PHYSICAL REVIEW D 102, 035002 (2020)

Enhancing scalar productions with leptoquarks at the LHC

† ‡ Arvind Bhaskar ,1,* Debottam Das,2,3, Bibhabasu De,2,3, and Subhadip Mitra 1,§ 1Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India 2Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India 3Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 085, India

(Received 2 May 2020; revised 15 July 2020; accepted 17 July 2020; published 4 August 2020)

The (SM), when extended with a leptoquark (LQ) and right-handed , can have interesting new implications for Higgs physics. We show that sterile neutrinos can induce a boost to the down-type Yukawa interactions through a diagonal coupling associated with the and a scalar LQ of electromagnetic charge 1=3. The relative change is moderately larger in the case of the first two generations of quarks, as they have vanishingly small Yukawa couplings in the SM. The enhancement in the couplings would also lead to a non-negligible contribution from the quark fusion process to the production of the 125 GeV Higgs scalar in the SM, though the fusion always dominates. However, this may not be true for a general scalar. As an example, we consider a scenario with a SM-gauge-singlet scalar ϕ where an Oð1Þ coupling between ϕ and the LQ is allowed. The ϕqq¯ Yukawa couplings can be generated radiatively only through a loop of LQ and sterile neutrinos. Here, the quark fusion process can have a significant cross section, especially for a light ϕ. It can even supersede the normally dominant gluon fusion process for a moderate to large value of the LQ mass. This model can be tested/constrained at the high luminosity run of the LHC through a potentially large branching fraction of the scalar to two jets.

DOI: 10.1103/PhysRevD.102.035002

I. INTRODUCTION production of a Higgs. It motivates us to investigate whether it is possible to enhance the Yukawa couplings The discovery of a Standard Model–(SM-)like Higgs of the first two generation quarks in some existing of mass 125 GeV at the LHC [1,2] and the minimal extension of the SM. subsequent measurements of its couplings to other SM Therefore, in this paper, we study a simple extension of have played a significant role in understanding the SM augmented with a scalar leptoquark (LQ) of the possible physics beyond the Standard Model (BSM). 1=3 S1 The Higgs couplings to the third generation electromagnetic charge (generally denoted as ) and the vector have already been measured and right-handed neutrinos. We find that the Yukawa within 10%–20% of their SM predictions [3]. couplings of the down-type quarks receive some new However, it is difficult to put strong bounds on the contributions and, for perturbative values of the free coupling parameters, can be moderately enhanced, espe- Yukawa couplings (yf) of the first two generations of fermions. This is an interesting point since, at the LHC, cially for a SM-like Higgs (h125). However, for a singlet ϕ a change in the light-quark Yukawa couplings opens up Higgs ( ), this enhancement could be more significant ¯ → ϕ the possibility of light quarks contributions to the and could open up the qq production channel. Here, we systematically study the production of both h125 and ϕ at the 14 TeV LHC through the quark and gluon fusion channels in the presence of a S1 and right-handed *[email protected] † neutrinos. [email protected] ‡ [email protected] LQs are bosons that couple simultaneously to a quark §[email protected] and a . They appear quite naturally in several extensions of the SM, especially in theories of grand Published by the American Physical Society under the terms of unification like the Pati-Salam model [4], SUð5Þ [5],or the Creative Commons Attribution 4.0 International license. 10 Further distribution of this work must maintain attribution to SOð Þ [6] (for a review, see [7]). Though, in principle, the author(s) and the published article’s title, journal citation, LQs can be either scalar or vector in local quantum field and DOI. Funded by SCOAP3. theories, the scalar states are more attractive, as the vector

2470-0010=2020=102(3)=035002(15) 035002-1 Published by the American Physical Society BHASKAR, DAS, DE, and MITRA PHYS. REV. D 102, 035002 (2020) ones may lead to some problems with loops [8–10].In our model2 and, as we shall see, for perturbative recent times, LQ models (with or without right-handed new couplings and TeV scale new physics masses, the neutrinos) have drawn attention for various reasons. For boosts are moderate and lead to some enhancement of example, they can be used to explain different B- both production and decays of h125 at the LHC. anomalies [11–20] or to enhance flavor violating decays (b) A singlet scalar ϕ (BSM Higgs). We also study the of Higgs and like τ → μγ and h → τμ [21].LQs productions and decays of a scalar ϕ that is a singlet may also play a role to accommodate dark under the SM gauge group. Such a scalar has been abundance [22,23] or to mitigate the discrepancy in the considered in different contexts in the literature. For anomalous magnetic moment of ðg − 2Þμ [24–26]. example, it may serve as a dark matter candidate. Direct production of TeV scale right-handed neutrinos at Similarly, a singlet scalar can help solve the so-called the LHC can be strongly enhanced if one considers μ problem in the Minimal Supersymmetric Standard the mass generated at tree level via the Model [55]. To produce such a singlet at the LHC, one inverse-seesaw mechanism within LQ scenarios [27]. generally relies upon its mixing with the doubletlike An S1-Higgs coupling can help to stabilize the electro- Higgs states present in the theory. If the mixing is non- weak vacuum [28]. The phenomenology of negligible, then the leading order production process variousLQshasalsobeenextensivelydiscussedinthe turns out to be the gluon fusion (though literature [7,29–38]. fusion may also become relevant in specific cases In the scenario that we consider, there are three gen- [56]). One may also consider the production of ϕ erations of right chiral neutrinos in addition to the S1. through cascade decays of the doublet Higgs state(s). Generically, such a scenario is not very difficult to realize However, such a process is generally much sup- within the grand unified frameworks. In fact, considering pressed. Now, as we shall see, in the presence of a sterile neutrinos in this context is rather well motivated scalar LQ and sterile neutrinos we could have a new because of the existence of nonzero neutrino masses and loop contribution to the quark fusion production mixings, which have been firmly established by now. It is process (qqF). The LQ would also contribute to the known that an Oð1Þ Yukawa coupling between the chiral gluon fusion process. In such a setup, the singlet Higgs neutrinos and TeV scale masses for the right-handed can potentially be tested at the LHC via its decays to neutrinos can explain the experimental observations related the light-quark states. to neutrino masses and mixing angles even at tree level if The rest of the paper is organized as follows. In Sec. II, one extends SM to a simple setup like the inverse seesaw we introduce the model Lagrangian and discuss the new mechanism (ISSM) [39–41]. Of course, this requires the interactions. In Sec. III, we discuss additional contributions presence of an additional singlet neutrino state X in the model.1 2This may be possible in an effective theory with free Interestingly, the production cross sections of sterile parameters. For example, Ref. [52] considers a dimension-6 † Λ2 ¯ neutrinos at the LHC can be enhanced significantly if the operator of the form fdðH H= ÞðqLHdRÞþH:c: (where ISSM is embedded in a LQ scenario [27]. Similarly, as Λ ∼ TeV) in addition to the SM Yukawa terms that contribute differently to the physical quark masses and effective quark indicated earlier, a νR state in a loop accompanied with Yukawa couplings. Thus, by choosing f one may raise the S1 may influence the production of a Higgs at the LHC d Yukawa parameters while keeping the physical masses un- and its decays to the SM fermions, especially to the light changed, though this may require some fine-tuning among the ones. Observable effects can be seen in scenarios with a parameters of the model. It is important to note that in the general scalar sector that may include additional Higgs presence of higher-dimensional operators, a large Yukawa cou- states, a TeV scale ν , and an Oð1Þ Yukawa couplings pling need not induce large correction to the corresponding quark R mass always. between the left and right chiral neutrinos. In this paper, Such enhancements of the light-quark Yukawa couplings can we shall explore this in some detail. Notably, the gluon even be probed at the LHC. An analysis of pair fusion process (ggF) for producing a Higgs scalar gets production suggests that in the future the High Luminosity LHC boosted in presence of a LQ [51]. Our study is general— (HL-LHC) may offer a handle on this [53]. An updated analysis, 3000 −1 it can be applied to both SM-like and BSM Higgs with fb of integrated luminosity suggests (though not in a fully model independent way) that it may be possible to narrow bosons. Specifically, we consider the following two down the d- and s-quark Yukawa couplings to about 260 and 13 cases: times to their SM values, respectively [54], i.e., (a) A 125 GeV SM-like Higgs boson (h125). We inves- tigate how the light-quark Yukawa couplings can jκdj ≤ 260; jκsj ≤ 13; ð1Þ get some positive boosts. However, obtaining a free κ rise of the Yukawa parameters is not possible in where the Yukawa coupling modifier q is defined as

yeff 1 κ ¼ q : ð2Þ ISSM or inverse seesaw extended supersymmetric models q ySM may lead to interesting phenomenology at low energy [42–50]. q

035002-2 ENHANCING SCALAR PRODUCTIONS WITH LEPTOQUARKS AT … PHYS. REV. D 102, 035002 (2020)

L ⊃ LL − ¯Cν ¯C RR ¯C to the production and decays of h125. In Sec. IV, we discuss fy1 ð dL L þ uLeLÞS1 þ y1 uReRS1 bounds on the parameters. In Sec. V, we investigate the case RR ¯Cν λ † of the singlet scalar ϕ. Finally we summarize our results þ y1 dR RS1 þ H:c:gþ vhðS1S1Þ 1 and conclude in Sec. VI. 0 † 2 2 2 † þ λ ϕðS S1Þþ M ϕ þ M ðS S1Þ; ð7Þ 1 2 ϕ S1 1 II. THE MODEL: A SIMPLE EXTENSION X X OF THE SM where we have simplified ðy1 Þii as yi . Since the flavor of the neutrino is irrelevant for the LHC, from here on we shall As explained in the Introduction, our model is a simple simply write ν to denote neutrinos. extension of the SM with chiral neutrinos and an additional The terms in Eq. (7) have the potential to boost up some 1=3 scalar LQ of electromagnetic charge , normally denoted production/decay modes for h and ϕ. For example, it would as S1. The LQ transforms under the SM gauge group as ¯ lead to an additional contribution to the effective hgg ð3; 1; 1=3Þ with Q ¼ T3 þ Y. In the notation of Ref. [7], EM coupling (see Fig. 1) [51]. Similarly, the decay h → dd¯, the general fermionic interaction Lagrangian for S1 can be which is negligible in the SM, may get a boost now, as long written as as some of the new couplings are not negligible. The – LL ¯ Cia ab jb RR Ci j processes are illustrated in Figs. 1(a) 1(c) [the first diagram L ¼ðy1 Þ ðQ ϵ L ÞS1 þðy1 Þ ðu¯ e ÞS1 F ij L L ij R R is independent of v, while the other two are of Oðv2Þ], RR ¯Ciνj ¯ þðy1 ÞijðdR RÞS1 þ H:c:; ð3Þ where the Higgs is shown to be decaying to a dd pair via a triangle loop mediated by S1 and chiral neutrinos. There are where we have suppressed the color indices. The super- two possibilities: the Higgs directly couples with either the script C denotes charge conjugation; fi; jg and fa; bg are chiral neutrinos or the LQ. Since the contributions of these flavor and SU 2 indices, respectively. The SM quark and ð Þ diagrams appear as corrections to yd, it is easy to see that lepton doublets are denoted by QL and LL, respectively. We the in the loop (i.e., the neutrino) has to go through now add the scalar interaction terms to the Lagrangian in a chirality flip. In this case, the right-handed neutrino from Eq. (3), the third term in Eq. (3) helps to get a nonzero contribution. One can, of course, imagine similar diagrams with L ⊃ L λ † † λ0ϕ † F þ ðH HÞðS1S1Þþ ðS1S1Þ charged leptons in the loops, contributing to the h → uu¯ 1 † 2 2 2 ¯ 2 † (or any other up-type quark-antiquark pair) decay. þ μðH HÞϕ þ M ϕ þ M ðS S1Þ: ð4Þ 2 ϕ S1 1 However, the contributions of such diagrams would be ¯ small as they are suppressed by the tiny charged lepton Here, H denotes the SM Higgs doublet, and Mϕ and MS1 Yukawa couplings, at least for the first two generations. If define the bare mass parameters for ϕ and S1, respectively. we restrict ourselves only to flavor diagonal couplings in We denote the physical Higgs field after the electroweak Eq. (3) (i.e., we allow only i ¼ j terms), only the top symmetry breaking as h ≡ h125. The singlet ϕ does not Yukawa yt would be modified appreciably. If we allow off- acquire any vacuum expectation value (VEV). Physical diagonal couplings, one can get contributions for the first masses can be obtained via two generations of Yukawa couplings—namely, yu and yc,   1 0 respectively. However, one needs to be careful as off- H ¼ pffiffiffi ; ϕ ¼ ϕ; ð5Þ diagonal LQ-quark-lepton couplings are constrained, par- 2 v þ h ticularly for the first two generations [7,57]. In this case, we consider only flavor diagonal couplings and look only at ≃ 246 where the SM Higgs VEV v GeV. We assume the the modification of Higgs couplings to down-type quarks. mixing between H and ϕ, controlled by the dimensionless Thus, one may always set ðyRRÞ ¼ 0 for all values of coupling μ to be small to ensure that the presence of a 1 ij singlet Higgs does not affect the production and decays of i and j. This may lead to a somewhat favorable situation in some cases to accommodate rare decays of fermions h125 significantly via mixing. Notice that, unlike dimen- sionless λ or μ, λ0 is a dimension-1 parameter. We define the through LQ exchange. Before we discuss productions and decays of h125 and ϕ physical mass of S1 to be MS1 as in our model, a few comments are in order. As we shall see 1 in the next section, an order 1 hν¯LνR coupling, i.e., yν ∼ M2 ¼ M¯ 2 þ λv2: ð6Þ O 1 ν S1 S1 2 ð Þ and a TeV scale mass for the R would be helpful to raise the Yukawa couplings of the light quarks. Typically, The above Lagrangian simplifies a bit if we ignore the the models like ISSM would be able to accommodate such V mixing among quarks and neutrinos (i.e., set CKM ¼ a scenario. In the ISSM, an additional gauge singlet U I PMNS ¼ ). For example, we can expand Eq. (4) for the neutrino, usually denoted by X, is assigned a Majorana first generation as mass term μXXX, while νR receives a Dirac mass term of

035002-3 BHASKAR, DAS, DE, and MITRA PHYS. REV. D 102, 035002 (2020) the form Mν¯RX. For our purposes, we may assume that this with two publicly available packages, FeynCalc [60] and singlet X cannot directly interact with any other we LoopTools [61]. consider. However, since it interacts exclusively with the νR ν fields via M, it would modify the R propagators. In this A. Correction to Yukawa couplings “ ν case, it may be useful to define something called a fat R of the down-type quarks propagator” [58] that includes all the effects of the sequential insertions of the X field. For simplicity, we In our calculation, we assume that left-handed neutrinos do not display this interaction and mass term of the right- are massless while right-handed ones are massive. Also, handed neutrinos explicitly in Eq. (3). One can explicitly since we consider Higgs decays to down-type quarks only, we can safely ignore the quark masses (mq ¼ 0) consider an ISSM in the backdrop of our analysis and easily 2 2 and set m ¼ðp1 þ p2Þ ¼ 2p1:p2 (see Fig. 1). The accommodate fat νR propagators without any change in our h results. correction to yd coming from the diagram shown in Fig. 1(a) is given by Z  III. CONTRIBUTION TO THE PRODUCTION 4 d l P =lðp=1 þ p=2 − =l þ Mν ÞP h ˜ðaÞ − 2 R R R AND DECAYS OF 125 yd ¼ ig1yν 4 2 2 2 ð2πÞ l fðp1 þ p2 − lÞ − Mν g  R In this section, we first look into the additional con- 1 tributions to the Yukawa couplings of the down-type quarks × 2 2 ; ð8Þ fðp1 − lÞ − M g with h125. The relevant interactions can be read from S1 Eq. (7). We shall then discuss the role of these loops in 2 LL RR¯ the production of h125 and its decays to the down-type where g1 ¼ gLgR ¼ y1 y1 and PL=R are the chirality quarks. In this paper, we compute all the loop diagrams projectors. From here on, we shall suppress the generation 2 2 using dimensional regularization and Feynman parametri- index of the leptoquark couplings and simply write gi as g . zation and then match the results using the Passarino- After Feynman parametrization and dimensional regulari- Veltman (PV) integrals [59]. We evaluate the PV integrals zation, we get

(a) (b) (c)

(d) (e)

FIG. 1. Feynman diagrams showing the SM-like Higgs (h125) decaying to (a)–(c) down quarks and (d), (e) gluon pairs through loop diagrams mediated by S1 and chiral neutrinos. Only in (a) and (c) does the Higgs couple to ν, whereas it couples to S1 in all the other diagrams. The couplings g ¼ yLL and g ¼ yRR [see Eq. (7)]. The diagrams for s- and b-quarks are similar to the last two diagrams. L 1 pffiffiffi R 1 pffiffiffi Note that we absorb a factor of 1= 2 in the definition of Yukawa couplings in the mass basis, i.e., we write yν instead of yν= 2.

035002-4 ENHANCING SCALAR PRODUCTIONS WITH LEPTOQUARKS AT … PHYS. REV. D 102, 035002 (2020) Z Z   Z Z   2 1 1−x 2 2 1 1−x 2 ˜ðaÞ − g yν xmh ðaÞ − g yν xmh yd ¼ 2 dx dy yd ¼ 2 dx dy : ð13Þ 16π 0 0 D1 16π 0 0 D1 Z  1 − dz ln D2 þ Δϵ ; ð9Þ Now, proceeding along the same lines, we get the correc- 0 tion from the diagram in Fig. 1(b) as Z  where 4 ðbÞ 2 2 d l 1 y ig λyνv d ¼ 2π 4 l2 − 2 l − 2 − 2 2 2 2 2 ð Þ ð Mν Þfð p1Þ MS1 g D1ðx; yÞ¼xym þ xðx − 1Þm þ xMν þ yM ð10Þ  R h h R S1 1 × 2 2 and fðl þ p2Þ − M g Z Z S1   2 2 1 1− g λyνv x 1 2 2 D2ðzÞ¼zM þð1 − zÞMν : ð11Þ ¼ 2 dx dy ; ð14Þ S1 R 16π 0 0 D0

0 2 2 2 2 2 The divergent piece at O v , Δϵ − γ ln 4π O ϵ − − ð Þ ¼ ϵ þ ð Þþ ð Þ where D0ðx;yÞ¼MνR þðxþyÞðMS1 MνR Þ xymh. Simi- is canceled by a similar contribution from diagrams with a larly, the correction term corresponding to Fig. 1(c) can be bubble in an external quark line. The bubble in the quark obtained as lines is obtained by replacing the Higgs field in Fig. 1(a)  2 2 Z 4 with v and amputating the external quark lines; see Fig. 2 ig yνλv d l P =lðp=1 þ p=2 − =l þ Mν ÞP ˜ðcÞ R R R yd ¼ 4 2 2 2 (a). This extra contribution is given as 2 ð2πÞ l fðp1 þ p2 − lÞ − Mν g  R Z 1 2 1 leg g yν 2 2 × 2 2 2 y j 0 ¼ dz½Δϵ − ln fzM þð1 − zÞMν g: − l − d Oðv Þ 2 S1 R fðp1 Þ MS1 g 16π 0 Z Z   2 λ 2 1 1−x 2 ð12Þ − g yν v 1 − − ymh ¼ 2 dx dyð x yÞ 2 32π 0 0 D Z Z   3 Putting these two together, we get 1 1−x 1 þ dx dy ; ð15Þ 0 0 D4

− 2 2 1 − − 2 where D3ðx; yÞ¼ xymh þ yMνR þð x yÞMS1 and 2 1 − 2 ðbÞ D4ðxÞ¼xMνR þð xÞMS1 . This is finite like y . The last term of Eq. (15) is actually canceled by the Oðv2Þ correction to the external quark propagators, as shown in Fig. 2(b). This is similar to the cancellation at Oðv0Þ in yðaÞ; in this case, the bubble is obtained by replacing the Higgs field in Fig. 1(b) with v and amputating the external quark (a) lines. However, one has to be careful with the factors here. After electroweak symmetry breaking, one can expand the Higgs-S1 interaction term in Eq. (4) as λ λ † † 2 2 2 † ðH HÞðS1S1Þ¼2 ðh þ hv þ v ÞðS1S1Þþ: ð16Þ

† ðbÞ The λvhðS1S1Þ term contributes to yq , but the propagator 2 † correction would come from the λv ðS1S1Þ=2 term, i.e., with a different prefactor. The Oðv2Þ external leg correction (b) 2 † to the Yukawa coupling is proportional to λv ðS1S1Þ=2 and FIG. 2. Feynman diagrams showing the (a) Oðv0Þ and (b) can be written as Oðv2Þ corrections to the quark propagator from loop diagrams Z   2 2 1 LL g yνλv 1 − x mediated by S1 and chiral neutrinos. The couplings gL ¼ y1 and leg ¯ yd jOðv2Þ ¼ 2 dx 2 2 : ð17Þ RR 32π 0 1 − gR ¼ y1 [see Eq. (7)]. The diagrams for s- and b-quarks are xMνR þð xÞMS1 similar. These corrections are independent of the external momentum (p) and hence contribute as mass corrections. Once this is added, we get

035002-5 BHASKAR, DAS, DE, and MITRA PHYS. REV. D 102, 035002 (2020) Z Z   2 λ 2 1 1−x 2 TABLE I. Contributions of the three diagrams shown in Fig. 1 ðcÞ − g yν v 1 − − ymh yd ¼ 2 dx dyð x yÞ 2 : ð18Þ to the Yukawa couplings obtained from Eq. (19) or (20) for some 32π 0 0 D3 illustrative choices of the mass of the right-handed neutrino Mν 2 R ¯ and the leptoquark mass M while keeping g yν ¼ 1 and λ ¼ 1. Therefore, the effective hdd coupling can be written as S1 Mν (GeV) M (GeV) yðaÞ yðbÞ yðcÞ eff SM δ R S1 yd ¼ yd þ y Z Z  600 1000 −0.000046 0.000255 −6 3 10−7 2 1 1− 2 2 . × g yν x λv xm −7 SM − h 1500 −0.000031 0.000132 −2.2 × 10 ¼ yd þ 2 dx dy 16π 0 0 D0 D1   1100 1000 −0.000022 0.000180 −2.1 × 10−7 λ 2 2 −0 000016 −0 9 10−7 − 1 − − v × ymh 1500 . 0.000103 . × ð x yÞ 2 ; ð19Þ 2D3

SM κ 1 λ where yd ¼ md=v is the d-quark Yukawa coupling in the Eq. (20), we see that q depends linearly on =mq, , δ ðaÞ 2 SM (with md being the physical mass) and y ¼ yd þ and the combination g yν, but, a priori, its dependence on ðbÞ ðcÞ M or Mν is not so simple. In Table I, we show the y þ y is the total loop correction. This results in a finite S1 R d d – shift to the SM down-quark Yukawa couplings which contributions of the three loop diagrams [Figs. 1(a) 1(c)] for some illustrative choices of MνR and MS1 . With cannot be absorbed in a redefinition of the quark masses 2 since the corrections corresponding to the mass terms g yν ¼ λ ¼ 1, we see that there is some cancellation between these contributions. Note that this choice of (Fig. 2) are already accounted for in md, the physical mass, through Eqs. (12) and (17). ‘This is similar to the coupling is not restricted by the rare decays [7,57]. κ κ κ case in which the SM is augmented with dimension-6 In Fig. 3, we show the variations of d, s, and b for 500 ≤ M ≤ 3000 Mν operators [52]. S1 GeV for three different choices of R . Equation (19) can also be written in terms of the As expected, we see the lightest among the three quarks, κ following PV integrals, i.e., the d-quark, getting the maximum deviation in q from  unity. The b-quark coupling hardly moves from the SM 2 eff SM g yν 2 2 2 2 value for the considered parameter range. However, all the y ¼ y þ B0ð0;Mν ;M Þ − B0ðm ; 0;Mν Þ d d 16π2 R S1 h R deviations are well within the ranges allowed by Eq. (1). − 2 0 0 2 0 2 2 MS1 C0ð ; ;mh; ;MS1 ;MνR Þ C. Decays of h125 2 2 2 2 2 − λv C0ð0; 0;m ;M ;Mν ;M Þ h S1 R S1 As mentioned before, we shall use h and h125 inter- 2 λv 2 2 2 changeably to denote the 125 GeV SM-like Higgs boson. þ fC0ð0; 0;m ; 0;M ;Mν Þ 2 h S1 R In the SM, the total decay width of the 125 GeV Higgs SM −3 2 2 2 2 2 boson is computed as Γ ¼ 4.07 × 10 GeV, with a M D0 0; 0;m ; 0; 0; 0;M ;M ; 0;Mν h þ S1 ð h S1 S1 R Þ þ4.0%  relative theoretical uncertainty of −3.9% [62]. Now, because 2 2 2 of the additional loop contribution, the total decay width − C0ð0; 0; 0;M ;M ;Mν Þg ; ð20Þ S1 S1 R would increase in our model. We can use Eq. (19) or (20) to compute the partial decay width for the h → qq¯ decay in where D0, C0, and B0 are the four-point, triangle, and the rest frame of the Higgs as bubble integrals, respectively. The expressions for the s- Z and b-quarks would be exactly the same as the above with jp⃗qj 2 2 Γ M 2 Ω h→qq¯ ¼ Nc × 2 2 j totj d md and g ¼ gi suitably modified. 32π mh N B. Relative couplings ¼ c jyeffj2ðm2 − 4m2Þ3=2; ð22Þ 8πm2 q h q To get some idea about how the extra contributions from h the loops depend on the parameters, we use the Yukawa M eff ¯ where i tot ¼ yq qq is the invariant amplitude and Nc ¼ coupling modifiers [Eq. (2)], 3 accounts for the colors of the quark. Similarly, the h → gg δy partial width would also get a positive boost in the presence κ ¼ 1 þ : ð21Þ of S1 [7]. The relevant diagrams can be seen in Figs. 1(d) q ySM q and 1(e). In our model, the h → gg partial width can be Since we ignore the mass of the quarks, δy is independent expressed as [7,63], of the flavor of the down-type quark that the Higgs is α2 3 λ 2 2 2 GF smh v coupling to as long as g yν remains the same. Hence, Γ ffiffiffi A A h→gg ¼ p 3 1=2ðxtÞþ 2 0ðxS1 Þ ; ð23Þ SM SM 64 2π 2M δy=yq should go as 1=yq ∼ 1=mq. Using this and S1

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35 M = 600 GeV − R ½x fðxÞ M = 1100 GeV A − R 0ðxÞ¼ ; ð25Þ 30 M = 2100 GeV 2 R x ( pffiffiffi ) 25 arcsin2ð xÞ;x≤ 1 h  pffiffiffiffiffiffiffiffiffi i fðxÞ¼ 1 1 1− −1 2 : ð26Þ 20 − þpffiffiffiffiffiffiffiffiffix − π 1 4 ln −1 i ;x> d 1− 1−x 15 Now, Eqs. (22) and (23) can be used to obtain the total 10 width in our model, 5  X  Γ ΓSM − ΓSM − ΓSMðtreeÞ Γ 0 h ¼ h h→gg h→qq¯ þ h→gg 500 1000 1500 2000 2500 3000 q¼d;s;b M (GeV) X S1 Γ (a) þ h→qq¯: ð27Þ q¼d;s;b 3 M = 600 GeV R M = 1100 GeV R Ideally, we should also include corrections to partial widths M = 2100 GeV R of other decay modes, like h → γγ or other three body 2.5 decays in the above expression. However, since their con- tributions to the total width are relatively small, we

s ignore them. 2 From Eqs. (22) and (27), we compute the new branching ratios (BRs) of the h → qq¯ modes in our model as 1.5 Γ → ¯ BRðh → qq¯Þ¼ h qq : ð28Þ Γh 1 500 1000 1500 2000 2500 3000 → ¯ M (GeV) In Fig. 4, we show BRðh qqÞ for different quarks for S1 2 g yν ¼ 1 (for all generations) and λ ¼ 1. Equation (22) (b) ¯ SM 2 indicates BRðh → qqÞ ∼ jyq þ δyj ; i.e., it increases 1.04 2 M = 600 GeV SM 1 δ R with yq (remember, for g yν ¼ , y is the same M = 1100 GeV 1.035 R M = 2100 GeV → ¯ R for all the quarks). Hence, we expect BRðh bbÞ > ¯ SM 1.03 BRðh → ss¯Þ > BRðh → ddÞ,asyq increases with the 1.025 mass of the quark. This can be seen in Fig. 4. However, even for order 1 yν couplings and TeV scale S1 and νR, the b 1.02 relative shift in branching ratio of the h → bb¯ decay to that 1.015 of SM is not large (as expected from Fig. 3). For the lighter

1.01 quarks, the branching ratios become much larger than their SM values, even though they remain small compared to 1.005 other decay modes like h → bb¯. The branching fraction 1 h → gg is almost unaffected with the variation in S1, as the 500 1000 1500 2000 2500 3000 M (GeV) SM contribution always dominates. S1 (c) D. Production of h125 κ κ FIG. 3. Variation of the coupling modifiers (a) d, (b) s, For a quantitative understanding of the quark-gluon κ and (c) b [defined in Eq. (2)] with MS1 for different values of 2 fusion production of h125, we normalize the fusion cross Mν . Here we set g yν ¼ 1 for all three generations and R section with respect to its SM value. We define the keep λ ¼ 1. “ ” μ normalized production factor F as P σðgg → hÞþ σðqq¯ → hÞ 2 2 2 2 μ ≡ μggþqq¯ q¼d;s;b where x ¼ m =4m and x ¼ m =4M . The relevant F ¼ : ð29Þ t h t S1 h S1 F σðgg → hÞ one-loop functions are given by SM It is a function of the BSM parameters and measures the 2½x þðx − 1ÞfðxÞ relative enhancement of production cross section in the A1 2ðxÞ¼ ; ð24Þ = x2 fusion channel. The subscript “F” stands for the fusion

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M =600 GeV 1.07 R 100 1.06 10-1 1.05 10-2 1.04 -3 10 F

BR 1.03 10-4 1.02 10-5 Br(h gg) - Br(h dd) - -6 Br(h ss) 1.01 10 - Br(h - bb) Br(h bb)SM 10-7 1 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 M (GeV) MS (GeV) S1 1 (a) (a) 101

M =2100 GeV 100 R 100 10-1 10-1 -2

h) 10 10-2 (ii h 10-3 R 10-3 -4

BR 10 10-4 R (gg h) -5 h - R (dd h) -5 10 h - 10 R (ss h) Br(h gg) h - - Rh(bb h) Br(h dd) - -6 -6 Br(h ss) 10 10 - 500 1000 1500 2000 2500 3000 Br(h - bb) Br(h bb) SM MS (GeV) 10-7 1 500 1000 1500 2000 2500 3000 (b) M (GeV) S1 -3 (b) 10

→ -4 FIG. 4. Variation of BRðh iiÞ with MS1 for i ¼ d, s, b, and 10 gluon and two values of MνR : (a) 600 GeV and (b) 2100 GeV. We 2 1 λ 1 -5 have set g yν ¼ for all generations and taken ¼ . h) 10

¯ (ii

σ → BSM -6 channel. In the denominator, we ignore ðbb hÞSM,asit h 10 σ → R is much smaller than ðgg hÞSM because of the small b-quark parton distribution function (PDF) in the initial -7 10 R (gg h) h - R (dd h) states. h - R (ss h) h - In our model, the leading order gluon fusion cross Rh(bb h) 10-8 section at parton level can be expressed as [7,63–65] 500 1000 1500 2000 2500 3000 M (GeV) S1 2 π mh 2 (c) σˆðgg → hÞ¼ Γ → δðsˆ − m Þ; ð30Þ 8sˆ h gg h FIG. 5. (a) The normalized production cross section of h125 as a where Γ → is given in Eq. (23). Similarly, the quark 1 1 2 1 h gg function of MS1 for MνR ¼ . TeV. Here also, we take g yν ¼ fusion cross section at parton level can be expressed in for all the generations and λ ¼ 1. (b) Relative production factor Γ terms of h→qq¯ from Eq. (22) as [62] (Rh) (defined in the text) for the SM þ LQ scenario as a function 1 1 BSM of MS1 for MνR ¼ . TeV. (c) Relative production factor Rh 2 4π M Mν 1 1 hqq¯ hgg mh 2 as a function of S1 for R ¼ . TeV when the ( ) σˆðqq¯ → hÞ¼ Γ → ¯δðsˆ − m Þ: ð31Þ 9sˆ h qq h coupling at leading order in the SM is assumed to be zero.

Naively, one would expect σˆðqq¯ → hÞ for the heavier PDFs, as the heavier quarks PDFs are suppressed compared Γ quarks to be larger than the lighter ones, as h→qq¯ is to their lighter counterparts. We compute σðqq¯ → hÞ at the eff proportional to the square of yq (which increases linearly 14 TeV LHC using the NNPDF2.3QED LO [66] PDF. with mq). However, there is a trade-off between mq and the Similarly, we use the next-to-next-to-leading-order plus

035002-8 ENHANCING SCALAR PRODUCTIONS WITH LEPTOQUARKS AT … PHYS. REV. D 102, 035002 (2020) next-to-next-to-leading-logarithmic QCD prediction for the limit on S1 would get much weaker. A conservative σ → ≃ 49 47 14 TeV LHC which leads to ðgg hÞSM . pb [67]. estimation indicates that the limit goes below a TeV when μ μ 1 6 We use these results to compute F. We show F as a the BR decreases to about = . Also, pair productions of 2 1 function of MS1 in Fig. 5(a) while assuming that g yν ¼ leptoquarks are QCD driven and thus cannot be used to put for all the generations and λ ¼ 1. For this plot, we set limits on the fermion couplings. The CMS Collaboration 1 has performed a search with the 8 TeV data for single MνR ¼ TeV. However, since the gluon fusion cross μ production of scalar leptoquarks that excludes up to section is much larger than the quark fusion ones, F is 1.75 TeV for order 1 coupling to the first generation largely insensitive to MνR . To get an idea of the contributions of the different modes [77]. However, even that limit comes down below 1 TeV to μ , we define the following two ratios: once we account for the reduction in the BR. However, a F recast of CMS 8 TeV data for the first generation (eejj=eνjj) indicates that for order 1 g , M ≳ σðii → hÞ ðL=RÞ S1 R ðii → hÞ¼ ðfull modelÞ; ð32Þ 1 1 3 h σ gg → h . TeV [78]. To be on the conservative side, we may ð ÞSM ≳ 1 5 2 1 use MS1 . TeV as a mass limit for S1 with g yν ¼ for σ ii → h all generations. BSM → ð ÞBSM Rh ðii hÞ¼ ðBSM onlyÞ: ð33Þ If, however, M >Mν , the LQ can decay to three more σðgg → hÞ S1 R SM final states with right-handed neutrinos. Thus, we would The difference between these two ratios lies in the inter- expect a further reduction of the limits on S1 [27]. ference between the SM and BSM contributions. We show Moreover, specifically for first generation fermions, the these ratios in Figs. 5(b) and 5(c). We find that, even choices of gL and gR are restricted further. The atomic ¯ parity violation measurements in Cs133 [79] put a strong after the PDF suppression, Rhðbb → hÞ >Rhðss¯ → hÞ > R ðdd¯ → hÞ. On the other hand, if we take RBSM, the constraint on them. Typically, all existing constraints h h may be satisfied easily for M ≳ 2 TeV and g2 ≈ 1 hierarchy is reversed. This can be understood from the S1 fact that the loop contribution δy is equal for all three with gL ¼ gR. of the quarks and hence the PDF suppression makes BSM ¯ → BSM ¯ → BSM ¯ → V. THE SINGLET HIGGS ϕ Rh ðbb hÞ

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loop-level interaction with the SM quarks, the effective coupling is the same for all three generations of down-type 2 quarks for the same value of g yν.

B. Branching ratios and cross sections The expressions for the partial decay widths and pro- duction cross section of ϕ are essentially identical to the eff eff ones for h125 if we replace yq → Yq and mh → Mϕ. Thus, the expressions for the partial decay widths would look like

3jYeffj2 3 Γ q 2 − 4 2 3=2 ≈ eff 2 FIG. 6. The singlet scalar, ϕ decaying to down-type quarks. ϕ→qq¯ ¼ 2 ðMϕ mqÞ jYq j Mϕ; ð37Þ 8πMϕ 8π   ϕ ϕν¯ ν 2 3 2 2 nature of , the tree-level L R coupling does not exist, so G α M λ0 M Γ F Sffiffiffi ϕ v A ϕ in this case there is no diagram like the one shown in Fig. 1 ϕ→gg ¼ p 2 0 2 ; ð38Þ 64 2π3 2M 4M (a). Proceeding as before, we get S1 S1   Z Z   α2 3 0 2 2 2 0 1 1− GF emMϕ λ v Mϕ g λ yνv x 1 Γ ffiffiffi A eff ϕ→γγ ¼ p 3 2 0 2 : ð39Þ Yq ¼ 2 dx dy ; 128 2π 6M 4M 16π 0 0 Dϕ S1 S1 The Feynman diagrams for the ϕ → γγ process will be where similar to those in Figs. 1(d) and 1(e), with the gluons 2 2 2 2 replaced by two and the αs coupling substituted for Dϕ x; y Mν x y M − Mν − xyM : 35 ð Þ¼ R þð þ Þð S1 R Þ ϕ ð Þ α the em coupling. As earlier, we can now express the cross sections in these modes in terms of the partial widths. In the Written in terms of PV integrals, this becomes gg channel,

2λ0 2 eff g yνv 2 2 2 2 π Mϕ Y − C0 0; 0;M ;M ;Mν ;M : 2 q ¼ 2 ð ϕ S1 R S1 Þ ð36Þ σˆðgg → ϕÞ¼ Γ → δðsˆ − M Þ; ð40Þ 16π 8sˆ h gg ϕ We present our results in Fig. 7, which shows the and in the qq¯ channel eff variation of Yq as a function of MS1 for two values of 500 λ0 4π2 MνR and Mϕ ¼ GeV. Here, is a dimensionful Mϕ 2 σˆðqq¯ → ϕÞ¼ Γϕ→ ¯δðsˆ − M Þ: ð41Þ parameter [see Eq. (4)] that can be taken to be of the 9sˆ qq ϕ order of the largest mass in the model spectrum. The eff ϕ The total width for ϕ can be expressed as coupling Yq decreases as MS1 increases. Since has only  X  0.004 Γϕ Γϕ→ ¯ Γϕ→ Γϕ→γγ : 42 M = 1 TeV ¼ qq þ gg þ ð Þ R M = 2 TeV q¼d;s;b R 0.003 We now present our numerical results. We begin with Fig. 8, where we show the variation of BRs of different ϕ

eff decay modes of . For the most part, the plots for the

q 0.002 Y quarks overlap, as Γϕ→qq¯ is essentially independent of mq [see Eq. (37)]. Here, without any singlet-doublet mixing, ϕ 0.001 can decay only to down-type quarks or gluon or ϕ → γγ pairs. As a result, when MS1 increases, BRð gg= Þ ϕ → ¯ decreases and BRð qqÞ goes up if MνR is held fixed. 0 We see that for a 2 TeV S1, ϕ → qq¯ is the dominant decay 600 800 1000 1200 1400 1600 1800 2000 2 M (GeV) mode for g yν ¼ 1, Mν ¼ 1 TeV (the BRs are indepen- S1 R dent of λ0). ϕ ¯ FIG. 7. Variation of qq coupling as a function of MS1 for In Figs. 9(a) and 9(b), we plot the scattering cross 1 2 1 λ0 2 ϕ MνR ¼ TeV and 2 TeV, g yν ¼ , ¼ TeV, and sections of in different decay modes at the 14 TeV LHC, Mϕ ¼ 500 GeV. considering both the gluon and quark fusion processes. We

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M = 500 GeV M = 500 GeV 100 102

101 10-1 100

-1 10-2 10 - ii) [fb] Br( dd-) -2 Br( ss) 10 BR - - Br( bb) x Br( dd) -3 Br( gg) x Br( ss-) 10 -3 - Br( ) x Br( 10 x Br( bb) x Br( ) 10-4 gg) 10-4 10-5

10-5 10-6 600 800 1000 1200 1400 1600 1800 2000 600 800 1000 1200 1400 1600 1800 2000 M (GeV) M (GeV) S1 S1 (a) (a)

M = 2000 GeV S1 M = 2000 GeV S1 100 102 - -1 x Br( dd) 10 - 1 x Br( ss) 10 - 10-2 bb) x Br( ) 100 10-3 gg) -1 -4 10

10 ii) [fb]

BR -2 10-5 10 -6 -3

10 x Br( 10 - -7 -4 10 Br( dd-) 10 Br( ss-) -8 Br( bb) 10 Br( gg) -5 Br( ) 10 -9 10 -6 0 100 200 300 400 500 600 700 800 900 1000 10 100 200 300 400 500 600 700 800 900 1000 M (GeV) M (GeV) (b) (b) FIG. 8. Variation of BR ðϕ → qq¯Þ,BRðϕ → ggÞ, and BR ðϕ → 2 FIG. 9. Variation of the production cross section of ϕ times the γγÞ as a function of (a) M and (b) Mϕ for g yν ¼ 1 and S1 2 1 0 0 branching ratios as functions of (a) MS1 and (b) Mϕ for g yν ¼ , Mν 1 TeV. The ratios are independent of λ . We set λ R ¼ ¼ 0 λ ¼ 2 TeV, and Mν ¼ 1 TeV at the 14 TeV LHC. 2 TeV to compute the partial decay widths of ϕ. R show the production cross section times the branching ratio In Figs. 10(a) and 10(b), we show the variation of Rϕ ϕ for all the modes against MS1 and Mϕ. Note that, in the with MS1 and Mϕ. Recall that a SM singlet cannot be parameter space that we consider, we find Γϕ ≪ Mϕ, which produced at tree level. The leading order contribution to makes the narrow width approximation used in our com- σðii → ϕÞ starts at one-loop level. In Fig. 10(b),we putation a valid one. Here, we use the same set of PDFs as observe a crossover where the qqF becomes the dominant σ ¯ → ϕ σ → ϕ in the h125 case. To have some intuition about the strengths process over the ggF, i.e., ðqq Þ > ðgg Þ for a of different production channels, we scale the cross sec- fixed value of LQ mass (¼ 2 TeV). This is not a generic σ → pattern and can be understood from Eqs. (37) and (38) by tions by ðgg hMϕ Þ, where hMϕ represents a BSM Higgs whose couplings with the SM particles are the same as varying a few of the free parameters. For example, for a relatively large value of LQ mass (M ≥ 2 TeV), one those of h125. Its production cross section in the gluon S1 Γ ≤ Γ ϕ fusion mode can be computed from Eq. (30), after taking may obtain ϕ→gg ϕ→qq¯ when is not large, i.e., → ∞ Mϕ ≤ 250 GeV. In this case, the quark fusion process MS1 in Eq. (23),as   would have leading contributions. If one increases MS1 α2 4 2 2 GF SMϕ Mϕ 2 further, Γϕ→gg decreases more rapidly than Γϕ→qq¯, with σˆ gg → h ≃ pffiffiffi A1 2 δ sˆ − M : 43 ð Mϕ Þ = 2 ð ϕÞ ð Þ ¯ → ϕ 512 2πsˆ 4mt Mϕ ensuring that the qq process remains the dominant one for a larger range of Mϕ. For example, Then we define the scaled cross sections as ∼ 3 if one sets MS1 TeV, we find that quark fusion ≤ 350 σðii → ϕÞ becomes dominant for Mϕ GeV. However, the Rϕðii → ϕÞ¼ : ð44Þ relative contributions are insensitive to the value of λ0 σðgg → h Þ Mϕ chosen.

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M = 500 GeV searched for such a state in the γγ final states, though the 10-1 R (gg ) present bound from this channel is weaker [81] than the - R (dd ) -2 R (ss- ) dijet one. In our model, this channel is not at all promising, 10 - R (bb ) as can be seen in Figs. 9 and 10. Even the HL-LHC might γγ -3 not be able to probe the singlet state in the mode.

) 10

(ii -4 R 10 VI. CONCLUSION In this paper, we have considered a simple extension to -5 10 the SM, in which we have a scalar LQ (S1) with electro- magnetic charge 1=3 and heavy right chiral neutrinos. 10-6 600 800 1000 1200 1400 1600 1800 2000 While the presence of both BSM particles may have its M (GeV) S1 origin in a grand unified framework, we have simply considered their interactions at the TeV scale. The moti- (a) vation for considering such an extension comes from the M = 2000 GeV S1 fact that it can accommodate Yukawa couplings of the 10-3 down-type quarks that are enhanced compared to SM expectations. We have shown that the LQ and the right chiral neutrinos 10-4 can enhance the production cross section of the SM-like

) Higgs through a triangle loop. We have calculated the one-

10-5

(ii loop contributions to the Yukawa couplings of the down-

R type quarks. We have found the enhancements (which we have parametrized by the usual κ ) for order 1 new 10-6 R d;s;b - R (dd ) couplings and TeV scale new particles. We have then R (ss- ) - R (bb ) further extended our analysis to include a SM-singlet scalar -7 10 ϕ in the model with a dimension-1 coupling with S1 but no 100 200 300 400 500 600 700 800 900 1000 M (GeV) tree-level mixing with the SM-like Higgs. We have found that, for a similar choice of parameters, the gluon fusion (b) (through a LQ in the loop) and the quark fusion (mediated by a LQ and neutrinos in a loop) processes can lead to a FIG. 10. Variation of Rϕ ii → ϕ [Eq. (44)] with (a) M and ð Þ S1 ϕ 2 0 significant cross section to produce at the LHC. They also (b) Mϕ for g yν ¼ 1, λ ¼ 2 TeV, and Mν ¼ 1 TeV. R enhance the decay width of the singlet. Interestingly, we have found that for a light ϕ, the quark fusion can become C. Prospects at the LHC more important than the gluon fusion process as long as the ∼ It is clear that the scalar ϕ in our model would offer mass of the LQ remains high ( TeV). In both cases, precise some novel and interesting phenomenology at the LHC. measurements of branching fractions or partial widths of the 125 GeV SM-like Higgs or the singlet scalar, i.e., h125, However, a detailed analysis is beyond the scope of this ¯ ¯ paper. Instead we now simply make a few comments on its ϕ → dd, ss¯, bb, would be crucial for testing or constraining prospects. the model at the high luminosity run of the LHC. It may be possible to put a bound on σϕðMϕÞ from the dijet resonance searches. For example, the one performed ACKNOWLEDGMENTS by the CMS Collaboration at the 13 TeV LHC [80] Our computations were supported in part by indicates that σϕ ×BR ϕ → gg has to be less than about ð Þ SAMKHYA: the high performance computing facility 1 pb for Mϕ ¼ 1 TeV and about 20 pb for Mϕ ¼ 600 GeV. ¯ ¯ provided by the Institute of Physics (IoP), Bhubaneswar, Similarly, in the quark mode, σϕ×BRðϕ → dd þ ss¯ þ bbÞ India. A. B. and S. M. acknowledge support from the is less than about 1 pb for Mϕ ¼ 1 TeV and about 5 pb for Science and Engineering Research Board (SERB), DST, Mϕ ¼ 600 GeV. Figure 9(b) (which is obtained for the India, under Grant No. ECR/2017/000517. We thank 14 TeV LHC) indicates that our choice of parameters easily P. Agrawal for the helpful discussion. S. M. also acknowl- satisfies this limit. Future searches in this channel would edges the local hospitality at IoP, Bhubaneswar during the put stronger bounds on σϕ and/or Mϕ. The LHC has also meeting IMHEP-19, where this work was initiated.

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