THIS is virgin territory for Glasgow. New ground they have been waiting to break for some time. Two years on from their PRO12 title, and a couple of decades after their first foray into European competition, they are at last playing in the quarter-finals of the Champions Cup.

The task that awaits them today could hardly be tougher. Saracens, the cup-holders and English champions, are formidable opponents anywhere, but at home they have acquired an aura of near-invincibility. The Warriors know that if they are to upset the odds and go through to a semi-final at Murrayfield they will have to be at their very best - which means better than at any time this season.

And to be at their best, of course, they will need their mental preparation to be spot-on. That PRO12 triumph was a long time in the making: they lost three semi-finals before reaching a final, then lost their first final before at last beating Munster in 2015. They must show today that they can take more than one stride at a time when it comes to European competition; that they have matured to the point where they do not need to rest to acclimatise after every step on the way to the summit.

Rob Harley, for one, is convinced they can do so. The blindside flanker believes that that maturing process has already taken place in European competition, and is demonstrated by the improved results they have shown over the past few years, culminating in the extraordinary 43-0 victory at Leicester in January that took then through to the last eight as one of the best runners-up from the pool stages.

The Tigers are former champions, while Racing 92, who Glasgow also beat home and away, were runners-up to Saracens last season. Harley, who has a crucial role to play at the breakdown this afternoon, is sure that such results prove to himself and his team-mates that they can come out on top at Allianz Park.

“There have been a few games in Europe this season which have laid a marker of what we can do,” he said. “The games against Leicester and against Racing were about putting in good performances for the 80 minutes in those games. That laid down a marker for how we can play.

“We’ve shown we can do it. As a squad we’ve had big occasions, we’ve had finals and semi-finals. We’ve played and won big games in Europe for a couple of years now. We do have that mindset that we can beat any team in Europe: it’s about going through the right processes and being accurate enough.”

Although this is only a quarter-final and Glasgow have no intention of ending the journey here, this match is arguably even bigger than that PRO12 final itself. Nearly 6000 supporters are travelling with the team to north London, which is extraordinary enough in itself given it is not that long since only a couple of thousand turned up for home games, and the semi-final at Murrayfield, should the Warriors get there, would attract a home support several times that morning.

“It would be huge for us,” Harley agreed when asked what a win would mean for his team. “It would be new ground in Europe. We’ve won the PRO12 Final and that’s right up there, but in terms of the new frontier for us, it’s about Europe and what we can achieve there.”

As they face this quarter-final frontier, the Warriors are well aware of how strong Saracens are: having had two months to prepare for this match - the demands of regular PRO12 fixtures notwithstanding - Gregor Townsend and the coaching team have been able to analyse their opponents in unusually thorough detail. But at the same time, as Harley warned, the Warriors must ensure they do not become so concerned with nullifying Saracens’ weaknesses that they forget to give vent to their own strengths.

“When you analyse Saracens you see that they’re a very strong team,” Harley added. “They have a lot of quality players, and it’s a massive challenge for us to go down there, but we believe we can get a result.

“Although we’ve done a bit of work on them, we’ll be talking about what we can do well and how we can impose ourselves. We won’t get too carried away by what they can do, and try and look at our own performance. It’s about putting the performance together in order to do that.

“We know Saracens are a big physical side. They play on a pitch which is similar to ours and they’re confident in kicking the ball. They’ll have the ability to switch between styles.

“We will be looking to impose our game as well. It’s about how well we deal with the physicality of what we want to do and how well we adapt.”

Glasgow Warriors: S Hogg; T Seymour, P Horne, A Dunbar, L Jones; F Russell, H Pyrgos; G Reid, F Brown, Z Fagerson, B Alainu’uese, J Gray, R Harley, R Wilson, A Ashe. Substitutes: C Flynn, A Allan, S Puafisi, G Peterson, C Fusaro, A Price, N Grigg, R Hughes.

Saracens: A Goode; C Ashton, M Bosch, B Barritt, S Maitland; O Farrell, R Wigglesworth; M Vunipola, J George, J Figallo, M Itoje, J Hamilton, M Rhodes, J Wray, B Vunipola. Substitutes: S Brits, T Lamositele, V Koch, K Brown, J Conlon, B Spencer, A Lozowski, D Taylor.