String resonances at hadron colliders

We consider extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Assuming that the fundamental string mass scale $M_s$ is in the TeV range and that the theory is weakly coupled, we discuss possible signals of string physics at the upcoming HL-LHC run (integrated $\mathrm{luminosity}=3000{\mathrm{fb}}^{-1}$) with a center-of-mass energy of $\sqrt{s}=14\mathrm{TeV}$ and at potential future $pp$ colliders, HE-LHC and VLHC, operating at $\sqrt{s}=33$ and 100 TeV, respectively (with the same integrated luminosity). In such D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets and $\gamma +\mathrm{jet}$ are completely independent of the details of compactification and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first $(n=1)$ and second $(n=2)$ resonant poles to determine the discovery potential for Regge excitations of the quark, the gluon, and the color singlet living on the QCD stack. We show that for string scales as large as 7.1 TeV (6.1 TeV) lowest massive Regge excitations are open to discovery at the $\ge 5\sigma$ in dijet ($\gamma +\mathrm{jet}$) HL-LHC data. We also show that for $n=1$ the dijet discovery potential at HE-LHC and VLHC exceedingly improves: up to 15 TeV and 41 TeV, respectively. To compute the signal-to-noise ratio for $n=2$ resonances, we first carry out a complete calculation of all relevant decay widths of the second massive level string states (including decays into massless particles and a massive $n=1$ and a massless particle), where we rely on factorization and conformal field theory techniques. Helicity wave functions of arbitrary higher spin massive bosons are also constructed. We demonstrate that for string scales $M_s\lesssim 10.5\mathrm{TeV}$ ($M_s\lesssim 28\mathrm{TeV}$) detection of $n=2$ Regge recurrences at HE-LHC (VLHC) would become the smoking gun for D-brane string compactifications. Our calculations have been performed using a semianalytic parton model approach which is cross checked against an original software package. The string event generator interfaces with HERWIG and Pythia through BlackMax. The source code is publicly available in the hepforge repository.

Figure 1

D-brane setup with $d_{\parallel }$ parallel and $d_{\perp }$ transverse internal directions.

Figure 2

Pictorial representation of the $U(1{)}_C\times Sp(1{)}_L\times U(1{)}_L\times U(1{)}_R$ D-brane model.

Figure 3

Factorization of the amplitude $\mathcal{A}(G^{(1)},g,g,g)$ gives different group factors on two sides. The doubled wavy line presents the first massive level bosonic string state, whereas the single lines present massless bosonic string states. $G^{(2)}$ or $C^{(2)}$ are the second massive level intermediate string states obtained from factorization.

Figure 4

Signal-to-noise ratio of the lowest massive Regge excitations for the HL-LHC in the dijet (left) and $\gamma +\mathrm{jet}$ (right) topologies. For comparison, we also show ATLAS and CMS upper limits on $M_s$ from unsuccessful searches of new particles decaying to pairs of partons (quarks, antiquarks, or gluons) [30, 31, 32, 33]. For LHC phase I, the signal-to-noise ratio is suppressed by $\simeq 0.32$.

Figure 5

Dijet signal-to-noise ratio of the lowest massive Regge excitations for the HE-LHC (left) and VLHC (right).

Figure 6

Dijet signal-to-noise ratio of $n=2$ Regge excitations for the HE-LHC (left) and VLHC (right).

Figure 7

$d\sigma /dM$ vs $M$ of first resonance string signal as obtained through the semianalytic parton model calculation (dots) and with SEGI (solid). We have taken $M_s=5\mathrm{TeV}$.

Figure 8

Systematic uncertainty of the dijet (left) and $\gamma +\mathrm{jet}$ (right) string signal due to PDFs as obtained with SEGI.

Figure 9

Dijet (left) and $\gamma +\mathrm{jet}$ (right) pseudorapidity distributions.