Single- and central-diffractive production of open charm and bottom mesons at the LHC
aa r X i v : . [ h e p - ph ] O c t Single- and central-diffractive productionof open charm and bottom mesons at the LHC ∗ Marta Luszczak, Rafa l Maciu la and Antoni Szczurek
University of Rzesz´ow, Rejtana 16, 35-959 Rzesz´ow, PolandandH.Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences,Radzikowskiego 152, 31-342 Krak´ow, PolandWe discuss diffractive production of open charm and bottom mesons atthe LHC. The differential cross sections for single- and central-diffractivemechanisms for c ¯ c and b ¯ b pair production are calculated in the frameworkof the Ingelman-Schlein model corrected for absorption effects. The LOgluon-gluon fusion and quark-antiquark anihilation partonic subprocessesare taken into consideration, which are calculated within standard collinearapproximation. The extra corrections from reggeon exchanges are takeninto account. The hadronization of charm and bottom quarks is taken intoaccount by means of fragmentation functions. Predictions for single- andcentral-diffractive production in the case of D and B mesons, as well as D ¯ D pairs are presented, including detector acceptance of the ATLAS, CMS andLHCb Collaborations.PACS numbers: 13.87.Ce,14.65.Dw
1. Introduction
On theoretical side diffractive processes are related with exchange ofpomeron or processes with the QCD amplitude without net color exchange.In such processes pomeron must be treated rather technically, dependingon the formulation of the approach. Experimentally such processes are de-fined by special requirement(s) on the final state. The most popular is arequirement of rapidity gap starting from the final proton(s) on one (single-diffrative process) or both (central-diffractive process) sides. Several pro-cesses with different final states were studied at HERA, such as dijet, charm ∗ Presented at the 16th conference on Elastic and Diffractive scattering, EDS Blois2015 (1)
Marta˙Luszczak printed on July 11, 2018 production, etc. The H1 Collaboration has found a set of so-called diffractiveparton distributions in the proton inspired by the Ingelman-Schlein model[1], which we will use in the presented studies. In this fit both pomeron andreggeon contributions were included.In hadronic processes so far only some selected diffractive processes werediscussed in the literature such as diffractive production of dijets [2], produc-tion of W [3] and Z [4] bosons, production of W + W − pairs [5] or productionof c ¯ c [6]. The latter was done there only for illustration of the general sit-uation at the parton level. The cross section for diffractive processes are ingeneral rather small, (e.g. the single-diffractive processes are of the orderof a few percent compared to inclusive cross sections).
2. Theoretical framework
The mechanisms of the diffractive production of heavy quarks ( c ¯ c , b ¯ b )discussed here are shown in Figs. 1 and 2. Both, LO gg-fusion and q ¯ q -anihilation partonic subprocesses are taken into account in the calculations. a) b) IP,IRp p p ′ Y XQ ¯ Qgg IP,IRp p p ′ Y XQ ¯ Qq f (¯ q f )¯ q f ( q f ) IP,IRp p p ′ Y XQ ¯ Qgg IP,IRp p p ′ Y XQ ¯ Q ¯ q f ( q f ) q f (¯ q f ) Fig. 1. The mechanisms of single-diffractive production of heavy quarks.
IP,IRp p p ′ Y Y Q ¯ Qg p ′ IP,IR g IP,IRp p p ′ Y Y Q ¯ Q ¯ q f ( q f ) p ′ IP,IR q f (¯ q f ) Fig. 2. The mechanisms of central-diffractive production of heavy quarks.
In the following we apply the Ingelman-Schlein approach [1]. Details ofour calculations of corresponding differential cross sections can be found inRef. [7]. arta˙Luszczak printed on July 11, 2018 In Fig. 3 we show the transverse momentum distribution of c quarks (an-tiquarks) and b quarks (antiquarks) for single-diffractive production at √ s =14 TeV. Components of the pomeron-gluon (and gluon-pomeron) are almosttwo orders of magnitude larger than the pomeron-quark(antiquark) andquark(antiquark)-pomeron. The estimated reggeon contribution is slightlysmaller.Different models of absorption corrections (one-, two- or three-channelapproaches) for diffractive processes were presented in the literature. Theabsorption effects for the diffractive processes were calculated e.g. in [8, 9, 4].The different models give slightly different predictions. Usually an averagevalue of the gap survival probability < | S G | > is calculated first and thenthe cross sections for different processes is multiplied by this value. Wefollow this somewhat simplified approach. Numerical values of the gapsurvival probability can be found in [8, 9, 4]. The multiplicative factorsare S G = 0.05 for single-diffractive production and S G = 0.02 for central-diffractive one for the nominal LHC energy ( √ s = 14 TeV). (GeV) t p ( nb / G e V ) t / dp σ d -3 -2 -1 X (SD)c p c → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq I P - g l uon I R - g l uon I P - qua r k I R - qua r k = 0.05 G S = m µ |y| < 8.0 (GeV) t p ( nb / G e V ) t / dp σ d -3 -2 -1 X (SD)b p b → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq I P - g l uon I R - g l uon I P - qua r k I R - qua r k = 0.05 G S = m µ |y| < 8.0 Fig. 3. Transverse momentum distribution of c quarks (antiquarks) (left) and b quarks (antiquarks) (right) for single-diffractive production at √ s = 14 TeV. In Fig. 4 we show the transverse momentum distribution of c quarks(antiquarks) and b quarks (antiquarks) for central-diffractive production at √ s = 14 TeV. The distributions for central-dffractive component is smallerthan that for the single-diffractive distributions by almost two orders ofmagnitude.In Fig. 5 we show separately contributions for different upper limitsfor the value of x IP and x IR . The shape of these distributions are rathersimilar. As a default, in the case of pomeron exchange the upper limit inthe convolution formula is taken to be 0.1 and for reggeon exchange 0.2.Figures 6 and 7 show rapidity distributions for c quarks (antiquarks)(left panels) and b quarks (antiquarks) (right panels) production for single- Marta˙Luszczak printed on July 11, 2018 (GeV) t p ( nb / G e V ) t / dp σ d -3 -2 -1 X (CD)c p c → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq I P - I P I R - I R I P - I P I R - I R = 0.05 G S = m µ |y| < 8.0 I P - I R and I R - I P I P - I R and I R - I P (GeV) t p ( nb / G e V ) t / dp σ d -3 -2 -1 X (CD)b p p b → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq I P - I P I R - I R I P - I P I R - I R = 0.02 G S = m µ |y| < 8.0 I P - I R and I R - I P I P - I R and I R - I P Fig. 4. Transverse momentum distribution of c quarks (antiquarks) (left) and b quarks (antiquarks) (right) for the central-diffractive production at √ s = 14 TeV. (GeV) t p ( nb / G e V ) t / dp σ d -2 -1 X (SD)c p c → p p = 14 TeVs IP-gluon (solid)IR-gluon (dashed) < . po m x < . po m x < . r eg x < . r eg x = 0.05 G S = m µ |y| < 8.0 (GeV) t p ( nb / G e V ) t / dp σ d -2 -1 X (SD)b p b → p p = 14 TeVs IP-gluon (solid)IR-gluon (dashed) < . po m x < . po m x < . r eg x < . r eg x = 0.05 G S = m µ |y| < 8.0 Fig. 5. Transverse momentum distribution of c quarks (antiquarks) (left) and b quarks (antiquarks) (right) for single-diffractive production at √ s = 14 TeV fordifferent maximal x IP (solid) and x IR (dashed). and central-diffractive mechanisms, respectively. The rapidity distribu-tions for pomeron-gluon (and gluon-pomeron), pomeron-quark(antiquark)(and quark(antiquark)-pomeron) and reggeon-gluon (and gluon-reggeon),reggeon-quark(antiquark) (and quark(antiquark)-reggeon) mechanisms inthe single-diffractive case are shifted to forward and backward rapidities,respectively. The distributions for the individual single-diffractive mecha-nisms have maxima at large rapidities, while the central-diffractive contri-bution is concentrated at midrapidities. This is a consequence of limitingintegration: 0.0 < x IP < x IR to 0.0 < x IR < D and B ± mesons production Measurements of charm and bottom cross sections at hadron collidersis based on full reconstruction of all decay products of open charm and arta˙Luszczak printed on July 11, 2018 y -8 -6 -4 -2 0 2 4 6 8 ( nb ) / d y } σ d -1 X (SD)c p c → p p X (SD)c p c → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq IP-gluon IR-gluonIP-quarkIR-quark gluon-IPgluon-IR quark-IPquark-IR = 0.05 G S = m µ < 30.0 t p y -8 -6 -4 -2 0 2 4 6 8 ( nb ) / d y } σ d -2 -1 X (SD)b p b → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq IP-gluonIR-gluonIP-quarkIR-quark gluon-IPgluon-IRquark-IPquark-IR = 0.05 G S t = m µ < 30.0 t p Fig. 6. Rapidity distribution of c quarks (antiquarks) (left) and b quarks (anti-quarks) (right) for single-diffractive production at √ s = 14 TeV. y -8 -6 -4 -2 0 2 4 6 8 ( nb ) / d y } σ d -1 X (CD)c p p c → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq IP-IPsumIR-IRIP-IPIR-IRIP-IR and IR-IPIP-IR and IR-IP = 0.02 G S = m µ < 30.0 t p y -8 -6 -4 -2 0 2 4 6 8 ( nb ) / d y } σ d -3 -2 -1 X (CD)b p p b → p p = 14 TeVs gg-fusion (solid)-annihilation (dashed)qq IP-IPsumIR-IRIP-IPIR-IRIP-IR and IR-IPIP-IR and IR-IP = 0.02 G S = m µ < 30.0 t p Fig. 7. Rapidity distribution of c quarks (antiquarks) (left) and b quarks (anti-quarks) (right) for the central-diffractive production at √ s = 14 TeV. bottom mesons, for instance in the D → K − π + , D + → K − π + π + or B + → J/ψK + → K + µ + µ − channels. The decay products with an invariant massfrom the expected hadron decay combinations, permit direct observationof D or B meson as a peak in relevant invariant mass spectrum. Then,after a substraction of invariant mass continuum background the relevantcross section for the meson production is obtained. The same method canbe applied for measurement of charm and bottom production rates for thediffractive events.Numerical predictions of the integrated cross sections for the single-and central-diffractive production of D and B ± mesons, including rele-vant experimental acceptance of the ATLAS, LHCb and CMS detectors,are collected in Table 1. The kinematical cuts are taken to be identical tothose which have been already used in the standard non-diffractive measure-ments. The corresponding experimental cross sections for non-diffractiveprocesses are shown for reference. In the case of inclusive production of Marta˙Luszczak printed on July 11, 2018
Table 1. Integrated cross sections for diffractive production of open charm andbottom mesons in different measurement modes for ATLAS, LHCb and CMS ex-periments at √ s = 14 TeV. Acceptance Mode Integrated cross sections, [nb]single-diffractive central-diffractive non-diffractiveEXP dataATLAS, | y | < . D + D IR : 25%) 177.35 ( IR : 43%) − p ⊥ > . < y < . D + D IR : 31%) 2526.7 ( IR : 50%) 1488000 ± p ⊥ < | y | < . B + + B − ) / IR : 24%) 14.24 ( IR : 42%) 28100 ± ± p ⊥ > < y < . B + + B − IR : 27%) 31.03 ( IR : 43%) 41400 ± ± p ⊥ <
40 GeVLHCb, 2 < y < D D IR : 28%) 7.67 ( IR : 45%) 6230 ± ± < p ⊥ <
12 GeV single D or B meson the ratio of the diffractive integrated cross sections tothe non-diffractive one is about ∼
2% for single- and only about ∼ .
07% forcentral-diffractive mechanism. This ratio is only slightly bigger for D D pair production, becoming of about ∼
3% and 0 . ∼ −
31% for single-diffractive (
IRIP + IR ) and ∼ − IP IR + IRIP + IRIRIP IP + IP IR + IRIP + IRIR ) for both, charm andbottom flavoured mesons.
3. Conclusion
In the present study we discuss in detail single- and central- diffrac-tive production of charm and bottom quark-antiquark pairs as well as opencharmed and bottom mesons. The corresponding cross sections are ratherlarge. First we have presented cross sections for c ¯ c and b ¯ b production insingle and central production. Several quark-level differential distributionsare shown and discussed. We have compared pomeron and reggeon contri-butions. In order to make predictions which could be compared with futureexperimental data we have included hadronization to charmed ( D ) and bot-tom ( B ) mesons using hadronization functions known for other processes.We have shown several inclusive differential distributions for the mesonsas well as correlations of D and ¯ D mesons. In these calculations we haveincluded detector acceptance of the ATLAS, CMS and LHCb collaborationexperiments. The production of charmed mesons is interesting because ofthe cross section of the order of a few microbarns for ATLAS and CMS and arta˙Luszczak printed on July 11, 2018 of the order of tens of microbarns for the LHCb acceptance and could bemeasured. We have shown that the pomeron contribution is much largerthan the subleading reggeon contribution. Acknowledgments
This study was partially supported by the Polish National Science Cen-tre grant DEC-2013/09/D/ST2/03724.REFERENCES [1] G. Ingelman, P.E. Schlein, Phys. Lett. B152 256 (1985).[2] M. Klasen, G. Kramer, Phys. Rev.
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