Is pīti physical and sukha emotional?

My answer below is not definitive but mere consideration.

The 1st four jhanas are called "rupa" jhana however I have never read a compelling explanation for this. However, it is known via experience that rupa jhana arises from the calming of the physical processes (breath & physical body) that are stressed by mental formations (sankhara). Thus, as the physical body is purified of mental stress, the nerves of the physical body start to bliss out. Once the breathing completely calms and the physical body is purified of stress, all the mind can be conscious of is the bliss (which is jhana). It appears the bliss of jhana has its basis in the nervous system of the physical body and possibly is physical in its basis. MN 111 refers to two types of feelings in rupa jhana, bolded below. The 2nd feeling is part of "nama" (refer to SN 12.2) and is definitely mental in it basis (because it remains in the arupa jhana) but the piti and sukha of rupa jhana could be feelings arising from/towards the rupa sense base (kāyāyatanaṃ).

There was the case where Sariputta — quite secluded from sensuality, secluded from unskillful qualities — entered & remained in the first jhana: rapture & pleasure born of seclusion, accompanied by directed thought & evaluation. Whatever qualities there are in the first jhana — directed thought, evaluation, rapture, pleasure, singleness of mind, contact, feeling, perception, intention, consciousness, desire, decision, persistence, mindfulness, equanimity, & attention — he ferreted them out one after another. Known to him they arose, known to him they remained, known to him they subsided. He discerned, 'So this is how these qualities, not having been, come into play. Having been, they vanish.' He remained unattracted & unrepelled with regard to those qualities, independent, detached, released, dissociated, with an awareness rid of barriers. He discerned that 'There is a further escape,' and pursuing it there really was for him.

Furthermore, with the complete transcending of perceptions of [physical] form, with the disappearance of perceptions of resistance, and not heeding perceptions of diversity, [perceiving,] 'Infinite space,' Sariputta entered & remained in the dimension of the infinitude of space. Whatever qualities there are in the dimension of the infinitude of space — the perception of the dimension of the infinitude of space, singleness of mind, contact, feeling, perception, intention, consciousness, desire, decision, persistence, mindfulness, equanimity & attention — he ferreted them out one after another. Known to him they arose, known to him they remained, known to him they subsided. He discerned, 'So this is how these qualities, not having been, come into play. Having been, they vanish.' He remained unattracted & unrepelled with regard to those qualities, independent, detached, released, dissociated, with an awareness rid of barriers. He discerned that 'There is a further escape,' and pursuing it there really was for him.

I think the right difference between pīti and sukha is that pīti is subjective. whereas sukha/dukha is objective. pīti always caused by pamudita. as written many time in jhana definition.

here pamudita is also subjective.in fact all brahmavihara are subjective.

Responding to Andriy Volkov answer, which is partially correct but has a major error: As part of 7 factors of awakening and 4 jhāna formula, Pīti is mentally originated, sukha is physical. The formula in SN 46.3, which occurs in slightly different variations at least 50 times in the suttas, says Pīti-man-assa (with) en-raptured mind, kāyo-pi passambhati, (the) body-also becomes-pacified, cittam-pi passambhati (the) mind-also becomes-pacified And with body pacified, sukha (physical happiness) is experienced as part of samādhi awakening factor, a.k.a. four jhānas.

What makes pīti coarser is because it's an optional mental emotional response, and is not engaged in order to progress from second to third jhāna. Sukha is physical, linked to the pleasure chemicals of the brain. You can't turn it on or off at will like you can with pīti. Sukha automatically disappears and is replaced with neutral (neither sukha nor dukkha) sensations in fourth jhāna, when you put in enough time meditating and charging up your jhāna battery. Similar to how when you each too much food, it stops tasting good.

A few useful links that could help distinguishing the two: Piti definition; sukha definition; and detailed analysis at Vism Chapter IV.94

With this sutta, it is Vinnana which is secluded, which means fewer objects cognized, then it is mano which has piti and the kaya has passambhati then sukhaṃ vediyati, and the citta has sukhha then samadhi.

Here is the pali version.

Sukha as well as piti are both mental factors. The bodily unpleasant or pleasant sensations are domanassa and somanassa.

If you want to dive deeper into mental states and their accompanying factors you might want to read the Abhidhamma. A free pdf version can be downloaded here.