Anomalous dimension of transverse momentum broadening in planar N=4\mathcal{N}=4 SYM

The typical transverse momentum $Q_s(t)$ (or "saturation" momentum) acquired by a hard particle propagating through a $\mathcal{N}=4$ SYM plasma increases over time like $t^\gamma$, with an anomalous exponent $\gamma>1/2$ characteristic of super-diffusion. This anomalous exponent is a function of the 't Hooft coupling $\lambda=g^2N_c$. Recently, a method has been proposed to systematically compute the perturbative series of $\gamma(\lambda)$ at weak coupling. This method relies on the traveling wave interpretation of the time evolution of $Q_s(t)$ and on the dominance of soft-collinear radiative corrections at large times. In this paper, we compute $\gamma(\lambda)$ up to $\mathcal{O}(\lambda^{2})$ using the double logarithmic behaviour of the BFKL equation in planar $\mathcal{N}=4$ SYM at three loops. This calculation allows us to discuss the transition towards the strong coupling regime where AdS/CFT calculations predict $\gamma\to 1$.Comment: 8 pages, 1 figure, contribution to the proceedings of the "XVth International Conference on Quark Confinement and the Hadron Spectrum

Universality aspects of quantum corrections to transverse momentum broadening in QCD media

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with L\'{e}vy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient $\hat q$ and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.Comment: 57 pages, 15 figure

Towards a cosmological neutrino mass detection

Future cosmological measurements should enable the sum of neutrino masses to be determined indirectly through their effects on the expansion rate of the Universe and the clustering of matter. We consider prospects for the gravitationally lensed Cosmic Microwave Background anisotropies and Baryon Acoustic Oscillations in the galaxy distribution, examining how the projected uncertainty of $\approx15$ meV on the neutrino mass sum (a 4$\sigma$ detection of the minimal mass) might be reached over the next decade. The current 1$\sigma$ uncertainty of $\approx 103$ meV (Planck-2015+BAO-15) will be improved by upcoming 'Stage-3' CMB experiments (S3+BAO-15: 44 meV), then upcoming BAO measurements (S3+DESI: 22 meV), and planned next-generation 'Stage 4' CMB experiments (S4+DESI: 15-19 meV, depending on angular range). An improved optical depth measurement is important: the projected neutrino mass uncertainty increases to $26$ meV if S4 is limited to $\ell>20$ and combined with current large-scale polarization data. Looking beyond $\Lambda$CDM, including curvature uncertainty increases the forecast mass error by $\approx$ 50% for S4+DESI, and more than doubles the error with a two-parameter dark energy equation of state. Complementary low-redshift probes including galaxy lensing will play a role in distinguishing between massive neutrinos and a departure from a $w=-1$, flat geometry.Comment: Submitted to PRD. 15 pages, 10 figure

Transverse momentum broadening from NLL BFKL to all orders in pQCD

We study, to all orders in perturbative QCD, the universal behavior of the saturation momentum $Q_s(L)$ controlling the transverse momentum distribution of a fast parton propagating through a dense QCD medium with large size $L$. Due to the double logarithmic nature of the quantum evolution of the saturation momentum, its large $L$ asymptotics is obtained by slightly departing from the double logarithmic limit of either next-to-leading log (NLL) BFKL or leading order DGLAP evolution equations. At fixed coupling, or in conformal $\mathcal{N}=4$ SYM theory, we derive the large $L$ expansion of $Q_s(L)$ up to order $\alpha_s^{3/2}$. In QCD with massless quarks, where conformal symmetry is broken by the running of the strong coupling constant, the one-loop QCD $\beta$-function fully accounts for the universal terms in the $Q_s(L)$ expansion. Therefore, the universal coefficients of this series are known exactly to all orders in $\alpha_s$.Comment: 13 pages, 4 figures, 3 appendice

Anomalous diffusion in QCD matter

We study the effects of quantum corrections on transverse momentum broadening of a fast parton passing through dense QCD matter. We show that, at leading logarithmic accuracy the broadening distribution tends at late times or equivalently for large system sizes $L$ to a universal distribution that only depends on a single scaling variable $k^2_\perp/Q^2_s$ where the typical transverse momentum scale increases with time as $\ln Q_s^2 \simeq (1+2 \beta ) \ln L - \frac{3}{2}(1+\beta )\,\ln\ln L$ up to non-universal terms, with an anomalous dimension $\beta \sim \sqrt{\alpha_s}$. This property is analogous to geometric scaling of gluon distributions in the saturation regime and traveling waves solutions to reaction-diffusion processes. We note that since $\beta >0$ the process is super-diffusive, which is also reflected at large transverse momentum where the scaling distribution exhibits a heavy tail $k_\perp^{4-2\beta }$ akin to L\'{e}vy random walks.Comment: 10 pages, 3 figures, 3 supplemental material

Anomalous dimension of transverse momentum broadening in planar = 4 SYM

The typical transverse momentum Qs(t) (or "saturation" momentum) acquired by a hard particle propagating through a N = 4 SYM plasma increases over time like tγ, with an anomalous exponent γ > 1/2 characteristic of super-diffusion. This anomalous exponent is a function of the ’t Hooft coupling λ = g2Nc. Recently, a method has been proposed to systematically compute the perturbative series of γ(λ) at weak coupling. This method relies on the traveling wave interpretation of the time evolution of Qs(t) and on the dominance of softcollinear radiative corrections at large times. In this paper, we compute γ(λ) up to (λ2) using the double logarithmic behaviour of the BFKL equation in planar = 4 SYM at three loops. This calculation allows us to discuss the transition towards the strong coupling regime where AdS/CFT calculations predict γ→1

Back-to-back inclusive dijets in DIS at small xx: Complete NLO results and predictions

We compute the back-to-back dijet cross-section in deep inelastic scattering (DIS) at small $x$ to next-to-leading order (NLO) in the Color Glass Condensate effective field theory. Our result can be factorized into a convolution of the Weizs\"{a}cker-Williams gluon transverse momentum dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum $P_\perp$ of the dijet pair to the dijet momentum imbalance $q_\perp$; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in $x$ that is kinematically constrained to satisfy both lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.Comment: 41 pages, 9 figures, 5 supplemental materials, to be published in Physical Review Letter

Cold gas and a Milky Way-type 2175 {\AA} bump in a metal-rich and highly depleted absorption system

We report the detection of a strong Milky Way-type 2175 \AA$$ extinction bump at $z$ = 2.1166 in the quasar spectrum towards SDSS J121143.42+083349.7 from the Sloan Digital Sky Survey (SDSS) Data Release 10. We conduct follow up observations with the Echelle Spectrograph and Imager (ESI) onboard the Keck-II telescope and the Ultraviolet and Visual Echelle Spectrograph (UVES) on the VLT. This 2175 \AA$$ absorber is remarkable in that we simultaneously detect neutral carbon (C I), neutral chlorine (Cl I), and carbon monoxide (CO). It also qualifies as a damped Lyman alpha system. The J1211+0833 absorber is found to be metal-rich and has a dust depletion pattern resembling that of the Milky Way disk clouds. We use the column densities of the C I fine structure states and the C II/C I ratio (under the assumption of ionization equilibrium) to derive the temperature and volume density in the absorbing gas. A Cloudy photoionization model is constructed, which utilizes additional atoms/ions to constrain the physical conditions. The inferred physical conditions are consistent with a canonical cold (T $\sim$ 100 K) neutral medium with a high density ($n$(H I) $\sim$ 100 cm$^{-3}$) and a slightly higher pressure than the local interstellar medium. Given the simultaneous presence of C I, CO, and the 2175 \AA$$ bump, combined with the high metallicity, high dust depletion level and overall low ionization state of the gas, the absorber towards J1211+0833 supports the scenario that the presence of the bump requires an evolved stellar population.Comment: 18 pages, 17 figures, to be published in MNRA

Anomalous dimension of transverse momentum broadening in planar N=4\mathcal{N}=4 SYM

International audienceThe typical transverse momentum $Q_s(t)$ (or "saturation" momentum) acquired by a hard particle propagating through a $\mathcal{N}=4$ SYM plasma increases over time like $t^\gamma$, with an anomalous exponent $\gamma>1/2$ characteristic of super-diffusion. This anomalous exponent is a function of the 't Hooft coupling $\lambda=g^2N_c$. Recently, a method has been proposed to systematically compute the perturbative series of $\gamma(\lambda)$ at weak coupling. This method relies on the traveling wave interpretation of the time evolution of $Q_s(t)$ and on the dominance of soft-collinear radiative corrections at large times. In this paper, we compute $\gamma(\lambda)$ up to $\mathcal{O}(\lambda^{2})$ using the double logarithmic behaviour of the BFKL equation in planar $\mathcal{N}=4$ SYM at three loops. This calculation allows us to discuss the transition towards the strong coupling regime where AdS/CFT calculations predict $\gamma\to 1$