PHYSICAL REVIEW D 98, 036014 (2018) Heavy P-wave quarkonium production via Higgs decays † ‡ Qi-Li Liao,1,* Ya Deng,1, Yan Yu, 1, Guang-Chuan Wang,1 and Guo-Ya Xie2 1College of Mobile Telecommunications Chongqing University of Posts and Telecom, Chongqing 401520, People’s Republic of China 2Chongqing University of Posts and Telecom, Chongqing 400065, People’s Republic of China (Received 6 July 2018; published 21 August 2018) The production of the heavy quarkonium, i.e., jðcb¯Þ½ni (or jðbc¯Þ½ni), jðcc¯Þ½ni, and jðbb¯Þ½ni- ¯ 0 0 quarkonium [jðQQ Þ½ni-quarkonium for short], through Higgs H boson semiexclusive decays is evaluated within the nonrelativistic quantum chromodynamics (NRQCD) framework, where [n] stands ¯ 0 1 ¯ 0 3 for the production of the two color-singlet S-wave states, jðQQ Þ½ S01i and jðQQ Þ½ S11i, the production ¯ 0 1 ¯ 0 3 of the four color-singlet P-wave states, i.e., jðQQ Þ½ P01i, jðQQ Þ½ PJ1i (with J ¼½0; 1; 2). Moreover, according to the velocity scaling rule of the NRQCD, the production of the two color-octet components, ¯ 0 1 ¯ 0 3 jðQQ Þg½ S08i and jðQQ Þg½ S18i, are also taken into account. The “improved trace technology” to derive the simplified analytic expressions at the amplitude level is adopted, which shall be useful for dealing with these decay channels. If all higher heavy quarkonium states decay completely to the ground states, 0 ¯ 1 0 1 it should be obtained ΓðH → jðcbÞ½ S01iÞ ¼ 15.14 KeV, ΓðH → jðcc¯Þ½ S01iÞ ¼ 1.547 KeV, and 0 ¯ 1 5 4 ΓðH → jðbbÞ½ S01iÞ ¼ 1.311 KeV. The production of 5.6 × 10 Bc meson, 4.7 × 10 charmonium meson, and 4.9 × 104 bottomonium meson per year in Higgs decays at the HE/HL-LHC can be obtained. DOI: 10.1103/PhysRevD.98.036014 I. INTRODUCTION eþe− → H0Z0 and the WþW− fusion process eþe− → ν ν¯ 0 Since the Higgs boson of the standard model (SM) has e eH . The cross section for the Higgs-strahlungpffiffiffi process is dominant at the low energy. For s ¼ 500 GeV, the been found by CMS [1] and ATLAS [2] at the Large Hadron þ − Collider (LHC) in July 2012. The lots of experimental cross section for the W W fusion is dominant. The cross 0 0 þ − → þ − 0 results and review papers on the Higgs boson production and section for the Z Z fusion process e e e e H increases significantly with the center-of-mass (c.m.) decay were obtained by the CMS and ATLAS at the LHC 0 0 [3–5]. With the growingly accumulated date, the properties energy increasing,pffiffiffi and can exceeds that of Z H production of a new particle are consistent with those of Higgs boson around s ¼ 1 TeV. These processes can be well used to predicted by SM [6,7]. Though the LHC offers obvious test the Higgs-gauge couplings. The Higgs self-coupling advantages in proving very high energy and very large rates can be studied through the double Higgs boson production þ − → 0 0 0 þ − → ν ν¯ 0 0 in typical reactions, the measuring precision will be processes e e Z H H and e e e eH H at the restricted due to the complicated background. ILC. The absolute values of the Higgs coupling to bosons, The most precise measurements will be performed in the gluons and heavy fermions can also be measured. When clean environment of the future electron-positron collider updated to the Super Proton-Proton Collider (SPPC), for the proposed Higgs factory, like the International Linear researchers can even measure the Higgs self-coupling, Collider (ILC) [8] and the Circular Electron-Positron which is regarded as the holy grail of experimental particle Collider (CEPC) [9]. It is well known that the main physics high luminosity/energy (HL/HE-LHC) scenarios production processes of the Higgs boson in electron- are designed forpffiffiffi the LHC [10,11]. Running at center-of- positron collider collisions are the Higgs-strahlung process mass energy s ¼ 14 TeV, cross-section of the Higgs boson production at the LHC is about 55 pb (gluon-gluon * fusion process dominates). Given that the integrated lumi- [email protected] −1 8 † 1 65 10 [email protected] nosity is 3 ab , the HL-LHC would produce . × ‡ [email protected] pHiggsffiffiffi events [11]. While at the HE-LHC who runs at s ¼ 33 TeV, the cross-section of the Higgs boson pro- Published by the American Physical Society under the terms of duction would be about 200 pb, hence the Higgs boson the Creative Commons Attribution 4.0 International license. 6 0 108 Further distribution of this work must maintain attribution to events per year can be obtained . × . the author(s) and the published article’s title, journal citation, With the above mentioned excellent platforms, rare and DOI. Funded by SCOAP3. Higgs boson decay processes, like the heavy quarkonium 2470-0010=2018=98(3)=036014(9) 036014-1 Published by the American Physical Society LIAO, DENG, YU, WANG, and XIE PHYS. REV. D 98, 036014 (2018) 1 3 1 3 production in the Higgs boson decays, might be observed for NRQCD, where [n] stands for 1 S0, 1 S1, 1 P0, n PJ the first time. Pioneer investigation on the search of H0 → (J ¼½0; 1; 2). To deal with heavy quarkonium production J=Ψγ and H0 → ϒðnSÞγ has been carried out by ATLAS through H0 semiexclusive decays, one needs to derive the [12]. Theoretically, some related calculations have been pQCD calculable squared amplitudes. But the analytical done [13–17]. Within the nonrelativistic quantum chromo- expression for the usual squared amplitude jΣj2 becomes dynamics (NRQCD) formulism [18] and light-cone meth- too complex and lengthy for more (massive) particles in the ods [19], both direct and indirect production mechanism and final states and for higher-level Fock states to be generated relativistic corrections to H0 → J=Ψγ and H0 → ϒðnSÞγ for the emergence of massive-fermion lines in the Feynman à are studied [16]. In Ref. [20], the Bc (Bc) meson production diagrams, especially to derive the amplitudes of the via Higgs boson decays under the NRQCD [18] is system- P-wave states. To solve the problem, the “improved trace atic investigated. Where both the quantum chromodynamics technology” is suggested and developed in the literature (QCD) and the quantum electrodynamics (QED) contribu- [37–43]; it deals with the process directly at the amplitude à tions are included. It is found that the production of Bc (Bc) level. We will continue to adopt improved trace technology meson through the QED contributions is very smaller to derive the analytical expression for all the above- Γð 0 → jð ¯Þ½ i þ ¯ Þ mentioned decay channels. than through the QCD, e.g., H bc n bc QED= 0 −5 The rest of the paper is organized as follows. We ΓðH → jðbc¯Þ½ni þ bc¯ Þ ∼ 10 . In comparison with QCD introduce the calculation techniques for the H0 boson the QCD one, QED contribution is negligible for production ¯ 0 semiexclusive decays to jðQQ Þ½ni-quarkonium within the heavy quarkonium through the Higgs boson decays. So it the NRQCD formulism in Sec. II. In Sec. III, we calculate is only studied the QCD contribution for the Higgs boson the production of jðcb¯Þ½ni (or jðbc¯Þ½ni), jðcc¯Þ½ni, and decays production the heavy quarkonium in this paper. jð ¯Þ½ i 0 The LHCb, ATLAS, and CMS Collaboration experi- bb n -quarkonium through H decay channels, i.e., H0 → jðcb¯Þ½ni þ cb¯ , H0 → jðcc¯Þ½ni þ cc¯ , and H0 → ments have published studies of the Bc meson production ¯ ¯ and of the double J=Ψ production [12,21,22]. Since its jðbbÞ½ni þ bb, with new parameters [37] for the jð ¯ 0Þ½ i discovery by the CDF Collaboration [23], the Bc meson QQ n -quarkonium, an estimation of events at the being the unique “doubly heavy-flavored” meson in the SM HL/HE-LHC. Then we make some discussions on has aroused great interest. The direct hadronic production the theoretical uncertainties of the decays widths by the jð ¯Þ½ i of the Bc meson has been studied systematically in masses of the cb n -quarkonium. The final section is Refs. [24–29]. Therefore, investigation of the heavy quar- reserved for a summary. konium production through H0 decays is worthwhile and meaningful. The heavy quarkonium is presumed to be a II. CALCULATION TECHNIQUES nonrelativistic bound state of the heavy quark and anti- AND FORMULATION quark. The study of the heavy quarkonium, e.g., jðbc¯Þ½ni The H0 boson decays semiexclusive processes for the (or jðcb¯Þ½ni), jðcc¯Þ½ni, and jðbb¯Þ½ni-quarkonium, can heavy quarkonium production can be analogous dealt with, help us to achieve a deeper understanding of the QCD in 0 → jð ¯Þ½ i þ ¯ 0 → jð ¯Þ½ i þ ¯ 0 → both the perturbative and nonperturbative sectors. A very i.e., H cb n cb (or H bc n bc), H jð ¯Þ½ i þ ¯ 0 → jð ¯Þ½ i þ ¯ practical theoretical tool to deal with the processes involv- cc n cc, and H bb n bb. According to the ing heavy quarkonium is the NRQCD [18], in which the NRQCD factorization formula [18], the square of the low-energy interactions are organized by the expansion in semiexclusive amplitude can be written as the production v, where v stands for the typical relative velocity of the of the perturbatively calculable short-distance coefficients heavy quark and antiquark inside of the heavy quarkonium.