Small x behavior of parton distributions with soft initial conditions

Kotikov, A. V.; Parente, G.

doi:10.1016/s0550-3213(99)00107-8

Cited by 99 publications

(209 citation statements)

References 66 publications

Supporting

Mentioning

199

Contrasting

Order By: Relevance

“…(13)- (15) (dashed lines) and the BBT results evaluated from Eqs. (17) and (18) (dash-dotted line), which are hardly distinguishable from one another, are shown in Fig. 1.…”

mentioning

confidence: 94%

See 1 more Smart Citation

Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

2011

View full text Add to dashboard Cite

We present a simple formula for the total cross section σ νN of neutral-and charged-current deepinelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F νN 2 (M 2 V /s, M 2 V ), where MV is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in the front of F νN 2 (x, Q 2 ) depends on the asymptotic low-x behavior of F νN 2 . It contains an additional ln s term if F νN 2 scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F νN 2 ∝ ln 2 (1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on σ νN .PACS numbers: 13.15.+g, 13.85.Hd, 25.30.Pt, 95.85.Ry For more than a decade, large experiments have been searching for ultrahigh-energy (UHE) cosmic neutrinos (ν), with energies E ν > 10 6 GeV, using detectors scanning for events in large volumes of water, ice, the Earth's atmosphere, and the lunar regolith [1]. While no clear indication of such an event has yet been reported, experimental bounds on UHE-neutrino fluxes could be established, which, put together, now cover energies way up to 10 12 GeV and start to constrain scenarios of astrophysical interest. Since these limits directly depend on the total cross section σ νN (E ν ) of UHE-neutrino deep-inelastic scattering (DIS) off nucleons (N ), it is an urgent task to provide reliable theoretical predictions for the latter in the asymptotic high-E ν regime, which lies far beyond the one explored by laboratory-based νN DIS experiments and corresponds to asymptotically low values of Bjorken's scaling variable x. This requires extrapolation over several orders of magnitude in E ν , for which various approaches exist [2][3][4][5][6][7][8]. These are based on successful descriptions of the terrestrial data within the framework of perturbative QCD and frequently impose the Froissart bound [9] on σ νN . According to the latter, unitarity and analyticity limit the total cross section of a scattering process not to grow faster with energy than ln 2 s.In this Letter, we derive a general formula for σ νN that is remarkably concise and correctly accounts for the asymptotic high-energy behavior making it perfectly suitable for UHE-neutrino phenomenology. It is proportional to the DIS structure function F νN 2 (x, Q 2 ), which has a well-known representation in terms of parton distribution functions (PDFs) within the parton model (PM) of QCD, with x and the typical energy scale Q appropriately defined in terms of E ν and M V (V = W, Z). To be on the conservative side, we assume for the time being, as in Refs. [2][3][4][5][6][7][8], that the available experimental data on DIS allow for an extrapolation to very high (low) values of E ν (x) using an appropriate parameterization of F νN 2 . If the latter rises too steeply as x → 0, then possible new QCD phenomena, such as gluon saturation or recombination, color glass condensates, multiple pomeron exchanges, etc., are expected to enter the stage as a ...

show abstract

“…(13)- (15) (dashed lines) and the BBT results evaluated from Eqs. (17) and (18) (dash-dotted line), which are hardly distinguishable from one another, are shown in Fig. 1.…”

mentioning

confidence: 94%

“…This violation of the Froissart bound is attributed to the presence of the ln 2 x term in Eq. (17). On the other hand, if In fact, this is the case for the original H ansatz [20], B ln(x 0 /x) ln(1 + Q 2 /Q 2 0 ), which contains just three fit parameters.…”

mentioning

confidence: 98%

Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

2011

View full text Add to dashboard Cite

show abstract

“…The original study of [11] was extended in [12,13,14] to include the finite parts of anomalous dimensions of Wilson operators 1 . This has led to predictions [13,14] of the small-x asymptotic form of parton distribution functions (PDFs) in the framework of the DGLAP dynamics starting at some Q 2 0 with the flat function…”

Section: Generalized Doubled Asymptotic Scaling Approachmentioning

confidence: 99%

“…This has led to predictions [13,14] of the small-x asymptotic form of parton distribution functions (PDFs) in the framework of the DGLAP dynamics starting at some Q 2 0 with the flat function…”

Section: Generalized Doubled Asymptotic Scaling Approachmentioning

confidence: 99%

See 1 more Smart Citation

Q2-evolution of parton densities at small x values and H1 and ZEUS experimental data

Kotikov¹,

Shaikhatdenov²

2014

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. It is shown that in the leading twist approximation of the Wilson operator product expansion with "frozen" and analytic strong coupling constants, considering the Bessel-inspired behavior of the structure functions F 2 and the derivative ∂ ln F 2 /∂ ln(1/x) at small x values, obtained for a flat initial condition in the DGLAP evolution equations, leads to a good agreement with the deep inelastic scattering H1 and ZEUS experimental data from HERA.

show abstract

The next-to-leading order (NLO) gluon distribution from DGLAP equation and the logarithmic derivatives of the proton structure functionF 2(x, Q 2) at lowx

Choudhury

Sahariah

2005

Pramana - J Phys

View full text Add to dashboard Cite

Small x behavior of parton distributions with soft initial conditions

Cited by 99 publications

References 66 publications

Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

Q2-evolution of parton densities at small x values and H1 and ZEUS experimental data

The next-to-leading order (NLO) gluon distribution from DGLAP equation and the logarithmic derivatives of the proton structure functionF 2(x, Q 2) at lowx

Contact Info

Product

Resources

About