theory

Jets and their substructure play a central role in many analyses at the Large Hadron Collider (LHC). To improve the precision of measurements, as well as to enable measurement of jet substructure at increasingly small angular scales, tracking information is often used due to its superior angular resolution and robustness to pile-up. Calculations of track-based observables involve non-perturbative track functions, that absorb infrared divergences in perturbative calculations and describe the transition to charged hadrons. The infrared divergences are directly related to the renormalization group evolution (RGE), and can be systematically computed in perturbation theory. Unlike the standard DGLAP evolution, the RGE of the track functions is non-linear, encoding correlations in the fragmentation process. We compute the next-to-leading order (NLO) evolution of the track functions, which involves in its kernel the full 1 → 3 splitting function. We discuss in detail how we implement the evolution equation numerically, and illustrate the size of the NLO corrections. We also show that our equation can be viewed as a master equation for collinear evolution at NLO, by illustrating that by integrating out specific terms, one can derive the evolution for any N -hadron fragmentation function. Our results provide a crucial ingredient for obtaining track-based predictions for generic measurements at the LHC, and for improving the description of the collinear dynamics of jets.

Multi-collinear splitting kernels for track function evolution

Track functions describe the collective effect of the fragmentation of quarks and gluons into charged hadrons, making them a key ingredient for jet substructure measurements at hadron colliders, where track-based measurements offer superior angular resolution. The first moment of the track function, describing the average energy deposited in charged particles, is a simple and well-studied object. However, measurements of higher-point correlations of energy flow necessitate a characterization of fluctuations in the hadronization process, described theoretically by higher moments of the track function. In this paper we derive the structure of the renormalization group (RG) evolution equations for track function moments. We show that energy conservation gives rise to a shift symmetry that allows the evolution equations to be written in terms of cumulants, κ(N), and the difference between the first moment of quark and gluon track functions, ∆. The uniqueness of the first three cumulants then fixes their all-order evolution to be DGLAP, up to corrections involving powers of ∆, that are numerically suppressed by an effective order in the perturbative expansion for phenomenological track functions. However, at the fourth cumulant and beyond there is non-trivial RG mixing into products of cumulants such as κ(4) into κ(2)2. We analytically compute the evolution equations up to the sixth moment at   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (  <math> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math>  $$ {\alpha}_s^2 $$ ), and study the associated RG flows. These results allow for the study of up to six-point correlations in energy flow using tracks, paving the way for precision jet substructure at the LHC.

Renormalization group flows for track function moments

Novel methods to reconstruct the slant depth of the maximum of the longitudinal profile ( $$X_{\mathrm{max}}$$  <math> <msub> <mi>X</mi> <mi>max</mi> </msub> </math>  ) of high-energy showers initiated by gamma-rays as well as their energy ( $$E_0$$  <math> <msub> <mi>E</mi> <mn>0</mn> </msub> </math>  ) are presented. The methods were developed for gamma rays with energies ranging from a few hundred GeV to  $$\sim 10$$  <math> <mrow> <mo>∼</mo> <mn>10</mn> </mrow> </math>   TeV. An estimator of  $$X_{\mathrm{max}}$$  <math> <msub> <mi>X</mi> <mi>max</mi> </msub> </math>   is obtained, event-by-event, from its correlation with the distribution of the arrival time of the particles at the ground, or the signal at the ground for lower energies. An estimator of  $$E_0$$  <math> <msub> <mi>E</mi> <mn>0</mn> </msub> </math>   is obtained, event-by-event, using a parametrization that has as inputs the total measured energy at the ground, the amount of energy contained in a region near to the shower core and the estimated  $$X_{\mathrm{max}}$$  <math> <msub> <mi>X</mi> <mi>max</mi> </msub> </math>  . Resolutions about  $$40 \, (20)\,\mathrm{g/cm^2}$$  <math> <mrow> <mn>40</mn> <mspace width="0.166667em"></mspace> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <mrow> <mi>g</mi> <mo>/</mo> <msup> <mi>cm</mi> <mn>2</mn> </msup> </mrow> </mrow> </math>   and about  $$30 \, (20)\%$$  <math> <mrow> <mn>30</mn> <mspace width="0.166667em"></mspace> <mo>(</mo> <mn>20</mn> <mo>)</mo> <mo>%</mo> </mrow> </math>   for, respectively,  $$X_{\mathrm{max}}$$  <math> <msub> <mi>X</mi> <mi>max</mi> </msub> </math>   and  $$E_0$$  <math> <msub> <mi>E</mi> <mn>0</mn> </msub> </math>   at  $$1 \, (10) \ \mathrm {TeV}$$  <math> <mrow> <mn>1</mn> <mspace width="0.166667em"></mspace> <mo>(</mo> <mn>10</mn> <mo>)</mo> <mspace width="4pt"></mspace> <mi>TeV</mi> </mrow> </math>   energies are obtained, considering vertical showers. The obtained results are auspicious and can lead to the opening of new physics avenues for large wide field-of-view gamma-ray observatories. The dependence of the resolutions with experimental conditions is discussed.

Portugal

R. Conceição

L. Peres

M. Pimenta

B. Tomé

New methods to reconstruct  $$X_{\mathrm{max}}$$  <math> <msub> <mi>X</mi> <mi>max</mi> </msub> </math>   and the energy of gamma-ray air showers with high accuracy in large wide-field observatories

The atmospheric depth where the energy deposit profile of secondary particles from extensive air showers (EAS) reaches its maximum, $$X_{\mathrm{max}}$$ <math><msub><mi>X</mi><mi>max</mi></msub></math> , is related to the primary particle mass. The mass composition of the ultra-high energy cosmic rays (UHECRs) can be inferred from measurements of $$X_{\mathrm{max}}$$ <math><msub><mi>X</mi><mi>max</mi></msub></math>  distributions in each energy interval, by fitting these distributions with Monte Carlo (MC) templates for four primary species (p, He, N and Fe). On the basis of simulations, we show that a high abundance of some intermediate elements in the $$X_{\mathrm{max}}$$ <math><msub><mi>X</mi><mi>max</mi></msub></math>  distributions, e.g. Ne or Si, may affect the quality of the fit and also the reconstructed fractions of different species with respect to their true values. We propose a method for finding the “best combination” of elements in each energy interval from a larger set of primaries (p, He, C, N, O, Ne, Si and Fe) which best describes the $$X_{\mathrm{max}}$$ <math><msub><mi>X</mi><mi>max</mi></msub></math>  distributions. Applying this method to the $$X_{\mathrm{max}}$$ <math><msub><mi>X</mi><mi>max</mi></msub></math>  distributions measured by the Pierre Auger Observatory (2014), we found that the “best combination” of elements which best describe the data suggest the presence of Ne or Si in some low energy bins for the EPOS-LHC model.

Romania

Nicusor Arsene

Octavian Sima

UHECRs mass composition from $$X_{\mathrm{max}}$$ <math><msub><mi>X</mi><mi>max</mi></msub></math>  distributions

In the context of massive (bi-)gravity, non-minimal matter couplings have been proposed. These couplings are special in the sense that they are free of the Boulware-Deser ghost below the strong coupling scale and can be used consistently as an effective field theory. Furthermore, they enrich the phenomenology of massive gravity. We consider these couplings in the framework of bimetric gravity and study the cosmological implications for background and linear tensor, vector, and scalar Previous works have investigated special branches of solutions. Here we perform a complete perturbation analysis for the general background equations of motion, completing previous analyses.

Japan

Xian Gao

Switzerland

Lavinia Heisenberg

Doubly coupled matter fields in massive bigravitySupported by the Chinese National Youth Thousand Talents Program (71000-41180003), JSPS Grant-in-Aid for Scientific Research (15H02082, 25287054, 26610062), L. H. Acknowledges Financial Support from Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation