Calculating b-quark production cross sections at hadron-hadron colliders

Fred Olness , Southern Methodist University
(Original posting: Summer 2000)

Large momentum transfer production of particles and jets provided some of the early tests of QCD. Indeed, by taking into account quark and gluon initiated scattering processes, QCD was able to explain the relatively large cross sections observed at the CERN ISR. However, as the precision of the experiments increased, there was a corresponding need for increased theoretical precision. Discrepancies now exist between theory and data for several large momentum transfer processes. One such long-standing problem in QCD is the calculation of the cross section for the production of b-quarks at high energy hadron colliders. The state of this problem is easily surmised by examining the figure shown below (taken from the 1999 CERN LHC Workshop hep-ph/0003142 ) which shows the integrated transverse momentum spectrum for b production at the Tevatron vs. p_T. Clearly, the Tevatron data are approximately a factor of 2 above the theoretical bands. Another unsettling feature of this plot is that there is large theoretical uncertainty, despite the fact that this is a NLO calculation. This problem has existed (in various forms) for more than 10 years; a similar discrepancy is also observed in UA1 data.

b-quark cross section vs. p_T.

Please feel free to send any solutions to this puzzle to PRL and the NY Times. Comments on this entry may be sent to Fred Olness.


Note Added (May 2002):

There has been quite a bit of work in this area recently.

A recent paper (R. Field PRD65 (2002) 094006 ) uses leading-order Monte Carlo calculations with both flavor creation (g g -> b b-bar) and flavor excitation (g b -> g b) including fragmentation. The result of the calculation is shown below.

See also Kuebel et al., (PRD43:767,1991 ; Fig.9 in particular) for a comparison of bottom-quark production rates in ISAJET with a full QCD 2-->3 calculation.

The  physics modelling for production and hadronization of heavy quarks is described by Norrbin and Sjostrand in EPJ.C17:137,2000.



In a separate study (Cacciari and Nason hep-ph/0204025), the B fragmentation function was re-analyzed. Using this updated fragmentation function, they obtain the following comparison with data.



Finally,in a recent report (hep-ex/0012061 ) John Womersley made the following interesting comparison between the b-jet data and the direct-photon data.

 

For the application of kt factorization supplemented with the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) small-x evolution equation,  see H. Jung, PRD.65.034015.

A recent paper (Berger et al., PRL 86 (2001) 4231 ) demonstrates that pair production of low-mass gluinos that decay into bottom quarks and bottom squarks provides a good description of the b-cross section and reproduces the measured ratio of like-sign to opposite-sign leptons with assumptions consistent with experimental constraints on SUSY particle masses.


Some References:

This list is not intended to be comprehensive, and only  serve as a starting point.  (See the Standard Disclaimer. )
 

THE ORIGINAL NLO CALCULATIONS

THE TOTAL CROSS-SECTION FOR THE PRODUCTION OF HEAVY QUARKS IN HADRONIC COLLISIONS.  By P. Nason, S. Dawson (Brookhaven), R.K. Ellis (Fermilab). FERMILAB-PUB-87-222-T, BNL-40718, Dec 1987. 41pp. Published in Nucl.Phys.B303:607,1988

QCD CORRECTIONS TO HEAVY QUARK PRODUCTION IN P ANTI-P COLLISIONS.  By W. Beenakker, H. Kuijf, W.L. van Neerven (Leiden U.), J. Smith (SUNY, Stony Brook). PRINT-88-0717 (LEIDEN), ITP-SB-88-13, Sep 1988. 82pp. Published in Phys.Rev.D40:54-82,1989

RECENT EXPERIMENTAL MEASUREMENTS

MEASUREMENT OF BOTTOM QUARK PRODUCTION IN 1.8-TEV P ANTI-P COLLISIONS USING SEMILEPTONIC DECAY MUONS.  By CDF Collaboration (F. Abe et al.). FERMILAB-PUB-93-145-E, Jun 1993. 14pp.  Published in Phys.Rev.Lett.71:2396-2400,1993

INCLUSIVE MU AND B QUARK PRODUCTION CROSS-SECTIONS IN P ANTI-P COLLISIONS AT S**(1/2) = 1.8-TEV.  By D0 Collaboration (S. Abachi et al.). FERMILAB-PUB-94-409-E, Dec 1994. 13pp.  Published in Phys.Rev.Lett.74:3548-3552,1995

TEVATRON RESULTS ON B-QUARK CROSS-SECTIONS AND CORRELATIONS. By D0 and CDF Collaborations (D.K. Fein for the collaboration). FERMILAB-CONF-99-050-E, Mar 1999. 5pp. Given at 13th Topical Conference on Hadron Collider Physics, Mumbai, India, 14-20 Jan 1999.

A COMPREHENSIVE REVIEW

HEAVY QUARK PRODUCTION. By Stefano Frixione (Zurich, ETH), Michelangelo L. Mangano, Paolo Nason (CERN), Giovanni Ridolfi (INFN, Genoa). CERN-TH-97-16, Feb 1997. 100pp.  in Heavy Flavours II, ed. by A.J. Buras and M. Lindner, World Scientific, p 609-706.

RECENT WORKSHOP REPORTS

BOTTOM PRODUCTION. By P. Nason, et al., May 1999. 74pp. To appear in the Report of the '1999 CERN Workshop on SM physics (and more) and the LHC'.  To be published in the proceedings of Workshop on Standard Model Physics (and more) at the LHC (First Plenary Meeting), Geneva, Switzerland, 25-26 May 1999.

HEAVY QUARK PRODUCTION AND PDF'S SUBGROUP REPORT. By R. Demina et al.,Jun 1999. 8pp.  Contributed to Physics at Run II: QCD and Weak Boson Physics Workshop: 2nd General Meeting, Batavia, Illinois, 3-4 Jun 1999.