Anticipating nonresonant new physics in dilepton angular spectra at the LHC

At the LHC, dileptonic events may turn up new physics interacting with quarks and leptons. The poster child for this scenario is a resonant $Z^{\prime }$, much anticipated in ${\ell }^{+}{\ell }^{-}$ invariant mass spectra. However, angular spectra of dileptons may play an equal or stronger role in discovering a nonresonant species. This paper avails their LHC measurements to corner the couplings and masses of leptoquarks (LQs) that can mediate $q\overline{q}\to {\ell }^{+}{\ell }^{-}$ in the $t$ channel and dramatically alter Standard Model (SM) angular spectra. Also derived are constraints from alterations to $m_{\ell \ell }$ distributions. These dilepton probes exploiting the high rates and small uncertainties of the Drell-Yan process, rival or outdo dedicated LHC searches for LQs in single and pair production modes. The couplings of LQs with electronic interactions are best bound today by low-energy measurements of atomic parity violation, but can be probed better by ${\ell }^{+}{\ell }^{-}$ measurements in the high luminosity runs of the LHC, with the angular spectra leading the way. This work also urges the experimental presentation of boost-invariant angular asymmetries that vanish in the SM.

Figure 1

Feynman diagrams that contribute to the Drell-Yan process at tree level. The $t$-channel leptoquark exchange amplitude on the right modifies dilepton production by the Standard Model $s$-channel $Z/{\gamma }^{*}$ exchange amplitude on the left. These modifications trackable in ${\ell }^{+}{\ell }^{-}$ kinematic and angular spectra are powerful indirect signals of leptoquarks at the LHC.

Figure 2

Effect of leptoquarks on dielectron production spectra depicted at the partonic level. An ElectroUp is chosen for illustration. As a function of $m_{\ell \ell }$, the top left plot shows the production cross section and the top right plot the parton level forward-backward asymmetry defined in Eq. (11). The bottom plots show the normalized angular distributions at $m_{\ell \ell }=500$ and 1500 GeV. Here the blue curves are obtained from the $Z/{\gamma }^{*}$-mediated diagrams in Fig. 1 with an up quark–antiquark initial state. The solid curves show deviations from the SM spectrum as $m_{\mathrm{LQ}}$ is kept fixed at 1 TeV and the LQ Yukawa $y_{ue}$ is varied, with {red, black, green}: $\{0.4,1,1.6\}$. The black curves show deviations as $y_{ue}$ is fixed at 1 and $m_{\mathrm{LQ}}$ is varied, with {dotted, solid, dashed}: $\{400,1000,1600\}\mathrm{GeV}$. More details are described in the text.

Figure 3

Contours of the ratio $d{\sigma }_{\mathrm{tot}}/d{\sigma }_{\mathrm{SM}}$ in the ElectroUp (left) and ElectroDown models (right) at $m_{\ell \ell }=1500\mathrm{GeV}$. Regions where the ratio $>1(<1)$ are shaded blue (red). This illustrates that destructive interference between SM and leptoquark-mediated Drell-Yan production (i.e., between the diagrams in Fig. 1) is possible for LeptoDowns. Since the up quark is denser in protons than the down quark, the dip in hadronic level cross sections is more subdued than at the partonic level. See text for more details.

Figure 4

The center-edge asymmetry $A_{\mathrm{CE}}$, as defined in Eq. (18), with the color code the same as in Fig. 2. The $A_{\mathrm{CE}}$ is a boost invariant that can be chosen to vanish in the SM at some perturbative order, so that a nonzero value may easily signal new physics. Here I have chosen $y_{\max }\to \infty$ for simplicity and $y_0=3.854$ to set the SM value to zero.

Figure 5

Feynman diagrams for pair production of leptoquarks denoted by $\varphi$. Leptoquarks shaded red are produced on shell, and those shaded green mediate production. Diagrams (a)–(d) are QCD driven while the diagram in (e) makes a Yukawa coupling-dependent contribution subjecting the coupling to a mild constraint.

Figure 6

Feynman diagrams for single production of leptoquarks denoted by $\varphi$. The LQs shaded green in diagrams (a), (b) and (c) play the role of mediators, whereas the LQs shaded red in diagrams (d) and (e) are produced on shell. In these latter diagrams the LQ width in Eq. (b3) plays a major role in determining the signal cross sections. LQs shaded green mediate processes giving the ${\ell }^{+}{\ell }^{-}j$ final state. Diagrams with all fermion arrows reversed are also present. Unlike pair production, which is QCD dominated and mostly unresponsive to LQ Yukawa couplings, this search channel is sensitive to both the couplings and masses of LQs.

Figure 7

Summary of all the constraints on LQ models considered in this work. Regions shaded brown and cyan are excluded at 95% C.L. by dedicated LHC searches in processes of LQ pair and single production respectively at $\sqrt{s}=8\mathrm{TeV}$ and $\mathcal{L}=20{\mathrm{fb}}^{-1}$. Regions shaded grey in the ElectroQuark plots are excluded at $2\sigma$ by low-energy measurements of atomic parity violation. The other curves are 95% C.L. limits derived from LHC measurements of dilepton spectra at $\sqrt{s}=8\mathrm{TeV}$, $\mathcal{L}=20{\mathrm{fb}}^{-1}$. The green curves are bounds from CMS measurements of the forward-backward asymmetry, and the red curves, from ATLAS data on $m_{\ell \ell }$ distributions. The magenta curves provided for comparison are limits extracted in Ref. [20] from ATLAS bins of $m_{\ell \ell }\ge 1.8\mathrm{TeV}$, where no events were observed. See text for further details.

Figure 8

Ninety-five percent C.L. sensitivities of future LHC dileptonic measurements compared with the current bound from atomic parity violation on ElectroQuarks (shaded grey). The green and red curves, as before, correspond to forward-backward asymmetries and $m_{\ell \ell }$ spectra respectively. The dashed (solid) curves correspond to an integrated luminosity of $300{\mathrm{fb}}^{-1}$ ($3000{\mathrm{fb}}^{-1}$). These forecasts are made with pseudodata obtained by Poisson-fluctuating background estimates 100 times. See text for further details.

Figure 9

${\ell }^{+}{\ell }^{-}$ angular distributions can clearly mark the spin of LQs. In these plots, blue, SM; green, scalar LQ; red, vector LQ. The LQ coupling and mass are taken 1 and 1 TeV, for illustration. The surest distinguisher is the center-edge asymmetry $A_{\mathrm{CE}}$ carrying an opposite sign for either spin. See Sec. 6 for more details.

Figure 10

Feynman diagrams for radiative Drell-Yan processes that produce threshold effects noticeable at large couplings. While analogues of the quark-initiated diagrams (b) and (c) were dealt with in Ref. [18], the gluon-initiated diagrams (a) and (d) must now be added. See Sec. 6 for more details.