Fri·Feb 25, 2022Friday·February 25, 2022

1. 01*

   Constraining the CP structure of Higgs-fermion couplings with a global LHC fit, the electron EDM and baryogenesis

   Henning Bahl🇺🇸 · Elina Fuchs🇨🇭 · Sven Heinemeyer🇪🇸 · Judith Katzy🇩🇪 · Marco Menen🇩🇪 · Krisztian Peters🇩🇪 · Matthias Saimpert🇫🇷 · Georg Weiglein🇩🇪

   CP violation in the Higgs couplings to fermions is an intriguing, but not yet extensively explored possibility. We use inclusive and differential LHC Higgs boson measurements to fit the CP structure of the Higgs Yukawa couplings. Starting with simple effective models featuring CP violation in a single Higgs-fermion coupling, we probe well-motivated models with up to nine free parameters. We also investigate the complementarity of LHC constraints with the electron electric dipole moment bound, taking into account the possibility of a modified electron Yukawa coupling, and assess to which extent CP violation in the Higgs-fermion couplings can contribute to the observed baryon asymmetry of the universe. Even after including the recent analysis of angular correlations in $H\to {\tau }^{+}{\tau }^{-}$ decays, we find that a complex tau Yukawa coupling alone may be able to account for the observed baryon asymmetry, but with large uncertainties in the baryogenesis calculation. A combination of complex top and bottom quark Yukawa couplings yields a result four times larger than the sum of their separate contributions, but remains insufficient to account for the observed baryon asymmetry.

   hep-phhep-exEPJC(2022)·53 citations
2. 02*

   Nuclear medium effects in lepton-nucleus DIS in the region of $x\gtrsim 1$

   M. Sajjad Athar🇮🇳 · S. K. Singh🇮🇳 · F. Zaidi🇮🇳

   The nuclear medium effects in the nuclear structure functions and differential cross sections in the deep inelastic scattering (DIS) of charged lepton and neutrino from nuclear targets are studied in the region of large $x$ including $x\ge 1$. The nuclear medium effects due to the Fermi motion and the binding energy of nucleons and the nucleon correlations are included using nucleon spectral function calculated in a microscopic field theoretical model. The numerical results for the nuclear structure functions and the cross sections are obtained using the nucleon structure function evaluated at the next-to-next-to-leading order (NNLO) with the Martin-Motylinski-Harland Lang-Thorne (MMHT) parameterization of the nucleonic parton distribution functions (PDFs) and are compared with the available experimental data on electron scattering from the Jefferson Lab (JLab) and SLAC Nuclear Physics Facility (NPAS). In the case of neutrino scattering the results are relevant for understanding the DIS contributions to the recent inclusive cross sections measured by the Main Injector Neutrino ExpeRiment to study v-A interactions (MINERvA) as well as theoretical predictions are made for Deep Underground Neutrino Experiment (DUNE). The importance of isoscalarity corrections in heavier nuclear targets as well as the effect of the kinematic cut on the CM energy $W$ in defining the DIS region have also been discussed.

   hep-phnucl-thPRD(2022)·5 citations
3. 03*

   Topological portals from matter to antimatter

   Andrea Addazi🇨🇳

   We discuss possibilities of generating a Majorana mass for the neutron from topological quantum gravity effects which survive at mesoscopic scales from decoherence. We show how virtual micro-black hole (BH) pairs with skyrme/baryon hairs induce a neutron-antineutron transition which can be tested in next generation of experiments. Such effects do not destabilize the proton. We also discuss how BHs with mix ordinary and mirror baryon hairs can mediate neutron-mirror neutron mixings.

   hep-phgr-qchep-thSymmetry(2022)·3 citations
4. 04*

   Looking for the exotic $X_0(2866)$ and its $J^P=1^{+}$ partner in the ${\bar{B}}^0\to D^{(\ast )+}{K}^{-}{K}^{(\ast )0}$ reactions

   L. R. Dai🇨🇳 · R. Molina🇪🇸 · E. Oset🇪🇸

   We propose two reactions, ${\bar{B}}^0\to K^0{D}^{+}{K}^{-}$ and ${\bar{B}}^0\to K^{\ast 0}{D}^{\ast +}{K}^{-}$, already measured at Belle, to look into the $J^P=0^{+}$, $X_0(2866)$ state and a $1^{+}$ partner of molecular $D^{\ast }{\bar{K}}^{\ast }$ nature, by looking at the $D^{+}{K}^{-}$ and $D^{\ast +}{K}^{-}$ invariant mass distributions, respectively. Very clear peaks over the background are predicted and the branching ratios for the production of these states are evaluated to facilitate the task of determining the needed statistics for their observation. The fact that the $K^{\ast 0}{K}^{-}$ mass distribution from accumulation of events of different reactions is already available, indicates that one is not far away from having the needed statistics to see peaks in the $D^{(\ast )+}{K}^{-}$ mass distributions, so far not yet analyzed.

   hep-phPRD(2022)·20 citations
5. 05*

   Hadronic effects in Møller scattering at NNLO

   Jens Erler🇩🇪 · Rodolfo Ferro-Hernández🇩🇪 · Ayres Freitas🇺🇸

   Two-loop electroweak corrections to polarized Moller scattering are studied in two different schemes at low energies. We find the finite $Q^2$ corrections to be well under control. The hadronic and perturbative QCD corrections to the $\gamma Z$ two-point function are incorporated through the weak mixing angle at low energies, which introduce an error of $0.08\times 10^{-3}$ in the weak charge of the electron $Q_W^e$. Furthermore, by studying the scheme dependence, we obtain an estimate of the current perturbative electroweak uncertainty, $\delta Q_W^e\approx 0.23\times 10^{-3}$, which is five times smaller than the precision estimated for the MOLLER experiment $(\delta Q_W^e=1.1\times 10^{-3})$. Future work is possible to reduce the theory error further.

   hep-phJHEP(2022)·7 citations
6. 06*

   Mass Spectra and Decay Properties of Singly Heavy Bottom-Strange Baryons

   Amee Kakadiya🇮🇳 · Zalak Shah🇮🇳 · Ajay Kumar Rai🇮🇳

   We enumerated ground and excited state masses of singly heavy bottom-strange baryons using the Hypercentral Constituent Quark Model (hCQM). The screening potential is used with color-Coulomb potential, as the confining potential. We determine the possible $J^P$ values to recently observed excited states like, ${\Xi }_b(6100)$, ${\Xi }_b(6227)$, ${\Xi }_b(6327)$, ${\Xi }_b(6333)$ and four ${\Omega }_b(6316,6330,6340,6350)$ states. The Regge trajectories are plotted in $(J,M^2)$ plane to assign the $J^P$ values and quantum numbers to recently observed states. Using the calculated spectroscopic data, properties such as magnetic moment, transition magnetic moment, radiative decay width, and strong decay width are also investigated for all singly heavy bottom-strange baryonic system.

   hep-phInt.J.Mod.Phys.A(2022)·32 citations
7. 07*

   Distinguishing two dark matter component particles at $e^{+}{e}^{-}$ colliders

   Subhaditya Bhattacharya🇮🇳 · Purusottam Ghosh🇮🇳 · Jayita Lahiri🇮🇳 · Biswarup Mukhopadhyaya🇮🇳

   In this work we demonstrate that a distorted double hump like missing energy ($\text{slashed}E$) or missing transverse momentum ($\text{slashed}{E}_T$) or missing mass ($\text{slashed}M$) distribution at $e^{+}{e}^{-}$ colliders may hint towards the presence of multipartite dark sector. We illustrate the phenomena using a two component dark matter (DM) model involving an inert scalar doublet stabilised under a ${\mathcal{Z}}_2$ symmetry providing a scalar DM, one vector like fermion doublet and a right handed fermion singlet both stabilised under a different ${\mathcal{Z}}_2^{{}^{\prime }}$ providing a fermion DM. We indicate the region of parameter space where the production of the heavy charged particles and their subsequent decay to DM yield double peak behaviour in $\text{slashed}E$ spectrum after satisfying DM constraints. Importantly, we illustrate why and how $\text{slashed}E$ serves as a better variable than $\text{slashed}{E}_T$ in distinguishing two component DM frameworks and therefore how International Linear Collider (ILC) does better than the ongoing Large Hadron Collider (LHC). We also chalk out a set of criteria to identify and segregate the second peak in $\text{slashed}E$ spectrum, after a careful analysis of the corresponding Standard Model (SM) background contribution, which plays a crucial role.

   hep-phhep-exJHEP(2022)·23 citations
8. 08*

   Gluon Fusion Production at NLO: Merging the Transverse Momentum and the High-Energy Expansions

   Luigi Bellafronte🇪🇸 · Giuseppe Degrassi🇮🇹 · Pier Paolo Giardino🇪🇸 · Ramona Gröber🇮🇹 · Marco Vitti🇮🇹

   The virtual corrections to $gg\to HH$ and $gg\to ZH$ are analytically evaluated combining an expansion in the small transverse momentum of the final particles with an expansion valid at high energies. The two expansion methods describe complementary regions of the phase space and we merge their results, extending the range of validity of both expansions using Padé approximants. We show that this approach can reproduce the available numerical results retaining the exact top quark mass dependence with an accuracy well below the 1% level. Our results allow a fast and flexible evaluation of the virtual corrections of the considered processes. Furthermore, they are available in different renormalisation schemes of the top quark mass.

   hep-phJHEP(2022)·50 citations
9. 09*

   Coherent $J/\psi$ electroproduction on ${}^4$He and ${}^3$He at the Electron-Ion Collider: probing nuclear shadowing one nucleon at a time

   V. Guzey (St. Petersburg, INP)🇷🇺 · M. Rinaldi (Perugia U. and INFN, Perugia)🇮🇹 · S. Scopetta (Perugia U. and INFN, Perugia)🇮🇹 · M. Strikman (Penn State U.)🇺🇸 · M. Viviani (INFN, Pisa)🇮🇹

   While the phenomenon of gluon nuclear shadowing at small $x$ has been getting confirmation in QCD analyses of various LHC measurements involving heavy nuclei, it has not been possible so far to establish experimentally the number of target nucleons responsible for nuclear shadowing in a given process. To address this issue, we study coherent $J/\psi$ electroproduction on ${}^4$He and ${}^3$He in the kinematics of a future electron-ion collider and show that this process has the power to disentangle the contributions of the interaction with a specific number of nucleons $k$, in particular, with two nucleons at the momentum transfer $t\ne 0$. We predict a dramatic shift of the $t$-dependence of the differential cross section toward smaller values of $|t|$ due to a non-trivial correlation between $x$ and $k$. This calculation, which makes use for the first time of realistic wave functions, provides a stringent test of models of nuclear shadowing and a novel probe of the 3D imaging of gluons in light nuclei. In addition, thanks to this analysis, unique information on the real part of the corresponding scattering amplitude could be accessed.

   hep-phhep-exnucl-thPRL(2022)·5 citations
10. 10*

    Diffractive semi-hard production of a $J/\psi$ or a ${\rm Y}$ from single-parton fragmentation plus a jet in hybrid factorization

    Francesco Giovanni Celiberto🇮🇹 · Michael Fucilla🇮🇹

    We investigate the inclusive hadroproduction of a heavy quarkonium ($J/\psi$ or ${\rm Y}$), in association with a light-flavored jet, as a testing ground for the semi-hard regime of QCD. Our theoretical setup is the hybrid high-energy and collinear factorization, where the standard collinear approach is supplemented by the $t$-channel resummation of leading and next-to-leading energy logarithms à la BFKL. We present predictions for rapidity and azimuthal-angle differential distributions, hunting for stabilizing effects of the high-energy series under higher-order corrections. Our reaction represents an additional channel to test the production mechanisms of quarkonia at high energies and large transverse momenta and to possibly shed light on the transition region from heavy-quark pair production to single-parton fragmentation of $J/\psi$ and ${\rm Y}$ states.

    hep-phEPJC(2022)·87 citations
11. 11*

    Illuminating the nucleon spin

    Miguel G. Echevarria🇪🇸

    In this short note the QED extension of the nucleon spin sum rule is considered. To this end, the leading-order (LO) QED evolution kernels for the quark/gluon helicity and orbital-angular-momentum (OAM) distributions are calculated, as well as their lepton and photon analogue distributions introduced for the first time. The LO evolution kernels of the latter are also calculated, both in QCD and QED. Putting all together, the nucleon spin sum rule remains scale-invariant in QCD$\times$QED, as expected, which represents a check of the newly obtained results. This theoretical development will allow in the future the quantification of the contributions of lepton and photon distributions to the nucleon spin, and a more precise control over the uncertainties.

    hep-phPRD(2022)·0 citations
12. 12*

    Exploring the QGP phase above the deconfinement temperature in $pp$ and $A-A$ collisions at LHC energies

    Aditya Nath Mishra🇭🇺 · Guy Paić🇲🇽 · Carlos Pajares🇪🇸 · Rolf P Scharenberg🇺🇸 · Brijesh K Srivastava🇺🇸

    In the present work we have analyzed the transverse momentum spectra of charged particles in high multiplicity $pp$ collisions at LHC energies $\sqrt{s}=$ 5.02 and 13 TeV published by the ALICE Collaboration using the Color String Percolation Model (CSPM). For heavy ions Pb-Pb at $\sqrt{s_{NN}}=$ 2.76 and 5.02 TeV along with Xe-Xe at $\sqrt{s_{NN}}=$ 5.44 TeV have been analyzed. The initial temperature is extracted both in low and high multiplicity events in $pp$ collisions. For $A-A$ collisions the temperature is obtained as a function of centrality. A universal scaling in the temperature from $pp$ and $A-A$ collisions is obtained when multiplicity is scaled by the transverse interaction area.From the measured energy density $\mathbf{\epsilon }$ and the temperature the dimensionless quantity $\mathbf{\epsilon }/T^4$ is obtained. Our results for Pb-Pb and Xe-Xe collisions show a sharp increase in $\mathbf{\epsilon }/T^4$ above T $\sim$ 210 MeV and reaching the ideal gas of quarks and gluons value of $\mathbf{\epsilon }/T^4\sim$ 16 at temperature $\sim$ 230 MeV. In case of $pp$ collisions only $\mathbf{\epsilon }/T^4\sim$ 10 corresponding to $\sim$ 30 degrees of freedom.

    hep-phhep-exnucl-exNPA(2024)·11 citations
13. 13*

    Probing New Gauge Forces with a High-Energy Muon Beam Dump

    Cari Cesarotti🇺🇸 · Samuel Homiller🇺🇸 · Rashmish K. Mishra🇺🇸 · Matthew Reece🇺🇸

    We propose a new beam dump experiment at a future TeV-scale muon collider. A beam dump would be an economical and effective way to increase the discovery potential of the collider complex in a complementary regime. In this work we consider vector models such as the dark photon and $L_{\mu }-L_{\tau }$ gauge boson as new physics candidates and explore which novel regions of parameter space can be probed with a muon beam dump. We find that for the dark photon model, we gain sensitivity in the moderate mass (MeV - GeV) range at both higher and lower couplings compared to existing and proposed experiments, and gain access to previously untouched areas of parameter space of the $L_{\mu }-L_{\tau }$ model.

    hep-phPRL(2023)·62 citations
14. 14*

    The width difference in \bbm\ at order ${\alpha }_s$ and beyond

    Marvin Gerlach🇩🇪 · Ulrich Nierste🇩🇪 · Vladyslav Shtabovenko🇩🇪 · Matthias Steinhauser🇩🇪

    We complete the calculation of the element ${\Gamma }_{12}^q$ of the decay matrix in $B_q-{\bar{B}}_q$ mixing, $q=d,s$, to order ${\alpha }_s$ in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order ${\alpha }_s^2$, i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction $\Delta {\Gamma }_s/\Delta M_s=(5.20\pm 0.69)\cdot 10^{-3}$ if ${\Gamma }_{12}^s$ is expressed in terms of the $\overline{\mathrm{MS}}$ b-quark mass, while we find $\Delta {\Gamma }_s/\Delta M_s=(4.70\pm 0.96)\cdot 10^{-3}$ instead for the use of the pole mass.

    hep-phJHEP(2022)·24 citations
15. 15*

    Neutrino flavor oscillations in a rotating spacetime

    Himanshu Swami🇮🇳

    We study neutrino oscillations in a rotating spacetime under the weak gravity limit for the trajectories of neutrinos which are constrained in the equatorial plane. Using the asymptotic form of the Kerr metric, we show that the rotation of the gravitational source non-trivially modifies the neutrino phase. We find that the oscillation probabilities deviate significantly from the corresponding results in the Schwarzschild spacetime when neutrinos are produced near the black hole (still in the weak-gravity limit) with non-zero angular momentum and detected on the same side, i.e., the non-lensed neutrino. Moreover, for a given gravitational body and geometric parameters, there exists a distance scale for every energy scale (and vice versa), after which the rotational contribution in the neutrino phase becomes significant. Using the sun-sized gravitational body in the numerical analysis of the one-sided neutrino propagation, we show that even a small rotation of the gravitational object can significantly change the survival or appearance events of a neutrino flavor registered by the detector, which is located on the earth. These effects are expected to be prominent for cosmological/astrophysical scenarios where neutrinos travel past by many (rotating) gravitational bodies and for large distances. Thus rotational effects of all such bodies must be incorporated in analyzing oscillations data.

    hep-phgr-qchep-thEPJC(2022)·18 citations
16. 16*

    Gauge dependence of the quark gap equation: an exploratory study

    José Roberto Lessa🇧🇷 · Fernando E. Serna🇧🇷 · Bruno El-Bennich🇧🇷 · Adnan Bashir🇲🇽 · Orlando Oliveira🇵🇹

    We study the gauge dependence of the quark propagator in quantum chromodynamics by solving the gap equation with a nonperturbative quark-gluon vertex which is constrained by longitudinal and transverse Slavnov-Taylor identities, the discrete charge conjugation and parity symmetries and which is free of kinematic singularities in the limit of equal incoming and outgoing quark momenta. We employ gluon propagators in renormalizable $R_{\xi }$ gauges obtained in lattice QCD studies. We report the dependence of the nonperturbative quark propagator on the gauge parameter, in particular we observe an increase, proportional to the gauge-fixing parameter, of the mass function in the infrared domain, whereas the wave renormalization decreases within the range $0\le \xi \le 1$ considered here. The chiral quark condensate reveals a mild gauge dependence in the region of $\xi$ investigated. We comment on how to build and improve upon this exploratory study in future in conjunction with generalized gauge covariance relations for QCD.

    hep-phhep-latnucl-thPRD(2023)·20 citations
17. 17*

    Prospects for measuring the Hubble constant and dark energy using gravitational-wave dark sirens with neutron star tidal deformation

    Shang-Jie Jin🇨🇳 · Tian-Nuo Li🇨🇳 · Jing-Fei Zhang🇨🇳 · Xin Zhang🇨🇳

    Using the measurements of tidal deformation in the binary neutron star (BNS) coalescences can obtain the information of redshifts of gravitational wave (GW) sources, and thus actually the cosmic expansion history can be investigated using solely such GW dark sirens. To do this, the key is to get a large number of accurate GW data, which can be achieved with the third-generation (3G) GW detectors. Here we wish to offer an answer to the question of whether the Hubble constant and the equation of state (EoS) of dark energy can be precisely measured using solely GW dark sirens. We find that in the era of 3G GW detectors $\mathcal{O}(10^5-10^6)$ dark siren data (with the NS tidal measurements) could be obtained in three-year observation if the EoS of NS is perfectly known, and thus using only dark sirens can actually achieve the precision cosmology. Based on a network of 3G detectors, we obtain the constraint precisions of $0.15\%$ and $0.95\%$ for the Hubble constant $H_0$ and the constant EoS of dark energy $w$, respectively; for a two-parameter EoS parametrization of dark energy, the precision of $w_0$ is $2.04\%$ and the error of $w_a$ is 0.13. We conclude that 3G GW detectors would lead to breakthroughs in solving the Hubble tension and revealing the nature of dark energy provided that the EoS of NS is perfectly known.

    ↳ gr-qcastro-ph.COhep-phJCAP(2023)·68 citations
18. 18*

    Lattice calculation of the pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$

    R. Frezzotti🇮🇹 · G. Gagliardi🇮🇹 · V. Lubicz🇮🇹 · G. Martinelli🇮🇹 · F. Sanfilippo🇮🇹 · S. Simula🇮🇹

    We present a lattice calculation of the charged/neutral pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$ using the gauge configurations produced by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quark flavours at three values of the lattice spacing ($a\simeq 0.062,0.082,0.089\mathrm{fm}$) and pion masses in the range $M_{\pi }\simeq 250-500\mathrm{MeV}$. We employ the RM123 method and expand the path-integral around the isospin symmetric point at leading order in the electromagnetic coupling ${\alpha }_{em}$. Making use of the recently proposed RTM scheme, we evaluate the full $\mathcal{O}({\alpha }_{em})$ contribution, with the inclusion of the disconnected diagram. At the physical point, after performing the continuum and infinite volume extrapolation, we obtain the value $M_{{\pi }^{+}}-M_{{\pi }^0}=4.622(95)\mathrm{MeV}$ which is in good agreement with the experimental result $[M_{{\pi }^{+}}-M_{{\pi }^0}{]}^{exp.}=4.5936(5)\mathrm{MeV}$.

    ↳ hep-lathep-phPRD(2022)·15 citations
19. 19*

    Constraints on dark matter self-interaction from galactic core size

    Tirtha Sankar Ray🇮🇳 · Sambo Sarkar🇮🇳 · Abinash Kumar Shaw🇮🇳

    Self-interaction of particulate dark matter may help thermalising the central region of the galactic halo and driving core formation. The core radius is expectedly sensitive to the self-interaction strength of dark matter (DM). In this paper we study the feasibility of constraining dark matter self-interaction from the distribution of the core radius in isolated haloes. We perform systematic DM only $N$-body simulations of spherically symmetric isolated galactic haloes in the mass range of $10^{10}$-$10^{15}{M}_{\odot }$, incorporating the impact of isotropic DM self-interaction. Comparing the simulated profiles with the observational data, we provide a conservative upper limit on the self-interaction cross-section, $\sigma /m<$ $9.8$ $\mathrm{c}{\mathrm{m}}^2/\mathrm{gm}$ at $95\%$ confidence level. We report significant dependence of the derived bounds on the galactic density distribution models assumed for the analysis.

    ↳ astro-ph.GAhep-phJCAP(2022)·15 citations
20. 20*

    ALP induced polarization effects on photons from galaxy clusters

    Giorgio Galanti🇮🇹 · Marco Roncadelli🇮🇹 · Fabrizio Tavecchio🇮🇹 · Enrico Costa🇮🇹

    Many extensions of the Standard Model of particle physics and in particular superstring and superbrane theories predict the existence of axion-like particles (ALPs). ALPs are very elusive, extremely light and interact primarily with photons. In the presence of an external magnetic field two effects show up: (i) photon-ALP oscillations and (ii) a change of the photon polarization state. The astrophysical context represents the best opportunity to get indirect evidence for the ALP existence thanks to various effects that the photon-ALP interaction produces in the sky. Great attention has been paid so far to photon-ALP oscillations, since they modify the transparency of the crossed media at very high energies and so the final spectra of faraway sources exhibit a flux excess and a characteristic oscillatory behavior. Two hints at the ALP existence have hitherto been discovered. But less interest has been attracted by the modification of the photon polarization. In this paper we address it in the X-ray and in the high energy (HE) bands. Specifically, we analyze the photon degree of linear polarization and the polarization angle induced by the photon-ALP interaction for photons generated in the central region of two galaxy clusters: Perseus and Coma. We find a substantial departure from conventional physics in both considered bands. We conclude that the ALP-induced polarization effects are more likely detectable with the proposed missions like COSI (approved to launch), e-ASTROGAM and AMEGO in the HE range. Still, possible ALP-induced effects on photon polarization could also be detected by IXPE (already operative) and by the proposed eXTP, XL-Calibur, NGXP and XPP in the X-ray band.

    ↳ astro-ph.HEhep-phPRD(2023)·24 citations
21. 21*

    Feynman Polytopes and the Tropical Geometry of UV and IR Divergences

    Nima Arkani-Hamed🇺🇸 · Aaron Hillman🇺🇸 · Sebastian Mizera🇺🇸

    We introduce a class of polytopes that concisely capture the structure of UV and IR divergences of general Feynman integrals in Schwinger parameter space, treating them in a unified way as worldline segments shrinking and expanding at different relative rates. While these polytopes conventionally arise as convex hulls - via Newton polytopes of Symanzik polynomials - we show that they also have a remarkably simple dual description as cut out by linear inequalities defining the facets. It is this dual definition that makes it possible to transparently understand and efficiently compute leading UV and IR divergences for any Feynman integral. In the case of the UV, this provides a transparent geometric understanding of the familiar nested and overlapping divergences. In the IR, the polytope exposes a new perspective on soft/collinear singularities and their intricate generalizations. Tropical geometry furnishes a simple framework for calculating the leading UV/IR divergences of any Feynman integral, associating them with the volumes of certain dual cones. As concrete applications, we generalize Weinberg's theorem to include a characterization of IR divergences, and classify space-time dimensions in which general IR divergences (logarithmic as well as power-law) can occur. We also compute the leading IR divergence of rectangular fishnet diagrams at all loop orders, which turn out to have a surprisingly simple combinatorial description.

    ↳ hep-thhep-phPRD(2022)·69 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.