Time-reversal asymmetry in particle physics has finally been clearly seen

When it was discovered in 1957 that the weak interactions of elementary particles are not symmetric under the parity operation P, theorists retreated to the seemingly safe presumption that the combined operation CP remained an inviolate symmetry. (The charge-conjugation operation C replaces all particles by their antiparticles.) But seven years later came a second rude awakening: The decay of neutral K mesons revealed a minuscule but undeniable violation of CP symmetry. So particles viewed in a mirror don’t behave exactly like their antiparticles.

The violation of CP symmetry strongly implies that the weak interactions must also be asymmetric under time reversal T. That’s because inviolate CPT symmetry was, and still remains, a bedrock theorem of particle theory. In 1999 experimenters thought they had found the first direct evidence of T violation in the observed difference in the forward and backward rates for the oscillatory metamorphosis K⁰ ↔ K⁰ (see Physics Today, February 1999, page 19 ).

But theorist Lincoln Wolfenstein soon pointed out that because K⁰ and K⁰ are antiparticles, such rate comparisons can’t disentangle the contributions of T and CP violation. ¹ He suggested instead that less ambiguous evidence of T violation be sought in decay cascades of the much heavier neutral B mesons soon to be produced in great profusion at the “B factories,” small, special-purpose electron–positron colliders just then starting up at SLAC and at KEK in Japan. “Though accepted theory insisted on the CPT theorem,” Wolfenstein recalls, “testing it has long been a goal.”

From 1999 to its final shutdown in 2008, SLAC’s B factory produced several hundred million pairs of neutral B mesons quantum-entangled in such a way that, sometimes, the decay of one instantaneously fixes the state of its partner, perhaps a millimeter away. Having combed through all those B pairs, the international collaboration that ran the B factory’s BaBar detector now reports the first clear, direct evidence of T-symmetry violation. ² In transitions between neutral-B states not connected by CP, they find transition rates that depend on temporal direction in a way that can only be attributed to T violation. And the observed level of T asymmetry is consistent with what’s expected from the known violation of CP symmetry. To no one’s surprise, then, the CPT theorem emerges unscathed.

B factories

B mesons are bound states of the heavy b quark (or its antiquark b) and one of the ordinary light antiquarks (or quarks). Therefore, the B meson’s mass (5.28 GeV) is about five times that of the proton. To create B pairs at the highest possible rate, the countercirculating e⁻ and e⁺ beams in the SLAC collider were tuned so that their center-of-mass collision energy was 10.58 GeV, the mass of an upsilon meson [the s-wave bb bound state Υ(4s)] that immediately decays, with roughly equal probability, into a pair of neutral or oppositely charged B mesons.

The B mesons then decay with a half-life of about a picosecond. Much like its Japanese rival, the SLAC collider employed a trick to better observe the individual B decays: The beam electrons are accelerated to three times the momentum of the positrons that run into them. In a conventional collider with equal and opposite beam momenta, the B mesons would be born almost at rest. But the asymmetric SLAC collider imparts a hefty 6-GeV net momentum to the B pair. Thus a measurable distance between the two B-decay vertices in the BaBar detector reveals the time interval between them (see Physics Today, May 2001, page 17 ).

Looking for violation

Symmetry under time reversal would require the transition rate between two different neutral-B states to be independent of the time order. The internal quantum state of a neutral B meson can be described in terms of either the quark-flavor eigenstates B⁰ and B⁰ (depending on whether the heavy quark is a b or b) or the even and odd CP eigenstates B₊ and B₋ , which are orthogonal superpositions of the flavor states:

B_± = (B⁰ ± B⁰)/√2 .

Like neutral kaons and neutrinos, neutral B mesons exhibit flavor oscillation as they travel. Born, say, as a pure B⁰, a neutral B can later show itself in a revealing decay as a B⁰, or even as one of the CP eigenstates.

The entanglement imposed on the neutral-B pair by the parent Υ(4s) dictates that if the first decay of a daughter reveals it to have been in a specific flavor or CP eigenstate, her still undecayed sister must—at that instant—be in the opposite state. “That’s the kind of Einstein-Podolsky-Rosen quantum weirdness we exploited in search of T violation,” says BaBar spokesman Michael Roney.

To that end, a BaBar analysis team led by Fernando Martinez-Vidal (University of Valencia, Spain) sought the rare neutral-B pairs in which the decay of one B clearly revealed a CP eigenstate and the decay of the other, a flavor eigenstate. Decays that reveal a neutral B’s quark flavor are not rare. The charge of an energetic lepton among the decay products can serve as a flavor tag. If it’s an e⁻ or a μ⁻, the progenitor was a B⁰; but if it’s an e⁺ or a μ⁺, the decay began with a B⁰.

Much rarer are the decays that unambiguously reveal a CP eigenstate. The gold standard is

B_+/− → ψ(1s) + K_L/S .

The ψ(1s) meson is the first discovered bound state of the charmed quark and its antiquark. The B meson’s CP state is revealed by the subsequent decay of the neutral K. Its subscripts L and S, for long and short, denote the very disparate half-lives of the neutral kaon’s two mass eigenstates.

In the example sketched in figure 1, at the moment of the first tagged B decay, the survivor must have been a B⁰. Its subsequent tagged demise, then, shows the transformation of a B⁰ into a B₋ after a time interval Δt of a few picoseconds, measured by Δz, the beam-direction component of the displacement between the two decay vertices in the detector.

If time-reversal symmetry holds, the transition rate, as a function of Δt, must precisely equal the rate for its time reverse, B₋ → B⁰. Figure 2 shows the results of the team’s tests of that symmetry for four different neutral-B transformations. The data were gleaned from a few thousand appropriately tagged decays of neutral-B pairs.

The asymmetry parameter A, plotted as a function of Δt in each of the figure 2 panels, is defined as the difference between the rates of the transition and its time reverse, divided by their sum. Even in the absence of any T-symmetry violation, instrumental effects would cause the small departures of the measured A from zero indicated by the blue curves. But the best global fit to the actual data (red curves) constitutes a 14-standard-deviation departure from the null hypothesis that T symmetry is not violated.

The level of T violation indicated by that fit agrees well with what one expects from inviolate CPT symmetry, given the well-characterized violation of CP symmetry in the neutral-B system. Indeed, the BaBar data also yield several direct tests of CPT symmetry. And none of them shows any evidence of its violation.