My answer is also ‘No’ but by direct construction: over the past few years, various research groups have understood new symmetries of the Standard Model.
Over the past decade, field theorists have understood an expanded paradigm for thinking about symmetries known as ‘Generalized Global Symmetries’. Recall that when you learned QFT you looked for symmetries by examining the Lagrangian data of your theory and thinking about transformations of pointlike operators (local fields). But indeed Lagrangians do not necessarily fully define QFTs, and often theories that we care about as particle physicists contain extended operators. You can have in mind objects like cosmic strings (1+1 dimensional) or domain walls (2 + 1 dimensional) which may have played a role in the early universe, or just Wilson or ’t Hooft lines which have long helped us understand gauge theories. For completeness, recall a Wilson line $W_q(\gamma) = \exp(i q \int_\gamma A^\mu dx_\mu)$ where $q$ is an electric charge, $\gamma$ is a one-dimensional closed loop or infinite worldline, $A_\mu$ is the photon field, and I remind you that this operator is gauge-invariant. 't Hooft lines are the magnetic dual of these, and either should be thought of physically as the 0 + 1 dimensional worldlines of heavy electrically or magnetically charged particles as you take their mass to infinity.
So it’s a natural question whether these extended operators may enjoy a notion of global symmetry—and the answer is yes! In this broader framework of Generalized Global Symmetries, which was formalized in Gaiotto, Kapustin, Seiberg, Willett (2014) but of course has earlier precursors, symmetries whose charged objects are n-dimensional operators are known as n-form symmetries.
Only in the past few years have particle physicists begun to catch on and examine what we can learn about fundamental physics from this expanded notion of symmetries. A very gentle introduction to the basic concepts of GGS can be found in Koren & Martin (2024) section 7. And indeed there are generalized global symmetries in the Standard Model (and in well-studied theories Beyond the Standard Model) from which we can learn more about particle physics.
A first such example is that there is a global $U(1)^{(1)}$ magnetic one-form symmetry which acts on the ’t Hooft lines of hypercharge because the Standard Model does not contain any magnetic monopoles. And at energies below the mass of the electron (the lightest electrically charged particle), there is an emergent $U(1)^{(1)}$ electric one-form symmetry under which the QED Wilson lines are charged. Intriguingly, the photon can be understood as a Goldstone boson for these one-form symmetries which are spontaneously broken by the vacuum [GKSW].
Note from those statements that the existence of these symmetries requires a lack of dynamical particles in the representations of those line operators, which conversely means these symmetries are explicitly broken when we go to energies where those charged particles become dynamical---this is a novel and interesting feature of higher-form symmetries. Roughly this is because once we have those dynamical charged particles, we can write gauge-invariant line operators which end on those local operators which create/destroy the charged particle, and resultingly these operators can no longer be used to define topological invariants, which is crucial for these symmetries. If that statement was confusing just think about how in 3d space two rings are clearly either linked or not and this cannot be smoothly changed, but a ring can be smoothly taken off the end of a finite rod.
In fact we don’t know whether this is all of the one-form symmetry possessed by the SM, or whether there is additional discrete $\mathbb{Z}^{(1)}_n$ electric one-form symmetry. This is something we could potentially learn at the Large Hadron Collider if we discover a heavy fractionally-charged particle, which would mean there are Wilson line operators at energies below its mass which cannot end on any of the SM particles [KM]. This is a general possibility, but especially well-motivated is the existence of particles with electric charge an integer multiple of $e/6$ because of an ambiguity in the 'global structure' of the SM gauge group $SU(3)_C \times SU(2)_L \times U(1)_Y / \mathbb{Z}_q$ where we do not know which of $q = 1,2,3,6$ is realized in nature.
The spectrum of line operators in the SM was also discussed influentially in Tong (2017), see also J. Wang, Wan, You (2021). The possibility to uncover this by discovering an axion was discussed in Reece (2023) and Choi, Forslund, Lam, Shao (2023), and the effects of the one-form symmetry if the SM is studied on a torus in Anber & Poppitz (2021).
Past learning about new sorts of symmetries that act on operators of different dimensions, it turns out that once you admit such symmetries there are further subtle sorts of symmetry structures which can exist which in some sense ‘intertwine’ symmetries which act on operators of different dimensions. One such structure is known as a ‘2-group’ Cordova, Dumitrescu, Intriligator (2019). It turns out in the Standard Model the zero-form $SU(3)^5$ flavor symmetries which act among the three generations of fermions, and the aforementioned magnetic one-form symmetry of hypercharge are in fact intertwined in just such a structure Cordova & Koren (2023). Now the flavor symmetries were only ever approximate, but of course have been extremely useful in organizing and guiding our understanding of SM physics. The approximate 2-group likewise still circumscribes the patterns of grand unification that can appear in the ultraviolet, as elucidated in that work. And this is a good place to remark that by understanding global symmetries we learn information which is fully nonperturbative---unlike for gauge symmetries, where at strong coupling we may be forced to reckon with the fact that these are really only 'redundancies'.
With symmetries that can act on operators of different dimensions, there are even more surprising structures to find which go further past group theoretic symmetries. One such structure is known as a ‘noninvertible’ symmetry (Choi, Lam, Shao (2022a), Cordova, Ohmori (2022) for 4d continuum field theory understanding) because indeed these symmetries are not realized by unitary operators. As described in the former of these, it turns out the SM enjoys an approximate noninvertible symmetry which intertwines chiral zero-form rotations of quarks with the one-form magnetic symmetry, which can be used to give a genuine symmetry argument for the decay of the pion into two photons. Furthermore, due to the absence of right-handed neutrinos in the SM, after coupling to gravity there is a noninvertible symmetry involving the gravitational Chern-Simons term Putrov & J. Wang (2023) which can be responsible for interesting effects in the early universe like the creation of a lepton asymmetry from gravitational waves Alexander, Peskin, Sheikh-Jabbari (2004). There are further emergent, approximate, noninvertible global symmetries in the far infrared of QED when one considers time-reversal symmetry Choi, Lam, Shao (2022b) or electric-magnetic duality Cordova & Ohmori (2023).
Going Beyond the SM, it turns out that theories of axions have a rich spectrum of global symmetries that have been explored by a number of groups e.g. Brennan & Cordova (2020), Hidaka, Nitta, Yokokura (2020), Choi, Lam, Shao (2022c), Brennan, Hong, L.-T. Wang (2023), Cordova, Hong, L.-T. Wang (2023), Aloni, Garcia-Valdecasas, Reece, Suzuki (2024). In another direction, understanding non-invertible symmetries in Z’ extensions of the SM has been useful for model-building to point to interesting theories of flavor unification which have been missed. In the lepton sector this yielded a Dirac natural model of Dirac neutrino masses which are automatically exponentially suppressed Cordova, Hong, Koren, Ohmori (2022), and in the quark sector it pointed to a flavor-symmetric 'massless quark solution' to the strong CP problem in color-flavor unification Cordova, Hong, Koren (2024).
As a final point, returning to old-school zero-form symmetries, there may easily be new discrete symmetries of the theory of Standard Model fermions. It was explained in Koren (2022a) that in the SM itself the proton is stable due to an exact, anomaly-free $\mathbb{Z}_3$ lepton number symmetry which exists because we have 3 generations of SM fermions (see also J. Wang, Wan, You (2022)). In fact this symmetry could be a gauge symmetry rather than a global symmetry, since its ’t Hooft anomaly vanishes as well as its ABJ anomalies, and there’s likewise a discrete $\mathbb{Z}_9$ subgroup of baryon minus lepton number symmetry which can be gauged with only the SM fermions, see Koren (2022b) appendix B. These being gauged would ensure the proton is stable against even putative quantum gravitational effects (QG is thought to violate global symmetries). Davighi, Greljo, Thomsen (2022) constructed flavorful ultraviolet models in which such a discrete gauge symmetry protects the proton in the infrared. And if we’re happy to add right-handed neutrinos as well, then a larger discrete subgroup of baryon minus lepton number may be an unbroken gauge symmetry of the far infrared Dvali, Redi, Sibiryakov, Vainshtein (2008), Craig, Garcia Garcia, Koren (2018) (of course anomaly-theoretically the entire $U(1)$ can now be gauged, but empirically only a discrete subgroup can be a gauge symmetry of the infrared universe). Theories of discrete gauge symmetries possess a two-form global symmetry in the infrared which is broken in the ultraviolet by the existence of dynamical cosmic strings, and it was suggested in [Koren (2022b)] that the cosmic strings of discrete gauged baryon minus lepton number may be able to resolve the cosmological lithium problem.
TL;DR: Deeply examining the symmetries of the Standard Model remains an active topic of research, and in the past few years we have indeed understood a variety of new symmetries of the Standard Model which have various interesting implications for particle physics.
