Excited Quarks Production at FCC and S$pp$C $pp$ Colliders

TL;DR

This paper investigates the potential to discover or exclude excited u and d quarks at future multi-TeV colliders FCC and SppC, estimating discovery reach, compositeness scale, and effects of coupling parameters.

Contribution

It provides the first detailed analysis of excited quark discovery prospects at FCC and SppC colliders, including mass reach and compositeness scale determination.

Findings

Discovery potential up to 42.1 TeV for u* at FCC

Discovery potential up to 55.2 TeV for u* at SppC

Excited quarks could be observed with small coupling constants

Abstract

Potential discovery, observation and exclusion limits of excited $u$ and $d$ quarks with gamma+jet final state are researched at the multi-TeV scale colliders, FCC and S$pp$C in this work. Both colliders, FCC and S$pp$C, show that excited $u$ and $d$ quarks could be discovered up to 42.1 TeV and 55.2 TeV for $u^\star$, 30.3 TeV and 39.4 TeV for $d^\star$ and 42.3 TeV and 55.5 TeV mass values for degenerate case (m$_{u^\star}$ = m$_{d^\star}$), respectively. Determination of excited quarks compositeness scale is examined, which will be up to multi-PeV level. Beside these analysis, free parameters ($f_s,\;f\;\text{and}\; f^\prime$) are scanned from around 0.1 up to 1 that show excited quark could be discovered at dozens of TeV with even coupling constants under 0.1.

Tables

Table 1. Table 1: Attainable mass limits of excited quarks at FCC and S p ​ p 𝑝 𝑝 pp C corresponding to integrated luminosity values by selecting Λ Λ \Lambda = m Q ⋆ superscript 𝑄 ⋆ {}_{Q^{\star}} .

Colliders :		FCC-Phase I			FCC-Phase II			S$pp$C
${ℒ}_{\text{int}}$ (fb-1) :		2500			17500			22500
Significance :		$5\sigma$	$3\sigma$	$2\sigma$	$5\sigma$	$3\sigma$	$2\sigma$	$5\sigma$	$3\sigma$	$2\sigma$
m${}_{u^{\star }}$		35.1	38.8	41.7	42.1	45.7	48.5	55.2	60.1	64.0
m${}_{d^{\star }}$	(TeV)	24.3	27.4	29.9	30.3	33.5	36.1	39.4	43.8	47.3
m${}_{q^{\star }}$		35.4	39.0	41.9	42.3	45.9	48.7	55.5	60.4	64.2

Table 2. Table 2: Achievable compositeness scale values for selected mass quantities for all three cases at FCC with final integrated luminosity values.

Mass (TeV)	Compositeness Scale $\Lambda$ (TeV) at FCC
	$u^{\star }$			$d^{\star }$			$q^{\star }$
	$5\sigma$	$3\sigma$	$2\sigma$	$5\sigma$	$3\sigma$	$2\sigma$	$5\sigma$	$3\sigma$	$2\sigma$
5.5	2559	4265	6398	796	1327	1991	2798	4663	6995
10	1564	2607	3911	429	716	1074	1690	2817	4226
20	485	808	1213	111	185	278	516	859	1289
30	162	270	406	31	52	77	165	275	412

Table 3. Table 3: Achievable compositeness scale values for selected mass quantities for all three cases at S p ​ p 𝑝 𝑝 pp C with final integrated luminosity values.

Mass (TeV)	Compositeness Scale $\Lambda$ (TeV) at S$pp$C
	$u^{\star }$			$d^{\star }$			$q^{\star }$
	$5\sigma$	$3\sigma$	$2\sigma$	$5\sigma$	$3\sigma$	$2\sigma$	$5\sigma$	$3\sigma$	$2\sigma$
5.5	3631	6051	9077	1183	1972	2958	3913	6521	9781
10	2485	4142	6213	726	1210	1815	2646	4411	6616
20	988	1646	2469	248	413	620	1040	1733	2599
30	430	716	1074	96	160	239	449	748	1122
40	192	321	481	38	63	95	200	334	500

Equations

$$\begin{bmatrix}u\\ d\end{bmatrix}_{L},\begin{array}[]{c}u_{R}\;d_{R},\end{array}\begin{bmatrix}u^{\star}\\ d^{\star}\end{bmatrix}_{L},\begin{bmatrix}u^{\star}\\ d^{\star}\end{bmatrix}_{R}.$$

$$L_{eff}=\frac{1}{2\Lambda }\overline{Q_R^{\star }}{\sigma }^{\mu \nu }[g_s{f}_s\frac{{\lambda }_a}{2}{G}_{\mu \nu }^a+gf\frac{\overrightarrow{\tau }}{2}{\overrightarrow{W}}_{\mu \nu }+g^{{}^{\prime }}{f}^{{}^{\prime }}\frac{Y}{2}{B}_{\mu \nu }]Q_L+h.c.$$

$${\Gamma }_{(Q^{\star }\to Qg)}$$

$${\Gamma }_{(Q^{\star }\to Q\gamma )}$$

$${\Gamma }_{(Q^{\star }\to QV)}$$

$${\text{m}}_{u^{\star }}$$

$${\text{m}}_{d^{\star }}$$

$${\text{m}}_{u^{\star }}$$

$$S_{stat}=\frac{{\sigma }_s}{\sqrt{{\sigma }_s+{\sigma }_b}}\sqrt{{\mathcal{L}}_{int}}$$

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I Introduction

The historical development of the elementary particles Sahin et al. (2011) suggest that there could be more fundamental particles than Standard Model (SM) fermions. Therefore, over the last four decades, both experimental and theoretical particle physicists have proposed new models claiming that SM fermions could have composite substructure which are called preons Pati and Salam (1974); Shupe (1979); Harari (1979); Terazawa (1980); Fritzsch and Mandelbaum (1981); Terazawa et al. (1982); Terazawa (1983); Eichten et al. (1983); D’Souza and Kalman (1992); Çelikel et al. (1998); De Souza (2008); Fritzsch (2016). Preonic interactions bring into such new hypothetical particles like diquarks, dileptons, leptogluons, leptoquarks, excited quarks ($Q^{\star}$) and excited leptons ($l^{\star}$). As the matter of fact in the SM, there should be three possible families for excited fermions. This paper focuses on analysis of the first family spin-1/2 excited quarks ($u^{\star}$ and $d^{\star}$). Existence of the excited quark will be strong verification of such a state that composite structure of the fundamental particle might be possible. Excited quark mass is expected much heavier than the SM quark mass.

The LHC working plan will be ended in the 2020s and the more energetic particle colliders are required to observe and discover this unstable and heavy particles. After that, two new energy frontier particle collider machines, Future Circular Collider (FCC) at CERN and Super Proton Proton Collider (S$pp$C) at China, are planned for the deep investigation on hypothetical particles. FCC working plan will be carried out in two phases. It is expected to reach its final integrated luminosity as 2.5 ab*-1* at Phase I in 10 years and 15 ab*-1* at Phase II in 15 years. Overall, integrated luminosity of the FCC is expected as 17.5 ab*-1* in 25 years Abada et al. (2019). On the other hand, S$pp$C is presumed to reach 22.5 ab*-1* in 15 years Su et al. (2016).

There are some experimental Abe et al. (1995); Abazov et al. (2006); Abdallah et al. (2006); Chatrchyan et al. (2011); Khachatryan et al. (2014, 2016); CMS Authors (2016); Aad et al. (2016a, b); Sirunyan et al. (2017); CMS Authors (2017); Aaboud et al. (2017); Sirunyan et al. (2018a, b, c) and phenomenological Low (1965); Pati and Salam (1974); Terazawa et al. (1977); Harari (1979); Shupe (1979); Terazawa (1980); Fritzsch and Mandelbaum (1981); Terazawa et al. (1982); Eichten et al. (1983); Lyons (1983); Renard (1983); Terazawa (1983); Kühn and Zerwas (1984); Pancheri and Srivastava (1984); de Rújula et al. (1984); Hagiwara et al. (1985); Kühn et al. (1985); Baur et al. (1987); Spira and Zerwas (1989); Baur et al. (1990); Jikia (1990); D’Souza and Kalman (1992); Boudjema et al. (1993); Çelikel et al. (1998); Çakır and Mehdiyev (1999); Çakır et al. (2000, 2001); Éboli et al. (2002); Çakır et al. (2004a, b); Çakır and Ozansoy (2008); Harris and K. (2011); Biondini et al. (2012); Terazawa and Yasuè (2014); Terazawa and Yasue (2016); Biondini and Panella (2015); Fritzsch (2016); Panella et al. (2017); Caliskan et al. (2017); Caliskan (2017); De Souza (2008); Günaydin et al. (2018); Kaya et al. (2018); Caliskan and Kara (2018); Akay et al. (2019) research that investigate excited fermions and provide mass limits of excited quarks based on final state particles. Currently, CERN LHC collaborations (ATLAS and CMS) hold experimental exclusion limits on excited quark mass in proton-proton collisions as m${}_{q^{\star}}=6.0$ TeV at $jj$, m${}_{q^{\star}}=5.5$ TeV at $\gamma j$ final states according to both experiments, and m${}_{q^{\star}}=3.2$ TeV at $Wj$ and m${}_{q^{\star}}=2.9$ TeV at $Zj$ final states for the ATLAS experiment, m${}_{q^{\star}}=5.0$ TeV at $Wj$ and m${}_{q^{\star}}=4.7$ TeV at $Zj$ final states for the CMS experiment.

In this research, production cross section of spin-1/2 excited $u$ and $d$ quark ($u^{\star}$ and $d^{\star}$) decaying into gamma+jet final states are analyzed at the FCC and the S$pp$C with their expected integrated luminosities. To do so, interaction Lagrangian of spin-1/2 excited quark and its decay widths are presented in following section II. Then, cross section values in section III, signal-background analysis to determine cuts in section IV, and attainable mass, compositeness scale ($\Lambda$) limits, free parameters’ scan and conclusions in section V are introduced.

II Interaction Lagrangian of Spin 1/2 Excited Quarks and Decay Widths

The first generation SM and excited quarks’ isospin structure are described by Baur et al. (1990)

[TABLE]

Interaction Lagrangian of spin-1/2 excited quarks, which interact with SM gauge bosons and quarks, is presented in Eq. 1. Here, $\Lambda$ represents compositeness scale, $Q_{R}^{\star}$ is right-handed excited quark, $Q_{L}$ is SM quark, $g_{s},\;g\;\text{and}\;g^{{}^{\prime}}$ are gauge coupling constants, $F^{a}_{\mu\nu}$, $\overrightarrow{W}_{\mu\nu}$, $B_{\mu\nu}$ are the field strength tensors for gluon, SU(2) and U(1), $\lambda^{a}$ are 3$\times$3 Gell-Mann matrices, $\vec{\tau}$ is the Pauli spin matrices, $Y=1/3$ is weak hypercharge and $f_{s}$, $f$ and $f^{\prime}$ are free parameters. Eq. 1 have been implemented to CalcHEP Belyaev et al. (2013) simulation software via LanHEP Semenov (2002, 2016).

[TABLE]

The analytical formulae for excited up- and down-quark partial decay width are presented in Eq. 2, 3, 4. In these equations, SM quark mass is neglected because the experimental limits on excited quark mass are at TeV scales Aad et al. (2016a); CMS Authors (2016):

[TABLE]

where, $V$ denotes $W\;\text{or}\;Z$ bosons, $Q$ represents $u\;\text{or}\;d$ quarks and $Q^{\star}$ symbolizes $u^{\star}\;\text{or}\;d^{\star}$ excited quarks and then considering $T_{3}$ is a third component of weak isospin and $Y$ is a weak hyper charge of an excited quark; $f_{\gamma}=fT_{3}+f^{\prime}(Y/2)$, $f_{Z}=fT_{3}\cos^{2}\theta_{W}-f^{\prime}(Y/2)\sin^{2}\theta_{W}$, $f_{W}=f/\sqrt{2}$.

The decay width values obtained via CalcHEP are summarized in Fig 1. Total and partial decay widths for $u^{\star}\;\text{and}\;d^{\star}$ are examined starting from 5.5 TeV to 100 TeV mass ranges with $f=f_{s}=f^{\prime}=1$. Besides two different flavors used in analysis, decay widths are plotted in terms of different compositeness values. In Fig. 1, compositeness scale was chosen 100 TeV at the first row and it was selected equal to excited quark mass at the second row. It is apparent from Fig. 1 that $Q^{\star}\rightarrow\gamma+Q$ channel makes the lowest contribution to total decay width unlike $Q^{\star}\rightarrow g+Q$ channel. While the latter channel corresponds to dijet final states, the former channel corresponds to gamma+jet final state which is studied in this work.

III Excited Quarks Production Cross Sections at Multi-TeV Scale

In this paper, three different cases as the signal process, which are listed in Eq. 5 are considered to be studied where $q^{\star}$ means $u^{\star}+d^{\star}$. Firstly, production cross section values are computed via CalcHEP simulation software in which cross section plots (Fig. 3) are generated by using CTEQ6L1 Pumplin et al. (2002); Stump et al. (2003) quark distribution function and taking renormalization and factorization scales equal to excited quark masses. At proton-proton colliders, resonance production of excited quarks cross section values obtained at LO level are as high as next-to-leading order (NLO) level cross section values due to QCD interactions. Therefore, LO level cross section values are used in experimental studies without computation of any $k$-factor Gumus et al. (2006); Chatrchyan et al. (2011); Harris and K. (2011) for excited quarks. So, all calculations are done at a leading order (LO) level. According to LHC experiments Aad et al. (2016a); Aaboud et al. (2017) using different selections of PDF, factorization and renormalization scales cause less than 1% contribution on systematic uncertainties for $Q^{\star}\rightarrow\gamma Q$ channel. Figure 2 illustrates four Feynman diagrams that contribute to signal cross section for the case described in Eq. 5a. Besides these diagrams, cases described in Eq. 5b and 5c contribute to signal cross section with four and eight Feynman diagrams, respectively.

[TABLE]

As shown in Fig. 3, excited $u$-quark cross section values are significantly higher than excited $d$-quark due to proton’s two valance up quarks and electric charge difference of excited up (2/3) and down (-1/3) quarks. It is roughly estimated that for 10 events, $u^{\star}$ and $d^{\star}$ can be produced up to 46 TeV, 36 TeV mass limits at FCC and 58 TeV and 45 TeV at S$pp$C, respectively.

IV Signal Background Analysis of Excited Quarks

As it is declared in previous section, three signal processes, $pp\rightarrow u^{\star}+X\rightarrow\gamma u+X$, $pp\rightarrow d^{\star}+X\rightarrow\gamma d+X$ and $pp\rightarrow q^{\star}+X\rightarrow\gamma q+X\;\text{(degenerate state)}$ are analyzed along with background process $pp\rightarrow\gamma j+X$. Here, $j$ indicates $u,\,\bar{u},\,d,\,\bar{d},\,c,\,\bar{c},\,s,\,\bar{s},\,b,\,\bar{b}$ and $g$. Considering four different signal mass values with gamma+jet final state, transverse momentum and pseudo-rapidity distributions that depending on normalized differential cross sections are plotted for both colliders.

Transverse momentum ($P_{T}$), pseudo-rapidity ($\eta_{j}\;\text{or}\;\eta_{\gamma}$) and invariant mass (mγj) cuts that distinguish the signal process from the background process are implemented. Both final state particle’s transverse momentum distributions show almost the same characteristic. For this reason, one distribution plot is presented for illustration. As shown in Fig. 4, 2000 GeV cut significantly reduces the background while the signal remains almost unchanged. This cut is far beyond the experimental $P_{T}$ cut because if $P_{T}>150$ GeV and events contain at least one photon and one jet candidate, photon and jet registration is nearly 100% Aad et al. (2016a). Pseudo-rapidity regions are selected between -2.5 and 2.5 for jet and between -1.44 and 1.44 for photon based on Fig. 5.

Invariant mass cut is applied as $\text{m}^{\star}-2\Gamma^{\star}<\text{m}_{\gamma j}<\text{m}^{\star}+2\Gamma^{\star}$ mass window, here m*⋆* indicates excited quark mass and $\Gamma^{\star}$ denotes total decay width of corresponding excited quark. Additionally, to differentiate photon and jet, cone angle radius ($\Delta R$) cut is used as $\Delta R>0.5$.

[TABLE]

To obtain statistical significance values, Eq. 6 is utilized, where $\sigma_{s}$ depicts signal cross section, $\sigma_{b}$ means background cross section and $\mathcal{L}_{int}$ is integrated luminosity. By using this formula, all confidence levels, discovery ($5\sigma$), observation ($3\sigma$) and exclusion ($2\sigma$) are computed with applied cuts as mentioned above for FCC and S$pp$C colliders.

V Results and Conclusions

In this analysis, excited quark mass limits depending on integrated luminosity is calculated by implementing cut values and utilizing statistical significance formula mentioned in previous section for both collider options. These limits are presented in Fig. 6 based on expected operation time of FCC and S$pp$C colliders. Excited quarks’ discovery ($5\sigma$), observation ($3\sigma$) and exclusion ($2\sigma$) mass limits are listed in Tab. 1, which reveals both colliders’ physics potentials in terms of final luminosity values. At the end of FCC-Phase I operational time, excited quarks discovery limit will be at 35.4 TeV. FCC-Phase II will make this discovery limit further up to 42.3 TeV. On the other hand, S$pp$C with 22500 fb*-1* luminosity will take the discovery limits of Q⋆ up to 55.5 TeV.

Determining compositeness scale value is an important matter that could be decouple of the excited quark mass, so this parameter can be scanned starting from experimental mass limit of excited quark. Figure 7 provides attainable compositeness scale values of excited quarks at the both energy frontier machines with their final luminosities. As can be seen from Fig. 7, degenerate cases held the highest compositeness scale values if the m${}_{q^{\star}}$ = 5.5 TeV: 2798 TeV (5$\sigma$), 4663 TeV (3$\sigma$) and 6995 TeV (2$\sigma$) at the FCC with $\mathcal{L}_{int}$ = 17500 fb*-1* and 3913 TeV (5$\sigma$), 6521 TeV (3$\sigma$) and 9781 TeV (2$\sigma$) at the S$pp$C with $\mathcal{L}_{int}$ = 22500 fb*-1*. For some selected mass quantities, attainable compositeness scale values are listed in Tab. 2 and 3.

Up to now, free parameters were taken as $f=f_{s}=f^{\prime}=1$; however, these parameters could have different values which can be lower than 1. Mass limits of excited quark at all confidence level are presented in Fig. 8, using both colliders’ final luminosity values and taking $\Lambda$ = m${}_{Q^{\star}}$ for different coupling free parameters from around 0.1 up to 1. It is clearly seen in Fig. 8, even free parameters are taken 0.1, degenerate case excited quark, $q^{\star}$, could be discovered at 19.4 TeV at FCC and 24.8 TeV at S$pp$C.

The presented results show that FCC and S$pp$C will have significant physics potential as new frontier machines. They will potentially discover excited quarks up to 42.3 TeV at FCC and 55.5 TeV at S$pp$C. If excited quarks are discovered at these colliders, compositeness scale of excited quarks will be determined.

ACKNOWLEDGMENTS

This study is supported by TUBITAK under the grant No [114F337]. Authors are grateful to the Usak University, Energy, Environment and Sustainability Application and Research Center for their support. We also wish to acknowledge Assist. Prof. Yunus Emre Akbana for language editing and Dr. Hasan Eskalen for technical support.